By using this site, you agree to our updated Privacy Policy and our Terms of Use. Manage your Cookies Settings.
459,680 Members | 1,666 Online
Bytes IT Community
+ Ask a Question
Need help? Post your question and get tips & solutions from a community of 459,680 IT Pros & Developers. It's quick & easy.

Unwinding a loop: why can't .NET add 1 + 2 + 3 ... ?

P: n/a
Take some standard code such as shown below. It simply loops to add up a
series of terms and it produces the correct result.

// sum numbers with a loop
public int DoSumLooping(int iterations)
{
int result = 0;
for(int i = 1;i <=iterations;i++)
{
result += i;
}
return result;
}

Now translate this into a specific solution that doesn't use looping (and
use the same value for the number of iterations the loop performs). This
code returns an incorrect result. The method consists entirely of a very
straightforward code statement, but in this case .NET adds the numbers
incorrectly.
public double ComputeSum( )
{
// Brute force sum method
// For iterations == 10000
double sum = 0+ 1+ 2+ 3+ 4+ 5+ 6+ 7+ 8+ 9+ 10+ 11+ 12+ 13+ 14+ 15+ ...
+ 9997+ 9998+ 9999+ 10000;
return sum;
}
The above method returns an incorrect result with any number of terms above
about 200. It will correctly add 1 + 2 + ... + 200, but it will NOT
correctly add 1 + 2 + ... + 1000.

I have just run across this, and I have not yet researched the possible
reasons for this behavior. It may be a known issue related to either stack
size or the length of a code line, but to my knowledge it hasn't been
discussed in any of the "popular" literature on C# and .NET. I need to write
code like this, so if anyone has already encountered this issue, please
advise me.
Here's another example that also creates problems, but of a somewhat
different nature. Take the following code and translate it into a specific,
non-looping method and try to execute it using reflection. It fails.

public double LoopToCompute()
{
double sumOfProducts = 0;
double grandTotal = 0;
for (int i = 0; i < maxRows; ++i)
{
for (int j = 0; j < maxCols; ++j)
{
sumOfProducts += coeff[j] * table[i][j];
}
a_point[i] = sumOfProducts;
grandTotal += sumOfProducts;
sumOfProducts = 0;
}
return grandTotal;
}//LoopToCompute

The above code works -- but it's equivalent code with loops unrolled (shown
below) doesn't work unless the maxRows is set very small. For small values,
the 2 methods (above and below) produce identical results. There is nothing
"wrong" with the code in that sense. It's similar to the above situation. If
the "size" of the code statement or the number of code statements is too
large, .NET fails. In this case (using reflection) it doesn't return the
incorrect result, as the first example did. In this case, reflection calls
it an invalid program and refuses to run it (but only when the value of
maxRows is above about 250). The reason for this is probably
straightforward. However, I have the need to make statements like this for
performance reasons so I need a work-around. Any suggestions are
appreciated! All comments are appreciated.

public double DoBruteForceCompute()
{
double bruteForceSum = 0;

point1=coeff1*table[0][0] +coeff2*table[0][1] +coeff3*table[0][2]
+coeff4*table[0][3] +coeff5*table[0][4] +coeff6*table[0][5]
+coeff7*table[0][6] +coeff8*table[0][7] +coeff9*table[0][8]
+coeff10*table[0][9] +coeff11*table[0][10] +coeff12*table[0][11]
+coeff13*table[0][12] +coeff14*table[0][13] +coeff15*table[0][14]
+coeff16*table[0][15] +coeff17*table[0][16] +coeff18*table[0][17]
+coeff19*table[0][18] +coeff20*table[0][19] +coeff21*table[0][20]
+coeff22*table[0][21] +coeff23*table[0][22] +coeff24*table[0][23]
+coeff25*table[0][24] +coeff26*table[0][25] +coeff27*table[0][26]
+coeff28*table[0][27] +coeff29*table[0][28] +coeff30*table[0][29]
+coeff31*table[0][30] +coeff32*table[0][31] +coeff33*table[0][32]
+coeff34*table[0][33] +coeff35*table[0][34] ;

point2=coeff1*table[1][0] +coeff2*table[1][1] +coeff3*table[1][2]
+coeff4*table[1][3] +coeff5*table[1][4] +coeff6*table[1][5]
+coeff7*table[1][6] +coeff8*table[1][7] +coeff9*table[1][8]
+coeff10*table[1][9] +coeff11*table[1][10] +coeff12*table[1][11]
+coeff13*table[1][12] +coeff14*table[1][13] +coeff15*table[1][14]
+coeff16*table[1][15] +coeff17*table[1][16] +coeff18*table[1][17]
+coeff19*table[1][18] +coeff20*table[1][19] +coeff21*table[1][20]
+coeff22*table[1][21] +coeff23*table[1][22] +coeff24*table[1][23]
+coeff25*table[1][24] +coeff26*table[1][25] +coeff27*table[1][26]
+coeff28*table[1][27] +coeff29*table[1][28] +coeff30*table[1][29]
+coeff31*table[1][30] +coeff32*table[1][31] +coeff33*table[1][32]
+coeff34*table[1][33] +coeff35*table[1][34] ;
[...]

point500=coeff1*table[499][0] +coeff2*table[499][1] +coeff3*table[499][2]
+coeff4*table[499][3] +coeff5*table[499][4] +coeff6*table[499][5]
+coeff7*table[499][6] +coeff8*table[499][7] +coeff9*table[499][8]
+coeff10*table[499][9] +coeff11*table[499][10] +coeff12*table[499][11]
+coeff13*table[499][12] +coeff14*table[499][13] +coeff15*table[499][14]
+coeff16*table[499][15] +coeff17*table[499][16] +coeff18*table[499][17]
+coeff19*table[499][18] +coeff20*table[499][19] +coeff21*table[499][20]
+coeff22*table[499][21] +coeff23*table[499][22] +coeff24*table[499][23]
+coeff25*table[499][24] +coeff26*table[499][25] +coeff27*table[499][26]
+coeff28*table[499][27] +coeff29*table[499][28] +coeff30*table[499][29]
+coeff31*table[499][30] +coeff32*table[499][31] +coeff33*table[499][32]
+coeff34*table[499][33] +coeff35*table[499][34] ;

bruteForceSum =
point1 +
point2 + ... +

point499 +
point500
;

return bruteForceSum;

}//DoBruteForceCompute
Jul 21 '05 #1
Share this Question
Share on Google+
47 Replies


P: n/a
100
You use variables of diferent type for the result.

result is *int*
// sum numbers with a loop
public int DoSumLooping(int iterations)
{
int result = 0;
for(int i = 1;i <=iterations;i++)
{
result += i;
}
return result;
} public double ComputeSum( )
{
// Brute force sum method
// For iterations == 10000
double sum = 0+ 1+ 2+ 3+ 4+ 5+ 6+ 7+ 8+ 9+ 10+ 11+ 12+ 13+ 14+ 15+ .... + 9997+ 9998+ 9999+ 10000;
return sum;
}


result is *double*

Can it be de reason for the different results?

B\rgds
100
Jul 21 '05 #2

P: n/a
I just did it going with 200 Hard coded ints, then 390, then 300. Each time
I got the correct results. Are you positive of the input numbers? I know
that's a stupid question, but I first did each one by loading them into an
Int Array and adding them like that. It worked. Then I actually used
straight hard coding, and I used the number 10 each time and added 100000 to
the last one for good measure (just to make sure the value I had was
similarly high). No problems whatsoever. Inasmuch as you can load those
values in an array and iterate it successfully, couldn't you just load the
array and use an iterative approach? I understand that's what you are
asking about...why should you have to do this, but it's probably easier than
verifying the math each time when you know it will work. If I can find
anything, I'll repost.

HTH,

Bill
"Mountain Bikn' Guy" <vc@attbi.com> wrote in message
news:NZUjb.795942$YN5.793228@sccrnsc01...
Take some standard code such as shown below. It simply loops to add up a
series of terms and it produces the correct result.

// sum numbers with a loop
public int DoSumLooping(int iterations)
{
int result = 0;
for(int i = 1;i <=iterations;i++)
{
result += i;
}
return result;
}

Now translate this into a specific solution that doesn't use looping (and
use the same value for the number of iterations the loop performs). This
code returns an incorrect result. The method consists entirely of a very
straightforward code statement, but in this case .NET adds the numbers
incorrectly.
public double ComputeSum( )
{
// Brute force sum method
// For iterations == 10000
double sum = 0+ 1+ 2+ 3+ 4+ 5+ 6+ 7+ 8+ 9+ 10+ 11+ 12+ 13+ 14+ 15+ .... + 9997+ 9998+ 9999+ 10000;
return sum;
}
The above method returns an incorrect result with any number of terms above about 200. It will correctly add 1 + 2 + ... + 200, but it will NOT
correctly add 1 + 2 + ... + 1000.

I have just run across this, and I have not yet researched the possible
reasons for this behavior. It may be a known issue related to either stack
size or the length of a code line, but to my knowledge it hasn't been
discussed in any of the "popular" literature on C# and .NET. I need to write code like this, so if anyone has already encountered this issue, please
advise me.
Here's another example that also creates problems, but of a somewhat
different nature. Take the following code and translate it into a specific, non-looping method and try to execute it using reflection. It fails.

public double LoopToCompute()
{
double sumOfProducts = 0;
double grandTotal = 0;
for (int i = 0; i < maxRows; ++i)
{
for (int j = 0; j < maxCols; ++j)
{
sumOfProducts += coeff[j] * table[i][j];
}
a_point[i] = sumOfProducts;
grandTotal += sumOfProducts;
sumOfProducts = 0;
}
return grandTotal;
}//LoopToCompute

The above code works -- but it's equivalent code with loops unrolled (shown below) doesn't work unless the maxRows is set very small. For small values, the 2 methods (above and below) produce identical results. There is nothing "wrong" with the code in that sense. It's similar to the above situation. If the "size" of the code statement or the number of code statements is too
large, .NET fails. In this case (using reflection) it doesn't return the
incorrect result, as the first example did. In this case, reflection calls
it an invalid program and refuses to run it (but only when the value of
maxRows is above about 250). The reason for this is probably
straightforward. However, I have the need to make statements like this for
performance reasons so I need a work-around. Any suggestions are
appreciated! All comments are appreciated.

public double DoBruteForceCompute()
{
double bruteForceSum = 0;

point1=coeff1*table[0][0] +coeff2*table[0][1] +coeff3*table[0][2]
+coeff4*table[0][3] +coeff5*table[0][4] +coeff6*table[0][5]
+coeff7*table[0][6] +coeff8*table[0][7] +coeff9*table[0][8]
+coeff10*table[0][9] +coeff11*table[0][10] +coeff12*table[0][11]
+coeff13*table[0][12] +coeff14*table[0][13] +coeff15*table[0][14]
+coeff16*table[0][15] +coeff17*table[0][16] +coeff18*table[0][17]
+coeff19*table[0][18] +coeff20*table[0][19] +coeff21*table[0][20]
+coeff22*table[0][21] +coeff23*table[0][22] +coeff24*table[0][23]
+coeff25*table[0][24] +coeff26*table[0][25] +coeff27*table[0][26]
+coeff28*table[0][27] +coeff29*table[0][28] +coeff30*table[0][29]
+coeff31*table[0][30] +coeff32*table[0][31] +coeff33*table[0][32]
+coeff34*table[0][33] +coeff35*table[0][34] ;

point2=coeff1*table[1][0] +coeff2*table[1][1] +coeff3*table[1][2]
+coeff4*table[1][3] +coeff5*table[1][4] +coeff6*table[1][5]
+coeff7*table[1][6] +coeff8*table[1][7] +coeff9*table[1][8]
+coeff10*table[1][9] +coeff11*table[1][10] +coeff12*table[1][11]
+coeff13*table[1][12] +coeff14*table[1][13] +coeff15*table[1][14]
+coeff16*table[1][15] +coeff17*table[1][16] +coeff18*table[1][17]
+coeff19*table[1][18] +coeff20*table[1][19] +coeff21*table[1][20]
+coeff22*table[1][21] +coeff23*table[1][22] +coeff24*table[1][23]
+coeff25*table[1][24] +coeff26*table[1][25] +coeff27*table[1][26]
+coeff28*table[1][27] +coeff29*table[1][28] +coeff30*table[1][29]
+coeff31*table[1][30] +coeff32*table[1][31] +coeff33*table[1][32]
+coeff34*table[1][33] +coeff35*table[1][34] ;
[...]

point500=coeff1*table[499][0] +coeff2*table[499][1] +coeff3*table[499][2]
+coeff4*table[499][3] +coeff5*table[499][4] +coeff6*table[499][5]
+coeff7*table[499][6] +coeff8*table[499][7] +coeff9*table[499][8]
+coeff10*table[499][9] +coeff11*table[499][10] +coeff12*table[499][11]
+coeff13*table[499][12] +coeff14*table[499][13] +coeff15*table[499][14]
+coeff16*table[499][15] +coeff17*table[499][16] +coeff18*table[499][17]
+coeff19*table[499][18] +coeff20*table[499][19] +coeff21*table[499][20]
+coeff22*table[499][21] +coeff23*table[499][22] +coeff24*table[499][23]
+coeff25*table[499][24] +coeff26*table[499][25] +coeff27*table[499][26]
+coeff28*table[499][27] +coeff29*table[499][28] +coeff30*table[499][29]
+coeff31*table[499][30] +coeff32*table[499][31] +coeff33*table[499][32]
+coeff34*table[499][33] +coeff35*table[499][34] ;

bruteForceSum =
point1 +
point2 + ... +

point499 +
point500
;

return bruteForceSum;

}//DoBruteForceCompute

Jul 21 '05 #3

P: n/a
That's not the issue -- the return type doesn't affect the issue I'm
describing, and if you read my post you would have noticed that I said I had
validated that the results were identical for small problems. It's only when
the problem is large that the answers are different (and it is not a
rounding issue). The answers become vastly different -- by orders of
magnitude.

"100" <10*@100.com> wrote in message
news:OJ*************@TK2MSFTNGP11.phx.gbl...
You use variables of diferent type for the result.

result is *int*
// sum numbers with a loop
public int DoSumLooping(int iterations)
{
int result = 0;
for(int i = 1;i <=iterations;i++)
{
result += i;
}
return result;
}

public double ComputeSum( )
{
// Brute force sum method
// For iterations == 10000
double sum = 0+ 1+ 2+ 3+ 4+ 5+ 6+ 7+ 8+ 9+ 10+ 11+ 12+ 13+ 14+ 15+

...
+ 9997+ 9998+ 9999+ 10000;
return sum;
}


result is *double*

Can it be de reason for the different results?

B\rgds
100

Jul 21 '05 #4

P: n/a
I thought that it might be the problem too and I tried it both ways. Since
I didn't test with decimals (it looks like his case, he didn't have any
decimals) the only difference was the .0 at the end of it if I declared it
as double.

I suspect that there may be decimals in there b/c it sure seems that if you
iterate with a loop, you should get the same numbers.

"100" <10*@100.com> wrote in message
news:OJ*************@TK2MSFTNGP11.phx.gbl...
You use variables of diferent type for the result.

result is *int*
// sum numbers with a loop
public int DoSumLooping(int iterations)
{
int result = 0;
for(int i = 1;i <=iterations;i++)
{
result += i;
}
return result;
}

public double ComputeSum( )
{
// Brute force sum method
// For iterations == 10000
double sum = 0+ 1+ 2+ 3+ 4+ 5+ 6+ 7+ 8+ 9+ 10+ 11+ 12+ 13+ 14+ 15+

...
+ 9997+ 9998+ 9999+ 10000;
return sum;
}


result is *double*

Can it be de reason for the different results?

B\rgds
100

Jul 21 '05 #5

P: n/a
Yes, I'm positive. I will post the exact code. Here is the test anyone can
do:
1. paste this code, compile and run. Check the result.
2. Use Excel and do the same thing and compare the result. In Excel, simply
enter 1 on row 1 and 2 on row 2, then copy down to 10000 (or whatever size
you wish). Then use the sum function to get the sum. You will see that the
C# code is vastly in error.

Here's the code (sorry, but it's long):
public double ComputeSum( )

