SRM 741, D1, 250-Pointer (DigitStringDiv1)

James S. Plank

Sat Nov 3 11:57:31 EDT 2018

Problem Statement.
A main() with the examples compiled in.
A skeleton that compiles with main.cpp.
tests.sh MD5 hash = df512b1887fa2cc1c4ea6a85d0e6b81f
answers.txt MD5 hash = f738e7de6c4a5672c42e06c7f9d7ec6b
Problem Given in Topcoder: November, 2018
Competitors who opened the problem: 99
Competitors who submitted a solution: 82
Number of correct solutions: 42
Accuracy (percentage correct vs those who opened): 49.4%
Average Correct Time: 24.59

In case Topcoder's servers are down, here is a summary of the problem:

You are given a string S, which contains characters from '0' through '9' and is at most 47 characters in length.
You are also given a number X, which will be between 0 and 777,444,111.
A subsequence of S is a string that results when you erase some subset of indices of S.
For example, if S is "12356", then "13" and "256" are subsequences. "61" is not.
Suppose we enumerate all subsequences of S. When we turn them into numbers, how many are greater than X, and do not start with the digit '0"?
Calculate and return this number (it's a long long).

Examples and Answers:

Again, in case the servers are down, here are 14 examples plus answers. These are compiled into the main.cpp as examples 0 through 13. Also, if you give main.cpp two arguments it will treat them as S and X, so you can test your code that way too. If you get examples 0 through 13 correct and they are fast enough, you can be satisfied that you solved this problem.

Number	S	X	Answer
0	0	1	0
1	101	9	3
2	471	47	2
3	2222	97	5
4	95847362	436	216
5	102030405	85	316
6	8034151889109199226907	368249157	2582766
7	54019091675924410392006963001976	33857108	3685790257
8	949778566115406970397000000000000000000079641169	694874013	281455487794133
9	990450814731595674899314817951534213891202482671	777444111	241891551624992
10	906708300000000816661861190246822256891226113143	13879163	200119655333575
11	547371145238239979608276364147467162445006834154	26862	281474707766866
12	550000096205335065730009666579861000000769420768	75676722	213163063953684
13	957837542544882028114572037810101728066730780324	536624519	281469731899716

The tests.sh script tests these cases.

The really dumb solution won't work

This problem has a "power set enumeration" feel to it:

Enumerate the power set of the digits of S.
Any set with more digits than X will add one to the total.
Any set with fewer digits than X will be ignored.
Any set with the same number of digits as X can be turned into an integer and compared with X.

If the constraints had S with, say, 22 digits or less, then this approach would be fast enough. But at 47 digits, this enumearation is 2⁴⁷, which is going to take a few days, to say the least.

On the flip side, you can implement this enumeration pretty quickly, so it's not a bad idea to do so, so that you can double-check your answer later.

So, back to the drawing board.

Doing those three subcases a little faster

Those three subcases seem like a good place to start. Let's try a different approach, based on them. First, some variables: SD is the number of digits of S, and XD is the number of digits of X. Then, our approach should be:

Count the number of substrings of S that don't start with zero, and have more than XD digits.
Count the number of substrings of S that don't start with zero, have exactly XD digits, and are greater than X.
Ignore the rest.

Here was my class definition, and procedure prototype:

long long comb(long long N, long long K);           // Return N-choose-K.

class DigitStringDiv1 {
  public:
    long long count(string s, int x);               // The topcoder problem.
    int X;                                          // The parameter X
    string S;                                       // The parameter S
    string XS;                                      // X as a string of digits
    int SD;                                         // Number of digits in S
    int XD;                                         // Number of digits in X
    long long ngtr_digits(int sindex);              // Counting strings whose sizes are > XD.
    long long neq_digits(int sindex, int xindex);   // Counting strings whose sizes are == XD
    long long Cache[50][15];                        // Memoization cache for neq_digits()
};

Your first job is to write comb() -- when you do this, do both the multiplication and the division in the same for loop. For example, if you're implementing 6-choose-3, you'll do the operations in the following order:

Set rv = 1.
Multiply rv = by 6.
Divide rv = by 1.
Multiply rv = by 5.
Divide rv = by 2.
Multiply rv = by 4.
Divide rv = by 3.

That keeps the return value small, and you're guaranteed that whenver you divide rv by y, rv will be divisible by y.

Test it, and the move onto ngtr_digits(). For this procedure, you want to count the number of strings that start with S[sindex] and that have more than XD digits. This is not a recursive procedure -- you can simply use comb() above to do that calculation.

Go ahead and test this one, too. It will get the correct answer for examples 0, 1 and 3. I'll give you another example to try, and put it into main.cpp as example 5:

S = "102030405";    X = 85;    count(S, X) = 316;

Now, the harder part -- to implement neq_digits(int sindex, int xindex). What this method does is return the number of strings, starting with S[sindex] that are the exact same size as XD-xindex and, when viewed as a number, are greater than atoi(XS.substr(xindex).c_str()). Let's use example 2 to illustrate. In this example, S is "471" and X is 47. So, let's break down the recursive calls of neq_digits():

neq_digits(0,0) will return neq_digits(1,1) + neq_digits(2,1).
neq_digits(1,1) will return 0, because "7" == "7".
neq_digits(2,1) will return 0, because "1" < "7".
neq_digits(1,0) will return 1, because "7" > "4", and there is one substring whose starting index is > 1 and whose size is 1.
neq_digits(2,0) will return 0, because (SD-2) < (XD-0).

You can memoize this on sindex and xindex. To help you out, I've put the following into example 4:

S = "95847362";    X = 436;    count(S, X) = 216;

And here is the memoization cache:

sindex xindex neq_digits(sindex,xindex) 
------ ------ -------------------------
   0      0              21
   1      0              15
   2      0              10
   3      0               4
   4      0               3
   4      1               3
   5      0               0
   5      1               0
   6      0               0
   6      1               1
   6      2               0
   7      0               0
   7      1               0
   7      2               0

Have fun with this one!