{

// Brute force sum method

// For value = 10000

double sum = 0+ 1+ 2+ 3+ 4+ 5+ 6+ 7+ 8+ 9+ 10+ 11+ 12+ 13+ 14+ 15+ 16+ 17+
18+ 19+ 20+ 21+ 22+ 23+ 24+ 25+ 26+ 27+ 28+ 29+ 30+ 31+ 32+ 33+ 34+ 35+ 36+
37+ 38+ 39+ 40+ 41+ 42+ 43+ 44+ 45+ 46+ 47+ 48+ 49+ 50+ 51+ 52+ 53+ 54+ 55+
56+ 57+ 58+ 59+ 60+ 61+ 62+ 63+ 64+ 65+ 66+ 67+ 68+ 69+ 70+ 71+ 72+ 73+ 74+
75+ 76+ 77+ 78+ 79+ 80+ 81+ 82+ 83+ 84+ 85+ 86+ 87+ 88+ 89+ 90+ 91+ 92+ 93+
94+ 95+ 96+ 97+ 98+ 99+ 100+ 101+ 102+ 103+ 104+ 105+ 106+ 107+ 108+ 109+
110+ 111+ 112+ 113+ 114+ 115+ 116+ 117+ 118+ 119+ 120+ 121+ 122+ 123+ 124+
125+ 126+ 127+ 128+ 129+ 130+ 131+ 132+ 133+ 134+ 135+ 136+ 137+ 138+ 139+
140+ 141+ 142+ 143+ 144+ 145+ 146+ 147+ 148+ 149+ 150+ 151+ 152+ 153+ 154+
155+ 156+ 157+ 158+ 159+ 160+ 161+ 162+ 163+ 164+ 165+ 166+ 167+ 168+ 169+
170+ 171+ 172+ 173+ 174+ 175+ 176+ 177+ 178+ 179+ 180+ 181+ 182+ 183+ 184+
185+ 186+ 187+ 188+ 189+ 190+ 191+ 192+ 193+ 194+ 195+ 196+ 197+ 198+ 199+
200+ 201+ 202+ 203+ 204+ 205+ 206+ 207+ 208+ 209+ 210+ 211+ 212+ 213+ 214+
215+ 216+ 217+ 218+ 219+ 220+ 221+ 222+ 223+ 224+ 225+ 226+ 227+ 228+ 229+
230+ 231+ 232+ 233+ 234+ 235+ 236+ 237+ 238+ 239+ 240+ 241+ 242+ 243+ 244+
245+ 246+ 247+ 248+ 249+ 250+ 251+ 252+ 253+ 254+ 255+ 256+ 257+ 258+ 259+
260+ 261+ 262+ 263+ 264+ 265+ 266+ 267+ 268+ 269+ 270+ 271+ 272+ 273+ 274+
275+ 276+ 277+ 278+ 279+ 280+ 281+ 282+ 283+ 284+ 285+ 286+ 287+ 288+ 289+
290+ 291+ 292+ 293+ 294+ 295+ 296+ 297+ 298+ 299+ 300+ 301+ 302+ 303+ 304+
305+ 306+ 307+ 308+ 309+ 310+ 311+ 312+ 313+ 314+ 315+ 316+ 317+ 318+ 319+
320+ 321+ 322+ 323+ 324+ 325+ 326+ 327+ 328+ 329+ 330+ 331+ 332+ 333+ 334+
335+ 336+ 337+ 338+ 339+ 340+ 341+ 342+ 343+ 344+ 345+ 346+ 347+ 348+ 349+
350+ 351+ 352+ 353+ 354+ 355+ 356+ 357+ 358+ 359+ 360+ 361+ 362+ 363+ 364+
365+ 366+ 367+ 368+ 369+ 370+ 371+ 372+ 373+ 374+ 375+ 376+ 377+ 378+ 379+
380+ 381+ 382+ 383+ 384+ 385+ 386+ 387+ 388+ 389+ 390+ 391+ 392+ 393+ 394+
395+ 396+ 397+ 398+ 399+ 400+ 401+ 402+ 403+ 404+ 405+ 406+ 407+ 408+ 409+
410+ 411+ 412+ 413+ 414+ 415+ 416+ 417+ 418+ 419+ 420+ 421+ 422+ 423+ 424+
425+ 426+ 427+ 428+ 429+ 430+ 431+ 432+ 433+ 434+ 435+ 436+ 437+ 438+ 439+
440+ 441+ 442+ 443+ 444+ 445+ 446+ 447+ 448+ 449+ 450+ 451+ 452+ 453+ 454+
455+ 456+ 457+ 458+ 459+ 460+ 461+ 462+ 463+ 464+ 465+ 466+ 467+ 468+ 469+
470+ 471+ 472+ 473+ 474+ 475+ 476+ 477+ 478+ 479+ 480+ 481+ 482+ 483+ 484+
485+ 486+ 487+ 488+ 489+ 490+ 491+ 492+ 493+ 494+ 495+ 496+ 497+ 498+ 499+
500+ 501+ 502+ 503+ 504+ 505+ 506+ 507+ 508+ 509+ 510+ 511+ 512+ 513+ 514+
515+ 516+ 517+ 518+ 519+ 520+ 521+ 522+ 523+ 524+ 525+ 526+ 527+ 528+ 529+
530+ 531+ 532+ 533+ 534+ 535+ 536+ 537+ 538+ 539+ 540+ 541+ 542+ 543+ 544+
545+ 546+ 547+ 548+ 549+ 550+ 551+ 552+ 553+ 554+ 555+ 556+ 557+ 558+ 559+
560+ 561+ 562+ 563+ 564+ 565+ 566+ 567+ 568+ 569+ 570+ 571+ 572+ 573+ 574+
575+ 576+ 577+ 578+ 579+ 580+ 581+ 582+ 583+ 584+ 585+ 586+ 587+ 588+ 589+
590+ 591+ 592+ 593+ 594+ 595+ 596+ 597+ 598+ 599+ 600+ 601+ 602+ 603+ 604+
605+ 606+ 607+ 608+ 609+ 610+ 611+ 612+ 613+ 614+ 615+ 616+ 617+ 618+ 619+
620+ 621+ 622+ 623+ 624+ 625+ 626+ 627+ 628+ 629+ 630+ 631+ 632+ 633+ 634+
635+ 636+ 637+ 638+ 639+ 640+ 641+ 642+ 643+ 644+ 645+ 646+ 647+ 648+ 649+
650+ 651+ 652+ 653+ 654+ 655+ 656+ 657+ 658+ 659+ 660+ 661+ 662+ 663+ 664+
665+ 666+ 667+ 668+ 669+ 670+ 671+ 672+ 673+ 674+ 675+ 676+ 677+ 678+ 679+
680+ 681+ 682+ 683+ 684+ 685+ 686+ 687+ 688+ 689+ 690+ 691+ 692+ 693+ 694+
695+ 696+ 697+ 698+ 699+ 700+ 701+ 702+ 703+ 704+ 705+ 706+ 707+ 708+ 709+
710+ 711+ 712+ 713+ 714+ 715+ 716+ 717+ 718+ 719+ 720+ 721+ 722+ 723+ 724+
725+ 726+ 727+ 728+ 729+ 730+ 731+ 732+ 733+ 734+ 735+ 736+ 737+ 738+ 739+
740+ 741+ 742+ 743+ 744+ 745+ 746+ 747+ 748+ 749+ 750+ 751+ 752+ 753+ 754+
755+ 756+ 757+ 758+ 759+ 760+ 761+ 762+ 763+ 764+ 765+ 766+ 767+ 768+ 769+
770+ 771+ 772+ 773+ 774+ 775+ 776+ 777+ 778+ 779+ 780+ 781+ 782+ 783+ 784+
785+ 786+ 787+ 788+ 789+ 790+ 791+ 792+ 793+ 794+ 795+ 796+ 797+ 798+ 799+
800+ 801+ 802+ 803+ 804+ 805+ 806+ 807+ 808+ 809+ 810+ 811+ 812+ 813+ 814+
815+ 816+ 817+ 818+ 819+ 820+ 821+ 822+ 823+ 824+ 825+ 826+ 827+ 828+ 829+
830+ 831+ 832+ 833+ 834+ 835+ 836+ 837+ 838+ 839+ 840+ 841+ 842+ 843+ 844+
845+ 846+ 847+ 848+ 849+ 850+ 851+ 852+ 853+ 854+ 855+ 856+ 857+ 858+ 859+
860+ 861+ 862+ 863+ 864+ 865+ 866+ 867+ 868+ 869+ 870+ 871+ 872+ 873+ 874+
875+ 876+ 877+ 878+ 879+ 880+ 881+ 882+ 883+ 884+ 885+ 886+ 887+ 888+ 889+
890+ 891+ 892+ 893+ 894+ 895+ 896+ 897+ 898+ 899+ 900+ 901+ 902+ 903+ 904+
905+ 906+ 907+ 908+ 909+ 910+ 911+ 912+ 913+ 914+ 915+ 916+ 917+ 918+ 919+
920+ 921+ 922+ 923+ 924+ 925+ 926+ 927+ 928+ 929+ 930+ 931+ 932+ 933+ 934+
935+ 936+ 937+ 938+ 939+ 940+ 941+ 942+ 943+ 944+ 945+ 946+ 947+ 948+ 949+
950+ 951+ 952+ 953+ 954+ 955+ 956+ 957+ 958+ 959+ 960+ 961+ 962+ 963+ 964+
965+ 966+ 967+ 968+ 969+ 970+ 971+ 972+ 973+ 974+ 975+ 976+ 977+ 978+ 979+
980+ 981+ 982+ 983+ 984+ 985+ 986+ 987+ 988+ 989+ 990+ 991+ 992+ 993+ 994+
995+ 996+ 997+ 998+ 999+ 1000+ 1001+ 1002+ 1003+ 1004+ 1005+ 1006+ 1007+
1008+ 1009+ 1010+ 1011+ 1012+ 1013+ 1014+ 1015+ 1016+ 1017+ 1018+ 1019+
1020+ 1021+ 1022+ 1023+ 1024+ 1025+ 1026+ 1027+ 1028+ 1029+ 1030+ 1031+
1032+ 1033+ 1034+ 1035+ 1036+ 1037+ 1038+ 1039+ 1040+ 1041+ 1042+ 1043+
1044+ 1045+ 1046+ 1047+ 1048+ 1049+ 1050+ 1051+ 1052+ 1053+ 1054+ 1055+
1056+ 1057+ 1058+ 1059+ 1060+ 1061+ 1062+ 1063+ 1064+ 1065+ 1066+ 1067+
1068+ 1069+ 1070+ 1071+ 1072+ 1073+ 1074+ 1075+ 1076+ 1077+ 1078+ 1079+
1080+ 1081+ 1082+ 1083+ 1084+ 1085+ 1086+ 1087+ 1088+ 1089+ 1090+ 1091+
1092+ 1093+ 1094+ 1095+ 1096+ 1097+ 1098+ 1099+ 1100+ 1101+ 1102+ 1103+
1104+ 1105+ 1106+ 1107+ 1108+ 1109+ 1110+ 1111+ 1112+ 1113+ 1114+ 1115+
1116+ 1117+ 1118+ 1119+ 1120+ 1121+ 1122+ 1123+ 1124+ 1125+ 1126+ 1127+
1128+ 1129+ 1130+ 1131+ 1132+ 1133+ 1134+ 1135+ 1136+ 1137+ 1138+ 1139+
1140+ 1141+ 1142+ 1143+ 1144+ 1145+ 1146+ 1147+ 1148+ 1149+ 1150+ 1151+
1152+ 1153+ 1154+ 1155+ 1156+ 1157+ 1158+ 1159+ 1160+ 1161+ 1162+ 1163+
1164+ 1165+ 1166+ 1167+ 1168+ 1169+ 1170+ 1171+ 1172+ 1173+ 1174+ 1175+
1176+ 1177+ 1178+ 1179+ 1180+ 1181+ 1182+ 1183+ 1184+ 1185+ 1186+ 1187+
1188+ 1189+ 1190+ 1191+ 1192+ 1193+ 1194+ 1195+ 1196+ 1197+ 1198+ 1199+
1200+ 1201+ 1202+ 1203+ 1204+ 1205+ 1206+ 1207+ 1208+ 1209+ 1210+ 1211+
1212+ 1213+ 1214+ 1215+ 1216+ 1217+ 1218+ 1219+ 1220+ 1221+ 1222+ 1223+
1224+ 1225+ 1226+ 1227+ 1228+ 1229+ 1230+ 1231+ 1232+ 1233+ 1234+ 1235+
1236+ 1237+ 1238+ 1239+ 1240+ 1241+ 1242+ 1243+ 1244+ 1245+ 1246+ 1247+
1248+ 1249+ 1250+ 1251+ 1252+ 1253+ 1254+ 1255+ 1256+ 1257+ 1258+ 1259+
1260+ 1261+ 1262+ 1263+ 1264+ 1265+ 1266+ 1267+ 1268+ 1269+ 1270+ 1271+
1272+ 1273+ 1274+ 1275+ 1276+ 1277+ 1278+ 1279+ 1280+ 1281+ 1282+ 1283+
1284+ 1285+ 1286+ 1287+ 1288+ 1289+ 1290+ 1291+ 1292+ 1293+ 1294+ 1295+
1296+ 1297+ 1298+ 1299+ 1300+ 1301+ 1302+ 1303+ 1304+ 1305+ 1306+ 1307+
1308+ 1309+ 1310+ 1311+ 1312+ 1313+ 1314+ 1315+ 1316+ 1317+ 1318+ 1319+
1320+ 1321+ 1322+ 1323+ 1324+ 1325+ 1326+ 1327+ 1328+ 1329+ 1330+ 1331+
1332+ 1333+ 1334+ 1335+ 1336+ 1337+ 1338+ 1339+ 1340+ 1341+ 1342+ 1343+
1344+ 1345+ 1346+ 1347+ 1348+ 1349+ 1350+ 1351+ 1352+ 1353+ 1354+ 1355+
1356+ 1357+ 1358+ 1359+ 1360+ 1361+ 1362+ 1363+ 1364+ 1365+ 1366+ 1367+
1368+ 1369+ 1370+ 1371+ 1372+ 1373+ 1374+ 1375+ 1376+ 1377+ 1378+ 1379+
1380+ 1381+ 1382+ 1383+ 1384+ 1385+ 1386+ 1387+ 1388+ 1389+ 1390+ 1391+
1392+ 1393+ 1394+ 1395+ 1396+ 1397+ 1398+ 1399+ 1400+ 1401+ 1402+ 1403+
1404+ 1405+ 1406+ 1407+ 1408+ 1409+ 1410+ 1411+ 1412+ 1413+ 1414+ 1415+
1416+ 1417+ 1418+ 1419+ 1420+ 1421+ 1422+ 1423+ 1424+ 1425+ 1426+ 1427+
1428+ 1429+ 1430+ 1431+ 1432+ 1433+ 1434+ 1435+ 1436+ 1437+ 1438+ 1439+
1440+ 1441+ 1442+ 1443+ 1444+ 1445+ 1446+ 1447+ 1448+ 1449+ 1450+ 1451+
1452+ 1453+ 1454+ 1455+ 1456+ 1457+ 1458+ 1459+ 1460+ 1461+ 1462+ 1463+
1464+ 1465+ 1466+ 1467+ 1468+ 1469+ 1470+ 1471+ 1472+ 1473+ 1474+ 1475+
1476+ 1477+ 1478+ 1479+ 1480+ 1481+ 1482+ 1483+ 1484+ 1485+ 1486+ 1487+
1488+ 1489+ 1490+ 1491+ 1492+ 1493+ 1494+ 1495+ 1496+ 1497+ 1498+ 1499+
1500+ 1501+ 1502+ 1503+ 1504+ 1505+ 1506+ 1507+ 1508+ 1509+ 1510+ 1511+
1512+ 1513+ 1514+ 1515+ 1516+ 1517+ 1518+ 1519+ 1520+ 1521+ 1522+ 1523+
1524+ 1525+ 1526+ 1527+ 1528+ 1529+ 1530+ 1531+ 1532+ 1533+ 1534+ 1535+
1536+ 1537+ 1538+ 1539+ 1540+ 1541+ 1542+ 1543+ 1544+ 1545+ 1546+ 1547+
1548+ 1549+ 1550+ 1551+ 1552+ 1553+ 1554+ 1555+ 1556+ 1557+ 1558+ 1559+
1560+ 1561+ 1562+ 1563+ 1564+ 1565+ 1566+ 1567+ 1568+ 1569+ 1570+ 1571+
1572+ 1573+ 1574+ 1575+ 1576+ 1577+ 1578+ 1579+ 1580+ 1581+ 1582+ 1583+
1584+ 1585+ 1586+ 1587+ 1588+ 1589+ 1590+ 1591+ 1592+ 1593+ 1594+ 1595+
1596+ 1597+ 1598+ 1599+ 1600+ 1601+ 1602+ 1603+ 1604+ 1605+ 1606+ 1607+
1608+ 1609+ 1610+ 1611+ 1612+ 1613+ 1614+ 1615+ 1616+ 1617+ 1618+ 1619+
1620+ 1621+ 1622+ 1623+ 1624+ 1625+ 1626+ 1627+ 1628+ 1629+ 1630+ 1631+
1632+ 1633+ 1634+ 1635+ 1636+ 1637+ 1638+ 1639+ 1640+ 1641+ 1642+ 1643+
1644+ 1645+ 1646+ 1647+ 1648+ 1649+ 1650+ 1651+ 1652+ 1653+ 1654+ 1655+
1656+ 1657+ 1658+ 1659+ 1660+ 1661+ 1662+ 1663+ 1664+ 1665+ 1666+ 1667+
1668+ 1669+ 1670+ 1671+ 1672+ 1673+ 1674+ 1675+ 1676+ 1677+ 1678+ 1679+
1680+ 1681+ 1682+ 1683+ 1684+ 1685+ 1686+ 1687+ 1688+ 1689+ 1690+ 1691+
1692+ 1693+ 1694+ 1695+ 1696+ 1697+ 1698+ 1699+ 1700+ 1701+ 1702+ 1703+
1704+ 1705+ 1706+ 1707+ 1708+ 1709+ 1710+ 1711+ 1712+ 1713+ 1714+ 1715+
1716+ 1717+ 1718+ 1719+ 1720+ 1721+ 1722+ 1723+ 1724+ 1725+ 1726+ 1727+
1728+ 1729+ 1730+ 1731+ 1732+ 1733+ 1734+ 1735+ 1736+ 1737+ 1738+ 1739+
1740+ 1741+ 1742+ 1743+ 1744+ 1745+ 1746+ 1747+ 1748+ 1749+ 1750+ 1751+
1752+ 1753+ 1754+ 1755+ 1756+ 1757+ 1758+ 1759+ 1760+ 1761+ 1762+ 1763+
1764+ 1765+ 1766+ 1767+ 1768+ 1769+ 1770+ 1771+ 1772+ 1773+ 1774+ 1775+
1776+ 1777+ 1778+ 1779+ 1780+ 1781+ 1782+ 1783+ 1784+ 1785+ 1786+ 1787+
1788+ 1789+ 1790+ 1791+ 1792+ 1793+ 1794+ 1795+ 1796+ 1797+ 1798+ 1799+
1800+ 1801+ 1802+ 1803+ 1804+ 1805+ 1806+ 1807+ 1808+ 1809+ 1810+ 1811+
1812+ 1813+ 1814+ 1815+ 1816+ 1817+ 1818+ 1819+ 1820+ 1821+ 1822+ 1823+
1824+ 1825+ 1826+ 1827+ 1828+ 1829+ 1830+ 1831+ 1832+ 1833+ 1834+ 1835+
1836+ 1837+ 1838+ 1839+ 1840+ 1841+ 1842+ 1843+ 1844+ 1845+ 1846+ 1847+
1848+ 1849+ 1850+ 1851+ 1852+ 1853+ 1854+ 1855+ 1856+ 1857+ 1858+ 1859+
1860+ 1861+ 1862+ 1863+ 1864+ 1865+ 1866+ 1867+ 1868+ 1869+ 1870+ 1871+
1872+ 1873+ 1874+ 1875+ 1876+ 1877+ 1878+ 1879+ 1880+ 1881+ 1882+ 1883+
1884+ 1885+ 1886+ 1887+ 1888+ 1889+ 1890+ 1891+ 1892+ 1893+ 1894+ 1895+
1896+ 1897+ 1898+ 1899+ 1900+ 1901+ 1902+ 1903+ 1904+ 1905+ 1906+ 1907+
1908+ 1909+ 1910+ 1911+ 1912+ 1913+ 1914+ 1915+ 1916+ 1917+ 1918+ 1919+
1920+ 1921+ 1922+ 1923+ 1924+ 1925+ 1926+ 1927+ 1928+ 1929+ 1930+ 1931+
1932+ 1933+ 1934+ 1935+ 1936+ 1937+ 1938+ 1939+ 1940+ 1941+ 1942+ 1943+
1944+ 1945+ 1946+ 1947+ 1948+ 1949+ 1950+ 1951+ 1952+ 1953+ 1954+ 1955+
1956+ 1957+ 1958+ 1959+ 1960+ 1961+ 1962+ 1963+ 1964+ 1965+ 1966+ 1967+
1968+ 1969+ 1970+ 1971+ 1972+ 1973+ 1974+ 1975+ 1976+ 1977+ 1978+ 1979+
1980+ 1981+ 1982+ 1983+ 1984+ 1985+ 1986+ 1987+ 1988+ 1989+ 1990+ 1991+
1992+ 1993+ 1994+ 1995+ 1996+ 1997+ 1998+ 1999+ 2000+ 2001+ 2002+ 2003+
2004+ 2005+ 2006+ 2007+ 2008+ 2009+ 2010+ 2011+ 2012+ 2013+ 2014+ 2015+
2016+ 2017+ 2018+ 2019+ 2020+ 2021+ 2022+ 2023+ 2024+ 2025+ 2026+ 2027+
2028+ 2029+ 2030+ 2031+ 2032+ 2033+ 2034+ 2035+ 2036+ 2037+ 2038+ 2039+
2040+ 2041+ 2042+ 2043+ 2044+ 2045+ 2046+ 2047+ 2048+ 2049+ 2050+ 2051+
2052+ 2053+ 2054+ 2055+ 2056+ 2057+ 2058+ 2059+ 2060+ 2061+ 2062+ 2063+
2064+ 2065+ 2066+ 2067+ 2068+ 2069+ 2070+ 2071+ 2072+ 2073+ 2074+ 2075+
2076+ 2077+ 2078+ 2079+ 2080+ 2081+ 2082+ 2083+ 2084+ 2085+ 2086+ 2087+
2088+ 2089+ 2090+ 2091+ 2092+ 2093+ 2094+ 2095+ 2096+ 2097+ 2098+ 2099+
2100+ 2101+ 2102+ 2103+ 2104+ 2105+ 2106+ 2107+ 2108+ 2109+ 2110+ 2111+
2112+ 2113+ 2114+ 2115+ 2116+ 2117+ 2118+ 2119+ 2120+ 2121+ 2122+ 2123+
2124+ 2125+ 2126+ 2127+ 2128+ 2129+ 2130+ 2131+ 2132+ 2133+ 2134+ 2135+
2136+ 2137+ 2138+ 2139+ 2140+ 2141+ 2142+ 2143+ 2144+ 2145+ 2146+ 2147+
2148+ 2149+ 2150+ 2151+ 2152+ 2153+ 2154+ 2155+ 2156+ 2157+ 2158+ 2159+
2160+ 2161+ 2162+ 2163+ 2164+ 2165+ 2166+ 2167+ 2168+ 2169+ 2170+ 2171+
2172+ 2173+ 2174+ 2175+ 2176+ 2177+ 2178+ 2179+ 2180+ 2181+ 2182+ 2183+
2184+ 2185+ 2186+ 2187+ 2188+ 2189+ 2190+ 2191+ 2192+ 2193+ 2194+ 2195+
2196+ 2197+ 2198+ 2199+ 2200+ 2201+ 2202+ 2203+ 2204+ 2205+ 2206+ 2207+
2208+ 2209+ 2210+ 2211+ 2212+ 2213+ 2214+ 2215+ 2216+ 2217+ 2218+ 2219+
2220+ 2221+ 2222+ 2223+ 2224+ 2225+ 2226+ 2227+ 2228+ 2229+ 2230+ 2231+
2232+ 2233+ 2234+ 2235+ 2236+ 2237+ 2238+ 2239+ 2240+ 2241+ 2242+ 2243+
2244+ 2245+ 2246+ 2247+ 2248+ 2249+ 2250+ 2251+ 2252+ 2253+ 2254+ 2255+
2256+ 2257+ 2258+ 2259+ 2260+ 2261+ 2262+ 2263+ 2264+ 2265+ 2266+ 2267+
2268+ 2269+ 2270+ 2271+ 2272+ 2273+ 2274+ 2275+ 2276+ 2277+ 2278+ 2279+
2280+ 2281+ 2282+ 2283+ 2284+ 2285+ 2286+ 2287+ 2288+ 2289+ 2290+ 2291+
2292+ 2293+ 2294+ 2295+ 2296+ 2297+ 2298+ 2299+ 2300+ 2301+ 2302+ 2303+
2304+ 2305+ 2306+ 2307+ 2308+ 2309+ 2310+ 2311+ 2312+ 2313+ 2314+ 2315+
2316+ 2317+ 2318+ 2319+ 2320+ 2321+ 2322+ 2323+ 2324+ 2325+ 2326+ 2327+
2328+ 2329+ 2330+ 2331+ 2332+ 2333+ 2334+ 2335+ 2336+ 2337+ 2338+ 2339+
2340+ 2341+ 2342+ 2343+ 2344+ 2345+ 2346+ 2347+ 2348+ 2349+ 2350+ 2351+
2352+ 2353+ 2354+ 2355+ 2356+ 2357+ 2358+ 2359+ 2360+ 2361+ 2362+ 2363+
2364+ 2365+ 2366+ 2367+ 2368+ 2369+ 2370+ 2371+ 2372+ 2373+ 2374+ 2375+
2376+ 2377+ 2378+ 2379+ 2380+ 2381+ 2382+ 2383+ 2384+ 2385+ 2386+ 2387+
2388+ 2389+ 2390+ 2391+ 2392+ 2393+ 2394+ 2395+ 2396+ 2397+ 2398+ 2399+
2400+ 2401+ 2402+ 2403+ 2404+ 2405+ 2406+ 2407+ 2408+ 2409+ 2410+ 2411+
2412+ 2413+ 2414+ 2415+ 2416+ 2417+ 2418+ 2419+ 2420+ 2421+ 2422+ 2423+
2424+ 2425+ 2426+ 2427+ 2428+ 2429+ 2430+ 2431+ 2432+ 2433+ 2434+ 2435+
2436+ 2437+ 2438+ 2439+ 2440+ 2441+ 2442+ 2443+ 2444+ 2445+ 2446+ 2447+
2448+ 2449+ 2450+ 2451+ 2452+ 2453+ 2454+ 2455+ 2456+ 2457+ 2458+ 2459+
2460+ 2461+ 2462+ 2463+ 2464+ 2465+ 2466+ 2467+ 2468+ 2469+ 2470+ 2471+
2472+ 2473+ 2474+ 2475+ 2476+ 2477+ 2478+ 2479+ 2480+ 2481+ 2482+ 2483+
2484+ 2485+ 2486+ 2487+ 2488+ 2489+ 2490+ 2491+ 2492+ 2493+ 2494+ 2495+
2496+ 2497+ 2498+ 2499+ 2500+ 2501+ 2502+ 2503+ 2504+ 2505+ 2506+ 2507+
2508+ 2509+ 2510+ 2511+ 2512+ 2513+ 2514+ 2515+ 2516+ 2517+ 2518+ 2519+
2520+ 2521+ 2522+ 2523+ 2524+ 2525+ 2526+ 2527+ 2528+ 2529+ 2530+ 2531+
2532+ 2533+ 2534+ 2535+ 2536+ 2537+ 2538+ 2539+ 2540+ 2541+ 2542+ 2543+
2544+ 2545+ 2546+ 2547+ 2548+ 2549+ 2550+ 2551+ 2552+ 2553+ 2554+ 2555+
2556+ 2557+ 2558+ 2559+ 2560+ 2561+ 2562+ 2563+ 2564+ 2565+ 2566+ 2567+
2568+ 2569+ 2570+ 2571+ 2572+ 2573+ 2574+ 2575+ 2576+ 2577+ 2578+ 2579+
2580+ 2581+ 2582+ 2583+ 2584+ 2585+ 2586+ 2587+ 2588+ 2589+ 2590+ 2591+
2592+ 2593+ 2594+ 2595+ 2596+ 2597+ 2598+ 2599+ 2600+ 2601+ 2602+ 2603+
2604+ 2605+ 2606+ 2607+ 2608+ 2609+ 2610+ 2611+ 2612+ 2613+ 2614+ 2615+
2616+ 2617+ 2618+ 2619+ 2620+ 2621+ 2622+ 2623+ 2624+ 2625+ 2626+ 2627+
2628+ 2629+ 2630+ 2631+ 2632+ 2633+ 2634+ 2635+ 2636+ 2637+ 2638+ 2639+
2640+ 2641+ 2642+ 2643+ 2644+ 2645+ 2646+ 2647+ 2648+ 2649+ 2650+ 2651+
2652+ 2653+ 2654+ 2655+ 2656+ 2657+ 2658+ 2659+ 2660+ 2661+ 2662+ 2663+
2664+ 2665+ 2666+ 2667+ 2668+ 2669+ 2670+ 2671+ 2672+ 2673+ 2674+ 2675+
2676+ 2677+ 2678+ 2679+ 2680+ 2681+ 2682+ 2683+ 2684+ 2685+ 2686+ 2687+
2688+ 2689+ 2690+ 2691+ 2692+ 2693+ 2694+ 2695+ 2696+ 2697+ 2698+ 2699+
2700+ 2701+ 2702+ 2703+ 2704+ 2705+ 2706+ 2707+ 2708+ 2709+ 2710+ 2711+
2712+ 2713+ 2714+ 2715+ 2716+ 2717+ 2718+ 2719+ 2720+ 2721+ 2722+ 2723+
2724+ 2725+ 2726+ 2727+ 2728+ 2729+ 2730+ 2731+ 2732+ 2733+ 2734+ 2735+
2736+ 2737+ 2738+ 2739+ 2740+ 2741+ 2742+ 2743+ 2744+ 2745+ 2746+ 2747+
2748+ 2749+ 2750+ 2751+ 2752+ 2753+ 2754+ 2755+ 2756+ 2757+ 2758+ 2759+
2760+ 2761+ 2762+ 2763+ 2764+ 2765+ 2766+ 2767+ 2768+ 2769+ 2770+ 2771+
2772+ 2773+ 2774+ 2775+ 2776+ 2777+ 2778+ 2779+ 2780+ 2781+ 2782+ 2783+
2784+ 2785+ 2786+ 2787+ 2788+ 2789+ 2790+ 2791+ 2792+ 2793+ 2794+ 2795+
2796+ 2797+ 2798+ 2799+ 2800+ 2801+ 2802+ 2803+ 2804+ 2805+ 2806+ 2807+
2808+ 2809+ 2810+ 2811+ 2812+ 2813+ 2814+ 2815+ 2816+ 2817+ 2818+ 2819+
2820+ 2821+ 2822+ 2823+ 2824+ 2825+ 2826+ 2827+ 2828+ 2829+ 2830+ 2831+
2832+ 2833+ 2834+ 2835+ 2836+ 2837+ 2838+ 2839+ 2840+ 2841+ 2842+ 2843+
2844+ 2845+ 2846+ 2847+ 2848+ 2849+ 2850+ 2851+ 2852+ 2853+ 2854+ 2855+
2856+ 2857+ 2858+ 2859+ 2860+ 2861+ 2862+ 2863+ 2864+ 2865+ 2866+ 2867+
2868+ 2869+ 2870+ 2871+ 2872+ 2873+ 2874+ 2875+ 2876+ 2877+ 2878+ 2879+
2880+ 2881+ 2882+ 2883+ 2884+ 2885+ 2886+ 2887+ 2888+ 2889+ 2890+ 2891+
2892+ 2893+ 2894+ 2895+ 2896+ 2897+ 2898+ 2899+ 2900+ 2901+ 2902+ 2903+
2904+ 2905+ 2906+ 2907+ 2908+ 2909+ 2910+ 2911+ 2912+ 2913+ 2914+ 2915+
2916+ 2917+ 2918+ 2919+ 2920+ 2921+ 2922+ 2923+ 2924+ 2925+ 2926+ 2927+
2928+ 2929+ 2930+ 2931+ 2932+ 2933+ 2934+ 2935+ 2936+ 2937+ 2938+ 2939+
2940+ 2941+ 2942+ 2943+ 2944+ 2945+ 2946+ 2947+ 2948+ 2949+ 2950+ 2951+
2952+ 2953+ 2954+ 2955+ 2956+ 2957+ 2958+ 2959+ 2960+ 2961+ 2962+ 2963+
2964+ 2965+ 2966+ 2967+ 2968+ 2969+ 2970+ 2971+ 2972+ 2973+ 2974+ 2975+
2976+ 2977+ 2978+ 2979+ 2980+ 2981+ 2982+ 2983+ 2984+ 2985+ 2986+ 2987+
2988+ 2989+ 2990+ 2991+ 2992+ 2993+ 2994+ 2995+ 2996+ 2997+ 2998+ 2999+
3000+ 3001+ 3002+ 3003+ 3004+ 3005+ 3006+ 3007+ 3008+ 3009+ 3010+ 3011+
3012+ 3013+ 3014+ 3015+ 3016+ 3017+ 3018+ 3019+ 3020+ 3021+ 3022+ 3023+
3024+ 3025+ 3026+ 3027+ 3028+ 3029+ 3030+ 3031+ 3032+ 3033+ 3034+ 3035+
3036+ 3037+ 3038+ 3039+ 3040+ 3041+ 3042+ 3043+ 3044+ 3045+ 3046+ 3047+
3048+ 3049+ 3050+ 3051+ 3052+ 3053+ 3054+ 3055+ 3056+ 3057+ 3058+ 3059+
3060+ 3061+ 3062+ 3063+ 3064+ 3065+ 3066+ 3067+ 3068+ 3069+ 3070+ 3071+
3072+ 3073+ 3074+ 3075+ 3076+ 3077+ 3078+ 3079+ 3080+ 3081+ 3082+ 3083+
3084+ 3085+ 3086+ 3087+ 3088+ 3089+ 3090+ 3091+ 3092+ 3093+ 3094+ 3095+
3096+ 3097+ 3098+ 3099+ 3100+ 3101+ 3102+ 3103+ 3104+ 3105+ 3106+ 3107+
3108+ 3109+ 3110+ 3111+ 3112+ 3113+ 3114+ 3115+ 3116+ 3117+ 3118+ 3119+
3120+ 3121+ 3122+ 3123+ 3124+ 3125+ 3126+ 3127+ 3128+ 3129+ 3130+ 3131+
3132+ 3133+ 3134+ 3135+ 3136+ 3137+ 3138+ 3139+ 3140+ 3141+ 3142+ 3143+
3144+ 3145+ 3146+ 3147+ 3148+ 3149+ 3150+ 3151+ 3152+ 3153+ 3154+ 3155+
3156+ 3157+ 3158+ 3159+ 3160+ 3161+ 3162+ 3163+ 3164+ 3165+ 3166+ 3167+
3168+ 3169+ 3170+ 3171+ 3172+ 3173+ 3174+ 3175+ 3176+ 3177+ 3178+ 3179+
3180+ 3181+ 3182+ 3183+ 3184+ 3185+ 3186+ 3187+ 3188+ 3189+ 3190+ 3191+
3192+ 3193+ 3194+ 3195+ 3196+ 3197+ 3198+ 3199+ 3200+ 3201+ 3202+ 3203+
3204+ 3205+ 3206+ 3207+ 3208+ 3209+ 3210+ 3211+ 3212+ 3213+ 3214+ 3215+
3216+ 3217+ 3218+ 3219+ 3220+ 3221+ 3222+ 3223+ 3224+ 3225+ 3226+ 3227+
3228+ 3229+ 3230+ 3231+ 3232+ 3233+ 3234+ 3235+ 3236+ 3237+ 3238+ 3239+
3240+ 3241+ 3242+ 3243+ 3244+ 3245+ 3246+ 3247+ 3248+ 3249+ 3250+ 3251+
3252+ 3253+ 3254+ 3255+ 3256+ 3257+ 3258+ 3259+ 3260+ 3261+ 3262+ 3263+
3264+ 3265+ 3266+ 3267+ 3268+ 3269+ 3270+ 3271+ 3272+ 3273+ 3274+ 3275+
3276+ 3277+ 3278+ 3279+ 3280+ 3281+ 3282+ 3283+ 3284+ 3285+ 3286+ 3287+
3288+ 3289+ 3290+ 3291+ 3292+ 3293+ 3294+ 3295+ 3296+ 3297+ 3298+ 3299+
3300+ 3301+ 3302+ 3303+ 3304+ 3305+ 3306+ 3307+ 3308+ 3309+ 3310+ 3311+
3312+ 3313+ 3314+ 3315+ 3316+ 3317+ 3318+ 3319+ 3320+ 3321+ 3322+ 3323+
3324+ 3325+ 3326+ 3327+ 3328+ 3329+ 3330+ 3331+ 3332+ 3333+ 3334+ 3335+
3336+ 3337+ 3338+ 3339+ 3340+ 3341+ 3342+ 3343+ 3344+ 3345+ 3346+ 3347+
3348+ 3349+ 3350+ 3351+ 3352+ 3353+ 3354+ 3355+ 3356+ 3357+ 3358+ 3359+
3360+ 3361+ 3362+ 3363+ 3364+ 3365+ 3366+ 3367+ 3368+ 3369+ 3370+ 3371+
3372+ 3373+ 3374+ 3375+ 3376+ 3377+ 3378+ 3379+ 3380+ 3381+ 3382+ 3383+
3384+ 3385+ 3386+ 3387+ 3388+ 3389+ 3390+ 3391+ 3392+ 3393+ 3394+ 3395+
3396+ 3397+ 3398+ 3399+ 3400+ 3401+ 3402+ 3403+ 3404+ 3405+ 3406+ 3407+
3408+ 3409+ 3410+ 3411+ 3412+ 3413+ 3414+ 3415+ 3416+ 3417+ 3418+ 3419+
3420+ 3421+ 3422+ 3423+ 3424+ 3425+ 3426+ 3427+ 3428+ 3429+ 3430+ 3431+
3432+ 3433+ 3434+ 3435+ 3436+ 3437+ 3438+ 3439+ 3440+ 3441+ 3442+ 3443+
3444+ 3445+ 3446+ 3447+ 3448+ 3449+ 3450+ 3451+ 3452+ 3453+ 3454+ 3455+
3456+ 3457+ 3458+ 3459+ 3460+ 3461+ 3462+ 3463+ 3464+ 3465+ 3466+ 3467+
3468+ 3469+ 3470+ 3471+ 3472+ 3473+ 3474+ 3475+ 3476+ 3477+ 3478+ 3479+
3480+ 3481+ 3482+ 3483+ 3484+ 3485+ 3486+ 3487+ 3488+ 3489+ 3490+ 3491+
3492+ 3493+ 3494+ 3495+ 3496+ 3497+ 3498+ 3499+ 3500+ 3501+ 3502+ 3503+
3504+ 3505+ 3506+ 3507+ 3508+ 3509+ 3510+ 3511+ 3512+ 3513+ 3514+ 3515+
3516+ 3517+ 3518+ 3519+ 3520+ 3521+ 3522+ 3523+ 3524+ 3525+ 3526+ 3527+
3528+ 3529+ 3530+ 3531+ 3532+ 3533+ 3534+ 3535+ 3536+ 3537+ 3538+ 3539+
3540+ 3541+ 3542+ 3543+ 3544+ 3545+ 3546+ 3547+ 3548+ 3549+ 3550+ 3551+
3552+ 3553+ 3554+ 3555+ 3556+ 3557+ 3558+ 3559+ 3560+ 3561+ 3562+ 3563+
3564+ 3565+ 3566+ 3567+ 3568+ 3569+ 3570+ 3571+ 3572+ 3573+ 3574+ 3575+
3576+ 3577+ 3578+ 3579+ 3580+ 3581+ 3582+ 3583+ 3584+ 3585+ 3586+ 3587+
3588+ 3589+ 3590+ 3591+ 3592+ 3593+ 3594+ 3595+ 3596+ 3597+ 3598+ 3599+
3600+ 3601+ 3602+ 3603+ 3604+ 3605+ 3606+ 3607+ 3608+ 3609+ 3610+ 3611+
3612+ 3613+ 3614+ 3615+ 3616+ 3617+ 3618+ 3619+ 3620+ 3621+ 3622+ 3623+
3624+ 3625+ 3626+ 3627+ 3628+ 3629+ 3630+ 3631+ 3632+ 3633+ 3634+ 3635+
3636+ 3637+ 3638+ 3639+ 3640+ 3641+ 3642+ 3643+ 3644+ 3645+ 3646+ 3647+
3648+ 3649+ 3650+ 3651+ 3652+ 3653+ 3654+ 3655+ 3656+ 3657+ 3658+ 3659+
3660+ 3661+ 3662+ 3663+ 3664+ 3665+ 3666+ 3667+ 3668+ 3669+ 3670+ 3671+
3672+ 3673+ 3674+ 3675+ 3676+ 3677+ 3678+ 3679+ 3680+ 3681+ 3682+ 3683+
3684+ 3685+ 3686+ 3687+ 3688+ 3689+ 3690+ 3691+ 3692+ 3693+ 3694+ 3695+
3696+ 3697+ 3698+ 3699+ 3700+ 3701+ 3702+ 3703+ 3704+ 3705+ 3706+ 3707+
3708+ 3709+ 3710+ 3711+ 3712+ 3713+ 3714+ 3715+ 3716+ 3717+ 3718+ 3719+
3720+ 3721+ 3722+ 3723+ 3724+ 3725+ 3726+ 3727+ 3728+ 3729+ 3730+ 3731+
3732+ 3733+ 3734+ 3735+ 3736+ 3737+ 3738+ 3739+ 3740+ 3741+ 3742+ 3743+
3744+ 3745+ 3746+ 3747+ 3748+ 3749+ 3750+ 3751+ 3752+ 3753+ 3754+ 3755+
3756+ 3757+ 3758+ 3759+ 3760+ 3761+ 3762+ 3763+ 3764+ 3765+ 3766+ 3767+
3768+ 3769+ 3770+ 3771+ 3772+ 3773+ 3774+ 3775+ 3776+ 3777+ 3778+ 3779+
3780+ 3781+ 3782+ 3783+ 3784+ 3785+ 3786+ 3787+ 3788+ 3789+ 3790+ 3791+
3792+ 3793+ 3794+ 3795+ 3796+ 3797+ 3798+ 3799+ 3800+ 3801+ 3802+ 3803+
3804+ 3805+ 3806+ 3807+ 3808+ 3809+ 3810+ 3811+ 3812+ 3813+ 3814+ 3815+
3816+ 3817+ 3818+ 3819+ 3820+ 3821+ 3822+ 3823+ 3824+ 3825+ 3826+ 3827+
3828+ 3829+ 3830+ 3831+ 3832+ 3833+ 3834+ 3835+ 3836+ 3837+ 3838+ 3839+
3840+ 3841+ 3842+ 3843+ 3844+ 3845+ 3846+ 3847+ 3848+ 3849+ 3850+ 3851+
3852+ 3853+ 3854+ 3855+ 3856+ 3857+ 3858+ 3859+ 3860+ 3861+ 3862+ 3863+
3864+ 3865+ 3866+ 3867+ 3868+ 3869+ 3870+ 3871+ 3872+ 3873+ 3874+ 3875+
3876+ 3877+ 3878+ 3879+ 3880+ 3881+ 3882+ 3883+ 3884+ 3885+ 3886+ 3887+
3888+ 3889+ 3890+ 3891+ 3892+ 3893+ 3894+ 3895+ 3896+ 3897+ 3898+ 3899+
3900+ 3901+ 3902+ 3903+ 3904+ 3905+ 3906+ 3907+ 3908+ 3909+ 3910+ 3911+
3912+ 3913+ 3914+ 3915+ 3916+ 3917+ 3918+ 3919+ 3920+ 3921+ 3922+ 3923+
3924+ 3925+ 3926+ 3927+ 3928+ 3929+ 3930+ 3931+ 3932+ 3933+ 3934+ 3935+
3936+ 3937+ 3938+ 3939+ 3940+ 3941+ 3942+ 3943+ 3944+ 3945+ 3946+ 3947+
3948+ 3949+ 3950+ 3951+ 3952+ 3953+ 3954+ 3955+ 3956+ 3957+ 3958+ 3959+
3960+ 3961+ 3962+ 3963+ 3964+ 3965+ 3966+ 3967+ 3968+ 3969+ 3970+ 3971+
3972+ 3973+ 3974+ 3975+ 3976+ 3977+ 3978+ 3979+ 3980+ 3981+ 3982+ 3983+
3984+ 3985+ 3986+ 3987+ 3988+ 3989+ 3990+ 3991+ 3992+ 3993+ 3994+ 3995+
3996+ 3997+ 3998+ 3999+ 4000+ 4001+ 4002+ 4003+ 4004+ 4005+ 4006+ 4007+
4008+ 4009+ 4010+ 4011+ 4012+ 4013+ 4014+ 4015+ 4016+ 4017+ 4018+ 4019+
4020+ 4021+ 4022+ 4023+ 4024+ 4025+ 4026+ 4027+ 4028+ 4029+ 4030+ 4031+
4032+ 4033+ 4034+ 4035+ 4036+ 4037+ 4038+ 4039+ 4040+ 4041+ 4042+ 4043+
4044+ 4045+ 4046+ 4047+ 4048+ 4049+ 4050+ 4051+ 4052+ 4053+ 4054+ 4055+
4056+ 4057+ 4058+ 4059+ 4060+ 4061+ 4062+ 4063+ 4064+ 4065+ 4066+ 4067+
4068+ 4069+ 4070+ 4071+ 4072+ 4073+ 4074+ 4075+ 4076+ 4077+ 4078+ 4079+
4080+ 4081+ 4082+ 4083+ 4084+ 4085+ 4086+ 4087+ 4088+ 4089+ 4090+ 4091+
4092+ 4093+ 4094+ 4095+ 4096+ 4097+ 4098+ 4099+ 4100+ 4101+ 4102+ 4103+
4104+ 4105+ 4106+ 4107+ 4108+ 4109+ 4110+ 4111+ 4112+ 4113+ 4114+ 4115+
4116+ 4117+ 4118+ 4119+ 4120+ 4121+ 4122+ 4123+ 4124+ 4125+ 4126+ 4127+
4128+ 4129+ 4130+ 4131+ 4132+ 4133+ 4134+ 4135+ 4136+ 4137+ 4138+ 4139+
4140+ 4141+ 4142+ 4143+ 4144+ 4145+ 4146+ 4147+ 4148+ 4149+ 4150+ 4151+
4152+ 4153+ 4154+ 4155+ 4156+ 4157+ 4158+ 4159+ 4160+ 4161+ 4162+ 4163+
4164+ 4165+ 4166+ 4167+ 4168+ 4169+ 4170+ 4171+ 4172+ 4173+ 4174+ 4175+
4176+ 4177+ 4178+ 4179+ 4180+ 4181+ 4182+ 4183+ 4184+ 4185+ 4186+ 4187+
4188+ 4189+ 4190+ 4191+ 4192+ 4193+ 4194+ 4195+ 4196+ 4197+ 4198+ 4199+
4200+ 4201+ 4202+ 4203+ 4204+ 4205+ 4206+ 4207+ 4208+ 4209+ 4210+ 4211+
4212+ 4213+ 4214+ 4215+ 4216+ 4217+ 4218+ 4219+ 4220+ 4221+ 4222+ 4223+
4224+ 4225+ 4226+ 4227+ 4228+ 4229+ 4230+ 4231+ 4232+ 4233+ 4234+ 4235+
4236+ 4237+ 4238+ 4239+ 4240+ 4241+ 4242+ 4243+ 4244+ 4245+ 4246+ 4247+
4248+ 4249+ 4250+ 4251+ 4252+ 4253+ 4254+ 4255+ 4256+ 4257+ 4258+ 4259+
4260+ 4261+ 4262+ 4263+ 4264+ 4265+ 4266+ 4267+ 4268+ 4269+ 4270+ 4271+
4272+ 4273+ 4274+ 4275+ 4276+ 4277+ 4278+ 4279+ 4280+ 4281+ 4282+ 4283+
4284+ 4285+ 4286+ 4287+ 4288+ 4289+ 4290+ 4291+ 4292+ 4293+ 4294+ 4295+
4296+ 4297+ 4298+ 4299+ 4300+ 4301+ 4302+ 4303+ 4304+ 4305+ 4306+ 4307+
4308+ 4309+ 4310+ 4311+ 4312+ 4313+ 4314+ 4315+ 4316+ 4317+ 4318+ 4319+
4320+ 4321+ 4322+ 4323+ 4324+ 4325+ 4326+ 4327+ 4328+ 4329+ 4330+ 4331+
4332+ 4333+ 4334+ 4335+ 4336+ 4337+ 4338+ 4339+ 4340+ 4341+ 4342+ 4343+
4344+ 4345+ 4346+ 4347+ 4348+ 4349+ 4350+ 4351+ 4352+ 4353+ 4354+ 4355+
4356+ 4357+ 4358+ 4359+ 4360+ 4361+ 4362+ 4363+ 4364+ 4365+ 4366+ 4367+
4368+ 4369+ 4370+ 4371+ 4372+ 4373+ 4374+ 4375+ 4376+ 4377+ 4378+ 4379+
4380+ 4381+ 4382+ 4383+ 4384+ 4385+ 4386+ 4387+ 4388+ 4389+ 4390+ 4391+
4392+ 4393+ 4394+ 4395+ 4396+ 4397+ 4398+ 4399+ 4400+ 4401+ 4402+ 4403+
4404+ 4405+ 4406+ 4407+ 4408+ 4409+ 4410+ 4411+ 4412+ 4413+ 4414+ 4415+
4416+ 4417+ 4418+ 4419+ 4420+ 4421+ 4422+ 4423+ 4424+ 4425+ 4426+ 4427+
4428+ 4429+ 4430+ 4431+ 4432+ 4433+ 4434+ 4435+ 4436+ 4437+ 4438+ 4439+
4440+ 4441+ 4442+ 4443+ 4444+ 4445+ 4446+ 4447+ 4448+ 4449+ 4450+ 4451+
4452+ 4453+ 4454+ 4455+ 4456+ 4457+ 4458+ 4459+ 4460+ 4461+ 4462+ 4463+
4464+ 4465+ 4466+ 4467+ 4468+ 4469+ 4470+ 4471+ 4472+ 4473+ 4474+ 4475+
4476+ 4477+ 4478+ 4479+ 4480+ 4481+ 4482+ 4483+ 4484+ 4485+ 4486+ 4487+
4488+ 4489+ 4490+ 4491+ 4492+ 4493+ 4494+ 4495+ 4496+ 4497+ 4498+ 4499+
4500+ 4501+ 4502+ 4503+ 4504+ 4505+ 4506+ 4507+ 4508+ 4509+ 4510+ 4511+
4512+ 4513+ 4514+ 4515+ 4516+ 4517+ 4518+ 4519+ 4520+ 4521+ 4522+ 4523+
4524+ 4525+ 4526+ 4527+ 4528+ 4529+ 4530+ 4531+ 4532+ 4533+ 4534+ 4535+
4536+ 4537+ 4538+ 4539+ 4540+ 4541+ 4542+ 4543+ 4544+ 4545+ 4546+ 4547+
4548+ 4549+ 4550+ 4551+ 4552+ 4553+ 4554+ 4555+ 4556+ 4557+ 4558+ 4559+
4560+ 4561+ 4562+ 4563+ 4564+ 4565+ 4566+ 4567+ 4568+ 4569+ 4570+ 4571+
4572+ 4573+ 4574+ 4575+ 4576+ 4577+ 4578+ 4579+ 4580+ 4581+ 4582+ 4583+
4584+ 4585+ 4586+ 4587+ 4588+ 4589+ 4590+ 4591+ 4592+ 4593+ 4594+ 4595+
4596+ 4597+ 4598+ 4599+ 4600+ 4601+ 4602+ 4603+ 4604+ 4605+ 4606+ 4607+
4608+ 4609+ 4610+ 4611+ 4612+ 4613+ 4614+ 4615+ 4616+ 4617+ 4618+ 4619+
4620+ 4621+ 4622+ 4623+ 4624+ 4625+ 4626+ 4627+ 4628+ 4629+ 4630+ 4631+
4632+ 4633+ 4634+ 4635+ 4636+ 4637+ 4638+ 4639+ 4640+ 4641+ 4642+ 4643+
4644+ 4645+ 4646+ 4647+ 4648+ 4649+ 4650+ 4651+ 4652+ 4653+ 4654+ 4655+
4656+ 4657+ 4658+ 4659+ 4660+ 4661+ 4662+ 4663+ 4664+ 4665+ 4666+ 4667+
4668+ 4669+ 4670+ 4671+ 4672+ 4673+ 4674+ 4675+ 4676+ 4677+ 4678+ 4679+
4680+ 4681+ 4682+ 4683+ 4684+ 4685+ 4686+ 4687+ 4688+ 4689+ 4690+ 4691+
4692+ 4693+ 4694+ 4695+ 4696+ 4697+ 4698+ 4699+ 4700+ 4701+ 4702+ 4703+
4704+ 4705+ 4706+ 4707+ 4708+ 4709+ 4710+ 4711+ 4712+ 4713+ 4714+ 4715+
4716+ 4717+ 4718+ 4719+ 4720+ 4721+ 4722+ 4723+ 4724+ 4725+ 4726+ 4727+
4728+ 4729+ 4730+ 4731+ 4732+ 4733+ 4734+ 4735+ 4736+ 4737+ 4738+ 4739+
4740+ 4741+ 4742+ 4743+ 4744+ 4745+ 4746+ 4747+ 4748+ 4749+ 4750+ 4751+
4752+ 4753+ 4754+ 4755+ 4756+ 4757+ 4758+ 4759+ 4760+ 4761+ 4762+ 4763+
4764+ 4765+ 4766+ 4767+ 4768+ 4769+ 4770+ 4771+ 4772+ 4773+ 4774+ 4775+
4776+ 4777+ 4778+ 4779+ 4780+ 4781+ 4782+ 4783+ 4784+ 4785+ 4786+ 4787+
4788+ 4789+ 4790+ 4791+ 4792+ 4793+ 4794+ 4795+ 4796+ 4797+ 4798+ 4799+
4800+ 4801+ 4802+ 4803+ 4804+ 4805+ 4806+ 4807+ 4808+ 4809+ 4810+ 4811+
4812+ 4813+ 4814+ 4815+ 4816+ 4817+ 4818+ 4819+ 4820+ 4821+ 4822+ 4823+
4824+ 4825+ 4826+ 4827+ 4828+ 4829+ 4830+ 4831+ 4832+ 4833+ 4834+ 4835+
4836+ 4837+ 4838+ 4839+ 4840+ 4841+ 4842+ 4843+ 4844+ 4845+ 4846+ 4847+
4848+ 4849+ 4850+ 4851+ 4852+ 4853+ 4854+ 4855+ 4856+ 4857+ 4858+ 4859+
4860+ 4861+ 4862+ 4863+ 4864+ 4865+ 4866+ 4867+ 4868+ 4869+ 4870+ 4871+
4872+ 4873+ 4874+ 4875+ 4876+ 4877+ 4878+ 4879+ 4880+ 4881+ 4882+ 4883+
4884+ 4885+ 4886+ 4887+ 4888+ 4889+ 4890+ 4891+ 4892+ 4893+ 4894+ 4895+
4896+ 4897+ 4898+ 4899+ 4900+ 4901+ 4902+ 4903+ 4904+ 4905+ 4906+ 4907+
4908+ 4909+ 4910+ 4911+ 4912+ 4913+ 4914+ 4915+ 4916+ 4917+ 4918+ 4919+
4920+ 4921+ 4922+ 4923+ 4924+ 4925+ 4926+ 4927+ 4928+ 4929+ 4930+ 4931+
4932+ 4933+ 4934+ 4935+ 4936+ 4937+ 4938+ 4939+ 4940+ 4941+ 4942+ 4943+
4944+ 4945+ 4946+ 4947+ 4948+ 4949+ 4950+ 4951+ 4952+ 4953+ 4954+ 4955+
4956+ 4957+ 4958+ 4959+ 4960+ 4961+ 4962+ 4963+ 4964+ 4965+ 4966+ 4967+
4968+ 4969+ 4970+ 4971+ 4972+ 4973+ 4974+ 4975+ 4976+ 4977+ 4978+ 4979+
4980+ 4981+ 4982+ 4983+ 4984+ 4985+ 4986+ 4987+ 4988+ 4989+ 4990+ 4991+
4992+ 4993+ 4994+ 4995+ 4996+ 4997+ 4998+ 4999+ 5000+ 5001+ 5002+ 5003+
5004+ 5005+ 5006+ 5007+ 5008+ 5009+ 5010+ 5011+ 5012+ 5013+ 5014+ 5015+
5016+ 5017+ 5018+ 5019+ 5020+ 5021+ 5022+ 5023+ 5024+ 5025+ 5026+ 5027+
5028+ 5029+ 5030+ 5031+ 5032+ 5033+ 5034+ 5035+ 5036+ 5037+ 5038+ 5039+
5040+ 5041+ 5042+ 5043+ 5044+ 5045+ 5046+ 5047+ 5048+ 5049+ 5050+ 5051+
5052+ 5053+ 5054+ 5055+ 5056+ 5057+ 5058+ 5059+ 5060+ 5061+ 5062+ 5063+
5064+ 5065+ 5066+ 5067+ 5068+ 5069+ 5070+ 5071+ 5072+ 5073+ 5074+ 5075+
5076+ 5077+ 5078+ 5079+ 5080+ 5081+ 5082+ 5083+ 5084+ 5085+ 5086+ 5087+
5088+ 5089+ 5090+ 5091+ 5092+ 5093+ 5094+ 5095+ 5096+ 5097+ 5098+ 5099+
5100+ 5101+ 5102+ 5103+ 5104+ 5105+ 5106+ 5107+ 5108+ 5109+ 5110+ 5111+
5112+ 5113+ 5114+ 5115+ 5116+ 5117+ 5118+ 5119+ 5120+ 5121+ 5122+ 5123+
5124+ 5125+ 5126+ 5127+ 5128+ 5129+ 5130+ 5131+ 5132+ 5133+ 5134+ 5135+
5136+ 5137+ 5138+ 5139+ 5140+ 5141+ 5142+ 5143+ 5144+ 5145+ 5146+ 5147+
5148+ 5149+ 5150+ 5151+ 5152+ 5153+ 5154+ 5155+ 5156+ 5157+ 5158+ 5159+
5160+ 5161+ 5162+ 5163+ 5164+ 5165+ 5166+ 5167+ 5168+ 5169+ 5170+ 5171+
5172+ 5173+ 5174+ 5175+ 5176+ 5177+ 5178+ 5179+ 5180+ 5181+ 5182+ 5183+
5184+ 5185+ 5186+ 5187+ 5188+ 5189+ 5190+ 5191+ 5192+ 5193+ 5194+ 5195+
5196+ 5197+ 5198+ 5199+ 5200+ 5201+ 5202+ 5203+ 5204+ 5205+ 5206+ 5207+
5208+ 5209+ 5210+ 5211+ 5212+ 5213+ 5214+ 5215+ 5216+ 5217+ 5218+ 5219+
5220+ 5221+ 5222+ 5223+ 5224+ 5225+ 5226+ 5227+ 5228+ 5229+ 5230+ 5231+
5232+ 5233+ 5234+ 5235+ 5236+ 5237+ 5238+ 5239+ 5240+ 5241+ 5242+ 5243+
5244+ 5245+ 5246+ 5247+ 5248+ 5249+ 5250+ 5251+ 5252+ 5253+ 5254+ 5255+
5256+ 5257+ 5258+ 5259+ 5260+ 5261+ 5262+ 5263+ 5264+ 5265+ 5266+ 5267+
5268+ 5269+ 5270+ 5271+ 5272+ 5273+ 5274+ 5275+ 5276+ 5277+ 5278+ 5279+
5280+ 5281+ 5282+ 5283+ 5284+ 5285+ 5286+ 5287+ 5288+ 5289+ 5290+ 5291+
5292+ 5293+ 5294+ 5295+ 5296+ 5297+ 5298+ 5299+ 5300+ 5301+ 5302+ 5303+
5304+ 5305+ 5306+ 5307+ 5308+ 5309+ 5310+ 5311+ 5312+ 5313+ 5314+ 5315+
5316+ 5317+ 5318+ 5319+ 5320+ 5321+ 5322+ 5323+ 5324+ 5325+ 5326+ 5327+
5328+ 5329+ 5330+ 5331+ 5332+ 5333+ 5334+ 5335+ 5336+ 5337+ 5338+ 5339+
5340+ 5341+ 5342+ 5343+ 5344+ 5345+ 5346+ 5347+ 5348+ 5349+ 5350+ 5351+
5352+ 5353+ 5354+ 5355+ 5356+ 5357+ 5358+ 5359+ 5360+ 5361+ 5362+ 5363+
5364+ 5365+ 5366+ 5367+ 5368+ 5369+ 5370+ 5371+ 5372+ 5373+ 5374+ 5375+
5376+ 5377+ 5378+ 5379+ 5380+ 5381+ 5382+ 5383+ 5384+ 5385+ 5386+ 5387+
5388+ 5389+ 5390+ 5391+ 5392+ 5393+ 5394+ 5395+ 5396+ 5397+ 5398+ 5399+
5400+ 5401+ 5402+ 5403+ 5404+ 5405+ 5406+ 5407+ 5408+ 5409+ 5410+ 5411+
5412+ 5413+ 5414+ 5415+ 5416+ 5417+ 5418+ 5419+ 5420+ 5421+ 5422+ 5423+
5424+ 5425+ 5426+ 5427+ 5428+ 5429+ 5430+ 5431+ 5432+ 5433+ 5434+ 5435+
5436+ 5437+ 5438+ 5439+ 5440+ 5441+ 5442+ 5443+ 5444+ 5445+ 5446+ 5447+
5448+ 5449+ 5450+ 5451+ 5452+ 5453+ 5454+ 5455+ 5456+ 5457+ 5458+ 5459+
5460+ 5461+ 5462+ 5463+ 5464+ 5465+ 5466+ 5467+ 5468+ 5469+ 5470+ 5471+
5472+ 5473+ 5474+ 5475+ 5476+ 5477+ 5478+ 5479+ 5480+ 5481+ 5482+ 5483+
5484+ 5485+ 5486+ 5487+ 5488+ 5489+ 5490+ 5491+ 5492+ 5493+ 5494+ 5495+
5496+ 5497+ 5498+ 5499+ 5500+ 5501+ 5502+ 5503+ 5504+ 5505+ 5506+ 5507+
5508+ 5509+ 5510+ 5511+ 5512+ 5513+ 5514+ 5515+ 5516+ 5517+ 5518+ 5519+
5520+ 5521+ 5522+ 5523+ 5524+ 5525+ 5526+ 5527+ 5528+ 5529+ 5530+ 5531+
5532+ 5533+ 5534+ 5535+ 5536+ 5537+ 5538+ 5539+ 5540+ 5541+ 5542+ 5543+
5544+ 5545+ 5546+ 5547+ 5548+ 5549+ 5550+ 5551+ 5552+ 5553+ 5554+ 5555+
5556+ 5557+ 5558+ 5559+ 5560+ 5561+ 5562+ 5563+ 5564+ 5565+ 5566+ 5567+
5568+ 5569+ 5570+ 5571+ 5572+ 5573+ 5574+ 5575+ 5576+ 5577+ 5578+ 5579+
5580+ 5581+ 5582+ 5583+ 5584+ 5585+ 5586+ 5587+ 5588+ 5589+ 5590+ 5591+
5592+ 5593+ 5594+ 5595+ 5596+ 5597+ 5598+ 5599+ 5600+ 5601+ 5602+ 5603+
5604+ 5605+ 5606+ 5607+ 5608+ 5609+ 5610+ 5611+ 5612+ 5613+ 5614+ 5615+
5616+ 5617+ 5618+ 5619+ 5620+ 5621+ 5622+ 5623+ 5624+ 5625+ 5626+ 5627+
5628+ 5629+ 5630+ 5631+ 5632+ 5633+ 5634+ 5635+ 5636+ 5637+ 5638+ 5639+
5640+ 5641+ 5642+ 5643+ 5644+ 5645+ 5646+ 5647+ 5648+ 5649+ 5650+ 5651+
5652+ 5653+ 5654+ 5655+ 5656+ 5657+ 5658+ 5659+ 5660+ 5661+ 5662+ 5663+
5664+ 5665+ 5666+ 5667+ 5668+ 5669+ 5670+ 5671+ 5672+ 5673+ 5674+ 5675+
5676+ 5677+ 5678+ 5679+ 5680+ 5681+ 5682+ 5683+ 5684+ 5685+ 5686+ 5687+
5688+ 5689+ 5690+ 5691+ 5692+ 5693+ 5694+ 5695+ 5696+ 5697+ 5698+ 5699+
5700+ 5701+ 5702+ 5703+ 5704+ 5705+ 5706+ 5707+ 5708+ 5709+ 5710+ 5711+
5712+ 5713+ 5714+ 5715+ 5716+ 5717+ 5718+ 5719+ 5720+ 5721+ 5722+ 5723+
5724+ 5725+ 5726+ 5727+ 5728+ 5729+ 5730+ 5731+ 5732+ 5733+ 5734+ 5735+
5736+ 5737+ 5738+ 5739+ 5740+ 5741+ 5742+ 5743+ 5744+ 5745+ 5746+ 5747+
5748+ 5749+ 5750+ 5751+ 5752+ 5753+ 5754+ 5755+ 5756+ 5757+ 5758+ 5759+
5760+ 5761+ 5762+ 5763+ 5764+ 5765+ 5766+ 5767+ 5768+ 5769+ 5770+ 5771+
5772+ 5773+ 5774+ 5775+ 5776+ 5777+ 5778+ 5779+ 5780+ 5781+ 5782+ 5783+
5784+ 5785+ 5786+ 5787+ 5788+ 5789+ 5790+ 5791+ 5792+ 5793+ 5794+ 5795+
5796+ 5797+ 5798+ 5799+ 5800+ 5801+ 5802+ 5803+ 5804+ 5805+ 5806+ 5807+
5808+ 5809+ 5810+ 5811+ 5812+ 5813+ 5814+ 5815+ 5816+ 5817+ 5818+ 5819+
5820+ 5821+ 5822+ 5823+ 5824+ 5825+ 5826+ 5827+ 5828+ 5829+ 5830+ 5831+
5832+ 5833+ 5834+ 5835+ 5836+ 5837+ 5838+ 5839+ 5840+ 5841+ 5842+ 5843+
5844+ 5845+ 5846+ 5847+ 5848+ 5849+ 5850+ 5851+ 5852+ 5853+ 5854+ 5855+
5856+ 5857+ 5858+ 5859+ 5860+ 5861+ 5862+ 5863+ 5864+ 5865+ 5866+ 5867+
5868+ 5869+ 5870+ 5871+ 5872+ 5873+ 5874+ 5875+ 5876+ 5877+ 5878+ 5879+
5880+ 5881+ 5882+ 5883+ 5884+ 5885+ 5886+ 5887+ 5888+ 5889+ 5890+ 5891+
5892+ 5893+ 5894+ 5895+ 5896+ 5897+ 5898+ 5899+ 5900+ 5901+ 5902+ 5903+
5904+ 5905+ 5906+ 5907+ 5908+ 5909+ 5910+ 5911+ 5912+ 5913+ 5914+ 5915+
5916+ 5917+ 5918+ 5919+ 5920+ 5921+ 5922+ 5923+ 5924+ 5925+ 5926+ 5927+
5928+ 5929+ 5930+ 5931+ 5932+ 5933+ 5934+ 5935+ 5936+ 5937+ 5938+ 5939+
5940+ 5941+ 5942+ 5943+ 5944+ 5945+ 5946+ 5947+ 5948+ 5949+ 5950+ 5951+
5952+ 5953+ 5954+ 5955+ 5956+ 5957+ 5958+ 5959+ 5960+ 5961+ 5962+ 5963+
5964+ 5965+ 5966+ 5967+ 5968+ 5969+ 5970+ 5971+ 5972+ 5973+ 5974+ 5975+
5976+ 5977+ 5978+ 5979+ 5980+ 5981+ 5982+ 5983+ 5984+ 5985+ 5986+ 5987+
5988+ 5989+ 5990+ 5991+ 5992+ 5993+ 5994+ 5995+ 5996+ 5997+ 5998+ 5999+
6000+ 6001+ 6002+ 6003+ 6004+ 6005+ 6006+ 6007+ 6008+ 6009+ 6010+ 6011+
6012+ 6013+ 6014+ 6015+ 6016+ 6017+ 6018+ 6019+ 6020+ 6021+ 6022+ 6023+
6024+ 6025+ 6026+ 6027+ 6028+ 6029+ 6030+ 6031+ 6032+ 6033+ 6034+ 6035+
6036+ 6037+ 6038+ 6039+ 6040+ 6041+ 6042+ 6043+ 6044+ 6045+ 6046+ 6047+
6048+ 6049+ 6050+ 6051+ 6052+ 6053+ 6054+ 6055+ 6056+ 6057+ 6058+ 6059+
6060+ 6061+ 6062+ 6063+ 6064+ 6065+ 6066+ 6067+ 6068+ 6069+ 6070+ 6071+
6072+ 6073+ 6074+ 6075+ 6076+ 6077+ 6078+ 6079+ 6080+ 6081+ 6082+ 6083+
6084+ 6085+ 6086+ 6087+ 6088+ 6089+ 6090+ 6091+ 6092+ 6093+ 6094+ 6095+
6096+ 6097+ 6098+ 6099+ 6100+ 6101+ 6102+ 6103+ 6104+ 6105+ 6106+ 6107+
6108+ 6109+ 6110+ 6111+ 6112+ 6113+ 6114+ 6115+ 6116+ 6117+ 6118+ 6119+
6120+ 6121+ 6122+ 6123+ 6124+ 6125+ 6126+ 6127+ 6128+ 6129+ 6130+ 6131+
6132+ 6133+ 6134+ 6135+ 6136+ 6137+ 6138+ 6139+ 6140+ 6141+ 6142+ 6143+
6144+ 6145+ 6146+ 6147+ 6148+ 6149+ 6150+ 6151+ 6152+ 6153+ 6154+ 6155+
6156+ 6157+ 6158+ 6159+ 6160+ 6161+ 6162+ 6163+ 6164+ 6165+ 6166+ 6167+
6168+ 6169+ 6170+ 6171+ 6172+ 6173+ 6174+ 6175+ 6176+ 6177+ 6178+ 6179+
6180+ 6181+ 6182+ 6183+ 6184+ 6185+ 6186+ 6187+ 6188+ 6189+ 6190+ 6191+
6192+ 6193+ 6194+ 6195+ 6196+ 6197+ 6198+ 6199+ 6200+ 6201+ 6202+ 6203+
6204+ 6205+ 6206+ 6207+ 6208+ 6209+ 6210+ 6211+ 6212+ 6213+ 6214+ 6215+
6216+ 6217+ 6218+ 6219+ 6220+ 6221+ 6222+ 6223+ 6224+ 6225+ 6226+ 6227+
6228+ 6229+ 6230+ 6231+ 6232+ 6233+ 6234+ 6235+ 6236+ 6237+ 6238+ 6239+
6240+ 6241+ 6242+ 6243+ 6244+ 6245+ 6246+ 6247+ 6248+ 6249+ 6250+ 6251+
6252+ 6253+ 6254+ 6255+ 6256+ 6257+ 6258+ 6259+ 6260+ 6261+ 6262+ 6263+
6264+ 6265+ 6266+ 6267+ 6268+ 6269+ 6270+ 6271+ 6272+ 6273+ 6274+ 6275+
6276+ 6277+ 6278+ 6279+ 6280+ 6281+ 6282+ 6283+ 6284+ 6285+ 6286+ 6287+
6288+ 6289+ 6290+ 6291+ 6292+ 6293+ 6294+ 6295+ 6296+ 6297+ 6298+ 6299+
6300+ 6301+ 6302+ 6303+ 6304+ 6305+ 6306+ 6307+ 6308+ 6309+ 6310+ 6311+
6312+ 6313+ 6314+ 6315+ 6316+ 6317+ 6318+ 6319+ 6320+ 6321+ 6322+ 6323+
6324+ 6325+ 6326+ 6327+ 6328+ 6329+ 6330+ 6331+ 6332+ 6333+ 6334+ 6335+
6336+ 6337+ 6338+ 6339+ 6340+ 6341+ 6342+ 6343+ 6344+ 6345+ 6346+ 6347+
6348+ 6349+ 6350+ 6351+ 6352+ 6353+ 6354+ 6355+ 6356+ 6357+ 6358+ 6359+
6360+ 6361+ 6362+ 6363+ 6364+ 6365+ 6366+ 6367+ 6368+ 6369+ 6370+ 6371+
6372+ 6373+ 6374+ 6375+ 6376+ 6377+ 6378+ 6379+ 6380+ 6381+ 6382+ 6383+
6384+ 6385+ 6386+ 6387+ 6388+ 6389+ 6390+ 6391+ 6392+ 6393+ 6394+ 6395+
6396+ 6397+ 6398+ 6399+ 6400+ 6401+ 6402+ 6403+ 6404+ 6405+ 6406+ 6407+
6408+ 6409+ 6410+ 6411+ 6412+ 6413+ 6414+ 6415+ 6416+ 6417+ 6418+ 6419+
6420+ 6421+ 6422+ 6423+ 6424+ 6425+ 6426+ 6427+ 6428+ 6429+ 6430+ 6431+
6432+ 6433+ 6434+ 6435+ 6436+ 6437+ 6438+ 6439+ 6440+ 6441+ 6442+ 6443+
6444+ 6445+ 6446+ 6447+ 6448+ 6449+ 6450+ 6451+ 6452+ 6453+ 6454+ 6455+
6456+ 6457+ 6458+ 6459+ 6460+ 6461+ 6462+ 6463+ 6464+ 6465+ 6466+ 6467+
6468+ 6469+ 6470+ 6471+ 6472+ 6473+ 6474+ 6475+ 6476+ 6477+ 6478+ 6479+
6480+ 6481+ 6482+ 6483+ 6484+ 6485+ 6486+ 6487+ 6488+ 6489+ 6490+ 6491+
6492+ 6493+ 6494+ 6495+ 6496+ 6497+ 6498+ 6499+ 6500+ 6501+ 6502+ 6503+
6504+ 6505+ 6506+ 6507+ 6508+ 6509+ 6510+ 6511+ 6512+ 6513+ 6514+ 6515+
6516+ 6517+ 6518+ 6519+ 6520+ 6521+ 6522+ 6523+ 6524+ 6525+ 6526+ 6527+
6528+ 6529+ 6530+ 6531+ 6532+ 6533+ 6534+ 6535+ 6536+ 6537+ 6538+ 6539+
6540+ 6541+ 6542+ 6543+ 6544+ 6545+ 6546+ 6547+ 6548+ 6549+ 6550+ 6551+
6552+ 6553+ 6554+ 6555+ 6556+ 6557+ 6558+ 6559+ 6560+ 6561+ 6562+ 6563+
6564+ 6565+ 6566+ 6567+ 6568+ 6569+ 6570+ 6571+ 6572+ 6573+ 6574+ 6575+
6576+ 6577+ 6578+ 6579+ 6580+ 6581+ 6582+ 6583+ 6584+ 6585+ 6586+ 6587+
6588+ 6589+ 6590+ 6591+ 6592+ 6593+ 6594+ 6595+ 6596+ 6597+ 6598+ 6599+
6600+ 6601+ 6602+ 6603+ 6604+ 6605+ 6606+ 6607+ 6608+ 6609+ 6610+ 6611+
6612+ 6613+ 6614+ 6615+ 6616+ 6617+ 6618+ 6619+ 6620+ 6621+ 6622+ 6623+
6624+ 6625+ 6626+ 6627+ 6628+ 6629+ 6630+ 6631+ 6632+ 6633+ 6634+ 6635+
6636+ 6637+ 6638+ 6639+ 6640+ 6641+ 6642+ 6643+ 6644+ 6645+ 6646+ 6647+
6648+ 6649+ 6650+ 6651+ 6652+ 6653+ 6654+ 6655+ 6656+ 6657+ 6658+ 6659+
6660+ 6661+ 6662+ 6663+ 6664+ 6665+ 6666+ 6667+ 6668+ 6669+ 6670+ 6671+
6672+ 6673+ 6674+ 6675+ 6676+ 6677+ 6678+ 6679+ 6680+ 6681+ 6682+ 6683+
6684+ 6685+ 6686+ 6687+ 6688+ 6689+ 6690+ 6691+ 6692+ 6693+ 6694+ 6695+
6696+ 6697+ 6698+ 6699+ 6700+ 6701+ 6702+ 6703+ 6704+ 6705+ 6706+ 6707+
6708+ 6709+ 6710+ 6711+ 6712+ 6713+ 6714+ 6715+ 6716+ 6717+ 6718+ 6719+
6720+ 6721+ 6722+ 6723+ 6724+ 6725+ 6726+ 6727+ 6728+ 6729+ 6730+ 6731+
6732+ 6733+ 6734+ 6735+ 6736+ 6737+ 6738+ 6739+ 6740+ 6741+ 6742+ 6743+
6744+ 6745+ 6746+ 6747+ 6748+ 6749+ 6750+ 6751+ 6752+ 6753+ 6754+ 6755+
6756+ 6757+ 6758+ 6759+ 6760+ 6761+ 6762+ 6763+ 6764+ 6765+ 6766+ 6767+
6768+ 6769+ 6770+ 6771+ 6772+ 6773+ 6774+ 6775+ 6776+ 6777+ 6778+ 6779+
6780+ 6781+ 6782+ 6783+ 6784+ 6785+ 6786+ 6787+ 6788+ 6789+ 6790+ 6791+
6792+ 6793+ 6794+ 6795+ 6796+ 6797+ 6798+ 6799+ 6800+ 6801+ 6802+ 6803+
6804+ 6805+ 6806+ 6807+ 6808+ 6809+ 6810+ 6811+ 6812+ 6813+ 6814+ 6815+
6816+ 6817+ 6818+ 6819+ 6820+ 6821+ 6822+ 6823+ 6824+ 6825+ 6826+ 6827+
6828+ 6829+ 6830+ 6831+ 6832+ 6833+ 6834+ 6835+ 6836+ 6837+ 6838+ 6839+
6840+ 6841+ 6842+ 6843+ 6844+ 6845+ 6846+ 6847+ 6848+ 6849+ 6850+ 6851+
6852+ 6853+ 6854+ 6855+ 6856+ 6857+ 6858+ 6859+ 6860+ 6861+ 6862+ 6863+
6864+ 6865+ 6866+ 6867+ 6868+ 6869+ 6870+ 6871+ 6872+ 6873+ 6874+ 6875+
6876+ 6877+ 6878+ 6879+ 6880+ 6881+ 6882+ 6883+ 6884+ 6885+ 6886+ 6887+
6888+ 6889+ 6890+ 6891+ 6892+ 6893+ 6894+ 6895+ 6896+ 6897+ 6898+ 6899+
6900+ 6901+ 6902+ 6903+ 6904+ 6905+ 6906+ 6907+ 6908+ 6909+ 6910+ 6911+
6912+ 6913+ 6914+ 6915+ 6916+ 6917+ 6918+ 6919+ 6920+ 6921+ 6922+ 6923+
6924+ 6925+ 6926+ 6927+ 6928+ 6929+ 6930+ 6931+ 6932+ 6933+ 6934+ 6935+
6936+ 6937+ 6938+ 6939+ 6940+ 6941+ 6942+ 6943+ 6944+ 6945+ 6946+ 6947+
6948+ 6949+ 6950+ 6951+ 6952+ 6953+ 6954+ 6955+ 6956+ 6957+ 6958+ 6959+
6960+ 6961+ 6962+ 6963+ 6964+ 6965+ 6966+ 6967+ 6968+ 6969+ 6970+ 6971+
6972+ 6973+ 6974+ 6975+ 6976+ 6977+ 6978+ 6979+ 6980+ 6981+ 6982+ 6983+
6984+ 6985+ 6986+ 6987+ 6988+ 6989+ 6990+ 6991+ 6992+ 6993+ 6994+ 6995+
6996+ 6997+ 6998+ 6999+ 7000+ 7001+ 7002+ 7003+ 7004+ 7005+ 7006+ 7007+
7008+ 7009+ 7010+ 7011+ 7012+ 7013+ 7014+ 7015+ 7016+ 7017+ 7018+ 7019+
7020+ 7021+ 7022+ 7023+ 7024+ 7025+ 7026+ 7027+ 7028+ 7029+ 7030+ 7031+
7032+ 7033+ 7034+ 7035+ 7036+ 7037+ 7038+ 7039+ 7040+ 7041+ 7042+ 7043+
7044+ 7045+ 7046+ 7047+ 7048+ 7049+ 7050+ 7051+ 7052+ 7053+ 7054+ 7055+
7056+ 7057+ 7058+ 7059+ 7060+ 7061+ 7062+ 7063+ 7064+ 7065+ 7066+ 7067+
7068+ 7069+ 7070+ 7071+ 7072+ 7073+ 7074+ 7075+ 7076+ 7077+ 7078+ 7079+
7080+ 7081+ 7082+ 7083+ 7084+ 7085+ 7086+ 7087+ 7088+ 7089+ 7090+ 7091+
7092+ 7093+ 7094+ 7095+ 7096+ 7097+ 7098+ 7099+ 7100+ 7101+ 7102+ 7103+
7104+ 7105+ 7106+ 7107+ 7108+ 7109+ 7110+ 7111+ 7112+ 7113+ 7114+ 7115+
7116+ 7117+ 7118+ 7119+ 7120+ 7121+ 7122+ 7123+ 7124+ 7125+ 7126+ 7127+
7128+ 7129+ 7130+ 7131+ 7132+ 7133+ 7134+ 7135+ 7136+ 7137+ 7138+ 7139+
7140+ 7141+ 7142+ 7143+ 7144+ 7145+ 7146+ 7147+ 7148+ 7149+ 7150+ 7151+
7152+ 7153+ 7154+ 7155+ 7156+ 7157+ 7158+ 7159+ 7160+ 7161+ 7162+ 7163+
7164+ 7165+ 7166+ 7167+ 7168+ 7169+ 7170+ 7171+ 7172+ 7173+ 7174+ 7175+
7176+ 7177+ 7178+ 7179+ 7180+ 7181+ 7182+ 7183+ 7184+ 7185+ 7186+ 7187+
7188+ 7189+ 7190+ 7191+ 7192+ 7193+ 7194+ 7195+ 7196+ 7197+ 7198+ 7199+
7200+ 7201+ 7202+ 7203+ 7204+ 7205+ 7206+ 7207+ 7208+ 7209+ 7210+ 7211+
7212+ 7213+ 7214+ 7215+ 7216+ 7217+ 7218+ 7219+ 7220+ 7221+ 7222+ 7223+
7224+ 7225+ 7226+ 7227+ 7228+ 7229+ 7230+ 7231+ 7232+ 7233+ 7234+ 7235+
7236+ 7237+ 7238+ 7239+ 7240+ 7241+ 7242+ 7243+ 7244+ 7245+ 7246+ 7247+
7248+ 7249+ 7250+ 7251+ 7252+ 7253+ 7254+ 7255+ 7256+ 7257+ 7258+ 7259+
7260+ 7261+ 7262+ 7263+ 7264+ 7265+ 7266+ 7267+ 7268+ 7269+ 7270+ 7271+
7272+ 7273+ 7274+ 7275+ 7276+ 7277+ 7278+ 7279+ 7280+ 7281+ 7282+ 7283+
7284+ 7285+ 7286+ 7287+ 7288+ 7289+ 7290+ 7291+ 7292+ 7293+ 7294+ 7295+
7296+ 7297+ 7298+ 7299+ 7300+ 7301+ 7302+ 7303+ 7304+ 7305+ 7306+ 7307+
7308+ 7309+ 7310+ 7311+ 7312+ 7313+ 7314+ 7315+ 7316+ 7317+ 7318+ 7319+
7320+ 7321+ 7322+ 7323+ 7324+ 7325+ 7326+ 7327+ 7328+ 7329+ 7330+ 7331+
7332+ 7333+ 7334+ 7335+ 7336+ 7337+ 7338+ 7339+ 7340+ 7341+ 7342+ 7343+
7344+ 7345+ 7346+ 7347+ 7348+ 7349+ 7350+ 7351+ 7352+ 7353+ 7354+ 7355+
7356+ 7357+ 7358+ 7359+ 7360+ 7361+ 7362+ 7363+ 7364+ 7365+ 7366+ 7367+
7368+ 7369+ 7370+ 7371+ 7372+ 7373+ 7374+ 7375+ 7376+ 7377+ 7378+ 7379+
7380+ 7381+ 7382+ 7383+ 7384+ 7385+ 7386+ 7387+ 7388+ 7389+ 7390+ 7391+
7392+ 7393+ 7394+ 7395+ 7396+ 7397+ 7398+ 7399+ 7400+ 7401+ 7402+ 7403+
7404+ 7405+ 7406+ 7407+ 7408+ 7409+ 7410+ 7411+ 7412+ 7413+ 7414+ 7415+
7416+ 7417+ 7418+ 7419+ 7420+ 7421+ 7422+ 7423+ 7424+ 7425+ 7426+ 7427+
7428+ 7429+ 7430+ 7431+ 7432+ 7433+ 7434+ 7435+ 7436+ 7437+ 7438+ 7439+
7440+ 7441+ 7442+ 7443+ 7444+ 7445+ 7446+ 7447+ 7448+ 7449+ 7450+ 7451+
7452+ 7453+ 7454+ 7455+ 7456+ 7457+ 7458+ 7459+ 7460+ 7461+ 7462+ 7463+
7464+ 7465+ 7466+ 7467+ 7468+ 7469+ 7470+ 7471+ 7472+ 7473+ 7474+ 7475+
7476+ 7477+ 7478+ 7479+ 7480+ 7481+ 7482+ 7483+ 7484+ 7485+ 7486+ 7487+
7488+ 7489+ 7490+ 7491+ 7492+ 7493+ 7494+ 7495+ 7496+ 7497+ 7498+ 7499+
7500+ 7501+ 7502+ 7503+ 7504+ 7505+ 7506+ 7507+ 7508+ 7509+ 7510+ 7511+
7512+ 7513+ 7514+ 7515+ 7516+ 7517+ 7518+ 7519+ 7520+ 7521+ 7522+ 7523+
7524+ 7525+ 7526+ 7527+ 7528+ 7529+ 7530+ 7531+ 7532+ 7533+ 7534+ 7535+
7536+ 7537+ 7538+ 7539+ 7540+ 7541+ 7542+ 7543+ 7544+ 7545+ 7546+ 7547+
7548+ 7549+ 7550+ 7551+ 7552+ 7553+ 7554+ 7555+ 7556+ 7557+ 7558+ 7559+
7560+ 7561+ 7562+ 7563+ 7564+ 7565+ 7566+ 7567+ 7568+ 7569+ 7570+ 7571+
7572+ 7573+ 7574+ 7575+ 7576+ 7577+ 7578+ 7579+ 7580+ 7581+ 7582+ 7583+
7584+ 7585+ 7586+ 7587+ 7588+ 7589+ 7590+ 7591+ 7592+ 7593+ 7594+ 7595+
7596+ 7597+ 7598+ 7599+ 7600+ 7601+ 7602+ 7603+ 7604+ 7605+ 7606+ 7607+
7608+ 7609+ 7610+ 7611+ 7612+ 7613+ 7614+ 7615+ 7616+ 7617+ 7618+ 7619+
7620+ 7621+ 7622+ 7623+ 7624+ 7625+ 7626+ 7627+ 7628+ 7629+ 7630+ 7631+
7632+ 7633+ 7634+ 7635+ 7636+ 7637+ 7638+ 7639+ 7640+ 7641+ 7642+ 7643+
7644+ 7645+ 7646+ 7647+ 7648+ 7649+ 7650+ 7651+ 7652+ 7653+ 7654+ 7655+
7656+ 7657+ 7658+ 7659+ 7660+ 7661+ 7662+ 7663+ 7664+ 7665+ 7666+ 7667+
7668+ 7669+ 7670+ 7671+ 7672+ 7673+ 7674+ 7675+ 7676+ 7677+ 7678+ 7679+
7680+ 7681+ 7682+ 7683+ 7684+ 7685+ 7686+ 7687+ 7688+ 7689+ 7690+ 7691+
7692+ 7693+ 7694+ 7695+ 7696+ 7697+ 7698+ 7699+ 7700+ 7701+ 7702+ 7703+
7704+ 7705+ 7706+ 7707+ 7708+ 7709+ 7710+ 7711+ 7712+ 7713+ 7714+ 7715+
7716+ 7717+ 7718+ 7719+ 7720+ 7721+ 7722+ 7723+ 7724+ 7725+ 7726+ 7727+
7728+ 7729+ 7730+ 7731+ 7732+ 7733+ 7734+ 7735+ 7736+ 7737+ 7738+ 7739+
7740+ 7741+ 7742+ 7743+ 7744+ 7745+ 7746+ 7747+ 7748+ 7749+ 7750+ 7751+
7752+ 7753+ 7754+ 7755+ 7756+ 7757+ 7758+ 7759+ 7760+ 7761+ 7762+ 7763+
7764+ 7765+ 7766+ 7767+ 7768+ 7769+ 7770+ 7771+ 7772+ 7773+ 7774+ 7775+
7776+ 7777+ 7778+ 7779+ 7780+ 7781+ 7782+ 7783+ 7784+ 7785+ 7786+ 7787+
7788+ 7789+ 7790+ 7791+ 7792+ 7793+ 7794+ 7795+ 7796+ 7797+ 7798+ 7799+
7800+ 7801+ 7802+ 7803+ 7804+ 7805+ 7806+ 7807+ 7808+ 7809+ 7810+ 7811+
7812+ 7813+ 7814+ 7815+ 7816+ 7817+ 7818+ 7819+ 7820+ 7821+ 7822+ 7823+
7824+ 7825+ 7826+ 7827+ 7828+ 7829+ 7830+ 7831+ 7832+ 7833+ 7834+ 7835+
7836+ 7837+ 7838+ 7839+ 7840+ 7841+ 7842+ 7843+ 7844+ 7845+ 7846+ 7847+
7848+ 7849+ 7850+ 7851+ 7852+ 7853+ 7854+ 7855+ 7856+ 7857+ 7858+ 7859+
7860+ 7861+ 7862+ 7863+ 7864+ 7865+ 7866+ 7867+ 7868+ 7869+ 7870+ 7871+
7872+ 7873+ 7874+ 7875+ 7876+ 7877+ 7878+ 7879+ 7880+ 7881+ 7882+ 7883+
7884+ 7885+ 7886+ 7887+ 7888+ 7889+ 7890+ 7891+ 7892+ 7893+ 7894+ 7895+
7896+ 7897+ 7898+ 7899+ 7900+ 7901+ 7902+ 7903+ 7904+ 7905+ 7906+ 7907+
7908+ 7909+ 7910+ 7911+ 7912+ 7913+ 7914+ 7915+ 7916+ 7917+ 7918+ 7919+
7920+ 7921+ 7922+ 7923+ 7924+ 7925+ 7926+ 7927+ 7928+ 7929+ 7930+ 7931+
7932+ 7933+ 7934+ 7935+ 7936+ 7937+ 7938+ 7939+ 7940+ 7941+ 7942+ 7943+
7944+ 7945+ 7946+ 7947+ 7948+ 7949+ 7950+ 7951+ 7952+ 7953+ 7954+ 7955+
7956+ 7957+ 7958+ 7959+ 7960+ 7961+ 7962+ 7963+ 7964+ 7965+ 7966+ 7967+
7968+ 7969+ 7970+ 7971+ 7972+ 7973+ 7974+ 7975+ 7976+ 7977+ 7978+ 7979+
7980+ 7981+ 7982+ 7983+ 7984+ 7985+ 7986+ 7987+ 7988+ 7989+ 7990+ 7991+
7992+ 7993+ 7994+ 7995+ 7996+ 7997+ 7998+ 7999+ 8000+ 8001+ 8002+ 8003+
8004+ 8005+ 8006+ 8007+ 8008+ 8009+ 8010+ 8011+ 8012+ 8013+ 8014+ 8015+
8016+ 8017+ 8018+ 8019+ 8020+ 8021+ 8022+ 8023+ 8024+ 8025+ 8026+ 8027+
8028+ 8029+ 8030+ 8031+ 8032+ 8033+ 8034+ 8035+ 8036+ 8037+ 8038+ 8039+
8040+ 8041+ 8042+ 8043+ 8044+ 8045+ 8046+ 8047+ 8048+ 8049+ 8050+ 8051+
8052+ 8053+ 8054+ 8055+ 8056+ 8057+ 8058+ 8059+ 8060+ 8061+ 8062+ 8063+
8064+ 8065+ 8066+ 8067+ 8068+ 8069+ 8070+ 8071+ 8072+ 8073+ 8074+ 8075+
8076+ 8077+ 8078+ 8079+ 8080+ 8081+ 8082+ 8083+ 8084+ 8085+ 8086+ 8087+
8088+ 8089+ 8090+ 8091+ 8092+ 8093+ 8094+ 8095+ 8096+ 8097+ 8098+ 8099+
8100+ 8101+ 8102+ 8103+ 8104+ 8105+ 8106+ 8107+ 8108+ 8109+ 8110+ 8111+
8112+ 8113+ 8114+ 8115+ 8116+ 8117+ 8118+ 8119+ 8120+ 8121+ 8122+ 8123+
8124+ 8125+ 8126+ 8127+ 8128+ 8129+ 8130+ 8131+ 8132+ 8133+ 8134+ 8135+
8136+ 8137+ 8138+ 8139+ 8140+ 8141+ 8142+ 8143+ 8144+ 8145+ 8146+ 8147+
8148+ 8149+ 8150+ 8151+ 8152+ 8153+ 8154+ 8155+ 8156+ 8157+ 8158+ 8159+
8160+ 8161+ 8162+ 8163+ 8164+ 8165+ 8166+ 8167+ 8168+ 8169+ 8170+ 8171+
8172+ 8173+ 8174+ 8175+ 8176+ 8177+ 8178+ 8179+ 8180+ 8181+ 8182+ 8183+
8184+ 8185+ 8186+ 8187+ 8188+ 8189+ 8190+ 8191+ 8192+ 8193+ 8194+ 8195+
8196+ 8197+ 8198+ 8199+ 8200+ 8201+ 8202+ 8203+ 8204+ 8205+ 8206+ 8207+
8208+ 8209+ 8210+ 8211+ 8212+ 8213+ 8214+ 8215+ 8216+ 8217+ 8218+ 8219+
8220+ 8221+ 8222+ 8223+ 8224+ 8225+ 8226+ 8227+ 8228+ 8229+ 8230+ 8231+
8232+ 8233+ 8234+ 8235+ 8236+ 8237+ 8238+ 8239+ 8240+ 8241+ 8242+ 8243+
8244+ 8245+ 8246+ 8247+ 8248+ 8249+ 8250+ 8251+ 8252+ 8253+ 8254+ 8255+
8256+ 8257+ 8258+ 8259+ 8260+ 8261+ 8262+ 8263+ 8264+ 8265+ 8266+ 8267+
8268+ 8269+ 8270+ 8271+ 8272+ 8273+ 8274+ 8275+ 8276+ 8277+ 8278+ 8279+
8280+ 8281+ 8282+ 8283+ 8284+ 8285+ 8286+ 8287+ 8288+ 8289+ 8290+ 8291+
8292+ 8293+ 8294+ 8295+ 8296+ 8297+ 8298+ 8299+ 8300+ 8301+ 8302+ 8303+
8304+ 8305+ 8306+ 8307+ 8308+ 8309+ 8310+ 8311+ 8312+ 8313+ 8314+ 8315+
8316+ 8317+ 8318+ 8319+ 8320+ 8321+ 8322+ 8323+ 8324+ 8325+ 8326+ 8327+
8328+ 8329+ 8330+ 8331+ 8332+ 8333+ 8334+ 8335+ 8336+ 8337+ 8338+ 8339+
8340+ 8341+ 8342+ 8343+ 8344+ 8345+ 8346+ 8347+ 8348+ 8349+ 8350+ 8351+
8352+ 8353+ 8354+ 8355+ 8356+ 8357+ 8358+ 8359+ 8360+ 8361+ 8362+ 8363+
8364+ 8365+ 8366+ 8367+ 8368+ 8369+ 8370+ 8371+ 8372+ 8373+ 8374+ 8375+
8376+ 8377+ 8378+ 8379+ 8380+ 8381+ 8382+ 8383+ 8384+ 8385+ 8386+ 8387+
8388+ 8389+ 8390+ 8391+ 8392+ 8393+ 8394+ 8395+ 8396+ 8397+ 8398+ 8399+
8400+ 8401+ 8402+ 8403+ 8404+ 8405+ 8406+ 8407+ 8408+ 8409+ 8410+ 8411+
8412+ 8413+ 8414+ 8415+ 8416+ 8417+ 8418+ 8419+ 8420+ 8421+ 8422+ 8423+
8424+ 8425+ 8426+ 8427+ 8428+ 8429+ 8430+ 8431+ 8432+ 8433+ 8434+ 8435+
8436+ 8437+ 8438+ 8439+ 8440+ 8441+ 8442+ 8443+ 8444+ 8445+ 8446+ 8447+
8448+ 8449+ 8450+ 8451+ 8452+ 8453+ 8454+ 8455+ 8456+ 8457+ 8458+ 8459+
8460+ 8461+ 8462+ 8463+ 8464+ 8465+ 8466+ 8467+ 8468+ 8469+ 8470+ 8471+
8472+ 8473+ 8474+ 8475+ 8476+ 8477+ 8478+ 8479+ 8480+ 8481+ 8482+ 8483+
8484+ 8485+ 8486+ 8487+ 8488+ 8489+ 8490+ 8491+ 8492+ 8493+ 8494+ 8495+
8496+ 8497+ 8498+ 8499+ 8500+ 8501+ 8502+ 8503+ 8504+ 8505+ 8506+ 8507+
8508+ 8509+ 8510+ 8511+ 8512+ 8513+ 8514+ 8515+ 8516+ 8517+ 8518+ 8519+
8520+ 8521+ 8522+ 8523+ 8524+ 8525+ 8526+ 8527+ 8528+ 8529+ 8530+ 8531+
8532+ 8533+ 8534+ 8535+ 8536+ 8537+ 8538+ 8539+ 8540+ 8541+ 8542+ 8543+
8544+ 8545+ 8546+ 8547+ 8548+ 8549+ 8550+ 8551+ 8552+ 8553+ 8554+ 8555+
8556+ 8557+ 8558+ 8559+ 8560+ 8561+ 8562+ 8563+ 8564+ 8565+ 8566+ 8567+
8568+ 8569+ 8570+ 8571+ 8572+ 8573+ 8574+ 8575+ 8576+ 8577+ 8578+ 8579+
8580+ 8581+ 8582+ 8583+ 8584+ 8585+ 8586+ 8587+ 8588+ 8589+ 8590+ 8591+
8592+ 8593+ 8594+ 8595+ 8596+ 8597+ 8598+ 8599+ 8600+ 8601+ 8602+ 8603+
8604+ 8605+ 8606+ 8607+ 8608+ 8609+ 8610+ 8611+ 8612+ 8613+ 8614+ 8615+
8616+ 8617+ 8618+ 8619+ 8620+ 8621+ 8622+ 8623+ 8624+ 8625+ 8626+ 8627+
8628+ 8629+ 8630+ 8631+ 8632+ 8633+ 8634+ 8635+ 8636+ 8637+ 8638+ 8639+
8640+ 8641+ 8642+ 8643+ 8644+ 8645+ 8646+ 8647+ 8648+ 8649+ 8650+ 8651+
8652+ 8653+ 8654+ 8655+ 8656+ 8657+ 8658+ 8659+ 8660+ 8661+ 8662+ 8663+
8664+ 8665+ 8666+ 8667+ 8668+ 8669+ 8670+ 8671+ 8672+ 8673+ 8674+ 8675+
8676+ 8677+ 8678+ 8679+ 8680+ 8681+ 8682+ 8683+ 8684+ 8685+ 8686+ 8687+
8688+ 8689+ 8690+ 8691+ 8692+ 8693+ 8694+ 8695+ 8696+ 8697+ 8698+ 8699+
8700+ 8701+ 8702+ 8703+ 8704+ 8705+ 8706+ 8707+ 8708+ 8709+ 8710+ 8711+
8712+ 8713+ 8714+ 8715+ 8716+ 8717+ 8718+ 8719+ 8720+ 8721+ 8722+ 8723+
8724+ 8725+ 8726+ 8727+ 8728+ 8729+ 8730+ 8731+ 8732+ 8733+ 8734+ 8735+
8736+ 8737+ 8738+ 8739+ 8740+ 8741+ 8742+ 8743+ 8744+ 8745+ 8746+ 8747+
8748+ 8749+ 8750+ 8751+ 8752+ 8753+ 8754+ 8755+ 8756+ 8757+ 8758+ 8759+
8760+ 8761+ 8762+ 8763+ 8764+ 8765+ 8766+ 8767+ 8768+ 8769+ 8770+ 8771+
8772+ 8773+ 8774+ 8775+ 8776+ 8777+ 8778+ 8779+ 8780+ 8781+ 8782+ 8783+
8784+ 8785+ 8786+ 8787+ 8788+ 8789+ 8790+ 8791+ 8792+ 8793+ 8794+ 8795+
8796+ 8797+ 8798+ 8799+ 8800+ 8801+ 8802+ 8803+ 8804+ 8805+ 8806+ 8807+
8808+ 8809+ 8810+ 8811+ 8812+ 8813+ 8814+ 8815+ 8816+ 8817+ 8818+ 8819+
8820+ 8821+ 8822+ 8823+ 8824+ 8825+ 8826+ 8827+ 8828+ 8829+ 8830+ 8831+
8832+ 8833+ 8834+ 8835+ 8836+ 8837+ 8838+ 8839+ 8840+ 8841+ 8842+ 8843+
8844+ 8845+ 8846+ 8847+ 8848+ 8849+ 8850+ 8851+ 8852+ 8853+ 8854+ 8855+
8856+ 8857+ 8858+ 8859+ 8860+ 8861+ 8862+ 8863+ 8864+ 8865+ 8866+ 8867+
8868+ 8869+ 8870+ 8871+ 8872+ 8873+ 8874+ 8875+ 8876+ 8877+ 8878+ 8879+
8880+ 8881+ 8882+ 8883+ 8884+ 8885+ 8886+ 8887+ 8888+ 8889+ 8890+ 8891+
8892+ 8893+ 8894+ 8895+ 8896+ 8897+ 8898+ 8899+ 8900+ 8901+ 8902+ 8903+
8904+ 8905+ 8906+ 8907+ 8908+ 8909+ 8910+ 8911+ 8912+ 8913+ 8914+ 8915+
8916+ 8917+ 8918+ 8919+ 8920+ 8921+ 8922+ 8923+ 8924+ 8925+ 8926+ 8927+
8928+ 8929+ 8930+ 8931+ 8932+ 8933+ 8934+ 8935+ 8936+ 8937+ 8938+ 8939+
8940+ 8941+ 8942+ 8943+ 8944+ 8945+ 8946+ 8947+ 8948+ 8949+ 8950+ 8951+
8952+ 8953+ 8954+ 8955+ 8956+ 8957+ 8958+ 8959+ 8960+ 8961+ 8962+ 8963+
8964+ 8965+ 8966+ 8967+ 8968+ 8969+ 8970+ 8971+ 8972+ 8973+ 8974+ 8975+
8976+ 8977+ 8978+ 8979+ 8980+ 8981+ 8982+ 8983+ 8984+ 8985+ 8986+ 8987+
8988+ 8989+ 8990+ 8991+ 8992+ 8993+ 8994+ 8995+ 8996+ 8997+ 8998+ 8999+
9000+ 9001+ 9002+ 9003+ 9004+ 9005+ 9006+ 9007+ 9008+ 9009+ 9010+ 9011+
9012+ 9013+ 9014+ 9015+ 9016+ 9017+ 9018+ 9019+ 9020+ 9021+ 9022+ 9023+
9024+ 9025+ 9026+ 9027+ 9028+ 9029+ 9030+ 9031+ 9032+ 9033+ 9034+ 9035+
9036+ 9037+ 9038+ 9039+ 9040+ 9041+ 9042+ 9043+ 9044+ 9045+ 9046+ 9047+
9048+ 9049+ 9050+ 9051+ 9052+ 9053+ 9054+ 9055+ 9056+ 9057+ 9058+ 9059+
9060+ 9061+ 9062+ 9063+ 9064+ 9065+ 9066+ 9067+ 9068+ 9069+ 9070+ 9071+
9072+ 9073+ 9074+ 9075+ 9076+ 9077+ 9078+ 9079+ 9080+ 9081+ 9082+ 9083+
9084+ 9085+ 9086+ 9087+ 9088+ 9089+ 9090+ 9091+ 9092+ 9093+ 9094+ 9095+
9096+ 9097+ 9098+ 9099+ 9100+ 9101+ 9102+ 9103+ 9104+ 9105+ 9106+ 9107+
9108+ 9109+ 9110+ 9111+ 9112+ 9113+ 9114+ 9115+ 9116+ 9117+ 9118+ 9119+
9120+ 9121+ 9122+ 9123+ 9124+ 9125+ 9126+ 9127+ 9128+ 9129+ 9130+ 9131+
9132+ 9133+ 9134+ 9135+ 9136+ 9137+ 9138+ 9139+ 9140+ 9141+ 9142+ 9143+
9144+ 9145+ 9146+ 9147+ 9148+ 9149+ 9150+ 9151+ 9152+ 9153+ 9154+ 9155+
9156+ 9157+ 9158+ 9159+ 9160+ 9161+ 9162+ 9163+ 9164+ 9165+ 9166+ 9167+
9168+ 9169+ 9170+ 9171+ 9172+ 9173+ 9174+ 9175+ 9176+ 9177+ 9178+ 9179+
9180+ 9181+ 9182+ 9183+ 9184+ 9185+ 9186+ 9187+ 9188+ 9189+ 9190+ 9191+
9192+ 9193+ 9194+ 9195+ 9196+ 9197+ 9198+ 9199+ 9200+ 9201+ 9202+ 9203+
9204+ 9205+ 9206+ 9207+ 9208+ 9209+ 9210+ 9211+ 9212+ 9213+ 9214+ 9215+
9216+ 9217+ 9218+ 9219+ 9220+ 9221+ 9222+ 9223+ 9224+ 9225+ 9226+ 9227+
9228+ 9229+ 9230+ 9231+ 9232+ 9233+ 9234+ 9235+ 9236+ 9237+ 9238+ 9239+
9240+ 9241+ 9242+ 9243+ 9244+ 9245+ 9246+ 9247+ 9248+ 9249+ 9250+ 9251+
9252+ 9253+ 9254+ 9255+ 9256+ 9257+ 9258+ 9259+ 9260+ 9261+ 9262+ 9263+
9264+ 9265+ 9266+ 9267+ 9268+ 9269+ 9270+ 9271+ 9272+ 9273+ 9274+ 9275+
9276+ 9277+ 9278+ 9279+ 9280+ 9281+ 9282+ 9283+ 9284+ 9285+ 9286+ 9287+
9288+ 9289+ 9290+ 9291+ 9292+ 9293+ 9294+ 9295+ 9296+ 9297+ 9298+ 9299+
9300+ 9301+ 9302+ 9303+ 9304+ 9305+ 9306+ 9307+ 9308+ 9309+ 9310+ 9311+
9312+ 9313+ 9314+ 9315+ 9316+ 9317+ 9318+ 9319+ 9320+ 9321+ 9322+ 9323+
9324+ 9325+ 9326+ 9327+ 9328+ 9329+ 9330+ 9331+ 9332+ 9333+ 9334+ 9335+
9336+ 9337+ 9338+ 9339+ 9340+ 9341+ 9342+ 9343+ 9344+ 9345+ 9346+ 9347+
9348+ 9349+ 9350+ 9351+ 9352+ 9353+ 9354+ 9355+ 9356+ 9357+ 9358+ 9359+
9360+ 9361+ 9362+ 9363+ 9364+ 9365+ 9366+ 9367+ 9368+ 9369+ 9370+ 9371+
9372+ 9373+ 9374+ 9375+ 9376+ 9377+ 9378+ 9379+ 9380+ 9381+ 9382+ 9383+
9384+ 9385+ 9386+ 9387+ 9388+ 9389+ 9390+ 9391+ 9392+ 9393+ 9394+ 9395+
9396+ 9397+ 9398+ 9399+ 9400+ 9401+ 9402+ 9403+ 9404+ 9405+ 9406+ 9407+
9408+ 9409+ 9410+ 9411+ 9412+ 9413+ 9414+ 9415+ 9416+ 9417+ 9418+ 9419+
9420+ 9421+ 9422+ 9423+ 9424+ 9425+ 9426+ 9427+ 9428+ 9429+ 9430+ 9431+
9432+ 9433+ 9434+ 9435+ 9436+ 9437+ 9438+ 9439+ 9440+ 9441+ 9442+ 9443+
9444+ 9445+ 9446+ 9447+ 9448+ 9449+ 9450+ 9451+ 9452+ 9453+ 9454+ 9455+
9456+ 9457+ 9458+ 9459+ 9460+ 9461+ 9462+ 9463+ 9464+ 9465+ 9466+ 9467+
9468+ 9469+ 9470+ 9471+ 9472+ 9473+ 9474+ 9475+ 9476+ 9477+ 9478+ 9479+
9480+ 9481+ 9482+ 9483+ 9484+ 9485+ 9486+ 9487+ 9488+ 9489+ 9490+ 9491+
9492+ 9493+ 9494+ 9495+ 9496+ 9497+ 9498+ 9499+ 9500+ 9501+ 9502+ 9503+
9504+ 9505+ 9506+ 9507+ 9508+ 9509+ 9510+ 9511+ 9512+ 9513+ 9514+ 9515+
9516+ 9517+ 9518+ 9519+ 9520+ 9521+ 9522+ 9523+ 9524+ 9525+ 9526+ 9527+
9528+ 9529+ 9530+ 9531+ 9532+ 9533+ 9534+ 9535+ 9536+ 9537+ 9538+ 9539+
9540+ 9541+ 9542+ 9543+ 9544+ 9545+ 9546+ 9547+ 9548+ 9549+ 9550+ 9551+
9552+ 9553+ 9554+ 9555+ 9556+ 9557+ 9558+ 9559+ 9560+ 9561+ 9562+ 9563+
9564+ 9565+ 9566+ 9567+ 9568+ 9569+ 9570+ 9571+ 9572+ 9573+ 9574+ 9575+
9576+ 9577+ 9578+ 9579+ 9580+ 9581+ 9582+ 9583+ 9584+ 9585+ 9586+ 9587+
9588+ 9589+ 9590+ 9591+ 9592+ 9593+ 9594+ 9595+ 9596+ 9597+ 9598+ 9599+
9600+ 9601+ 9602+ 9603+ 9604+ 9605+ 9606+ 9607+ 9608+ 9609+ 9610+ 9611+
9612+ 9613+ 9614+ 9615+ 9616+ 9617+ 9618+ 9619+ 9620+ 9621+ 9622+ 9623+
9624+ 9625+ 9626+ 9627+ 9628+ 9629+ 9630+ 9631+ 9632+ 9633+ 9634+ 9635+
9636+ 9637+ 9638+ 9639+ 9640+ 9641+ 9642+ 9643+ 9644+ 9645+ 9646+ 9647+
9648+ 9649+ 9650+ 9651+ 9652+ 9653+ 9654+ 9655+ 9656+ 9657+ 9658+ 9659+
9660+ 9661+ 9662+ 9663+ 9664+ 9665+ 9666+ 9667+ 9668+ 9669+ 9670+ 9671+
9672+ 9673+ 9674+ 9675+ 9676+ 9677+ 9678+ 9679+ 9680+ 9681+ 9682+ 9683+
9684+ 9685+ 9686+ 9687+ 9688+ 9689+ 9690+ 9691+ 9692+ 9693+ 9694+ 9695+
9696+ 9697+ 9698+ 9699+ 9700+ 9701+ 9702+ 9703+ 9704+ 9705+ 9706+ 9707+
9708+ 9709+ 9710+ 9711+ 9712+ 9713+ 9714+ 9715+ 9716+ 9717+ 9718+ 9719+
9720+ 9721+ 9722+ 9723+ 9724+ 9725+ 9726+ 9727+ 9728+ 9729+ 9730+ 9731+
9732+ 9733+ 9734+ 9735+ 9736+ 9737+ 9738+ 9739+ 9740+ 9741+ 9742+ 9743+
9744+ 9745+ 9746+ 9747+ 9748+ 9749+ 9750+ 9751+ 9752+ 9753+ 9754+ 9755+
9756+ 9757+ 9758+ 9759+ 9760+ 9761+ 9762+ 9763+ 9764+ 9765+ 9766+ 9767+
9768+ 9769+ 9770+ 9771+ 9772+ 9773+ 9774+ 9775+ 9776+ 9777+ 9778+ 9779+
9780+ 9781+ 9782+ 9783+ 9784+ 9785+ 9786+ 9787+ 9788+ 9789+ 9790+ 9791+
9792+ 9793+ 9794+ 9795+ 9796+ 9797+ 9798+ 9799+ 9800+ 9801+ 9802+ 9803+
9804+ 9805+ 9806+ 9807+ 9808+ 9809+ 9810+ 9811+ 9812+ 9813+ 9814+ 9815+
9816+ 9817+ 9818+ 9819+ 9820+ 9821+ 9822+ 9823+ 9824+ 9825+ 9826+ 9827+
9828+ 9829+ 9830+ 9831+ 9832+ 9833+ 9834+ 9835+ 9836+ 9837+ 9838+ 9839+
9840+ 9841+ 9842+ 9843+ 9844+ 9845+ 9846+ 9847+ 9848+ 9849+ 9850+ 9851+
9852+ 9853+ 9854+ 9855+ 9856+ 9857+ 9858+ 9859+ 9860+ 9861+ 9862+ 9863+
9864+ 9865+ 9866+ 9867+ 9868+ 9869+ 9870+ 9871+ 9872+ 9873+ 9874+ 9875+
9876+ 9877+ 9878+ 9879+ 9880+ 9881+ 9882+ 9883+ 9884+ 9885+ 9886+ 9887+
9888+ 9889+ 9890+ 9891+ 9892+ 9893+ 9894+ 9895+ 9896+ 9897+ 9898+ 9899+
9900+ 9901+ 9902+ 9903+ 9904+ 9905+ 9906+ 9907+ 9908+ 9909+ 9910+ 9911+
9912+ 9913+ 9914+ 9915+ 9916+ 9917+ 9918+ 9919+ 9920+ 9921+ 9922+ 9923+
9924+ 9925+ 9926+ 9927+ 9928+ 9929+ 9930+ 9931+ 9932+ 9933+ 9934+ 9935+
9936+ 9937+ 9938+ 9939+ 9940+ 9941+ 9942+ 9943+ 9944+ 9945+ 9946+ 9947+
9948+ 9949+ 9950+ 9951+ 9952+ 9953+ 9954+ 9955+ 9956+ 9957+ 9958+ 9959+
9960+ 9961+ 9962+ 9963+ 9964+ 9965+ 9966+ 9967+ 9968+ 9969+ 9970+ 9971+
9972+ 9973+ 9974+ 9975+ 9976+ 9977+ 9978+ 9979+ 9980+ 9981+ 9982+ 9983+
9984+ 9985+ 9986+ 9987+ 9988+ 9989+ 9990+ 9991+ 9992+ 9993+ 9994+ 9995+
9996+ 9997+ 9998+ 9999+ 10000;

return sum;

}

"William Ryan" <do********@comcast.nospam.net> wrote in message
news:%2***************@TK2MSFTNGP09.phx.gbl...
I just did it going with 200 Hard coded ints, then 390, then 300. Each time I got the correct results. Are you positive of the input numbers? I know
that's a stupid question, but I first did each one by loading them into an
Int Array and adding them like that. It worked. Then I actually used
straight hard coding, and I used the number 10 each time and added 100000 to the last one for good measure (just to make sure the value I had was
similarly high). No problems whatsoever. Inasmuch as you can load those
values in an array and iterate it successfully, couldn't you just load the
array and use an iterative approach? I understand that's what you are
asking about...why should you have to do this, but it's probably easier than verifying the math each time when you know it will work. If I can find
anything, I'll repost.

HTH,

Bill
"Mountain Bikn' Guy" <vc@attbi.com> wrote in message
news:NZUjb.795942$YN5.793228@sccrnsc01...
Take some standard code such as shown below. It simply loops to add up a
series of terms and it produces the correct result.

// sum numbers with a loop
public int DoSumLooping(int iterations)
{
int result = 0;
for(int i = 1;i <=iterations;i++)
{
result += i;
}
return result;
}

Now translate this into a specific solution that doesn't use looping (and use the same value for the number of iterations the loop performs). This
code returns an incorrect result. The method consists entirely of a very
straightforward code statement, but in this case .NET adds the numbers
incorrectly.
public double ComputeSum( )
{
// Brute force sum method
// For iterations == 10000
double sum = 0+ 1+ 2+ 3+ 4+ 5+ 6+ 7+ 8+ 9+ 10+ 11+ 12+ 13+ 14+ 15+ ...
+ 9997+ 9998+ 9999+ 10000;
return sum;
}
The above method returns an incorrect result with any number of terms

above
about 200. It will correctly add 1 + 2 + ... + 200, but it will NOT
correctly add 1 + 2 + ... + 1000.

I have just run across this, and I have not yet researched the possible
reasons for this behavior. It may be a known issue related to either stack size or the length of a code line, but to my knowledge it hasn't been
discussed in any of the "popular" literature on C# and .NET. I need to

write
code like this, so if anyone has already encountered this issue, please
advise me.
Here's another example that also creates problems, but of a somewhat
different nature. Take the following code and translate it into a

specific,
non-looping method and try to execute it using reflection. It fails.

public double LoopToCompute()
{
double sumOfProducts = 0;
double grandTotal = 0;
for (int i = 0; i < maxRows; ++i)
{
for (int j = 0; j < maxCols; ++j)
{
sumOfProducts += coeff[j] * table[i][j];
}
a_point[i] = sumOfProducts;
grandTotal += sumOfProducts;
sumOfProducts = 0;
}
return grandTotal;
}//LoopToCompute

The above code works -- but it's equivalent code with loops unrolled

(shown
below) doesn't work unless the maxRows is set very small. For small

values,
the 2 methods (above and below) produce identical results. There is

nothing
"wrong" with the code in that sense. It's similar to the above situation. If
the "size" of the code statement or the number of code statements is too
large, .NET fails. In this case (using reflection) it doesn't return the
incorrect result, as the first example did. In this case, reflection

calls it an invalid program and refuses to run it (but only when the value of
maxRows is above about 250). The reason for this is probably
straightforward. However, I have the need to make statements like this for performance reasons so I need a work-around. Any suggestions are
appreciated! All comments are appreciated.

public double DoBruteForceCompute()
{
double bruteForceSum = 0;

point1=coeff1*table[0][0] +coeff2*table[0][1] +coeff3*table[0][2]
+coeff4*table[0][3] +coeff5*table[0][4] +coeff6*table[0][5]
+coeff7*table[0][6] +coeff8*table[0][7] +coeff9*table[0][8]
+coeff10*table[0][9] +coeff11*table[0][10] +coeff12*table[0][11]
+coeff13*table[0][12] +coeff14*table[0][13] +coeff15*table[0][14]
+coeff16*table[0][15] +coeff17*table[0][16] +coeff18*table[0][17]
+coeff19*table[0][18] +coeff20*table[0][19] +coeff21*table[0][20]
+coeff22*table[0][21] +coeff23*table[0][22] +coeff24*table[0][23]
+coeff25*table[0][24] +coeff26*table[0][25] +coeff27*table[0][26]
+coeff28*table[0][27] +coeff29*table[0][28] +coeff30*table[0][29]
+coeff31*table[0][30] +coeff32*table[0][31] +coeff33*table[0][32]
+coeff34*table[0][33] +coeff35*table[0][34] ;

point2=coeff1*table[1][0] +coeff2*table[1][1] +coeff3*table[1][2]
+coeff4*table[1][3] +coeff5*table[1][4] +coeff6*table[1][5]
+coeff7*table[1][6] +coeff8*table[1][7] +coeff9*table[1][8]
+coeff10*table[1][9] +coeff11*table[1][10] +coeff12*table[1][11]
+coeff13*table[1][12] +coeff14*table[1][13] +coeff15*table[1][14]
+coeff16*table[1][15] +coeff17*table[1][16] +coeff18*table[1][17]
+coeff19*table[1][18] +coeff20*table[1][19] +coeff21*table[1][20]
+coeff22*table[1][21] +coeff23*table[1][22] +coeff24*table[1][23]
+coeff25*table[1][24] +coeff26*table[1][25] +coeff27*table[1][26]
+coeff28*table[1][27] +coeff29*table[1][28] +coeff30*table[1][29]
+coeff31*table[1][30] +coeff32*table[1][31] +coeff33*table[1][32]
+coeff34*table[1][33] +coeff35*table[1][34] ;
[...]

point500=coeff1*table[499][0] +coeff2*table[499][1] +coeff3*table[499][2] +coeff4*table[499][3] +coeff5*table[499][4] +coeff6*table[499][5]
+coeff7*table[499][6] +coeff8*table[499][7] +coeff9*table[499][8]
+coeff10*table[499][9] +coeff11*table[499][10] +coeff12*table[499][11]
+coeff13*table[499][12] +coeff14*table[499][13] +coeff15*table[499][14]
+coeff16*table[499][15] +coeff17*table[499][16] +coeff18*table[499][17]
+coeff19*table[499][18] +coeff20*table[499][19] +coeff21*table[499][20]
+coeff22*table[499][21] +coeff23*table[499][22] +coeff24*table[499][23]
+coeff25*table[499][24] +coeff26*table[499][25] +coeff27*table[499][26]
+coeff28*table[499][27] +coeff29*table[499][28] +coeff30*table[499][29]
+coeff31*table[499][30] +coeff32*table[499][31] +coeff33*table[499][32]
+coeff34*table[499][33] +coeff35*table[499][34] ;

bruteForceSum =
point1 +
point2 + ... +

point499 +
point500
;

return bruteForceSum;

}//DoBruteForceCompute


Jul 21 '05 #6

P: n/a
Hi,

Maybe not the issue, tough it unwinds the loop, the sum of the first n
consecutive numbers:

(n+1)*n
= ---------
2

Greetings
"Mountain Bikn' Guy" <vc@attbi.com> wrote in message
news:NZUjb.795942$YN5.793228@sccrnsc01...
Take some standard code such as shown below. It simply loops to add up a
series of terms and it produces the correct result.

// sum numbers with a loop
public int DoSumLooping(int iterations)
{
int result = 0;
for(int i = 1;i <=iterations;i++)
{
result += i;
}
return result;
}

Now translate this into a specific solution that doesn't use looping (and
use the same value for the number of iterations the loop performs). This
code returns an incorrect result. The method consists entirely of a very
straightforward code statement, but in this case .NET adds the numbers
incorrectly.
public double ComputeSum( )
{
// Brute force sum method
// For iterations == 10000
double sum = 0+ 1+ 2+ 3+ 4+ 5+ 6+ 7+ 8+ 9+ 10+ 11+ 12+ 13+ 14+ 15+ .... + 9997+ 9998+ 9999+ 10000;
return sum;
}
The above method returns an incorrect result with any number of terms above about 200. It will correctly add 1 + 2 + ... + 200, but it will NOT
correctly add 1 + 2 + ... + 1000.