More Help

So, below, I have annotated my calls to ngtr_digits() and my calls to neq_digits(x, 0). If you're feeling stuck, see if you can implement these two methods and have their output match mine:

UNIX> a.out 0
ngtr_digits(0) = 0.     Total = 0
neq_digits(0) = 0.     Total = 0
S=0    X=1    Answer=0
UNIX> a.out 1
ngtr_digits(0) = 3.     Total = 3
ngtr_digits(1) = 0.     Total = 3
ngtr_digits(2) = 0.     Total = 3
neq_digits(0) = 0.     Total = 3
neq_digits(1) = 0.     Total = 3
neq_digits(2) = 0.     Total = 3
S=101    X=9    Answer=3
UNIX> a.out 2
ngtr_digits(0) = 1.     Total = 1
ngtr_digits(1) = 0.     Total = 1
ngtr_digits(2) = 0.     Total = 1
neq_digits(0) = 0.     Total = 1
neq_digits(1) = 1.     Total = 2
neq_digits(2) = 0.     Total = 2
S=471    X=47    Answer=2
UNIX> a.out 3
ngtr_digits(0) = 4.     Total = 4
ngtr_digits(1) = 1.     Total = 5
ngtr_digits(2) = 0.     Total = 5
ngtr_digits(3) = 0.     Total = 5
neq_digits(0) = 0.     Total = 5
neq_digits(1) = 0.     Total = 5
neq_digits(2) = 0.     Total = 5
neq_digits(3) = 0.     Total = 5
S=2222    X=97    Answer=5
UNIX> a.out 4
ngtr_digits(0) = 99.     Total = 99
ngtr_digits(1) = 42.     Total = 141
ngtr_digits(2) = 16.     Total = 157
ngtr_digits(3) = 5.     Total = 162
ngtr_digits(4) = 1.     Total = 163
ngtr_digits(5) = 0.     Total = 163
ngtr_digits(6) = 0.     Total = 163
ngtr_digits(7) = 0.     Total = 163
neq_digits(0) = 21.     Total = 184
neq_digits(1) = 15.     Total = 199
neq_digits(2) = 10.     Total = 209
neq_digits(3) = 4.     Total = 213
neq_digits(4) = 3.     Total = 216
neq_digits(5) = 0.     Total = 216
neq_digits(6) = 0.     Total = 216
neq_digits(7) = 0.     Total = 216
S=95847362    X=436    Answer=216
UNIX> a.out 5
ngtr_digits(0) = 247.     Total = 247
ngtr_digits(1) = 0.     Total = 247
ngtr_digits(2) = 57.     Total = 304
ngtr_digits(3) = 0.     Total = 304
ngtr_digits(4) = 11.     Total = 315
ngtr_digits(5) = 0.     Total = 315
ngtr_digits(6) = 1.     Total = 316
ngtr_digits(7) = 0.     Total = 316
ngtr_digits(8) = 0.     Total = 316
neq_digits(0) = 0.     Total = 316
neq_digits(1) = 0.     Total = 316
neq_digits(2) = 0.     Total = 316
neq_digits(3) = 0.     Total = 316
neq_digits(4) = 0.     Total = 316
neq_digits(5) = 0.     Total = 316
neq_digits(6) = 0.     Total = 316
neq_digits(7) = 0.     Total = 316
neq_digits(8) = 0.     Total = 316
S=102030405    X=85    Answer=316
UNIX> a.out 6
ngtr_digits(0) = 1695222.     Total = 1695222
ngtr_digits(1) = 0.     Total = 1695222
ngtr_digits(2) = 354522.     Total = 2049744
ngtr_digits(3) = 155382.     Total = 2205126
ngtr_digits(4) = 65536.     Total = 2270662
ngtr_digits(5) = 26333.     Total = 2296995
ngtr_digits(6) = 9949.     Total = 2306944
ngtr_digits(7) = 3473.     Total = 2310417
ngtr_digits(8) = 1093.     Total = 2311510
ngtr_digits(9) = 299.     Total = 2311809
ngtr_digits(10) = 67.     Total = 2311876
ngtr_digits(11) = 0.     Total = 2311876
ngtr_digits(12) = 1.     Total = 2311877
ngtr_digits(13) = 0.     Total = 2311877
ngtr_digits(14) = 0.     Total = 2311877
ngtr_digits(15) = 0.     Total = 2311877
ngtr_digits(16) = 0.     Total = 2311877
ngtr_digits(17) = 0.     Total = 2311877
ngtr_digits(18) = 0.     Total = 2311877
ngtr_digits(19) = 0.     Total = 2311877
ngtr_digits(20) = 0.     Total = 2311877
ngtr_digits(21) = 0.     Total = 2311877
neq_digits(0) = 203490.     Total = 2515367
neq_digits(1) = 0.     Total = 2515367
neq_digits(2) = 5977.     Total = 2521344
neq_digits(3) = 43758.     Total = 2565102
neq_digits(4) = 0.     Total = 2565102
neq_digits(5) = 12870.     Total = 2577972
neq_digits(6) = 0.     Total = 2577972
neq_digits(7) = 3003.     Total = 2580975
neq_digits(8) = 1287.     Total = 2582262
neq_digits(9) = 495.     Total = 2582757
neq_digits(10) = 0.     Total = 2582757
neq_digits(11) = 0.     Total = 2582757
neq_digits(12) = 9.     Total = 2582766
neq_digits(13) = 0.     Total = 2582766
neq_digits(14) = 0.     Total = 2582766
neq_digits(15) = 0.     Total = 2582766
neq_digits(16) = 0.     Total = 2582766
neq_digits(17) = 0.     Total = 2582766
neq_digits(18) = 0.     Total = 2582766
neq_digits(19) = 0.     Total = 2582766
neq_digits(20) = 0.     Total = 2582766
neq_digits(21) = 0.     Total = 2582766
S=8034151889109199226907    X=368249157    Answer=2582766
UNIX> a.out 7
ngtr_digits(0) = 2143911424.     Total = 2143911424
ngtr_digits(1) = 1070937812.     Total = 3214849236
ngtr_digits(2) = 0.     Total = 3214849236
ngtr_digits(3) = 266752238.     Total = 3481601474
ngtr_digits(4) = 132932104.     Total = 3614533578
ngtr_digits(5) = 0.     Total = 3614533578
ngtr_digits(6) = 32828226.     Total = 3647361804
ngtr_digits(7) = 16241061.     Total = 3663602865
ngtr_digits(8) = 7997952.     Total = 3671600817
ngtr_digits(9) = 3913704.     Total = 3675514521
ngtr_digits(10) = 1898712.     Total = 3677413233
ngtr_digits(11) = 910596.     Total = 3678323829
ngtr_digits(12) = 430104.     Total = 3678753933
ngtr_digits(13) = 199140.     Total = 3678953073
ngtr_digits(14) = 89846.     Total = 3679042919
ngtr_digits(15) = 39203.     Total = 3679082122
ngtr_digits(16) = 0.     Total = 3679082122
ngtr_digits(17) = 6476.     Total = 3679088598
ngtr_digits(18) = 2380.     Total = 3679090978
ngtr_digits(19) = 794.     Total = 3679091772
ngtr_digits(20) = 0.     Total = 3679091772
ngtr_digits(21) = 0.     Total = 3679091772
ngtr_digits(22) = 10.     Total = 3679091782
ngtr_digits(23) = 1.     Total = 3679091783
ngtr_digits(24) = 0.     Total = 3679091783
ngtr_digits(25) = 0.     Total = 3679091783
ngtr_digits(26) = 0.     Total = 3679091783
ngtr_digits(27) = 0.     Total = 3679091783
ngtr_digits(28) = 0.     Total = 3679091783
ngtr_digits(29) = 0.     Total = 3679091783
ngtr_digits(30) = 0.     Total = 3679091783
ngtr_digits(31) = 0.     Total = 3679091783
neq_digits(0) = 2629575.     Total = 3681721358
neq_digits(1) = 2035800.     Total = 3683757158
neq_digits(2) = 0.     Total = 3683757158
neq_digits(3) = 0.     Total = 3683757158
neq_digits(4) = 888030.     Total = 3684645188
neq_digits(5) = 0.     Total = 3684645188
neq_digits(6) = 480700.     Total = 3685125888
neq_digits(7) = 0.     Total = 3685125888
neq_digits(8) = 245157.     Total = 3685371045
neq_digits(9) = 170544.     Total = 3685541589
neq_digits(10) = 116280.     Total = 3685657869
neq_digits(11) = 77520.     Total = 3685735389
neq_digits(12) = 0.     Total = 3685735389
neq_digits(13) = 31824.     Total = 3685767213
neq_digits(14) = 19448.     Total = 3685786661
neq_digits(15) = 0.     Total = 3685786661
neq_digits(16) = 0.     Total = 3685786661
neq_digits(17) = 1835.     Total = 3685788496
neq_digits(18) = 1716.     Total = 3685790212
neq_digits(19) = 0.     Total = 3685790212
neq_digits(20) = 0.     Total = 3685790212
neq_digits(21) = 0.     Total = 3685790212
neq_digits(22) = 36.     Total = 3685790248
neq_digits(23) = 8.     Total = 3685790256
neq_digits(24) = 1.     Total = 3685790257
neq_digits(25) = 0.     Total = 3685790257
neq_digits(26) = 0.     Total = 3685790257
neq_digits(27) = 0.     Total = 3685790257
neq_digits(28) = 0.     Total = 3685790257
neq_digits(29) = 0.     Total = 3685790257
neq_digits(30) = 0.     Total = 3685790257
neq_digits(31) = 0.     Total = 3685790257
S=54019091675924410392006963001976    X=33857108    Answer=3685790257
UNIX> a.out 8
ngtr_digits(0) = 140737098539113.     Total = 140737098539113
ngtr_digits(1) = 70368418803149.     Total = 211105517342262
ngtr_digits(2) = 35184101624977.     Total = 246289618967239
ngtr_digits(3) = 17591962196175.     Total = 263881581163414
ngtr_digits(4) = 8795908593831.     Total = 272677489757245
ngtr_digits(5) = 4397895281823.     Total = 277075385039068
ngtr_digits(6) = 2198899866789.     Total = 279274284905857
ngtr_digits(7) = 1099411481052.     Total = 280373696386909
ngtr_digits(8) = 549674978652.     Total = 280923371365561
ngtr_digits(9) = 274813037580.     Total = 281198184403141
ngtr_digits(10) = 137387214780.     Total = 281335571617921
ngtr_digits(11) = 68678477220.     Total = 281404250095141
ngtr_digits(12) = 34327470700.     Total = 281438577565841
ngtr_digits(13) = 0.     Total = 281438577565841
ngtr_digits(14) = 8570386546.     Total = 281447147952387
ngtr_digits(15) = 4279934123.     Total = 281451427886510
ngtr_digits(16) = 2136022699.     Total = 281453563909209
ngtr_digits(17) = 0.     Total = 281453563909209
ngtr_digits(18) = 530396371.     Total = 281454094305580
ngtr_digits(19) = 263644133.     Total = 281454357949713
ngtr_digits(20) = 130712029.     Total = 281454488661742
ngtr_digits(21) = 0.     Total = 281454488661742
ngtr_digits(22) = 0.     Total = 281454488661742
ngtr_digits(23) = 0.     Total = 281454488661742
ngtr_digits(24) = 0.     Total = 281454488661742
ngtr_digits(25) = 0.     Total = 281454488661742
ngtr_digits(26) = 0.     Total = 281454488661742
ngtr_digits(27) = 0.     Total = 281454488661742
ngtr_digits(28) = 0.     Total = 281454488661742
ngtr_digits(29) = 0.     Total = 281454488661742
ngtr_digits(30) = 0.     Total = 281454488661742
ngtr_digits(31) = 0.     Total = 281454488661742
ngtr_digits(32) = 0.     Total = 281454488661742
ngtr_digits(33) = 0.     Total = 281454488661742
ngtr_digits(34) = 0.     Total = 281454488661742
ngtr_digits(35) = 0.     Total = 281454488661742
ngtr_digits(36) = 0.     Total = 281454488661742
ngtr_digits(37) = 0.     Total = 281454488661742
ngtr_digits(38) = 0.     Total = 281454488661742
ngtr_digits(39) = 0.     Total = 281454488661742
ngtr_digits(40) = 0.     Total = 281454488661742
ngtr_digits(41) = 0.     Total = 281454488661742
ngtr_digits(42) = 0.     Total = 281454488661742
ngtr_digits(43) = 0.     Total = 281454488661742
ngtr_digits(44) = 0.     Total = 281454488661742
ngtr_digits(45) = 0.     Total = 281454488661742
ngtr_digits(46) = 0.     Total = 281454488661742
ngtr_digits(47) = 0.     Total = 281454488661742
neq_digits(0) = 314457495.     Total = 281454803119237
neq_digits(1) = 0.     Total = 281454803119237