I have just run across this, and I have not yet researched the possible
reasons for this behavior. It may be a known issue related to either stack
size or the length of a code line, but to my knowledge it hasn't been
discussed in any of the "popular" literature on C# and .NET. I need to write code like this, so if anyone has already encountered this issue, please
advise me.
Here's another example that also creates problems, but of a somewhat
different nature. Take the following code and translate it into a specific, non-looping method and try to execute it using reflection. It fails.

public double LoopToCompute()
{
double sumOfProducts = 0;
double grandTotal = 0;
for (int i = 0; i < maxRows; ++i)
{
for (int j = 0; j < maxCols; ++j)
{
sumOfProducts += coeff[j] * table[i][j];
}
a_point[i] = sumOfProducts;
grandTotal += sumOfProducts;
sumOfProducts = 0;
}
return grandTotal;
}//LoopToCompute

The above code works -- but it's equivalent code with loops unrolled (shown below) doesn't work unless the maxRows is set very small. For small values, the 2 methods (above and below) produce identical results. There is nothing "wrong" with the code in that sense. It's similar to the above situation. If the "size" of the code statement or the number of code statements is too
large, .NET fails. In this case (using reflection) it doesn't return the
incorrect result, as the first example did. In this case, reflection calls
it an invalid program and refuses to run it (but only when the value of
maxRows is above about 250). The reason for this is probably
straightforward. However, I have the need to make statements like this for
performance reasons so I need a work-around. Any suggestions are
appreciated! All comments are appreciated.

public double DoBruteForceCompute()
{
double bruteForceSum = 0;

point1=coeff1*table[0][0] +coeff2*table[0][1] +coeff3*table[0][2]
+coeff4*table[0][3] +coeff5*table[0][4] +coeff6*table[0][5]
+coeff7*table[0][6] +coeff8*table[0][7] +coeff9*table[0][8]
+coeff10*table[0][9] +coeff11*table[0][10] +coeff12*table[0][11]
+coeff13*table[0][12] +coeff14*table[0][13] +coeff15*table[0][14]
+coeff16*table[0][15] +coeff17*table[0][16] +coeff18*table[0][17]
+coeff19*table[0][18] +coeff20*table[0][19] +coeff21*table[0][20]
+coeff22*table[0][21] +coeff23*table[0][22] +coeff24*table[0][23]
+coeff25*table[0][24] +coeff26*table[0][25] +coeff27*table[0][26]
+coeff28*table[0][27] +coeff29*table[0][28] +coeff30*table[0][29]
+coeff31*table[0][30] +coeff32*table[0][31] +coeff33*table[0][32]
+coeff34*table[0][33] +coeff35*table[0][34] ;

point2=coeff1*table[1][0] +coeff2*table[1][1] +coeff3*table[1][2]
+coeff4*table[1][3] +coeff5*table[1][4] +coeff6*table[1][5]
+coeff7*table[1][6] +coeff8*table[1][7] +coeff9*table[1][8]
+coeff10*table[1][9] +coeff11*table[1][10] +coeff12*table[1][11]
+coeff13*table[1][12] +coeff14*table[1][13] +coeff15*table[1][14]
+coeff16*table[1][15] +coeff17*table[1][16] +coeff18*table[1][17]
+coeff19*table[1][18] +coeff20*table[1][19] +coeff21*table[1][20]
+coeff22*table[1][21] +coeff23*table[1][22] +coeff24*table[1][23]
+coeff25*table[1][24] +coeff26*table[1][25] +coeff27*table[1][26]
+coeff28*table[1][27] +coeff29*table[1][28] +coeff30*table[1][29]
+coeff31*table[1][30] +coeff32*table[1][31] +coeff33*table[1][32]
+coeff34*table[1][33] +coeff35*table[1][34] ;
[...]

point500=coeff1*table[499][0] +coeff2*table[499][1] +coeff3*table[499][2]
+coeff4*table[499][3] +coeff5*table[499][4] +coeff6*table[499][5]
+coeff7*table[499][6] +coeff8*table[499][7] +coeff9*table[499][8]
+coeff10*table[499][9] +coeff11*table[499][10] +coeff12*table[499][11]
+coeff13*table[499][12] +coeff14*table[499][13] +coeff15*table[499][14]
+coeff16*table[499][15] +coeff17*table[499][16] +coeff18*table[499][17]
+coeff19*table[499][18] +coeff20*table[499][19] +coeff21*table[499][20]
+coeff22*table[499][21] +coeff23*table[499][22] +coeff24*table[499][23]
+coeff25*table[499][24] +coeff26*table[499][25] +coeff27*table[499][26]
+coeff28*table[499][27] +coeff29*table[499][28] +coeff30*table[499][29]
+coeff31*table[499][30] +coeff32*table[499][31] +coeff33*table[499][32]
+coeff34*table[499][33] +coeff35*table[499][34] ;

bruteForceSum =
point1 +
point2 + ... +

point499 +
point500
;

return bruteForceSum;

}//DoBruteForceCompute

Jul 21 '05 #7

P: n/a
maybe there is some sort of limit on the ammount of +s and length of your
line, have you tried splitting it on small chunks?
"Mountain Bikn' Guy" <vc@attbi.com> wrote in message
news:NZUjb.795942$YN5.793228@sccrnsc01...
Take some standard code such as shown below. It simply loops to add up a
series of terms and it produces the correct result.

// sum numbers with a loop
public int DoSumLooping(int iterations)
{
int result = 0;
for(int i = 1;i <=iterations;i++)
{
result += i;
}
return result;
}

Now translate this into a specific solution that doesn't use looping (and
use the same value for the number of iterations the loop performs). This
code returns an incorrect result. The method consists entirely of a very
straightforward code statement, but in this case .NET adds the numbers
incorrectly.
public double ComputeSum( )
{
// Brute force sum method
// For iterations == 10000
double sum = 0+ 1+ 2+ 3+ 4+ 5+ 6+ 7+ 8+ 9+ 10+ 11+ 12+ 13+ 14+ 15+ .... + 9997+ 9998+ 9999+ 10000;
return sum;
}
The above method returns an incorrect result with any number of terms above about 200. It will correctly add 1 + 2 + ... + 200, but it will NOT
correctly add 1 + 2 + ... + 1000.

I have just run across this, and I have not yet researched the possible
reasons for this behavior. It may be a known issue related to either stack
size or the length of a code line, but to my knowledge it hasn't been
discussed in any of the "popular" literature on C# and .NET. I need to write code like this, so if anyone has already encountered this issue, please
advise me.
Here's another example that also creates problems, but of a somewhat
different nature. Take the following code and translate it into a specific, non-looping method and try to execute it using reflection. It fails.

public double LoopToCompute()
{
double sumOfProducts = 0;
double grandTotal = 0;
for (int i = 0; i < maxRows; ++i)
{
for (int j = 0; j < maxCols; ++j)
{
sumOfProducts += coeff[j] * table[i][j];
}
a_point[i] = sumOfProducts;
grandTotal += sumOfProducts;
sumOfProducts = 0;
}
return grandTotal;
}//LoopToCompute

The above code works -- but it's equivalent code with loops unrolled (shown below) doesn't work unless the maxRows is set very small. For small values, the 2 methods (above and below) produce identical results. There is nothing "wrong" with the code in that sense. It's similar to the above situation. If the "size" of the code statement or the number of code statements is too
large, .NET fails. In this case (using reflection) it doesn't return the
incorrect result, as the first example did. In this case, reflection calls
it an invalid program and refuses to run it (but only when the value of
maxRows is above about 250). The reason for this is probably
straightforward. However, I have the need to make statements like this for
performance reasons so I need a work-around. Any suggestions are
appreciated! All comments are appreciated.

public double DoBruteForceCompute()
{
double bruteForceSum = 0;

point1=coeff1*table[0][0] +coeff2*table[0][1] +coeff3*table[0][2]
+coeff4*table[0][3] +coeff5*table[0][4] +coeff6*table[0][5]
+coeff7*table[0][6] +coeff8*table[0][7] +coeff9*table[0][8]
+coeff10*table[0][9] +coeff11*table[0][10] +coeff12*table[0][11]
+coeff13*table[0][12] +coeff14*table[0][13] +coeff15*table[0][14]
+coeff16*table[0][15] +coeff17*table[0][16] +coeff18*table[0][17]
+coeff19*table[0][18] +coeff20*table[0][19] +coeff21*table[0][20]
+coeff22*table[0][21] +coeff23*table[0][22] +coeff24*table[0][23]
+coeff25*table[0][24] +coeff26*table[0][25] +coeff27*table[0][26]
+coeff28*table[0][27] +coeff29*table[0][28] +coeff30*table[0][29]
+coeff31*table[0][30] +coeff32*table[0][31] +coeff33*table[0][32]
+coeff34*table[0][33] +coeff35*table[0][34] ;

point2=coeff1*table[1][0] +coeff2*table[1][1] +coeff3*table[1][2]
+coeff4*table[1][3] +coeff5*table[1][4] +coeff6*table[1][5]
+coeff7*table[1][6] +coeff8*table[1][7] +coeff9*table[1][8]
+coeff10*table[1][9] +coeff11*table[1][10] +coeff12*table[1][11]
+coeff13*table[1][12] +coeff14*table[1][13] +coeff15*table[1][14]
+coeff16*table[1][15] +coeff17*table[1][16] +coeff18*table[1][17]
+coeff19*table[1][18] +coeff20*table[1][19] +coeff21*table[1][20]
+coeff22*table[1][21] +coeff23*table[1][22] +coeff24*table[1][23]
+coeff25*table[1][24] +coeff26*table[1][25] +coeff27*table[1][26]
+coeff28*table[1][27] +coeff29*table[1][28] +coeff30*table[1][29]
+coeff31*table[1][30] +coeff32*table[1][31] +coeff33*table[1][32]
+coeff34*table[1][33] +coeff35*table[1][34] ;
[...]

point500=coeff1*table[499][0] +coeff2*table[499][1] +coeff3*table[499][2]
+coeff4*table[499][3] +coeff5*table[499][4] +coeff6*table[499][5]
+coeff7*table[499][6] +coeff8*table[499][7] +coeff9*table[499][8]
+coeff10*table[499][9] +coeff11*table[499][10] +coeff12*table[499][11]
+coeff13*table[499][12] +coeff14*table[499][13] +coeff15*table[499][14]
+coeff16*table[499][15] +coeff17*table[499][16] +coeff18*table[499][17]
+coeff19*table[499][18] +coeff20*table[499][19] +coeff21*table[499][20]
+coeff22*table[499][21] +coeff23*table[499][22] +coeff24*table[499][23]
+coeff25*table[499][24] +coeff26*table[499][25] +coeff27*table[499][26]
+coeff28*table[499][27] +coeff29*table[499][28] +coeff30*table[499][29]
+coeff31*table[499][30] +coeff32*table[499][31] +coeff33*table[499][32]
+coeff34*table[499][33] +coeff35*table[499][34] ;

bruteForceSum =
point1 +
point2 + ... +

point499 +
point500
;

return bruteForceSum;

}//DoBruteForceCompute

Jul 21 '05 #8

P: n/a
Ok, I just ran it and after my IDE finished choking, I'm getting 50005000
whether I loop through it or use your code. That is the same number Excel
is giving me.

Are you getting 50005000 in your computations? From this machine, it looks
like it's working correctly.
"Mountain Bikn' Guy" <vc@attbi.com> wrote in message
news:tuVjb.806880$uu5.142280@sccrnsc04...
Yes, I'm positive. I will post the exact code. Here is the test anyone can
do:
1. paste this code, compile and run. Check the result.
2. Use Excel and do the same thing and compare the result. In Excel, simply enter 1 on row 1 and 2 on row 2, then copy down to 10000 (or whatever size
you wish). Then use the sum function to get the sum. You will see that the
C# code is vastly in error.

Here's the code (sorry, but it's long):
public double ComputeSum( )

{

// Brute force sum method

// For value = 10000

double sum = 0+ 1+ 2+ 3+ 4+ 5+ 6+ 7+ 8+ 9+ 10+ 11+ 12+ 13+ 14+ 15+ 16+ 17+
18+ 19+ 20+ 21+ 22+ 23+ 24+ 25+ 26+ 27+ 28+ 29+ 30+ 31+ 32+ 33+ 34+ 35+ 36+ 37+ 38+ 39+ 40+ 41+ 42+ 43+ 44+ 45+ 46+ 47+ 48+ 49+ 50+ 51+ 52+ 53+ 54+ 55+ 56+ 57+ 58+ 59+ 60+ 61+ 62+ 63+ 64+ 65+ 66+ 67+ 68+ 69+ 70+ 71+ 72+ 73+ 74+ 75+ 76+ 77+ 78+ 79+ 80+ 81+ 82+ 83+ 84+ 85+ 86+ 87+ 88+ 89+ 90+ 91+ 92+ 93+ 94+ 95+ 96+ 97+ 98+ 99+ 100+ 101+ 102+ 103+ 104+ 105+ 106+ 107+ 108+ 109+
110+ 111+ 112+ 113+ 114+ 115+ 116+ 117+ 118+ 119+ 120+ 121+ 122+ 123+ 124+
125+ 126+ 127+ 128+ 129+ 130+ 131+ 132+ 133+ 134+ 135+ 136+ 137+ 138+ 139+
140+ 141+ 142+ 143+ 144+ 145+ 146+ 147+ 148+ 149+ 150+ 151+ 152+ 153+ 154+
155+ 156+ 157+ 158+ 159+ 160+ 161+ 162+ 163+ 164+ 165+ 166+ 167+ 168+ 169+
170+ 171+ 172+ 173+ 174+ 175+ 176+ 177+ 178+ 179+ 180+ 181+ 182+ 183+ 184+
185+ 186+ 187+ 188+ 189+ 190+ 191+ 192+ 193+ 194+ 195+ 196+ 197+ 198+ 199+
200+ 201+ 202+ 203+ 204+ 205+ 206+ 207+ 208+ 209+ 210+ 211+ 212+ 213+ 214+
215+ 216+ 217+ 218+ 219+ 220+ 221+ 222+ 223+ 224+ 225+ 226+ 227+ 228+ 229+
230+ 231+ 232+ 233+ 234+ 235+ 236+ 237+ 238+ 239+ 240+ 241+ 242+ 243+ 244+
245+ 246+ 247+ 248+ 249+ 250+ 251+ 252+ 253+ 254+ 255+ 256+ 257+ 258+ 259+
260+ 261+ 262+ 263+ 264+ 265+ 266+ 267+ 268+ 269+ 270+ 271+ 272+ 273+ 274+
275+ 276+ 277+ 278+ 279+ 280+ 281+ 282+ 283+ 284+ 285+ 286+ 287+ 288+ 289+
290+ 291+ 292+ 293+ 294+ 295+ 296+ 297+ 298+ 299+ 300+ 301+ 302+ 303+ 304+
305+ 306+ 307+ 308+ 309+ 310+ 311+ 312+ 313+ 314+ 315+ 316+ 317+ 318+ 319+
320+ 321+ 322+ 323+ 324+ 325+ 326+ 327+ 328+ 329+ 330+ 331+ 332+ 333+ 334+
335+ 336+ 337+ 338+ 339+ 340+ 341+ 342+ 343+ 344+ 345+ 346+ 347+ 348+ 349+
350+ 351+ 352+ 353+ 354+ 355+ 356+ 357+ 358+ 359+ 360+ 361+ 362+ 363+ 364+
365+ 366+ 367+ 368+ 369+ 370+ 371+ 372+ 373+ 374+ 375+ 376+ 377+ 378+ 379+
380+ 381+ 382+ 383+ 384+ 385+ 386+ 387+ 388+ 389+ 390+ 391+ 392+ 393+ 394+
395+ 396+ 397+ 398+ 399+ 400+ 401+ 402+ 403+ 404+ 405+ 406+ 407+ 408+ 409+
410+ 411+ 412+ 413+ 414+ 415+ 416+ 417+ 418+ 419+ 420+ 421+ 422+ 423+ 424+
425+ 426+ 427+ 428+ 429+ 430+ 431+ 432+ 433+ 434+ 435+ 436+ 437+ 438+ 439+
440+ 441+ 442+ 443+ 444+ 445+ 446+ 447+ 448+ 449+ 450+ 451+ 452+ 453+ 454+
455+ 456+ 457+ 458+ 459+ 460+ 461+ 462+ 463+ 464+ 465+ 466+ 467+ 468+ 469+
470+ 471+ 472+ 473+ 474+ 475+ 476+ 477+ 478+ 479+ 480+ 481+ 482+ 483+ 484+
485+ 486+ 487+ 488+ 489+ 490+ 491+ 492+ 493+ 494+ 495+ 496+ 497+ 498+ 499+
500+ 501+ 502+ 503+ 504+ 505+ 506+ 507+ 508+ 509+ 510+ 511+ 512+ 513+ 514+
515+ 516+ 517+ 518+ 519+ 520+ 521+ 522+ 523+ 524+ 525+ 526+ 527+ 528+ 529+
530+ 531+ 532+ 533+ 534+ 535+ 536+ 537+ 538+ 539+ 540+ 541+ 542+ 543+ 544+
545+ 546+ 547+ 548+ 549+ 550+ 551+ 552+ 553+ 554+ 555+ 556+ 557+ 558+ 559+
560+ 561+ 562+ 563+ 564+ 565+ 566+ 567+ 568+ 569+ 570+ 571+ 572+ 573+ 574+
575+ 576+ 577+ 578+ 579+ 580+ 581+ 582+ 583+ 584+ 585+ 586+ 587+ 588+ 589+
590+ 591+ 592+ 593+ 594+ 595+ 596+ 597+ 598+ 599+ 600+ 601+ 602+ 603+ 604+
605+ 606+ 607+ 608+ 609+ 610+ 611+ 612+ 613+ 614+ 615+ 616+ 617+ 618+ 619+
620+ 621+ 622+ 623+ 624+ 625+ 626+ 627+ 628+ 629+ 630+ 631+ 632+ 633+ 634+
635+ 636+ 637+ 638+ 639+ 640+ 641+ 642+ 643+ 644+ 645+ 646+ 647+ 648+ 649+
650+ 651+ 652+ 653+ 654+ 655+ 656+ 657+ 658+ 659+ 660+ 661+ 662+ 663+ 664+
665+ 666+ 667+ 668+ 669+ 670+ 671+ 672+ 673+ 674+ 675+ 676+ 677+ 678+ 679+
680+ 681+ 682+ 683+ 684+ 685+ 686+ 687+ 688+ 689+ 690+ 691+ 692+ 693+ 694+
695+ 696+ 697+ 698+ 699+ 700+ 701+ 702+ 703+ 704+ 705+ 706+ 707+ 708+ 709+
710+ 711+ 712+ 713+ 714+ 715+ 716+ 717+ 718+ 719+ 720+ 721+ 722+ 723+ 724+
725+ 726+ 727+ 728+ 729+ 730+ 731+ 732+ 733+ 734+ 735+ 736+ 737+ 738+ 739+
740+ 741+ 742+ 743+ 744+ 745+ 746+ 747+ 748+ 749+ 750+ 751+ 752+ 753+ 754+
755+ 756+ 757+ 758+ 759+ 760+ 761+ 762+ 763+ 764+ 765+ 766+ 767+ 768+ 769+
770+ 771+ 772+ 773+ 774+ 775+ 776+ 777+ 778+ 779+ 780+ 781+ 782+ 783+ 784+
785+ 786+ 787+ 788+ 789+ 790+ 791+ 792+ 793+ 794+ 795+ 796+ 797+ 798+ 799+
800+ 801+ 802+ 803+ 804+ 805+ 806+ 807+ 808+ 809+ 810+ 811+ 812+ 813+ 814+
815+ 816+ 817+ 818+ 819+ 820+ 821+ 822+ 823+ 824+ 825+ 826+ 827+ 828+ 829+
830+ 831+ 832+ 833+ 834+ 835+ 836+ 837+ 838+ 839+ 840+ 841+ 842+ 843+ 844+
845+ 846+ 847+ 848+ 849+ 850+ 851+ 852+ 853+ 854+ 855+ 856+ 857+ 858+ 859+
860+ 861+ 862+ 863+ 864+ 865+ 866+ 867+ 868+ 869+ 870+ 871+ 872+ 873+ 874+
875+ 876+ 877+ 878+ 879+ 880+ 881+ 882+ 883+ 884+ 885+ 886+ 887+ 888+ 889+
890+ 891+ 892+ 893+ 894+ 895+ 896+ 897+ 898+ 899+ 900+ 901+ 902+ 903+ 904+
905+ 906+ 907+ 908+ 909+ 910+ 911+ 912+ 913+ 914+ 915+ 916+ 917+ 918+ 919+
920+ 921+ 922+ 923+ 924+ 925+ 926+ 927+ 928+ 929+ 930+ 931+ 932+ 933+ 934+
935+ 936+ 937+ 938+ 939+ 940+ 941+ 942+ 943+ 944+ 945+ 946+ 947+ 948+ 949+
950+ 951+ 952+ 953+ 954+ 955+ 956+ 957+ 958+ 959+ 960+ 961+ 962+ 963+ 964+
965+ 966+ 967+ 968+ 969+ 970+ 971+ 972+ 973+ 974+ 975+ 976+ 977+ 978+ 979+
980+ 981+ 982+ 983+ 984+ 985+ 986+ 987+ 988+ 989+ 990+ 991+ 992+ 993+ 994+
995+ 996+ 997+ 998+ 999+ 1000+ 1001+ 1002+ 1003+ 1004+ 1005+ 1006+ 1007+
1008+ 1009+ 1010+ 1011+ 1012+ 1013+ 1014+ 1015+ 1016+ 1017+ 1018+ 1019+
1020+ 1021+ 1022+ 1023+ 1024+ 1025+ 1026+ 1027+ 1028+ 1029+ 1030+ 1031+
1032+ 1033+ 1034+ 1035+ 1036+ 1037+ 1038+ 1039+ 1040+ 1041+ 1042+ 1043+
1044+ 1045+ 1046+ 1047+ 1048+ 1049+ 1050+ 1051+ 1052+ 1053+ 1054+ 1055+
1056+ 1057+ 1058+ 1059+ 1060+ 1061+ 1062+ 1063+ 1064+ 1065+ 1066+ 1067+
1068+ 1069+ 1070+ 1071+ 1072+ 1073+ 1074+ 1075+ 1076+ 1077+ 1078+ 1079+
1080+ 1081+ 1082+ 1083+ 1084+ 1085+ 1086+ 1087+ 1088+ 1089+ 1090+ 1091+
1092+ 1093+ 1094+ 1095+ 1096+ 1097+ 1098+ 1099+ 1100+ 1101+ 1102+ 1103+
1104+ 1105+ 1106+ 1107+ 1108+ 1109+ 1110+ 1111+ 1112+ 1113+ 1114+ 1115+
1116+ 1117+ 1118+ 1119+ 1120+ 1121+ 1122+ 1123+ 1124+ 1125+ 1126+ 1127+
1128+ 1129+ 1130+ 1131+ 1132+ 1133+ 1134+ 1135+ 1136+ 1137+ 1138+ 1139+
1140+ 1141+ 1142+ 1143+ 1144+ 1145+ 1146+ 1147+ 1148+ 1149+ 1150+ 1151+
1152+ 1153+ 1154+ 1155+ 1156+ 1157+ 1158+ 1159+ 1160+ 1161+ 1162+ 1163+
1164+ 1165+ 1166+ 1167+ 1168+ 1169+ 1170+ 1171+ 1172+ 1173+ 1174+ 1175+
1176+ 1177+ 1178+ 1179+ 1180+ 1181+ 1182+ 1183+ 1184+ 1185+ 1186+ 1187+
1188+ 1189+ 1190+ 1191+ 1192+ 1193+ 1194+ 1195+ 1196+ 1197+ 1198+ 1199+
1200+ 1201+ 1202+ 1203+ 1204+ 1205+ 1206+ 1207+ 1208+ 1209+ 1210+ 1211+
1212+ 1213+ 1214+ 1215+ 1216+ 1217+ 1218+ 1219+ 1220+ 1221+ 1222+ 1223+
1224+ 1225+ 1226+ 1227+ 1228+ 1229+ 1230+ 1231+ 1232+ 1233+ 1234+ 1235+
1236+ 1237+ 1238+ 1239+ 1240+ 1241+ 1242+ 1243+ 1244+ 1245+ 1246+ 1247+
1248+ 1249+ 1250+ 1251+ 1252+ 1253+ 1254+ 1255+ 1256+ 1257+ 1258+ 1259+
1260+ 1261+ 1262+ 1263+ 1264+ 1265+ 1266+ 1267+ 1268+ 1269+ 1270+ 1271+
1272+ 1273+ 1274+ 1275+ 1276+ 1277+ 1278+ 1279+ 1280+ 1281+ 1282+ 1283+
1284+ 1285+ 1286+ 1287+ 1288+ 1289+ 1290+ 1291+ 1292+ 1293+ 1294+ 1295+
1296+ 1297+ 1298+ 1299+ 1300+ 1301+ 1302+ 1303+ 1304+ 1305+ 1306+ 1307+
1308+ 1309+ 1310+ 1311+ 1312+ 1313+ 1314+ 1315+ 1316+ 1317+ 1318+ 1319+
1320+ 1321+ 1322+ 1323+ 1324+ 1325+ 1326+ 1327+ 1328+ 1329+ 1330+ 1331+
1332+ 1333+ 1334+ 1335+ 1336+ 1337+ 1338+ 1339+ 1340+ 1341+ 1342+ 1343+
1344+ 1345+ 1346+ 1347+ 1348+ 1349+ 1350+ 1351+ 1352+ 1353+ 1354+ 1355+
1356+ 1357+ 1358+ 1359+ 1360+ 1361+ 1362+ 1363+ 1364+ 1365+ 1366+ 1367+
1368+ 1369+ 1370+ 1371+ 1372+ 1373+ 1374+ 1375+ 1376+ 1377+ 1378+ 1379+
1380+ 1381+ 1382+ 1383+ 1384+ 1385+ 1386+ 1387+ 1388+ 1389+ 1390+ 1391+
1392+ 1393+ 1394+ 1395+ 1396+ 1397+ 1398+ 1399+ 1400+ 1401+ 1402+ 1403+
1404+ 1405+ 1406+ 1407+ 1408+ 1409+ 1410+ 1411+ 1412+ 1413+ 1414+ 1415+
1416+ 1417+ 1418+ 1419+ 1420+ 1421+ 1422+ 1423+ 1424+ 1425+ 1426+ 1427+
1428+ 1429+ 1430+ 1431+ 1432+ 1433+ 1434+ 1435+ 1436+ 1437+ 1438+ 1439+
1440+ 1441+ 1442+ 1443+ 1444+ 1445+ 1446+ 1447+ 1448+ 1449+ 1450+ 1451+
1452+ 1453+ 1454+ 1455+ 1456+ 1457+ 1458+ 1459+ 1460+ 1461+ 1462+ 1463+
1464+ 1465+ 1466+ 1467+ 1468+ 1469+ 1470+ 1471+ 1472+ 1473+ 1474+ 1475+
1476+ 1477+ 1478+ 1479+ 1480+ 1481+ 1482+ 1483+ 1484+ 1485+ 1486+ 1487+
1488+ 1489+ 1490+ 1491+ 1492+ 1493+ 1494+ 1495+ 1496+ 1497+ 1498+ 1499+
1500+ 1501+ 1502+ 1503+ 1504+ 1505+ 1506+ 1507+ 1508+ 1509+ 1510+ 1511+
1512+ 1513+ 1514+ 1515+ 1516+ 1517+ 1518+ 1519+ 1520+ 1521+ 1522+ 1523+
1524+ 1525+ 1526+ 1527+ 1528+ 1529+ 1530+ 1531+ 1532+ 1533+ 1534+ 1535+
1536+ 1537+ 1538+ 1539+ 1540+ 1541+ 1542+ 1543+ 1544+ 1545+ 1546+ 1547+
1548+ 1549+ 1550+ 1551+ 1552+ 1553+ 1554+ 1555+ 1556+ 1557+ 1558+ 1559+
1560+ 1561+ 1562+ 1563+ 1564+ 1565+ 1566+ 1567+ 1568+ 1569+ 1570+ 1571+
1572+ 1573+ 1574+ 1575+ 1576+ 1577+ 1578+ 1579+ 1580+ 1581+ 1582+ 1583+
1584+ 1585+ 1586+ 1587+ 1588+ 1589+ 1590+ 1591+ 1592+ 1593+ 1594+ 1595+
1596+ 1597+ 1598+ 1599+ 1600+ 1601+ 1602+ 1603+ 1604+ 1605+ 1606+ 1607+
1608+ 1609+ 1610+ 1611+ 1612+ 1613+ 1614+ 1615+ 1616+ 1617+ 1618+ 1619+
1620+ 1621+ 1622+ 1623+ 1624+ 1625+ 1626+ 1627+ 1628+ 1629+ 1630+ 1631+
1632+ 1633+ 1634+ 1635+ 1636+ 1637+ 1638+ 1639+ 1640+ 1641+ 1642+ 1643+
1644+ 1645+ 1646+ 1647+ 1648+ 1649+ 1650+ 1651+ 1652+ 1653+ 1654+ 1655+
1656+ 1657+ 1658+ 1659+ 1660+ 1661+ 1662+ 1663+ 1664+ 1665+ 1666+ 1667+
1668+ 1669+ 1670+ 1671+ 1672+ 1673+ 1674+ 1675+ 1676+ 1677+ 1678+ 1679+
1680+ 1681+ 1682+ 1683+ 1684+ 1685+ 1686+ 1687+ 1688+ 1689+ 1690+ 1691+
1692+ 1693+ 1694+ 1695+ 1696+ 1697+ 1698+ 1699+ 1700+ 1701+ 1702+ 1703+
1704+ 1705+ 1706+ 1707+ 1708+ 1709+ 1710+ 1711+ 1712+ 1713+ 1714+ 1715+
1716+ 1717+ 1718+ 1719+ 1720+ 1721+ 1722+ 1723+ 1724+ 1725+ 1726+ 1727+
1728+ 1729+ 1730+ 1731+ 1732+ 1733+ 1734+ 1735+ 1736+ 1737+ 1738+ 1739+
1740+ 1741+ 1742+ 1743+ 1744+ 1745+ 1746+ 1747+ 1748+ 1749+ 1750+ 1751+
1752+ 1753+ 1754+ 1755+ 1756+ 1757+ 1758+ 1759+ 1760+ 1761+ 1762+ 1763+
1764+ 1765+ 1766+ 1767+ 1768+ 1769+ 1770+ 1771+ 1772+ 1773+ 1774+ 1775+
1776+ 1777+ 1778+ 1779+ 1780+ 1781+ 1782+ 1783+ 1784+ 1785+ 1786+ 1787+
1788+ 1789+ 1790+ 1791+ 1792+ 1793+ 1794+ 1795+ 1796+ 1797+ 1798+ 1799+
1800+ 1801+ 1802+ 1803+ 1804+ 1805+ 1806+ 1807+ 1808+ 1809+ 1810+ 1811+
1812+ 1813+ 1814+ 1815+ 1816+ 1817+ 1818+ 1819+ 1820+ 1821+ 1822+ 1823+
1824+ 1825+ 1826+ 1827+ 1828+ 1829+ 1830+ 1831+ 1832+ 1833+ 1834+ 1835+
1836+ 1837+ 1838+ 1839+ 1840+ 1841+ 1842+ 1843+ 1844+ 1845+ 1846+ 1847+
1848+ 1849+ 1850+ 1851+ 1852+ 1853+ 1854+ 1855+ 1856+ 1857+ 1858+ 1859+
1860+ 1861+ 1862+ 1863+ 1864+ 1865+ 1866+ 1867+ 1868+ 1869+ 1870+ 1871+
1872+ 1873+ 1874+ 1875+ 1876+ 1877+ 1878+ 1879+ 1880+ 1881+ 1882+ 1883+
1884+ 1885+ 1886+ 1887+ 1888+ 1889+ 1890+ 1891+ 1892+ 1893+ 1894+ 1895+
1896+ 1897+ 1898+ 1899+ 1900+ 1901+ 1902+ 1903+ 1904+ 1905+ 1906+ 1907+
1908+ 1909+ 1910+ 1911+ 1912+ 1913+ 1914+ 1915+ 1916+ 1917+ 1918+ 1919+
1920+ 1921+ 1922+ 1923+ 1924+ 1925+ 1926+ 1927+ 1928+ 1929+ 1930+ 1931+
1932+ 1933+ 1934+ 1935+ 1936+ 1937+ 1938+ 1939+ 1940+ 1941+ 1942+ 1943+
1944+ 1945+ 1946+ 1947+ 1948+ 1949+ 1950+ 1951+ 1952+ 1953+ 1954+ 1955+
1956+ 1957+ 1958+ 1959+ 1960+ 1961+ 1962+ 1963+ 1964+ 1965+ 1966+ 1967+
1968+ 1969+ 1970+ 1971+ 1972+ 1973+ 1974+ 1975+ 1976+ 1977+ 1978+ 1979+
1980+ 1981+ 1982+ 1983+ 1984+ 1985+ 1986+ 1987+ 1988+ 1989+ 1990+ 1991+
1992+ 1993+ 1994+ 1995+ 1996+ 1997+ 1998+ 1999+ 2000+ 2001+ 2002+ 2003+
2004+ 2005+ 2006+ 2007+ 2008+ 2009+ 2010+ 2011+ 2012+ 2013+ 2014+ 2015+
2016+ 2017+ 2018+ 2019+ 2020+ 2021+ 2022+ 2023+ 2024+ 2025+ 2026+ 2027+
2028+ 2029+ 2030+ 2031+ 2032+ 2033+ 2034+ 2035+ 2036+ 2037+ 2038+ 2039+
2040+ 2041+ 2042+ 2043+ 2044+ 2045+ 2046+ 2047+ 2048+ 2049+ 2050+ 2051+
2052+ 2053+ 2054+ 2055+ 2056+ 2057+ 2058+ 2059+ 2060+ 2061+ 2062+ 2063+
2064+ 2065+ 2066+ 2067+ 2068+ 2069+ 2070+ 2071+ 2072+ 2073+ 2074+ 2075+
2076+ 2077+ 2078+ 2079+ 2080+ 2081+ 2082+ 2083+ 2084+ 2085+ 2086+ 2087+
2088+ 2089+ 2090+ 2091+ 2092+ 2093+ 2094+ 2095+ 2096+ 2097+ 2098+ 2099+
2100+ 2101+ 2102+ 2103+ 2104+ 2105+ 2106+ 2107+ 2108+ 2109+ 2110+ 2111+
2112+ 2113+ 2114+ 2115+ 2116+ 2117+ 2118+ 2119+ 2120+ 2121+ 2122+ 2123+
2124+ 2125+ 2126+ 2127+ 2128+ 2129+ 2130+ 2131+ 2132+ 2133+ 2134+ 2135+
2136+ 2137+ 2138+ 2139+ 2140+ 2141+ 2142+ 2143+ 2144+ 2145+ 2146+ 2147+
2148+ 2149+ 2150+ 2151+ 2152+ 2153+ 2154+ 2155+ 2156+ 2157+ 2158+ 2159+
2160+ 2161+ 2162+ 2163+ 2164+ 2165+ 2166+ 2167+ 2168+ 2169+ 2170+ 2171+
2172+ 2173+ 2174+ 2175+ 2176+ 2177+ 2178+ 2179+ 2180+ 2181+ 2182+ 2183+
2184+ 2185+ 2186+ 2187+ 2188+ 2189+ 2190+ 2191+ 2192+ 2193+ 2194+ 2195+
2196+ 2197+ 2198+ 2199+ 2200+ 2201+ 2202+ 2203+ 2204+ 2205+ 2206+ 2207+
2208+ 2209+ 2210+ 2211+ 2212+ 2213+ 2214+ 2215+ 2216+ 2217+ 2218+ 2219+
2220+ 2221+ 2222+ 2223+ 2224+ 2225+ 2226+ 2227+ 2228+ 2229+ 2230+ 2231+
2232+ 2233+ 2234+ 2235+ 2236+ 2237+ 2238+ 2239+ 2240+ 2241+ 2242+ 2243+
2244+ 2245+ 2246+ 2247+ 2248+ 2249+ 2250+ 2251+ 2252+ 2253+ 2254+ 2255+
2256+ 2257+ 2258+ 2259+ 2260+ 2261+ 2262+ 2263+ 2264+ 2265+ 2266+ 2267+
2268+ 2269+ 2270+ 2271+ 2272+ 2273+ 2274+ 2275+ 2276+ 2277+ 2278+ 2279+
2280+ 2281+ 2282+ 2283+ 2284+ 2285+ 2286+ 2287+ 2288+ 2289+ 2290+ 2291+
2292+ 2293+ 2294+ 2295+ 2296+ 2297+ 2298+ 2299+ 2300+ 2301+ 2302+ 2303+
2304+ 2305+ 2306+ 2307+ 2308+ 2309+ 2310+ 2311+ 2312+ 2313+ 2314+ 2315+
2316+ 2317+ 2318+ 2319+ 2320+ 2321+ 2322+ 2323+ 2324+ 2325+ 2326+ 2327+
2328+ 2329+ 2330+ 2331+ 2332+ 2333+ 2334+ 2335+ 2336+ 2337+ 2338+ 2339+
2340+ 2341+ 2342+ 2343+ 2344+ 2345+ 2346+ 2347+ 2348+ 2349+ 2350+ 2351+
2352+ 2353+ 2354+ 2355+ 2356+ 2357+ 2358+ 2359+ 2360+ 2361+ 2362+ 2363+
2364+ 2365+ 2366+ 2367+ 2368+ 2369+ 2370+ 2371+ 2372+ 2373+ 2374+ 2375+
2376+ 2377+ 2378+ 2379+ 2380+ 2381+ 2382+ 2383+ 2384+ 2385+ 2386+ 2387+
2388+ 2389+ 2390+ 2391+ 2392+ 2393+ 2394+ 2395+ 2396+ 2397+ 2398+ 2399+
2400+ 2401+ 2402+ 2403+ 2404+ 2405+ 2406+ 2407+ 2408+ 2409+ 2410+ 2411+
2412+ 2413+ 2414+ 2415+ 2416+ 2417+ 2418+ 2419+ 2420+ 2421+ 2422+ 2423+
2424+ 2425+ 2426+ 2427+ 2428+ 2429+ 2430+ 2431+ 2432+ 2433+ 2434+ 2435+
2436+ 2437+ 2438+ 2439+ 2440+ 2441+ 2442+ 2443+ 2444+ 2445+ 2446+ 2447+
2448+ 2449+ 2450+ 2451+ 2452+ 2453+ 2454+ 2455+ 2456+ 2457+ 2458+ 2459+
2460+ 2461+ 2462+ 2463+ 2464+ 2465+ 2466+ 2467+ 2468+ 2469+ 2470+ 2471+
2472+ 2473+ 2474+ 2475+ 2476+ 2477+ 2478+ 2479+ 2480+ 2481+ 2482+ 2483+
2484+ 2485+ 2486+ 2487+ 2488+ 2489+ 2490+ 2491+ 2492+ 2493+ 2494+ 2495+
2496+ 2497+ 2498+ 2499+ 2500+ 2501+ 2502+ 2503+ 2504+ 2505+ 2506+ 2507+
2508+ 2509+ 2510+ 2511+ 2512+ 2513+ 2514+ 2515+ 2516+ 2517+ 2518+ 2519+
2520+ 2521+ 2522+ 2523+ 2524+ 2525+ 2526+ 2527+ 2528+ 2529+ 2530+ 2531+
2532+ 2533+ 2534+ 2535+ 2536+ 2537+ 2538+ 2539+ 2540+ 2541+ 2542+ 2543+
2544+ 2545+ 2546+ 2547+ 2548+ 2549+ 2550+ 2551+ 2552+ 2553+ 2554+ 2555+
2556+ 2557+ 2558+ 2559+ 2560+ 2561+ 2562+ 2563+ 2564+ 2565+ 2566+ 2567+
2568+ 2569+ 2570+ 2571+ 2572+ 2573+ 2574+ 2575+ 2576+ 2577+ 2578+ 2579+
2580+ 2581+ 2582+ 2583+ 2584+ 2585+ 2586+ 2587+ 2588+ 2589+ 2590+ 2591+
2592+ 2593+ 2594+ 2595+ 2596+ 2597+ 2598+ 2599+ 2600+ 2601+ 2602+ 2603+
2604+ 2605+ 2606+ 2607+ 2608+ 2609+ 2610+ 2611+ 2612+ 2613+ 2614+ 2615+
2616+ 2617+ 2618+ 2619+ 2620+ 2621+ 2622+ 2623+ 2624+ 2625+ 2626+ 2627+
2628+ 2629+ 2630+ 2631+ 2632+ 2633+ 2634+ 2635+ 2636+ 2637+ 2638+ 2639+
2640+ 2641+ 2642+ 2643+ 2644+ 2645+ 2646+ 2647+ 2648+ 2649+ 2650+ 2651+
2652+ 2653+ 2654+ 2655+ 2656+ 2657+ 2658+ 2659+ 2660+ 2661+ 2662+ 2663+
2664+ 2665+ 2666+ 2667+ 2668+ 2669+ 2670+ 2671+ 2672+ 2673+ 2674+ 2675+
2676+ 2677+ 2678+ 2679+ 2680+ 2681+ 2682+ 2683+ 2684+ 2685+ 2686+ 2687+
2688+ 2689+ 2690+ 2691+ 2692+ 2693+ 2694+ 2695+ 2696+ 2697+ 2698+ 2699+
2700+ 2701+ 2702+ 2703+ 2704+ 2705+ 2706+ 2707+ 2708+ 2709+ 2710+ 2711+
2712+ 2713+ 2714+ 2715+ 2716+ 2717+ 2718+ 2719+ 2720+ 2721+ 2722+ 2723+
2724+ 2725+ 2726+ 2727+ 2728+ 2729+ 2730+ 2731+ 2732+ 2733+ 2734+ 2735+
2736+ 2737+ 2738+ 2739+ 2740+ 2741+ 2742+ 2743+ 2744+ 2745+ 2746+ 2747+
2748+ 2749+ 2750+ 2751+ 2752+ 2753+ 2754+ 2755+ 2756+ 2757+ 2758+ 2759+
2760+ 2761+ 2762+ 2763+ 2764+ 2765+ 2766+ 2767+ 2768+ 2769+ 2770+ 2771+
2772+ 2773+ 2774+ 2775+ 2776+ 2777+ 2778+ 2779+ 2780+ 2781+ 2782+ 2783+
2784+ 2785+ 2786+ 2787+ 2788+ 2789+ 2790+ 2791+ 2792+ 2793+ 2794+ 2795+
2796+ 2797+ 2798+ 2799+ 2800+ 2801+ 2802+ 2803+ 2804+ 2805+ 2806+ 2807+
2808+ 2809+ 2810+ 2811+ 2812+ 2813+ 2814+ 2815+ 2816+ 2817+ 2818+ 2819+
2820+ 2821+ 2822+ 2823+ 2824+ 2825+ 2826+ 2827+ 2828+ 2829+ 2830+ 2831+
2832+ 2833+ 2834+ 2835+ 2836+ 2837+ 2838+ 2839+ 2840+ 2841+ 2842+ 2843+
2844+ 2845+ 2846+ 2847+ 2848+ 2849+ 2850+ 2851+ 2852+ 2853+ 2854+ 2855+
2856+ 2857+ 2858+ 2859+ 2860+ 2861+ 2862+ 2863+ 2864+ 2865+ 2866+ 2867+
2868+ 2869+ 2870+ 2871+ 2872+ 2873+ 2874+ 2875+ 2876+ 2877+ 2878+ 2879+
2880+ 2881+ 2882+ 2883+ 2884+ 2885+ 2886+ 2887+ 2888+ 2889+ 2890+ 2891+
2892+ 2893+ 2894+ 2895+ 2896+ 2897+ 2898+ 2899+ 2900+ 2901+ 2902+ 2903+
2904+ 2905+ 2906+ 2907+ 2908+ 2909+ 2910+ 2911+ 2912+ 2913+ 2914+ 2915+
2916+ 2917+ 2918+ 2919+ 2920+ 2921+ 2922+ 2923+ 2924+ 2925+ 2926+ 2927+
2928+ 2929+ 2930+ 2931+ 2932+ 2933+ 2934+ 2935+ 2936+ 2937+ 2938+ 2939+
2940+ 2941+ 2942+ 2943+ 2944+ 2945+ 2946+ 2947+ 2948+ 2949+ 2950+ 2951+
2952+ 2953+ 2954+ 2955+ 2956+ 2957+ 2958+ 2959+ 2960+ 2961+ 2962+ 2963+
2964+ 2965+ 2966+ 2967+ 2968+ 2969+ 2970+ 2971+ 2972+ 2973+ 2974+ 2975+
2976+ 2977+ 2978+ 2979+ 2980+ 2981+ 2982+ 2983+ 2984+ 2985+ 2986+ 2987+
2988+ 2989+ 2990+ 2991+ 2992+ 2993+ 2994+ 2995+ 2996+ 2997+ 2998+ 2999+
3000+ 3001+ 3002+ 3003+ 3004+ 3005+ 3006+ 3007+ 3008+ 3009+ 3010+ 3011+
3012+ 3013+ 3014+ 3015+ 3016+ 3017+ 3018+ 3019+ 3020+ 3021+ 3022+ 3023+
3024+ 3025+ 3026+ 3027+ 3028+ 3029+ 3030+ 3031+ 3032+ 3033+ 3034+ 3035+
3036+ 3037+ 3038+ 3039+ 3040+ 3041+ 3042+ 3043+ 3044+ 3045+ 3046+ 3047+
3048+ 3049+ 3050+ 3051+ 3052+ 3053+ 3054+ 3055+ 3056+ 3057+ 3058+ 3059+
3060+ 3061+ 3062+ 3063+ 3064+ 3065+ 3066+ 3067+ 3068+ 3069+ 3070+ 3071+
3072+ 3073+ 3074+ 3075+ 3076+ 3077+ 3078+ 3079+ 3080+ 3081+ 3082+ 3083+
3084+ 3085+ 3086+ 3087+ 3088+ 3089+ 3090+ 3091+ 3092+ 3093+ 3094+ 3095+
3096+ 3097+ 3098+ 3099+ 3100+ 3101+ 3102+ 3103+ 3104+ 3105+ 3106+ 3107+
3108+ 3109+ 3110+ 3111+ 3112+ 3113+ 3114+ 3115+ 3116+ 3117+ 3118+ 3119+
3120+ 3121+ 3122+ 3123+ 3124+ 3125+ 3126+ 3127+ 3128+ 3129+ 3130+ 3131+
3132+ 3133+ 3134+ 3135+ 3136+ 3137+ 3138+ 3139+ 3140+ 3141+ 3142+ 3143+
3144+ 3145+ 3146+ 3147+ 3148+ 3149+ 3150+ 3151+ 3152+ 3153+ 3154+ 3155+
3156+ 3157+ 3158+ 3159+ 3160+ 3161+ 3162+ 3163+ 3164+ 3165+ 3166+ 3167+
3168+ 3169+ 3170+ 3171+ 3172+ 3173+ 3174+ 3175+ 3176+ 3177+ 3178+ 3179+
3180+ 3181+ 3182+ 3183+ 3184+ 3185+ 3186+ 3187+ 3188+ 3189+ 3190+ 3191+
3192+ 3193+ 3194+ 3195+ 3196+ 3197+ 3198+ 3199+ 3200+ 3201+ 3202+ 3203+
3204+ 3205+ 3206+ 3207+ 3208+ 3209+ 3210+ 3211+ 3212+ 3213+ 3214+ 3215+
3216+ 3217+ 3218+ 3219+ 3220+ 3221+ 3222+ 3223+ 3224+ 3225+ 3226+ 3227+
3228+ 3229+ 3230+ 3231+ 3232+ 3233+ 3234+ 3235+ 3236+ 3237+ 3238+ 3239+
3240+ 3241+ 3242+ 3243+ 3244+ 3245+ 3246+ 3247+ 3248+ 3249+ 3250+ 3251+
3252+ 3253+ 3254+ 3255+ 3256+ 3257+ 3258+ 3259+ 3260+ 3261+ 3262+ 3263+
3264+ 3265+ 3266+ 3267+ 3268+ 3269+ 3270+ 3271+ 3272+ 3273+ 3274+ 3275+
3276+ 3277+ 3278+ 3279+ 3280+ 3281+ 3282+ 3283+ 3284+ 3285+ 3286+ 3287+
3288+ 3289+ 3290+ 3291+ 3292+ 3293+ 3294+ 3295+ 3296+ 3297+ 3298+ 3299+
3300+ 3301+ 3302+ 3303+ 3304+ 3305+ 3306+ 3307+ 3308+ 3309+ 3310+ 3311+
3312+ 3313+ 3314+ 3315+ 3316+ 3317+ 3318+ 3319+ 3320+ 3321+ 3322+ 3323+
3324+ 3325+ 3326+ 3327+ 3328+ 3329+ 3330+ 3331+ 3332+ 3333+ 3334+ 3335+
3336+ 3337+ 3338+ 3339+ 3340+ 3341+ 3342+ 3343+ 3344+ 3345+ 3346+ 3347+
3348+ 3349+ 3350+ 3351+ 3352+ 3353+ 3354+ 3355+ 3356+ 3357+ 3358+ 3359+
3360+ 3361+ 3362+ 3363+ 3364+ 3365+ 3366+ 3367+ 3368+ 3369+ 3370+ 3371+
3372+ 3373+ 3374+ 3375+ 3376+ 3377+ 3378+ 3379+ 3380+ 3381+ 3382+ 3383+
3384+ 3385+ 3386+ 3387+ 3388+ 3389+ 3390+ 3391+ 3392+ 3393+ 3394+ 3395+
3396+ 3397+ 3398+ 3399+ 3400+ 3401+ 3402+ 3403+ 3404+ 3405+ 3406+ 3407+
3408+ 3409+ 3410+ 3411+ 3412+ 3413+ 3414+ 3415+ 3416+ 3417+ 3418+ 3419+
3420+ 3421+ 3422+ 3423+ 3424+ 3425+ 3426+ 3427+ 3428+ 3429+ 3430+ 3431+
3432+ 3433+ 3434+ 3435+ 3436+ 3437+ 3438+ 3439+ 3440+ 3441+ 3442+ 3443+
3444+ 3445+ 3446+ 3447+ 3448+ 3449+ 3450+ 3451+ 3452+ 3453+ 3454+ 3455+
3456+ 3457+ 3458+ 3459+ 3460+ 3461+ 3462+ 3463+ 3464+ 3465+ 3466+ 3467+
3468+ 3469+ 3470+ 3471+ 3472+ 3473+ 3474+ 3475+ 3476+ 3477+ 3478+ 3479+
3480+ 3481+ 3482+ 3483+ 3484+ 3485+ 3486+ 3487+ 3488+ 3489+ 3490+ 3491+
3492+ 3493+ 3494+ 3495+ 3496+ 3497+ 3498+ 3499+ 3500+ 3501+ 3502+ 3503+
3504+ 3505+ 3506+ 3507+ 3508+ 3509+ 3510+ 3511+ 3512+ 3513+ 3514+ 3515+
3516+ 3517+ 3518+ 3519+ 3520+ 3521+ 3522+ 3523+ 3524+ 3525+ 3526+ 3527+
3528+ 3529+ 3530+ 3531+ 3532+ 3533+ 3534+ 3535+ 3536+ 3537+ 3538+ 3539+
3540+ 3541+ 3542+ 3543+ 3544+ 3545+ 3546+ 3547+ 3548+ 3549+ 3550+ 3551+
3552+ 3553+ 3554+ 3555+ 3556+ 3557+ 3558+ 3559+ 3560+ 3561+ 3562+ 3563+
3564+ 3565+ 3566+ 3567+ 3568+ 3569+ 3570+ 3571+ 3572+ 3573+ 3574+ 3575+
3576+ 3577+ 3578+ 3579+ 3580+ 3581+ 3582+ 3583+ 3584+ 3585+ 3586+ 3587+
3588+ 3589+ 3590+ 3591+ 3592+ 3593+ 3594+ 3595+ 3596+ 3597+ 3598+ 3599+
3600+ 3601+ 3602+ 3603+ 3604+ 3605+ 3606+ 3607+ 3608+ 3609+ 3610+ 3611+
3612+ 3613+ 3614+ 3615+ 3616+ 3617+ 3618+ 3619+ 3620+ 3621+ 3622+ 3623+
3624+ 3625+ 3626+ 3627+ 3628+ 3629+ 3630+ 3631+ 3632+ 3633+ 3634+ 3635+
3636+ 3637+ 3638+ 3639+ 3640+ 3641+ 3642+ 3643+ 3644+ 3645+ 3646+ 3647+
3648+ 3649+ 3650+ 3651+ 3652+ 3653+ 3654+ 3655+ 3656+ 3657+ 3658+ 3659+
3660+ 3661+ 3662+ 3663+ 3664+ 3665+ 3666+ 3667+ 3668+ 3669+ 3670+ 3671+
3672+ 3673+ 3674+ 3675+ 3676+ 3677+ 3678+ 3679+ 3680+ 3681+ 3682+ 3683+
3684+ 3685+ 3686+ 3687+ 3688+ 3689+ 3690+ 3691+ 3692+ 3693+ 3694+ 3695+
3696+ 3697+ 3698+ 3699+ 3700+ 3701+ 3702+ 3703+ 3704+ 3705+ 3706+ 3707+
3708+ 3709+ 3710+ 3711+ 3712+ 3713+ 3714+ 3715+ 3716+ 3717+ 3718+ 3719+
3720+ 3721+ 3722+ 3723+ 3724+ 3725+ 3726+ 3727+ 3728+ 3729+ 3730+ 3731+
3732+ 3733+ 3734+ 3735+ 3736+ 3737+ 3738+ 3739+ 3740+ 3741+ 3742+ 3743+
3744+ 3745+ 3746+ 3747+ 3748+ 3749+ 3750+ 3751+ 3752+ 3753+ 3754+ 3755+
3756+ 3757+ 3758+ 3759+ 3760+ 3761+ 3762+ 3763+ 3764+ 3765+ 3766+ 3767+
3768+ 3769+ 3770+ 3771+ 3772+ 3773+ 3774+ 3775+ 3776+ 3777+ 3778+ 3779+
3780+ 3781+ 3782+ 3783+ 3784+ 3785+ 3786+ 3787+ 3788+ 3789+ 3790+ 3791+
3792+ 3793+ 3794+ 3795+ 3796+ 3797+ 3798+ 3799+ 3800+ 3801+ 3802+ 3803+
3804+ 3805+ 3806+ 3807+ 3808+ 3809+ 3810+ 3811+ 3812+ 3813+ 3814+ 3815+
3816+ 3817+ 3818+ 3819+ 3820+ 3821+ 3822+ 3823+ 3824+ 3825+ 3826+ 3827+
3828+ 3829+ 3830+ 3831+ 3832+ 3833+ 3834+ 3835+ 3836+ 3837+ 3838+ 3839+
3840+ 3841+ 3842+ 3843+ 3844+ 3845+ 3846+ 3847+ 3848+ 3849+ 3850+ 3851+
3852+ 3853+ 3854+ 3855+ 3856+ 3857+ 3858+ 3859+ 3860+ 3861+ 3862+ 3863+
3864+ 3865+ 3866+ 3867+ 3868+ 3869+ 3870+ 3871+ 3872+ 3873+ 3874+ 3875+
3876+ 3877+ 3878+ 3879+ 3880+ 3881+ 3882+ 3883+ 3884+ 3885+ 3886+ 3887+
3888+ 3889+ 3890+ 3891+ 3892+ 3893+ 3894+ 3895+ 3896+ 3897+ 3898+ 3899+
3900+ 3901+ 3902+ 3903+ 3904+ 3905+ 3906+ 3907+ 3908+ 3909+ 3910+ 3911+
3912+ 3913+ 3914+ 3915+ 3916+ 3917+ 3918+ 3919+ 3920+ 3921+ 3922+ 3923+
3924+ 3925+ 3926+ 3927+ 3928+ 3929+ 3930+ 3931+ 3932+ 3933+ 3934+ 3935+
3936+ 3937+ 3938+ 3939+ 3940+ 3941+ 3942+ 3943+ 3944+ 3945+ 3946+ 3947+
3948+ 3949+ 3950+ 3951+ 3952+ 3953+ 3954+ 3955+ 3956+ 3957+ 3958+ 3959+
3960+ 3961+ 3962+ 3963+ 3964+ 3965+ 3966+ 3967+ 3968+ 3969+ 3970+ 3971+
3972+ 3973+ 3974+ 3975+ 3976+ 3977+ 3978+ 3979+ 3980+ 3981+ 3982+ 3983+
3984+ 3985+ 3986+ 3987+ 3988+ 3989+ 3990+ 3991+ 3992+ 3993+ 3994+ 3995+
3996+ 3997+ 3998+ 3999+ 4000+ 4001+ 4002+ 4003+ 4004+ 4005+ 4006+ 4007+
4008+ 4009+ 4010+ 4011+ 4012+ 4013+ 4014+ 4015+ 4016+ 4017+ 4018+ 4019+
4020+ 4021+ 4022+ 4023+ 4024+ 4025+ 4026+ 4027+ 4028+ 4029+ 4030+ 4031+
4032+ 4033+ 4034+ 4035+ 4036+ 4037+ 4038+ 4039+ 4040+ 4041+ 4042+ 4043+
4044+ 4045+ 4046+ 4047+ 4048+ 4049+ 4050+ 4051+ 4052+ 4053+ 4054+ 4055+
4056+ 4057+ 4058+ 4059+ 4060+ 4061+ 4062+ 4063+ 4064+ 4065+ 4066+ 4067+
4068+ 4069+ 4070+ 4071+ 4072+ 4073+ 4074+ 4075+ 4076+ 4077+ 4078+ 4079+
4080+ 4081+ 4082+ 4083+ 4084+ 4085+ 4086+ 4087+ 4088+ 4089+ 4090+ 4091+
4092+ 4093+ 4094+ 4095+ 4096+ 4097+ 4098+ 4099+ 4100+ 4101+ 4102+ 4103+
4104+ 4105+ 4106+ 4107+ 4108+ 4109+ 4110+ 4111+ 4112+ 4113+ 4114+ 4115+
4116+ 4117+ 4118+ 4119+ 4120+ 4121+ 4122+ 4123+ 4124+ 4125+ 4126+ 4127+
4128+ 4129+ 4130+ 4131+ 4132+ 4133+ 4134+ 4135+ 4136+ 4137+ 4138+ 4139+
4140+ 4141+ 4142+ 4143+ 4144+ 4145+ 4146+ 4147+ 4148+ 4149+ 4150+ 4151+
4152+ 4153+ 4154+ 4155+ 4156+ 4157+ 4158+ 4159+ 4160+ 4161+ 4162+ 4163+
4164+ 4165+ 4166+ 4167+ 4168+ 4169+ 4170+ 4171+ 4172+ 4173+ 4174+ 4175+
4176+ 4177+ 4178+ 4179+ 4180+ 4181+ 4182+ 4183+ 4184+ 4185+ 4186+ 4187+
4188+ 4189+ 4190+ 4191+ 4192+ 4193+ 4194+ 4195+ 4196+ 4197+ 4198+ 4199+
4200+ 4201+ 4202+ 4203+ 4204+ 4205+ 4206+ 4207+ 4208+ 4209+ 4210+ 4211+
4212+ 4213+ 4214+ 4215+ 4216+ 4217+ 4218+ 4219+ 4220+ 4221+ 4222+ 4223+
4224+ 4225+ 4226+ 4227+ 4228+ 4229+ 4230+ 4231+ 4232+ 4233+ 4234+ 4235+
4236+ 4237+ 4238+ 4239+ 4240+ 4241+ 4242+ 4243+ 4244+ 4245+ 4246+ 4247+
4248+ 4249+ 4250+ 4251+ 4252+ 4253+ 4254+ 4255+ 4256+ 4257+ 4258+ 4259+
4260+ 4261+ 4262+ 4263+ 4264+ 4265+ 4266+ 4267+ 4268+ 4269+ 4270+ 4271+
4272+ 4273+ 4274+ 4275+ 4276+ 4277+ 4278+ 4279+ 4280+ 4281+ 4282+ 4283+
4284+ 4285+ 4286+ 4287+ 4288+ 4289+ 4290+ 4291+ 4292+ 4293+ 4294+ 4295+
4296+ 4297+ 4298+ 4299+ 4300+ 4301+ 4302+ 4303+ 4304+ 4305+ 4306+ 4307+
4308+ 4309+ 4310+ 4311+ 4312+ 4313+ 4314+ 4315+ 4316+ 4317+ 4318+ 4319+
4320+ 4321+ 4322+ 4323+ 4324+ 4325+ 4326+ 4327+ 4328+ 4329+ 4330+ 4331+
4332+ 4333+ 4334+ 4335+ 4336+ 4337+ 4338+ 4339+ 4340+ 4341+ 4342+ 4343+
4344+ 4345+ 4346+ 4347+ 4348+ 4349+ 4350+ 4351+ 4352+ 4353+ 4354+ 4355+
4356+ 4357+ 4358+ 4359+ 4360+ 4361+ 4362+ 4363+ 4364+ 4365+ 4366+ 4367+
4368+ 4369+ 4370+ 4371+ 4372+ 4373+ 4374+ 4375+ 4376+ 4377+ 4378+ 4379+
4380+ 4381+ 4382+ 4383+ 4384+ 4385+ 4386+ 4387+ 4388+ 4389+ 4390+ 4391+
4392+ 4393+ 4394+ 4395+ 4396+ 4397+ 4398+ 4399+ 4400+ 4401+ 4402+ 4403+
4404+ 4405+ 4406+ 4407+ 4408+ 4409+ 4410+ 4411+ 4412+ 4413+ 4414+ 4415+
4416+ 4417+ 4418+ 4419+ 4420+ 4421+ 4422+ 4423+ 4424+ 4425+ 4426+ 4427+
4428+ 4429+ 4430+ 4431+ 4432+ 4433+ 4434+ 4435+ 4436+ 4437+ 4438+ 4439+
4440+ 4441+ 4442+ 4443+ 4444+ 4445+ 4446+ 4447+ 4448+ 4449+ 4450+ 4451+
4452+ 4453+ 4454+ 4455+ 4456+ 4457+ 4458+ 4459+ 4460+ 4461+ 4462+ 4463+
4464+ 4465+ 4466+ 4467+ 4468+ 4469+ 4470+ 4471+ 4472+ 4473+ 4474+ 4475+
4476+ 4477+ 4478+ 4479+ 4480+ 4481+ 4482+ 4483+ 4484+ 4485+ 4486+ 4487+
4488+ 4489+ 4490+ 4491+ 4492+ 4493+ 4494+ 4495+ 4496+ 4497+ 4498+ 4499+
4500+ 4501+ 4502+ 4503+ 4504+ 4505+ 4506+ 4507+ 4508+ 4509+ 4510+ 4511+
4512+ 4513+ 4514+ 4515+ 4516+ 4517+ 4518+ 4519+ 4520+ 4521+ 4522+ 4523+
4524+ 4525+ 4526+ 4527+ 4528+ 4529+ 4530+ 4531+ 4532+ 4533+ 4534+ 4535+
4536+ 4537+ 4538+ 4539+ 4540+ 4541+ 4542+ 4543+ 4544+ 4545+ 4546+ 4547+
4548+ 4549+ 4550+ 4551+ 4552+ 4553+ 4554+ 4555+ 4556+ 4557+ 4558+ 4559+
4560+ 4561+ 4562+ 4563+ 4564+ 4565+ 4566+ 4567+ 4568+ 4569+ 4570+ 4571+
4572+ 4573+ 4574+ 4575+ 4576+ 4577+ 4578+ 4579+ 4580+ 4581+ 4582+ 4583+
4584+ 4585+ 4586+ 4587+ 4588+ 4589+ 4590+ 4591+ 4592+ 4593+ 4594+ 4595+
4596+ 4597+ 4598+ 4599+ 4600+ 4601+ 4602+ 4603+ 4604+ 4605+ 4606+ 4607+
4608+ 4609+ 4610+ 4611+ 4612+ 4613+ 4614+ 4615+ 4616+ 4617+ 4618+ 4619+
4620+ 4621+ 4622+ 4623+ 4624+ 4625+ 4626+ 4627+ 4628+ 4629+ 4630+ 4631+
4632+ 4633+ 4634+ 4635+ 4636+ 4637+ 4638+ 4639+ 4640+ 4641+ 4642+ 4643+
4644+ 4645+ 4646+ 4647+ 4648+ 4649+ 4650+ 4651+ 4652+ 4653+ 4654+ 4655+
4656+ 4657+ 4658+ 4659+ 4660+ 4661+ 4662+ 4663+ 4664+ 4665+ 4666+ 4667+
4668+ 4669+ 4670+ 4671+ 4672+ 4673+ 4674+ 4675+ 4676+ 4677+ 4678+ 4679+
4680+ 4681+ 4682+ 4683+ 4684+ 4685+ 4686+ 4687+ 4688+ 4689+ 4690+ 4691+
4692+ 4693+ 4694+ 4695+ 4696+ 4697+ 4698+ 4699+ 4700+ 4701+ 4702+ 4703+
4704+ 4705+ 4706+ 4707+ 4708+ 4709+ 4710+ 4711+ 4712+ 4713+ 4714+ 4715+
4716+ 4717+ 4718+ 4719+ 4720+ 4721+ 4722+ 4723+ 4724+ 4725+ 4726+ 4727+
4728+ 4729+ 4730+ 4731+ 4732+ 4733+ 4734+ 4735+ 4736+ 4737+ 4738+ 4739+
4740+ 4741+ 4742+ 4743+ 4744+ 4745+ 4746+ 4747+ 4748+ 4749+ 4750+ 4751+
4752+ 4753+ 4754+ 4755+ 4756+ 4757+ 4758+ 4759+ 4760+ 4761+ 4762+ 4763+
4764+ 4765+ 4766+ 4767+ 4768+ 4769+ 4770+ 4771+ 4772+ 4773+ 4774+ 4775+
4776+ 4777+ 4778+ 4779+ 4780+ 4781+ 4782+ 4783+ 4784+ 4785+ 4786+ 4787+
4788+ 4789+ 4790+ 4791+ 4792+ 4793+ 4794+ 4795+ 4796+ 4797+ 4798+ 4799+
4800+ 4801+ 4802+ 4803+ 4804+ 4805+ 4806+ 4807+ 4808+ 4809+ 4810+ 4811+
4812+ 4813+ 4814+ 4815+ 4816+ 4817+ 4818+ 4819+ 4820+ 4821+ 4822+ 4823+
4824+ 4825+ 4826+ 4827+ 4828+ 4829+ 4830+ 4831+ 4832+ 4833+ 4834+ 4835+
4836+ 4837+ 4838+ 4839+ 4840+ 4841+ 4842+ 4843+ 4844+ 4845+ 4846+ 4847+
4848+ 4849+ 4850+ 4851+ 4852+ 4853+ 4854+ 4855+ 4856+ 4857+ 4858+ 4859+
4860+ 4861+ 4862+ 4863+ 4864+ 4865+ 4866+ 4867+ 4868+ 4869+ 4870+ 4871+
4872+ 4873+ 4874+ 4875+ 4876+ 4877+ 4878+ 4879+ 4880+ 4881+ 4882+ 4883+
4884+ 4885+ 4886+ 4887+ 4888+ 4889+ 4890+ 4891+ 4892+ 4893+ 4894+ 4895+
4896+ 4897+ 4898+ 4899+ 4900+ 4901+ 4902+ 4903+ 4904+ 4905+ 4906+ 4907+
4908+ 4909+ 4910+ 4911+ 4912+ 4913+ 4914+ 4915+ 4916+ 4917+ 4918+ 4919+
4920+ 4921+ 4922+ 4923+ 4924+ 4925+ 4926+ 4927+ 4928+ 4929+ 4930+ 4931+
4932+ 4933+ 4934+ 4935+ 4936+ 4937+ 4938+ 4939+ 4940+ 4941+ 4942+ 4943+
4944+ 4945+ 4946+ 4947+ 4948+ 4949+ 4950+ 4951+ 4952+ 4953+ 4954+ 4955+
4956+ 4957+ 4958+ 4959+ 4960+ 4961+ 4962+ 4963+ 4964+ 4965+ 4966+ 4967+
4968+ 4969+ 4970+ 4971+ 4972+ 4973+ 4974+ 4975+ 4976+ 4977+ 4978+ 4979+
4980+ 4981+ 4982+ 4983+ 4984+ 4985+ 4986+ 4987+ 4988+ 4989+ 4990+ 4991+
4992+ 4993+ 4994+ 4995+ 4996+ 4997+ 4998+ 4999+ 5000+ 5001+ 5002+ 5003+
5004+ 5005+ 5006+ 5007+ 5008+ 5009+ 5010+ 5011+ 5012+ 5013+ 5014+ 5015+
5016+ 5017+ 5018+ 5019+ 5020+ 5021+ 5022+ 5023+ 5024+ 5025+ 5026+ 5027+
5028+ 5029+ 5030+ 5031+ 5032+ 5033+ 5034+ 5035+ 5036+ 5037+ 5038+ 5039+
5040+ 5041+ 5042+ 5043+ 5044+ 5045+ 5046+ 5047+ 5048+ 5049+ 5050+ 5051+
5052+ 5053+ 5054+ 5055+ 5056+ 5057+ 5058+ 5059+ 5060+ 5061+ 5062+ 5063+
5064+ 5065+ 5066+ 5067+ 5068+ 5069+ 5070+ 5071+ 5072+ 5073+ 5074+ 5075+
5076+ 5077+ 5078+ 5079+ 5080+ 5081+ 5082+ 5083+ 5084+ 5085+ 5086+ 5087+
5088+ 5089+ 5090+ 5091+ 5092+ 5093+ 5094+ 5095+ 5096+ 5097+ 5098+ 5099+
5100+ 5101+ 5102+ 5103+ 5104+ 5105+ 5106+ 5107+ 5108+ 5109+ 5110+ 5111+
5112+ 5113+ 5114+ 5115+ 5116+ 5117+ 5118+ 5119+ 5120+ 5121+ 5122+ 5123+
5124+ 5125+ 5126+ 5127+ 5128+ 5129+ 5130+ 5131+ 5132+ 5133+ 5134+ 5135+
5136+ 5137+ 5138+ 5139+ 5140+ 5141+ 5142+ 5143+ 5144+ 5145+ 5146+ 5147+
5148+ 5149+ 5150+ 5151+ 5152+ 5153+ 5154+ 5155+ 5156+ 5157+ 5158+ 5159+
5160+ 5161+ 5162+ 5163+ 5164+ 5165+ 5166+ 5167+ 5168+ 5169+ 5170+ 5171+
5172+ 5173+ 5174+ 5175+ 5176+ 5177+ 5178+ 5179+ 5180+ 5181+ 5182+ 5183+
5184+ 5185+ 5186+ 5187+ 5188+ 5189+ 5190+ 5191+ 5192+ 5193+ 5194+ 5195+
5196+ 5197+ 5198+ 5199+ 5200+ 5201+ 5202+ 5203+ 5204+ 5205+ 5206+ 5207+
5208+ 5209+ 5210+ 5211+ 5212+ 5213+ 5214+ 5215+ 5216+ 5217+ 5218+ 5219+
5220+ 5221+ 5222+ 5223+ 5224+ 5225+ 5226+ 5227+ 5228+ 5229+ 5230+ 5231+
5232+ 5233+ 5234+ 5235+ 5236+ 5237+ 5238+ 5239+ 5240+ 5241+ 5242+ 5243+
5244+ 5245+ 5246+ 5247+ 5248+ 5249+ 5250+ 5251+ 5252+ 5253+ 5254+ 5255+
5256+ 5257+ 5258+ 5259+ 5260+ 5261+ 5262+ 5263+ 5264+ 5265+ 5266+ 5267+
5268+ 5269+ 5270+ 5271+ 5272+ 5273+ 5274+ 5275+ 5276+ 5277+ 5278+ 5279+
5280+ 5281+ 5282+ 5283+ 5284+ 5285+ 5286+ 5287+ 5288+ 5289+ 5290+ 5291+
5292+ 5293+ 5294+ 5295+ 5296+ 5297+ 5298+ 5299+ 5300+ 5301+ 5302+ 5303+
5304+ 5305+ 5306+ 5307+ 5308+ 5309+ 5310+ 5311+ 5312+ 5313+ 5314+ 5315+
5316+ 5317+ 5318+ 5319+ 5320+ 5321+ 5322+ 5323+ 5324+ 5325+ 5326+ 5327+
5328+ 5329+ 5330+ 5331+ 5332+ 5333+ 5334+ 5335+ 5336+ 5337+ 5338+ 5339+
5340+ 5341+ 5342+ 5343+ 5344+ 5345+ 5346+ 5347+ 5348+ 5349+ 5350+ 5351+
5352+ 5353+ 5354+ 5355+ 5356+ 5357+ 5358+ 5359+ 5360+ 5361+ 5362+ 5363+
5364+ 5365+ 5366+ 5367+ 5368+ 5369+ 5370+ 5371+ 5372+ 5373+ 5374+ 5375+
5376+ 5377+ 5378+ 5379+ 5380+ 5381+ 5382+ 5383+ 5384+ 5385+ 5386+ 5387+
5388+ 5389+ 5390+ 5391+ 5392+ 5393+ 5394+ 5395+ 5396+ 5397+ 5398+ 5399+
5400+ 5401+ 5402+ 5403+ 5404+ 5405+ 5406+ 5407+ 5408+ 5409+ 5410+ 5411+
5412+ 5413+ 5414+ 5415+ 5416+ 5417+ 5418+ 5419+ 5420+ 5421+ 5422+ 5423+
5424+ 5425+ 5426+ 5427+ 5428+ 5429+ 5430+ 5431+ 5432+ 5433+ 5434+ 5435+
5436+ 5437+ 5438+ 5439+ 5440+ 5441+ 5442+ 5443+ 5444+ 5445+ 5446+ 5447+
5448+ 5449+ 5450+ 5451+ 5452+ 5453+ 5454+ 5455+ 5456+ 5457+ 5458+ 5459+
5460+ 5461+ 5462+ 5463+ 5464+ 5465+ 5466+ 5467+ 5468+ 5469+ 5470+ 5471+
5472+ 5473+ 5474+ 5475+ 5476+ 5477+ 5478+ 5479+ 5480+ 5481+ 5482+ 5483+
5484+ 5485+ 5486+ 5487+ 5488+ 5489+ 5490+ 5491+ 5492+ 5493+ 5494+ 5495+
5496+ 5497+ 5498+ 5499+ 5500+ 5501+ 5502+ 5503+ 5504+ 5505+ 5506+ 5507+
5508+ 5509+ 5510+ 5511+ 5512+ 5513+ 5514+ 5515+ 5516+ 5517+ 5518+ 5519+
5520+ 5521+ 5522+ 5523+ 5524+ 5525+ 5526+ 5527+ 5528+ 5529+ 5530+ 5531+
5532+ 5533+ 5534+ 5535+ 5536+ 5537+ 5538+ 5539+ 5540+ 5541+ 5542+ 5543+
5544+ 5545+ 5546+ 5547+ 5548+ 5549+ 5550+ 5551+ 5552+ 5553+ 5554+ 5555+
5556+ 5557+ 5558+ 5559+ 5560+ 5561+ 5562+ 5563+ 5564+ 5565+ 5566+ 5567+
5568+ 5569+ 5570+ 5571+ 5572+ 5573+ 5574+ 5575+ 5576+ 5577+ 5578+ 5579+
5580+ 5581+ 5582+ 5583+ 5584+ 5585+ 5586+ 5587+ 5588+ 5589+ 5590+ 5591+
5592+ 5593+ 5594+ 5595+ 5596+ 5597+ 5598+ 5599+ 5600+ 5601+ 5602+ 5603+
5604+ 5605+ 5606+ 5607+ 5608+ 5609+ 5610+ 5611+ 5612+ 5613+ 5614+ 5615+
5616+ 5617+ 5618+ 5619+ 5620+ 5621+ 5622+ 5623+ 5624+ 5625+ 5626+ 5627+
5628+ 5629+ 5630+ 5631+ 5632+ 5633+ 5634+ 5635+ 5636+ 5637+ 5638+ 5639+
5640+ 5641+ 5642+ 5643+ 5644+ 5645+ 5646+ 5647+ 5648+ 5649+ 5650+ 5651+
5652+ 5653+ 5654+ 5655+ 5656+ 5657+ 5658+ 5659+ 5660+ 5661+ 5662+ 5663+
5664+ 5665+ 5666+ 5667+ 5668+ 5669+ 5670+ 5671+ 5672+ 5673+ 5674+ 5675+
5676+ 5677+ 5678+ 5679+ 5680+ 5681+ 5682+ 5683+ 5684+ 5685+ 5686+ 5687+
5688+ 5689+ 5690+ 5691+ 5692+ 5693+ 5694+ 5695+ 5696+ 5697+ 5698+ 5699+
5700+ 5701+ 5702+ 5703+ 5704+ 5705+ 5706+ 5707+ 5708+ 5709+ 5710+ 5711+
5712+ 5713+ 5714+ 5715+ 5716+ 5717+ 5718+ 5719+ 5720+ 5721+ 5722+ 5723+
5724+ 5725+ 5726+ 5727+ 5728+ 5729+ 5730+ 5731+ 5732+ 5733+ 5734+ 5735+
5736+ 5737+ 5738+ 5739+ 5740+ 5741+ 5742+ 5743+ 5744+ 5745+ 5746+ 5747+
5748+ 5749+ 5750+ 5751+ 5752+ 5753+ 5754+ 5755+ 5756+ 5757+ 5758+ 5759+
5760+ 5761+ 5762+ 5763+ 5764+ 5765+ 5766+ 5767+ 5768+ 5769+ 5770+ 5771+
5772+ 5773+ 5774+ 5775+ 5776+ 5777+ 5778+ 5779+ 5780+ 5781+ 5782+ 5783+
5784+ 5785+ 5786+ 5787+ 5788+ 5789+ 5790+ 5791+ 5792+ 5793+ 5794+ 5795+
5796+ 5797+ 5798+ 5799+ 5800+ 5801+ 5802+ 5803+ 5804+ 5805+ 5806+ 5807+
5808+ 5809+ 5810+ 5811+ 5812+ 5813+ 5814+ 5815+ 5816+ 5817+ 5818+ 5819+
5820+ 5821+ 5822+ 5823+ 5824+ 5825+ 5826+ 5827+ 5828+ 5829+ 5830+ 5831+
5832+ 5833+ 5834+ 5835+ 5836+ 5837+ 5838+ 5839+ 5840+ 5841+ 5842+ 5843+
5844+ 5845+ 5846+ 5847+ 5848+ 5849+ 5850+ 5851+ 5852+ 5853+ 5854+ 5855+
5856+ 5857+ 5858+ 5859+ 5860+ 5861+ 5862+ 5863+ 5864+ 5865+ 5866+ 5867+
5868+ 5869+ 5870+ 5871+ 5872+ 5873+ 5874+ 5875+ 5876+ 5877+ 5878+ 5879+
5880+ 5881+ 5882+ 5883+ 5884+ 5885+ 5886+ 5887+ 5888+ 5889+ 5890+ 5891+
5892+ 5893+ 5894+ 5895+ 5896+ 5897+ 5898+ 5899+ 5900+ 5901+ 5902+ 5903+
5904+ 5905+ 5906+ 5907+ 5908+ 5909+ 5910+ 5911+ 5912+ 5913+ 5914+ 5915+
5916+ 5917+ 5918+ 5919+ 5920+ 5921+ 5922+ 5923+ 5924+ 5925+ 5926+ 5927+
5928+ 5929+ 5930+ 5931+ 5932+ 5933+ 5934+ 5935+ 5936+ 5937+ 5938+ 5939+
5940+ 5941+ 5942+ 5943+ 5944+ 5945+ 5946+ 5947+ 5948+ 5949+ 5950+ 5951+
5952+ 5953+ 5954+ 5955+ 5956+ 5957+ 5958+ 5959+ 5960+ 5961+ 5962+ 5963+
5964+ 5965+ 5966+ 5967+ 5968+ 5969+ 5970+ 5971+ 5972+ 5973+ 5974+ 5975+
5976+ 5977+ 5978+ 5979+ 5980+ 5981+ 5982+ 5983+ 5984+ 5985+ 5986+ 5987+
5988+ 5989+ 5990+ 5991+ 5992+ 5993+ 5994+ 5995+ 5996+ 5997+ 5998+ 5999+
6000+ 6001+ 6002+ 6003+ 6004+ 6005+ 6006+ 6007+ 6008+ 6009+ 6010+ 6011+
6012+ 6013+ 6014+ 6015+ 6016+ 6017+ 6018+ 6019+ 6020+ 6021+ 6022+ 6023+
6024+ 6025+ 6026+ 6027+ 6028+ 6029+ 6030+ 6031+ 6032+ 6033+ 6034+ 6035+
6036+ 6037+ 6038+ 6039+ 6040+ 6041+ 6042+ 6043+ 6044+ 6045+ 6046+ 6047+
6048+ 6049+ 6050+ 6051+ 6052+ 6053+ 6054+ 6055+ 6056+ 6057+ 6058+ 6059+
6060+ 6061+ 6062+ 6063+ 6064+ 6065+ 6066+ 6067+ 6068+ 6069+ 6070+ 6071+
6072+ 6073+ 6074+ 6075+ 6076+ 6077+ 6078+ 6079+ 6080+ 6081+ 6082+ 6083+
6084+ 6085+ 6086+ 6087+ 6088+ 6089+ 6090+ 6091+ 6092+ 6093+ 6094+ 6095+
6096+ 6097+ 6098+ 6099+ 6100+ 6101+ 6102+ 6103+ 6104+ 6105+ 6106+ 6107+
6108+ 6109+ 6110+ 6111+ 6112+ 6113+ 6114+ 6115+ 6116+ 6117+ 6118+ 6119+
6120+ 6121+ 6122+ 6123+ 6124+ 6125+ 6126+ 6127+ 6128+ 6129+ 6130+ 6131+
6132+ 6133+ 6134+ 6135+ 6136+ 6137+ 6138+ 6139+ 6140+ 6141+ 6142+ 6143+
6144+ 6145+ 6146+ 6147+ 6148+ 6149+ 6150+ 6151+ 6152+ 6153+ 6154+ 6155+
6156+ 6157+ 6158+ 6159+ 6160+ 6161+ 6162+ 6163+ 6164+ 6165+ 6166+ 6167+
6168+ 6169+ 6170+ 6171+ 6172+ 6173+ 6174+ 6175+ 6176+ 6177+ 6178+ 6179+
6180+ 6181+ 6182+ 6183+ 6184+ 6185+ 6186+ 6187+ 6188+ 6189+ 6190+ 6191+
6192+ 6193+ 6194+ 6195+ 6196+ 6197+ 6198+ 6199+ 6200+ 6201+ 6202+ 6203+
6204+ 6205+ 6206+ 6207+ 6208+ 6209+ 6210+ 6211+ 6212+ 6213+ 6214+ 6215+
6216+ 6217+ 6218+ 6219+ 6220+ 6221+ 6222+ 6223+ 6224+ 6225+ 6226+ 6227+
6228+ 6229+ 6230+ 6231+ 6232+ 6233+ 6234+ 6235+ 6236+ 6237+ 6238+ 6239+
6240+ 6241+ 6242+ 6243+ 6244+ 6245+ 6246+ 6247+ 6248+ 6249+ 6250+ 6251+
6252+ 6253+ 6254+ 6255+ 6256+ 6257+ 6258+ 6259+ 6260+ 6261+ 6262+ 6263+
6264+ 6265+ 6266+ 6267+ 6268+ 6269+ 6270+ 6271+ 6272+ 6273+ 6274+ 6275+
6276+ 6277+ 6278+ 6279+ 6280+ 6281+ 6282+ 6283+ 6284+ 6285+ 6286+ 6287+
6288+ 6289+ 6290+ 6291+ 6292+ 6293+ 6294+ 6295+ 6296+ 6297+ 6298+ 6299+
6300+ 6301+ 6302+ 6303+ 6304+ 6305+ 6306+ 6307+ 6308+ 6309+ 6310+ 6311+
6312+ 6313+ 6314+ 6315+ 6316+ 6317+ 6318+ 6319+ 6320+ 6321+ 6322+ 6323+
6324+ 6325+ 6326+ 6327+ 6328+ 6329+ 6330+ 6331+ 6332+ 6333+ 6334+ 6335+
6336+ 6337+ 6338+ 6339+ 6340+ 6341+ 6342+ 6343+ 6344+ 6345+ 6346+ 6347+
6348+ 6349+ 6350+ 6351+ 6352+ 6353+ 6354+ 6355+ 6356+ 6357+ 6358+ 6359+
6360+ 6361+ 6362+ 6363+ 6364+ 6365+ 6366+ 6367+ 6368+ 6369+ 6370+ 6371+
6372+ 6373+ 6374+ 6375+ 6376+ 6377+ 6378+ 6379+ 6380+ 6381+ 6382+ 6383+
6384+ 6385+ 6386+ 6387+ 6388+ 6389+ 6390+ 6391+ 6392+ 6393+ 6394+ 6395+
6396+ 6397+ 6398+ 6399+ 6400+ 6401+ 6402+ 6403+ 6404+ 6405+ 6406+ 6407+
6408+ 6409+ 6410+ 6411+ 6412+ 6413+ 6414+ 6415+ 6416+ 6417+ 6418+ 6419+
6420+ 6421+ 6422+ 6423+ 6424+ 6425+ 6426+ 6427+ 6428+ 6429+ 6430+ 6431+
6432+ 6433+ 6434+ 6435+ 6436+ 6437+ 6438+ 6439+ 6440+ 6441+ 6442+ 6443+
6444+ 6445+ 6446+ 6447+ 6448+ 6449+ 6450+ 6451+ 6452+ 6453+ 6454+ 6455+
6456+ 6457+ 6458+ 6459+ 6460+ 6461+ 6462+ 6463+ 6464+ 6465+ 6466+ 6467+
6468+ 6469+ 6470+ 6471+ 6472+ 6473+ 6474+ 6475+ 6476+ 6477+ 6478+ 6479+
6480+ 6481+ 6482+ 6483+ 6484+ 6485+ 6486+ 6487+ 6488+ 6489+ 6490+ 6491+
6492+ 6493+ 6494+ 6495+ 6496+ 6497+ 6498+ 6499+ 6500+ 6501+ 6502+ 6503+
6504+ 6505+ 6506+ 6507+ 6508+ 6509+ 6510+ 6511+ 6512+ 6513+ 6514+ 6515+
6516+ 6517+ 6518+ 6519+ 6520+ 6521+ 6522+ 6523+ 6524+ 6525+ 6526+ 6527+
6528+ 6529+ 6530+ 6531+ 6532+ 6533+ 6534+ 6535+ 6536+ 6537+ 6538+ 6539+
6540+ 6541+ 6542+ 6543+ 6544+ 6545+ 6546+ 6547+ 6548+ 6549+ 6550+ 6551+
6552+ 6553+ 6554+ 6555+ 6556+ 6557+ 6558+ 6559+ 6560+ 6561+ 6562+ 6563+
6564+ 6565+ 6566+ 6567+ 6568+ 6569+ 6570+ 6571+ 6572+ 6573+ 6574+ 6575+
6576+ 6577+ 6578+ 6579+ 6580+ 6581+ 6582+ 6583+ 6584+ 6585+ 6586+ 6587+
6588+ 6589+ 6590+ 6591+ 6592+ 6593+ 6594+ 6595+ 6596+ 6597+ 6598+ 6599+
6600+ 6601+ 6602+ 6603+ 6604+ 6605+ 6606+ 6607+ 6608+ 6609+ 6610+ 6611+
6612+ 6613+ 6614+ 6615+ 6616+ 6617+ 6618+ 6619+ 6620+ 6621+ 6622+ 6623+
6624+ 6625+ 6626+ 6627+ 6628+ 6629+ 6630+ 6631+ 6632+ 6633+ 6634+ 6635+
6636+ 6637+ 6638+ 6639+ 6640+ 6641+ 6642+ 6643+ 6644+ 6645+ 6646+ 6647+
6648+ 6649+ 6650+ 6651+ 6652+ 6653+ 6654+ 6655+ 6656+ 6657+ 6658+ 6659+
6660+ 6661+ 6662+ 6663+ 6664+ 6665+ 6666+ 6667+ 6668+ 6669+ 6670+ 6671+
6672+ 6673+ 6674+ 6675+ 6676+ 6677+ 6678+ 6679+ 6680+ 6681+ 6682+ 6683+
6684+ 6685+ 6686+ 6687+ 6688+ 6689+ 6690+ 6691+ 6692+ 6693+ 6694+ 6695+
6696+ 6697+ 6698+ 6699+ 6700+ 6701+ 6702+ 6703+ 6704+ 6705+ 6706+ 6707+
6708+ 6709+ 6710+ 6711+ 6712+ 6713+ 6714+ 6715+ 6716+ 6717+ 6718+ 6719+
6720+ 6721+ 6722+ 6723+ 6724+ 6725+ 6726+ 6727+ 6728+ 6729+ 6730+ 6731+
6732+ 6733+ 6734+ 6735+ 6736+ 6737+ 6738+ 6739+ 6740+ 6741+ 6742+ 6743+
6744+ 6745+ 6746+ 6747+ 6748+ 6749+ 6750+ 6751+ 6752+ 6753+ 6754+ 6755+
6756+ 6757+ 6758+ 6759+ 6760+ 6761+ 6762+ 6763+ 6764+ 6765+ 6766+ 6767+
6768+ 6769+ 6770+ 6771+ 6772+ 6773+ 6774+ 6775+ 6776+ 6777+ 6778+ 6779+
6780+ 6781+ 6782+ 6783+ 6784+ 6785+ 6786+ 6787+ 6788+ 6789+ 6790+ 6791+
6792+ 6793+ 6794+ 6795+ 6796+ 6797+ 6798+ 6799+ 6800+ 6801+ 6802+ 6803+
6804+ 6805+ 6806+ 6807+ 6808+ 6809+ 6810+ 6811+ 6812+ 6813+ 6814+ 6815+
6816+ 6817+ 6818+ 6819+ 6820+ 6821+ 6822+ 6823+ 6824+ 6825+ 6826+ 6827+
6828+ 6829+ 6830+ 6831+ 6832+ 6833+ 6834+ 6835+ 6836+ 6837+ 6838+ 6839+
6840+ 6841+ 6842+ 6843+ 6844+ 6845+ 6846+ 6847+ 6848+ 6849+ 6850+ 6851+
6852+ 6853+ 6854+ 6855+ 6856+ 6857+ 6858+ 6859+ 6860+ 6861+ 6862+ 6863+
6864+ 6865+ 6866+ 6867+ 6868+ 6869+ 6870+ 6871+ 6872+ 6873+ 6874+ 6875+
6876+ 6877+ 6878+ 6879+ 6880+ 6881+ 6882+ 6883+ 6884+ 6885+ 6886+ 6887+
6888+ 6889+ 6890+ 6891+ 6892+ 6893+ 6894+ 6895+ 6896+ 6897+ 6898+ 6899+
6900+ 6901+ 6902+ 6903+ 6904+ 6905+ 6906+ 6907+ 6908+ 6909+ 6910+ 6911+
6912+ 6913+ 6914+ 6915+ 6916+ 6917+ 6918+ 6919+ 6920+ 6921+ 6922+ 6923+
6924+ 6925+ 6926+ 6927+ 6928+ 6929+ 6930+ 6931+ 6932+ 6933+ 6934+ 6935+
6936+ 6937+ 6938+ 6939+ 6940+ 6941+ 6942+ 6943+ 6944+ 6945+ 6946+ 6947+
6948+ 6949+ 6950+ 6951+ 6952+ 6953+ 6954+ 6955+ 6956+ 6957+ 6958+ 6959+
6960+ 6961+ 6962+ 6963+ 6964+ 6965+ 6966+ 6967+ 6968+ 6969+ 6970+ 6971+
6972+ 6973+ 6974+ 6975+ 6976+ 6977+ 6978+ 6979+ 6980+ 6981+ 6982+ 6983+
6984+ 6985+ 6986+ 6987+ 6988+ 6989+ 6990+ 6991+ 6992+ 6993+ 6994+ 6995+
6996+ 6997+ 6998+ 6999+ 7000+ 7001+ 7002+ 7003+ 7004+ 7005+ 7006+ 7007+
7008+ 7009+ 7010+ 7011+ 7012+ 7013+ 7014+ 7015+ 7016+ 7017+ 7018+ 7019+
7020+ 7021+ 7022+ 7023+ 7024+ 7025+ 7026+ 7027+ 7028+ 7029+ 7030+ 7031+
7032+ 7033+ 7034+ 7035+ 7036+ 7037+ 7038+ 7039+ 7040+ 7041+ 7042+ 7043+
7044+ 7045+ 7046+ 7047+ 7048+ 7049+ 7050+ 7051+ 7052+ 7053+ 7054+ 7055+
7056+ 7057+ 7058+ 7059+ 7060+ 7061+ 7062+ 7063+ 7064+ 7065+ 7066+ 7067+
7068+ 7069+ 7070+ 7071+ 7072+ 7073+ 7074+ 7075+ 7076+ 7077+ 7078+ 7079+
7080+ 7081+ 7082+ 7083+ 7084+ 7085+ 7086+ 7087+ 7088+ 7089+ 7090+ 7091+
7092+ 7093+ 7094+ 7095+ 7096+ 7097+ 7098+ 7099+ 7100+ 7101+ 7102+ 7103+
7104+ 7105+ 7106+ 7107+ 7108+ 7109+ 7110+ 7111+ 7112+ 7113+ 7114+ 7115+
7116+ 7117+ 7118+ 7119+ 7120+ 7121+ 7122+ 7123+ 7124+ 7125+ 7126+ 7127+
7128+ 7129+ 7130+ 7131+ 7132+ 7133+ 7134+ 7135+ 7136+ 7137+ 7138+ 7139+
7140+ 7141+ 7142+ 7143+ 7144+ 7145+ 7146+ 7147+ 7148+ 7149+ 7150+ 7151+
7152+ 7153+ 7154+ 7155+ 7156+ 7157+ 7158+ 7159+ 7160+ 7161+ 7162+ 7163+
7164+ 7165+ 7166+ 7167+ 7168+ 7169+ 7170+ 7171+ 7172+ 7173+ 7174+ 7175+
7176+ 7177+ 7178+ 7179+ 7180+ 7181+ 7182+ 7183+ 7184+ 7185+ 7186+ 7187+
7188+ 7189+ 7190+ 7191+ 7192+ 7193+ 7194+ 7195+ 7196+ 7197+ 7198+ 7199+
7200+ 7201+ 7202+ 7203+ 7204+ 7205+ 7206+ 7207+ 7208+ 7209+ 7210+ 7211+
7212+ 7213+ 7214+ 7215+ 7216+ 7217+ 7218+ 7219+ 7220+ 7221+ 7222+ 7223+
7224+ 7225+ 7226+ 7227+ 7228+ 7229+ 7230+ 7231+ 7232+ 7233+ 7234+ 7235+
7236+ 7237+ 7238+ 7239+ 7240+ 7241+ 7242+ 7243+ 7244+ 7245+ 7246+ 7247+
7248+ 7249+ 7250+ 7251+ 7252+ 7253+ 7254+ 7255+ 7256+ 7257+ 7258+ 7259+
7260+ 7261+ 7262+ 7263+ 7264+ 7265+ 7266+ 7267+ 7268+ 7269+ 7270+ 7271+
7272+ 7273+ 7274+ 7275+ 7276+ 7277+ 7278+ 7279+ 7280+ 7281+ 7282+ 7283+
7284+ 7285+ 7286+ 7287+ 7288+ 7289+ 7290+ 7291+ 7292+ 7293+ 7294+ 7295+
7296+ 7297+ 7298+ 7299+ 7300+ 7301+ 7302+ 7303+ 7304+ 7305+ 7306+ 7307+
7308+ 7309+ 7310+ 7311+ 7312+ 7313+ 7314+ 7315+ 7316+ 7317+ 7318+ 7319+
7320+ 7321+ 7322+ 7323+ 7324+ 7325+ 7326+ 7327+ 7328+ 7329+ 7330+ 7331+
7332+ 7333+ 7334+ 7335+ 7336+ 7337+ 7338+ 7339+ 7340+ 7341+ 7342+ 7343+
7344+ 7345+ 7346+ 7347+ 7348+ 7349+ 7350+ 7351+ 7352+ 7353+ 7354+ 7355+
7356+ 7357+ 7358+ 7359+ 7360+ 7361+ 7362+ 7363+ 7364+ 7365+ 7366+ 7367+
7368+ 7369+ 7370+ 7371+ 7372+ 7373+ 7374+ 7375+ 7376+ 7377+ 7378+ 7379+
7380+ 7381+ 7382+ 7383+ 7384+ 7385+ 7386+ 7387+ 7388+ 7389+ 7390+ 7391+
7392+ 7393+ 7394+ 7395+ 7396+ 7397+ 7398+ 7399+ 7400+ 7401+ 7402+ 7403+
7404+ 7405+ 7406+ 7407+ 7408+ 7409+ 7410+ 7411+ 7412+ 7413+ 7414+ 7415+
7416+ 7417+ 7418+ 7419+ 7420+ 7421+ 7422+ 7423+ 7424+ 7425+ 7426+ 7427+
7428+ 7429+ 7430+ 7431+ 7432+ 7433+ 7434+ 7435+ 7436+ 7437+ 7438+ 7439+
7440+ 7441+ 7442+ 7443+ 7444+ 7445+ 7446+ 7447+ 7448+ 7449+ 7450+ 7451+
7452+ 7453+ 7454+ 7455+ 7456+ 7457+ 7458+ 7459+ 7460+ 7461+ 7462+ 7463+
7464+ 7465+ 7466+ 7467+ 7468+ 7469+ 7470+ 7471+ 7472+ 7473+ 7474+ 7475+
7476+ 7477+ 7478+ 7479+ 7480+ 7481+ 7482+ 7483+ 7484+ 7485+ 7486+ 7487+
7488+ 7489+ 7490+ 7491+ 7492+ 7493+ 7494+ 7495+ 7496+ 7497+ 7498+ 7499+
7500+ 7501+ 7502+ 7503+ 7504+ 7505+ 7506+ 7507+ 7508+ 7509+ 7510+ 7511+
7512+ 7513+ 7514+ 7515+ 7516+ 7517+ 7518+ 7519+ 7520+ 7521+ 7522+ 7523+
7524+ 7525+ 7526+ 7527+ 7528+ 7529+ 7530+ 7531+ 7532+ 7533+ 7534+ 7535+
7536+ 7537+ 7538+ 7539+ 7540+ 7541+ 7542+ 7543+ 7544+ 7545+ 7546+ 7547+
7548+ 7549+ 7550+ 7551+ 7552+ 7553+ 7554+ 7555+ 7556+ 7557+ 7558+ 7559+
7560+ 7561+ 7562+ 7563+ 7564+ 7565+ 7566+ 7567+ 7568+ 7569+ 7570+ 7571+
7572+ 7573+ 7574+ 7575+ 7576+ 7577+ 7578+ 7579+ 7580+ 7581+ 7582+ 7583+
7584+ 7585+ 7586+ 7587+ 7588+ 7589+ 7590+ 7591+ 7592+ 7593+ 7594+ 7595+
7596+ 7597+ 7598+ 7599+ 7600+ 7601+ 7602+ 7603+ 7604+ 7605+ 7606+ 7607+
7608+ 7609+ 7610+ 7611+ 7612+ 7613+ 7614+ 7615+ 7616+ 7617+ 7618+ 7619+
7620+ 7621+ 7622+ 7623+ 7624+ 7625+ 7626+ 7627+ 7628+ 7629+ 7630+ 7631+
7632+ 7633+ 7634+ 7635+ 7636+ 7637+ 7638+ 7639+ 7640+ 7641+ 7642+ 7643+
7644+ 7645+ 7646+ 7647+ 7648+ 7649+ 7650+ 7651+ 7652+ 7653+ 7654+ 7655+
7656+ 7657+ 7658+ 7659+ 7660+ 7661+ 7662+ 7663+ 7664+ 7665+ 7666+ 7667+
7668+ 7669+ 7670+ 7671+ 7672+ 7673+ 7674+ 7675+ 7676+ 7677+ 7678+ 7679+
7680+ 7681+ 7682+ 7683+ 7684+ 7685+ 7686+ 7687+ 7688+ 7689+ 7690+ 7691+
7692+ 7693+ 7694+ 7695+ 7696+ 7697+ 7698+ 7699+ 7700+ 7701+ 7702+ 7703+
7704+ 7705+ 7706+ 7707+ 7708+ 7709+ 7710+ 7711+ 7712+ 7713+ 7714+ 7715+
7716+ 7717+ 7718+ 7719+ 7720+ 7721+ 7722+ 7723+ 7724+ 7725+ 7726+ 7727+
7728+ 7729+ 7730+ 7731+ 7732+ 7733+ 7734+ 7735+ 7736+ 7737+ 7738+ 7739+
7740+ 7741+ 7742+ 7743+ 7744+ 7745+ 7746+ 7747+ 7748+ 7749+ 7750+ 7751+
7752+ 7753+ 7754+ 7755+ 7756+ 7757+ 7758+ 7759+ 7760+ 7761+ 7762+ 7763+
7764+ 7765+ 7766+ 7767+ 7768+ 7769+ 7770+ 7771+ 7772+ 7773+ 7774+ 7775+
7776+ 7777+ 7778+ 7779+ 7780+ 7781+ 7782+ 7783+ 7784+ 7785+ 7786+ 7787+
7788+ 7789+ 7790+ 7791+ 7792+ 7793+ 7794+ 7795+ 7796+ 7797+ 7798+ 7799+
7800+ 7801+ 7802+ 7803+ 7804+ 7805+ 7806+ 7807+ 7808+ 7809+ 7810+ 7811+
7812+ 7813+ 7814+ 7815+ 7816+ 7817+ 7818+ 7819+ 7820+ 7821+ 7822+ 7823+
7824+ 7825+ 7826+ 7827+ 7828+ 7829+ 7830+ 7831+ 7832+ 7833+ 7834+ 7835+
7836+ 7837+ 7838+ 7839+ 7840+ 7841+ 7842+ 7843+ 7844+ 7845+ 7846+ 7847+
7848+ 7849+ 7850+ 7851+ 7852+ 7853+ 7854+ 7855+ 7856+ 7857+ 7858+ 7859+
7860+ 7861+ 7862+ 7863+ 7864+ 7865+ 7866+ 7867+ 7868+ 7869+ 7870+ 7871+
7872+ 7873+ 7874+ 7875+ 7876+ 7877+ 7878+ 7879+ 7880+ 7881+ 7882+ 7883+
7884+ 7885+ 7886+ 7887+ 7888+ 7889+ 7890+ 7891+ 7892+ 7893+ 7894+ 7895+
7896+ 7897+ 7898+ 7899+ 7900+ 7901+ 7902+ 7903+ 7904+ 7905+ 7906+ 7907+
7908+ 7909+ 7910+ 7911+ 7912+ 7913+ 7914+ 7915+ 7916+ 7917+ 7918+ 7919+
7920+ 7921+ 7922+ 7923+ 7924+ 7925+ 7926+ 7927+ 7928+ 7929+ 7930+ 7931+
7932+ 7933+ 7934+ 7935+ 7936+ 7937+ 7938+ 7939+ 7940+ 7941+ 7942+ 7943+
7944+ 7945+ 7946+ 7947+ 7948+ 7949+ 7950+ 7951+ 7952+ 7953+ 7954+ 7955+
7956+ 7957+ 7958+ 7959+ 7960+ 7961+ 7962+ 7963+ 7964+ 7965+ 7966+ 7967+
7968+ 7969+ 7970+ 7971+ 7972+ 7973+ 7974+ 7975+ 7976+ 7977+ 7978+ 7979+
7980+ 7981+ 7982+ 7983+ 7984+ 7985+ 7986+ 7987+ 7988+ 7989+ 7990+ 7991+
7992+ 7993+ 7994+ 7995+ 7996+ 7997+ 7998+ 7999+ 8000+ 8001+ 8002+ 8003+
8004+ 8005+ 8006+ 8007+ 8008+ 8009+ 8010+ 8011+ 8012+ 8013+ 8014+ 8015+
8016+ 8017+ 8018+ 8019+ 8020+ 8021+ 8022+ 8023+ 8024+ 8025+ 8026+ 8027+
8028+ 8029+ 8030+ 8031+ 8032+ 8033+ 8034+ 8035+ 8036+ 8037+ 8038+ 8039+
8040+ 8041+ 8042+ 8043+ 8044+ 8045+ 8046+ 8047+ 8048+ 8049+ 8050+ 8051+
8052+ 8053+ 8054+ 8055+ 8056+ 8057+ 8058+ 8059+ 8060+ 8061+ 8062+ 8063+
8064+ 8065+ 8066+ 8067+ 8068+ 8069+ 8070+ 8071+ 8072+ 8073+ 8074+ 8075+
8076+ 8077+ 8078+ 8079+ 8080+ 8081+ 8082+ 8083+ 8084+ 8085+ 8086+ 8087+
8088+ 8089+ 8090+ 8091+ 8092+ 8093+ 8094+ 8095+ 8096+ 8097+ 8098+ 8099+
8100+ 8101+ 8102+ 8103+ 8104+ 8105+ 8106+ 8107+ 8108+ 8109+ 8110+ 8111+
8112+ 8113+ 8114+ 8115+ 8116+ 8117+ 8118+ 8119+ 8120+ 8121+ 8122+ 8123+
8124+ 8125+ 8126+ 8127+ 8128+ 8129+ 8130+ 8131+ 8132+ 8133+ 8134+ 8135+
8136+ 8137+ 8138+ 8139+ 8140+ 8141+ 8142+ 8143+ 8144+ 8145+ 8146+ 8147+
8148+ 8149+ 8150+ 8151+ 8152+ 8153+ 8154+ 8155+ 8156+ 8157+ 8158+ 8159+
8160+ 8161+ 8162+ 8163+ 8164+ 8165+ 8166+ 8167+ 8168+ 8169+ 8170+ 8171+
8172+ 8173+ 8174+ 8175+ 8176+ 8177+ 8178+ 8179+ 8180+ 8181+ 8182+ 8183+
8184+ 8185+ 8186+ 8187+ 8188+ 8189+ 8190+ 8191+ 8192+ 8193+ 8194+ 8195+
8196+ 8197+ 8198+ 8199+ 8200+ 8201+ 8202+ 8203+ 8204+ 8205+ 8206+ 8207+
8208+ 8209+ 8210+ 8211+ 8212+ 8213+ 8214+ 8215+ 8216+ 8217+ 8218+ 8219+
8220+ 8221+ 8222+ 8223+ 8224+ 8225+ 8226+ 8227+ 8228+ 8229+ 8230+ 8231+
8232+ 8233+ 8234+ 8235+ 8236+ 8237+ 8238+ 8239+ 8240+ 8241+ 8242+ 8243+
8244+ 8245+ 8246+ 8247+ 8248+ 8249+ 8250+ 8251+ 8252+ 8253+ 8254+ 8255+
8256+ 8257+ 8258+ 8259+ 8260+ 8261+ 8262+ 8263+ 8264+ 8265+ 8266+ 8267+
8268+ 8269+ 8270+ 8271+ 8272+ 8273+ 8274+ 8275+ 8276+ 8277+ 8278+ 8279+
8280+ 8281+ 8282+ 8283+ 8284+ 8285+ 8286+ 8287+ 8288+ 8289+ 8290+ 8291+
8292+ 8293+ 8294+ 8295+ 8296+ 8297+ 8298+ 8299+ 8300+ 8301+ 8302+ 8303+
8304+ 8305+ 8306+ 8307+ 8308+ 8309+ 8310+ 8311+ 8312+ 8313+ 8314+ 8315+
8316+ 8317+ 8318+ 8319+ 8320+ 8321+ 8322+ 8323+ 8324+ 8325+ 8326+ 8327+
8328+ 8329+ 8330+ 8331+ 8332+ 8333+ 8334+ 8335+ 8336+ 8337+ 8338+ 8339+
8340+ 8341+ 8342+ 8343+ 8344+ 8345+ 8346+ 8347+ 8348+ 8349+ 8350+ 8351+
8352+ 8353+ 8354+ 8355+ 8356+ 8357+ 8358+ 8359+ 8360+ 8361+ 8362+ 8363+
8364+ 8365+ 8366+ 8367+ 8368+ 8369+ 8370+ 8371+ 8372+ 8373+ 8374+ 8375+
8376+ 8377+ 8378+ 8379+ 8380+ 8381+ 8382+ 8383+ 8384+ 8385+ 8386+ 8387+
8388+ 8389+ 8390+ 8391+ 8392+ 8393+ 8394+ 8395+ 8396+ 8397+ 8398+ 8399+
8400+ 8401+ 8402+ 8403+ 8404+ 8405+ 8406+ 8407+ 8408+ 8409+ 8410+ 8411+
8412+ 8413+ 8414+ 8415+ 8416+ 8417+ 8418+ 8419+ 8420+ 8421+ 8422+ 8423+
8424+ 8425+ 8426+ 8427+ 8428+ 8429+ 8430+ 8431+ 8432+ 8433+ 8434+ 8435+
8436+ 8437+ 8438+ 8439+ 8440+ 8441+ 8442+ 8443+ 8444+ 8445+ 8446+ 8447+
8448+ 8449+ 8450+ 8451+ 8452+ 8453+ 8454+ 8455+ 8456+ 8457+ 8458+ 8459+
8460+ 8461+ 8462+ 8463+ 8464+ 8465+ 8466+ 8467+ 8468+ 8469+ 8470+ 8471+
8472+ 8473+ 8474+ 8475+ 8476+ 8477+ 8478+ 8479+ 8480+ 8481+ 8482+ 8483+
8484+ 8485+ 8486+ 8487+ 8488+ 8489+ 8490+ 8491+ 8492+ 8493+ 8494+ 8495+
8496+ 8497+ 8498+ 8499+ 8500+ 8501+ 8502+ 8503+ 8504+ 8505+ 8506+ 8507+
8508+ 8509+ 8510+ 8511+ 8512+ 8513+ 8514+ 8515+ 8516+ 8517+ 8518+ 8519+
8520+ 8521+ 8522+ 8523+ 8524+ 8525+ 8526+ 8527+ 8528+ 8529+ 8530+ 8531+
8532+ 8533+ 8534+ 8535+ 8536+ 8537+ 8538+ 8539+ 8540+ 8541+ 8542+ 8543+
8544+ 8545+ 8546+ 8547+ 8548+ 8549+ 8550+ 8551+ 8552+ 8553+ 8554+ 8555+
8556+ 8557+ 8558+ 8559+ 8560+ 8561+ 8562+ 8563+ 8564+ 8565+ 8566+ 8567+
8568+ 8569+ 8570+ 8571+ 8572+ 8573+ 8574+ 8575+ 8576+ 8577+ 8578+ 8579+
8580+ 8581+ 8582+ 8583+ 8584+ 8585+ 8586+ 8587+ 8588+ 8589+ 8590+ 8591+
8592+ 8593+ 8594+ 8595+ 8596+ 8597+ 8598+ 8599+ 8600+ 8601+ 8602+ 8603+
8604+ 8605+ 8606+ 8607+ 8608+ 8609+ 8610+ 8611+ 8612+ 8613+ 8614+ 8615+
8616+ 8617+ 8618+ 8619+ 8620+ 8621+ 8622+ 8623+ 8624+ 8625+ 8626+ 8627+
8628+ 8629+ 8630+ 8631+ 8632+ 8633+ 8634+ 8635+ 8636+ 8637+ 8638+ 8639+
8640+ 8641+ 8642+ 8643+ 8644+ 8645+ 8646+ 8647+ 8648+ 8649+ 8650+ 8651+
8652+ 8653+ 8654+ 8655+ 8656+ 8657+ 8658+ 8659+ 8660+ 8661+ 8662+ 8663+
8664+ 8665+ 8666+ 8667+ 8668+ 8669+ 8670+ 8671+ 8672+ 8673+ 8674+ 8675+
8676+ 8677+ 8678+ 8679+ 8680+ 8681+ 8682+ 8683+ 8684+ 8685+ 8686+ 8687+
8688+ 8689+ 8690+ 8691+ 8692+ 8693+ 8694+ 8695+ 8696+ 8697+ 8698+ 8699+
8700+ 8701+ 8702+ 8703+ 8704+ 8705+ 8706+ 8707+ 8708+ 8709+ 8710+ 8711+
8712+ 8713+ 8714+ 8715+ 8716+ 8717+ 8718+ 8719+ 8720+ 8721+ 8722+ 8723+
8724+ 8725+ 8726+ 8727+ 8728+ 8729+ 8730+ 8731+ 8732+ 8733+ 8734+ 8735+
8736+ 8737+ 8738+ 8739+ 8740+ 8741+ 8742+ 8743+ 8744+ 8745+ 8746+ 8747+
8748+ 8749+ 8750+ 8751+ 8752+ 8753+ 8754+ 8755+ 8756+ 8757+ 8758+ 8759+
8760+ 8761+ 8762+ 8763+ 8764+ 8765+ 8766+ 8767+ 8768+ 8769+ 8770+ 8771+
8772+ 8773+ 8774+ 8775+ 8776+ 8777+ 8778+ 8779+ 8780+ 8781+ 8782+ 8783+
8784+ 8785+ 8786+ 8787+ 8788+ 8789+ 8790+ 8791+ 8792+ 8793+ 8794+ 8795+
8796+ 8797+ 8798+ 8799+ 8800+ 8801+ 8802+ 8803+ 8804+ 8805+ 8806+ 8807+
8808+ 8809+ 8810+ 8811+ 8812+ 8813+ 8814+ 8815+ 8816+ 8817+ 8818+ 8819+
8820+ 8821+ 8822+ 8823+ 8824+ 8825+ 8826+ 8827+ 8828+ 8829+ 8830+ 8831+
8832+ 8833+ 8834+ 8835+ 8836+ 8837+ 8838+ 8839+ 8840+ 8841+ 8842+ 8843+
8844+ 8845+ 8846+ 8847+ 8848+ 8849+ 8850+ 8851+ 8852+ 8853+ 8854+ 8855+
8856+ 8857+ 8858+ 8859+ 8860+ 8861+ 8862+ 8863+ 8864+ 8865+ 8866+ 8867+
8868+ 8869+ 8870+ 8871+ 8872+ 8873+ 8874+ 8875+ 8876+ 8877+ 8878+ 8879+
8880+ 8881+ 8882+ 8883+ 8884+ 8885+ 8886+ 8887+ 8888+ 8889+ 8890+ 8891+
8892+ 8893+ 8894+ 8895+ 8896+ 8897+ 8898+ 8899+ 8900+ 8901+ 8902+ 8903+
8904+ 8905+ 8906+ 8907+ 8908+ 8909+ 8910+ 8911+ 8912+ 8913+ 8914+ 8915+
8916+ 8917+ 8918+ 8919+ 8920+ 8921+ 8922+ 8923+ 8924+ 8925+ 8926+ 8927+
8928+ 8929+ 8930+ 8931+ 8932+ 8933+ 8934+ 8935+ 8936+ 8937+ 8938+ 8939+
8940+ 8941+ 8942+ 8943+ 8944+ 8945+ 8946+ 8947+ 8948+ 8949+ 8950+ 8951+
8952+ 8953+ 8954+ 8955+ 8956+ 8957+ 8958+ 8959+ 8960+ 8961+ 8962+ 8963+
8964+ 8965+ 8966+ 8967+ 8968+ 8969+ 8970+ 8971+ 8972+ 8973+ 8974+ 8975+
8976+ 8977+ 8978+ 8979+ 8980+ 8981+ 8982+ 8983+ 8984+ 8985+ 8986+ 8987+
8988+ 8989+ 8990+ 8991+ 8992+ 8993+ 8994+ 8995+ 8996+ 8997+ 8998+ 8999+
9000+ 9001+ 9002+ 9003+ 9004+ 9005+ 9006+ 9007+ 9008+ 9009+ 9010+ 9011+
9012+ 9013+ 9014+ 9015+ 9016+ 9017+ 9018+ 9019+ 9020+ 9021+ 9022+ 9023+
9024+ 9025+ 9026+ 9027+ 9028+ 9029+ 9030+ 9031+ 9032+ 9033+ 9034+ 9035+
9036+ 9037+ 9038+ 9039+ 9040+ 9041+ 9042+ 9043+ 9044+ 9045+ 9046+ 9047+
9048+ 9049+ 9050+ 9051+ 9052+ 9053+ 9054+ 9055+ 9056+ 9057+ 9058+ 9059+
9060+ 9061+ 9062+ 9063+ 9064+ 9065+ 9066+ 9067+ 9068+ 9069+ 9070+ 9071+
9072+ 9073+ 9074+ 9075+ 9076+ 9077+ 9078+ 9079+ 9080+ 9081+ 9082+ 9083+
9084+ 9085+ 9086+ 9087+ 9088+ 9089+ 9090+ 9091+ 9092+ 9093+ 9094+ 9095+
9096+ 9097+ 9098+ 9099+ 9100+ 9101+ 9102+ 9103+ 9104+ 9105+ 9106+ 9107+
9108+ 9109+ 9110+ 9111+ 9112+ 9113+ 9114+ 9115+ 9116+ 9117+ 9118+ 9119+
9120+ 9121+ 9122+ 9123+ 9124+ 9125+ 9126+ 9127+ 9128+ 9129+ 9130+ 9131+
9132+ 9133+ 9134+ 9135+ 9136+ 9137+ 9138+ 9139+ 9140+ 9141+ 9142+ 9143+
9144+ 9145+ 9146+ 9147+ 9148+ 9149+ 9150+ 9151+ 9152+ 9153+ 9154+ 9155+
9156+ 9157+ 9158+ 9159+ 9160+ 9161+ 9162+ 9163+ 9164+ 9165+ 9166+ 9167+
9168+ 9169+ 9170+ 9171+ 9172+ 9173+ 9174+ 9175+ 9176+ 9177+ 9178+ 9179+
9180+ 9181+ 9182+ 9183+ 9184+ 9185+ 9186+ 9187+ 9188+ 9189+ 9190+ 9191+
9192+ 9193+ 9194+ 9195+ 9196+ 9197+ 9198+ 9199+ 9200+ 9201+ 9202+ 9203+
9204+ 9205+ 9206+ 9207+ 9208+ 9209+ 9210+ 9211+ 9212+ 9213+ 9214+ 9215+
9216+ 9217+ 9218+ 9219+ 9220+ 9221+ 9222+ 9223+ 9224+ 9225+ 9226+ 9227+
9228+ 9229+ 9230+ 9231+ 9232+ 9233+ 9234+ 9235+ 9236+ 9237+ 9238+ 9239+
9240+ 9241+ 9242+ 9243+ 9244+ 9245+ 9246+ 9247+ 9248+ 9249+ 9250+ 9251+
9252+ 9253+ 9254+ 9255+ 9256+ 9257+ 9258+ 9259+ 9260+ 9261+ 9262+ 9263+
9264+ 9265+ 9266+ 9267+ 9268+ 9269+ 9270+ 9271+ 9272+ 9273+ 9274+ 9275+
9276+ 9277+ 9278+ 9279+ 9280+ 9281+ 9282+ 9283+ 9284+ 9285+ 9286+ 9287+
9288+ 9289+ 9290+ 9291+ 9292+ 9293+ 9294+ 9295+ 9296+ 9297+ 9298+ 9299+
9300+ 9301+ 9302+ 9303+ 9304+ 9305+ 9306+ 9307+ 9308+ 9309+ 9310+ 9311+
9312+ 9313+ 9314+ 9315+ 9316+ 9317+ 9318+ 9319+ 9320+ 9321+ 9322+ 9323+
9324+ 9325+ 9326+ 9327+ 9328+ 9329+ 9330+ 9331+ 9332+ 9333+ 9334+ 9335+
9336+ 9337+ 9338+ 9339+ 9340+ 9341+ 9342+ 9343+ 9344+ 9345+ 9346+ 9347+
9348+ 9349+ 9350+ 9351+ 9352+ 9353+ 9354+ 9355+ 9356+ 9357+ 9358+ 9359+
9360+ 9361+ 9362+ 9363+ 9364+ 9365+ 9366+ 9367+ 9368+ 9369+ 9370+ 9371+
9372+ 9373+ 9374+ 9375+ 9376+ 9377+ 9378+ 9379+ 9380+ 9381+ 9382+ 9383+
9384+ 9385+ 9386+ 9387+ 9388+ 9389+ 9390+ 9391+ 9392+ 9393+ 9394+ 9395+
9396+ 9397+ 9398+ 9399+ 9400+ 9401+ 9402+ 9403+ 9404+ 9405+ 9406+ 9407+
9408+ 9409+ 9410+ 9411+ 9412+ 9413+ 9414+ 9415+ 9416+ 9417+ 9418+ 9419+
9420+ 9421+ 9422+ 9423+ 9424+ 9425+ 9426+ 9427+ 9428+ 9429+ 9430+ 9431+
9432+ 9433+ 9434+ 9435+ 9436+ 9437+ 9438+ 9439+ 9440+ 9441+ 9442+ 9443+
9444+ 9445+ 9446+ 9447+ 9448+ 9449+ 9450+ 9451+ 9452+ 9453+ 9454+ 9455+
9456+ 9457+ 9458+ 9459+ 9460+ 9461+ 9462+ 9463+ 9464+ 9465+ 9466+ 9467+
9468+ 9469+ 9470+ 9471+ 9472+ 9473+ 9474+ 9475+ 9476+ 9477+ 9478+ 9479+
9480+ 9481+ 9482+ 9483+ 9484+ 9485+ 9486+ 9487+ 9488+ 9489+ 9490+ 9491+
9492+ 9493+ 9494+ 9495+ 9496+ 9497+ 9498+ 9499+ 9500+ 9501+ 9502+ 9503+
9504+ 9505+ 9506+ 9507+ 9508+ 9509+ 9510+ 9511+ 9512+ 9513+ 9514+ 9515+
9516+ 9517+ 9518+ 9519+ 9520+ 9521+ 9522+ 9523+ 9524+ 9525+ 9526+ 9527+
9528+ 9529+ 9530+ 9531+ 9532+ 9533+ 9534+ 9535+ 9536+ 9537+ 9538+ 9539+
9540+ 9541+ 9542+ 9543+ 9544+ 9545+ 9546+ 9547+ 9548+ 9549+ 9550+ 9551+
9552+ 9553+ 9554+ 9555+ 9556+ 9557+ 9558+ 9559+ 9560+ 9561+ 9562+ 9563+
9564+ 9565+ 9566+ 9567+ 9568+ 9569+ 9570+ 9571+ 9572+ 9573+ 9574+ 9575+
9576+ 9577+ 9578+ 9579+ 9580+ 9581+ 9582+ 9583+ 9584+ 9585+ 9586+ 9587+
9588+ 9589+ 9590+ 9591+ 9592+ 9593+ 9594+ 9595+ 9596+ 9597+ 9598+ 9599+
9600+ 9601+ 9602+ 9603+ 9604+ 9605+ 9606+ 9607+ 9608+ 9609+ 9610+ 9611+
9612+ 9613+ 9614+ 9615+ 9616+ 9617+ 9618+ 9619+ 9620+ 9621+ 9622+ 9623+
9624+ 9625+ 9626+ 9627+ 9628+ 9629+ 9630+ 9631+ 9632+ 9633+ 9634+ 9635+
9636+ 9637+ 9638+ 9639+ 9640+ 9641+ 9642+ 9643+ 9644+ 9645+ 9646+ 9647+
9648+ 9649+ 9650+ 9651+ 9652+ 9653+ 9654+ 9655+ 9656+ 9657+ 9658+ 9659+
9660+ 9661+ 9662+ 9663+ 9664+ 9665+ 9666+ 9667+ 9668+ 9669+ 9670+ 9671+
9672+ 9673+ 9674+ 9675+ 9676+ 9677+ 9678+ 9679+ 9680+ 9681+ 9682+ 9683+
9684+ 9685+ 9686+ 9687+ 9688+ 9689+ 9690+ 9691+ 9692+ 9693+ 9694+ 9695+
9696+ 9697+ 9698+ 9699+ 9700+ 9701+ 9702+ 9703+ 9704+ 9705+ 9706+ 9707+
9708+ 9709+ 9710+ 9711+ 9712+ 9713+ 9714+ 9715+ 9716+ 9717+ 9718+ 9719+
9720+ 9721+ 9722+ 9723+ 9724+ 9725+ 9726+ 9727+ 9728+ 9729+ 9730+ 9731+
9732+ 9733+ 9734+ 9735+ 9736+ 9737+ 9738+ 9739+ 9740+ 9741+ 9742+ 9743+
9744+ 9745+ 9746+ 9747+ 9748+ 9749+ 9750+ 9751+ 9752+ 9753+ 9754+ 9755+
9756+ 9757+ 9758+ 9759+ 9760+ 9761+ 9762+ 9763+ 9764+ 9765+ 9766+ 9767+
9768+ 9769+ 9770+ 9771+ 9772+ 9773+ 9774+ 9775+ 9776+ 9777+ 9778+ 9779+
9780+ 9781+ 9782+ 9783+ 9784+ 9785+ 9786+ 9787+ 9788+ 9789+ 9790+ 9791+
9792+ 9793+ 9794+ 9795+ 9796+ 9797+ 9798+ 9799+ 9800+ 9801+ 9802+ 9803+
9804+ 9805+ 9806+ 9807+ 9808+ 9809+ 9810+ 9811+ 9812+ 9813+ 9814+ 9815+
9816+ 9817+ 9818+ 9819+ 9820+ 9821+ 9822+ 9823+ 9824+ 9825+ 9826+ 9827+
9828+ 9829+ 9830+ 9831+ 9832+ 9833+ 9834+ 9835+ 9836+ 9837+ 9838+ 9839+
9840+ 9841+ 9842+ 9843+ 9844+ 9845+ 9846+ 9847+ 9848+ 9849+ 9850+ 9851+
9852+ 9853+ 9854+ 9855+ 9856+ 9857+ 9858+ 9859+ 9860+ 9861+ 9862+ 9863+
9864+ 9865+ 9866+ 9867+ 9868+ 9869+ 9870+ 9871+ 9872+ 9873+ 9874+ 9875+
9876+ 9877+ 9878+ 9879+ 9880+ 9881+ 9882+ 9883+ 9884+ 9885+ 9886+ 9887+
9888+ 9889+ 9890+ 9891+ 9892+ 9893+ 9894+ 9895+ 9896+ 9897+ 9898+ 9899+
9900+ 9901+ 9902+ 9903+ 9904+ 9905+ 9906+ 9907+ 9908+ 9909+ 9910+ 9911+
9912+ 9913+ 9914+ 9915+ 9916+ 9917+ 9918+ 9919+ 9920+ 9921+ 9922+ 9923+
9924+ 9925+ 9926+ 9927+ 9928+ 9929+ 9930+ 9931+ 9932+ 9933+ 9934+ 9935+
9936+ 9937+ 9938+ 9939+ 9940+ 9941+ 9942+ 9943+ 9944+ 9945+ 9946+ 9947+
9948+ 9949+ 9950+ 9951+ 9952+ 9953+ 9954+ 9955+ 9956+ 9957+ 9958+ 9959+
9960+ 9961+ 9962+ 9963+ 9964+ 9965+ 9966+ 9967+ 9968+ 9969+ 9970+ 9971+
9972+ 9973+ 9974+ 9975+ 9976+ 9977+ 9978+ 9979+ 9980+ 9981+ 9982+ 9983+
9984+ 9985+ 9986+ 9987+ 9988+ 9989+ 9990+ 9991+ 9992+ 9993+ 9994+ 9995+
9996+ 9997+ 9998+ 9999+ 10000;

return sum;

}

"William Ryan" <do********@comcast.nospam.net> wrote in message
news:%2***************@TK2MSFTNGP09.phx.gbl...
I just did it going with 200 Hard coded ints, then 390, then 300. Each time
I got the correct results. Are you positive of the input numbers? I know
that's a stupid question, but I first did each one by loading them into an Int Array and adding them like that. It worked. Then I actually used
straight hard coding, and I used the number 10 each time and added 100000 to
the last one for good measure (just to make sure the value I had was
similarly high). No problems whatsoever. Inasmuch as you can load

those values in an array and iterate it successfully, couldn't you just load the array and use an iterative approach? I understand that's what you are
asking about...why should you have to do this, but it's probably easier

than
verifying the math each time when you know it will work. If I can find
anything, I'll repost.

HTH,

Bill
"Mountain Bikn' Guy" <vc@attbi.com> wrote in message
news:NZUjb.795942$YN5.793228@sccrnsc01...
Take some standard code such as shown below. It simply loops to add up a series of terms and it produces the correct result.

// sum numbers with a loop
public int DoSumLooping(int iterations)
{
int result = 0;
for(int i = 1;i <=iterations;i++)
{
result += i;
}
return result;
}

Now translate this into a specific solution that doesn't use looping (and use the same value for the number of iterations the loop performs). This code returns an incorrect result. The method consists entirely of a very straightforward code statement, but in this case .NET adds the numbers
incorrectly.
public double ComputeSum( )
{
// Brute force sum method
// For iterations == 10000
double sum = 0+ 1+ 2+ 3+ 4+ 5+ 6+ 7+ 8+ 9+ 10+ 11+ 12+ 13+ 14+ 15+ ...
+ 9997+ 9998+ 9999+ 10000;
return sum;
}
The above method returns an incorrect result with any number of terms

above
about 200. It will correctly add 1 + 2 + ... + 200, but it will NOT
correctly add 1 + 2 + ... + 1000.

I have just run across this, and I have not yet researched the
possible reasons for this behavior. It may be a known issue related to either

stack size or the length of a code line, but to my knowledge it hasn't been
discussed in any of the "popular" literature on C# and .NET. I need to

write
code like this, so if anyone has already encountered this issue, please advise me.
Here's another example that also creates problems, but of a somewhat
different nature. Take the following code and translate it into a

specific,
non-looping method and try to execute it using reflection. It fails.

public double LoopToCompute()
{
double sumOfProducts = 0;
double grandTotal = 0;
for (int i = 0; i < maxRows; ++i)
{
for (int j = 0; j < maxCols; ++j)
{
sumOfProducts += coeff[j] * table[i][j];
}
a_point[i] = sumOfProducts;
grandTotal += sumOfProducts;
sumOfProducts = 0;
}
return grandTotal;
}//LoopToCompute

The above code works -- but it's equivalent code with loops unrolled

(shown
below) doesn't work unless the maxRows is set very small. For small

values,
the 2 methods (above and below) produce identical results. There is

nothing
"wrong" with the code in that sense. It's similar to the above situation.
If
the "size" of the code statement or the number of code statements is too large, .NET fails. In this case (using reflection) it doesn't return the incorrect result, as the first example did. In this case, reflection

calls it an invalid program and refuses to run it (but only when the value of maxRows is above about 250). The reason for this is probably
straightforward. However, I have the need to make statements like this for performance reasons so I need a work-around. Any suggestions are
appreciated! All comments are appreciated.

public double DoBruteForceCompute()
{
double bruteForceSum = 0;

point1=coeff1*table[0][0] +coeff2*table[0][1] +coeff3*table[0][2]
+coeff4*table[0][3] +coeff5*table[0][4] +coeff6*table[0][5]
+coeff7*table[0][6] +coeff8*table[0][7] +coeff9*table[0][8]
+coeff10*table[0][9] +coeff11*table[0][10] +coeff12*table[0][11]
+coeff13*table[0][12] +coeff14*table[0][13] +coeff15*table[0][14]
+coeff16*table[0][15] +coeff17*table[0][16] +coeff18*table[0][17]
+coeff19*table[0][18] +coeff20*table[0][19] +coeff21*table[0][20]
+coeff22*table[0][21] +coeff23*table[0][22] +coeff24*table[0][23]
+coeff25*table[0][24] +coeff26*table[0][25] +coeff27*table[0][26]
+coeff28*table[0][27] +coeff29*table[0][28] +coeff30*table[0][29]
+coeff31*table[0][30] +coeff32*table[0][31] +coeff33*table[0][32]
+coeff34*table[0][33] +coeff35*table[0][34] ;

point2=coeff1*table[1][0] +coeff2*table[1][1] +coeff3*table[1][2]
+coeff4*table[1][3] +coeff5*table[1][4] +coeff6*table[1][5]
+coeff7*table[1][6] +coeff8*table[1][7] +coeff9*table[1][8]
+coeff10*table[1][9] +coeff11*table[1][10] +coeff12*table[1][11]
+coeff13*table[1][12] +coeff14*table[1][13] +coeff15*table[1][14]
+coeff16*table[1][15] +coeff17*table[1][16] +coeff18*table[1][17]
+coeff19*table[1][18] +coeff20*table[1][19] +coeff21*table[1][20]
+coeff22*table[1][21] +coeff23*table[1][22] +coeff24*table[1][23]
+coeff25*table[1][24] +coeff26*table[1][25] +coeff27*table[1][26]
+coeff28*table[1][27] +coeff29*table[1][28] +coeff30*table[1][29]
+coeff31*table[1][30] +coeff32*table[1][31] +coeff33*table[1][32]
+coeff34*table[1][33] +coeff35*table[1][34] ;
[...]

point500=coeff1*table[499][0] +coeff2*table[499][1] +coeff3*table[499][2] +coeff4*table[499][3] +coeff5*table[499][4] +coeff6*table[499][5]
+coeff7*table[499][6] +coeff8*table[499][7] +coeff9*table[499][8]
+coeff10*table[499][9] +coeff11*table[499][10] +coeff12*table[499][11]
+coeff13*table[499][12] +coeff14*table[499][13] +coeff15*table[499][14] +coeff16*table[499][15] +coeff17*table[499][16] +coeff18*table[499][17] +coeff19*table[499][18] +coeff20*table[499][19] +coeff21*table[499][20] +coeff22*table[499][21] +coeff23*table[499][22] +coeff24*table[499][23] +coeff25*table[499][24] +coeff26*table[499][25] +coeff27*table[499][26] +coeff28*table[499][27] +coeff29*table[499][28] +coeff30*table[499][29] +coeff31*table[499][30] +coeff32*table[499][31] +coeff33*table[499][32] +coeff34*table[499][33] +coeff35*table[499][34] ;

bruteForceSum =
point1 +
point2 + ... +

point499 +
point500
;

return bruteForceSum;

}//DoBruteForceCompute



Jul 21 '05 #9

P: n/a
Funny. Now, can we get back to the issue? This is fundamentally about
reflection emit and specific, optimized solutions to any problem.
Dave

"Jhon" <Jh**@a.a> wrote in message
news:Iv*********************@phobos.telenet-ops.be...
Hi,

Maybe not the issue, tough it unwinds the loop, the sum of the first n
consecutive numbers:

(n+1)*n
= ---------
2

Greetings
"Mountain Bikn' Guy" <vc@attbi.com> wrote in message
news:NZUjb.795942$YN5.793228@sccrnsc01...
Take some standard code such as shown below. It simply loops to add up a
series of terms and it produces the correct result.

// sum numbers with a loop
public int DoSumLooping(int iterations)
{
int result = 0;
for(int i = 1;i <=iterations;i++)
{
result += i;
}
return result;
}

Now translate this into a specific solution that doesn't use looping (and use the same value for the number of iterations the loop performs). This
code returns an incorrect result. The method consists entirely of a very
straightforward code statement, but in this case .NET adds the numbers
incorrectly.
public double ComputeSum( )
{
// Brute force sum method
// For iterations == 10000
double sum = 0+ 1+ 2+ 3+ 4+ 5+ 6+ 7+ 8+ 9+ 10+ 11+ 12+ 13+ 14+ 15+ ...
+ 9997+ 9998+ 9999+ 10000;
return sum;
}
The above method returns an incorrect result with any number of terms

above
about 200. It will correctly add 1 + 2 + ... + 200, but it will NOT
correctly add 1 + 2 + ... + 1000.

I have just run across this, and I have not yet researched the possible
reasons for this behavior. It may be a known issue related to either stack size or the length of a code line, but to my knowledge it hasn't been
discussed in any of the "popular" literature on C# and .NET. I need to

write
code like this, so if anyone has already encountered this issue, please
advise me.
Here's another example that also creates problems, but of a somewhat
different nature. Take the following code and translate it into a

specific,
non-looping method and try to execute it using reflection. It fails.

public double LoopToCompute()
{
double sumOfProducts = 0;
double grandTotal = 0;
for (int i = 0; i < maxRows; ++i)
{
for (int j = 0; j < maxCols; ++j)
{
sumOfProducts += coeff[j] * table[i][j];
}
a_point[i] = sumOfProducts;
grandTotal += sumOfProducts;
sumOfProducts = 0;
}
return grandTotal;
}//LoopToCompute

The above code works -- but it's equivalent code with loops unrolled

(shown
below) doesn't work unless the maxRows is set very small. For small

values,
the 2 methods (above and below) produce identical results. There is

nothing
"wrong" with the code in that sense. It's similar to the above situation. If
the "size" of the code statement or the number of code statements is too
large, .NET fails. In this case (using reflection) it doesn't return the
incorrect result, as the first example did. In this case, reflection

calls it an invalid program and refuses to run it (but only when the value of
maxRows is above about 250). The reason for this is probably
straightforward. However, I have the need to make statements like this for performance reasons so I need a work-around. Any suggestions are
appreciated! All comments are appreciated.

public double DoBruteForceCompute()
{
double bruteForceSum = 0;

point1=coeff1*table[0][0] +coeff2*table[0][1] +coeff3*table[0][2]
+coeff4*table[0][3] +coeff5*table[0][4] +coeff6*table[0][5]
+coeff7*table[0][6] +coeff8*table[0][7] +coeff9*table[0][8]
+coeff10*table[0][9] +coeff11*table[0][10] +coeff12*table[0][11]
+coeff13*table[0][12] +coeff14*table[0][13] +coeff15*table[0][14]
+coeff16*table[0][15] +coeff17*table[0][16] +coeff18*table[0][17]
+coeff19*table[0][18] +coeff20*table[0][19] +coeff21*table[0][20]
+coeff22*table[0][21] +coeff23*table[0][22] +coeff24*table[0][23]
+coeff25*table[0][24] +coeff26*table[0][25] +coeff27*table[0][26]
+coeff28*table[0][27] +coeff29*table[0][28] +coeff30*table[0][29]
+coeff31*table[0][30] +coeff32*table[0][31] +coeff33*table[0][32]
+coeff34*table[0][33] +coeff35*table[0][34] ;

point2=coeff1*table[1][0] +coeff2*table[1][1] +coeff3*table[1][2]
+coeff4*table[1][3] +coeff5*table[1][4] +coeff6*table[1][5]
+coeff7*table[1][6] +coeff8*table[1][7] +coeff9*table[1][8]
+coeff10*table[1][9] +coeff11*table[1][10] +coeff12*table[1][11]
+coeff13*table[1][12] +coeff14*table[1][13] +coeff15*table[1][14]
+coeff16*table[1][15] +coeff17*table[1][16] +coeff18*table[1][17]
+coeff19*table[1][18] +coeff20*table[1][19] +coeff21*table[1][20]
+coeff22*table[1][21] +coeff23*table[1][22] +coeff24*table[1][23]
+coeff25*table[1][24] +coeff26*table[1][25] +coeff27*table[1][26]
+coeff28*table[1][27] +coeff29*table[1][28] +coeff30*table[1][29]
+coeff31*table[1][30] +coeff32*table[1][31] +coeff33*table[1][32]
+coeff34*table[1][33] +coeff35*table[1][34] ;
[...]

point500=coeff1*table[499][0] +coeff2*table[499][1] +coeff3*table[499][2] +coeff4*table[499][3] +coeff5*table[499][4] +coeff6*table[499][5]
+coeff7*table[499][6] +coeff8*table[499][7] +coeff9*table[499][8]
+coeff10*table[499][9] +coeff11*table[499][10] +coeff12*table[499][11]
+coeff13*table[499][12] +coeff14*table[499][13] +coeff15*table[499][14]
+coeff16*table[499][15] +coeff17*table[499][16] +coeff18*table[499][17]
+coeff19*table[499][18] +coeff20*table[499][19] +coeff21*table[499][20]
+coeff22*table[499][21] +coeff23*table[499][22] +coeff24*table[499][23]
+coeff25*table[499][24] +coeff26*table[499][25] +coeff27*table[499][26]
+coeff28*table[499][27] +coeff29*table[499][28] +coeff30*table[499][29]
+coeff31*table[499][30] +coeff32*table[499][31] +coeff33*table[499][32]
+coeff34*table[499][33] +coeff35*table[499][34] ;

bruteForceSum =
point1 +
point2 + ... +

point499 +
point500
;

return bruteForceSum;

}//DoBruteForceCompute


Jul 21 '05 #10

P: n/a
Wow, that's interesting. And I appreciate you checking the code I pasted. I
get 50005000 in Excel and the same with the loop. When I run the unrolled
code I always get 5050. If you aren't reproducing the problem, and the code
I pasted gave you correct results, then maybe the problem is related to my
machine or my installation of the framework... very strange. (BTW, I'm doing
this on a dual Xeon with 4GB of RAM and VS.NET 2003 on W2K).

Any other comments are appreciated.

"William Ryan" <do********@comcast.nospam.net> wrote in message
news:eO**************@TK2MSFTNGP10.phx.gbl...
Ok, I just ran it and after my IDE finished choking, I'm getting 50005000
whether I loop through it or use your code. That is the same number Excel
is giving me.