neq_digits(2) = 215553195.     Total = 281455018672432
neq_digits(3) = 177232627.     Total = 281455195905059
neq_digits(4) = 145008513.     Total = 281455340913572
neq_digits(5) = 118030185.     Total = 281455458943757
neq_digits(6) = 0.     Total = 281455458943757
neq_digits(7) = 1705057.     Total = 281455460648814
neq_digits(8) = 1705057.     Total = 281455462353871
neq_digits(9) = 0.     Total = 281455462353871
neq_digits(10) = 0.     Total = 281455462353871
neq_digits(11) = 0.     Total = 281455462353871
neq_digits(12) = 0.     Total = 281455462353871
neq_digits(13) = 0.     Total = 281455462353871
neq_digits(14) = 1705057.     Total = 281455464058928
neq_digits(15) = 10518300.     Total = 281455474577228
neq_digits(16) = 7888725.     Total = 281455482465953
neq_digits(17) = 0.     Total = 281455482465953
neq_digits(18) = 0.     Total = 281455482465953
neq_digits(19) = 3108105.     Total = 281455485574058
neq_digits(20) = 2220075.     Total = 281455487794133
neq_digits(21) = 0.     Total = 281455487794133
neq_digits(22) = 0.     Total = 281455487794133
neq_digits(23) = 0.     Total = 281455487794133
neq_digits(24) = 0.     Total = 281455487794133
neq_digits(25) = 0.     Total = 281455487794133
neq_digits(26) = 0.     Total = 281455487794133
neq_digits(27) = 0.     Total = 281455487794133
neq_digits(28) = 0.     Total = 281455487794133
neq_digits(29) = 0.     Total = 281455487794133
neq_digits(30) = 0.     Total = 281455487794133
neq_digits(31) = 0.     Total = 281455487794133
neq_digits(32) = 0.     Total = 281455487794133
neq_digits(33) = 0.     Total = 281455487794133
neq_digits(34) = 0.     Total = 281455487794133
neq_digits(35) = 0.     Total = 281455487794133
neq_digits(36) = 0.     Total = 281455487794133
neq_digits(37) = 0.     Total = 281455487794133
neq_digits(38) = 0.     Total = 281455487794133
neq_digits(39) = 0.     Total = 281455487794133
neq_digits(40) = 0.     Total = 281455487794133
neq_digits(41) = 0.     Total = 281455487794133
neq_digits(42) = 0.     Total = 281455487794133
neq_digits(43) = 0.     Total = 281455487794133
neq_digits(44) = 0.     Total = 281455487794133
neq_digits(45) = 0.     Total = 281455487794133
neq_digits(46) = 0.     Total = 281455487794133
neq_digits(47) = 0.     Total = 281455487794133
S=949778566115406970397000000000000000000079641169    X=694874013    Answer=281455487794133
UNIX> a.out 9
ngtr_digits(0) = 140737098539113.     Total = 140737098539113
ngtr_digits(1) = 70368418803149.     Total = 211105517342262
ngtr_digits(2) = 0.     Total = 211105517342262
ngtr_digits(3) = 17591962196175.     Total = 228697479538437
ngtr_digits(4) = 8795908593831.     Total = 237493388132268
ngtr_digits(5) = 0.     Total = 237493388132268
ngtr_digits(6) = 2198899866789.     Total = 239692287999057
ngtr_digits(7) = 1099411481052.     Total = 240791699480109
ngtr_digits(8) = 549674978652.     Total = 241341374458761
ngtr_digits(9) = 274813037580.     Total = 241616187496341
ngtr_digits(10) = 137387214780.     Total = 241753574711121
ngtr_digits(11) = 68678477220.     Total = 241822253188341
ngtr_digits(12) = 34327470700.     Total = 241856580659041
ngtr_digits(13) = 17154657248.     Total = 241873735316289
ngtr_digits(14) = 8570386546.     Total = 241882305702835
ngtr_digits(15) = 4279934123.     Total = 241886585636958
ngtr_digits(16) = 2136022699.     Total = 241888721659657
ngtr_digits(17) = 1065084887.     Total = 241889786744544
ngtr_digits(18) = 530396371.     Total = 241890317140915
ngtr_digits(19) = 263644133.     Total = 241890580785048
ngtr_digits(20) = 130712029.     Total = 241890711497077
ngtr_digits(21) = 64574877.     Total = 241890776071954
ngtr_digits(22) = 31746651.     Total = 241890807818605
ngtr_digits(23) = 15505590.     Total = 241890823324195
ngtr_digits(24) = 7507638.     Total = 241890830831833
ngtr_digits(25) = 3593934.     Total = 241890834425767
ngtr_digits(26) = 1695222.     Total = 241890836120989
ngtr_digits(27) = 784626.     Total = 241890836905615
ngtr_digits(28) = 354522.     Total = 241890837260137
ngtr_digits(29) = 155382.     Total = 241890837415519
ngtr_digits(30) = 65536.     Total = 241890837481055
ngtr_digits(31) = 26333.     Total = 241890837507388
ngtr_digits(32) = 9949.     Total = 241890837517337
ngtr_digits(33) = 3473.     Total = 241890837520810
ngtr_digits(34) = 1093.     Total = 241890837521903
ngtr_digits(35) = 299.     Total = 241890837522202
ngtr_digits(36) = 67.     Total = 241890837522269
ngtr_digits(37) = 11.     Total = 241890837522280
ngtr_digits(38) = 1.     Total = 241890837522281
ngtr_digits(39) = 0.     Total = 241890837522281
ngtr_digits(40) = 0.     Total = 241890837522281
ngtr_digits(41) = 0.     Total = 241890837522281
ngtr_digits(42) = 0.     Total = 241890837522281
ngtr_digits(43) = 0.     Total = 241890837522281
ngtr_digits(44) = 0.     Total = 241890837522281
ngtr_digits(45) = 0.     Total = 241890837522281
ngtr_digits(46) = 0.     Total = 241890837522281