Are you getting 50005000 in your computations? From this machine, it looks like it's working correctly.
"Mountain Bikn' Guy" <vc@attbi.com> wrote in message
news:tuVjb.806880$uu5.142280@sccrnsc04...
Yes, I'm positive. I will post the exact code. Here is the test anyone can do:
1. paste this code, compile and run. Check the result.
2. Use Excel and do the same thing and compare the result. In Excel,

simply
enter 1 on row 1 and 2 on row 2, then copy down to 10000 (or whatever size you wish). Then use the sum function to get the sum. You will see that the C# code is vastly in error.

Here's the code (sorry, but it's long):

Jul 21 '05 #11

P: n/a
[Removed microsoft.public.dotnet.csharp.general which isn't a valid
group, at least not on the MS server.]

Mountain Bikn' Guy <vc@attbi.com> wrote:
Take some standard code such as shown below. It simply loops to add up a
series of terms and it produces the correct result.

// sum numbers with a loop
public int DoSumLooping(int iterations)
{
int result = 0;
for(int i = 1;i <=iterations;i++)
{
result += i;
}
return result;
}

Now translate this into a specific solution that doesn't use looping (and
use the same value for the number of iterations the loop performs). This
code returns an incorrect result.


Not for me it doesn't (going up to 10000). Could you produce a
*complete* example somewhere which gives the incorrect result, either
posting it or giving a link to it on the web?

--
Jon Skeet - <sk***@pobox.com>
http://www.pobox.com/~skeet
If replying to the group, please do not mail me too
Jul 21 '05 #12

P: n/a
[Removed microsoft.public.dotnet.csharp.general which isn't a valid
group, at least not on the MS server.]

Mountain Bikn' Guy <vc@attbi.com> wrote:
Yes, I'm positive. I will post the exact code. Here is the test anyone can
do:
1. paste this code, compile and run. Check the result.
Yup: 50005000, which is the correct amount.
2. Use Excel and do the same thing and compare the result. In Excel, simply
enter 1 on row 1 and 2 on row 2, then copy down to 10000 (or whatever size
you wish). Then use the sum function to get the sum. You will see that the
C# code is vastly in error.


Nope - what result do you get from the C#?

--
Jon Skeet - <sk***@pobox.com>
http://www.pobox.com/~skeet
If replying to the group, please do not mail me too
Jul 21 '05 #13

P: n/a

"Mountain Bikn' Guy" <vc@attbi.com> wrote in message
news:VPVjb.807103$uu5.142258@sccrnsc04...
Funny. Now, can we get back to the issue? This is fundamentally about
reflection emit and specific, optimized solutions to any problem.
Yes I could smell that
Funny, optimized solutions to any problem
Dave

"Jhon" <Jh**@a.a> wrote in message
news:Iv*********************@phobos.telenet-ops.be...
Hi,

Maybe not the issue, tough it unwinds the loop, the sum of the first n
consecutive numbers:

(n+1)*n
= ---------
2

Greetings
"Mountain Bikn' Guy" <vc@attbi.com> wrote in message
news:NZUjb.795942$YN5.793228@sccrnsc01...
Take some standard code such as shown below. It simply loops to add up a series of terms and it produces the correct result.

// sum numbers with a loop
public int DoSumLooping(int iterations)
{
int result = 0;
for(int i = 1;i <=iterations;i++)
{
result += i;
}
return result;
}

Now translate this into a specific solution that doesn't use looping (and use the same value for the number of iterations the loop performs). This code returns an incorrect result. The method consists entirely of a very straightforward code statement, but in this case .NET adds the numbers
incorrectly.
public double ComputeSum( )
{
// Brute force sum method
// For iterations == 10000
double sum = 0+ 1+ 2+ 3+ 4+ 5+ 6+ 7+ 8+ 9+ 10+ 11+ 12+ 13+ 14+ 15+
...
+ 9997+ 9998+ 9999+ 10000;
return sum;
}
The above method returns an incorrect result with any number of terms

above
about 200. It will correctly add 1 + 2 + ... + 200, but it will NOT
correctly add 1 + 2 + ... + 1000.

I have just run across this, and I have not yet researched the
possible reasons for this behavior. It may be a known issue related to either

stack size or the length of a code line, but to my knowledge it hasn't been
discussed in any of the "popular" literature on C# and .NET. I need to

write
code like this, so if anyone has already encountered this issue, please advise me.
Here's another example that also creates problems, but of a somewhat
different nature. Take the following code and translate it into a

specific,
non-looping method and try to execute it using reflection. It fails.

public double LoopToCompute()
{
double sumOfProducts = 0;
double grandTotal = 0;
for (int i = 0; i < maxRows; ++i)
{
for (int j = 0; j < maxCols; ++j)
{
sumOfProducts += coeff[j] * table[i][j];
}
a_point[i] = sumOfProducts;
grandTotal += sumOfProducts;
sumOfProducts = 0;
}
return grandTotal;
}//LoopToCompute

The above code works -- but it's equivalent code with loops unrolled

(shown
below) doesn't work unless the maxRows is set very small. For small

values,
the 2 methods (above and below) produce identical results. There is

nothing
"wrong" with the code in that sense. It's similar to the above situation.
If
the "size" of the code statement or the number of code statements is too large, .NET fails. In this case (using reflection) it doesn't return the incorrect result, as the first example did. In this case, reflection

calls it an invalid program and refuses to run it (but only when the value of maxRows is above about 250). The reason for this is probably
straightforward. However, I have the need to make statements like this for performance reasons so I need a work-around. Any suggestions are
appreciated! All comments are appreciated.

public double DoBruteForceCompute()
{
double bruteForceSum = 0;

point1=coeff1*table[0][0] +coeff2*table[0][1] +coeff3*table[0][2]
+coeff4*table[0][3] +coeff5*table[0][4] +coeff6*table[0][5]
+coeff7*table[0][6] +coeff8*table[0][7] +coeff9*table[0][8]
+coeff10*table[0][9] +coeff11*table[0][10] +coeff12*table[0][11]
+coeff13*table[0][12] +coeff14*table[0][13] +coeff15*table[0][14]
+coeff16*table[0][15] +coeff17*table[0][16] +coeff18*table[0][17]
+coeff19*table[0][18] +coeff20*table[0][19] +coeff21*table[0][20]
+coeff22*table[0][21] +coeff23*table[0][22] +coeff24*table[0][23]
+coeff25*table[0][24] +coeff26*table[0][25] +coeff27*table[0][26]
+coeff28*table[0][27] +coeff29*table[0][28] +coeff30*table[0][29]
+coeff31*table[0][30] +coeff32*table[0][31] +coeff33*table[0][32]
+coeff34*table[0][33] +coeff35*table[0][34] ;

point2=coeff1*table[1][0] +coeff2*table[1][1] +coeff3*table[1][2]
+coeff4*table[1][3] +coeff5*table[1][4] +coeff6*table[1][5]
+coeff7*table[1][6] +coeff8*table[1][7] +coeff9*table[1][8]
+coeff10*table[1][9] +coeff11*table[1][10] +coeff12*table[1][11]
+coeff13*table[1][12] +coeff14*table[1][13] +coeff15*table[1][14]
+coeff16*table[1][15] +coeff17*table[1][16] +coeff18*table[1][17]
+coeff19*table[1][18] +coeff20*table[1][19] +coeff21*table[1][20]
+coeff22*table[1][21] +coeff23*table[1][22] +coeff24*table[1][23]
+coeff25*table[1][24] +coeff26*table[1][25] +coeff27*table[1][26]
+coeff28*table[1][27] +coeff29*table[1][28] +coeff30*table[1][29]
+coeff31*table[1][30] +coeff32*table[1][31] +coeff33*table[1][32]
+coeff34*table[1][33] +coeff35*table[1][34] ;
[...]

point500=coeff1*table[499][0] +coeff2*table[499][1] +coeff3*table[499][2] +coeff4*table[499][3] +coeff5*table[499][4] +coeff6*table[499][5]
+coeff7*table[499][6] +coeff8*table[499][7] +coeff9*table[499][8]
+coeff10*table[499][9] +coeff11*table[499][10] +coeff12*table[499][11]
+coeff13*table[499][12] +coeff14*table[499][13] +coeff15*table[499][14] +coeff16*table[499][15] +coeff17*table[499][16] +coeff18*table[499][17] +coeff19*table[499][18] +coeff20*table[499][19] +coeff21*table[499][20] +coeff22*table[499][21] +coeff23*table[499][22] +coeff24*table[499][23] +coeff25*table[499][24] +coeff26*table[499][25] +coeff27*table[499][26] +coeff28*table[499][27] +coeff29*table[499][28] +coeff30*table[499][29] +coeff31*table[499][30] +coeff32*table[499][31] +coeff33*table[499][32] +coeff34*table[499][33] +coeff35*table[499][34] ;

bruteForceSum =
point1 +
point2 + ... +

point499 +
point500
;

return bruteForceSum;

}//DoBruteForceCompute



Jul 21 '05 #14

P: n/a
Jon,
I will work on a complete example. I think I made an assumption about where
the problem was coming from and simplified my posting too much. I'm actually
generating the specific "unrolled" code in code, writing it out, compiling
it, and using reflection to invoke the object. Now I'm guessing the problem
lies somewhere other than C#'s inability to add. I'll have to eat my words
on that one. ;) But I feel better knowing that this isn't a fundamental
problem and that I will probably be able to get my solution working
correctly with a bit more troubleshooting.

I'll try to make a short example showing the error and paste it here.
Dave

"Jon Skeet [C# MVP]" <sk***@pobox.com> wrote in message
news:MP************************@msnews.microsoft.c om...
[Removed microsoft.public.dotnet.csharp.general which isn't a valid
group, at least not on the MS server.]

Mountain Bikn' Guy <vc@attbi.com> wrote:
Take some standard code such as shown below. It simply loops to add up a
series of terms and it produces the correct result.

// sum numbers with a loop
public int DoSumLooping(int iterations)
{
int result = 0;
for(int i = 1;i <=iterations;i++)
{
result += i;
}
return result;
}

Now translate this into a specific solution that doesn't use looping (and use the same value for the number of iterations the loop performs). This
code returns an incorrect result.


Not for me it doesn't (going up to 10000). Could you produce a
*complete* example somewhere which gives the incorrect result, either
posting it or giving a link to it on the web?

--
Jon Skeet - <sk***@pobox.com>
http://www.pobox.com/~skeet
If replying to the group, please do not mail me too

Jul 21 '05 #15

P: n/a
I'm using Win2000Pro, VS2003, 1 gig or Ram (man you are lucky) and only one
processor. I've done it on an older machine as well, and I'm getting the
right results..not really sure what it can be, but definitely interested in
finding out.
"Mountain Bikn' Guy" <vc@attbi.com> wrote in message
news:hUVjb.796541$YN5.793655@sccrnsc01...
Wow, that's interesting. And I appreciate you checking the code I pasted. I get 50005000 in Excel and the same with the loop. When I run the unrolled
code I always get 5050. If you aren't reproducing the problem, and the code I pasted gave you correct results, then maybe the problem is related to my
machine or my installation of the framework... very strange. (BTW, I'm doing this on a dual Xeon with 4GB of RAM and VS.NET 2003 on W2K).

Any other comments are appreciated.

"William Ryan" <do********@comcast.nospam.net> wrote in message
news:eO**************@TK2MSFTNGP10.phx.gbl...
Ok, I just ran it and after my IDE finished choking, I'm getting 50005000
whether I loop through it or use your code. That is the same number Excel is giving me.

Are you getting 50005000 in your computations? From this machine, it

looks
like it's working correctly.
"Mountain Bikn' Guy" <vc@attbi.com> wrote in message
news:tuVjb.806880$uu5.142280@sccrnsc04...
Yes, I'm positive. I will post the exact code. Here is the test anyone

can do:
1. paste this code, compile and run. Check the result.
2. Use Excel and do the same thing and compare the result. In Excel,

simply
enter 1 on row 1 and 2 on row 2, then copy down to 10000 (or whatever size you wish). Then use the sum function to get the sum. You will see that the C# code is vastly in error.

Here's the code (sorry, but it's long):


Jul 21 '05 #16

P: n/a
Mountain Bikn' Guy,

I couldn't reproduce the errors you encountered. I tried both the
1.0 and 1.1 C# compilers, and tried using both ints and doubles as
return values. Could you post a complete program demonstrating the
problem?

TIA,

Chris.
-------------
C.R. Timmons Consulting, Inc.
http://www.crtimmonsinc.com/
Jul 21 '05 #17

P: n/a
I am pasting an example that reproduces the error. I apologize for two
things in advance:
1. the code is a bit long;
2. I hard-coded paths specific to my machine.
This example comes from Programming C# by Jesse Liberty. His code wouldn't
run at all, and in the process of debugging it initially I used the
hard-coded paths and I ended up leaving them in because I got involved in
the current issue. At this point I don't want to change anything and risk
introducing new errors, so I'm posting the code as it is. Please change the
hard coded paths as required by your machine, and I apologize again for
having these hard coded paths in the file.

To set up the solution, first I create and compile a class library
containing the following interface. I set a reference to this in my main
project. I also reference it in the command line args for csc (as seen in
the main code below this).
namespace Programming_CSharp
{
public interface IComputer
{
double ComputeSum( );
}
}

Then I have another console app project containing the following code
(remember to reference the class library containing the above interface). It
should run and I would assume it will produce the incorrect results for
others, as it does for me -- and as shown in my screen shot attached to
another message in this thread.

// Example 18-10 of Programming C# by Liberty: Dynamic invocation with
interfaces
namespace Programming_CSharp
{
using System;
using System.Diagnostics;
using System.IO;
using System.Reflection;
using System.Runtime.InteropServices; // provides RuntimeEnvironment
// used to benchmark the looping approach
public class MyMath
{
// sum numbers with a loop
public int DoSumLooping(int iterations)
{
int result = 0;
for(int i = 1;i <=iterations;i++)
{
result += i;
}
return result;
}
public double CheckMyResults( )
{
// Brute force sum method
// For value = 10000
double sum = 0+ 1+ 2+ 3+ 4+ 5+ 6+ 7+ 8+ 9+ 10+ 11+ 12+ 13+ 14+ 15+ 16+ 17+
18+ 19+ 20+ 21+ 22+ 23+ 24+ 25+ 26+ 27+ 28+ 29+ 30+ 31+ 32+ 33+ 34+ 35+ 36+
37+ 38+ 39+ 40+ 41+ 42+ 43+ 44+ 45+ 46+ 47+ 48+ 49+ 50+ 51+ 52+ 53+ 54+ 55+
56+ 57+ 58+ 59+ 60+ 61+ 62+ 63+ 64+ 65+ 66+ 67+ 68+ 69+ 70+ 71+ 72+ 73+ 74+
75+ 76+ 77+ 78+ 79+ 80+ 81+ 82+ 83+ 84+ 85+ 86+ 87+ 88+ 89+ 90+ 91+ 92+ 93+
94+ 95+ 96+ 97+ 98+ 99+ 100+ 101+ 102+ 103+ 104+ 105+ 106+ 107+ 108+ 109+
110+ 111+ 112+ 113+ 114+ 115+ 116+ 117+ 118+ 119+ 120+ 121+ 122+ 123+ 124+
125+ 126+ 127+ 128+ 129+ 130+ 131+ 132+ 133+ 134+ 135+ 136+ 137+ 138+ 139+
140+ 141+ 142+ 143+ 144+ 145+ 146+ 147+ 148+ 149+ 150+ 151+ 152+ 153+ 154+
155+ 156+ 157+ 158+ 159+ 160+ 161+ 162+ 163+ 164+ 165+ 166+ 167+ 168+ 169+
170+ 171+ 172+ 173+ 174+ 175+ 176+ 177+ 178+ 179+ 180+ 181+ 182+ 183+ 184+
185+ 186+ 187+ 188+ 189+ 190+ 191+ 192+ 193+ 194+ 195+ 196+ 197+ 198+ 199+
200+ 201+ 202+ 203+ 204+ 205+ 206+ 207+ 208+ 209+ 210+ 211+ 212+ 213+ 214+
215+ 216+ 217+ 218+ 219+ 220+ 221+ 222+ 223+ 224+ 225+ 226+ 227+ 228+ 229+
230+ 231+ 232+ 233+ 234+ 235+ 236+ 237+ 238+ 239+ 240+ 241+ 242+ 243+ 244+
245+ 246+ 247+ 248+ 249+ 250+ 251+ 252+ 253+ 254+ 255+ 256+ 257+ 258+ 259+
260+ 261+ 262+ 263+ 264+ 265+ 266+ 267+ 268+ 269+ 270+ 271+ 272+ 273+ 274+
275+ 276+ 277+ 278+ 279+ 280+ 281+ 282+ 283+ 284+ 285+ 286+ 287+ 288+ 289+
290+ 291+ 292+ 293+ 294+ 295+ 296+ 297+ 298+ 299+ 300+ 301+ 302+ 303+ 304+
305+ 306+ 307+ 308+ 309+ 310+ 311+ 312+ 313+ 314+ 315+ 316+ 317+ 318+ 319+
320+ 321+ 322+ 323+ 324+ 325+ 326+ 327+ 328+ 329+ 330+ 331+ 332+ 333+ 334+
335+ 336+ 337+ 338+ 339+ 340+ 341+ 342+ 343+ 344+ 345+ 346+ 347+ 348+ 349+
350+ 351+ 352+ 353+ 354+ 355+ 356+ 357+ 358+ 359+ 360+ 361+ 362+ 363+ 364+
365+ 366+ 367+ 368+ 369+ 370+ 371+ 372+ 373+ 374+ 375+ 376+ 377+ 378+ 379+
380+ 381+ 382+ 383+ 384+ 385+ 386+ 387+ 388+ 389+ 390+ 391+ 392+ 393+ 394+
395+ 396+ 397+ 398+ 399+ 400
+ 401+ 402+ 403+ 404+ 405+ 406+ 407+ 408+ 409+ 410+ 411+ 412+ 413+ 414+ 415+
416+ 417+ 418+ 419+ 420+ 421+ 422+ 423+ 424+ 425+ 426+ 427+ 428+ 429+ 430+
431+ 432+ 433+ 434+ 435+ 436+ 437+ 438+ 439+ 440+ 441+ 442+ 443+ 444+ 445+
446+ 447+ 448+ 449+ 450+ 451+ 452+ 453+ 454+ 455+ 456+ 457+ 458+ 459+ 460+
461+ 462+ 463+ 464+ 465+ 466+ 467+ 468+ 469+ 470+ 471+ 472+ 473+ 474+ 475+
476+ 477+ 478+ 479+ 480+ 481+ 482+ 483+ 484+ 485+ 486+ 487+ 488+ 489+ 490+
491+ 492+ 493+ 494+ 495+ 496+ 497+ 498+ 499+ 500+ 501+ 502+ 503+ 504+ 505+
506+ 507+ 508+ 509+ 510+ 511+ 512+ 513+ 514+ 515+ 516+ 517+ 518+ 519+ 520+
521+ 522+ 523+ 524+ 525+ 526+ 527+ 528+ 529+ 530+ 531+ 532+ 533+ 534+ 535+
536+ 537+ 538+ 539+ 540+ 541+ 542+ 543+ 544+ 545+ 546+ 547+ 548+ 549+ 550+
551+ 552+ 553+ 554+ 555+ 556+ 557+ 558+ 559+ 560+ 561+ 562+ 563+ 564+ 565+
566+ 567+ 568+ 569+ 570+ 571+ 572+ 573+ 574+ 575+ 576+ 577+ 578+ 579+ 580+
581+ 582+ 583+ 584+ 585+ 586+ 587+ 588+ 589+ 590+ 591+ 592+ 593+ 594+ 595+
596+ 597+ 598+ 599+ 600+ 601+ 602+ 603+ 604+ 605+ 606+ 607+ 608+ 609+ 610+
611+ 612+ 613+ 614+ 615+ 616+ 617+ 618+ 619+ 620+ 621+ 622+ 623+ 624+ 625+
626+ 627+ 628+ 629+ 630+ 631+ 632+ 633+ 634+ 635+ 636+ 637+ 638+ 639+ 640+
641+ 642+ 643+ 644+ 645+ 646+ 647+ 648+ 649+ 650+ 651+ 652+ 653+ 654+ 655+
656+ 657+ 658+ 659+ 660+ 661+ 662+ 663+ 664+ 665+ 666+ 667+ 668+ 669+ 670+
671+ 672+ 673+ 674+ 675+ 676+ 677+ 678+ 679+ 680+ 681+ 682+ 683+ 684+ 685+
686+ 687+ 688+ 689+ 690+ 691+ 692+ 693+ 694+ 695+ 696+ 697+ 698+ 699+ 700+
701+ 702+ 703+ 704+ 705+ 706+ 707+ 708+ 709+ 710+ 711+ 712+ 713+ 714+ 715+
716+ 717+ 718+ 719+ 720+ 721+ 722+ 723+ 724+ 725+ 726+ 727+ 728+ 729+ 730+
731+ 732+ 733+ 734+ 735+ 736+ 737+ 738+ 739+ 740+ 741+ 742+ 743+ 744+ 745+
746+ 747+ 748+ 749+ 750+ 751+ 752+ 753+ 754+ 755+ 756+ 757+ 758+ 759+ 760+
761+ 762+ 763+ 764+ 765+ 766+ 767+ 768+ 769+ 770+ 771+ 772+ 773+ 774+ 775+
776+ 777+ 778+ 779+ 780+ 781+
782+ 783+ 784+ 785+ 786+ 787+ 788+ 789+ 790+ 791+ 792+ 793+ 794+ 795+ 796+
797+ 798+ 799+ 800+ 801+ 802+ 803+ 804+ 805+ 806+ 807+ 808+ 809+ 810+ 811+
812+ 813+ 814+ 815+ 816+ 817+ 818+ 819+ 820+ 821+ 822+ 823+ 824+ 825+ 826+
827+ 828+ 829+ 830+ 831+ 832+ 833+ 834+ 835+ 836+ 837+ 838+ 839+ 840+ 841+
842+ 843+ 844+ 845+ 846+ 847+ 848+ 849+ 850+ 851+ 852+ 853+ 854+ 855+ 856+
857+ 858+ 859+ 860+ 861+ 862+ 863+ 864+ 865+ 866+ 867+ 868+ 869+ 870+ 871+
872+ 873+ 874+ 875+ 876+ 877+ 878+ 879+ 880+ 881+ 882+ 883+ 884+ 885+ 886+
887+ 888+ 889+ 890+ 891+ 892+ 893+ 894+ 895+ 896+ 897+ 898+ 899+ 900+ 901+
902+ 903+ 904+ 905+ 906+ 907+ 908+ 909+ 910+ 911+ 912+ 913+ 914+ 915+ 916+
917+ 918+ 919+ 920+ 921+ 922+ 923+ 924+ 925+ 926+ 927+ 928+ 929+ 930+ 931+
932+ 933+ 934+ 935+ 936+ 937+ 938+ 939+ 940+ 941+ 942+ 943+ 944+ 945+ 946+
947+ 948+ 949+ 950+ 951+ 952+ 953+ 954+ 955+ 956+ 957+ 958+ 959+ 960+ 961+
962+ 963+ 964+ 965+ 966+ 967+ 968+ 969+ 970+ 971+ 972+ 973+ 974+ 975+ 976+
977+ 978+ 979+ 980+ 981+ 982+ 983+ 984+ 985+ 986+ 987+ 988+ 989+ 990+ 991+
992+ 993+ 994+ 995+ 996+ 997+ 998+ 999+ 1000+ 1001+ 1002+ 1003+ 1004+ 1005+
1006+ 1007+ 1008+ 1009+ 1010+ 1011+ 1012+ 1013+ 1014+ 1015+ 1016+ 1017+
1018+ 1019+ 1020+ 1021+ 1022+ 1023+ 1024+ 1025+ 1026+ 1027+ 1028+ 1029+
1030+ 1031+ 1032+ 1033+ 1034+ 1035+ 1036+ 1037+ 1038+ 1039+ 1040+ 1041+
1042+ 1043+ 1044+ 1045+ 1046+ 1047+ 1048+ 1049+ 1050+ 1051+ 1052+ 1053+
1054+ 1055+ 1056+ 1057+ 1058+ 1059+ 1060+ 1061+ 1062+ 1063+ 1064+ 1065+
1066+ 1067+ 1068+ 1069+ 1070+ 1071+ 1072+ 1073+ 1074+ 1075+ 1076+ 1077+
1078+ 1079+ 1080+ 1081+ 1082+ 1083+ 1084+ 1085+ 1086+ 1087+ 1088+ 1089+
1090+ 1091+ 1092+ 1093+ 1094+ 1095+ 1096+ 1097+ 1098+ 1099+ 1100+ 1101+
1102+ 1103+ 1104+ 1105+ 1106+ 1107+ 1108+ 1109+ 1110+ 1111+ 1112+ 1113+
1114+ 1115+ 1116+ 1117+ 1118+ 1119+ 1120+ 1121+ 1122+ 1123+ 1124+ 1125+
1126+ 1127+ 1128+ 1129+ 1130+ 1131+ 1132+ 1133+ 1134+ 1135+ 1136+
1137+ 1138+ 1139+ 1140+ 1141+ 1142+ 1143+ 1144+ 1145+ 1146+ 1147+ 1148+
1149+ 1150+ 1151+ 1152+ 1153+ 1154+ 1155+ 1156+ 1157+ 1158+ 1159+ 1160+
1161+ 1162+ 1163+ 1164+ 1165+ 1166+ 1167+ 1168+ 1169+ 1170+ 1171+ 1172+
1173+ 1174+ 1175+ 1176+ 1177+ 1178+ 1179+ 1180+ 1181+ 1182+ 1183+ 1184+
1185+ 1186+ 1187+ 1188+ 1189+ 1190+ 1191+ 1192+ 1193+ 1194+ 1195+ 1196+
1197+ 1198+ 1199+ 1200+ 1201+ 1202+ 1203+ 1204+ 1205+ 1206+ 1207+ 1208+
1209+ 1210+ 1211+ 1212+ 1213+ 1214+ 1215+ 1216+ 1217+ 1218+ 1219+ 1220+
1221+ 1222+ 1223+ 1224+ 1225+ 1226+ 1227+ 1228+ 1229+ 1230+ 1231+ 1232+
1233+ 1234+ 1235+ 1236+ 1237+ 1238+ 1239+ 1240+ 1241+ 1242+ 1243+ 1244+
1245+ 1246+ 1247+ 1248+ 1249+ 1250+ 1251+ 1252+ 1253+ 1254+ 1255+ 1256+
1257+ 1258+ 1259+ 1260+ 1261+ 1262+ 1263+ 1264+ 1265+ 1266+ 1267+ 1268+
1269+ 1270+ 1271+ 1272+ 1273+ 1274+ 1275+ 1276+ 1277+ 1278+ 1279+ 1280+
1281+ 1282+ 1283+ 1284+ 1285+ 1286+ 1287+ 1288+ 1289+ 1290+ 1291+ 1292+
1293+ 1294+ 1295+ 1296+ 1297+ 1298+ 1299+ 1300+ 1301+ 1302+ 1303+ 1304+
1305+ 1306+ 1307+ 1308+ 1309+ 1310+ 1311+ 1312+ 1313+ 1314+ 1315+ 1316+
1317+ 1318+ 1319+ 1320+ 1321+ 1322+ 1323+ 1324+ 1325+ 1326+ 1327+ 1328+
1329+ 1330+ 1331+ 1332+ 1333+ 1334+ 1335+ 1336+ 1337+ 1338+ 1339+ 1340+
1341+ 1342+ 1343+ 1344+ 1345+ 1346+ 1347+ 1348+ 1349+ 1350+ 1351+ 1352+
1353+ 1354+ 1355+ 1356+ 1357+ 1358+ 1359+ 1360+ 1361+ 1362+ 1363+ 1364+
1365+ 1366+ 1367+ 1368+ 1369+ 1370+ 1371+ 1372+ 1373+ 1374+ 1375+ 1376+
1377+ 1378+ 1379+ 1380+ 1381+ 1382+ 1383+ 1384+ 1385+ 1386+ 1387+ 1388+
1389+ 1390+ 1391+ 1392+ 1393+ 1394+ 1395+ 1396+ 1397+ 1398+ 1399+ 1400+
1401+ 1402+ 1403+ 1404+ 1405+ 1406+ 1407+ 1408+ 1409+ 1410+ 1411+ 1412+
1413+ 1414+ 1415+ 1416+ 1417+ 1418+ 1419+ 1420+ 1421+ 1422+ 1423+ 1424+
1425+ 1426+ 1427+ 1428+ 1429+ 1430+ 1431+ 1432+ 1433+ 1434+ 1435+ 1436+
1437+ 1438+ 1439+ 1440+ 1441+ 1442+ 1443+ 1444+ 1445+ 1446+ 1447+ 1448+
1449+ 1450+ 1451+ 1452+ 1453+ 1454+ 1455+
1456+ 1457+ 1458+ 1459+ 1460+ 1461+ 1462+ 1463+ 1464+ 1465+ 1466+ 1467+
1468+ 1469+ 1470+ 1471+ 1472+ 1473+ 1474+ 1475+ 1476+ 1477+ 1478+ 1479+
1480+ 1481+ 1482+ 1483+ 1484+ 1485+ 1486+ 1487+ 1488+ 1489+ 1490+ 1491+
1492+ 1493+ 1494+ 1495+ 1496+ 1497+ 1498+ 1499+ 1500+ 1501+ 1502+ 1503+
1504+ 1505+ 1506+ 1507+ 1508+ 1509+ 1510+ 1511+ 1512+ 1513+ 1514+ 1515+
1516+ 1517+ 1518+ 1519+ 1520+ 1521+ 1522+ 1523+ 1524+ 1525+ 1526+ 1527+
1528+ 1529+ 1530+ 1531+ 1532+ 1533+ 1534+ 1535+ 1536+ 1537+ 1538+ 1539+
1540+ 1541+ 1542+ 1543+ 1544+ 1545+ 1546+ 1547+ 1548+ 1549+ 1550+ 1551+
1552+ 1553+ 1554+ 1555+ 1556+ 1557+ 1558+ 1559+ 1560+ 1561+ 1562+ 1563+
1564+ 1565+ 1566+ 1567+ 1568+ 1569+ 1570+ 1571+ 1572+ 1573+ 1574+ 1575+
1576+ 1577+ 1578+ 1579+ 1580+ 1581+ 1582+ 1583+ 1584+ 1585+ 1586+ 1587+
1588+ 1589+ 1590+ 1591+ 1592+ 1593+ 1594+ 1595+ 1596+ 1597+ 1598+ 1599+
1600+ 1601+ 1602+ 1603+ 1604+ 1605+ 1606+ 1607+ 1608+ 1609+ 1610+ 1611+
1612+ 1613+ 1614+ 1615+ 1616+ 1617+ 1618+ 1619+ 1620+ 1621+ 1622+ 1623+
1624+ 1625+ 1626+ 1627+ 1628+ 1629+ 1630+ 1631+ 1632+ 1633+ 1634+ 1635+
1636+ 1637+ 1638+ 1639+ 1640+ 1641+ 1642+ 1643+ 1644+ 1645+ 1646+ 1647+
1648+ 1649+ 1650+ 1651+ 1652+ 1653+ 1654+ 1655+ 1656+ 1657+ 1658+ 1659+
1660+ 1661+ 1662+ 1663+ 1664+ 1665+ 1666+ 1667+ 1668+ 1669+ 1670+ 1671+
1672+ 1673+ 1674+ 1675+ 1676+ 1677+ 1678+ 1679+ 1680+ 1681+ 1682+ 1683+
1684+ 1685+ 1686+ 1687+ 1688+ 1689+ 1690+ 1691+ 1692+ 1693+ 1694+ 1695+
1696+ 1697+ 1698+ 1699+ 1700+ 1701+ 1702+ 1703+ 1704+ 1705+ 1706+ 1707+
1708+ 1709+ 1710+ 1711+ 1712+ 1713+ 1714+ 1715+ 1716+ 1717+ 1718+ 1719+
1720+ 1721+ 1722+ 1723+ 1724+ 1725+ 1726+ 1727+ 1728+ 1729+ 1730+ 1731+
1732+ 1733+ 1734+ 1735+ 1736+ 1737+ 1738+ 1739+ 1740+ 1741+ 1742+ 1743+
1744+ 1745+ 1746+ 1747+ 1748+ 1749+ 1750+ 1751+ 1752+ 1753+ 1754+ 1755+
1756+ 1757+ 1758+ 1759+ 1760+ 1761+ 1762+ 1763+ 1764+ 1765+ 1766+ 1767+
1768+ 1769+ 1770+ 1771+ 1772+ 1773+ 1774+
1775+ 1776+ 1777+ 1778+ 1779+ 1780+ 1781+ 1782+ 1783+ 1784+ 1785+ 1786+
1787+ 1788+ 1789+ 1790+ 1791+ 1792+ 1793+ 1794+ 1795+ 1796+ 1797+ 1798+
1799+ 1800+ 1801+ 1802+ 1803+ 1804+ 1805+ 1806+ 1807+ 1808+ 1809+ 1810+
1811+ 1812+ 1813+ 1814+ 1815+ 1816+ 1817+ 1818+ 1819+ 1820+ 1821+ 1822+
1823+ 1824+ 1825+ 1826+ 1827+ 1828+ 1829+ 1830+ 1831+ 1832+ 1833+ 1834+
1835+ 1836+ 1837+ 1838+ 1839+ 1840+ 1841+ 1842+ 1843+ 1844+ 1845+ 1846+
1847+ 1848+ 1849+ 1850+ 1851+ 1852+ 1853+ 1854+ 1855+ 1856+ 1857+ 1858+
1859+ 1860+ 1861+ 1862+ 1863+ 1864+ 1865+ 1866+ 1867+ 1868+ 1869+ 1870+
1871+ 1872+ 1873+ 1874+ 1875+ 1876+ 1877+ 1878+ 1879+ 1880+ 1881+ 1882+
1883+ 1884+ 1885+ 1886+ 1887+ 1888+ 1889+ 1890+ 1891+ 1892+ 1893+ 1894+
1895+ 1896+ 1897+ 1898+ 1899+ 1900+ 1901+ 1902+ 1903+ 1904+ 1905+ 1906+
1907+ 1908+ 1909+ 1910+ 1911+ 1912+ 1913+ 1914+ 1915+ 1916+ 1917+ 1918+
1919+ 1920+ 1921+ 1922+ 1923+ 1924+ 1925+ 1926+ 1927+ 1928+ 1929+ 1930+
1931+ 1932+ 1933+ 1934+ 1935+ 1936+ 1937+ 1938+ 1939+ 1940+ 1941+ 1942+
1943+ 1944+ 1945+ 1946+ 1947+ 1948+ 1949+ 1950+ 1951+ 1952+ 1953+ 1954+
1955+ 1956+ 1957+ 1958+ 1959+ 1960+ 1961+ 1962+ 1963+ 1964+ 1965+ 1966+
1967+ 1968+ 1969+ 1970+ 1971+ 1972+ 1973+ 1974+ 1975+ 1976+ 1977+ 1978+
1979+ 1980+ 1981+ 1982+ 1983+ 1984+ 1985+ 1986+ 1987+ 1988+ 1989+ 1990+
1991+ 1992+ 1993+ 1994+ 1995+ 1996+ 1997+ 1998+ 1999+ 2000+ 2001+ 2002+
2003+ 2004+ 2005+ 2006+ 2007+ 2008+ 2009+ 2010+ 2011+ 2012+ 2013+ 2014+
2015+ 2016+ 2017+ 2018+ 2019+ 2020+ 2021+ 2022+ 2023+ 2024+ 2025+ 2026+
2027+ 2028+ 2029+ 2030+ 2031+ 2032+ 2033+ 2034+ 2035+ 2036+ 2037+ 2038+
2039+ 2040+ 2041+ 2042+ 2043+ 2044+ 2045+ 2046+ 2047+ 2048+ 2049+ 2050+
2051+ 2052+ 2053+ 2054+ 2055+ 2056+ 2057+ 2058+ 2059+ 2060+ 2061+ 2062+
2063+ 2064+ 2065+ 2066+ 2067+ 2068+ 2069+ 2070+ 2071+ 2072+ 2073+ 2074+
2075+ 2076+ 2077+ 2078+ 2079+ 2080+ 2081+ 2082+ 2083+ 2084+ 2085+ 2086+
2087+ 2088+ 2089+ 2090+ 2091+ 2092+ 2093+
2094+ 2095+ 2096+ 2097+ 2098+ 2099+ 2100+ 2101+ 2102+ 2103+ 2104+ 2105+
2106+ 2107+ 2108+ 2109+ 2110+ 2111+ 2112+ 2113+ 2114+ 2115+ 2116+ 2117+
2118+ 2119+ 2120+ 2121+ 2122+ 2123+ 2124+ 2125+ 2126+ 2127+ 2128+ 2129+
2130+ 2131+ 2132+ 2133+ 2134+ 2135+ 2136+ 2137+ 2138+ 2139+ 2140+ 2141+
2142+ 2143+ 2144+ 2145+ 2146+ 2147+ 2148+ 2149+ 2150+ 2151+ 2152+ 2153+
2154+ 2155+ 2156+ 2157+ 2158+ 2159+ 2160+ 2161+ 2162+ 2163+ 2164+ 2165+
2166+ 2167+ 2168+ 2169+ 2170+ 2171+ 2172+ 2173+ 2174+ 2175+ 2176+ 2177+
2178+ 2179+ 2180+ 2181+ 2182+ 2183+ 2184+ 2185+ 2186+ 2187+ 2188+ 2189+
2190+ 2191+ 2192+ 2193+ 2194+ 2195+ 2196+ 2197+ 2198+ 2199+ 2200+ 2201+
2202+ 2203+ 2204+ 2205+ 2206+ 2207+ 2208+ 2209+ 2210+ 2211+ 2212+ 2213+
2214+ 2215+ 2216+ 2217+ 2218+ 2219+ 2220+ 2221+ 2222+ 2223+ 2224+ 2225+
2226+ 2227+ 2228+ 2229+ 2230+ 2231+ 2232+ 2233+ 2234+ 2235+ 2236+ 2237+
2238+ 2239+ 2240+ 2241+ 2242+ 2243+ 2244+ 2245+ 2246+ 2247+ 2248+ 2249+
2250+ 2251+ 2252+ 2253+ 2254+ 2255+ 2256+ 2257+ 2258+ 2259+ 2260+ 2261+
2262+ 2263+ 2264+ 2265+ 2266+ 2267+ 2268+ 2269+ 2270+ 2271+ 2272+ 2273+
2274+ 2275+ 2276+ 2277+ 2278+ 2279+ 2280+ 2281+ 2282+ 2283+ 2284+ 2285+
2286+ 2287+ 2288+ 2289+ 2290+ 2291+ 2292+ 2293+ 2294+ 2295+ 2296+ 2297+
2298+ 2299+ 2300+ 2301+ 2302+ 2303+ 2304+ 2305+ 2306+ 2307+ 2308+ 2309+
2310+ 2311+ 2312+ 2313+ 2314+ 2315+ 2316+ 2317+ 2318+ 2319+ 2320+ 2321+
2322+ 2323+ 2324+ 2325+ 2326+ 2327+ 2328+ 2329+ 2330+ 2331+ 2332+ 2333+
2334+ 2335+ 2336+ 2337+ 2338+ 2339+ 2340+ 2341+ 2342+ 2343+ 2344+ 2345+
2346+ 2347+ 2348+ 2349+ 2350+ 2351+ 2352+ 2353+ 2354+ 2355+ 2356+ 2357+
2358+ 2359+ 2360+ 2361+ 2362+ 2363+ 2364+ 2365+ 2366+ 2367+ 2368+ 2369+
2370+ 2371+ 2372+ 2373+ 2374+ 2375+ 2376+ 2377+ 2378+ 2379+ 2380+ 2381+
2382+ 2383+ 2384+ 2385+ 2386+ 2387+ 2388+ 2389+ 2390+ 2391+ 2392+ 2393+
2394+ 2395+ 2396+ 2397+ 2398+ 2399+ 2400+ 2401+ 2402+ 2403+ 2404+ 2405+
2406+ 2407+ 2408+ 2409+ 2410+ 2411+ 2412+
2413+ 2414+ 2415+ 2416+ 2417+ 2418+ 2419+ 2420+ 2421+ 2422+ 2423+ 2424+
2425+ 2426+ 2427+ 2428+ 2429+ 2430+ 2431+ 2432+ 2433+ 2434+ 2435+ 2436+
2437+ 2438+ 2439+ 2440+ 2441+ 2442+ 2443+ 2444+ 2445+ 2446+ 2447+ 2448+
2449+ 2450+ 2451+ 2452+ 2453+ 2454+ 2455+ 2456+ 2457+ 2458+ 2459+ 2460+
2461+ 2462+ 2463+ 2464+ 2465+ 2466+ 2467+ 2468+ 2469+ 2470+ 2471+ 2472+
2473+ 2474+ 2475+ 2476+ 2477+ 2478+ 2479+ 2480+ 2481+ 2482+ 2483+ 2484+
2485+ 2486+ 2487+ 2488+ 2489+ 2490+ 2491+ 2492+ 2493+ 2494+ 2495+ 2496+
2497+ 2498+ 2499+ 2500+ 2501+ 2502+ 2503+ 2504+ 2505+ 2506+ 2507+ 2508+
2509+ 2510+ 2511+ 2512+ 2513+ 2514+ 2515+ 2516+ 2517+ 2518+ 2519+ 2520+
2521+ 2522+ 2523+ 2524+ 2525+ 2526+ 2527+ 2528+ 2529+ 2530+ 2531+ 2532+
2533+ 2534+ 2535+ 2536+ 2537+ 2538+ 2539+ 2540+ 2541+ 2542+ 2543+ 2544+
2545+ 2546+ 2547+ 2548+ 2549+ 2550+ 2551+ 2552+ 2553+ 2554+ 2555+ 2556+
2557+ 2558+ 2559+ 2560+ 2561+ 2562+ 2563+ 2564+ 2565+ 2566+ 2567+ 2568+
2569+ 2570+ 2571+ 2572+ 2573+ 2574+ 2575+ 2576+ 2577+ 2578+ 2579+ 2580+
2581+ 2582+ 2583+ 2584+ 2585+ 2586+ 2587+ 2588+ 2589+ 2590+ 2591+ 2592+
2593+ 2594+ 2595+ 2596+ 2597+ 2598+ 2599+ 2600+ 2601+ 2602+ 2603+ 2604+
2605+ 2606+ 2607+ 2608+ 2609+ 2610+ 2611+ 2612+ 2613+ 2614+ 2615+ 2616+
2617+ 2618+ 2619+ 2620+ 2621+ 2622+ 2623+ 2624+ 2625+ 2626+ 2627+ 2628+
2629+ 2630+ 2631+ 2632+ 2633+ 2634+ 2635+ 2636+ 2637+ 2638+ 2639+ 2640+
2641+ 2642+ 2643+ 2644+ 2645+ 2646+ 2647+ 2648+ 2649+ 2650+ 2651+ 2652+
2653+ 2654+ 2655+ 2656+ 2657+ 2658+ 2659+ 2660+ 2661+ 2662+ 2663+ 2664+
2665+ 2666+ 2667+ 2668+ 2669+ 2670+ 2671+ 2672+ 2673+ 2674+ 2675+ 2676+
2677+ 2678+ 2679+ 2680+ 2681+ 2682+ 2683+ 2684+ 2685+ 2686+ 2687+ 2688+
2689+ 2690+ 2691+ 2692+ 2693+ 2694+ 2695+ 2696+ 2697+ 2698+ 2699+ 2700+
2701+ 2702+ 2703+ 2704+ 2705+ 2706+ 2707+ 2708+ 2709+ 2710+ 2711+ 2712+
2713+ 2714+ 2715+ 2716+ 2717+ 2718+ 2719+ 2720+ 2721+ 2722+ 2723+ 2724+
2725+ 2726+ 2727+ 2728+ 2729+ 2730+ 2731+
2732+ 2733+ 2734+ 2735+ 2736+ 2737+ 2738+ 2739+ 2740+ 2741+ 2742+ 2743+
2744+ 2745+ 2746+ 2747+ 2748+ 2749+ 2750+ 2751+ 2752+ 2753+ 2754+ 2755+
2756+ 2757+ 2758+ 2759+ 2760+ 2761+ 2762+ 2763+ 2764+ 2765+ 2766+ 2767+
2768+ 2769+ 2770+ 2771+ 2772+ 2773+ 2774+ 2775+ 2776+ 2777+ 2778+ 2779+
2780+ 2781+ 2782+ 2783+ 2784+ 2785+ 2786+ 2787+ 2788+ 2789+ 2790+ 2791+
2792+ 2793+ 2794+ 2795+ 2796+ 2797+ 2798+ 2799+ 2800+ 2801+ 2802+ 2803+
2804+ 2805+ 2806+ 2807+ 2808+ 2809+ 2810+ 2811+ 2812+ 2813+ 2814+ 2815+
2816+ 2817+ 2818+ 2819+ 2820+ 2821+ 2822+ 2823+ 2824+ 2825+ 2826+ 2827+
2828+ 2829+ 2830+ 2831+ 2832+ 2833+ 2834+ 2835+ 2836+ 2837+ 2838+ 2839+
2840+ 2841+ 2842+ 2843+ 2844+ 2845+ 2846+ 2847+ 2848+ 2849+ 2850+ 2851+
2852+ 2853+ 2854+ 2855+ 2856+ 2857+ 2858+ 2859+ 2860+ 2861+ 2862+ 2863+
2864+ 2865+ 2866+ 2867+ 2868+ 2869+ 2870+ 2871+ 2872+ 2873+ 2874+ 2875+
2876+ 2877+ 2878+ 2879+ 2880+ 2881+ 2882+ 2883+ 2884+ 2885+ 2886+ 2887+
2888+ 2889+ 2890+ 2891+ 2892+ 2893+ 2894+ 2895+ 2896+ 2897+ 2898+ 2899+
2900+ 2901+ 2902+ 2903+ 2904+ 2905+ 2906+ 2907+ 2908+ 2909+ 2910+ 2911+
2912+ 2913+ 2914+ 2915+ 2916+ 2917+ 2918+ 2919+ 2920+ 2921+ 2922+ 2923+
2924+ 2925+ 2926+ 2927+ 2928+ 2929+ 2930+ 2931+ 2932+ 2933+ 2934+ 2935+
2936+ 2937+ 2938+ 2939+ 2940+ 2941+ 2942+ 2943+ 2944+ 2945+ 2946+ 2947+
2948+ 2949+ 2950+ 2951+ 2952+ 2953+ 2954+ 2955+ 2956+ 2957+ 2958+ 2959+
2960+ 2961+ 2962+ 2963+ 2964+ 2965+ 2966+ 2967+ 2968+ 2969+ 2970+ 2971+
2972+ 2973+ 2974+ 2975+ 2976+ 2977+ 2978+ 2979+ 2980+ 2981+ 2982+ 2983+
2984+ 2985+ 2986+ 2987+ 2988+ 2989+ 2990+ 2991+ 2992+ 2993+ 2994+ 2995+
2996+ 2997+ 2998+ 2999+ 3000+ 3001+ 3002+ 3003+ 3004+ 3005+ 3006+ 3007+
3008+ 3009+ 3010+ 3011+ 3012+ 3013+ 3014+ 3015+ 3016+ 3017+ 3018+ 3019+
3020+ 3021+ 3022+ 3023+ 3024+ 3025+ 3026+ 3027+ 3028+ 3029+ 3030+ 3031+
3032+ 3033+ 3034+ 3035+ 3036+ 3037+ 3038+ 3039+ 3040+ 3041+ 3042+ 3043+
3044+ 3045+ 3046+ 3047+ 3048+ 3049+ 3050+
3051+ 3052+ 3053+ 3054+ 3055+ 3056+ 3057+ 3058+ 3059+ 3060+ 3061+ 3062+
3063+ 3064+ 3065+ 3066+ 3067+ 3068+ 3069+ 3070+ 3071+ 3072+ 3073+ 3074+
3075+ 3076+ 3077+ 3078+ 3079+ 3080+ 3081+ 3082+ 3083+ 3084+ 3085+ 3086+
3087+ 3088+ 3089+ 3090+ 3091+ 3092+ 3093+ 3094+ 3095+ 3096+ 3097+ 3098+
3099+ 3100+ 3101+ 3102+ 3103+ 3104+ 3105+ 3106+ 3107+ 3108+ 3109+ 3110+
3111+ 3112+ 3113+ 3114+ 3115+ 3116+ 3117+ 3118+ 3119+ 3120+ 3121+ 3122+
3123+ 3124+ 3125+ 3126+ 3127+ 3128+ 3129+ 3130+ 3131+ 3132+ 3133+ 3134+
3135+ 3136+ 3137+ 3138+ 3139+ 3140+ 3141+ 3142+ 3143+ 3144+ 3145+ 3146+
3147+ 3148+ 3149+ 3150+ 3151+ 3152+ 3153+ 3154+ 3155+ 3156+ 3157+ 3158+
3159+ 3160+ 3161+ 3162+ 3163+ 3164+ 3165+ 3166+ 3167+ 3168+ 3169+ 3170+
3171+ 3172+ 3173+ 3174+ 3175+ 3176+ 3177+ 3178+ 3179+ 3180+ 3181+ 3182+
3183+ 3184+ 3185+ 3186+ 3187+ 3188+ 3189+ 3190+ 3191+ 3192+ 3193+ 3194+
3195+ 3196+ 3197+ 3198+ 3199+ 3200+ 3201+ 3202+ 3203+ 3204+ 3205+ 3206+
3207+ 3208+ 3209+ 3210+ 3211+ 3212+ 3213+ 3214+ 3215+ 3216+ 3217+ 3218+
3219+ 3220+ 3221+ 3222+ 3223+ 3224+ 3225+ 3226+ 3227+ 3228+ 3229+ 3230+
3231+ 3232+ 3233+ 3234+ 3235+ 3236+ 3237+ 3238+ 3239+ 3240+ 3241+ 3242+
3243+ 3244+ 3245+ 3246+ 3247+ 3248+ 3249+ 3250+ 3251+ 3252+ 3253+ 3254+
3255+ 3256+ 3257+ 3258+ 3259+ 3260+ 3261+ 3262+ 3263+ 3264+ 3265+ 3266+
3267+ 3268+ 3269+ 3270+ 3271+ 3272+ 3273+ 3274+ 3275+ 3276+ 3277+ 3278+
3279+ 3280+ 3281+ 3282+ 3283+ 3284+ 3285+ 3286+ 3287+ 3288+ 3289+ 3290+
3291+ 3292+ 3293+ 3294+ 3295+ 3296+ 3297+ 3298+ 3299+ 3300+ 3301+ 3302+
3303+ 3304+ 3305+ 3306+ 3307+ 3308+ 3309+ 3310+ 3311+ 3312+ 3313+ 3314+
3315+ 3316+ 3317+ 3318+ 3319+ 3320+ 3321+ 3322+ 3323+ 3324+ 3325+ 3326+
3327+ 3328+ 3329+ 3330+ 3331+ 3332+ 3333+ 3334+ 3335+ 3336+ 3337+ 3338+
3339+ 3340+ 3341+ 3342+ 3343+ 3344+ 3345+ 3346+ 3347+ 3348+ 3349+ 3350+
3351+ 3352+ 3353+ 3354+ 3355+ 3356+ 3357+ 3358+ 3359+ 3360+ 3361+ 3362+
3363+ 3364+ 3365+ 3366+ 3367+ 3368+ 3369+
3370+ 3371+ 3372+ 3373+ 3374+ 3375+ 3376+ 3377+ 3378+ 3379+ 3380+ 3381+
3382+ 3383+ 3384+ 3385+ 3386+ 3387+ 3388+ 3389+ 3390+ 3391+ 3392+ 3393+
3394+ 3395+ 3396+ 3397+ 3398+ 3399+ 3400+ 3401+ 3402+ 3403+ 3404+ 3405+
3406+ 3407+ 3408+ 3409+ 3410+ 3411+ 3412+ 3413+ 3414+ 3415+ 3416+ 3417+
3418+ 3419+ 3420+ 3421+ 3422+ 3423+ 3424+ 3425+ 3426+ 3427+ 3428+ 3429+
3430+ 3431+ 3432+ 3433+ 3434+ 3435+ 3436+ 3437+ 3438+ 3439+ 3440+ 3441+
3442+ 3443+ 3444+ 3445+ 3446+ 3447+ 3448+ 3449+ 3450+ 3451+ 3452+ 3453+
3454+ 3455+ 3456+ 3457+ 3458+ 3459+ 3460+ 3461+ 3462+ 3463+ 3464+ 3465+
3466+ 3467+ 3468+ 3469+ 3470+ 3471+ 3472+ 3473+ 3474+ 3475+ 3476+ 3477+
3478+ 3479+ 3480+ 3481+ 3482+ 3483+ 3484+ 3485+ 3486+ 3487+ 3488+ 3489+
3490+ 3491+ 3492+ 3493+ 3494+ 3495+ 3496+ 3497+ 3498+ 3499+ 3500+ 3501+
3502+ 3503+ 3504+ 3505+ 3506+ 3507+ 3508+ 3509+ 3510+ 3511+ 3512+ 3513+
3514+ 3515+ 3516+ 3517+ 3518+ 3519+ 3520+ 3521+ 3522+ 3523+ 3524+ 3525+
3526+ 3527+ 3528+ 3529+ 3530+ 3531+ 3532+ 3533+ 3534+ 3535+ 3536+ 3537+
3538+ 3539+ 3540+ 3541+ 3542+ 3543+ 3544+ 3545+ 3546+ 3547+ 3548+ 3549+
3550+ 3551+ 3552+ 3553+ 3554+ 3555+ 3556+ 3557+ 3558+ 3559+ 3560+ 3561+
3562+ 3563+ 3564+ 3565+ 3566+ 3567+ 3568+ 3569+ 3570+ 3571+ 3572+ 3573+
3574+ 3575+ 3576+ 3577+ 3578+ 3579+ 3580+ 3581+ 3582+ 3583+ 3584+ 3585+
3586+ 3587+ 3588+ 3589+ 3590+ 3591+ 3592+ 3593+ 3594+ 3595+ 3596+ 3597+
3598+ 3599+ 3600+ 3601+ 3602+ 3603+ 3604+ 3605+ 3606+ 3607+ 3608+ 3609+
3610+ 3611+ 3612+ 3613+ 3614+ 3615+ 3616+ 3617+ 3618+ 3619+ 3620+ 3621+
3622+ 3623+ 3624+ 3625+ 3626+ 3627+ 3628+ 3629+ 3630+ 3631+ 3632+ 3633+
3634+ 3635+ 3636+ 3637+ 3638+ 3639+ 3640+ 3641+ 3642+ 3643+ 3644+ 3645+
3646+ 3647+ 3648+ 3649+ 3650+ 3651+ 3652+ 3653+ 3654+ 3655+ 3656+ 3657+
3658+ 3659+ 3660+ 3661+ 3662+ 3663+ 3664+ 3665+ 3666+ 3667+ 3668+ 3669+
3670+ 3671+ 3672+ 3673+ 3674+ 3675+ 3676+ 3677+ 3678+ 3679+ 3680+ 3681+
3682+ 3683+ 3684+ 3685+ 3686+ 3687+ 3688+
3689+ 3690+ 3691+ 3692+ 3693+ 3694+ 3695+ 3696+ 3697+ 3698+ 3699+ 3700+
3701+ 3702+ 3703+ 3704+ 3705+ 3706+ 3707+ 3708+ 3709+ 3710+ 3711+ 3712+
3713+ 3714+ 3715+ 3716+ 3717+ 3718+ 3719+ 3720+ 3721+ 3722+ 3723+ 3724+
3725+ 3726+ 3727+ 3728+ 3729+ 3730+ 3731+ 3732+ 3733+ 3734+ 3735+ 3736+
3737+ 3738+ 3739+ 3740+ 3741+ 3742+ 3743+ 3744+ 3745+ 3746+ 3747+ 3748+
3749+ 3750+ 3751+ 3752+ 3753+ 3754+ 3755+ 3756+ 3757+ 3758+ 3759+ 3760+
3761+ 3762+ 3763+ 3764+ 3765+ 3766+ 3767+ 3768+ 3769+ 3770+ 3771+ 3772+
3773+ 3774+ 3775+ 3776+ 3777+ 3778+ 3779+ 3780+ 3781+ 3782+ 3783+ 3784+
3785+ 3786+ 3787+ 3788+ 3789+ 3790+ 3791+ 3792+ 3793+ 3794+ 3795+ 3796+
3797+ 3798+ 3799+ 3800+ 3801+ 3802+ 3803+ 3804+ 3805+ 3806+ 3807+ 3808+
3809+ 3810+ 3811+ 3812+ 3813+ 3814+ 3815+ 3816+ 3817+ 3818+ 3819+ 3820+
3821+ 3822+ 3823+ 3824+ 3825+ 3826+ 3827+ 3828+ 3829+ 3830+ 3831+ 3832+
3833+ 3834+ 3835+ 3836+ 3837+ 3838+ 3839+ 3840+ 3841+ 3842+ 3843+ 3844+
3845+ 3846+ 3847+ 3848+ 3849+ 3850+ 3851+ 3852+ 3853+ 3854+ 3855+ 3856+
3857+ 3858+ 3859+ 3860+ 3861+ 3862+ 3863+ 3864+ 3865+ 3866+ 3867+ 3868+
3869+ 3870+ 3871+ 3872+ 3873+ 3874+ 3875+ 3876+ 3877+ 3878+ 3879+ 3880+
3881+ 3882+ 3883+ 3884+ 3885+ 3886+ 3887+ 3888+ 3889+ 3890+ 3891+ 3892+
3893+ 3894+ 3895+ 3896+ 3897+ 3898+ 3899+ 3900+ 3901+ 3902+ 3903+ 3904+
3905+ 3906+ 3907+ 3908+ 3909+ 3910+ 3911+ 3912+ 3913+ 3914+ 3915+ 3916+
3917+ 3918+ 3919+ 3920+ 3921+ 3922+ 3923+ 3924+ 3925+ 3926+ 3927+ 3928+
3929+ 3930+ 3931+ 3932+ 3933+ 3934+ 3935+ 3936+ 3937+ 3938+ 3939+ 3940+
3941+ 3942+ 3943+ 3944+ 3945+ 3946+ 3947+ 3948+ 3949+ 3950+ 3951+ 3952+
3953+ 3954+ 3955+ 3956+ 3957+ 3958+ 3959+ 3960+ 3961+ 3962+ 3963+ 3964+
3965+ 3966+ 3967+ 3968+ 3969+ 3970+ 3971+ 3972+ 3973+ 3974+ 3975+ 3976+
3977+ 3978+ 3979+ 3980+ 3981+ 3982+ 3983+ 3984+ 3985+ 3986+ 3987+ 3988+
3989+ 3990+ 3991+ 3992+ 3993+ 3994+ 3995+ 3996+ 3997+ 3998+ 3999+ 4000+
4001+ 4002+ 4003+ 4004+ 4005+ 4006+ 4007+
4008+ 4009+ 4010+ 4011+ 4012+ 4013+ 4014+ 4015+ 4016+ 4017+ 4018+ 4019+
4020+ 4021+ 4022+ 4023+ 4024+ 4025+ 4026+ 4027+ 4028+ 4029+ 4030+ 4031+
4032+ 4033+ 4034+ 4035+ 4036+ 4037+ 4038+ 4039+ 4040+ 4041+ 4042+ 4043+
4044+ 4045+ 4046+ 4047+ 4048+ 4049+ 4050+ 4051+ 4052+ 4053+ 4054+ 4055+
4056+ 4057+ 4058+ 4059+ 4060+ 4061+ 4062+ 4063+ 4064+ 4065+ 4066+ 4067+
4068+ 4069+ 4070+ 4071+ 4072+ 4073+ 4074+ 4075+ 4076+ 4077+ 4078+ 4079+
4080+ 4081+ 4082+ 4083+ 4084+ 4085+ 4086+ 4087+ 4088+ 4089+ 4090+ 4091+
4092+ 4093+ 4094+ 4095+ 4096+ 4097+ 4098+ 4099+ 4100+ 4101+ 4102+ 4103+
4104+ 4105+ 4106+ 4107+ 4108+ 4109+ 4110+ 4111+ 4112+ 4113+ 4114+ 4115+
4116+ 4117+ 4118+ 4119+ 4120+ 4121+ 4122+ 4123+ 4124+ 4125+ 4126+ 4127+
4128+ 4129+ 4130+ 4131+ 4132+ 4133+ 4134+ 4135+ 4136+ 4137+ 4138+ 4139+
4140+ 4141+ 4142+ 4143+ 4144+ 4145+ 4146+ 4147+ 4148+ 4149+ 4150+ 4151+
4152+ 4153+ 4154+ 4155+ 4156+ 4157+ 4158+ 4159+ 4160+ 4161+ 4162+ 4163+
4164+ 4165+ 4166+ 4167+ 4168+ 4169+ 4170+ 4171+ 4172+ 4173+ 4174+ 4175+
4176+ 4177+ 4178+ 4179+ 4180+ 4181+ 4182+ 4183+ 4184+ 4185+ 4186+ 4187+
4188+ 4189+ 4190+ 4191+ 4192+ 4193+ 4194+ 4195+ 4196+ 4197+ 4198+ 4199+
4200+ 4201+ 4202+ 4203+ 4204+ 4205+ 4206+ 4207+ 4208+ 4209+ 4210+ 4211+
4212+ 4213+ 4214+ 4215+ 4216+ 4217+ 4218+ 4219+ 4220+ 4221+ 4222+ 4223+
4224+ 4225+ 4226+ 4227+ 4228+ 4229+ 4230+ 4231+ 4232+ 4233+ 4234+ 4235+
4236+ 4237+ 4238+ 4239+ 4240+ 4241+ 4242+ 4243+ 4244+ 4245+ 4246+ 4247+
4248+ 4249+ 4250+ 4251+ 4252+ 4253+ 4254+ 4255+ 4256+ 4257+ 4258+ 4259+
4260+ 4261+ 4262+ 4263+ 4264+ 4265+ 4266+ 4267+ 4268+ 4269+ 4270+ 4271+
4272+ 4273+ 4274+ 4275+ 4276+ 4277+ 4278+ 4279+ 4280+ 4281+ 4282+ 4283+
4284+ 4285+ 4286+ 4287+ 4288+ 4289+ 4290+ 4291+ 4292+ 4293+ 4294+ 4295+
4296+ 4297+ 4298+ 4299+ 4300+ 4301+ 4302+ 4303+ 4304+ 4305+ 4306+ 4307+
4308+ 4309+ 4310+ 4311+ 4312+ 4313+ 4314+ 4315+ 4316+ 4317+ 4318+ 4319+
4320+ 4321+ 4322+ 4323+ 4324+ 4325+ 4326+
4327+ 4328+ 4329+ 4330+ 4331+ 4332+ 4333+ 4334+ 4335+ 4336+ 4337+ 4338+
4339+ 4340+ 4341+ 4342+ 4343+ 4344+ 4345+ 4346+ 4347+ 4348+ 4349+ 4350+
4351+ 4352+ 4353+ 4354+ 4355+ 4356+ 4357+ 4358+ 4359+ 4360+ 4361+ 4362+
4363+ 4364+ 4365+ 4366+ 4367+ 4368+ 4369+ 4370+ 4371+ 4372+ 4373+ 4374+
4375+ 4376+ 4377+ 4378+ 4379+ 4380+ 4381+ 4382+ 4383+ 4384+ 4385+ 4386+
4387+ 4388+ 4389+ 4390+ 4391+ 4392+ 4393+ 4394+ 4395+ 4396+ 4397+ 4398+
4399+ 4400+ 4401+ 4402+ 4403+ 4404+ 4405+ 4406+ 4407+ 4408+ 4409+ 4410+
4411+ 4412+ 4413+ 4414+ 4415+ 4416+ 4417+ 4418+ 4419+ 4420+ 4421+ 4422+
4423+ 4424+ 4425+ 4426+ 4427+ 4428+ 4429+ 4430+ 4431+ 4432+ 4433+ 4434+
4435+ 4436+ 4437+ 4438+ 4439+ 4440+ 4441+ 4442+ 4443+ 4444+ 4445+ 4446+
4447+ 4448+ 4449+ 4450+ 4451+ 4452+ 4453+ 4454+ 4455+ 4456+ 4457+ 4458+
4459+ 4460+ 4461+ 4462+ 4463+ 4464+ 4465+ 4466+ 4467+ 4468+ 4469+ 4470+
4471+ 4472+ 4473+ 4474+ 4475+ 4476+ 4477+ 4478+ 4479+ 4480+ 4481+ 4482+
4483+ 4484+ 4485+ 4486+ 4487+ 4488+ 4489+ 4490+ 4491+ 4492+ 4493+ 4494+
4495+ 4496+ 4497+ 4498+ 4499+ 4500+ 4501+ 4502+ 4503+ 4504+ 4505+ 4506+
4507+ 4508+ 4509+ 4510+ 4511+ 4512+ 4513+ 4514+ 4515+ 4516+ 4517+ 4518+
4519+ 4520+ 4521+ 4522+ 4523+ 4524+ 4525+ 4526+ 4527+ 4528+ 4529+ 4530+
4531+ 4532+ 4533+ 4534+ 4535+ 4536+ 4537+ 4538+ 4539+ 4540+ 4541+ 4542+
4543+ 4544+ 4545+ 4546+ 4547+ 4548+ 4549+ 4550+ 4551+ 4552+ 4553+ 4554+
4555+ 4556+ 4557+ 4558+ 4559+ 4560+ 4561+ 4562+ 4563+ 4564+ 4565+ 4566+
4567+ 4568+ 4569+ 4570+ 4571+ 4572+ 4573+ 4574+ 4575+ 4576+ 4577+ 4578+
4579+ 4580+ 4581+ 4582+ 4583+ 4584+ 4585+ 4586+ 4587+ 4588+ 4589+ 4590+
4591+ 4592+ 4593+ 4594+ 4595+ 4596+ 4597+ 4598+ 4599+ 4600+ 4601+ 4602+
4603+ 4604+ 4605+ 4606+ 4607+ 4608+ 4609+ 4610+ 4611+ 4612+ 4613+ 4614+
4615+ 4616+ 4617+ 4618+ 4619+ 4620+ 4621+ 4622+ 4623+ 4624+ 4625+ 4626+
4627+ 4628+ 4629+ 4630+ 4631+ 4632+ 4633+ 4634+ 4635+ 4636+ 4637+ 4638+
4639+ 4640+ 4641+ 4642+ 4643+ 4644+ 4645+
4646+ 4647+ 4648+ 4649+ 4650+ 4651+ 4652+ 4653+ 4654+ 4655+ 4656+ 4657+
4658+ 4659+ 4660+ 4661+ 4662+ 4663+ 4664+ 4665+ 4666+ 4667+ 4668+ 4669+
4670+ 4671+ 4672+ 4673+ 4674+ 4675+ 4676+ 4677+ 4678+ 4679+ 4680+ 4681+
4682+ 4683+ 4684+ 4685+ 4686+ 4687+ 4688+ 4689+ 4690+ 4691+ 4692+ 4693+
4694+ 4695+ 4696+ 4697+ 4698+ 4699+ 4700+ 4701+ 4702+ 4703+ 4704+ 4705+
4706+ 4707+ 4708+ 4709+ 4710+ 4711+ 4712+ 4713+ 4714+ 4715+ 4716+ 4717+
4718+ 4719+ 4720+ 4721+ 4722+ 4723+ 4724+ 4725+ 4726+ 4727+ 4728+ 4729+
4730+ 4731+ 4732+ 4733+ 4734+ 4735+ 4736+ 4737+ 4738+ 4739+ 4740+ 4741+
4742+ 4743+ 4744+ 4745+ 4746+ 4747+ 4748+ 4749+ 4750+ 4751+ 4752+ 4753+
4754+ 4755+ 4756+ 4757+ 4758+ 4759+ 4760+ 4761+ 4762+ 4763+ 4764+ 4765+
4766+ 4767+ 4768+ 4769+ 4770+ 4771+ 4772+ 4773+ 4774+ 4775+ 4776+ 4777+
4778+ 4779+ 4780+ 4781+ 4782+ 4783+ 4784+ 4785+ 4786+ 4787+ 4788+ 4789+
4790+ 4791+ 4792+ 4793+ 4794+ 4795+ 4796+ 4797+ 4798+ 4799+ 4800+ 4801+
4802+ 4803+ 4804+ 4805+ 4806+ 4807+ 4808+ 4809+ 4810+ 4811+ 4812+ 4813+
4814+ 4815+ 4816+ 4817+ 4818+ 4819+ 4820+ 4821+ 4822+ 4823+ 4824+ 4825+
4826+ 4827+ 4828+ 4829+ 4830+ 4831+ 4832+ 4833+ 4834+ 4835+ 4836+ 4837+
4838+ 4839+ 4840+ 4841+ 4842+ 4843+ 4844+ 4845+ 4846+ 4847+ 4848+ 4849+
4850+ 4851+ 4852+ 4853+ 4854+ 4855+ 4856+ 4857+ 4858+ 4859+ 4860+ 4861+
4862+ 4863+ 4864+ 4865+ 4866+ 4867+ 4868+ 4869+ 4870+ 4871+ 4872+ 4873+
4874+ 4875+ 4876+ 4877+ 4878+ 4879+ 4880+ 4881+ 4882+ 4883+ 4884+ 4885+
4886+ 4887+ 4888+ 4889+ 4890+ 4891+ 4892+ 4893+ 4894+ 4895+ 4896+ 4897+
4898+ 4899+ 4900+ 4901+ 4902+ 4903+ 4904+ 4905+ 4906+ 4907+ 4908+ 4909+
4910+ 4911+ 4912+ 4913+ 4914+ 4915+ 4916+ 4917+ 4918+ 4919+ 4920+ 4921+
4922+ 4923+ 4924+ 4925+ 4926+ 4927+ 4928+ 4929+ 4930+ 4931+ 4932+ 4933+
4934+ 4935+ 4936+ 4937+ 4938+ 4939+ 4940+ 4941+ 4942+ 4943+ 4944+ 4945+
4946+ 4947+ 4948+ 4949+ 4950+ 4951+ 4952+ 4953+ 4954+ 4955+ 4956+ 4957+
4958+ 4959+ 4960+ 4961+ 4962+ 4963+ 4964+
4965+ 4966+ 4967+ 4968+ 4969+ 4970+ 4971+ 4972+ 4973+ 4974+ 4975+ 4976+
4977+ 4978+ 4979+ 4980+ 4981+ 4982+ 4983+ 4984+ 4985+ 4986+ 4987+ 4988+
4989+ 4990+ 4991+ 4992+ 4993+ 4994+ 4995+ 4996+ 4997+ 4998+ 4999+ 5000+
5001+ 5002+ 5003+ 5004+ 5005+ 5006+ 5007+ 5008+ 5009+ 5010+ 5011+ 5012+
5013+ 5014+ 5015+ 5016+ 5017+ 5018+ 5019+ 5020+ 5021+ 5022+ 5023+ 5024+
5025+ 5026+ 5027+ 5028+ 5029+ 5030+ 5031+ 5032+ 5033+ 5034+ 5035+ 5036+
5037+ 5038+ 5039+ 5040+ 5041+ 5042+ 5043+ 5044+ 5045+ 5046+ 5047+ 5048+
5049+ 5050+ 5051+ 5052+ 5053+ 5054+ 5055+ 5056+ 5057+ 5058+ 5059+ 5060+
5061+ 5062+ 5063+ 5064+ 5065+ 5066+ 5067+ 5068+ 5069+ 5070+ 5071+ 5072+
5073+ 5074+ 5075+ 5076+ 5077+ 5078+ 5079+ 5080+ 5081+ 5082+ 5083+ 5084+
5085+ 5086+ 5087+ 5088+ 5089+ 5090+ 5091+ 5092+ 5093+ 5094+ 5095+ 5096+
5097+ 5098+ 5099+ 5100+ 5101+ 5102+ 5103+ 5104+ 5105+ 5106+ 5107+ 5108+
5109+ 5110+ 5111+ 5112+ 5113+ 5114+ 5115+ 5116+ 5117+ 5118+ 5119+ 5120+
5121+ 5122+ 5123+ 5124+ 5125+ 5126+ 5127+ 5128+ 5129+ 5130+ 5131+ 5132+
5133+ 5134+ 5135+ 5136+ 5137+ 5138+ 5139+ 5140+ 5141+ 5142+ 5143+ 5144+
5145+ 5146+ 5147+ 5148+ 5149+ 5150+ 5151+ 5152+ 5153+ 5154+ 5155+ 5156+
5157+ 5158+ 5159+ 5160+ 5161+ 5162+ 5163+ 5164+ 5165+ 5166+ 5167+ 5168+
5169+ 5170+ 5171+ 5172+ 5173+ 5174+ 5175+ 5176+ 5177+ 5178+ 5179+ 5180+
5181+ 5182+ 5183+ 5184+ 5185+ 5186+ 5187+ 5188+ 5189+ 5190+ 5191+ 5192+
5193+ 5194+ 5195+ 5196+ 5197+ 5198+ 5199+ 5200+ 5201+ 5202+ 5203+ 5204+
5205+ 5206+ 5207+ 5208+ 5209+ 5210+ 5211+ 5212+ 5213+ 5214+ 5215+ 5216+
5217+ 5218+ 5219+ 5220+ 5221+ 5222+ 5223+ 5224+ 5225+ 5226+ 5227+ 5228+
5229+ 5230+ 5231+ 5232+ 5233+ 5234+ 5235+ 5236+ 5237+ 5238+ 5239+ 5240+
5241+ 5242+ 5243+ 5244+ 5245+ 5246+ 5247+ 5248+ 5249+ 5250+ 5251+ 5252+
5253+ 5254+ 5255+ 5256+ 5257+ 5258+ 5259+ 5260+ 5261+ 5262+ 5263+ 5264+
5265+ 5266+ 5267+ 5268+ 5269+ 5270+ 5271+ 5272+ 5273+ 5274+ 5275+ 5276+
5277+ 5278+ 5279+ 5280+ 5281+ 5282+ 5283+
5284+ 5285+ 5286+ 5287+ 5288+ 5289+ 5290+ 5291+ 5292+ 5293+ 5294+ 5295+
5296+ 5297+ 5298+ 5299+ 5300+ 5301+ 5302+ 5303+ 5304+ 5305+ 5306+ 5307+
5308+ 5309+ 5310+ 5311+ 5312+ 5313+ 5314+ 5315+ 5316+ 5317+ 5318+ 5319+
5320+ 5321+ 5322+ 5323+ 5324+ 5325+ 5326+ 5327+ 5328+ 5329+ 5330+ 5331+
5332+ 5333+ 5334+ 5335+ 5336+ 5337+ 5338+ 5339+ 5340+ 5341+ 5342+ 5343+
5344+ 5345+ 5346+ 5347+ 5348+ 5349+ 5350+ 5351+ 5352+ 5353+ 5354+ 5355+
5356+ 5357+ 5358+ 5359+ 5360+ 5361+ 5362+ 5363+ 5364+ 5365+ 5366+ 5367+
5368+ 5369+ 5370+ 5371+ 5372+ 5373+ 5374+ 5375+ 5376+ 5377+ 5378+ 5379+
5380+ 5381+ 5382+ 5383+ 5384+ 5385+ 5386+ 5387+ 5388+ 5389+ 5390+ 5391+
5392+ 5393+ 5394+ 5395+ 5396+ 5397+ 5398+ 5399+ 5400+ 5401+ 5402+ 5403+
5404+ 5405+ 5406+ 5407+ 5408+ 5409+ 5410+ 5411+ 5412+ 5413+ 5414+ 5415+
5416+ 5417+ 5418+ 5419+ 5420+ 5421+ 5422+ 5423+ 5424+ 5425+ 5426+ 5427+
5428+ 5429+ 5430+ 5431+ 5432+ 5433+ 5434+ 5435+ 5436+ 5437+ 5438+ 5439+
5440+ 5441+ 5442+ 5443+ 5444+ 5445+ 5446+ 5447+ 5448+ 5449+ 5450+ 5451+
5452+ 5453+ 5454+ 5455+ 5456+ 5457+ 5458+ 5459+ 5460+ 5461+ 5462+ 5463+
5464+ 5465+ 5466+ 5467+ 5468+ 5469+ 5470+ 5471+ 5472+ 5473+ 5474+ 5475+
5476+ 5477+ 5478+ 5479+ 5480+ 5481+ 5482+ 5483+ 5484+ 5485+ 5486+ 5487+
5488+ 5489+ 5490+ 5491+ 5492+ 5493+ 5494+ 5495+ 5496+ 5497+ 5498+ 5499+
5500+ 5501+ 5502+ 5503+ 5504+ 5505+ 5506+ 5507+ 5508+ 5509+ 5510+ 5511+
5512+ 5513+ 5514+ 5515+ 5516+ 5517+ 5518+ 5519+ 5520+ 5521+ 5522+ 5523+
5524+ 5525+ 5526+ 5527+ 5528+ 5529+ 5530+ 5531+ 5532+ 5533+ 5534+ 5535+
5536+ 5537+ 5538+ 5539+ 5540+ 5541+ 5542+ 5543+ 5544+ 5545+ 5546+ 5547+
5548+ 5549+ 5550+ 5551+ 5552+ 5553+ 5554+ 5555+ 5556+ 5557+ 5558+ 5559+
5560+ 5561+ 5562+ 5563+ 5564+ 5565+ 5566+ 5567+ 5568+ 5569+ 5570+ 5571+
5572+ 5573+ 5574+ 5575+ 5576+ 5577+ 5578+ 5579+ 5580+ 5581+ 5582+ 5583+
5584+ 5585+ 5586+ 5587+ 5588+ 5589+ 5590+ 5591+ 5592+ 5593+ 5594+ 5595+
5596+ 5597+ 5598+ 5599+ 5600+ 5601+ 5602+
5603+ 5604+ 5605+ 5606+ 5607+ 5608+ 5609+ 5610+ 5611+ 5612+ 5613+ 5614+
5615+ 5616+ 5617+ 5618+ 5619+ 5620+ 5621+ 5622+ 5623+ 5624+ 5625+ 5626+
5627+ 5628+ 5629+ 5630+ 5631+ 5632+ 5633+ 5634+ 5635+ 5636+ 5637+ 5638+
5639+ 5640+ 5641+ 5642+ 5643+ 5644+ 5645+ 5646+ 5647+ 5648+ 5649+ 5650+
5651+ 5652+ 5653+ 5654+ 5655+ 5656+ 5657+ 5658+ 5659+ 5660+ 5661+ 5662+
5663+ 5664+ 5665+ 5666+ 5667+ 5668+ 5669+ 5670+ 5671+ 5672+ 5673+ 5674+
5675+ 5676+ 5677+ 5678+ 5679+ 5680+ 5681+ 5682+ 5683+ 5684+ 5685+ 5686+
5687+ 5688+ 5689+ 5690+ 5691+ 5692+ 5693+ 5694+ 5695+ 5696+ 5697+ 5698+
5699+ 5700+ 5701+ 5702+ 5703+ 5704+ 5705+ 5706+ 5707+ 5708+ 5709+ 5710+
5711+ 5712+ 5713+ 5714+ 5715+ 5716+ 5717+ 5718+ 5719+ 5720+ 5721+ 5722+
5723+ 5724+ 5725+ 5726+ 5727+ 5728+ 5729+ 5730+ 5731+ 5732+ 5733+ 5734+
5735+ 5736+ 5737+ 5738+ 5739+ 5740+ 5741+ 5742+ 5743+ 5744+ 5745+ 5746+
5747+ 5748+ 5749+ 5750+ 5751+ 5752+ 5753+ 5754+ 5755+ 5756+ 5757+ 5758+
5759+ 5760+ 5761+ 5762+ 5763+ 5764+ 5765+ 5766+ 5767+ 5768+ 5769+ 5770+
5771+ 5772+ 5773+ 5774+ 5775+ 5776+ 5777+ 5778+ 5779+ 5780+ 5781+ 5782+
5783+ 5784+ 5785+ 5786+ 5787+ 5788+ 5789+ 5790+ 5791+ 5792+ 5793+ 5794+
5795+ 5796+ 5797+ 5798+ 5799+ 5800+ 5801+ 5802+ 5803+ 5804+ 5805+ 5806+
5807+ 5808+ 5809+ 5810+ 5811+ 5812+ 5813+ 5814+ 5815+ 5816+ 5817+ 5818+
5819+ 5820+ 5821+ 5822+ 5823+ 5824+ 5825+ 5826+ 5827+ 5828+ 5829+ 5830+
5831+ 5832+ 5833+ 5834+ 5835+ 5836+ 5837+ 5838+ 5839+ 5840+ 5841+ 5842+
5843+ 5844+ 5845+ 5846+ 5847+ 5848+ 5849+ 5850+ 5851+ 5852+ 5853+ 5854+
5855+ 5856+ 5857+ 5858+ 5859+ 5860+ 5861+ 5862+ 5863+ 5864+ 5865+ 5866+
5867+ 5868+ 5869+ 5870+ 5871+ 5872+ 5873+ 5874+ 5875+ 5876+ 5877+ 5878+
5879+ 5880+ 5881+ 5882+ 5883+ 5884+ 5885+ 5886+ 5887+ 5888+ 5889+ 5890+
5891+ 5892+ 5893+ 5894+ 5895+ 5896+ 5897+ 5898+ 5899+ 5900+ 5901+ 5902+
5903+ 5904+ 5905+ 5906+ 5907+ 5908+ 5909+ 5910+ 5911+ 5912+ 5913+ 5914+
5915+ 5916+ 5917+ 5918+ 5919+ 5920+ 5921+
5922+ 5923+ 5924+ 5925+ 5926+ 5927+ 5928+ 5929+ 5930+ 5931+ 5932+ 5933+
5934+ 5935+ 5936+ 5937+ 5938+ 5939+ 5940+ 5941+ 5942+ 5943+ 5944+ 5945+
5946+ 5947+ 5948+ 5949+ 5950+ 5951+ 5952+ 5953+ 5954+ 5955+ 5956+ 5957+
5958+ 5959+ 5960+ 5961+ 5962+ 5963+ 5964+ 5965+ 5966+ 5967+ 5968+ 5969+
5970+ 5971+ 5972+ 5973+ 5974+ 5975+ 5976+ 5977+ 5978+ 5979+ 5980+ 5981+
5982+ 5983+ 5984+ 5985+ 5986+ 5987+ 5988+ 5989+ 5990+ 5991+ 5992+ 5993+
5994+ 5995+ 5996+ 5997+ 5998+ 5999+ 6000+ 6001+ 6002+ 6003+ 6004+ 6005+
6006+ 6007+ 6008+ 6009+ 6010+ 6011+ 6012+ 6013+ 6014+ 6015+ 6016+ 6017+
6018+ 6019+ 6020+ 6021+ 6022+ 6023+ 6024+ 6025+ 6026+ 6027+ 6028+ 6029+
6030+ 6031+ 6032+ 6033+ 6034+ 6035+ 6036+ 6037+ 6038+ 6039+ 6040+ 6041+
6042+ 6043+ 6044+ 6045+ 6046+ 6047+ 6048+ 6049+ 6050+ 6051+ 6052+ 6053+
6054+ 6055+ 6056+ 6057+ 6058+ 6059+ 6060+ 6061+ 6062+ 6063+ 6064+ 6065+
6066+ 6067+ 6068+ 6069+ 6070+ 6071+ 6072+ 6073+ 6074+ 6075+ 6076+ 6077+
6078+ 6079+ 6080+ 6081+ 6082+ 6083+ 6084+ 6085+ 6086+ 6087+ 6088+ 6089+
6090+ 6091+ 6092+ 6093+ 6094+ 6095+ 6096+ 6097+ 6098+ 6099+ 6100+ 6101+
6102+ 6103+ 6104+ 6105+ 6106+ 6107+ 6108+ 6109+ 6110+ 6111+ 6112+ 6113+
6114+ 6115+ 6116+ 6117+ 6118+ 6119+ 6120+ 6121+ 6122+ 6123+ 6124+ 6125+
6126+ 6127+ 6128+ 6129+ 6130+ 6131+ 6132+ 6133+ 6134+ 6135+ 6136+ 6137+
6138+ 6139+ 6140+ 6141+ 6142+ 6143+ 6144+ 6145+ 6146+ 6147+ 6148+ 6149+
6150+ 6151+ 6152+ 6153+ 6154+ 6155+ 6156+ 6157+ 6158+ 6159+ 6160+ 6161+
6162+ 6163+ 6164+ 6165+ 6166+ 6167+ 6168+ 6169+ 6170+ 6171+ 6172+ 6173+
6174+ 6175+ 6176+ 6177+ 6178+ 6179+ 6180+ 6181+ 6182+ 6183+ 6184+ 6185+
6186+ 6187+ 6188+ 6189+ 6190+ 6191+ 6192+ 6193+ 6194+ 6195+ 6196+ 6197+
6198+ 6199+ 6200+ 6201+ 6202+ 6203+ 6204+ 6205+ 6206+ 6207+ 6208+ 6209+
6210+ 6211+ 6212+ 6213+ 6214+ 6215+ 6216+ 6217+ 6218+ 6219+ 6220+ 6221+
6222+ 6223+ 6224+ 6225+ 6226+ 6227+ 6228+ 6229+ 6230+ 6231+ 6232+ 6233+
6234+ 6235+ 6236+ 6237+ 6238+ 6239+ 6240+
6241+ 6242+ 6243+ 6244+ 6245+ 6246+ 6247+ 6248+ 6249+ 6250+ 6251+ 6252+
6253+ 6254+ 6255+ 6256+ 6257+ 6258+ 6259+ 6260+ 6261+ 6262+ 6263+ 6264+
6265+ 6266+ 6267+ 6268+ 6269+ 6270+ 6271+ 6272+ 6273+ 6274+ 6275+ 6276+
6277+ 6278+ 6279+ 6280+ 6281+ 6282+ 6283+ 6284+ 6285+ 6286+ 6287+ 6288+
6289+ 6290+ 6291+ 6292+ 6293+ 6294+ 6295+ 6296+ 6297+ 6298+ 6299+ 6300+
6301+ 6302+ 6303+ 6304+ 6305+ 6306+ 6307+ 6308+ 6309+ 6310+ 6311+ 6312+
6313+ 6314+ 6315+ 6316+ 6317+ 6318+ 6319+ 6320+ 6321+ 6322+ 6323+ 6324+
6325+ 6326+ 6327+ 6328+ 6329+ 6330+ 6331+ 6332+ 6333+ 6334+ 6335+ 6336+
6337+ 6338+ 6339+ 6340+ 6341+ 6342+ 6343+ 6344+ 6345+ 6346+ 6347+ 6348+
6349+ 6350+ 6351+ 6352+ 6353+ 6354+ 6355+ 6356+ 6357+ 6358+ 6359+ 6360+
6361+ 6362+ 6363+ 6364+ 6365+ 6366+ 6367+ 6368+ 6369+ 6370+ 6371+ 6372+
6373+ 6374+ 6375+ 6376+ 6377+ 6378+ 6379+ 6380+ 6381+ 6382+ 6383+ 6384+
6385+ 6386+ 6387+ 6388+ 6389+ 6390+ 6391+ 6392+ 6393+ 6394+ 6395+ 6396+
6397+ 6398+ 6399+ 6400+ 6401+ 6402+ 6403+ 6404+ 6405+ 6406+ 6407+ 6408+
6409+ 6410+ 6411+ 6412+ 6413+ 6414+ 6415+ 6416+ 6417+ 6418+ 6419+ 6420+
6421+ 6422+ 6423+ 6424+ 6425+ 6426+ 6427+ 6428+ 6429+ 6430+ 6431+ 6432+
6433+ 6434+ 6435+ 6436+ 6437+ 6438+ 6439+ 6440+ 6441+ 6442+ 6443+ 6444+
6445+ 6446+ 6447+ 6448+ 6449+ 6450+ 6451+ 6452+ 6453+ 6454+ 6455+ 6456+
6457+ 6458+ 6459+ 6460+ 6461+ 6462+ 6463+ 6464+ 6465+ 6466+ 6467+ 6468+
6469+ 6470+ 6471+ 6472+ 6473+ 6474+ 6475+ 6476+ 6477+ 6478+ 6479+ 6480+
6481+ 6482+ 6483+ 6484+ 6485+ 6486+ 6487+ 6488+ 6489+ 6490+ 6491+ 6492+
6493+ 6494+ 6495+ 6496+ 6497+ 6498+ 6499+ 6500+ 6501+ 6502+ 6503+ 6504+
6505+ 6506+ 6507+ 6508+ 6509+ 6510+ 6511+ 6512+ 6513+ 6514+ 6515+ 6516+
6517+ 6518+ 6519+ 6520+ 6521+ 6522+ 6523+ 6524+ 6525+ 6526+ 6527+ 6528+
6529+ 6530+ 6531+ 6532+ 6533+ 6534+ 6535+ 6536+ 6537+ 6538+ 6539+ 6540+
6541+ 6542+ 6543+ 6544+ 6545+ 6546+ 6547+ 6548+ 6549+ 6550+ 6551+ 6552+
6553+ 6554+ 6555+ 6556+ 6557+ 6558+ 6559+
6560+ 6561+ 6562+ 6563+ 6564+ 6565+ 6566+ 6567+ 6568+ 6569+ 6570+ 6571+
6572+ 6573+ 6574+ 6575+ 6576+ 6577+ 6578+ 6579+ 6580+ 6581+ 6582+ 6583+
6584+ 6585+ 6586+ 6587+ 6588+ 6589+ 6590+ 6591+ 6592+ 6593+ 6594+ 6595+
6596+ 6597+ 6598+ 6599+ 6600+ 6601+ 6602+ 6603+ 6604+ 6605+ 6606+ 6607+
6608+ 6609+ 6610+ 6611+ 6612+ 6613+ 6614+ 6615+ 6616+ 6617+ 6618+ 6619+
6620+ 6621+ 6622+ 6623+ 6624+ 6625+ 6626+ 6627+ 6628+ 6629+ 6630+ 6631+
6632+ 6633+ 6634+ 6635+ 6636+ 6637+ 6638+ 6639+ 6640+ 6641+ 6642+ 6643+
6644+ 6645+ 6646+ 6647+ 6648+ 6649+ 6650+ 6651+ 6652+ 6653+ 6654+ 6655+
6656+ 6657+ 6658+ 6659+ 6660+ 6661+ 6662+ 6663+ 6664+ 6665+ 6666+ 6667+
6668+ 6669+ 6670+ 6671+ 6672+ 6673+ 6674+ 6675+ 6676+ 6677+ 6678+ 6679+
6680+ 6681+ 6682+ 6683+ 6684+ 6685+ 6686+ 6687+ 6688+ 6689+ 6690+ 6691+
6692+ 6693+ 6694+ 6695+ 6696+ 6697+ 6698+ 6699+ 6700+ 6701+ 6702+ 6703+
6704+ 6705+ 6706+ 6707+ 6708+ 6709+ 6710+ 6711+ 6712+ 6713+ 6714+ 6715+
6716+ 6717+ 6718+ 6719+ 6720+ 6721+ 6722+ 6723+ 6724+ 6725+ 6726+ 6727+
6728+ 6729+ 6730+ 6731+ 6732+ 6733+ 6734+ 6735+ 6736+ 6737+ 6738+ 6739+
6740+ 6741+ 6742+ 6743+ 6744+ 6745+ 6746+ 6747+ 6748+ 6749+ 6750+ 6751+
6752+ 6753+ 6754+ 6755+ 6756+ 6757+ 6758+ 6759+ 6760+ 6761+ 6762+ 6763+
6764+ 6765+ 6766+ 6767+ 6768+ 6769+ 6770+ 6771+ 6772+ 6773+ 6774+ 6775+
6776+ 6777+ 6778+ 6779+ 6780+ 6781+ 6782+ 6783+ 6784+ 6785+ 6786+ 6787+
6788+ 6789+ 6790+ 6791+ 6792+ 6793+ 6794+ 6795+ 6796+ 6797+ 6798+ 6799+
6800+ 6801+ 6802+ 6803+ 6804+ 6805+ 6806+ 6807+ 6808+ 6809+ 6810+ 6811+
6812+ 6813+ 6814+ 6815+ 6816+ 6817+ 6818+ 6819+ 6820+ 6821+ 6822+ 6823+
6824+ 6825+ 6826+ 6827+ 6828+ 6829+ 6830+ 6831+ 6832+ 6833+ 6834+ 6835+
6836+ 6837+ 6838+ 6839+ 6840+ 6841+ 6842+ 6843+ 6844+ 6845+ 6846+ 6847+
6848+ 6849+ 6850+ 6851+ 6852+ 6853+ 6854+ 6855+ 6856+ 6857+ 6858+ 6859+
6860+ 6861+ 6862+ 6863+ 6864+ 6865+ 6866+ 6867+ 6868+ 6869+ 6870+ 6871+
6872+ 6873+ 6874+ 6875+ 6876+ 6877+ 6878+
6879+ 6880+ 6881+ 6882+ 6883+ 6884+ 6885+ 6886+ 6887+ 6888+ 6889+ 6890+
6891+ 6892+ 6893+ 6894+ 6895+ 6896+ 6897+ 6898+ 6899+ 6900+ 6901+ 6902+
6903+ 6904+ 6905+ 6906+ 6907+ 6908+ 6909+ 6910+ 6911+ 6912+ 6913+ 6914+
6915+ 6916+ 6917+ 6918+ 6919+ 6920+ 6921+ 6922+ 6923+ 6924+ 6925+ 6926+
6927+ 6928+ 6929+ 6930+ 6931+ 6932+ 6933+ 6934+ 6935+ 6936+ 6937+ 6938+
6939+ 6940+ 6941+ 6942+ 6943+ 6944+ 6945+ 6946+ 6947+ 6948+ 6949+ 6950+
6951+ 6952+ 6953+ 6954+ 6955+ 6956+ 6957+ 6958+ 6959+ 6960+ 6961+ 6962+
6963+ 6964+ 6965+ 6966+ 6967+ 6968+ 6969+ 6970+ 6971+ 6972+ 6973+ 6974+
6975+ 6976+ 6977+ 6978+ 6979+ 6980+ 6981+ 6982+ 6983+ 6984+ 6985+ 6986+
6987+ 6988+ 6989+ 6990+ 6991+ 6992+ 6993+ 6994+ 6995+ 6996+ 6997+ 6998+
6999+ 7000+ 7001+ 7002+ 7003+ 7004+ 7005+ 7006+ 7007+ 7008+ 7009+ 7010+
7011+ 7012+ 7013+ 7014+ 7015+ 7016+ 7017+ 7018+ 7019+ 7020+ 7021+ 7022+
7023+ 7024+ 7025+ 7026+ 7027+ 7028+ 7029+ 7030+ 7031+ 7032+ 7033+ 7034+
7035+ 7036+ 7037+ 7038+ 7039+ 7040+ 7041+ 7042+ 7043+ 7044+ 7045+ 7046+
7047+ 7048+ 7049+ 7050+ 7051+ 7052+ 7053+ 7054+ 7055+ 7056+ 7057+ 7058+
7059+ 7060+ 7061+ 7062+ 7063+ 7064+ 7065+ 7066+ 7067+ 7068+ 7069+ 7070+
7071+ 7072+ 7073+ 7074+ 7075+ 7076+ 7077+ 7078+ 7079+ 7080+ 7081+ 7082+
7083+ 7084+ 7085+ 7086+ 7087+ 7088+ 7089+ 7090+ 7091+ 7092+ 7093+ 7094+
7095+ 7096+ 7097+ 7098+ 7099+ 7100+ 7101+ 7102+ 7103+ 7104+ 7105+ 7106+
7107+ 7108+ 7109+ 7110+ 7111+ 7112+ 7113+ 7114+ 7115+ 7116+ 7117+ 7118+
7119+ 7120+ 7121+ 7122+ 7123+ 7124+ 7125+ 7126+ 7127+ 7128+ 7129+ 7130+
7131+ 7132+ 7133+ 7134+ 7135+ 7136+ 7137+ 7138+ 7139+ 7140+ 7141+ 7142+
7143+ 7144+ 7145+ 7146+ 7147+ 7148+ 7149+ 7150+ 7151+ 7152+ 7153+ 7154+
7155+ 7156+ 7157+ 7158+ 7159+ 7160+ 7161+ 7162+ 7163+ 7164+ 7165+ 7166+
7167+ 7168+ 7169+ 7170+ 7171+ 7172+ 7173+ 7174+ 7175+ 7176+ 7177+ 7178+
7179+ 7180+ 7181+ 7182+ 7183+ 7184+ 7185+ 7186+ 7187+ 7188+ 7189+ 7190+
7191+ 7192+ 7193+ 7194+ 7195+ 7196+ 7197+
7198+ 7199+ 7200+ 7201+ 7202+ 7203+ 7204+ 7205+ 7206+ 7207+ 7208+ 7209+
7210+ 7211+ 7212+ 7213+ 7214+ 7215+ 7216+ 7217+ 7218+ 7219+ 7220+ 7221+
7222+ 7223+ 7224+ 7225+ 7226+ 7227+ 7228+ 7229+ 7230+ 7231+ 7232+ 7233+
7234+ 7235+ 7236+ 7237+ 7238+ 7239+ 7240+ 7241+ 7242+ 7243+ 7244+ 7245+
7246+ 7247+ 7248+ 7249+ 7250+ 7251+ 7252+ 7253+ 7254+ 7255+ 7256+ 7257+
7258+ 7259+ 7260+ 7261+ 7262+ 7263+ 7264+ 7265+ 7266+ 7267+ 7268+ 7269+
7270+ 7271+ 7272+ 7273+ 7274+ 7275+ 7276+ 7277+ 7278+ 7279+ 7280+ 7281+
7282+ 7283+ 7284+ 7285+ 7286+ 7287+ 7288+ 7289+ 7290+ 7291+ 7292+ 7293+
7294+ 7295+ 7296+ 7297+ 7298+ 7299+ 7300+ 7301+ 7302+ 7303+ 7304+ 7305+
7306+ 7307+ 7308+ 7309+ 7310+ 7311+ 7312+ 7313+ 7314+ 7315+ 7316+ 7317+
7318+ 7319+ 7320+ 7321+ 7322+ 7323+ 7324+ 7325+ 7326+ 7327+ 7328+ 7329+
7330+ 7331+ 7332+ 7333+ 7334+ 7335+ 7336+ 7337+ 7338+ 7339+ 7340+ 7341+
7342+ 7343+ 7344+ 7345+ 7346+ 7347+ 7348+ 7349+ 7350+ 7351+ 7352+ 7353+
7354+ 7355+ 7356+ 7357+ 7358+ 7359+ 7360+ 7361+ 7362+ 7363+ 7364+ 7365+
7366+ 7367+ 7368+ 7369+ 7370+ 7371+ 7372+ 7373+ 7374+ 7375+ 7376+ 7377+
7378+ 7379+ 7380+ 7381+ 7382+ 7383+ 7384+ 7385+ 7386+ 7387+ 7388+ 7389+
7390+ 7391+ 7392+ 7393+ 7394+ 7395+ 7396+ 7397+ 7398+ 7399+ 7400+ 7401+
7402+ 7403+ 7404+ 7405+ 7406+ 7407+ 7408+ 7409+ 7410+ 7411+ 7412+ 7413+
7414+ 7415+ 7416+ 7417+ 7418+ 7419+ 7420+ 7421+ 7422+ 7423+ 7424+ 7425+
7426+ 7427+ 7428+ 7429+ 7430+ 7431+ 7432+ 7433+ 7434+ 7435+ 7436+ 7437+
7438+ 7439+ 7440+ 7441+ 7442+ 7443+ 7444+ 7445+ 7446+ 7447+ 7448+ 7449+
7450+ 7451+ 7452+ 7453+ 7454+ 7455+ 7456+ 7457+ 7458+ 7459+ 7460+ 7461+
7462+ 7463+ 7464+ 7465+ 7466+ 7467+ 7468+ 7469+ 7470+ 7471+ 7472+ 7473+
7474+ 7475+ 7476+ 7477+ 7478+ 7479+ 7480+ 7481+ 7482+ 7483+ 7484+ 7485+
7486+ 7487+ 7488+ 7489+ 7490+ 7491+ 7492+ 7493+ 7494+ 7495+ 7496+ 7497+
7498+ 7499+ 7500+ 7501+ 7502+ 7503+ 7504+ 7505+ 7506+ 7507+ 7508+ 7509+
7510+ 7511+ 7512+ 7513+ 7514+ 7515+ 7516+
7517+ 7518+ 7519+ 7520+ 7521+ 7522+ 7523+ 7524+ 7525+ 7526+ 7527+ 7528+
7529+ 7530+ 7531+ 7532+ 7533+ 7534+ 7535+ 7536+ 7537+ 7538+ 7539+ 7540+
7541+ 7542+ 7543+ 7544+ 7545+ 7546+ 7547+ 7548+ 7549+ 7550+ 7551+ 7552+
7553+ 7554+ 7555+ 7556+ 7557+ 7558+ 7559+ 7560+ 7561+ 7562+ 7563+ 7564+
7565+ 7566+ 7567+ 7568+ 7569+ 7570+ 7571+ 7572+ 7573+ 7574+ 7575+ 7576+
7577+ 7578+ 7579+ 7580+ 7581+ 7582+ 7583+ 7584+ 7585+ 7586+ 7587+ 7588+
7589+ 7590+ 7591+ 7592+ 7593+ 7594+ 7595+ 7596+ 7597+ 7598+ 7599+ 7600+
7601+ 7602+ 7603+ 7604+ 7605+ 7606+ 7607+ 7608+ 7609+ 7610+ 7611+ 7612+
7613+ 7614+ 7615+ 7616+ 7617+ 7618+ 7619+ 7620+ 7621+ 7622+ 7623+ 7624+
7625+ 7626+ 7627+ 7628+ 7629+ 7630+ 7631+ 7632+ 7633+ 7634+ 7635+ 7636+
7637+ 7638+ 7639+ 7640+ 7641+ 7642+ 7643+ 7644+ 7645+ 7646+ 7647+ 7648+
7649+ 7650+ 7651+ 7652+ 7653+ 7654+ 7655+ 7656+ 7657+ 7658+ 7659+ 7660+
7661+ 7662+ 7663+ 7664+ 7665+ 7666+ 7667+ 7668+ 7669+ 7670+ 7671+ 7672+
7673+ 7674+ 7675+ 7676+ 7677+ 7678+ 7679+ 7680+ 7681+ 7682+ 7683+ 7684+
7685+ 7686+ 7687+ 7688+ 7689+ 7690+ 7691+ 7692+ 7693+ 7694+ 7695+ 7696+
7697+ 7698+ 7699+ 7700+ 7701+ 7702+ 7703+ 7704+ 7705+ 7706+ 7707+ 7708+
7709+ 7710+ 7711+ 7712+ 7713+ 7714+ 7715+ 7716+ 7717+ 7718+ 7719+ 7720+
7721+ 7722+ 7723+ 7724+ 7725+ 7726+ 7727+ 7728+ 7729+ 7730+ 7731+ 7732+
7733+ 7734+ 7735+ 7736+ 7737+ 7738+ 7739+ 7740+ 7741+ 7742+ 7743+ 7744+
7745+ 7746+ 7747+ 7748+ 7749+ 7750+ 7751+ 7752+ 7753+ 7754+ 7755+ 7756+
7757+ 7758+ 7759+ 7760+ 7761+ 7762+ 7763+ 7764+ 7765+ 7766+ 7767+ 7768+
7769+ 7770+ 7771+ 7772+ 7773+ 7774+ 7775+ 7776+ 7777+ 7778+ 7779+ 7780+
7781+ 7782+ 7783+ 7784+ 7785+ 7786+ 7787+ 7788+ 7789+ 7790+ 7791+ 7792+
7793+ 7794+ 7795+ 7796+ 7797+ 7798+ 7799+ 7800+ 7801+ 7802+ 7803+ 7804+
7805+ 7806+ 7807+ 7808+ 7809+ 7810+ 7811+ 7812+ 7813+ 7814+ 7815+ 7816+
7817+ 7818+ 7819+ 7820+ 7821+ 7822+ 7823+ 7824+ 7825+ 7826+ 7827+ 7828+
7829+ 7830+ 7831+ 7832+ 7833+ 7834+ 7835+
7836+ 7837+ 7838+ 7839+ 7840+ 7841+ 7842+ 7843+ 7844+ 7845+ 7846+ 7847+
7848+ 7849+ 7850+ 7851+ 7852+ 7853+ 7854+ 7855+ 7856+ 7857+ 7858+ 7859+
7860+ 7861+ 7862+ 7863+ 7864+ 7865+ 7866+ 7867+ 7868+ 7869+ 7870+ 7871+
7872+ 7873+ 7874+ 7875+ 7876+ 7877+ 7878+ 7879+ 7880+ 7881+ 7882+ 7883+
7884+ 7885+ 7886+ 7887+ 7888+ 7889+ 7890+ 7891+ 7892+ 7893+ 7894+ 7895+
7896+ 7897+ 7898+ 7899+ 7900+ 7901+ 7902+ 7903+ 7904+ 7905+ 7906+ 7907+
7908+ 7909+ 7910+ 7911+ 7912+ 7913+ 7914+ 7915+ 7916+ 7917+ 7918+ 7919+
7920+ 7921+ 7922+ 7923+ 7924+ 7925+ 7926+ 7927+ 7928+ 7929+ 7930+ 7931+
7932+ 7933+ 7934+ 7935+ 7936+ 7937+ 7938+ 7939+ 7940+ 7941+ 7942+ 7943+
7944+ 7945+ 7946+ 7947+ 7948+ 7949+ 7950+ 7951+ 7952+ 7953+ 7954+ 7955+
7956+ 7957+ 7958+ 7959+ 7960+ 7961+ 7962+ 7963+ 7964+ 7965+ 7966+ 7967+
7968+ 7969+ 7970+ 7971+ 7972+ 7973+ 7974+ 7975+ 7976+ 7977+ 7978+ 7979+
7980+ 7981+ 7982+ 7983+ 7984+ 7985+ 7986+ 7987+ 7988+ 7989+ 7990+ 7991+
7992+ 7993+ 7994+ 7995+ 7996+ 7997+ 7998+ 7999+ 8000+ 8001+ 8002+ 8003+
8004+ 8005+ 8006+ 8007+ 8008+ 8009+ 8010+ 8011+ 8012+ 8013+ 8014+ 8015+
8016+ 8017+ 8018+ 8019+ 8020+ 8021+ 8022+ 8023+ 8024+ 8025+ 8026+ 8027+
8028+ 8029+ 8030+ 8031+ 8032+ 8033+ 8034+ 8035+ 8036+ 8037+ 8038+ 8039+
8040+ 8041+ 8042+ 8043+ 8044+ 8045+ 8046+ 8047+ 8048+ 8049+ 8050+ 8051+
8052+ 8053+ 8054+ 8055+ 8056+ 8057+ 8058+ 8059+ 8060+ 8061+ 8062+ 8063+
8064+ 8065+ 8066+ 8067+ 8068+ 8069+ 8070+ 8071+ 8072+ 8073+ 8074+ 8075+
8076+ 8077+ 8078+ 8079+ 8080+ 8081+ 8082+ 8083+ 8084+ 8085+ 8086+ 8087+
8088+ 8089+ 8090+ 8091+ 8092+ 8093+ 8094+ 8095+ 8096+ 8097+ 8098+ 8099+
8100+ 8101+ 8102+ 8103+ 8104+ 8105+ 8106+ 8107+ 8108+ 8109+ 8110+ 8111+
8112+ 8113+ 8114+ 8115+ 8116+ 8117+ 8118+ 8119+ 8120+ 8121+ 8122+ 8123+
8124+ 8125+ 8126+ 8127+ 8128+ 8129+ 8130+ 8131+ 8132+ 8133+ 8134+ 8135+
8136+ 8137+ 8138+ 8139+ 8140+ 8141+ 8142+ 8143+ 8144+ 8145+ 8146+ 8147+
8148+ 8149+ 8150+ 8151+ 8152+ 8153+ 8154+
8155+ 8156+ 8157+ 8158+ 8159+ 8160+ 8161+ 8162+ 8163+ 8164+ 8165+ 8166+
8167+ 8168+ 8169+ 8170+ 8171+ 8172+ 8173+ 8174+ 8175+ 8176+ 8177+ 8178+
8179+ 8180+ 8181+ 8182+ 8183+ 8184+ 8185+ 8186+ 8187+ 8188+ 8189+ 8190+
8191+ 8192+ 8193+ 8194+ 8195+ 8196+ 8197+ 8198+ 8199+ 8200+ 8201+ 8202+
8203+ 8204+ 8205+ 8206+ 8207+ 8208+ 8209+ 8210+ 8211+ 8212+ 8213+ 8214+
8215+ 8216+ 8217+ 8218+ 8219+ 8220+ 8221+ 8222+ 8223+ 8224+ 8225+ 8226+
8227+ 8228+ 8229+ 8230+ 8231+ 8232+ 8233+ 8234+ 8235+ 8236+ 8237+ 8238+
8239+ 8240+ 8241+ 8242+ 8243+ 8244+ 8245+ 8246+ 8247+ 8248+ 8249+ 8250+
8251+ 8252+ 8253+ 8254+ 8255+ 8256+ 8257+ 8258+ 8259+ 8260+ 8261+ 8262+
8263+ 8264+ 8265+ 8266+ 8267+ 8268+ 8269+ 8270+ 8271+ 8272+ 8273+ 8274+
8275+ 8276+ 8277+ 8278+ 8279+ 8280+ 8281+ 8282+ 8283+ 8284+ 8285+ 8286+
8287+ 8288+ 8289+ 8290+ 8291+ 8292+ 8293+ 8294+ 8295+ 8296+ 8297+ 8298+
8299+ 8300+ 8301+ 8302+ 8303+ 8304+ 8305+ 8306+ 8307+ 8308+ 8309+ 8310+
8311+ 8312+ 8313+ 8314+ 8315+ 8316+ 8317+ 8318+ 8319+ 8320+ 8321+ 8322+
8323+ 8324+ 8325+ 8326+ 8327+ 8328+ 8329+ 8330+ 8331+ 8332+ 8333+ 8334+
8335+ 8336+ 8337+ 8338+ 8339+ 8340+ 8341+ 8342+ 8343+ 8344+ 8345+ 8346+
8347+ 8348+ 8349+ 8350+ 8351+ 8352+ 8353+ 8354+ 8355+ 8356+ 8357+ 8358+
8359+ 8360+ 8361+ 8362+ 8363+ 8364+ 8365+ 8366+ 8367+ 8368+ 8369+ 8370+
8371+ 8372+ 8373+ 8374+ 8375+ 8376+ 8377+ 8378+ 8379+ 8380+ 8381+ 8382+
8383+ 8384+ 8385+ 8386+ 8387+ 8388+ 8389+ 8390+ 8391+ 8392+ 8393+ 8394+
8395+ 8396+ 8397+ 8398+ 8399+ 8400+ 8401+ 8402+ 8403+ 8404+ 8405+ 8406+
8407+ 8408+ 8409+ 8410+ 8411+ 8412+ 8413+ 8414+ 8415+ 8416+ 8417+ 8418+
8419+ 8420+ 8421+ 8422+ 8423+ 8424+ 8425+ 8426+ 8427+ 8428+ 8429+ 8430+
8431+ 8432+ 8433+ 8434+ 8435+ 8436+ 8437+ 8438+ 8439+ 8440+ 8441+ 8442+
8443+ 8444+ 8445+ 8446+ 8447+ 8448+ 8449+ 8450+ 8451+ 8452+ 8453+ 8454+
8455+ 8456+ 8457+ 8458+ 8459+ 8460+ 8461+ 8462+ 8463+ 8464+ 8465+ 8466+
8467+ 8468+ 8469+ 8470+ 8471+ 8472+ 8473+
8474+ 8475+ 8476+ 8477+ 8478+ 8479+ 8480+ 8481+ 8482+ 8483+ 8484+ 8485+
8486+ 8487+ 8488+ 8489+ 8490+ 8491+ 8492+ 8493+ 8494+ 8495+ 8496+ 8497+
8498+ 8499+ 8500+ 8501+ 8502+ 8503+ 8504+ 8505+ 8506+ 8507+ 8508+ 8509+
8510+ 8511+ 8512+ 8513+ 8514+ 8515+ 8516+ 8517+ 8518+ 8519+ 8520+ 8521+
8522+ 8523+ 8524+ 8525+ 8526+ 8527+ 8528+ 8529+ 8530+ 8531+ 8532+ 8533+
8534+ 8535+ 8536+ 8537+ 8538+ 8539+ 8540+ 8541+ 8542+ 8543+ 8544+ 8545+
8546+ 8547+ 8548+ 8549+ 8550+ 8551+ 8552+ 8553+ 8554+ 8555+ 8556+ 8557+
8558+ 8559+ 8560+ 8561+ 8562+ 8563+ 8564+ 8565+ 8566+ 8567+ 8568+ 8569+
8570+ 8571+ 8572+ 8573+ 8574+ 8575+ 8576+ 8577+ 8578+ 8579+ 8580+ 8581+
8582+ 8583+ 8584+ 8585+ 8586+ 8587+ 8588+ 8589+ 8590+ 8591+ 8592+ 8593+
8594+ 8595+ 8596+ 8597+ 8598+ 8599+ 8600+ 8601+ 8602+ 8603+ 8604+ 8605+
8606+ 8607+ 8608+ 8609+ 8610+ 8611+ 8612+ 8613+ 8614+ 8615+ 8616+ 8617+
8618+ 8619+ 8620+ 8621+ 8622+ 8623+ 8624+ 8625+ 8626+ 8627+ 8628+ 8629+
8630+ 8631+ 8632+ 8633+ 8634+ 8635+ 8636+ 8637+ 8638+ 8639+ 8640+ 8641+
8642+ 8643+ 8644+ 8645+ 8646+ 8647+ 8648+ 8649+ 8650+ 8651+ 8652+ 8653+
8654+ 8655+ 8656+ 8657+ 8658+ 8659+ 8660+ 8661+ 8662+ 8663+ 8664+ 8665+
8666+ 8667+ 8668+ 8669+ 8670+ 8671+ 8672+ 8673+ 8674+ 8675+ 8676+ 8677+
8678+ 8679+ 8680+ 8681+ 8682+ 8683+ 8684+ 8685+ 8686+ 8687+ 8688+ 8689+
8690+ 8691+ 8692+ 8693+ 8694+ 8695+ 8696+ 8697+ 8698+ 8699+ 8700+ 8701+
8702+ 8703+ 8704+ 8705+ 8706+ 8707+ 8708+ 8709+ 8710+ 8711+ 8712+ 8713+
8714+ 8715+ 8716+ 8717+ 8718+ 8719+ 8720+ 8721+ 8722+ 8723+ 8724+ 8725+
8726+ 8727+ 8728+ 8729+ 8730+ 8731+ 8732+ 8733+ 8734+ 8735+ 8736+ 8737+
8738+ 8739+ 8740+ 8741+ 8742+ 8743+ 8744+ 8745+ 8746+ 8747+ 8748+ 8749+
8750+ 8751+ 8752+ 8753+ 8754+ 8755+ 8756+ 8757+ 8758+ 8759+ 8760+ 8761+
8762+ 8763+ 8764+ 8765+ 8766+ 8767+ 8768+ 8769+ 8770+ 8771+ 8772+ 8773+
8774+ 8775+ 8776+ 8777+ 8778+ 8779+ 8780+ 8781+ 8782+ 8783+ 8784+ 8785+
8786+ 8787+ 8788+ 8789+ 8790+ 8791+ 8792+
8793+ 8794+ 8795+ 8796+ 8797+ 8798+ 8799+ 8800+ 8801+ 8802+ 8803+ 8804+
8805+ 8806+ 8807+ 8808+ 8809+ 8810+ 8811+ 8812+ 8813+ 8814+ 8815+ 8816+
8817+ 8818+ 8819+ 8820+ 8821+ 8822+ 8823+ 8824+ 8825+ 8826+ 8827+ 8828+
8829+ 8830+ 8831+ 8832+ 8833+ 8834+ 8835+ 8836+ 8837+ 8838+ 8839+ 8840+
8841+ 8842+ 8843+ 8844+ 8845+ 8846+ 8847+ 8848+ 8849+ 8850+ 8851+ 8852+
8853+ 8854+ 8855+ 8856+ 8857+ 8858+ 8859+ 8860+ 8861+ 8862+ 8863+ 8864+
8865+ 8866+ 8867+ 8868+ 8869+ 8870+ 8871+ 8872+ 8873+ 8874+ 8875+ 8876+
8877+ 8878+ 8879+ 8880+ 8881+ 8882+ 8883+ 8884+ 8885+ 8886+ 8887+ 8888+
8889+ 8890+ 8891+ 8892+ 8893+ 8894+ 8895+ 8896+ 8897+ 8898+ 8899+ 8900+
8901+ 8902+ 8903+ 8904+ 8905+ 8906+ 8907+ 8908+ 8909+ 8910+ 8911+ 8912+
8913+ 8914+ 8915+ 8916+ 8917+ 8918+ 8919+ 8920+ 8921+ 8922+ 8923+ 8924+
8925+ 8926+ 8927+ 8928+ 8929+ 8930+ 8931+ 8932+ 8933+ 8934+ 8935+ 8936+
8937+ 8938+ 8939+ 8940+ 8941+ 8942+ 8943+ 8944+ 8945+ 8946+ 8947+ 8948+
8949+ 8950+ 8951+ 8952+ 8953+ 8954+ 8955+ 8956+ 8957+ 8958+ 8959+ 8960+
8961+ 8962+ 8963+ 8964+ 8965+ 8966+ 8967+ 8968+ 8969+ 8970+ 8971+ 8972+
8973+ 8974+ 8975+ 8976+ 8977+ 8978+ 8979+ 8980+ 8981+ 8982+ 8983+ 8984+
8985+ 8986+ 8987+ 8988+ 8989+ 8990+ 8991+ 8992+ 8993+ 8994+ 8995+ 8996+
8997+ 8998+ 8999+ 9000+ 9001+ 9002+ 9003+ 9004+ 9005+ 9006+ 9007+ 9008+
9009+ 9010+ 9011+ 9012+ 9013+ 9014+ 9015+ 9016+ 9017+ 9018+ 9019+ 9020+
9021+ 9022+ 9023+ 9024+ 9025+ 9026+ 9027+ 9028+ 9029+ 9030+ 9031+ 9032+
9033+ 9034+ 9035+ 9036+ 9037+ 9038+ 9039+ 9040+ 9041+ 9042+ 9043+ 9044+
9045+ 9046+ 9047+ 9048+ 9049+ 9050+ 9051+ 9052+ 9053+ 9054+ 9055+ 9056+
9057+ 9058+ 9059+ 9060+ 9061+ 9062+ 9063+ 9064+ 9065+ 9066+ 9067+ 9068+
9069+ 9070+ 9071+ 9072+ 9073+ 9074+ 9075+ 9076+ 9077+ 9078+ 9079+ 9080+
9081+ 9082+ 9083+ 9084+ 9085+ 9086+ 9087+ 9088+ 9089+ 9090+ 9091+ 9092+
9093+ 9094+ 9095+ 9096+ 9097+ 9098+ 9099+ 9100+ 9101+ 9102+ 9103+ 9104+
9105+ 9106+ 9107+ 9108+ 9109+ 9110+ 9111+
9112+ 9113+ 9114+ 9115+ 9116+ 9117+ 9118+ 9119+ 9120+ 9121+ 9122+ 9123+
9124+ 9125+ 9126+ 9127+ 9128+ 9129+ 9130+ 9131+ 9132+ 9133+ 9134+ 9135+
9136+ 9137+ 9138+ 9139+ 9140+ 9141+ 9142+ 9143+ 9144+ 9145+ 9146+ 9147+
9148+ 9149+ 9150+ 9151+ 9152+ 9153+ 9154+ 9155+ 9156+ 9157+ 9158+ 9159+
9160+ 9161+ 9162+ 9163+ 9164+ 9165+ 9166+ 9167+ 9168+ 9169+ 9170+ 9171+
9172+ 9173+ 9174+ 9175+ 9176+ 9177+ 9178+ 9179+ 9180+ 9181+ 9182+ 9183+
9184+ 9185+ 9186+ 9187+ 9188+ 9189+ 9190+ 9191+ 9192+ 9193+ 9194+ 9195+
9196+ 9197+ 9198+ 9199+ 9200+ 9201+ 9202+ 9203+ 9204+ 9205+ 9206+ 9207+
9208+ 9209+ 9210+ 9211+ 9212+ 9213+ 9214+ 9215+ 9216+ 9217+ 9218+ 9219+
9220+ 9221+ 9222+ 9223+ 9224+ 9225+ 9226+ 9227+ 9228+ 9229+ 9230+ 9231+
9232+ 9233+ 9234+ 9235+ 9236+ 9237+ 9238+ 9239+ 9240+ 9241+ 9242+ 9243+
9244+ 9245+ 9246+ 9247+ 9248+ 9249+ 9250+ 9251+ 9252+ 9253+ 9254+ 9255+
9256+ 9257+ 9258+ 9259+ 9260+ 9261+ 9262+ 9263+ 9264+ 9265+ 9266+ 9267+
9268+ 9269+ 9270+ 9271+ 9272+ 9273+ 9274+ 9275+ 9276+ 9277+ 9278+ 9279+
9280+ 9281+ 9282+ 9283+ 9284+ 9285+ 9286+ 9287+ 9288+ 9289+ 9290+ 9291+
9292+ 9293+ 9294+ 9295+ 9296+ 9297+ 9298+ 9299+ 9300+ 9301+ 9302+ 9303+
9304+ 9305+ 9306+ 9307+ 9308+ 9309+ 9310+ 9311+ 9312+ 9313+ 9314+ 9315+
9316+ 9317+ 9318+ 9319+ 9320+ 9321+ 9322+ 9323+ 9324+ 9325+ 9326+ 9327+
9328+ 9329+ 9330+ 9331+ 9332+ 9333+ 9334+ 9335+ 9336+ 9337+ 9338+ 9339+
9340+ 9341+ 9342+ 9343+ 9344+ 9345+ 9346+ 9347+ 9348+ 9349+ 9350+ 9351+
9352+ 9353+ 9354+ 9355+ 9356+ 9357+ 9358+ 9359+ 9360+ 9361+ 9362+ 9363+
9364+ 9365+ 9366+ 9367+ 9368+ 9369+ 9370+ 9371+ 9372+ 9373+ 9374+ 9375+
9376+ 9377+ 9378+ 9379+ 9380+ 9381+ 9382+ 9383+ 9384+ 9385+ 9386+ 9387+
9388+ 9389+ 9390+ 9391+ 9392+ 9393+ 9394+ 9395+ 9396+ 9397+ 9398+ 9399+
9400+ 9401+ 9402+ 9403+ 9404+ 9405+ 9406+ 9407+ 9408+ 9409+ 9410+ 9411+
9412+ 9413+ 9414+ 9415+ 9416+ 9417+ 9418+ 9419+ 9420+ 9421+ 9422+ 9423+
9424+ 9425+ 9426+ 9427+ 9428+ 9429+ 9430+
9431+ 9432+ 9433+ 9434+ 9435+ 9436+ 9437+ 9438+ 9439+ 9440+ 9441+ 9442+
9443+ 9444+ 9445+ 9446+ 9447+ 9448+ 9449+ 9450+ 9451+ 9452+ 9453+ 9454+
9455+ 9456+ 9457+ 9458+ 9459+ 9460+ 9461+ 9462+ 9463+ 9464+ 9465+ 9466+
9467+ 9468+ 9469+ 9470+ 9471+ 9472+ 9473+ 9474+ 9475+ 9476+ 9477+ 9478+
9479+ 9480+ 9481+ 9482+ 9483+ 9484+ 9485+ 9486+ 9487+ 9488+ 9489+ 9490+
9491+ 9492+ 9493+ 9494+ 9495+ 9496+ 9497+ 9498+ 9499+ 9500+ 9501+ 9502+
9503+ 9504+ 9505+ 9506+ 9507+ 9508+ 9509+ 9510+ 9511+ 9512+ 9513+ 9514+
9515+ 9516+ 9517+ 9518+ 9519+ 9520+ 9521+ 9522+ 9523+ 9524+ 9525+ 9526+
9527+ 9528+ 9529+ 9530+ 9531+ 9532+ 9533+ 9534+ 9535+ 9536+ 9537+ 9538+
9539+ 9540+ 9541+ 9542+ 9543+ 9544+ 9545+ 9546+ 9547+ 9548+ 9549+ 9550+
9551+ 9552+ 9553+ 9554+ 9555+ 9556+ 9557+ 9558+ 9559+ 9560+ 9561+ 9562+
9563+ 9564+ 9565+ 9566+ 9567+ 9568+ 9569+ 9570+ 9571+ 9572+ 9573+ 9574+
9575+ 9576+ 9577+ 9578+ 9579+ 9580+ 9581+ 9582+ 9583+ 9584+ 9585+ 9586+
9587+ 9588+ 9589+ 9590+ 9591+ 9592+ 9593+ 9594+ 9595+ 9596+ 9597+ 9598+
9599+ 9600+ 9601+ 9602+ 9603+ 9604+ 9605+ 9606+ 9607+ 9608+ 9609+ 9610+
9611+ 9612+ 9613+ 9614+ 9615+ 9616+ 9617+ 9618+ 9619+ 9620+ 9621+ 9622+
9623+ 9624+ 9625+ 9626+ 9627+ 9628+ 9629+ 9630+ 9631+ 9632+ 9633+ 9634+
9635+ 9636+ 9637+ 9638+ 9639+ 9640+ 9641+ 9642+ 9643+ 9644+ 9645+ 9646+
9647+ 9648+ 9649+ 9650+ 9651+ 9652+ 9653+ 9654+ 9655+ 9656+ 9657+ 9658+
9659+ 9660+ 9661+ 9662+ 9663+ 9664+ 9665+ 9666+ 9667+ 9668+ 9669+ 9670+
9671+ 9672+ 9673+ 9674+ 9675+ 9676+ 9677+ 9678+ 9679+ 9680+ 9681+ 9682+
9683+ 9684+ 9685+ 9686+ 9687+ 9688+ 9689+ 9690+ 9691+ 9692+ 9693+ 9694+
9695+ 9696+ 9697+ 9698+ 9699+ 9700+ 9701+ 9702+ 9703+ 9704+ 9705+ 9706+
9707+ 9708+ 9709+ 9710+ 9711+ 9712+ 9713+ 9714+ 9715+ 9716+ 9717+ 9718+
9719+ 9720+ 9721+ 9722+ 9723+ 9724+ 9725+ 9726+ 9727+ 9728+ 9729+ 9730+
9731+ 9732+ 9733+ 9734+ 9735+ 9736+ 9737+ 9738+ 9739+ 9740+ 9741+ 9742+
9743+ 9744+ 9745+ 9746+ 9747+ 9748+ 9749+
9750+ 9751+ 9752+ 9753+ 9754+ 9755+ 9756+ 9757+ 9758+ 9759+ 9760+ 9761+
9762+ 9763+ 9764+ 9765+ 9766+ 9767+ 9768+ 9769+ 9770+ 9771+ 9772+ 9773+
9774+ 9775+ 9776+ 9777+ 9778+ 9779+ 9780+ 9781+ 9782+ 9783+ 9784+ 9785+
9786+ 9787+ 9788+ 9789+ 9790+ 9791+ 9792+ 9793+ 9794+ 9795+ 9796+ 9797+
9798+ 9799+ 9800+ 9801+ 9802+ 9803+ 9804+ 9805+ 9806+ 9807+ 9808+ 9809+
9810+ 9811+ 9812+ 9813+ 9814+ 9815+ 9816+ 9817+ 9818+ 9819+ 9820+ 9821+
9822+ 9823+ 9824+ 9825+ 9826+ 9827+ 9828+ 9829+ 9830+ 9831+ 9832+ 9833+
9834+ 9835+ 9836+ 9837+ 9838+ 9839+ 9840+ 9841+ 9842+ 9843+ 9844+ 9845+
9846+ 9847+ 9848+ 9849+ 9850+ 9851+ 9852+ 9853+ 9854+ 9855+ 9856+ 9857+
9858+ 9859+ 9860+ 9861+ 9862+ 9863+ 9864+ 9865+ 9866+ 9867+ 9868+ 9869+
9870+ 9871+ 9872+ 9873+ 9874+ 9875+ 9876+ 9877+ 9878+ 9879+ 9880+ 9881+
9882+ 9883+ 9884+ 9885+ 9886+ 9887+ 9888+ 9889+ 9890+ 9891+ 9892+ 9893+
9894+ 9895+ 9896+ 9897+ 9898+ 9899+ 9900+ 9901+ 9902+ 9903+ 9904+ 9905+
9906+ 9907+ 9908+ 9909+ 9910+ 9911+ 9912+ 9913+ 9914+ 9915+ 9916+ 9917+
9918+ 9919+ 9920+ 9921+ 9922+ 9923+ 9924+ 9925+ 9926+ 9927+ 9928+ 9929+
9930+ 9931+ 9932+ 9933+ 9934+ 9935+ 9936+ 9937+ 9938+ 9939+ 9940+ 9941+
9942+ 9943+ 9944+ 9945+ 9946+ 9947+ 9948+ 9949+ 9950+ 9951+ 9952+ 9953+
9954+ 9955+ 9956+ 9957+ 9958+ 9959+ 9960+ 9961+ 9962+ 9963+ 9964+ 9965+
9966+ 9967+ 9968+ 9969+ 9970+ 9971+ 9972+ 9973+ 9974+ 9975+ 9976+ 9977+
9978+ 9979+ 9980+ 9981+ 9982+ 9983+ 9984+ 9985+ 9986+ 9987+ 9988+ 9989+
9990+ 9991+ 9992+ 9993+ 9994+ 9995+ 9996+ 9997+ 9998+ 9999+ 10000;
return sum;
}
}//MyMath
// responsible for creating the BruteForceSums
// class and compiling it and invoking the
// DoSums method dynamically
public class ReflectionTest
{
public static string fileName = "BruteForceSums";
// the public method called by the driver
public double DoSum(int theValue)
{
if (theComputer == null)
{
GenerateCode(theValue);
}
double retval = (theComputer.ComputeSum());
return retval;
}
// generate the code and compile it
private void GenerateCode(int theVal)
{
string className = "BruteForceSums";
Stream s =
File.Open(fileName + ".cs", FileMode.Create);
StreamWriter wrtr = new StreamWriter(s);
wrtr.WriteLine(
"// Dynamically created BruteForceSums class");
//open the namespace
wrtr.WriteLine("namespace Programming_CSharp {\n");
// create the class
wrtr.WriteLine(
"class {0} : Programming_CSharp.IComputer ",
className);
wrtr.WriteLine("{");
// create the method
wrtr.WriteLine("\tpublic double ComputeSum( )");
wrtr.WriteLine("\t{");
wrtr.WriteLine("\t// Brute force sum method");
wrtr.WriteLine("\t// For value = {0}", theVal);
// write the brute force additions
wrtr.Write("\tdouble sum = 0");
for (int i = 1;i<=theVal;i++)
{
wrtr.Write("+ {0}",i);
}
wrtr.WriteLine(";"); // finish method
wrtr.WriteLine("return sum;");
wrtr.WriteLine("\t}"); // end method
wrtr.WriteLine("}\n"); // end class
wrtr.WriteLine("}"); // end namespace
// close the writer and the stream
wrtr.Close( );
s.Close( );
// Build the file
ProcessStartInfo psi =
new ProcessStartInfo();
string compileString = " /optimize+ ";
compileString += "/r:" +
@"M:\WUTemp\ReflectionEmit\Example18_10\bin\Debug\ IComputer.dll ";
compileString += "/target:library ";
compileString += "/out:" +
@"M:\WUTemp\ReflectionEmit\Example18_10\bin\Debug\ " + fileName + ".dll ";
compileString += @"M:\WUTemp\ReflectionEmit\Example18_10\bin\Debug\ ";
compileString += fileName + ".cs > compile.out";
string frameworkDir = @"C:\WINNT\Microsoft.NET\Framework\v1.1.4322\";
Process proc = Process.Start(frameworkDir + "csc.exe", compileString);
Console.WriteLine(frameworkDir + "csc.exe" + compileString);
proc.WaitForExit();
Console.WriteLine("Exit Code: " + proc.ExitCode);
Assembly a = Assembly.Load(fileName);
Type BruteForceSums = a.GetType("Programming_CSharp.BruteForceSums");
object o = Activator.CreateInstance(BruteForceSums);
theComputer = (Programming_CSharp.IComputer)o;
}
IComputer theComputer = null;
}
public class TestDriver
{
public static void Main( )
{
const int val = 10000; // 1..200
const int iterations = 50;
double result = 0;
// run the benchmark
MyMath m = new MyMath( );
DateTime startTime = DateTime.Now;
for (int i = 0;i < iterations;i++)
{
result = m.DoSumLooping(val);
}
TimeSpan elapsed =
DateTime.Now - startTime;
Console.WriteLine(
"Sum of ({0}) = {1}",val, result);
Console.WriteLine(
"Looping. Elapsed milliseconds: " +
elapsed.TotalMilliseconds +
" for {0} iterations", iterations);
// run our reflection alternative
ReflectionTest t = new ReflectionTest( );
startTime = DateTime.Now;
for (int i = 0;i < iterations;i++)
{
result = t.DoSum(val);
}
elapsed = DateTime.Now - startTime;
Console.WriteLine(
"Sum of ({0}) = {1}",val, result);
Console.WriteLine(
"Brute Force. Elapsed milliseconds: " +
elapsed.TotalMilliseconds +
" for {0} iterations", iterations);
result = m.CheckMyResults();
Console.WriteLine(
"Checking brute force: Sum of ({0}) = {1}",10000, result);
Console.ReadLine();
}
}
}
Jul 21 '05 #18

P: n/a
A couple of ideas:
1) From the screenshot, I noticed "Exit Code: 1". It's not obvious where
it's coming from but if it's coming from csc.exe that means your program
didn't compile and you are running an old version. This would lead me to
believe the following is happening: The last program that compiled fine
correctly yielded a result of 5050, then you added more +'s to your
statement and the program stopped compiling. Check compile.out.
2) You are using a /optimize+ switch. Could that switch be mangling the code
and everyone else in the ns is testing without this switch?

- Santiago

"Mountain Bikn' Guy" <vc@attbi.com> wrote in message
news:CfWjb.796759$YN5.792640@sccrnsc01...
Here's a screen shot showing my results:

The first write line is for the loop. Then we see the statement that
compiles the runtime generated code (the brute force unrolled loop code).
Then we see the results -- the answer is 5050, which is obviously incorrect. And it's the exact same code I posted -- the code that you used to get the
correct result of 50005000. The only difference is the use of reflection.
The final Console.Writeline statment in the screen shot shows the same code again, but this time not executed with reflection. Now I also get the
correct answer.

I suspect that the line of runtime generated code is too long. I don't know yet, but that's my immediate guess.

Thanks again for the replies. They have helped me refine my search for the
solution.

Dave

"William Ryan" <do********@comcast.nospam.net> wrote in message
news:%2****************@tk2msftngp13.phx.gbl...
I'm using Win2000Pro, VS2003, 1 gig or Ram (man you are lucky) and only one
processor. I've done it on an older machine as well, and I'm getting the
right results..not really sure what it can be, but definitely interested

in
finding out.
"Mountain Bikn' Guy" <vc@attbi.com> wrote in message
news:hUVjb.796541$YN5.793655@sccrnsc01...
Wow, that's interesting. And I appreciate you checking the code I

pasted.
I
get 50005000 in Excel and the same with the loop. When I run the

unrolled code I always get 5050. If you aren't reproducing the problem, and the

code
I pasted gave you correct results, then maybe the problem is related to my
machine or my installation of the framework... very strange. (BTW, I'm

doing
this on a dual Xeon with 4GB of RAM and VS.NET 2003 on W2K).

Any other comments are appreciated.

"William Ryan" <do********@comcast.nospam.net> wrote in message
news:eO**************@TK2MSFTNGP10.phx.gbl...
> Ok, I just ran it and after my IDE finished choking, I'm getting

50005000
> whether I loop through it or use your code. That is the same number

Excel
> is giving me.
>
> Are you getting 50005000 in your computations? From this machine,
it looks
> like it's working correctly.
> "Mountain Bikn' Guy" <vc@attbi.com> wrote in message
> news:tuVjb.806880$uu5.142280@sccrnsc04...
> > Yes, I'm positive. I will post the exact code. Here is the test

anyone can
> > do:
> > 1. paste this code, compile and run. Check the result.
> > 2. Use Excel and do the same thing and compare the result. In Excel, > simply
> > enter 1 on row 1 and 2 on row 2, then copy down to 10000 (or whatever size
> > you wish). Then use the sum function to get the sum. You will see that the
> > C# code is vastly in error.
> >
> > Here's the code (sorry, but it's long):



Jul 21 '05 #19

P: n/a
Hi Santiago,
Thanks for your message. I found the solution. It's posted at the end of
this thread. The only thing I didn't figure out yet is why compile.out
didn't contain any error messages.
Dave

"Santiago" <replytonewsgroup> wrote in message
news:%2****************@TK2MSFTNGP12.phx.gbl...
A couple of ideas:
1) From the screenshot, I noticed "Exit Code: 1". It's not obvious where
it's coming from but if it's coming from csc.exe that means your program
didn't compile and you are running an old version. This would lead me to
believe the following is happening: The last program that compiled fine
correctly yielded a result of 5050, then you added more +'s to your
statement and the program stopped compiling. Check compile.out.
2) You are using a /optimize+ switch. Could that switch be mangling the code and everyone else in the ns is testing without this switch?

- Santiago

"Mountain Bikn' Guy" <vc@attbi.com> wrote in message
news:CfWjb.796759$YN5.792640@sccrnsc01...
Here's a screen shot showing my results:

The first write line is for the loop. Then we see the statement that
compiles the runtime generated code (the brute force unrolled loop code).
Then we see the results -- the answer is 5050, which is obviously

incorrect.
And it's the exact same code I posted -- the code that you used to get the correct result of 50005000. The only difference is the use of reflection. The final Console.Writeline statment in the screen shot shows the same

code
again, but this time not executed with reflection. Now I also get the
correct answer.

I suspect that the line of runtime generated code is too long. I don't

know
yet, but that's my immediate guess.

Thanks again for the replies. They have helped me refine my search for the solution.

Dave

"William Ryan" <do********@comcast.nospam.net> wrote in message
news:%2****************@tk2msftngp13.phx.gbl...
I'm using Win2000Pro, VS2003, 1 gig or Ram (man you are lucky) and only
one
processor. I've done it on an older machine as well, and I'm getting the right results..not really sure what it can be, but definitely
interested in
finding out.
"Mountain Bikn' Guy" <vc@attbi.com> wrote in message
news:hUVjb.796541$YN5.793655@sccrnsc01...
> Wow, that's interesting. And I appreciate you checking the code I

pasted.
I
> get 50005000 in Excel and the same with the loop. When I run the

unrolled
> code I always get 5050. If you aren't reproducing the problem, and
the code
> I pasted gave you correct results, then maybe the problem is related

to
my
> machine or my installation of the framework... very strange. (BTW, I'm doing
> this on a dual Xeon with 4GB of RAM and VS.NET 2003 on W2K).
>
> Any other comments are appreciated.
>
> "William Ryan" <do********@comcast.nospam.net> wrote in message
> news:eO**************@TK2MSFTNGP10.phx.gbl...
> > Ok, I just ran it and after my IDE finished choking, I'm getting
50005000
> > whether I loop through it or use your code. That is the same number Excel
> > is giving me.
> >
> > Are you getting 50005000 in your computations? From this machine,

it > looks
> > like it's working correctly.
> > "Mountain Bikn' Guy" <vc@attbi.com> wrote in message
> > news:tuVjb.806880$uu5.142280@sccrnsc04...
> > > Yes, I'm positive. I will post the exact code. Here is the test

anyone
> can
> > > do:
> > > 1. paste this code, compile and run. Check the result.
> > > 2. Use Excel and do the same thing and compare the result. In Excel, > > simply
> > > enter 1 on row 1 and 2 on row 2, then copy down to 10000 (or

whatever
> size
> > > you wish). Then use the sum function to get the sum. You will

see that
> the
> > > C# code is vastly in error.
> > >
> > > Here's the code (sorry, but it's long):
>
>



Jul 21 '05 #20

P: n/a
Good insight -- that was exactly the problem (but it was covered up because
I was using reflection techniques to generate/compile/load and run the
code). See my last message at the end of this thread.
Dave

"memememe" <[rem]casolorz[rem]@hot[rem]mail.com> wrote in message
news:sLVjb.14449$iq3.7768@okepread01...
maybe there is some sort of limit on the ammount of +s and length of your
line, have you tried splitting it on small chunks?
"Mountain Bikn' Guy" <vc@attbi.com> wrote in message
news:NZUjb.795942$YN5.793228@sccrnsc01...
Take some standard code such as shown below. It simply loops to add up a
series of terms and it produces the correct result.