ngtr_digits(47) = 0.     Total = 241890837522281
neq_digits(0) = 314457495.     Total = 241891151979776
neq_digits(1) = 260932815.     Total = 241891412912591
neq_digits(2) = 0.     Total = 241891412912591
neq_digits(3) = 0.     Total = 241891412912591
neq_digits(4) = 0.     Total = 241891412912591
neq_digits(5) = 0.     Total = 241891412912591
neq_digits(6) = 95548245.     Total = 241891508460836
neq_digits(7) = 0.     Total = 241891508460836
neq_digits(8) = 0.     Total = 241891508460836
neq_digits(9) = 10697754.     Total = 241891519158590
neq_digits(10) = 0.     Total = 241891519158590
neq_digits(11) = 0.     Total = 241891519158590
neq_digits(12) = 0.     Total = 241891519158590
neq_digits(13) = 18156204.     Total = 241891537314794
neq_digits(14) = 0.     Total = 241891537314794
neq_digits(15) = 0.     Total = 241891537314794
neq_digits(16) = 3995409.     Total = 241891541310203
neq_digits(17) = 0.     Total = 241891541310203
neq_digits(18) = 4292145.     Total = 241891545602348
neq_digits(19) = 3108105.     Total = 241891548710453
neq_digits(20) = 2220075.     Total = 241891550930528
neq_digits(21) = 0.     Total = 241891550930528
neq_digits(22) = 0.     Total = 241891550930528
neq_digits(23) = 0.     Total = 241891550930528
neq_digits(24) = 490314.     Total = 241891551420842
neq_digits(25) = 0.     Total = 241891551420842
neq_digits(26) = 77970.     Total = 241891551498812
neq_digits(27) = 125970.     Total = 241891551624782
neq_digits(28) = 0.     Total = 241891551624782
neq_digits(29) = 0.     Total = 241891551624782
neq_digits(30) = 0.     Total = 241891551624782
neq_digits(31) = 0.     Total = 241891551624782
neq_digits(32) = 0.     Total = 241891551624782
neq_digits(33) = 0.     Total = 241891551624782
neq_digits(34) = 0.     Total = 241891551624782
neq_digits(35) = 0.     Total = 241891551624782
neq_digits(36) = 165.     Total = 241891551624947
neq_digits(37) = 45.     Total = 241891551624992
neq_digits(38) = 0.     Total = 241891551624992
neq_digits(39) = 0.     Total = 241891551624992
neq_digits(40) = 0.     Total = 241891551624992
neq_digits(41) = 0.     Total = 241891551624992
neq_digits(42) = 0.     Total = 241891551624992
neq_digits(43) = 0.     Total = 241891551624992
neq_digits(44) = 0.     Total = 241891551624992
neq_digits(45) = 0.     Total = 241891551624992
neq_digits(46) = 0.     Total = 241891551624992
neq_digits(47) = 0.     Total = 241891551624992
S=990450814731595674899314817951534213891202482671    X=777444111    Answer=241891551624992
UNIX> a.out 10
ngtr_digits(0) = 140737412996608.     Total = 140737412996608
ngtr_digits(1) = 0.     Total = 140737412996608
ngtr_digits(2) = 35184317178172.     Total = 175921730174780
ngtr_digits(3) = 17592139428802.     Total = 193513869603582
ngtr_digits(4) = 0.     Total = 193513869603582
ngtr_digits(5) = 4398013312008.     Total = 197911882915590
ngtr_digits(6) = 2198995415034.     Total = 200110878330624
ngtr_digits(7) = 0.     Total = 200110878330624
ngtr_digits(8) = 0.     Total = 200110878330624
ngtr_digits(9) = 0.     Total = 200110878330624
ngtr_digits(10) = 0.     Total = 200110878330624
ngtr_digits(11) = 0.     Total = 200110878330624
ngtr_digits(12) = 0.     Total = 200110878330624
ngtr_digits(13) = 0.     Total = 200110878330624
ngtr_digits(14) = 0.     Total = 200110878330624
ngtr_digits(15) = 4290452423.     Total = 200115168783047
ngtr_digits(16) = 2143911424.     Total = 200117312694471
ngtr_digits(17) = 1070937812.     Total = 200118383632283
ngtr_digits(18) = 534688516.     Total = 200118918320799
ngtr_digits(19) = 266752238.     Total = 200119185073037
ngtr_digits(20) = 132932104.     Total = 200119318005141
ngtr_digits(21) = 66137152.     Total = 200119384142293
ngtr_digits(22) = 32828226.     Total = 200119416970519
ngtr_digits(23) = 16241061.     Total = 200119433211580
ngtr_digits(24) = 7997952.     Total = 200119441209532
ngtr_digits(25) = 3913704.     Total = 200119445123236
ngtr_digits(26) = 0.     Total = 200119445123236
ngtr_digits(27) = 910596.     Total = 200119446033832
ngtr_digits(28) = 430104.     Total = 200119446463936
ngtr_digits(29) = 199140.     Total = 200119446663076
ngtr_digits(30) = 89846.     Total = 200119446752922
ngtr_digits(31) = 39203.     Total = 200119446792125
ngtr_digits(32) = 16384.     Total = 200119446808509
ngtr_digits(33) = 6476.     Total = 200119446814985
ngtr_digits(34) = 2380.     Total = 200119446817365
ngtr_digits(35) = 794.     Total = 200119446818159
ngtr_digits(36) = 232.     Total = 200119446818391
ngtr_digits(37) = 56.     Total = 200119446818447
ngtr_digits(38) = 10.     Total = 200119446818457
ngtr_digits(39) = 1.     Total = 200119446818458
ngtr_digits(40) = 0.     Total = 200119446818458
ngtr_digits(41) = 0.     Total = 200119446818458
ngtr_digits(42) = 0.     Total = 200119446818458
ngtr_digits(43) = 0.     Total = 200119446818458
ngtr_digits(44) = 0.     Total = 200119446818458
ngtr_digits(45) = 0.     Total = 200119446818458