// sum numbers with a loop
public int DoSumLooping(int iterations)
{
int result = 0;
for(int i = 1;i <=iterations;i++)
{
result += i;
}
return result;
}

Now translate this into a specific solution that doesn't use looping (and use the same value for the number of iterations the loop performs). This
code returns an incorrect result. The method consists entirely of a very
straightforward code statement, but in this case .NET adds the numbers
incorrectly.
public double ComputeSum( )
{
// Brute force sum method
// For iterations == 10000
double sum = 0+ 1+ 2+ 3+ 4+ 5+ 6+ 7+ 8+ 9+ 10+ 11+ 12+ 13+ 14+ 15+ ...
+ 9997+ 9998+ 9999+ 10000;
return sum;
}
The above method returns an incorrect result with any number of terms

above
about 200. It will correctly add 1 + 2 + ... + 200, but it will NOT
correctly add 1 + 2 + ... + 1000.

I have just run across this, and I have not yet researched the possible
reasons for this behavior. It may be a known issue related to either stack size or the length of a code line, but to my knowledge it hasn't been
discussed in any of the "popular" literature on C# and .NET. I need to

write
code like this, so if anyone has already encountered this issue, please
advise me.
Here's another example that also creates problems, but of a somewhat
different nature. Take the following code and translate it into a

specific,
non-looping method and try to execute it using reflection. It fails.

public double LoopToCompute()
{
double sumOfProducts = 0;
double grandTotal = 0;
for (int i = 0; i < maxRows; ++i)
{
for (int j = 0; j < maxCols; ++j)
{
sumOfProducts += coeff[j] * table[i][j];
}
a_point[i] = sumOfProducts;
grandTotal += sumOfProducts;
sumOfProducts = 0;
}
return grandTotal;
}//LoopToCompute

The above code works -- but it's equivalent code with loops unrolled

(shown
below) doesn't work unless the maxRows is set very small. For small

values,
the 2 methods (above and below) produce identical results. There is

nothing
"wrong" with the code in that sense. It's similar to the above situation. If
the "size" of the code statement or the number of code statements is too
large, .NET fails. In this case (using reflection) it doesn't return the
incorrect result, as the first example did. In this case, reflection

calls it an invalid program and refuses to run it (but only when the value of
maxRows is above about 250). The reason for this is probably
straightforward. However, I have the need to make statements like this for performance reasons so I need a work-around. Any suggestions are
appreciated! All comments are appreciated.

public double DoBruteForceCompute()
{
double bruteForceSum = 0;

point1=coeff1*table[0][0] +coeff2*table[0][1] +coeff3*table[0][2]
+coeff4*table[0][3] +coeff5*table[0][4] +coeff6*table[0][5]
+coeff7*table[0][6] +coeff8*table[0][7] +coeff9*table[0][8]
+coeff10*table[0][9] +coeff11*table[0][10] +coeff12*table[0][11]
+coeff13*table[0][12] +coeff14*table[0][13] +coeff15*table[0][14]
+coeff16*table[0][15] +coeff17*table[0][16] +coeff18*table[0][17]
+coeff19*table[0][18] +coeff20*table[0][19] +coeff21*table[0][20]
+coeff22*table[0][21] +coeff23*table[0][22] +coeff24*table[0][23]
+coeff25*table[0][24] +coeff26*table[0][25] +coeff27*table[0][26]
+coeff28*table[0][27] +coeff29*table[0][28] +coeff30*table[0][29]
+coeff31*table[0][30] +coeff32*table[0][31] +coeff33*table[0][32]
+coeff34*table[0][33] +coeff35*table[0][34] ;

point2=coeff1*table[1][0] +coeff2*table[1][1] +coeff3*table[1][2]
+coeff4*table[1][3] +coeff5*table[1][4] +coeff6*table[1][5]
+coeff7*table[1][6] +coeff8*table[1][7] +coeff9*table[1][8]
+coeff10*table[1][9] +coeff11*table[1][10] +coeff12*table[1][11]
+coeff13*table[1][12] +coeff14*table[1][13] +coeff15*table[1][14]
+coeff16*table[1][15] +coeff17*table[1][16] +coeff18*table[1][17]
+coeff19*table[1][18] +coeff20*table[1][19] +coeff21*table[1][20]
+coeff22*table[1][21] +coeff23*table[1][22] +coeff24*table[1][23]
+coeff25*table[1][24] +coeff26*table[1][25] +coeff27*table[1][26]
+coeff28*table[1][27] +coeff29*table[1][28] +coeff30*table[1][29]
+coeff31*table[1][30] +coeff32*table[1][31] +coeff33*table[1][32]
+coeff34*table[1][33] +coeff35*table[1][34] ;
[...]

point500=coeff1*table[499][0] +coeff2*table[499][1] +coeff3*table[499][2] +coeff4*table[499][3] +coeff5*table[499][4] +coeff6*table[499][5]
+coeff7*table[499][6] +coeff8*table[499][7] +coeff9*table[499][8]
+coeff10*table[499][9] +coeff11*table[499][10] +coeff12*table[499][11]
+coeff13*table[499][12] +coeff14*table[499][13] +coeff15*table[499][14]
+coeff16*table[499][15] +coeff17*table[499][16] +coeff18*table[499][17]
+coeff19*table[499][18] +coeff20*table[499][19] +coeff21*table[499][20]
+coeff22*table[499][21] +coeff23*table[499][22] +coeff24*table[499][23]
+coeff25*table[499][24] +coeff26*table[499][25] +coeff27*table[499][26]
+coeff28*table[499][27] +coeff29*table[499][28] +coeff30*table[499][29]
+coeff31*table[499][30] +coeff32*table[499][31] +coeff33*table[499][32]
+coeff34*table[499][33] +coeff35*table[499][34] ;

bruteForceSum =
point1 +
point2 + ... +

point499 +
point500
;

return bruteForceSum;

}//DoBruteForceCompute


Jul 21 '05 #21

P: n/a
Hi Guys,

4GB Ram.
Super speed.
Modern OS.
Ultra-modern compiler.

Doh! Of course there's an arbitrary small liimit somewhere. ;-))

Regards,
Fergus
Jul 21 '05 #22

P: n/a
Anyone have any ideas why the following code "is not a valid program". It
compiles fine, but the runtime refuses to run it. I apologize for it being a
bit long (but I did cut out 497 of the 500 statement lines in the method).
FYI, this is part 2 of my initial question in this thread (and in this case,
the statement lines are not longer than the limit).
Thanks.
Dave

public double DoBruteForceCompute()
{
double bruteForceSum = 0;

point1=coeff1*table[0][0] +coeff2*table[0][1] +coeff3*table[0][2]
+coeff4*table[0][3] +coeff5*table[0][4] +coeff6*table[0][5]
+coeff7*table[0][6] +coeff8*table[0][7] +coeff9*table[0][8]
+coeff10*table[0][9] +coeff11*table[0][10] +coeff12*table[0][11]
+coeff13*table[0][12] +coeff14*table[0][13] +coeff15*table[0][14]
+coeff16*table[0][15] +coeff17*table[0][16] +coeff18*table[0][17]
+coeff19*table[0][18] +coeff20*table[0][19] +coeff21*table[0][20]
+coeff22*table[0][21] +coeff23*table[0][22] +coeff24*table[0][23]
+coeff25*table[0][24] +coeff26*table[0][25] +coeff27*table[0][26]
+coeff28*table[0][27] +coeff29*table[0][28] +coeff30*table[0][29]
+coeff31*table[0][30] +coeff32*table[0][31] +coeff33*table[0][32]
+coeff34*table[0][33] +coeff35*table[0][34] ;

point2=coeff1*table[1][0] +coeff2*table[1][1] +coeff3*table[1][2]
+coeff4*table[1][3] +coeff5*table[1][4] +coeff6*table[1][5]
+coeff7*table[1][6] +coeff8*table[1][7] +coeff9*table[1][8]
+coeff10*table[1][9] +coeff11*table[1][10] +coeff12*table[1][11]
+coeff13*table[1][12] +coeff14*table[1][13] +coeff15*table[1][14]
+coeff16*table[1][15] +coeff17*table[1][16] +coeff18*table[1][17]
+coeff19*table[1][18] +coeff20*table[1][19] +coeff21*table[1][20]
+coeff22*table[1][21] +coeff23*table[1][22] +coeff24*table[1][23]
+coeff25*table[1][24] +coeff26*table[1][25] +coeff27*table[1][26]
+coeff28*table[1][27] +coeff29*table[1][28] +coeff30*table[1][29]
+coeff31*table[1][30] +coeff32*table[1][31] +coeff33*table[1][32]
+coeff34*table[1][33] +coeff35*table[1][34] ;
[...]

point500=coeff1*table[499][0] +coeff2*table[499][1] +coeff3*table[499][2]
+coeff4*table[499][3] +coeff5*table[499][4] +coeff6*table[499][5]
+coeff7*table[499][6] +coeff8*table[499][7] +coeff9*table[499][8]
+coeff10*table[499][9] +coeff11*table[499][10] +coeff12*table[499][11]
+coeff13*table[499][12] +coeff14*table[499][13] +coeff15*table[499][14]
+coeff16*table[499][15] +coeff17*table[499][16] +coeff18*table[499][17]
+coeff19*table[499][18] +coeff20*table[499][19] +coeff21*table[499][20]
+coeff22*table[499][21] +coeff23*table[499][22] +coeff24*table[499][23]
+coeff25*table[499][24] +coeff26*table[499][25] +coeff27*table[499][26]
+coeff28*table[499][27] +coeff29*table[499][28] +coeff30*table[499][29]
+coeff31*table[499][30] +coeff32*table[499][31] +coeff33*table[499][32]
+coeff34*table[499][33] +coeff35*table[499][34] ;

bruteForceSum =
point1 +
point2 + ... +

point500
;

return bruteForceSum;

}//DoBruteForceCompute
"Jon Skeet [C# MVP]" <sk***@pobox.com> wrote in message
news:MP************************@msnews.microsoft.c om...
[Removed microsoft.public.dotnet.csharp.general which isn't a valid
group, at least not on the MS server.]

Mountain Bikn' Guy <vc@attbi.com> wrote:
Take some standard code such as shown below. It simply loops to add up a
series of terms and it produces the correct result.

// sum numbers with a loop
public int DoSumLooping(int iterations)
{
int result = 0;
for(int i = 1;i <=iterations;i++)
{
result += i;
}
return result;
}

Now translate this into a specific solution that doesn't use looping (and use the same value for the number of iterations the loop performs). This
code returns an incorrect result.


Not for me it doesn't (going up to 10000). Could you produce a
*complete* example somewhere which gives the incorrect result, either
posting it or giving a link to it on the web?

--
Jon Skeet - <sk***@pobox.com>
http://www.pobox.com/~skeet
If replying to the group, please do not mail me too

Jul 21 '05 #23

P: n/a
P.S. I forgot to mention that the problem is related to the number of
statements in the method. 1000 doesn't work. I think it works up to a few
hundred statements, then stops being "a valid program," according to the
runtime. The compiler never complains.
Jul 21 '05 #24

P: n/a
Mountain Bikn' Guy <vc@attbi.com> wrote:
Anyone have any ideas why the following code "is not a valid program". It
compiles fine, but the runtime refuses to run it. I apologize for it being a
bit long (but I did cut out 497 of the 500 statement lines in the method).
FYI, this is part 2 of my initial question in this thread (and in this case,
the statement lines are not longer than the limit).


<snip>

Presumably you do actually still *have* the full version around? I
appreciate it would be too long to post, but could you mail it to me or
put it on a website? It's easier to test that way :)

If you could make it a full program that we could just compile as-is
and then run, that would be great.

--
Jon Skeet - <sk***@pobox.com>
http://www.pobox.com/~skeet
If replying to the group, please do not mail me too
Jul 21 '05 #25

P: n/a
Hi Dave,

Breaks at 1000 per method?

There's the 'why' and there's the 'what to do about it'.

Here's a possibility for the latter:

public double DoBruteForceCompute_Part_01()

public double DoBruteForceCompute_Part_02()
: : :
public double DoBruteForceCompute_Part_NN()

.. where each gets, say, a mere 250.

Regards,
Fergus
Jul 21 '05 #26

P: n/a
Jon,
I will email it to you. Thanks for you interest.
If people wish, I'll also post it, but it IS long.
Dave

"Jon Skeet [C# MVP]" <sk***@pobox.com> wrote in message
news:MP************************@msnews.microsoft.c om...
Mountain Bikn' Guy <vc@attbi.com> wrote:
Anyone have any ideas why the following code "is not a valid program". It compiles fine, but the runtime refuses to run it. I apologize for it being a bit long (but I did cut out 497 of the 500 statement lines in the method). FYI, this is part 2 of my initial question in this thread (and in this case, the statement lines are not longer than the limit).


<snip>

Presumably you do actually still *have* the full version around? I
appreciate it would be too long to post, but could you mail it to me or
put it on a website? It's easier to test that way :)

If you could make it a full program that we could just compile as-is
and then run, that would be great.

--
Jon Skeet - <sk***@pobox.com>
http://www.pobox.com/~skeet
If replying to the group, please do not mail me too

Jul 21 '05 #27

P: n/a
how about....... putting it into a briefcase... or something like
that...... so those of us that subscribe to the board... don't pull it
down.. unless we want it..... then lost the location ?

"Mountain Bikn' Guy" <vc@attbi.com> wrote in message
news:qIekb.171193$%h1.163241@sccrnsc02...
Jon,
I will email it to you. Thanks for you interest.
If people wish, I'll also post it, but it IS long.
Dave

"Jon Skeet [C# MVP]" <sk***@pobox.com> wrote in message
news:MP************************@msnews.microsoft.c om...
Mountain Bikn' Guy <vc@attbi.com> wrote:
Anyone have any ideas why the following code "is not a valid program". It compiles fine, but the runtime refuses to run it. I apologize for it being a bit long (but I did cut out 497 of the 500 statement lines in the method). FYI, this is part 2 of my initial question in this thread (and in this case, the statement lines are not longer than the limit).


<snip>

Presumably you do actually still *have* the full version around? I
appreciate it would be too long to post, but could you mail it to me or
put it on a website? It's easier to test that way :)

If you could make it a full program that we could just compile as-is
and then run, that would be great.

--
Jon Skeet - <sk***@pobox.com>
http://www.pobox.com/~skeet
If replying to the group, please do not mail me too


Jul 21 '05 #28

P: n/a
I hope the zip file I attached to my other message is OK. If not, let me
know and I'll try something else.

"Steve S" <be*********@hotmail.com> wrote in message
news:eP**************@tk2msftngp13.phx.gbl...
how about....... putting it into a briefcase... or something like
that...... so those of us that subscribe to the board... don't pull it
down.. unless we want it..... then lost the location ?

"Mountain Bikn' Guy" <vc@attbi.com> wrote in message
news:qIekb.171193$%h1.163241@sccrnsc02...
Jon,
I will email it to you. Thanks for you interest.
If people wish, I'll also post it, but it IS long.
Dave


Jul 21 '05 #29

P: n/a
This link is interesting

http://groups.google.com/groups?hl=e...p09%26rnum%3D3

You can also get to the same place by searching Google Groups on "Common
Language Runtime detected an invalid program" if that URI is too long.

The little block of code posted back in 2002 still causes a compiler error
in VS 2003. Here it is:

I wrote this piece of code in the main method of a console application.

int myInteger = 5;
goto addval;
writeresult:
{
Console.WriteLine("My Integer = {0}", myInteger);
if (myInteger == 15)
{
goto Finish;
}
}

addval:
{
myInteger += 10;
goto writeresult;
}

Finish:
{
Console.WriteLine("End of Code");
}

"Mountain Bikn' Guy" <vc@attbi.com> wrote in message
news:OOfkb.812318$Ho3.221223@sccrnsc03...
Attached is a 137kb zip file (the "unrolled" code file alone is over 1MB!). It contains the full version of the program that shows more "arbitrary
limits" in .NET. (At least I think that's what it shows. Hopefully, it will just show that I made a stupid mistake somewhere and we won't have to
discover more arbitrary limits ;)

There is a method that unrolls some looping code. If the loop iterates 500
times, the unrolled method contains 500 statements. It runs fine.

However, if we go up to 1000 iterations/statements, I get the following
fatal exception:

Additional information: Common Language Runtime detected an invalid program.
I built my little test app using several Infragistics controls (toolbar,
grid, etc.). I jerked these out before posting this message. If anyone finds any problem in the code, let me know and I'll fix it. Thanks.
Dave

Jul 21 '05 #30

P: n/a
Jon,
I'm becoming convinced this issue is a compiler bug. I'm curious what you or
others find:
can you reproduce it using my code?
is there a work around (with equivalent performance advantages)?
is the bug present in both VS.NET 2002 and 2003?
Regards,
Dave

"Jon Skeet [C# MVP]" <sk***@pobox.com> wrote in message
news:MP************************@msnews.microsoft.c om...
Mountain Bikn' Guy <vc@attbi.com> wrote:
Anyone have any ideas why the following code "is not a valid program". It compiles fine, but the runtime refuses to run it. I apologize for it being a bit long (but I did cut out 497 of the 500 statement lines in the method). FYI, this is part 2 of my initial question in this thread (and in this case, the statement lines are not longer than the limit).


<snip>

Presumably you do actually still *have* the full version around? I
appreciate it would be too long to post, but could you mail it to me or
put it on a website? It's easier to test that way :)

If you could make it a full program that we could just compile as-is
and then run, that would be great.

--
Jon Skeet - <sk***@pobox.com>
http://www.pobox.com/~skeet
If replying to the group, please do not mail me too

Jul 21 '05 #31

P: n/a
Mountain Bikn' Guy <vc@attbi.com> wrote:
I'm becoming convinced this issue is a compiler bug. I'm curious what you or
others find:
can you reproduce it using my code?
Yup.
is there a work around (with equivalent performance advantages)?
is the bug present in both VS.NET 2002 and 2003?


I suspect it's actually in the framework itself (which is where the
guts of the compiler is) rather than VS.NET itself.

Is the simple looping code definitely too slow for your needs?

--
Jon Skeet - <sk***@pobox.com>
http://www.pobox.com/~skeet
If replying to the group, please do not mail me too
Jul 21 '05 #32

P: n/a
In the event anyone wishes to review this thread now or later, I thought I
would provide some conclusions that resulted from everyone's input and from
my reading:

1. unrolling loops often doesn't provide a performance gain on large (real
life size?) problems. In my experience, the unrolled loop was 5-10 times
SLOWER than the simple nested loop that I used as a reference. I found the
following quote in Eric Gunnerson's book (2nd ed). He said (about unrolled
loops), a "function is so big it doesn't fit into cache and therefore gets
slower performance."

Jon added the following info:
I suspect he means the processor's instruction
cache - if it's a small loop, the processor (not JIT, note!) can decode
the instructions once and keep the microcode available for further
iterations.

2. VS.NET has a 2048 char line limit in code files. In my experience, when
using runtime code generation and compiling, this can cause unusual trouble
if one isn't aware of it. I was able to compile and run an application that
was created from a code file with a line longer than this limit. The only
error I encountered was that the mathematical expression in the executing
program returned incorrect results! (The fix was simply inserting line
breaks into the code file.)

3. VS.NET has some compiler bugs that will result in the following error
message:
Additional information: Common Language Runtime detected an invalid program.

This appears to happen on complex mathematical expressions. However, in my
case the expression itself was not that complex. It was just long (but each
line wasn't too long). When I reached about 1000 subexpressions in a simple
sum of products expression, I encountered this compiler bug. Search on
Google Groups using the error message, and you'll see that others have
encountered it (frequently) when dealing with complex mathematical
expressions.

To my knowledge, there is no solution for this. Anyone from Microsoft care
to comment?

That about sums up (no pun intended) what I've learned so far. HTH.
Dave
"Mountain Bikn' Guy" <vc@attbi.com> wrote in message
news:NZUjb.795942$YN5.793228@sccrnsc01...
Take some standard code such as shown below. It simply loops to add up a
series of terms and it produces the correct result.

// sum numbers with a loop
public int DoSumLooping(int iterations)
{
int result = 0;
for(int i = 1;i <=iterations;i++)
{
result += i;
}
return result;
}

Now translate this into a specific solution that doesn't use looping (and
use the same value for the number of iterations the loop performs). This
code returns an incorrect result. The method consists entirely of a very
straightforward code statement, but in this case .NET adds the numbers
incorrectly.
public double ComputeSum( )
{
// Brute force sum method
// For iterations == 10000
double sum = 0+ 1+ 2+ 3+ 4+ 5+ 6+ 7+ 8+ 9+ 10+ 11+ 12+ 13+ 14+ 15+ .... + 9997+ 9998+ 9999+ 10000;
return sum;
}
The above method returns an incorrect result with any number of terms above about 200. It will correctly add 1 + 2 + ... + 200, but it will NOT
correctly add 1 + 2 + ... + 1000.

I have just run across this, and I have not yet researched the possible
reasons for this behavior. It may be a known issue related to either stack
size or the length of a code line, but to my knowledge it hasn't been
discussed in any of the "popular" literature on C# and .NET. I need to write code like this, so if anyone has already encountered this issue, please
advise me.
Here's another example that also creates problems, but of a somewhat
different nature. Take the following code and translate it into a specific, non-looping method and try to execute it using reflection. It fails.

public double LoopToCompute()
{
double sumOfProducts = 0;
double grandTotal = 0;
for (int i = 0; i < maxRows; ++i)
{
for (int j = 0; j < maxCols; ++j)
{
sumOfProducts += coeff[j] * table[i][j];
}
a_point[i] = sumOfProducts;
grandTotal += sumOfProducts;
sumOfProducts = 0;
}
return grandTotal;
}//LoopToCompute

The above code works -- but it's equivalent code with loops unrolled (shown below) doesn't work unless the maxRows is set very small. For small values, the 2 methods (above and below) produce identical results. There is nothing "wrong" with the code in that sense. It's similar to the above situation. If the "size" of the code statement or the number of code statements is too
large, .NET fails. In this case (using reflection) it doesn't return the
incorrect result, as the first example did. In this case, reflection calls
it an invalid program and refuses to run it (but only when the value of
maxRows is above about 250). The reason for this is probably
straightforward. However, I have the need to make statements like this for
performance reasons so I need a work-around. Any suggestions are
appreciated! All comments are appreciated.

public double DoBruteForceCompute()
{
double bruteForceSum = 0;

point1=coeff1*table[0][0] +coeff2*table[0][1] +coeff3*table[0][2]
+coeff4*table[0][3] +coeff5*table[0][4] +coeff6*table[0][5]
+coeff7*table[0][6] +coeff8*table[0][7] +coeff9*table[0][8]
+coeff10*table[0][9] +coeff11*table[0][10] +coeff12*table[0][11]
+coeff13*table[0][12] +coeff14*table[0][13] +coeff15*table[0][14]
+coeff16*table[0][15] +coeff17*table[0][16] +coeff18*table[0][17]
+coeff19*table[0][18] +coeff20*table[0][19] +coeff21*table[0][20]
+coeff22*table[0][21] +coeff23*table[0][22] +coeff24*table[0][23]
+coeff25*table[0][24] +coeff26*table[0][25] +coeff27*table[0][26]
+coeff28*table[0][27] +coeff29*table[0][28] +coeff30*table[0][29]
+coeff31*table[0][30] +coeff32*table[0][31] +coeff33*table[0][32]
+coeff34*table[0][33] +coeff35*table[0][34] ;

point2=coeff1*table[1][0] +coeff2*table[1][1] +coeff3*table[1][2]
+coeff4*table[1][3] +coeff5*table[1][4] +coeff6*table[1][5]
+coeff7*table[1][6] +coeff8*table[1][7] +coeff9*table[1][8]
+coeff10*table[1][9] +coeff11*table[1][10] +coeff12*table[1][11]
+coeff13*table[1][12] +coeff14*table[1][13] +coeff15*table[1][14]
+coeff16*table[1][15] +coeff17*table[1][16] +coeff18*table[1][17]
+coeff19*table[1][18] +coeff20*table[1][19] +coeff21*table[1][20]
+coeff22*table[1][21] +coeff23*table[1][22] +coeff24*table[1][23]
+coeff25*table[1][24] +coeff26*table[1][25] +coeff27*table[1][26]
+coeff28*table[1][27] +coeff29*table[1][28] +coeff30*table[1][29]
+coeff31*table[1][30] +coeff32*table[1][31] +coeff33*table[1][32]
+coeff34*table[1][33] +coeff35*table[1][34] ;
[...]

point500=coeff1*table[499][0] +coeff2*table[499][1] +coeff3*table[499][2]
+coeff4*table[499][3] +coeff5*table[499][4] +coeff6*table[499][5]
+coeff7*table[499][6] +coeff8*table[499][7] +coeff9*table[499][8]
+coeff10*table[499][9] +coeff11*table[499][10] +coeff12*table[499][11]
+coeff13*table[499][12] +coeff14*table[499][13] +coeff15*table[499][14]
+coeff16*table[499][15] +coeff17*table[499][16] +coeff18*table[499][17]
+coeff19*table[499][18] +coeff20*table[499][19] +coeff21*table[499][20]
+coeff22*table[499][21] +coeff23*table[499][22] +coeff24*table[499][23]
+coeff25*table[499][24] +coeff26*table[499][25] +coeff27*table[499][26]
+coeff28*table[499][27] +coeff29*table[499][28] +coeff30*table[499][29]
+coeff31*table[499][30] +coeff32*table[499][31] +coeff33*table[499][32]
+coeff34*table[499][33] +coeff35*table[499][34] ;

bruteForceSum =
point1 +
point2 + ... +

point499 +
point500
;

return bruteForceSum;

}//DoBruteForceCompute

Jul 21 '05 #33

P: n/a
I think I found the right balance:
Instead of using a nested loop, I unroll the inner loop but leave the outer
loop. This has resulted in the best performance so far (and it doesn't cause
any of the issues/bugs and have been discussed in this thread).

Thanks for all your replies.

Dave
"Jon Skeet [C# MVP]" <sk***@pobox.com> wrote in message
news:MP************************@msnews.microsoft.c om...
Mountain Bikn' Guy <vc@attbi.com> wrote:
I'm becoming convinced this issue is a compiler bug. I'm curious what you or others find:
can you reproduce it using my code?


Yup.
is there a work around (with equivalent performance advantages)?
is the bug present in both VS.NET 2002 and 2003?


I suspect it's actually in the framework itself (which is where the
guts of the compiler is) rather than VS.NET itself.

Is the simple looping code definitely too slow for your needs?

--
Jon Skeet - <sk***@pobox.com>
http://www.pobox.com/~skeet
If replying to the group, please do not mail me too

Jul 21 '05 #34

P: n/a
Did you make these unrolled loops manually or did you use a CodeDom to
generate them?

Curious.

Why do it the hard way:D
"Mountain Bikn' Guy" <vc@attbi.com> wrote in message
news:RAblb.196435$%h1.190498@sccrnsc02...
In the event anyone wishes to review this thread now or later, I thought I
would provide some conclusions that resulted from everyone's input and from my reading:

1. unrolling loops often doesn't provide a performance gain on large (real
life size?) problems. In my experience, the unrolled loop was 5-10 times
SLOWER than the simple nested loop that I used as a reference. I found the
following quote in Eric Gunnerson's book (2nd ed). He said (about unrolled
loops), a "function is so big it doesn't fit into cache and therefore gets
slower performance."

Jon added the following info:
I suspect he means the processor's instruction
cache - if it's a small loop, the processor (not JIT, note!) can decode
the instructions once and keep the microcode available for further
iterations.

2. VS.NET has a 2048 char line limit in code files. In my experience, when
using runtime code generation and compiling, this can cause unusual trouble if one isn't aware of it. I was able to compile and run an application that was created from a code file with a line longer than this limit. The only
error I encountered was that the mathematical expression in the executing
program returned incorrect results! (The fix was simply inserting line
breaks into the code file.)

3. VS.NET has some compiler bugs that will result in the following error
message:
Additional information: Common Language Runtime detected an invalid program.
This appears to happen on complex mathematical expressions. However, in my
case the expression itself was not that complex. It was just long (but each line wasn't too long). When I reached about 1000 subexpressions in a simple sum of products expression, I encountered this compiler bug. Search on
Google Groups using the error message, and you'll see that others have
encountered it (frequently) when dealing with complex mathematical
expressions.

To my knowledge, there is no solution for this. Anyone from Microsoft care
to comment?

That about sums up (no pun intended) what I've learned so far. HTH.
Dave
"Mountain Bikn' Guy" <vc@attbi.com> wrote in message
news:NZUjb.795942$YN5.793228@sccrnsc01...
Take some standard code such as shown below. It simply loops to add up a
series of terms and it produces the correct result.

// sum numbers with a loop
public int DoSumLooping(int iterations)
{
int result = 0;
for(int i = 1;i <=iterations;i++)
{
result += i;
}
return result;
}

Now translate this into a specific solution that doesn't use looping (and use the same value for the number of iterations the loop performs). This
code returns an incorrect result. The method consists entirely of a very
straightforward code statement, but in this case .NET adds the numbers
incorrectly.
public double ComputeSum( )
{
// Brute force sum method
// For iterations == 10000
double sum = 0+ 1+ 2+ 3+ 4+ 5+ 6+ 7+ 8+ 9+ 10+ 11+ 12+ 13+ 14+ 15+ ...
+ 9997+ 9998+ 9999+ 10000;
return sum;
}
The above method returns an incorrect result with any number of terms

above
about 200. It will correctly add 1 + 2 + ... + 200, but it will NOT
correctly add 1 + 2 + ... + 1000.

I have just run across this, and I have not yet researched the possible
reasons for this behavior. It may be a known issue related to either stack size or the length of a code line, but to my knowledge it hasn't been
discussed in any of the "popular" literature on C# and .NET. I need to

write
code like this, so if anyone has already encountered this issue, please
advise me.
Here's another example that also creates problems, but of a somewhat
different nature. Take the following code and translate it into a

specific,
non-looping method and try to execute it using reflection. It fails.

public double LoopToCompute()
{
double sumOfProducts = 0;
double grandTotal = 0;
for (int i = 0; i < maxRows; ++i)
{
for (int j = 0; j < maxCols; ++j)
{
sumOfProducts += coeff[j] * table[i][j];
}
a_point[i] = sumOfProducts;
grandTotal += sumOfProducts;
sumOfProducts = 0;
}
return grandTotal;
}//LoopToCompute

The above code works -- but it's equivalent code with loops unrolled

(shown
below) doesn't work unless the maxRows is set very small. For small

values,
the 2 methods (above and below) produce identical results. There is

nothing
"wrong" with the code in that sense. It's similar to the above situation. If
the "size" of the code statement or the number of code statements is too
large, .NET fails. In this case (using reflection) it doesn't return the
incorrect result, as the first example did. In this case, reflection

calls it an invalid program and refuses to run it (but only when the value of
maxRows is above about 250). The reason for this is probably
straightforward. However, I have the need to make statements like this for performance reasons so I need a work-around. Any suggestions are
appreciated! All comments are appreciated.

public double DoBruteForceCompute()
{
double bruteForceSum = 0;

point1=coeff1*table[0][0] +coeff2*table[0][1] +coeff3*table[0][2]
+coeff4*table[0][3] +coeff5*table[0][4] +coeff6*table[0][5]
+coeff7*table[0][6] +coeff8*table[0][7] +coeff9*table[0][8]
+coeff10*table[0][9] +coeff11*table[0][10] +coeff12*table[0][11]
+coeff13*table[0][12] +coeff14*table[0][13] +coeff15*table[0][14]
+coeff16*table[0][15] +coeff17*table[0][16] +coeff18*table[0][17]
+coeff19*table[0][18] +coeff20*table[0][19] +coeff21*table[0][20]
+coeff22*table[0][21] +coeff23*table[0][22] +coeff24*table[0][23]
+coeff25*table[0][24] +coeff26*table[0][25] +coeff27*table[0][26]
+coeff28*table[0][27] +coeff29*table[0][28] +coeff30*table[0][29]
+coeff31*table[0][30] +coeff32*table[0][31] +coeff33*table[0][32]
+coeff34*table[0][33] +coeff35*table[0][34] ;

point2=coeff1*table[1][0] +coeff2*table[1][1] +coeff3*table[1][2]
+coeff4*table[1][3] +coeff5*table[1][4] +coeff6*table[1][5]
+coeff7*table[1][6] +coeff8*table[1][7] +coeff9*table[1][8]
+coeff10*table[1][9] +coeff11*table[1][10] +coeff12*table[1][11]
+coeff13*table[1][12] +coeff14*table[1][13] +coeff15*table[1][14]
+coeff16*table[1][15] +coeff17*table[1][16] +coeff18*table[1][17]
+coeff19*table[1][18] +coeff20*table[1][19] +coeff21*table[1][20]
+coeff22*table[1][21] +coeff23*table[1][22] +coeff24*table[1][23]
+coeff25*table[1][24] +coeff26*table[1][25] +coeff27*table[1][26]
+coeff28*table[1][27] +coeff29*table[1][28] +coeff30*table[1][29]
+coeff31*table[1][30] +coeff32*table[1][31] +coeff33*table[1][32]
+coeff34*table[1][33] +coeff35*table[1][34] ;
[...]

point500=coeff1*table[499][0] +coeff2*table[499][1] +coeff3*table[499][2] +coeff4*table[499][3] +coeff5*table[499][4] +coeff6*table[499][5]
+coeff7*table[499][6] +coeff8*table[499][7] +coeff9*table[499][8]
+coeff10*table[499][9] +coeff11*table[499][10] +coeff12*table[499][11]
+coeff13*table[499][12] +coeff14*table[499][13] +coeff15*table[499][14]
+coeff16*table[499][15] +coeff17*table[499][16] +coeff18*table[499][17]
+coeff19*table[499][18] +coeff20*table[499][19] +coeff21*table[499][20]
+coeff22*table[499][21] +coeff23*table[499][22] +coeff24*table[499][23]
+coeff25*table[499][24] +coeff26*table[499][25] +coeff27*table[499][26]
+coeff28*table[499][27] +coeff29*table[499][28] +coeff30*table[499][29]
+coeff31*table[499][30] +coeff32*table[499][31] +coeff33*table[499][32]
+coeff34*table[499][33] +coeff35*table[499][34] ;

bruteForceSum =
point1 +
point2 + ... +

point499 +
point500
;

return bruteForceSum;

}//DoBruteForceCompute


Jul 21 '05 #35

P: n/a
Since you asked...

I could use some help with CodeDOM. Here is how I am generating these loops:

//
//TODO: generate this entire expression using CodeDOM classes:
StringBuilder formulaString = new StringBuilder();
formulaString.Append("dataPoints[row] = 0");
if (columns != null)
{
formulaString.Capacity = 40 * (columns.Count + 2);
for (int j = 0; j < columns.Count; ++j)
{
if ( ((MyColumnType)columns[j]).Role == RoleType.Independent)
{
formulaString.Append(System.Environment.NewLine);
formulaString.Append("+ coefficients[" + j + "] * table[row][" + j + "] ");
}
}
}
formulaString.Append(";");
//

The rest of the stuff (namespace, class, outer for loop, return statement,
etc.) is all generated purely without code snippet expressions (with 1
exception -- see bug below). Anyone want to show me how to do the above
expression without code snippets? (Note the need to break the lines to keep
them below the 2046 char limit.)

The one other issue I am having trouble with is this:

compute.ReturnType = new CodeTypeReference("public float[]"); //suggested
workaround for bug below
compute.Attributes |= MemberAttributes.Public;//has a bug

Is there an easy, language neutral way to work around the
MemberAttributes.Public bug when I return an array?

TIA,
Dave

"anonymouse" <an********@discussions.microsoft.com> wrote in message
news:Ol****************@TK2MSFTNGP12.phx.gbl...
Did you make these unrolled loops manually or did you use a CodeDom to
generate them?

Curious.

Why do it the hard way:D
"Mountain Bikn' Guy" <vc@attbi.com> wrote in message
news:RAblb.196435$%h1.190498@sccrnsc02...
In the event anyone wishes to review this thread now or later, I thought I
would provide some conclusions that resulted from everyone's input and

from
my reading:

1. unrolling loops often doesn't provide a performance gain on large (real life size?) problems. In my experience, the unrolled loop was 5-10 times
SLOWER than the simple nested loop that I used as a reference. I found the following quote in Eric Gunnerson's book (2nd ed). He said (about unrolled loops), a "function is so big it doesn't fit into cache and therefore gets slower performance."

Jon added the following info:
I suspect he means the processor's instruction
cache - if it's a small loop, the processor (not JIT, note!) can decode
the instructions once and keep the microcode available for further
iterations.

2. VS.NET has a 2048 char line limit in code files. In my experience, when using runtime code generation and compiling, this can cause unusual

trouble
if one isn't aware of it. I was able to compile and run an application

that
was created from a code file with a line longer than this limit. The only error I encountered was that the mathematical expression in the executing program returned incorrect results! (The fix was simply inserting line
breaks into the code file.)

3. VS.NET has some compiler bugs that will result in the following error
message:
Additional information: Common Language Runtime detected an invalid

program.

This appears to happen on complex mathematical expressions. However, in my case the expression itself was not that complex. It was just long (but

each
line wasn't too long). When I reached about 1000 subexpressions in a

simple
sum of products expression, I encountered this compiler bug. Search on
Google Groups using the error message, and you'll see that others have
encountered it (frequently) when dealing with complex mathematical
expressions.

To my knowledge, there is no solution for this. Anyone from Microsoft care to comment?

That about sums up (no pun intended) what I've learned so far. HTH.
Dave
"Mountain Bikn' Guy" <vc@attbi.com> wrote in message
news:NZUjb.795942$YN5.793228@sccrnsc01...
Take some standard code such as shown below. It simply loops to add up a series of terms and it produces the correct result.

// sum numbers with a loop
public int DoSumLooping(int iterations)
{
int result = 0;
for(int i = 1;i <=iterations;i++)
{
result += i;
}
return result;
}

Now translate this into a specific solution that doesn't use looping (and use the same value for the number of iterations the loop performs). This code returns an incorrect result. The method consists entirely of a very straightforward code statement, but in this case .NET adds the numbers
incorrectly.
public double ComputeSum( )
{
// Brute force sum method
// For iterations == 10000
double sum = 0+ 1+ 2+ 3+ 4+ 5+ 6+ 7+ 8+ 9+ 10+ 11+ 12+ 13+ 14+ 15+ ...
+ 9997+ 9998+ 9999+ 10000;
return sum;
}
The above method returns an incorrect result with any number of terms

above
about 200. It will correctly add 1 + 2 + ... + 200, but it will NOT
correctly add 1 + 2 + ... + 1000.

I have just run across this, and I have not yet researched the
possible reasons for this behavior. It may be a known issue related to either

stack size or the length of a code line, but to my knowledge it hasn't been
discussed in any of the "popular" literature on C# and .NET. I need to

write
code like this, so if anyone has already encountered this issue, please advise me.
Here's another example that also creates problems, but of a somewhat
different nature. Take the following code and translate it into a

specific,
non-looping method and try to execute it using reflection. It fails.

public double LoopToCompute()
{
double sumOfProducts = 0;
double grandTotal = 0;
for (int i = 0; i < maxRows; ++i)
{
for (int j = 0; j < maxCols; ++j)
{
sumOfProducts += coeff[j] * table[i][j];
}
a_point[i] = sumOfProducts;
grandTotal += sumOfProducts;
sumOfProducts = 0;
}
return grandTotal;
}//LoopToCompute

The above code works -- but it's equivalent code with loops unrolled

(shown
below) doesn't work unless the maxRows is set very small. For small

values,
the 2 methods (above and below) produce identical results. There is

nothing
"wrong" with the code in that sense. It's similar to the above situation.
If
the "size" of the code statement or the number of code statements is too large, .NET fails. In this case (using reflection) it doesn't return the incorrect result, as the first example did. In this case, reflection

calls it an invalid program and refuses to run it (but only when the value of maxRows is above about 250). The reason for this is probably
straightforward. However, I have the need to make statements like this for performance reasons so I need a work-around. Any suggestions are
appreciated! All comments are appreciated.

public double DoBruteForceCompute()
{
double bruteForceSum = 0;

point1=coeff1*table[0][0] +coeff2*table[0][1] +coeff3*table[0][2]
+coeff4*table[0][3] +coeff5*table[0][4] +coeff6*table[0][5]
+coeff7*table[0][6] +coeff8*table[0][7] +coeff9*table[0][8]
+coeff10*table[0][9] +coeff11*table[0][10] +coeff12*table[0][11]
+coeff13*table[0][12] +coeff14*table[0][13] +coeff15*table[0][14]
+coeff16*table[0][15] +coeff17*table[0][16] +coeff18*table[0][17]
+coeff19*table[0][18] +coeff20*table[0][19] +coeff21*table[0][20]
+coeff22*table[0][21] +coeff23*table[0][22] +coeff24*table[0][23]
+coeff25*table[0][24] +coeff26*table[0][25] +coeff27*table[0][26]
+coeff28*table[0][27] +coeff29*table[0][28] +coeff30*table[0][29]
+coeff31*table[0][30] +coeff32*table[0][31] +coeff33*table[0][32]
+coeff34*table[0][33] +coeff35*table[0][34] ;

point2=coeff1*table[1][0] +coeff2*table[1][1] +coeff3*table[1][2]
+coeff4*table[1][3] +coeff5*table[1][4] +coeff6*table[1][5]
+coeff7*table[1][6] +coeff8*table[1][7] +coeff9*table[1][8]
+coeff10*table[1][9] +coeff11*table[1][10] +coeff12*table[1][11]
+coeff13*table[1][12] +coeff14*table[1][13] +coeff15*table[1][14]
+coeff16*table[1][15] +coeff17*table[1][16] +coeff18*table[1][17]
+coeff19*table[1][18] +coeff20*table[1][19] +coeff21*table[1][20]
+coeff22*table[1][21] +coeff23*table[1][22] +coeff24*table[1][23]
+coeff25*table[1][24] +coeff26*table[1][25] +coeff27*table[1][26]
+coeff28*table[1][27] +coeff29*table[1][28] +coeff30*table[1][29]
+coeff31*table[1][30] +coeff32*table[1][31] +coeff33*table[1][32]
+coeff34*table[1][33] +coeff35*table[1][34] ;
[...]

point500=coeff1*table[499][0] +coeff2*table[499][1] +coeff3*table[499][2] +coeff4*table[499][3] +coeff5*table[499][4] +coeff6*table[499][5]
+coeff7*table[499][6] +coeff8*table[499][7] +coeff9*table[499][8]
+coeff10*table[499][9] +coeff11*table[499][10] +coeff12*table[499][11]
+coeff13*table[499][12] +coeff14*table[499][13] +coeff15*table[499][14] +coeff16*table[499][15] +coeff17*table[499][16] +coeff18*table[499][17] +coeff19*table[499][18] +coeff20*table[499][19] +coeff21*table[499][20] +coeff22*table[499][21] +coeff23*table[499][22] +coeff24*table[499][23] +coeff25*table[499][24] +coeff26*table[499][25] +coeff27*table[499][26] +coeff28*table[499][27] +coeff29*table[499][28] +coeff30*table[499][29] +coeff31*table[499][30] +coeff32*table[499][31] +coeff33*table[499][32] +coeff34*table[499][33] +coeff35*table[499][34] ;

bruteForceSum =
point1 +
point2 + ... +

point499 +
point500
;

return bruteForceSum;

}//DoBruteForceCompute



Jul 21 '05 #36

P: n/a
Comments inline

--
Eric Gunnerson

Visit the C# product team at http://www.csharp.net
Eric's blog is at http://blogs.gotdotnet.com/ericgu/

This posting is provided "AS IS" with no warranties, and confers no rights.
"Mountain Bikn' Guy" <vc@attbi.com> wrote in message
news:RAblb.196435$%h1.190498@sccrnsc02...
In the event anyone wishes to review this thread now or later, I thought I
would provide some conclusions that resulted from everyone's input and from my reading:

1. unrolling loops often doesn't provide a performance gain on large (real
life size?) problems. In my experience, the unrolled loop was 5-10 times
SLOWER than the simple nested loop that I used as a reference. I found the
following quote in Eric Gunnerson's book (2nd ed). He said (about unrolled
loops), a "function is so big it doesn't fit into cache and therefore gets
slower performance."

Jon added the following info:
I suspect he means the processor's instruction
cache - if it's a small loop, the processor (not JIT, note!) can decode
the instructions once and keep the microcode available for further
iterations.
I do mean the processor cache, but it's not necessarily just an instruction
effect.

Jan Gray's excellent article on managed code performance has a lot more
detail on this:

http://msdn.microsoft.com/library/?u...anagedcode.asp

2. VS.NET has a 2048 char line limit in code files. In my experience, when
using runtime code generation and compiling, this can cause unusual trouble if one isn't aware of it. I was able to compile and run an application that was created from a code file with a line longer than this limit. The only
error I encountered was that the mathematical expression in the executing
program returned incorrect results! (The fix was simply inserting line
breaks into the code file.)

3. VS.NET has some compiler bugs that will result in the following error
message:
Additional information: Common Language Runtime detected an invalid program.
This appears to happen on complex mathematical expressions. However, in my
case the expression itself was not that complex. It was just long (but each line wasn't too long). When I reached about 1000 subexpressions in a simple sum of products expression, I encountered this compiler bug. Search on
Google Groups using the error message, and you'll see that others have
encountered it (frequently) when dealing with complex mathematical
expressions.

To my knowledge, there is no solution for this. Anyone from Microsoft care
to comment?
I haven't heard of this before. Can you send me a program that demonstrates
the problem?
Er****@microsoft.com

That about sums up (no pun intended) what I've learned so far. HTH.
Dave
"Mountain Bikn' Guy" <vc@attbi.com> wrote in message
news:NZUjb.795942$YN5.793228@sccrnsc01...
Take some standard code such as shown below. It simply loops to add up a
series of terms and it produces the correct result.

// sum numbers with a loop
public int DoSumLooping(int iterations)
{
int result = 0;
for(int i = 1;i <=iterations;i++)
{
result += i;
}
return result;
}

Now translate this into a specific solution that doesn't use looping (and use the same value for the number of iterations the loop performs). This
code returns an incorrect result. The method consists entirely of a very
straightforward code statement, but in this case .NET adds the numbers
incorrectly.
public double ComputeSum( )
{
// Brute force sum method
// For iterations == 10000
double sum = 0+ 1+ 2+ 3+ 4+ 5+ 6+ 7+ 8+ 9+ 10+ 11+ 12+ 13+ 14+ 15+ ...
+ 9997+ 9998+ 9999+ 10000;
return sum;
}
The above method returns an incorrect result with any number of terms

above
about 200. It will correctly add 1 + 2 + ... + 200, but it will NOT
correctly add 1 + 2 + ... + 1000.

I have just run across this, and I have not yet researched the possible
reasons for this behavior. It may be a known issue related to either stack size or the length of a code line, but to my knowledge it hasn't been
discussed in any of the "popular" literature on C# and .NET. I need to

write
code like this, so if anyone has already encountered this issue, please
advise me.
Here's another example that also creates problems, but of a somewhat
different nature. Take the following code and translate it into a

specific,
non-looping method and try to execute it using reflection. It fails.

public double LoopToCompute()
{
double sumOfProducts = 0;
double grandTotal = 0;
for (int i = 0; i < maxRows; ++i)
{
for (int j = 0; j < maxCols; ++j)
{
sumOfProducts += coeff[j] * table[i][j];
}
a_point[i] = sumOfProducts;
grandTotal += sumOfProducts;
sumOfProducts = 0;
}
return grandTotal;
}//LoopToCompute

The above code works -- but it's equivalent code with loops unrolled

(shown
below) doesn't work unless the maxRows is set very small. For small

values,
the 2 methods (above and below) produce identical results. There is

nothing
"wrong" with the code in that sense. It's similar to the above situation. If
the "size" of the code statement or the number of code statements is too
large, .NET fails. In this case (using reflection) it doesn't return the
incorrect result, as the first example did. In this case, reflection

calls it an invalid program and refuses to run it (but only when the value of
maxRows is above about 250). The reason for this is probably
straightforward. However, I have the need to make statements like this for performance reasons so I need a work-around. Any suggestions are
appreciated! All comments are appreciated.

public double DoBruteForceCompute()
{
double bruteForceSum = 0;

point1=coeff1*table[0][0] +coeff2*table[0][1] +coeff3*table[0][2]
+coeff4*table[0][3] +coeff5*table[0][4] +coeff6*table[0][5]
+coeff7*table[0][6] +coeff8*table[0][7] +coeff9*table[0][8]
+coeff10*table[0][9] +coeff11*table[0][10] +coeff12*table[0][11]
+coeff13*table[0][12] +coeff14*table[0][13] +coeff15*table[0][14]
+coeff16*table[0][15] +coeff17*table[0][16] +coeff18*table[0][17]
+coeff19*table[0][18] +coeff20*table[0][19] +coeff21*table[0][20]
+coeff22*table[0][21] +coeff23*table[0][22] +coeff24*table[0][23]
+coeff25*table[0][24] +coeff26*table[0][25] +coeff27*table[0][26]
+coeff28*table[0][27] +coeff29*table[0][28] +coeff30*table[0][29]
+coeff31*table[0][30] +coeff32*table[0][31] +coeff33*table[0][32]
+coeff34*table[0][33] +coeff35*table[0][34] ;

point2=coeff1*table[1][0] +coeff2*table[1][1] +coeff3*table[1][2]
+coeff4*table[1][3] +coeff5*table[1][4] +coeff6*table[1][5]
+coeff7*table[1][6] +coeff8*table[1][7] +coeff9*table[1][8]
+coeff10*table[1][9] +coeff11*table[1][10] +coeff12*table[1][11]
+coeff13*table[1][12] +coeff14*table[1][13] +coeff15*table[1][14]
+coeff16*table[1][15] +coeff17*table[1][16] +coeff18*table[1][17]
+coeff19*table[1][18] +coeff20*table[1][19] +coeff21*table[1][20]
+coeff22*table[1][21] +coeff23*table[1][22] +coeff24*table[1][23]
+coeff25*table[1][24] +coeff26*table[1][25] +coeff27*table[1][26]
+coeff28*table[1][27] +coeff29*table[1][28] +coeff30*table[1][29]
+coeff31*table[1][30] +coeff32*table[1][31] +coeff33*table[1][32]
+coeff34*table[1][33] +coeff35*table[1][34] ;
[...]

point500=coeff1*table[499][0] +coeff2*table[499][1] +coeff3*table[499][2] +coeff4*table[499][3] +coeff5*table[499][4] +coeff6*table[499][5]
+coeff7*table[499][6] +coeff8*table[499][7] +coeff9*table[499][8]
+coeff10*table[499][9] +coeff11*table[499][10] +coeff12*table[499][11]
+coeff13*table[499][12] +coeff14*table[499][13] +coeff15*table[499][14]
+coeff16*table[499][15] +coeff17*table[499][16] +coeff18*table[499][17]
+coeff19*table[499][18] +coeff20*table[499][19] +coeff21*table[499][20]
+coeff22*table[499][21] +coeff23*table[499][22] +coeff24*table[499][23]
+coeff25*table[499][24] +coeff26*table[499][25] +coeff27*table[499][26]
+coeff28*table[499][27] +coeff29*table[499][28] +coeff30*table[499][29]
+coeff31*table[499][30] +coeff32*table[499][31] +coeff33*table[499][32]
+coeff34*table[499][33] +coeff35*table[499][34] ;

bruteForceSum =
point1 +
point2 + ... +

point499 +
point500
;

return bruteForceSum;

}//DoBruteForceCompute


Jul 21 '05 #37

P: n/a
"Mountain Bikn' Guy" <vc@attbi.com> wrote in
news:zcelb.838183$Ho3.244900@sccrnsc03:
Since you asked...

I could use some help with CodeDOM. Here is how I am generating
these loops:

//
//TODO: generate this entire expression using CodeDOM classes:
StringBuilder formulaString = new StringBuilder();
formulaString.Append("dataPoints[row] = 0");
if (columns != null)
{
formulaString.Capacity = 40 * (columns.Count + 2);
for (int j = 0; j < columns.Count; ++j)
{
if ( ((MyColumnType)columns[j]).Role == RoleType.Independent)
{
formulaString.Append(System.Environment.NewLine);
formulaString.Append("+ coefficients[" + j + "] * table[row][" +
j + "] "); }
}
}
formulaString.Append(";");
//

The rest of the stuff (namespace, class, outer for loop, return
statement, etc.) is all generated purely without code snippet
expressions (with 1 exception -- see bug below). Anyone want to
show me how to do the above expression without code snippets?
(Note the need to break the lines to keep them below the 2046
char limit.)

The one other issue I am having trouble with is this:

compute.ReturnType = new CodeTypeReference("public float[]");
//suggested workaround for bug below
compute.Attributes |= MemberAttributes.Public;//has a bug

Is there an easy, language neutral way to work around the
MemberAttributes.Public bug when I return an array?


Dave,

[I don't mean to come across as arrogant in the post below. This is
just my long-winded way of saying that there may be a much simpler
solution to your problem.]

I've read most of the messages in the threads that deal with the
problems you're runing into. I'm not going to pretend that I know
what all of your requirements are, or the reason why you're writing
this code (learning exercise or production code?). But I get the
feeling that you may be trying to pound a round peg through a square
hole.

Lately I've become a big fan of Occam's Razor
(http://pespmc1.vub.ac.be/OCCAMRAZ.html). Dynamically generating and
compiling code is usually the slowest and most complex way to
implement a solution. It's almost always my last choice. When
designing a solution to a complex and/or large problem, my solution
generally comes from a list like this (in order of simplicity):

1. structured (or non-polymorphic OOP code) code w/ a fixed data
structure
2. same code as #1, but w/ a dynamic data structure
3. polymorphic OOP and/or interfaced code w/ a fixed data structure
4. same code as #3, but w/ a dynamic data structure
5. database solution (SQL)
6. potentially very complex code and data (writing a custom
compiler, lengthy regular expressions, using CodeDOM, etc.)

Another way of looking at this list:

1. simple code and data.
2. simple code and moderately complex data.
3. moderately complex code and simple data.
4. moderately complex code and data.
5. range of simple-to-complex code and data, but has an external
dependency on a database engine. May also have performance
drawbacks.
6. very complex code and data.

Too often I've learned (the hard way) that a complex solution to a
seemingly simple problem is often an indicator of a design flaw.
Using lists like this has helped me catch design errors like that and
fix them before they infect the rest of the app.

Just my $0.02...

Chris.
-------------
C.R. Timmons Consulting, Inc.
http://www.crtimmonsinc.com/
Jul 21 '05 #38

P: n/a
sample program sent!
Thanks for your interest!
Dave

"Eric Gunnerson [MS]" <er****@online.microsoft.com> wrote in message
news:%2****************@TK2MSFTNGP10.phx.gbl...
Comments inline

--
Eric Gunnerson

Visit the C# product team at http://www.csharp.net
Eric's blog is at http://blogs.gotdotnet.com/ericgu/

This posting is provided "AS IS" with no warranties, and confers no rights. "Mountain Bikn' Guy" <vc@attbi.com> wrote in message
news:RAblb.196435$%h1.190498@sccrnsc02...
In the event anyone wishes to review this thread now or later, I thought I
would provide some conclusions that resulted from everyone's input and from
my reading:

1. unrolling loops often doesn't provide a performance gain on large (real life size?) problems. In my experience, the unrolled loop was 5-10 times
SLOWER than the simple nested loop that I used as a reference. I found the following quote in Eric Gunnerson's book (2nd ed). He said (about unrolled loops), a "function is so big it doesn't fit into cache and therefore gets slower performance."

Jon added the following info:
I suspect he means the processor's instruction
cache - if it's a small loop, the processor (not JIT, note!) can decode
the instructions once and keep the microcode available for further
iterations.


I do mean the processor cache, but it's not necessarily just an

instruction effect.

Jan Gray's excellent article on managed code performance has a lot more
detail on this:

http://msdn.microsoft.com/library/?u...anagedcode.asp

2. VS.NET has a 2048 char line limit in code files. In my experience, when using runtime code generation and compiling, this can cause unusual trouble
if one isn't aware of it. I was able to compile and run an application

that
was created from a code file with a line longer than this limit. The only error I encountered was that the mathematical expression in the executing program returned incorrect results! (The fix was simply inserting line
breaks into the code file.)

3. VS.NET has some compiler bugs that will result in the following error
message:
Additional information: Common Language Runtime detected an invalid

program.

This appears to happen on complex mathematical expressions. However, in my case the expression itself was not that complex. It was just long (but

each
line wasn't too long). When I reached about 1000 subexpressions in a

simple
sum of products expression, I encountered this compiler bug. Search on
Google Groups using the error message, and you'll see that others have
encountered it (frequently) when dealing with complex mathematical
expressions.

To my knowledge, there is no solution for this. Anyone from Microsoft care to comment?


I haven't heard of this before. Can you send me a program that

demonstrates the problem?
Er****@microsoft.com

That about sums up (no pun intended) what I've learned so far. HTH.
Dave
"Mountain Bikn' Guy" <vc@attbi.com> wrote in message
news:NZUjb.795942$YN5.793228@sccrnsc01...
Take some standard code such as shown below. It simply loops to add up a series of terms and it produces the correct result.

// sum numbers with a loop
public int DoSumLooping(int iterations)
{
int result = 0;
for(int i = 1;i <=iterations;i++)
{
result += i;
}
return result;
}

Now translate this into a specific solution that doesn't use looping (and use the same value for the number of iterations the loop performs). This code returns an incorrect result. The method consists entirely of a very straightforward code statement, but in this case .NET adds the numbers
incorrectly.
public double ComputeSum( )
{
// Brute force sum method
// For iterations == 10000
double sum = 0+ 1+ 2+ 3+ 4+ 5+ 6+ 7+ 8+ 9+ 10+ 11+ 12+ 13+ 14+ 15+ ...
+ 9997+ 9998+ 9999+ 10000;
return sum;
}
The above method returns an incorrect result with any number of terms

above
about 200. It will correctly add 1 + 2 + ... + 200, but it will NOT
correctly add 1 + 2 + ... + 1000.

I have just run across this, and I have not yet researched the
possible reasons for this behavior. It may be a known issue related to either

stack size or the length of a code line, but to my knowledge it hasn't been
discussed in any of the "popular" literature on C# and .NET. I need to

write
code like this, so if anyone has already encountered this issue, please advise me.
Here's another example that also creates problems, but of a somewhat
different nature. Take the following code and translate it into a

specific,
non-looping method and try to execute it using reflection. It fails.

public double LoopToCompute()
{
double sumOfProducts = 0;
double grandTotal = 0;
for (int i = 0; i < maxRows; ++i)
{
for (int j = 0; j < maxCols; ++j)
{
sumOfProducts += coeff[j] * table[i][j];
}
a_point[i] = sumOfProducts;
grandTotal += sumOfProducts;
sumOfProducts = 0;
}
return grandTotal;
}//LoopToCompute

The above code works -- but it's equivalent code with loops unrolled

(shown
below) doesn't work unless the maxRows is set very small. For small

values,
the 2 methods (above and below) produce identical results. There is

nothing
"wrong" with the code in that sense. It's similar to the above situation.
If
the "size" of the code statement or the number of code statements is too large, .NET fails. In this case (using reflection) it doesn't return the incorrect result, as the first example did. In this case, reflection

calls it an invalid program and refuses to run it (but only when the value of maxRows is above about 250). The reason for this is probably
straightforward. However, I have the need to make statements like this for performance reasons so I need a work-around. Any suggestions are
appreciated! All comments are appreciated.

public double DoBruteForceCompute()
{
double bruteForceSum = 0;

point1=coeff1*table[0][0] +coeff2*table[0][1] +coeff3*table[0][2]
+coeff4*table[0][3] +coeff5*table[0][4] +coeff6*table[0][5]
+coeff7*table[0][6] +coeff8*table[0][7] +coeff9*table[0][8]
+coeff10*table[0][9] +coeff11*table[0][10] +coeff12*table[0][11]
+coeff13*table[0][12] +coeff14*table[0][13] +coeff15*table[0][14]
+coeff16*table[0][15] +coeff17*table[0][16] +coeff18*table[0][17]
+coeff19*table[0][18] +coeff20*table[0][19] +coeff21*table[0][20]
+coeff22*table[0][21] +coeff23*table[0][22] +coeff24*table[0][23]
+coeff25*table[0][24] +coeff26*table[0][25] +coeff27*table[0][26]
+coeff28*table[0][27] +coeff29*table[0][28] +coeff30*table[0][29]
+coeff31*table[0][30] +coeff32*table[0][31] +coeff33*table[0][32]
+coeff34*table[0][33] +coeff35*table[0][34] ;

point2=coeff1*table[1][0] +coeff2*table[1][1] +coeff3*table[1][2]
+coeff4*table[1][3] +coeff5*table[1][4] +coeff6*table[1][5]
+coeff7*table[1][6] +coeff8*table[1][7] +coeff9*table[1][8]
+coeff10*table[1][9] +coeff11*table[1][10] +coeff12*table[1][11]
+coeff13*table[1][12] +coeff14*table[1][13] +coeff15*table[1][14]
+coeff16*table[1][15] +coeff17*table[1][16] +coeff18*table[1][17]
+coeff19*table[1][18] +coeff20*table[1][19] +coeff21*table[1][20]
+coeff22*table[1][21] +coeff23*table[1][22] +coeff24*table[1][23]
+coeff25*table[1][24] +coeff26*table[1][25] +coeff27*table[1][26]
+coeff28*table[1][27] +coeff29*table[1][28] +coeff30*table[1][29]
+coeff31*table[1][30] +coeff32*table[1][31] +coeff33*table[1][32]
+coeff34*table[1][33] +coeff35*table[1][34] ;
[...]

point500=coeff1*table[499][0] +coeff2*table[499][1] +coeff3*table[499][2] +coeff4*table[499][3] +coeff5*table[499][4] +coeff6*table[499][5]
+coeff7*table[499][6] +coeff8*table[499][7] +coeff9*table[499][8]
+coeff10*table[499][9] +coeff11*table[499][10] +coeff12*table[499][11]
+coeff13*table[499][12] +coeff14*table[499][13] +coeff15*table[499][14] +coeff16*table[499][15] +coeff17*table[499][16] +coeff18*table[499][17] +coeff19*table[499][18] +coeff20*table[499][19] +coeff21*table[499][20] +coeff22*table[499][21] +coeff23*table[499][22] +coeff24*table[499][23] +coeff25*table[499][24] +coeff26*table[499][25] +coeff27*table[499][26] +coeff28*table[499][27] +coeff29*table[499][28] +coeff30*table[499][29] +coeff31*table[499][30] +coeff32*table[499][31] +coeff33*table[499][32] +coeff34*table[499][33] +coeff35*table[499][34] ;

bruteForceSum =
point1 +
point2 + ... +

point499 +
point500
;

return bruteForceSum;

}//DoBruteForceCompute



Jul 21 '05 #39

P: n/a
I really don't want to make this thread any longer than it already is but I
found Chris' comments (above) interesting. And I thought I would add my own
$0.02.

If the nature of this app is such that every bit of performance is needed,
to the extent that even loops have to be unrolled (something that's usually
found in game engines but not business apps), I would question the use of
..NET. Using C++ (non-managed) you will shave a whole layer which will yield
further performance advantages if well done.

- Santiago

"Mountain Bikn' Guy" <vc@attbi.com> wrote in message
news:zcelb.838183$Ho3.244900@sccrnsc03...
Since you asked...

I could use some help with CodeDOM. Here is how I am generating these loops:
//
//TODO: generate this entire expression using CodeDOM classes:
StringBuilder formulaString = new StringBuilder();
formulaString.Append("dataPoints[row] = 0");
if (columns != null)
{
formulaString.Capacity = 40 * (columns.Count + 2);
for (int j = 0; j < columns.Count; ++j)
{
if ( ((MyColumnType)columns[j]).Role == RoleType.Independent)
{
formulaString.Append(System.Environment.NewLine);
formulaString.Append("+ coefficients[" + j + "] * table[row][" + j + "] "); }
}
}
formulaString.Append(";");
//

The rest of the stuff (namespace, class, outer for loop, return statement,
etc.) is all generated purely without code snippet expressions (with 1
exception -- see bug below). Anyone want to show me how to do the above
expression without code snippets? (Note the need to break the lines to keep them below the 2046 char limit.)

The one other issue I am having trouble with is this:

compute.ReturnType = new CodeTypeReference("public float[]"); //suggested
workaround for bug below
compute.Attributes |= MemberAttributes.Public;//has a bug

Is there an easy, language neutral way to work around the
MemberAttributes.Public bug when I return an array?

TIA,
Dave

"anonymouse" <an********@discussions.microsoft.com> wrote in message
news:Ol****************@TK2MSFTNGP12.phx.gbl...
Did you make these unrolled loops manually or did you use a CodeDom to
generate them?

Curious.

Why do it the hard way:D
"Mountain Bikn' Guy" <vc@attbi.com> wrote in message
news:RAblb.196435$%h1.190498@sccrnsc02...
In the event anyone wishes to review this thread now or later, I thought
I
would provide some conclusions that resulted from everyone's input and from
my reading:

1. unrolling loops often doesn't provide a performance gain on large (real life size?) problems. In my experience, the unrolled loop was 5-10
times SLOWER than the simple nested loop that I used as a reference. I found the following quote in Eric Gunnerson's book (2nd ed). He said (about unrolled loops), a "function is so big it doesn't fit into cache and therefore gets slower performance."

Jon added the following info:
I suspect he means the processor's instruction
cache - if it's a small loop, the processor (not JIT, note!) can decode the instructions once and keep the microcode available for further
iterations.

2. VS.NET has a 2048 char line limit in code files. In my experience, when using runtime code generation and compiling, this can cause unusual

trouble
if one isn't aware of it. I was able to compile and run an application

that
was created from a code file with a line longer than this limit. The only error I encountered was that the mathematical expression in the executing program returned incorrect results! (The fix was simply inserting line
breaks into the code file.)

3. VS.NET has some compiler bugs that will result in the following error message:
Additional information: Common Language Runtime detected an invalid

program.

This appears to happen on complex mathematical expressions. However, in my
case the expression itself was not that complex. It was just long (but each
line wasn't too long). When I reached about 1000 subexpressions in a

simple
sum of products expression, I encountered this compiler bug. Search on
Google Groups using the error message, and you'll see that others have
encountered it (frequently) when dealing with complex mathematical
expressions.

To my knowledge, there is no solution for this. Anyone from Microsoft care to comment?

That about sums up (no pun intended) what I've learned so far. HTH.
Dave
"Mountain Bikn' Guy" <vc@attbi.com> wrote in message
news:NZUjb.795942$YN5.793228@sccrnsc01...
> Take some standard code such as shown below. It simply loops to add
up a > series of terms and it produces the correct result.
>
> // sum numbers with a loop
> public int DoSumLooping(int iterations)
> {
> int result = 0;
> for(int i = 1;i <=iterations;i++)
> {
> result += i;
> }
> return result;
> }
>
> Now translate this into a specific solution that doesn't use looping

(and
> use the same value for the number of iterations the loop performs). This > code returns an incorrect result. The method consists entirely of a very > straightforward code statement, but in this case .NET adds the
numbers > incorrectly.
> public double ComputeSum( )
> {
> // Brute force sum method
> // For iterations == 10000
> double sum = 0+ 1+ 2+ 3+ 4+ 5+ 6+ 7+ 8+ 9+ 10+ 11+ 12+ 13+ 14+

15+ ...
> + 9997+ 9998+ 9999+ 10000;
> return sum;
> }
> The above method returns an incorrect result with any number of terms above
> about 200. It will correctly add 1 + 2 + ... + 200, but it will NOT
> correctly add 1 + 2 + ... + 1000.
>
> I have just run across this, and I have not yet researched the possible > reasons for this behavior. It may be a known issue related to either

stack
> size or the length of a code line, but to my knowledge it hasn't been > discussed in any of the "popular" literature on C# and .NET. I need to write
> code like this, so if anyone has already encountered this issue, please > advise me.
>
>
> Here's another example that also creates problems, but of a somewhat
> different nature. Take the following code and translate it into a
specific,
> non-looping method and try to execute it using reflection. It fails.
>
> public double LoopToCompute()
> {
> double sumOfProducts = 0;
> double grandTotal = 0;
> for (int i = 0; i < maxRows; ++i)
> {
> for (int j = 0; j < maxCols; ++j)
> {
> sumOfProducts += coeff[j] * table[i][j];
> }
> a_point[i] = sumOfProducts;
> grandTotal += sumOfProducts;
> sumOfProducts = 0;
> }
> return grandTotal;
> }//LoopToCompute
>
> The above code works -- but it's equivalent code with loops unrolled
(shown
> below) doesn't work unless the maxRows is set very small. For small
values,
> the 2 methods (above and below) produce identical results. There is
nothing
> "wrong" with the code in that sense. It's similar to the above

situation.
If
> the "size" of the code statement or the number of code statements is too > large, .NET fails. In this case (using reflection) it doesn't return the > incorrect result, as the first example did. In this case, reflection

calls
> it an invalid program and refuses to run it (but only when the value of > maxRows is above about 250). The reason for this is probably
> straightforward. However, I have the need to make statements like this for
> performance reasons so I need a work-around. Any suggestions are
> appreciated! All comments are appreciated.
>
> public double DoBruteForceCompute()
> {
> double bruteForceSum = 0;
>
> point1=coeff1*table[0][0] +coeff2*table[0][1] +coeff3*table[0][2]
> +coeff4*table[0][3] +coeff5*table[0][4] +coeff6*table[0][5]
> +coeff7*table[0][6] +coeff8*table[0][7] +coeff9*table[0][8]
> +coeff10*table[0][9] +coeff11*table[0][10] +coeff12*table[0][11]
> +coeff13*table[0][12] +coeff14*table[0][13] +coeff15*table[0][14]
> +coeff16*table[0][15] +coeff17*table[0][16] +coeff18*table[0][17]
> +coeff19*table[0][18] +coeff20*table[0][19] +coeff21*table[0][20]
> +coeff22*table[0][21] +coeff23*table[0][22] +coeff24*table[0][23]
> +coeff25*table[0][24] +coeff26*table[0][25] +coeff27*table[0][26]
> +coeff28*table[0][27] +coeff29*table[0][28] +coeff30*table[0][29]
> +coeff31*table[0][30] +coeff32*table[0][31] +coeff33*table[0][32]
> +coeff34*table[0][33] +coeff35*table[0][34] ;
>
> point2=coeff1*table[1][0] +coeff2*table[1][1] +coeff3*table[1][2]
> +coeff4*table[1][3] +coeff5*table[1][4] +coeff6*table[1][5]
> +coeff7*table[1][6] +coeff8*table[1][7] +coeff9*table[1][8]
> +coeff10*table[1][9] +coeff11*table[1][10] +coeff12*table[1][11]
> +coeff13*table[1][12] +coeff14*table[1][13] +coeff15*table[1][14]
> +coeff16*table[1][15] +coeff17*table[1][16] +coeff18*table[1][17]
> +coeff19*table[1][18] +coeff20*table[1][19] +coeff21*table[1][20]
> +coeff22*table[1][21] +coeff23*table[1][22] +coeff24*table[1][23]
> +coeff25*table[1][24] +coeff26*table[1][25] +coeff27*table[1][26]
> +coeff28*table[1][27] +coeff29*table[1][28] +coeff30*table[1][29]
> +coeff31*table[1][30] +coeff32*table[1][31] +coeff33*table[1][32]
> +coeff34*table[1][33] +coeff35*table[1][34] ;
>
>
> [...]
>
> point500=coeff1*table[499][0] +coeff2*table[499][1]

+coeff3*table[499][2]
> +coeff4*table[499][3] +coeff5*table[499][4] +coeff6*table[499][5]
> +coeff7*table[499][6] +coeff8*table[499][7] +coeff9*table[499][8]
> +coeff10*table[499][9] +coeff11*table[499][10]
+coeff12*table[499][11] > +coeff13*table[499][12] +coeff14*table[499][13]

+coeff15*table[499][14] > +coeff16*table[499][15] +coeff17*table[499][16] +coeff18*table[499][17] > +coeff19*table[499][18] +coeff20*table[499][19] +coeff21*table[499][20] > +coeff22*table[499][21] +coeff23*table[499][22] +coeff24*table[499][23] > +coeff25*table[499][24] +coeff26*table[499][25] +coeff27*table[499][26] > +coeff28*table[499][27] +coeff29*table[499][28] +coeff30*table[499][29] > +coeff31*table[499][30] +coeff32*table[499][31] +coeff33*table[499][32] > +coeff34*table[499][33] +coeff35*table[499][34] ;
>
> bruteForceSum =
> point1 +
> point2 + ... +
>
> point499 +
> point500
> ;
>
> return bruteForceSum;
>
> }//DoBruteForceCompute
>
>



Jul 21 '05 #40

P: n/a
My results so far indicate that C# can be just as fast as C++ on
mathematical expressions. (If I need to, I use pointers.) I don't see any
limitations that indicate C# can't do the job. It's a great language, IMO.