ngtr_digits(46) = 0.     Total = 200119446818458
ngtr_digits(47) = 0.     Total = 200119446818458
neq_digits(0) = 62891499.     Total = 200119509709957
neq_digits(1) = 0.     Total = 200119509709957
neq_digits(2) = 45379620.     Total = 200119555089577
neq_digits(3) = 38320568.     Total = 200119593410145
neq_digits(4) = 0.     Total = 200119593410145
neq_digits(5) = 26978328.     Total = 200119620388473
neq_digits(6) = 22481940.     Total = 200119642870413
neq_digits(7) = 0.     Total = 200119642870413
neq_digits(8) = 0.     Total = 200119642870413
neq_digits(9) = 0.     Total = 200119642870413
neq_digits(10) = 0.     Total = 200119642870413
neq_digits(11) = 0.     Total = 200119642870413
neq_digits(12) = 0.     Total = 200119642870413
neq_digits(13) = 0.     Total = 200119642870413
neq_digits(14) = 0.     Total = 200119642870413
neq_digits(15) = 3365856.     Total = 200119646236269
neq_digits(16) = 1988863.     Total = 200119648225132
neq_digits(17) = 2035800.     Total = 200119650260932
neq_digits(18) = 1560780.     Total = 200119651821712
neq_digits(19) = 1184040.     Total = 200119653005752
neq_digits(20) = 543328.     Total = 200119653549080
neq_digits(21) = 657800.     Total = 200119654206880
neq_digits(22) = 480700.     Total = 200119654687580
neq_digits(23) = 135998.     Total = 200119654823578
neq_digits(24) = 135998.     Total = 200119654959576
neq_digits(25) = 170544.     Total = 200119655130120
neq_digits(26) = 0.     Total = 200119655130120
neq_digits(27) = 77520.     Total = 200119655207640
neq_digits(28) = 50388.     Total = 200119655258028
neq_digits(29) = 31824.     Total = 200119655289852
neq_digits(30) = 19448.     Total = 200119655309300
neq_digits(31) = 11440.     Total = 200119655320740
neq_digits(32) = 6435.     Total = 200119655327175
neq_digits(33) = 3432.     Total = 200119655330607
neq_digits(34) = 1716.     Total = 200119655332323
neq_digits(35) = 792.     Total = 200119655333115
neq_digits(36) = 330.     Total = 200119655333445
neq_digits(37) = 120.     Total = 200119655333565
neq_digits(38) = 1.     Total = 200119655333566
neq_digits(39) = 8.     Total = 200119655333574
neq_digits(40) = 1.     Total = 200119655333575
neq_digits(41) = 0.     Total = 200119655333575
neq_digits(42) = 0.     Total = 200119655333575
neq_digits(43) = 0.     Total = 200119655333575
neq_digits(44) = 0.     Total = 200119655333575
neq_digits(45) = 0.     Total = 200119655333575
neq_digits(46) = 0.     Total = 200119655333575
neq_digits(47) = 0.     Total = 200119655333575
S=906708300000000816661861190246822256891226113143    X=13879163    Answer=200119655333575
UNIX> a.out 11
ngtr_digits(0) = 140737488159619.     Total = 140737488159619
ngtr_digits(1) = 70368743998217.     Total = 211106232157836
ngtr_digits(2) = 35184371924611.     Total = 246290604082447
ngtr_digits(3) = 17592185894430.     Total = 263882789976877
ngtr_digits(4) = 8796092885510.     Total = 272678882862387
ngtr_digits(5) = 4398046386790.     Total = 277076929249177
ngtr_digits(6) = 2199023142760.     Total = 279275952391937
ngtr_digits(7) = 1099511525685.     Total = 280375463917622
ngtr_digits(8) = 549755721717.     Total = 280925219639339
ngtr_digits(9) = 274877823951.     Total = 281200097463290
ngtr_digits(10) = 137438878953.     Total = 281337536342243
ngtr_digits(11) = 68719410024.     Total = 281406255752267
ngtr_digits(12) = 34359678832.     Total = 281440615431099
ngtr_digits(13) = 17179816228.     Total = 281457795247327
ngtr_digits(14) = 8589887654.     Total = 281466385134981
ngtr_digits(15) = 4294925847.     Total = 281470680060828
ngtr_digits(16) = 2147447191.     Total = 281472827508019
ngtr_digits(17) = 1073709893.     Total = 281473901217912
ngtr_digits(18) = 536843071.     Total = 281474438060983
ngtr_digits(19) = 0.     Total = 281474438060983
ngtr_digits(20) = 134196874.     Total = 281474572257857
ngtr_digits(21) = 67090962.     Total = 281474639348819
ngtr_digits(22) = 33539156.     Total = 281474672887975
ngtr_digits(23) = 16764265.     Total = 281474689652240
ngtr_digits(24) = 8377705.     Total = 281474698029945
ngtr_digits(25) = 4185195.     Total = 281474702215140
ngtr_digits(26) = 2089605.     Total = 281474704304745
ngtr_digits(27) = 1042380.     Total = 281474705347125
ngtr_digits(28) = 519252.     Total = 281474705866377
ngtr_digits(29) = 258096.     Total = 281474706124473
ngtr_digits(30) = 127858.     Total = 281474706252331
ngtr_digits(31) = 63019.     Total = 281474706315350
ngtr_digits(32) = 30827.     Total = 281474706346177
ngtr_digits(33) = 14913.     Total = 281474706361090
ngtr_digits(34) = 7099.     Total = 281474706368189
ngtr_digits(35) = 3302.     Total = 281474706371491
ngtr_digits(36) = 1486.     Total = 281474706372977
ngtr_digits(37) = 638.     Total = 281474706373615
ngtr_digits(38) = 256.     Total = 281474706373871
ngtr_digits(39) = 0.     Total = 281474706373871
ngtr_digits(40) = 0.     Total = 281474706373871
ngtr_digits(41) = 7.     Total = 281474706373878