"Santiago" <replytonewsgroup> wrote in message
news:Oq**************@TK2MSFTNGP09.phx.gbl...
I really don't want to make this thread any longer than it already is but I found Chris' comments (above) interesting. And I thought I would add my own $0.02.

If the nature of this app is such that every bit of performance is needed,
to the extent that even loops have to be unrolled (something that's usually found in game engines but not business apps), I would question the use of
.NET. Using C++ (non-managed) you will shave a whole layer which will yield further performance advantages if well done.

- Santiago

"Mountain Bikn' Guy" <vc@attbi.com> wrote in message
news:zcelb.838183$Ho3.244900@sccrnsc03...
Since you asked...

I could use some help with CodeDOM. Here is how I am generating these loops:

//
//TODO: generate this entire expression using CodeDOM classes:
StringBuilder formulaString = new StringBuilder();
formulaString.Append("dataPoints[row] = 0");
if (columns != null)
{
formulaString.Capacity = 40 * (columns.Count + 2);
for (int j = 0; j < columns.Count; ++j)
{
if ( ((MyColumnType)columns[j]).Role == RoleType.Independent)
{
formulaString.Append(System.Environment.NewLine);
formulaString.Append("+ coefficients[" + j + "] * table[row][" + j + "]

");
}
}
}
formulaString.Append(";");
//

The rest of the stuff (namespace, class, outer for loop, return statement,
etc.) is all generated purely without code snippet expressions (with 1
exception -- see bug below). Anyone want to show me how to do the above
expression without code snippets? (Note the need to break the lines to

keep
them below the 2046 char limit.)

The one other issue I am having trouble with is this:

compute.ReturnType = new CodeTypeReference("public float[]"); //suggested workaround for bug below
compute.Attributes |= MemberAttributes.Public;//has a bug

Is there an easy, language neutral way to work around the
MemberAttributes.Public bug when I return an array?

TIA,
Dave

"anonymouse" <an********@discussions.microsoft.com> wrote in message
news:Ol****************@TK2MSFTNGP12.phx.gbl...
Did you make these unrolled loops manually or did you use a CodeDom to
generate them?

Curious.

Why do it the hard way:D
"Mountain Bikn' Guy" <vc@attbi.com> wrote in message
news:RAblb.196435$%h1.190498@sccrnsc02...
> In the event anyone wishes to review this thread now or later, I thought
I
> would provide some conclusions that resulted from everyone's input and from
> my reading:
>
> 1. unrolling loops often doesn't provide a performance gain on large

(real
> life size?) problems. In my experience, the unrolled loop was 5-10

times > SLOWER than the simple nested loop that I used as a reference. I found the
> following quote in Eric Gunnerson's book (2nd ed). He said (about

unrolled
> loops), a "function is so big it doesn't fit into cache and
therefore
gets
> slower performance."
>
> Jon added the following info:
> I suspect he means the processor's instruction
> cache - if it's a small loop, the processor (not JIT, note!) can decode > the instructions once and keep the microcode available for further
> iterations.
>
> 2. VS.NET has a 2048 char line limit in code files. In my
experience, when
> using runtime code generation and compiling, this can cause unusual
trouble
> if one isn't aware of it. I was able to compile and run an
application that
> was created from a code file with a line longer than this limit. The

only
> error I encountered was that the mathematical expression in the

executing
> program returned incorrect results! (The fix was simply inserting line > breaks into the code file.)
>
> 3. VS.NET has some compiler bugs that will result in the following

error > message:
> Additional information: Common Language Runtime detected an invalid
program.
>
> This appears to happen on complex mathematical expressions. However, in
my
> case the expression itself was not that complex. It was just long (but each
> line wasn't too long). When I reached about 1000 subexpressions in a
simple
> sum of products expression, I encountered this compiler bug. Search on > Google Groups using the error message, and you'll see that others have > encountered it (frequently) when dealing with complex mathematical
> expressions.
>
> To my knowledge, there is no solution for this. Anyone from Microsoft care
> to comment?
>
> That about sums up (no pun intended) what I've learned so far. HTH.
> Dave
>
>
> "Mountain Bikn' Guy" <vc@attbi.com> wrote in message
> news:NZUjb.795942$YN5.793228@sccrnsc01...
> > Take some standard code such as shown below. It simply loops to
add up
a
> > series of terms and it produces the correct result.
> >
> > // sum numbers with a loop
> > public int DoSumLooping(int iterations)
> > {
> > int result = 0;
> > for(int i = 1;i <=iterations;i++)
> > {
> > result += i;
> > }
> > return result;
> > }
> >
> > Now translate this into a specific solution that doesn't use
looping (and
> > use the same value for the number of iterations the loop performs). This
> > code returns an incorrect result. The method consists entirely of
a very
> > straightforward code statement, but in this case .NET adds the numbers > > incorrectly.
> > public double ComputeSum( )
> > {
> > // Brute force sum method
> > // For iterations == 10000
> > double sum = 0+ 1+ 2+ 3+ 4+ 5+ 6+ 7+ 8+ 9+ 10+ 11+ 12+ 13+
14+ 15+
> ...
> > + 9997+ 9998+ 9999+ 10000;
> > return sum;
> > }
> > The above method returns an incorrect result with any number of terms > above
> > about 200. It will correctly add 1 + 2 + ... + 200, but it will
NOT > > correctly add 1 + 2 + ... + 1000.
> >
> > I have just run across this, and I have not yet researched the

possible
> > reasons for this behavior. It may be a known issue related to either stack
> > size or the length of a code line, but to my knowledge it hasn't

been > > discussed in any of the "popular" literature on C# and .NET. I need to
> write
> > code like this, so if anyone has already encountered this issue,

please
> > advise me.
> >
> >
> > Here's another example that also creates problems, but of a
somewhat > > different nature. Take the following code and translate it into a
> specific,
> > non-looping method and try to execute it using reflection. It fails. > >
> > public double LoopToCompute()
> > {
> > double sumOfProducts = 0;
> > double grandTotal = 0;
> > for (int i = 0; i < maxRows; ++i)
> > {
> > for (int j = 0; j < maxCols; ++j)
> > {
> > sumOfProducts += coeff[j] * table[i][j];
> > }
> > a_point[i] = sumOfProducts;
> > grandTotal += sumOfProducts;
> > sumOfProducts = 0;
> > }
> > return grandTotal;
> > }//LoopToCompute
> >
> > The above code works -- but it's equivalent code with loops unrolled > (shown
> > below) doesn't work unless the maxRows is set very small. For small > values,
> > the 2 methods (above and below) produce identical results. There is > nothing
> > "wrong" with the code in that sense. It's similar to the above
situation.
> If
> > the "size" of the code statement or the number of code statements is too
> > large, .NET fails. In this case (using reflection) it doesn't
return the
> > incorrect result, as the first example did. In this case,
reflection calls
> > it an invalid program and refuses to run it (but only when the

value of
> > maxRows is above about 250). The reason for this is probably
> > straightforward. However, I have the need to make statements like

this for
> > performance reasons so I need a work-around. Any suggestions are
> > appreciated! All comments are appreciated.
> >
> > public double DoBruteForceCompute()
> > {
> > double bruteForceSum = 0;
> >
> > point1=coeff1*table[0][0] +coeff2*table[0][1] +coeff3*table[0][2]
> > +coeff4*table[0][3] +coeff5*table[0][4] +coeff6*table[0][5]
> > +coeff7*table[0][6] +coeff8*table[0][7] +coeff9*table[0][8]
> > +coeff10*table[0][9] +coeff11*table[0][10] +coeff12*table[0][11]
> > +coeff13*table[0][12] +coeff14*table[0][13] +coeff15*table[0][14]
> > +coeff16*table[0][15] +coeff17*table[0][16] +coeff18*table[0][17]
> > +coeff19*table[0][18] +coeff20*table[0][19] +coeff21*table[0][20]
> > +coeff22*table[0][21] +coeff23*table[0][22] +coeff24*table[0][23]
> > +coeff25*table[0][24] +coeff26*table[0][25] +coeff27*table[0][26]
> > +coeff28*table[0][27] +coeff29*table[0][28] +coeff30*table[0][29]
> > +coeff31*table[0][30] +coeff32*table[0][31] +coeff33*table[0][32]
> > +coeff34*table[0][33] +coeff35*table[0][34] ;
> >
> > point2=coeff1*table[1][0] +coeff2*table[1][1] +coeff3*table[1][2]
> > +coeff4*table[1][3] +coeff5*table[1][4] +coeff6*table[1][5]
> > +coeff7*table[1][6] +coeff8*table[1][7] +coeff9*table[1][8]
> > +coeff10*table[1][9] +coeff11*table[1][10] +coeff12*table[1][11]
> > +coeff13*table[1][12] +coeff14*table[1][13] +coeff15*table[1][14]
> > +coeff16*table[1][15] +coeff17*table[1][16] +coeff18*table[1][17]
> > +coeff19*table[1][18] +coeff20*table[1][19] +coeff21*table[1][20]
> > +coeff22*table[1][21] +coeff23*table[1][22] +coeff24*table[1][23]
> > +coeff25*table[1][24] +coeff26*table[1][25] +coeff27*table[1][26]
> > +coeff28*table[1][27] +coeff29*table[1][28] +coeff30*table[1][29]
> > +coeff31*table[1][30] +coeff32*table[1][31] +coeff33*table[1][32]
> > +coeff34*table[1][33] +coeff35*table[1][34] ;
> >
> >
> > [...]
> >
> > point500=coeff1*table[499][0] +coeff2*table[499][1]
+coeff3*table[499][2]
> > +coeff4*table[499][3] +coeff5*table[499][4] +coeff6*table[499][5]
> > +coeff7*table[499][6] +coeff8*table[499][7] +coeff9*table[499][8]
> > +coeff10*table[499][9] +coeff11*table[499][10] +coeff12*table[499][11] > > +coeff13*table[499][12] +coeff14*table[499][13]

+coeff15*table[499][14]
> > +coeff16*table[499][15] +coeff17*table[499][16]

+coeff18*table[499][17]
> > +coeff19*table[499][18] +coeff20*table[499][19]

+coeff21*table[499][20]
> > +coeff22*table[499][21] +coeff23*table[499][22]

+coeff24*table[499][23]
> > +coeff25*table[499][24] +coeff26*table[499][25]

+coeff27*table[499][26]
> > +coeff28*table[499][27] +coeff29*table[499][28]

+coeff30*table[499][29]
> > +coeff31*table[499][30] +coeff32*table[499][31]

+coeff33*table[499][32]
> > +coeff34*table[499][33] +coeff35*table[499][34] ;
> >
> > bruteForceSum =
> > point1 +
> > point2 + ... +
> >
> > point499 +
> > point500
> > ;
> >
> > return bruteForceSum;
> >
> > }//DoBruteForceCompute
> >
> >
>
>



Jul 21 '05 #41

P: n/a

so long as you want to be dependent on m$oft patents and copyrights
and libraries that are not open ( unless you use mono ).
"Mountain Bikn' Guy" <vc@attbi.com> wrote in message
news:gQllb.837529$YN5.938550@sccrnsc01...
My results so far indicate that C# can be just as fast as C++ on
mathematical expressions. (If I need to, I use pointers.) I don't see any
limitations that indicate C# can't do the job. It's a great language, IMO.

"Santiago" <replytonewsgroup> wrote in message
news:Oq**************@TK2MSFTNGP09.phx.gbl...
I really don't want to make this thread any longer than it already is but
I
found Chris' comments (above) interesting. And I thought I would add my own
$0.02.

If the nature of this app is such that every bit of performance is needed, to the extent that even loops have to be unrolled (something that's

usually
found in game engines but not business apps), I would question the use of .NET. Using C++ (non-managed) you will shave a whole layer which will

yield
further performance advantages if well done.

- Santiago

"Mountain Bikn' Guy" <vc@attbi.com> wrote in message
news:zcelb.838183$Ho3.244900@sccrnsc03...
Since you asked...

I could use some help with CodeDOM. Here is how I am generating these

loops:

//
//TODO: generate this entire expression using CodeDOM classes:
StringBuilder formulaString = new StringBuilder();
formulaString.Append("dataPoints[row] = 0");
if (columns != null)
{
formulaString.Capacity = 40 * (columns.Count + 2);
for (int j = 0; j < columns.Count; ++j)
{
if ( ((MyColumnType)columns[j]).Role == RoleType.Independent)
{
formulaString.Append(System.Environment.NewLine);
formulaString.Append("+ coefficients[" + j + "] * table[row][" + j + "]
");
}
}
}
formulaString.Append(";");
//

The rest of the stuff (namespace, class, outer for loop, return statement, etc.) is all generated purely without code snippet expressions (with 1
exception -- see bug below). Anyone want to show me how to do the
above expression without code snippets? (Note the need to break the lines to

keep
them below the 2046 char limit.)

The one other issue I am having trouble with is this:

compute.ReturnType = new CodeTypeReference("public float[]");

//suggested workaround for bug below
compute.Attributes |= MemberAttributes.Public;//has a bug

Is there an easy, language neutral way to work around the
MemberAttributes.Public bug when I return an array?

TIA,
Dave

"anonymouse" <an********@discussions.microsoft.com> wrote in message
news:Ol****************@TK2MSFTNGP12.phx.gbl...
> Did you make these unrolled loops manually or did you use a CodeDom to > generate them?
>
> Curious.
>
> Why do it the hard way:D
>
>
> "Mountain Bikn' Guy" <vc@attbi.com> wrote in message
> news:RAblb.196435$%h1.190498@sccrnsc02...
> > In the event anyone wishes to review this thread now or later, I

thought
I
> > would provide some conclusions that resulted from everyone's input and > from
> > my reading:
> >
> > 1. unrolling loops often doesn't provide a performance gain on large (real
> > life size?) problems. In my experience, the unrolled loop was 5-10

times
> > SLOWER than the simple nested loop that I used as a reference. I found the
> > following quote in Eric Gunnerson's book (2nd ed). He said (about
unrolled
> > loops), a "function is so big it doesn't fit into cache and therefore gets
> > slower performance."
> >
> > Jon added the following info:
> > I suspect he means the processor's instruction
> > cache - if it's a small loop, the processor (not JIT, note!) can

decode
> > the instructions once and keep the microcode available for further
> > iterations.
> >
> > 2. VS.NET has a 2048 char line limit in code files. In my experience, when
> > using runtime code generation and compiling, this can cause unusual > trouble
> > if one isn't aware of it. I was able to compile and run an application > that
> > was created from a code file with a line longer than this limit. The only
> > error I encountered was that the mathematical expression in the
executing
> > program returned incorrect results! (The fix was simply inserting line > > breaks into the code file.)
> >
> > 3. VS.NET has some compiler bugs that will result in the following

error
> > message:
> > Additional information: Common Language Runtime detected an invalid > program.
> >
> > This appears to happen on complex mathematical expressions. However, in
my
> > case the expression itself was not that complex. It was just long (but > each
> > line wasn't too long). When I reached about 1000 subexpressions in
a > simple
> > sum of products expression, I encountered this compiler bug. Search on > > Google Groups using the error message, and you'll see that others have > > encountered it (frequently) when dealing with complex mathematical
> > expressions.
> >
> > To my knowledge, there is no solution for this. Anyone from Microsoft care
> > to comment?
> >
> > That about sums up (no pun intended) what I've learned so far.
HTH. > > Dave
> >
> >
> > "Mountain Bikn' Guy" <vc@attbi.com> wrote in message
> > news:NZUjb.795942$YN5.793228@sccrnsc01...
> > > Take some standard code such as shown below. It simply loops to add
up
a
> > > series of terms and it produces the correct result.
> > >
> > > // sum numbers with a loop
> > > public int DoSumLooping(int iterations)
> > > {
> > > int result = 0;
> > > for(int i = 1;i <=iterations;i++)
> > > {
> > > result += i;
> > > }
> > > return result;
> > > }
> > >
> > > Now translate this into a specific solution that doesn't use
looping > (and
> > > use the same value for the number of iterations the loop performs). This
> > > code returns an incorrect result. The method consists entirely of a
very
> > > straightforward code statement, but in this case .NET adds the numbers
> > > incorrectly.
> > > public double ComputeSum( )
> > > {
> > > // Brute force sum method
> > > // For iterations == 10000
> > > double sum = 0+ 1+ 2+ 3+ 4+ 5+ 6+ 7+ 8+ 9+ 10+ 11+ 12+ 13+ 14+ 15+
> > ...
> > > + 9997+ 9998+ 9999+ 10000;
> > > return sum;
> > > }
> > > The above method returns an incorrect result with any number of

terms
> > above
> > > about 200. It will correctly add 1 + 2 + ... + 200, but it will NOT > > > correctly add 1 + 2 + ... + 1000.
> > >
> > > I have just run across this, and I have not yet researched the
possible
> > > reasons for this behavior. It may be a known issue related to either > stack
> > > size or the length of a code line, but to my knowledge it hasn't

been
> > > discussed in any of the "popular" literature on C# and .NET. I need
to
> > write
> > > code like this, so if anyone has already encountered this issue,
please
> > > advise me.
> > >
> > >
> > > Here's another example that also creates problems, but of a

somewhat > > > different nature. Take the following code and translate it into
a > > specific,
> > > non-looping method and try to execute it using reflection. It

fails. > > >
> > > public double LoopToCompute()
> > > {
> > > double sumOfProducts = 0;
> > > double grandTotal = 0;
> > > for (int i = 0; i < maxRows; ++i)
> > > {
> > > for (int j = 0; j < maxCols; ++j)
> > > {
> > > sumOfProducts += coeff[j] * table[i][j];
> > > }
> > > a_point[i] = sumOfProducts;
> > > grandTotal += sumOfProducts;
> > > sumOfProducts = 0;
> > > }
> > > return grandTotal;
> > > }//LoopToCompute
> > >
> > > The above code works -- but it's equivalent code with loops unrolled > > (shown
> > > below) doesn't work unless the maxRows is set very small. For small > > values,
> > > the 2 methods (above and below) produce identical results. There is > > nothing
> > > "wrong" with the code in that sense. It's similar to the above
> situation.
> > If
> > > the "size" of the code statement or the number of code statements is
too
> > > large, .NET fails. In this case (using reflection) it doesn't return the
> > > incorrect result, as the first example did. In this case, reflection > calls
> > > it an invalid program and refuses to run it (but only when the value of
> > > maxRows is above about 250). The reason for this is probably
> > > straightforward. However, I have the need to make statements

like this
> for
> > > performance reasons so I need a work-around. Any suggestions are
> > > appreciated! All comments are appreciated.
> > >
> > > public double DoBruteForceCompute()
> > > {
> > > double bruteForceSum = 0;
> > >
> > > point1=coeff1*table[0][0] +coeff2*table[0][1]

+coeff3*table[0][2] > > > +coeff4*table[0][3] +coeff5*table[0][4] +coeff6*table[0][5]
> > > +coeff7*table[0][6] +coeff8*table[0][7] +coeff9*table[0][8]
> > > +coeff10*table[0][9] +coeff11*table[0][10] +coeff12*table[0][11]
> > > +coeff13*table[0][12] +coeff14*table[0][13] +coeff15*table[0][14] > > > +coeff16*table[0][15] +coeff17*table[0][16] +coeff18*table[0][17] > > > +coeff19*table[0][18] +coeff20*table[0][19] +coeff21*table[0][20] > > > +coeff22*table[0][21] +coeff23*table[0][22] +coeff24*table[0][23] > > > +coeff25*table[0][24] +coeff26*table[0][25] +coeff27*table[0][26] > > > +coeff28*table[0][27] +coeff29*table[0][28] +coeff30*table[0][29] > > > +coeff31*table[0][30] +coeff32*table[0][31] +coeff33*table[0][32] > > > +coeff34*table[0][33] +coeff35*table[0][34] ;
> > >
> > > point2=coeff1*table[1][0] +coeff2*table[1][1] +coeff3*table[1][2] > > > +coeff4*table[1][3] +coeff5*table[1][4] +coeff6*table[1][5]
> > > +coeff7*table[1][6] +coeff8*table[1][7] +coeff9*table[1][8]
> > > +coeff10*table[1][9] +coeff11*table[1][10] +coeff12*table[1][11]
> > > +coeff13*table[1][12] +coeff14*table[1][13] +coeff15*table[1][14] > > > +coeff16*table[1][15] +coeff17*table[1][16] +coeff18*table[1][17] > > > +coeff19*table[1][18] +coeff20*table[1][19] +coeff21*table[1][20] > > > +coeff22*table[1][21] +coeff23*table[1][22] +coeff24*table[1][23] > > > +coeff25*table[1][24] +coeff26*table[1][25] +coeff27*table[1][26] > > > +coeff28*table[1][27] +coeff29*table[1][28] +coeff30*table[1][29] > > > +coeff31*table[1][30] +coeff32*table[1][31] +coeff33*table[1][32] > > > +coeff34*table[1][33] +coeff35*table[1][34] ;
> > >
> > >
> > > [...]
> > >
> > > point500=coeff1*table[499][0] +coeff2*table[499][1]
> +coeff3*table[499][2]
> > > +coeff4*table[499][3] +coeff5*table[499][4] +coeff6*table[499][5] > > > +coeff7*table[499][6] +coeff8*table[499][7] +coeff9*table[499][8] > > > +coeff10*table[499][9] +coeff11*table[499][10]

+coeff12*table[499][11]
> > > +coeff13*table[499][12] +coeff14*table[499][13]
+coeff15*table[499][14]
> > > +coeff16*table[499][15] +coeff17*table[499][16]
+coeff18*table[499][17]
> > > +coeff19*table[499][18] +coeff20*table[499][19]
+coeff21*table[499][20]
> > > +coeff22*table[499][21] +coeff23*table[499][22]
+coeff24*table[499][23]
> > > +coeff25*table[499][24] +coeff26*table[499][25]
+coeff27*table[499][26]
> > > +coeff28*table[499][27] +coeff29*table[499][28]
+coeff30*table[499][29]
> > > +coeff31*table[499][30] +coeff32*table[499][31]
+coeff33*table[499][32]
> > > +coeff34*table[499][33] +coeff35*table[499][34] ;
> > >
> > > bruteForceSum =
> > > point1 +
> > > point2 + ... +
> > >
> > > point499 +
> > > point500
> > > ;
> > >
> > > return bruteForceSum;
> > >
> > > }//DoBruteForceCompute
> > >
> > >
> >
> >
>
>



Jul 21 '05 #42

P: n/a
inline

--
David Notario
Software Design Engineer, CLR JIT Compiler
http://devdiary.xplsv.com

"Mountain Bikn' Guy" <vc@attbi.com> wrote in message
news:RAblb.196435$%h1.190498@sccrnsc02...
In the event anyone wishes to review this thread now or later, I thought I
would provide some conclusions that resulted from everyone's input and from my reading:

1. unrolling loops often doesn't provide a performance gain on large (real
life size?) problems. In my experience, the unrolled loop was 5-10 times
SLOWER than the simple nested loop that I used as a reference. I found the
following quote in Eric Gunnerson's book (2nd ed). He said (about unrolled
loops), a "function is so big it doesn't fit into cache and therefore gets
slower performance."

Jon added the following info:
I suspect he means the processor's instruction
cache - if it's a small loop, the processor (not JIT, note!) can decode
the instructions once and keep the microcode available for further
iterations.
Unrolling should be performed by the compiler. It only makes sense for
extremely tight loops, where loop overhead matters (loop overhead is
typically 2 cycles, the cost of 'inc, cmp, jcc'. Unrolling more than 2-4
times has been something that has not been really that great since 386/486.
(any modern processor has branch prediction)

2. VS.NET has a 2048 char line limit in code files. In my experience, when
using runtime code generation and compiling, this can cause unusual trouble if one isn't aware of it. I was able to compile and run an application that was created from a code file with a line longer than this limit. The only
error I encountered was that the mathematical expression in the executing
program returned incorrect results! (The fix was simply inserting line
breaks into the code file.)
This would be a bug, attach a repro and send to the C# guys.

3. VS.NET has some compiler bugs that will result in the following error
message:
Additional information: Common Language Runtime detected an invalid program.
This appears to happen on complex mathematical expressions. However, in my
case the expression itself was not that complex. It was just long (but each line wasn't too long). When I reached about 1000 subexpressions in a simple sum of products expression, I encountered this compiler bug. Search on
Google Groups using the error message, and you'll see that others have
encountered it (frequently) when dealing with complex mathematical
expressions.

To my knowledge, there is no solution for this. Anyone from Microsoft care
to comment?


The JIT has a limit on local variables. You can get there in 2 ways, having
a lot of local variables in your code (goes over the 65534 IL limit) or the
compiler generating temps for evaluating expressions. Human written code
usually never hits these limits, although we do see them once in a while in
machine generated code (as nobody is really 'typing' down all that code).
When the JIT 'overflows', it will return an Invalid Program exception. The
only advice I can currently give you at the moment is write smaller
functions. I suspect you are hitting the temp limit.

Jul 21 '05 #43

P: n/a
Many people have commented on why the big statement might be hard for the
compiler to digest so I'm not going to add to that. But I thought I should
talk about loop unrolling a bit.

Remember the purpose of loop unrolling is to reduce the cost of testing the
loop variables on each iteration and the associated control flow. That's
all the overhead there is.

Generally when you unroll a loop you take several iterations and put it
directly into the body. Hopefully you can do this easily because you know
(for instance) that the number of iterations is always a multiple of 10, or
something like that (there's of course other ways too).

OK, so far all is goodness and joy. Here comes the but.

In the world of modern processors, bigger code is often slower code. At
some point the savings that you gained by having less control flow are not
sufficient to overcome the costs of extra cache misses due to having to load
in more code for the bigger (unrolled) algorithm.

So, the sweet spot is in between, you need to unroll enough to reduce the
cost (remember if you only unroll 10 iterations that's still at 90%
reduction in control flow cost, you'll have to unroll 100 iterations to get
to 99% and then 1000 to get to 99.9% -- diminishing returns if ever I saw
them) however you mustn't bloat the code to the point where you're taking an
undue number of cache misses in the course of running the program. I find
it unlikely that more than 10 unrolls would ever really be worth it, but of
course you'd have to measure to be sure for your case.

--
This posting is provided "AS IS" with no warranties, and confers no rights.

Rico Mariani
CLR Performance Architect


"Mountain Bikn' Guy" <vc@attbi.com> wrote in message
news:NZUjb.795942$YN5.793228@sccrnsc01...
Take some standard code such as shown below. It simply loops to add up a
series of terms and it produces the correct result.

// sum numbers with a loop
public int DoSumLooping(int iterations)
{
int result = 0;
for(int i = 1;i <=iterations;i++)
{
result += i;
}
return result;
}

Now translate this into a specific solution that doesn't use looping (and
use the same value for the number of iterations the loop performs). This
code returns an incorrect result. The method consists entirely of a very
straightforward code statement, but in this case .NET adds the numbers
incorrectly.
public double ComputeSum( )
{
// Brute force sum method
// For iterations == 10000
double sum = 0+ 1+ 2+ 3+ 4+ 5+ 6+ 7+ 8+ 9+ 10+ 11+ 12+ 13+ 14+ 15+ .... + 9997+ 9998+ 9999+ 10000;
return sum;
}
The above method returns an incorrect result with any number of terms above about 200. It will correctly add 1 + 2 + ... + 200, but it will NOT
correctly add 1 + 2 + ... + 1000.

I have just run across this, and I have not yet researched the possible
reasons for this behavior. It may be a known issue related to either stack
size or the length of a code line, but to my knowledge it hasn't been
discussed in any of the "popular" literature on C# and .NET. I need to write code like this, so if anyone has already encountered this issue, please
advise me.
Here's another example that also creates problems, but of a somewhat
different nature. Take the following code and translate it into a specific, non-looping method and try to execute it using reflection. It fails.

public double LoopToCompute()
{
double sumOfProducts = 0;
double grandTotal = 0;
for (int i = 0; i < maxRows; ++i)
{
for (int j = 0; j < maxCols; ++j)
{
sumOfProducts += coeff[j] * table[i][j];
}
a_point[i] = sumOfProducts;
grandTotal += sumOfProducts;
sumOfProducts = 0;
}
return grandTotal;
}//LoopToCompute

The above code works -- but it's equivalent code with loops unrolled (shown below) doesn't work unless the maxRows is set very small. For small values, the 2 methods (above and below) produce identical results. There is nothing "wrong" with the code in that sense. It's similar to the above situation. If the "size" of the code statement or the number of code statements is too
large, .NET fails. In this case (using reflection) it doesn't return the
incorrect result, as the first example did. In this case, reflection calls
it an invalid program and refuses to run it (but only when the value of
maxRows is above about 250). The reason for this is probably
straightforward. However, I have the need to make statements like this for
performance reasons so I need a work-around. Any suggestions are
appreciated! All comments are appreciated.

public double DoBruteForceCompute()
{
double bruteForceSum = 0;

point1=coeff1*table[0][0] +coeff2*table[0][1] +coeff3*table[0][2]
+coeff4*table[0][3] +coeff5*table[0][4] +coeff6*table[0][5]
+coeff7*table[0][6] +coeff8*table[0][7] +coeff9*table[0][8]
+coeff10*table[0][9] +coeff11*table[0][10] +coeff12*table[0][11]
+coeff13*table[0][12] +coeff14*table[0][13] +coeff15*table[0][14]
+coeff16*table[0][15] +coeff17*table[0][16] +coeff18*table[0][17]
+coeff19*table[0][18] +coeff20*table[0][19] +coeff21*table[0][20]
+coeff22*table[0][21] +coeff23*table[0][22] +coeff24*table[0][23]
+coeff25*table[0][24] +coeff26*table[0][25] +coeff27*table[0][26]
+coeff28*table[0][27] +coeff29*table[0][28] +coeff30*table[0][29]
+coeff31*table[0][30] +coeff32*table[0][31] +coeff33*table[0][32]
+coeff34*table[0][33] +coeff35*table[0][34] ;

point2=coeff1*table[1][0] +coeff2*table[1][1] +coeff3*table[1][2]
+coeff4*table[1][3] +coeff5*table[1][4] +coeff6*table[1][5]
+coeff7*table[1][6] +coeff8*table[1][7] +coeff9*table[1][8]
+coeff10*table[1][9] +coeff11*table[1][10] +coeff12*table[1][11]
+coeff13*table[1][12] +coeff14*table[1][13] +coeff15*table[1][14]
+coeff16*table[1][15] +coeff17*table[1][16] +coeff18*table[1][17]
+coeff19*table[1][18] +coeff20*table[1][19] +coeff21*table[1][20]
+coeff22*table[1][21] +coeff23*table[1][22] +coeff24*table[1][23]
+coeff25*table[1][24] +coeff26*table[1][25] +coeff27*table[1][26]
+coeff28*table[1][27] +coeff29*table[1][28] +coeff30*table[1][29]
+coeff31*table[1][30] +coeff32*table[1][31] +coeff33*table[1][32]
+coeff34*table[1][33] +coeff35*table[1][34] ;
[...]

point500=coeff1*table[499][0] +coeff2*table[499][1] +coeff3*table[499][2]
+coeff4*table[499][3] +coeff5*table[499][4] +coeff6*table[499][5]
+coeff7*table[499][6] +coeff8*table[499][7] +coeff9*table[499][8]
+coeff10*table[499][9] +coeff11*table[499][10] +coeff12*table[499][11]
+coeff13*table[499][12] +coeff14*table[499][13] +coeff15*table[499][14]
+coeff16*table[499][15] +coeff17*table[499][16] +coeff18*table[499][17]
+coeff19*table[499][18] +coeff20*table[499][19] +coeff21*table[499][20]
+coeff22*table[499][21] +coeff23*table[499][22] +coeff24*table[499][23]
+coeff25*table[499][24] +coeff26*table[499][25] +coeff27*table[499][26]
+coeff28*table[499][27] +coeff29*table[499][28] +coeff30*table[499][29]
+coeff31*table[499][30] +coeff32*table[499][31] +coeff33*table[499][32]
+coeff34*table[499][33] +coeff35*table[499][34] ;

bruteForceSum =
point1 +
point2 + ... +

point499 +
point500
;

return bruteForceSum;

}//DoBruteForceCompute

Jul 21 '05 #44

P: n/a
I'm going to add one person's actual experience into these posts about the
theoretical advantages of loop unrolling on modern processors. In the case
of a nested loop (2 for-loops) each iterating hundreds or thousands of
times, here is what I found:
1. unrolling both loops resulted in slower performance -- sometimes it was
significantly slower. It was the slowest of all variations I tested.
2. unrolling just the inner loop -- even when this resulted in a LOT of code
statements -- was the fastest of all options. I compared it against the
normal loop and several other variations. The unrolled inner loop had
hundreds of statements (typically about 500 or more). Yet, it was still the
fastest of all variations I could come up with. On average, it was 50% to
100% faster than the standard nested loop code.

In the end, I took a solution that was unusable because it was so slow (8
minutes+ to react to a single number change) to a solution that responds
virtually instantly (a fraction of a second now). Many things were part of
this -- unrolling the loop was just one of many.

BTW, I did the testing on a Xeon cpu machine.

"Rico Mariani [MSFT]" <ri***@online.microsoft.com> wrote in message
news:Od**************@TK2MSFTNGP10.phx.gbl...
Many people have commented on why the big statement might be hard for the
compiler to digest so I'm not going to add to that. But I thought I should talk about loop unrolling a bit.

Remember the purpose of loop unrolling is to reduce the cost of testing the loop variables on each iteration and the associated control flow. That's
all the overhead there is.

Generally when you unroll a loop you take several iterations and put it
directly into the body. Hopefully you can do this easily because you know
(for instance) that the number of iterations is always a multiple of 10, or something like that (there's of course other ways too).

OK, so far all is goodness and joy. Here comes the but.

In the world of modern processors, bigger code is often slower code. At
some point the savings that you gained by having less control flow are not
sufficient to overcome the costs of extra cache misses due to having to load in more code for the bigger (unrolled) algorithm.

So, the sweet spot is in between, you need to unroll enough to reduce the
cost (remember if you only unroll 10 iterations that's still at 90%
reduction in control flow cost, you'll have to unroll 100 iterations to get to 99% and then 1000 to get to 99.9% -- diminishing returns if ever I saw
them) however you mustn't bloat the code to the point where you're taking an undue number of cache misses in the course of running the program. I find
it unlikely that more than 10 unrolls would ever really be worth it, but of course you'd have to measure to be sure for your case.

--
This posting is provided "AS IS" with no warranties, and confers no rights.
Rico Mariani
CLR Performance Architect


"Mountain Bikn' Guy" <vc@attbi.com> wrote in message
news:NZUjb.795942$YN5.793228@sccrnsc01...
Take some standard code such as shown below. It simply loops to add up a
series of terms and it produces the correct result.

// sum numbers with a loop
public int DoSumLooping(int iterations)
{
int result = 0;
for(int i = 1;i <=iterations;i++)
{
result += i;
}
return result;
}

Now translate this into a specific solution that doesn't use looping (and use the same value for the number of iterations the loop performs). This
code returns an incorrect result. The method consists entirely of a very
straightforward code statement, but in this case .NET adds the numbers
incorrectly.
public double ComputeSum( )
{
// Brute force sum method
// For iterations == 10000
double sum = 0+ 1+ 2+ 3+ 4+ 5+ 6+ 7+ 8+ 9+ 10+ 11+ 12+ 13+ 14+ 15+ ...
+ 9997+ 9998+ 9999+ 10000;
return sum;
}
The above method returns an incorrect result with any number of terms

above
about 200. It will correctly add 1 + 2 + ... + 200, but it will NOT
correctly add 1 + 2 + ... + 1000.

I have just run across this, and I have not yet researched the possible
reasons for this behavior. It may be a known issue related to either stack size or the length of a code line, but to my knowledge it hasn't been
discussed in any of the "popular" literature on C# and .NET. I need to

write
code like this, so if anyone has already encountered this issue, please
advise me.
Here's another example that also creates problems, but of a somewhat
different nature. Take the following code and translate it into a

specific,
non-looping method and try to execute it using reflection. It fails.

public double LoopToCompute()
{
double sumOfProducts = 0;
double grandTotal = 0;
for (int i = 0; i < maxRows; ++i)
{
for (int j = 0; j < maxCols; ++j)
{
sumOfProducts += coeff[j] * table[i][j];
}
a_point[i] = sumOfProducts;
grandTotal += sumOfProducts;
sumOfProducts = 0;
}
return grandTotal;
}//LoopToCompute

The above code works -- but it's equivalent code with loops unrolled

(shown
below) doesn't work unless the maxRows is set very small. For small

values,
the 2 methods (above and below) produce identical results. There is

nothing
"wrong" with the code in that sense. It's similar to the above situation. If
the "size" of the code statement or the number of code statements is too
large, .NET fails. In this case (using reflection) it doesn't return the
incorrect result, as the first example did. In this case, reflection

calls it an invalid program and refuses to run it (but only when the value of
maxRows is above about 250). The reason for this is probably
straightforward. However, I have the need to make statements like this for performance reasons so I need a work-around. Any suggestions are
appreciated! All comments are appreciated.

public double DoBruteForceCompute()
{
double bruteForceSum = 0;

point1=coeff1*table[0][0] +coeff2*table[0][1] +coeff3*table[0][2]
+coeff4*table[0][3] +coeff5*table[0][4] +coeff6*table[0][5]
+coeff7*table[0][6] +coeff8*table[0][7] +coeff9*table[0][8]
+coeff10*table[0][9] +coeff11*table[0][10] +coeff12*table[0][11]
+coeff13*table[0][12] +coeff14*table[0][13] +coeff15*table[0][14]
+coeff16*table[0][15] +coeff17*table[0][16] +coeff18*table[0][17]
+coeff19*table[0][18] +coeff20*table[0][19] +coeff21*table[0][20]
+coeff22*table[0][21] +coeff23*table[0][22] +coeff24*table[0][23]
+coeff25*table[0][24] +coeff26*table[0][25] +coeff27*table[0][26]
+coeff28*table[0][27] +coeff29*table[0][28] +coeff30*table[0][29]
+coeff31*table[0][30] +coeff32*table[0][31] +coeff33*table[0][32]
+coeff34*table[0][33] +coeff35*table[0][34] ;

point2=coeff1*table[1][0] +coeff2*table[1][1] +coeff3*table[1][2]
+coeff4*table[1][3] +coeff5*table[1][4] +coeff6*table[1][5]
+coeff7*table[1][6] +coeff8*table[1][7] +coeff9*table[1][8]
+coeff10*table[1][9] +coeff11*table[1][10] +coeff12*table[1][11]
+coeff13*table[1][12] +coeff14*table[1][13] +coeff15*table[1][14]
+coeff16*table[1][15] +coeff17*table[1][16] +coeff18*table[1][17]
+coeff19*table[1][18] +coeff20*table[1][19] +coeff21*table[1][20]
+coeff22*table[1][21] +coeff23*table[1][22] +coeff24*table[1][23]
+coeff25*table[1][24] +coeff26*table[1][25] +coeff27*table[1][26]
+coeff28*table[1][27] +coeff29*table[1][28] +coeff30*table[1][29]
+coeff31*table[1][30] +coeff32*table[1][31] +coeff33*table[1][32]
+coeff34*table[1][33] +coeff35*table[1][34] ;
[...]

point500=coeff1*table[499][0] +coeff2*table[499][1] +coeff3*table[499][2] +coeff4*table[499][3] +coeff5*table[499][4] +coeff6*table[499][5]
+coeff7*table[499][6] +coeff8*table[499][7] +coeff9*table[499][8]
+coeff10*table[499][9] +coeff11*table[499][10] +coeff12*table[499][11]
+coeff13*table[499][12] +coeff14*table[499][13] +coeff15*table[499][14]
+coeff16*table[499][15] +coeff17*table[499][16] +coeff18*table[499][17]
+coeff19*table[499][18] +coeff20*table[499][19] +coeff21*table[499][20]
+coeff22*table[499][21] +coeff23*table[499][22] +coeff24*table[499][23]
+coeff25*table[499][24] +coeff26*table[499][25] +coeff27*table[499][26]
+coeff28*table[499][27] +coeff29*table[499][28] +coeff30*table[499][29]
+coeff31*table[499][30] +coeff32*table[499][31] +coeff33*table[499][32]
+coeff34*table[499][33] +coeff35*table[499][34] ;

bruteForceSum =
point1 +
point2 + ... +

point499 +
point500
;

return bruteForceSum;

}//DoBruteForceCompute


Jul 21 '05 #45

P: n/a
What amount of loop unrolling does the JIT perform? Does ngen perform any
more optimisations or is it just the JIT?

--
-----------
Got TidBits?
Get it here: www.networkip.net/tidbits
"Mountain Bikn' Guy" <vc@attbi.com> wrote in message
news:YWSnb.40504$mZ5.225768@attbi_s54...
I'm going to add one person's actual experience into these posts about the
theoretical advantages of loop unrolling on modern processors. In the case
of a nested loop (2 for-loops) each iterating hundreds or thousands of
times, here is what I found:
1. unrolling both loops resulted in slower performance -- sometimes it was
significantly slower. It was the slowest of all variations I tested.
2. unrolling just the inner loop -- even when this resulted in a LOT of code statements -- was the fastest of all options. I compared it against the
normal loop and several other variations. The unrolled inner loop had
hundreds of statements (typically about 500 or more). Yet, it was still the fastest of all variations I could come up with. On average, it was 50% to
100% faster than the standard nested loop code.

In the end, I took a solution that was unusable because it was so slow (8
minutes+ to react to a single number change) to a solution that responds
virtually instantly (a fraction of a second now). Many things were part of
this -- unrolling the loop was just one of many.

BTW, I did the testing on a Xeon cpu machine.

"Rico Mariani [MSFT]" <ri***@online.microsoft.com> wrote in message
news:Od**************@TK2MSFTNGP10.phx.gbl...
Many people have commented on why the big statement might be hard for the
compiler to digest so I'm not going to add to that. But I thought I should
talk about loop unrolling a bit.

Remember the purpose of loop unrolling is to reduce the cost of testing

the
loop variables on each iteration and the associated control flow. That's all the overhead there is.

Generally when you unroll a loop you take several iterations and put it
directly into the body. Hopefully you can do this easily because you know (for instance) that the number of iterations is always a multiple of 10,

or
something like that (there's of course other ways too).

OK, so far all is goodness and joy. Here comes the but.

In the world of modern processors, bigger code is often slower code. At
some point the savings that you gained by having less control flow are not sufficient to overcome the costs of extra cache misses due to having to

load
in more code for the bigger (unrolled) algorithm.

So, the sweet spot is in between, you need to unroll enough to reduce the cost (remember if you only unroll 10 iterations that's still at 90%
reduction in control flow cost, you'll have to unroll 100 iterations to

get
to 99% and then 1000 to get to 99.9% -- diminishing returns if ever I saw them) however you mustn't bloat the code to the point where you're taking an
undue number of cache misses in the course of running the program. I

find it unlikely that more than 10 unrolls would ever really be worth it, but

of
course you'd have to measure to be sure for your case.

--
This posting is provided "AS IS" with no warranties, and confers no

rights.

Rico Mariani
CLR Performance Architect


"Mountain Bikn' Guy" <vc@attbi.com> wrote in message
news:NZUjb.795942$YN5.793228@sccrnsc01...
Take some standard code such as shown below. It simply loops to add up a series of terms and it produces the correct result.

// sum numbers with a loop
public int DoSumLooping(int iterations)
{
int result = 0;
for(int i = 1;i <=iterations;i++)
{
result += i;
}
return result;
}

Now translate this into a specific solution that doesn't use looping (and use the same value for the number of iterations the loop performs). This code returns an incorrect result. The method consists entirely of a very straightforward code statement, but in this case .NET adds the numbers
incorrectly.
public double ComputeSum( )
{
// Brute force sum method
// For iterations == 10000
double sum = 0+ 1+ 2+ 3+ 4+ 5+ 6+ 7+ 8+ 9+ 10+ 11+ 12+ 13+ 14+ 15+ ...
+ 9997+ 9998+ 9999+ 10000;
return sum;
}
The above method returns an incorrect result with any number of terms

above
about 200. It will correctly add 1 + 2 + ... + 200, but it will NOT
correctly add 1 + 2 + ... + 1000.

I have just run across this, and I have not yet researched the
possible reasons for this behavior. It may be a known issue related to either

stack size or the length of a code line, but to my knowledge it hasn't been
discussed in any of the "popular" literature on C# and .NET. I need to

write
code like this, so if anyone has already encountered this issue, please advise me.
Here's another example that also creates problems, but of a somewhat
different nature. Take the following code and translate it into a

specific,
non-looping method and try to execute it using reflection. It fails.

public double LoopToCompute()
{
double sumOfProducts = 0;
double grandTotal = 0;
for (int i = 0; i < maxRows; ++i)
{
for (int j = 0; j < maxCols; ++j)
{
sumOfProducts += coeff[j] * table[i][j];
}
a_point[i] = sumOfProducts;
grandTotal += sumOfProducts;
sumOfProducts = 0;
}
return grandTotal;
}//LoopToCompute

The above code works -- but it's equivalent code with loops unrolled

(shown
below) doesn't work unless the maxRows is set very small. For small

values,
the 2 methods (above and below) produce identical results. There is

nothing
"wrong" with the code in that sense. It's similar to the above situation.
If
the "size" of the code statement or the number of code statements is too large, .NET fails. In this case (using reflection) it doesn't return the incorrect result, as the first example did. In this case, reflection

calls it an invalid program and refuses to run it (but only when the value of maxRows is above about 250). The reason for this is probably
straightforward. However, I have the need to make statements like this for performance reasons so I need a work-around. Any suggestions are
appreciated! All comments are appreciated.

public double DoBruteForceCompute()
{
double bruteForceSum = 0;

point1=coeff1*table[0][0] +coeff2*table[0][1] +coeff3*table[0][2]
+coeff4*table[0][3] +coeff5*table[0][4] +coeff6*table[0][5]
+coeff7*table[0][6] +coeff8*table[0][7] +coeff9*table[0][8]
+coeff10*table[0][9] +coeff11*table[0][10] +coeff12*table[0][11]
+coeff13*table[0][12] +coeff14*table[0][13] +coeff15*table[0][14]
+coeff16*table[0][15] +coeff17*table[0][16] +coeff18*table[0][17]
+coeff19*table[0][18] +coeff20*table[0][19] +coeff21*table[0][20]
+coeff22*table[0][21] +coeff23*table[0][22] +coeff24*table[0][23]
+coeff25*table[0][24] +coeff26*table[0][25] +coeff27*table[0][26]
+coeff28*table[0][27] +coeff29*table[0][28] +coeff30*table[0][29]
+coeff31*table[0][30] +coeff32*table[0][31] +coeff33*table[0][32]
+coeff34*table[0][33] +coeff35*table[0][34] ;

point2=coeff1*table[1][0] +coeff2*table[1][1] +coeff3*table[1][2]
+coeff4*table[1][3] +coeff5*table[1][4] +coeff6*table[1][5]
+coeff7*table[1][6] +coeff8*table[1][7] +coeff9*table[1][8]
+coeff10*table[1][9] +coeff11*table[1][10] +coeff12*table[1][11]
+coeff13*table[1][12] +coeff14*table[1][13] +coeff15*table[1][14]
+coeff16*table[1][15] +coeff17*table[1][16] +coeff18*table[1][17]
+coeff19*table[1][18] +coeff20*table[1][19] +coeff21*table[1][20]
+coeff22*table[1][21] +coeff23*table[1][22] +coeff24*table[1][23]
+coeff25*table[1][24] +coeff26*table[1][25] +coeff27*table[1][26]
+coeff28*table[1][27] +coeff29*table[1][28] +coeff30*table[1][29]
+coeff31*table[1][30] +coeff32*table[1][31] +coeff33*table[1][32]
+coeff34*table[1][33] +coeff35*table[1][34] ;
[...]

point500=coeff1*table[499][0] +coeff2*table[499][1] +coeff3*table[499][2] +coeff4*table[499][3] +coeff5*table[499][4] +coeff6*table[499][5]
+coeff7*table[499][6] +coeff8*table[499][7] +coeff9*table[499][8]
+coeff10*table[499][9] +coeff11*table[499][10] +coeff12*table[499][11]
+coeff13*table[499][12] +coeff14*table[499][13] +coeff15*table[499][14] +coeff16*table[499][15] +coeff17*table[499][16] +coeff18*table[499][17] +coeff19*table[499][18] +coeff20*table[499][19] +coeff21*table[499][20] +coeff22*table[499][21] +coeff23*table[499][22] +coeff24*table[499][23] +coeff25*table[499][24] +coeff26*table[499][25] +coeff27*table[499][26] +coeff28*table[499][27] +coeff29*table[499][28] +coeff30*table[499][29] +coeff31*table[499][30] +coeff32*table[499][31] +coeff33*table[499][32] +coeff34*table[499][33] +coeff35*table[499][34] ;

bruteForceSum =
point1 +
point2 + ... +

point499 +
point500
;

return bruteForceSum;

}//DoBruteForceCompute



Jul 21 '05 #46

P: n/a
Ignore this idiot. He is spoofing my email account.

--
-----------
Got TidBits?
Get it here: www.networkip.net/tidbits
"Alvin Bruney" <vapordan_spam_me_not@hotmail_no_spamhotmail.com > wrote in
message news:ef*************@TK2MSFTNGP10.phx.gbl...
What amount of loop unrolling does the JIT perform? Does ngen perform any
more optimisations or is it just the JIT?

--
-----------
Got TidBits?
Get it here: www.networkip.net/tidbits
"Mountain Bikn' Guy" <vc@attbi.com> wrote in message
news:YWSnb.40504$mZ5.225768@attbi_s54...
I'm going to add one person's actual experience into these posts about the
theoretical advantages of loop unrolling on modern processors. In the case of a nested loop (2 for-loops) each iterating hundreds or thousands of
times, here is what I found:
1. unrolling both loops resulted in slower performance -- sometimes it was significantly slower. It was the slowest of all variations I tested.
2. unrolling just the inner loop -- even when this resulted in a LOT of code
statements -- was the fastest of all options. I compared it against the
normal loop and several other variations. The unrolled inner loop had
hundreds of statements (typically about 500 or more). Yet, it was still

the
fastest of all variations I could come up with. On average, it was 50% to 100% faster than the standard nested loop code.

In the end, I took a solution that was unusable because it was so slow (8 minutes+ to react to a single number change) to a solution that responds
virtually instantly (a fraction of a second now). Many things were part of this -- unrolling the loop was just one of many.

BTW, I did the testing on a Xeon cpu machine.

"Rico Mariani [MSFT]" <ri***@online.microsoft.com> wrote in message
news:Od**************@TK2MSFTNGP10.phx.gbl...
Many people have commented on why the big statement might be hard for the compiler to digest so I'm not going to add to that. But I thought I

should
talk about loop unrolling a bit.

Remember the purpose of loop unrolling is to reduce the cost of testing the
loop variables on each iteration and the associated control flow. That's all the overhead there is.

Generally when you unroll a loop you take several iterations and put
it directly into the body. Hopefully you can do this easily because you know (for instance) that the number of iterations is always a multiple of 10, or
something like that (there's of course other ways too).

OK, so far all is goodness and joy. Here comes the but.

In the world of modern processors, bigger code is often slower code.
At some point the savings that you gained by having less control flow are not sufficient to overcome the costs of extra cache misses due to having to load
in more code for the bigger (unrolled) algorithm.

So, the sweet spot is in between, you need to unroll enough to reduce the cost (remember if you only unroll 10 iterations that's still at 90%
reduction in control flow cost, you'll have to unroll 100 iterations
to
get
to 99% and then 1000 to get to 99.9% -- diminishing returns if ever I saw them) however you mustn't bloat the code to the point where you're taking
an
undue number of cache misses in the course of running the program. I

find it unlikely that more than 10 unrolls would ever really be worth it,
but of
course you'd have to measure to be sure for your case.

--
This posting is provided "AS IS" with no warranties, and confers no

rights.

Rico Mariani
CLR Performance Architect


"Mountain Bikn' Guy" <vc@attbi.com> wrote in message
news:NZUjb.795942$YN5.793228@sccrnsc01...
> Take some standard code such as shown below. It simply loops to add
up a > series of terms and it produces the correct result.
>
> // sum numbers with a loop
> public int DoSumLooping(int iterations)
> {
> int result = 0;
> for(int i = 1;i <=iterations;i++)
> {
> result += i;
> }
> return result;
> }
>
> Now translate this into a specific solution that doesn't use looping

(and
> use the same value for the number of iterations the loop performs). This > code returns an incorrect result. The method consists entirely of a very > straightforward code statement, but in this case .NET adds the
numbers > incorrectly.
> public double ComputeSum( )
> {
> // Brute force sum method
> // For iterations == 10000
> double sum = 0+ 1+ 2+ 3+ 4+ 5+ 6+ 7+ 8+ 9+ 10+ 11+ 12+ 13+ 14+

15+ ...
> + 9997+ 9998+ 9999+ 10000;
> return sum;
> }
> The above method returns an incorrect result with any number of terms above
> about 200. It will correctly add 1 + 2 + ... + 200, but it will NOT
> correctly add 1 + 2 + ... + 1000.
>
> I have just run across this, and I have not yet researched the possible > reasons for this behavior. It may be a known issue related to either

stack
> size or the length of a code line, but to my knowledge it hasn't been > discussed in any of the "popular" literature on C# and .NET. I need to write
> code like this, so if anyone has already encountered this issue, please > advise me.
>
>
> Here's another example that also creates problems, but of a somewhat
> different nature. Take the following code and translate it into a
specific,
> non-looping method and try to execute it using reflection. It fails.
>
> public double LoopToCompute()
> {
> double sumOfProducts = 0;
> double grandTotal = 0;
> for (int i = 0; i < maxRows; ++i)
> {
> for (int j = 0; j < maxCols; ++j)
> {
> sumOfProducts += coeff[j] * table[i][j];
> }
> a_point[i] = sumOfProducts;
> grandTotal += sumOfProducts;
> sumOfProducts = 0;
> }
> return grandTotal;
> }//LoopToCompute
>
> The above code works -- but it's equivalent code with loops unrolled
(shown
> below) doesn't work unless the maxRows is set very small. For small
values,
> the 2 methods (above and below) produce identical results. There is
nothing
> "wrong" with the code in that sense. It's similar to the above

situation.
If
> the "size" of the code statement or the number of code statements is too > large, .NET fails. In this case (using reflection) it doesn't return the > incorrect result, as the first example did. In this case, reflection

calls
> it an invalid program and refuses to run it (but only when the value of > maxRows is above about 250). The reason for this is probably
> straightforward. However, I have the need to make statements like this for
> performance reasons so I need a work-around. Any suggestions are
> appreciated! All comments are appreciated.
>
> public double DoBruteForceCompute()
> {
> double bruteForceSum = 0;
>
> point1=coeff1*table[0][0] +coeff2*table[0][1] +coeff3*table[0][2]
> +coeff4*table[0][3] +coeff5*table[0][4] +coeff6*table[0][5]
> +coeff7*table[0][6] +coeff8*table[0][7] +coeff9*table[0][8]
> +coeff10*table[0][9] +coeff11*table[0][10] +coeff12*table[0][11]
> +coeff13*table[0][12] +coeff14*table[0][13] +coeff15*table[0][14]
> +coeff16*table[0][15] +coeff17*table[0][16] +coeff18*table[0][17]
> +coeff19*table[0][18] +coeff20*table[0][19] +coeff21*table[0][20]
> +coeff22*table[0][21] +coeff23*table[0][22] +coeff24*table[0][23]
> +coeff25*table[0][24] +coeff26*table[0][25] +coeff27*table[0][26]
> +coeff28*table[0][27] +coeff29*table[0][28] +coeff30*table[0][29]
> +coeff31*table[0][30] +coeff32*table[0][31] +coeff33*table[0][32]
> +coeff34*table[0][33] +coeff35*table[0][34] ;
>
> point2=coeff1*table[1][0] +coeff2*table[1][1] +coeff3*table[1][2]
> +coeff4*table[1][3] +coeff5*table[1][4] +coeff6*table[1][5]
> +coeff7*table[1][6] +coeff8*table[1][7] +coeff9*table[1][8]
> +coeff10*table[1][9] +coeff11*table[1][10] +coeff12*table[1][11]
> +coeff13*table[1][12] +coeff14*table[1][13] +coeff15*table[1][14]
> +coeff16*table[1][15] +coeff17*table[1][16] +coeff18*table[1][17]
> +coeff19*table[1][18] +coeff20*table[1][19] +coeff21*table[1][20]
> +coeff22*table[1][21] +coeff23*table[1][22] +coeff24*table[1][23]
> +coeff25*table[1][24] +coeff26*table[1][25] +coeff27*table[1][26]
> +coeff28*table[1][27] +coeff29*table[1][28] +coeff30*table[1][29]
> +coeff31*table[1][30] +coeff32*table[1][31] +coeff33*table[1][32]
> +coeff34*table[1][33] +coeff35*table[1][34] ;
>
>
> [...]
>
> point500=coeff1*table[499][0] +coeff2*table[499][1]

+coeff3*table[499][2]
> +coeff4*table[499][3] +coeff5*table[499][4] +coeff6*table[499][5]
> +coeff7*table[499][6] +coeff8*table[499][7] +coeff9*table[499][8]
> +coeff10*table[499][9] +coeff11*table[499][10]
+coeff12*table[499][11] > +coeff13*table[499][12] +coeff14*table[499][13]

+coeff15*table[499][14] > +coeff16*table[499][15] +coeff17*table[499][16] +coeff18*table[499][17] > +coeff19*table[499][18] +coeff20*table[499][19] +coeff21*table[499][20] > +coeff22*table[499][21] +coeff23*table[499][22] +coeff24*table[499][23] > +coeff25*table[499][24] +coeff26*table[499][25] +coeff27*table[499][26] > +coeff28*table[499][27] +coeff29*table[499][28] +coeff30*table[499][29] > +coeff31*table[499][30] +coeff32*table[499][31] +coeff33*table[499][32] > +coeff34*table[499][33] +coeff35*table[499][34] ;
>
> bruteForceSum =
> point1 +
> point2 + ... +
>
> point499 +
> point500
> ;
>
> return bruteForceSum;
>
> }//DoBruteForceCompute
>
>



Jul 21 '05 #47

P: n/a
Yes Ignore that idiot, like he thinks he owns the internet :D

--
-----------
Got TidBits?
Get it here: www.networkip.net/tidbits
"Alvin Bruney" <vapordan_spam_me_not@hotmail_no_spamhotmail.com > wrote in
message news:#d**************@TK2MSFTNGP12.phx.gbl...
Ignore this idiot. He is spoofing my email account.

--
-----------
Got TidBits?
Get it here: www.networkip.net/tidbits
"Alvin Bruney" <vapordan_spam_me_not@hotmail_no_spamhotmail.com > wrote in
message news:ef*************@TK2MSFTNGP10.phx.gbl...
What amount of loop unrolling does the JIT perform? Does ngen perform any
more optimisations or is it just the JIT?

--
-----------
Got TidBits?
Get it here: www.networkip.net/tidbits
"Mountain Bikn' Guy" <vc@attbi.com> wrote in message
news:YWSnb.40504$mZ5.225768@attbi_s54...
I'm going to add one person's actual experience into these posts about the theoretical advantages of loop unrolling on modern processors. In the case of a nested loop (2 for-loops) each iterating hundreds or thousands of
times, here is what I found:
1. unrolling both loops resulted in slower performance -- sometimes it was significantly slower. It was the slowest of all variations I tested.
2. unrolling just the inner loop -- even when this resulted in a LOT of code
statements -- was the fastest of all options. I compared it against
the normal loop and several other variations. The unrolled inner loop had
hundreds of statements (typically about 500 or more). Yet, it was still
the
fastest of all variations I could come up with. On average, it was 50% to 100% faster than the standard nested loop code.

In the end, I took a solution that was unusable because it was so slow (8 minutes+ to react to a single number change) to a solution that
responds virtually instantly (a fraction of a second now). Many things were part
of this -- unrolling the loop was just one of many.

BTW, I did the testing on a Xeon cpu machine.

"Rico Mariani [MSFT]" <ri***@online.microsoft.com> wrote in message
news:Od**************@TK2MSFTNGP10.phx.gbl...
> Many people have commented on why the big statement might be hard
for the
> compiler to digest so I'm not going to add to that. But I thought I
should
> talk about loop unrolling a bit.
>
> Remember the purpose of loop unrolling is to reduce the cost of testing the
> loop variables on each iteration and the associated control flow. That's
> all the overhead there is.
>
> Generally when you unroll a loop you take several iterations and put it > directly into the body. Hopefully you can do this easily because
you know
> (for instance) that the number of iterations is always a multiple of 10, or
> something like that (there's of course other ways too).
>
> OK, so far all is goodness and joy. Here comes the but.
>
> In the world of modern processors, bigger code is often slower code. At > some point the savings that you gained by having less control flow
are not
> sufficient to overcome the costs of extra cache misses due to having to load
> in more code for the bigger (unrolled) algorithm.
>
> So, the sweet spot is in between, you need to unroll enough to
reduce the
> cost (remember if you only unroll 10 iterations that's still at 90%
> reduction in control flow cost, you'll have to unroll 100 iterations to get
> to 99% and then 1000 to get to 99.9% -- diminishing returns if ever
I saw
> them) however you mustn't bloat the code to the point where you're

taking
an
> undue number of cache misses in the course of running the program.
I find
> it unlikely that more than 10 unrolls would ever really be worth it, but of
> course you'd have to measure to be sure for your case.
>
> --
> This posting is provided "AS IS" with no warranties, and confers no
rights.
>
> Rico Mariani
> CLR Performance Architect
>
>
>
>
> "Mountain Bikn' Guy" <vc@attbi.com> wrote in message
> news:NZUjb.795942$YN5.793228@sccrnsc01...
> > Take some standard code such as shown below. It simply loops to
add up
a
> > series of terms and it produces the correct result.
> >
> > // sum numbers with a loop
> > public int DoSumLooping(int iterations)
> > {
> > int result = 0;
> > for(int i = 1;i <=iterations;i++)
> > {
> > result += i;
> > }
> > return result;
> > }
> >
> > Now translate this into a specific solution that doesn't use
looping (and
> > use the same value for the number of iterations the loop performs). This
> > code returns an incorrect result. The method consists entirely of
a very
> > straightforward code statement, but in this case .NET adds the numbers > > incorrectly.
> > public double ComputeSum( )
> > {
> > // Brute force sum method
> > // For iterations == 10000
> > double sum = 0+ 1+ 2+ 3+ 4+ 5+ 6+ 7+ 8+ 9+ 10+ 11+ 12+ 13+
14+ 15+
> ...
> > + 9997+ 9998+ 9999+ 10000;
> > return sum;
> > }
> > The above method returns an incorrect result with any number of terms > above
> > about 200. It will correctly add 1 + 2 + ... + 200, but it will
NOT > > correctly add 1 + 2 + ... + 1000.
> >
> > I have just run across this, and I have not yet researched the

possible
> > reasons for this behavior. It may be a known issue related to either stack
> > size or the length of a code line, but to my knowledge it hasn't

been > > discussed in any of the "popular" literature on C# and .NET. I need to
> write
> > code like this, so if anyone has already encountered this issue,

please
> > advise me.
> >
> >
> > Here's another example that also creates problems, but of a
somewhat > > different nature. Take the following code and translate it into a
> specific,
> > non-looping method and try to execute it using reflection. It fails. > >
> > public double LoopToCompute()
> > {
> > double sumOfProducts = 0;
> > double grandTotal = 0;
> > for (int i = 0; i < maxRows; ++i)
> > {
> > for (int j = 0; j < maxCols; ++j)
> > {
> > sumOfProducts += coeff[j] * table[i][j];
> > }
> > a_point[i] = sumOfProducts;
> > grandTotal += sumOfProducts;
> > sumOfProducts = 0;
> > }
> > return grandTotal;
> > }//LoopToCompute
> >
> > The above code works -- but it's equivalent code with loops unrolled > (shown
> > below) doesn't work unless the maxRows is set very small. For small > values,
> > the 2 methods (above and below) produce identical results. There is > nothing
> > "wrong" with the code in that sense. It's similar to the above
situation.
> If
> > the "size" of the code statement or the number of code statements is too
> > large, .NET fails. In this case (using reflection) it doesn't
return the
> > incorrect result, as the first example did. In this case,
reflection calls
> > it an invalid program and refuses to run it (but only when the

value of
> > maxRows is above about 250). The reason for this is probably
> > straightforward. However, I have the need to make statements like

this for
> > performance reasons so I need a work-around. Any suggestions are
> > appreciated! All comments are appreciated.
> >
> > public double DoBruteForceCompute()
> > {
> > double bruteForceSum = 0;
> >
> > point1=coeff1*table[0][0] +coeff2*table[0][1] +coeff3*table[0][2]
> > +coeff4*table[0][3] +coeff5*table[0][4] +coeff6*table[0][5]
> > +coeff7*table[0][6] +coeff8*table[0][7] +coeff9*table[0][8]
> > +coeff10*table[0][9] +coeff11*table[0][10] +coeff12*table[0][11]
> > +coeff13*table[0][12] +coeff14*table[0][13] +coeff15*table[0][14]
> > +coeff16*table[0][15] +coeff17*table[0][16] +coeff18*table[0][17]
> > +coeff19*table[0][18] +coeff20*table[0][19] +coeff21*table[0][20]
> > +coeff22*table[0][21] +coeff23*table[0][22] +coeff24*table[0][23]
> > +coeff25*table[0][24] +coeff26*table[0][25] +coeff27*table[0][26]
> > +coeff28*table[0][27] +coeff29*table[0][28] +coeff30*table[0][29]
> > +coeff31*table[0][30] +coeff32*table[0][31] +coeff33*table[0][32]
> > +coeff34*table[0][33] +coeff35*table[0][34] ;
> >
> > point2=coeff1*table[1][0] +coeff2*table[1][1] +coeff3*table[1][2]
> > +coeff4*table[1][3] +coeff5*table[1][4] +coeff6*table[1][5]
> > +coeff7*table[1][6] +coeff8*table[1][7] +coeff9*table[1][8]
> > +coeff10*table[1][9] +coeff11*table[1][10] +coeff12*table[1][11]
> > +coeff13*table[1][12] +coeff14*table[1][13] +coeff15*table[1][14]
> > +coeff16*table[1][15] +coeff17*table[1][16] +coeff18*table[1][17]
> > +coeff19*table[1][18] +coeff20*table[1][19] +coeff21*table[1][20]
> > +coeff22*table[1][21] +coeff23*table[1][22] +coeff24*table[1][23]
> > +coeff25*table[1][24] +coeff26*table[1][25] +coeff27*table[1][26]
> > +coeff28*table[1][27] +coeff29*table[1][28] +coeff30*table[1][29]
> > +coeff31*table[1][30] +coeff32*table[1][31] +coeff33*table[1][32]
> > +coeff34*table[1][33] +coeff35*table[1][34] ;
> >
> >
> > [...]
> >
> > point500=coeff1*table[499][0] +coeff2*table[499][1]
+coeff3*table[499][2]
> > +coeff4*table[499][3] +coeff5*table[499][4] +coeff6*table[499][5]
> > +coeff7*table[499][6] +coeff8*table[499][7] +coeff9*table[499][8]
> > +coeff10*table[499][9] +coeff11*table[499][10] +coeff12*table[499][11] > > +coeff13*table[499][12] +coeff14*table[499][13]

+coeff15*table[499][14]
> > +coeff16*table[499][15] +coeff17*table[499][16]

+coeff18*table[499][17]
> > +coeff19*table[499][18] +coeff20*table[499][19]

+coeff21*table[499][20]
> > +coeff22*table[499][21] +coeff23*table[499][22]

+coeff24*table[499][23]
> > +coeff25*table[499][24] +coeff26*table[499][25]

+coeff27*table[499][26]
> > +coeff28*table[499][27] +coeff29*table[499][28]

+coeff30*table[499][29]
> > +coeff31*table[499][30] +coeff32*table[499][31]

+coeff33*table[499][32]
> > +coeff34*table[499][33] +coeff35*table[499][34] ;
> >
> > bruteForceSum =
> > point1 +
> > point2 + ... +
> >
> > point499 +
> > point500
> > ;
> >
> > return bruteForceSum;
> >
> > }//DoBruteForceCompute
> >
> >
>
>



Jul 21 '05 #48

This discussion thread is closed

Replies have been disabled for this discussion.