ngtr_digits(42) = 1.     Total = 281474706373879
ngtr_digits(43) = 0.     Total = 281474706373879
ngtr_digits(44) = 0.     Total = 281474706373879
ngtr_digits(45) = 0.     Total = 281474706373879
ngtr_digits(46) = 0.     Total = 281474706373879
ngtr_digits(47) = 0.     Total = 281474706373879
neq_digits(0) = 178365.     Total = 281474706552244
neq_digits(1) = 163185.     Total = 281474706715429
neq_digits(2) = 148995.     Total = 281474706864424
neq_digits(3) = 135751.     Total = 281474707000175
neq_digits(4) = 123410.     Total = 281474707123585
neq_digits(5) = 0.     Total = 281474707123585
neq_digits(6) = 0.     Total = 281474707123585
neq_digits(7) = 91390.     Total = 281474707214975
neq_digits(8) = 82251.     Total = 281474707297226
neq_digits(9) = 32739.     Total = 281474707329965
neq_digits(10) = 66045.     Total = 281474707396010
neq_digits(11) = 58905.     Total = 281474707454915
neq_digits(12) = 25599.     Total = 281474707480514
neq_digits(13) = 46376.     Total = 281474707526890
neq_digits(14) = 40920.     Total = 281474707567810
neq_digits(15) = 35960.     Total = 281474707603770
neq_digits(16) = 31465.     Total = 281474707635235
neq_digits(17) = 27405.     Total = 281474707662640
neq_digits(18) = 23751.     Total = 281474707686391
neq_digits(19) = 0.     Total = 281474707686391
neq_digits(20) = 17550.     Total = 281474707703941
neq_digits(21) = 3581.     Total = 281474707707522
neq_digits(22) = 12650.     Total = 281474707720172
neq_digits(23) = 10626.     Total = 281474707730798
neq_digits(24) = 8855.     Total = 281474707739653
neq_digits(25) = 7315.     Total = 281474707746968
neq_digits(26) = 5985.     Total = 281474707752953
neq_digits(27) = 0.     Total = 281474707752953
neq_digits(28) = 3876.     Total = 281474707756829
neq_digits(29) = 3060.     Total = 281474707759889
neq_digits(30) = 2380.     Total = 281474707762269
neq_digits(31) = 1820.     Total = 281474707764089
neq_digits(32) = 1365.     Total = 281474707765454
neq_digits(33) = 0.     Total = 281474707765454
neq_digits(34) = 715.     Total = 281474707766169
neq_digits(35) = 10.     Total = 281474707766179
neq_digits(36) = 330.     Total = 281474707766509
neq_digits(37) = 210.     Total = 281474707766719
neq_digits(38) = 126.     Total = 281474707766845
neq_digits(39) = 0.     Total = 281474707766845
neq_digits(40) = 0.     Total = 281474707766845
neq_digits(41) = 15.     Total = 281474707766860
neq_digits(42) = 5.     Total = 281474707766865
neq_digits(43) = 1.     Total = 281474707766866
neq_digits(44) = 0.     Total = 281474707766866
neq_digits(45) = 0.     Total = 281474707766866
neq_digits(46) = 0.     Total = 281474707766866
neq_digits(47) = 0.     Total = 281474707766866
S=547371145238239979608276364147467162445006834154    X=26862    Answer=281474707766866
UNIX> a.out 12
ngtr_digits(0) = 140737412996608.     Total = 140737412996608
ngtr_digits(1) = 70368679735964.     Total = 211106092732572
ngtr_digits(2) = 0.     Total = 211106092732572
ngtr_digits(3) = 0.     Total = 211106092732572
ngtr_digits(4) = 0.     Total = 211106092732572
ngtr_digits(5) = 0.     Total = 211106092732572
ngtr_digits(6) = 0.     Total = 211106092732572
ngtr_digits(7) = 1099488385737.     Total = 212205581118309
ngtr_digits(8) = 549736502400.     Total = 212755317620709
ngtr_digits(9) = 274861941072.     Total = 213030179561781
ngtr_digits(10) = 0.     Total = 213030179561781
ngtr_digits(11) = 68708737560.     Total = 213098888299341
ngtr_digits(12) = 34351006520.     Total = 213133239305861
ngtr_digits(13) = 17172813452.     Total = 213150412119313
ngtr_digits(14) = 8584270702.     Total = 213158996390015
ngtr_digits(15) = 0.     Total = 213158996390015
ngtr_digits(16) = 2143911424.     Total = 213161140301439
ngtr_digits(17) = 1070937812.     Total = 213162211239251
ngtr_digits(18) = 534688516.     Total = 213162745927767
ngtr_digits(19) = 266752238.     Total = 213163012680005
ngtr_digits(20) = 0.     Total = 213163012680005
ngtr_digits(21) = 0.     Total = 213163012680005
ngtr_digits(22) = 0.     Total = 213163012680005
ngtr_digits(23) = 16241061.     Total = 213163028921066
ngtr_digits(24) = 7997952.     Total = 213163036919018
ngtr_digits(25) = 3913704.     Total = 213163040832722
ngtr_digits(26) = 1898712.     Total = 213163042731434
ngtr_digits(27) = 910596.     Total = 213163043642030
ngtr_digits(28) = 430104.     Total = 213163044072134
ngtr_digits(29) = 199140.     Total = 213163044271274
ngtr_digits(30) = 89846.     Total = 213163044361120
ngtr_digits(31) = 39203.     Total = 213163044400323
ngtr_digits(32) = 16384.     Total = 213163044416707
ngtr_digits(33) = 0.     Total = 213163044416707
ngtr_digits(34) = 0.     Total = 213163044416707
ngtr_digits(35) = 0.     Total = 213163044416707
ngtr_digits(36) = 0.     Total = 213163044416707
ngtr_digits(37) = 0.     Total = 213163044416707
ngtr_digits(38) = 0.     Total = 213163044416707
ngtr_digits(39) = 1.     Total = 213163044416708
ngtr_digits(40) = 0.     Total = 213163044416708
ngtr_digits(41) = 0.     Total = 213163044416708
ngtr_digits(42) = 0.     Total = 213163044416708
ngtr_digits(43) = 0.     Total = 213163044416708
ngtr_digits(44) = 0.     Total = 213163044416708
ngtr_digits(45) = 0.     Total = 213163044416708
ngtr_digits(46) = 0.     Total = 213163044416708
ngtr_digits(47) = 0.     Total = 213163044416708
neq_digits(0) = 0.     Total = 213163044416708
neq_digits(1) = 0.     Total = 213163044416708
neq_digits(2) = 0.     Total = 213163044416708
neq_digits(3) = 0.     Total = 213163044416708
neq_digits(4) = 0.     Total = 213163044416708
neq_digits(5) = 0.     Total = 213163044416708
neq_digits(6) = 0.     Total = 213163044416708
neq_digits(7) = 18643560.     Total = 213163063060268
neq_digits(8) = 0.     Total = 213163063060268
neq_digits(9) = 0.     Total = 213163063060268
neq_digits(10) = 0.     Total = 213163063060268
neq_digits(11) = 0.     Total = 213163063060268
neq_digits(12) = 0.     Total = 213163063060268
neq_digits(13) = 0.     Total = 213163063060268
neq_digits(14) = 0.     Total = 213163063060268
neq_digits(15) = 0.     Total = 213163063060268
neq_digits(16) = 0.     Total = 213163063060268
neq_digits(17) = 0.     Total = 213163063060268
neq_digits(18) = 457048.     Total = 213163063517316
neq_digits(19) = 0.     Total = 213163063517316
neq_digits(20) = 0.     Total = 213163063517316
neq_digits(21) = 0.     Total = 213163063517316
neq_digits(22) = 0.     Total = 213163063517316
neq_digits(23) = 346104.     Total = 213163063863420
neq_digits(24) = 0.     Total = 213163063863420
neq_digits(25) = 0.     Total = 213163063863420
neq_digits(26) = 0.     Total = 213163063863420
neq_digits(27) = 0.     Total = 213163063863420
neq_digits(28) = 38984.     Total = 213163063902404
neq_digits(29) = 31824.     Total = 213163063934228
neq_digits(30) = 19448.     Total = 213163063953676
neq_digits(31) = 0.     Total = 213163063953676
neq_digits(32) = 0.     Total = 213163063953676
neq_digits(33) = 0.     Total = 213163063953676
neq_digits(34) = 0.     Total = 213163063953676
neq_digits(35) = 0.     Total = 213163063953676
neq_digits(36) = 0.     Total = 213163063953676
neq_digits(37) = 0.     Total = 213163063953676
neq_digits(38) = 0.     Total = 213163063953676
neq_digits(39) = 8.     Total = 213163063953684
neq_digits(40) = 0.     Total = 213163063953684
neq_digits(41) = 0.     Total = 213163063953684
neq_digits(42) = 0.     Total = 213163063953684
neq_digits(43) = 0.     Total = 213163063953684
neq_digits(44) = 0.     Total = 213163063953684
neq_digits(45) = 0.     Total = 213163063953684
neq_digits(46) = 0.     Total = 213163063953684
neq_digits(47) = 0.     Total = 213163063953684
S=550000096205335065730009666579861000000769420768    X=75676722    Answer=213163063953684
UNIX> a.out 13
ngtr_digits(0) = 140737098539113.     Total = 140737098539113
ngtr_digits(1) = 70368418803149.     Total = 211105517342262
ngtr_digits(2) = 35184101624977.     Total = 246289618967239
ngtr_digits(3) = 17591962196175.     Total = 263881581163414
ngtr_digits(4) = 8795908593831.     Total = 272677489757245
ngtr_digits(5) = 4397895281823.     Total = 277075385039068
ngtr_digits(6) = 2198899866789.     Total = 279274284905857
ngtr_digits(7) = 1099411481052.     Total = 280373696386909
ngtr_digits(8) = 549674978652.     Total = 280923371365561
ngtr_digits(9) = 274813037580.     Total = 281198184403141
ngtr_digits(10) = 137387214780.     Total = 281335571617921
ngtr_digits(11) = 68678477220.     Total = 281404250095141
ngtr_digits(12) = 34327470700.     Total = 281438577565841
ngtr_digits(13) = 17154657248.     Total = 281455732223089
ngtr_digits(14) = 8570386546.     Total = 281464302609635
ngtr_digits(15) = 0.     Total = 281464302609635
ngtr_digits(16) = 2136022699.     Total = 281466438632334
ngtr_digits(17) = 1065084887.     Total = 281467503717221
ngtr_digits(18) = 530396371.     Total = 281468034113592
ngtr_digits(19) = 263644133.     Total = 281468297757725
ngtr_digits(20) = 130712029.     Total = 281468428469754
ngtr_digits(21) = 64574877.     Total = 281468493044631
ngtr_digits(22) = 31746651.     Total = 281468524791282
ngtr_digits(23) = 15505590.     Total = 281468540296872
ngtr_digits(24) = 0.     Total = 281468540296872
ngtr_digits(25) = 3593934.     Total = 281468543890806
ngtr_digits(26) = 1695222.     Total = 281468545586028
ngtr_digits(27) = 784626.     Total = 281468546370654
ngtr_digits(28) = 354522.     Total = 281468546725176
ngtr_digits(29) = 0.     Total = 281468546725176
ngtr_digits(30) = 65536.     Total = 281468546790712
ngtr_digits(31) = 0.     Total = 281468546790712
ngtr_digits(32) = 9949.     Total = 281468546800661
ngtr_digits(33) = 3473.     Total = 281468546804134
ngtr_digits(34) = 1093.     Total = 281468546805227
ngtr_digits(35) = 299.     Total = 281468546805526
ngtr_digits(36) = 0.     Total = 281468546805526
ngtr_digits(37) = 11.     Total = 281468546805537
ngtr_digits(38) = 1.     Total = 281468546805538
ngtr_digits(39) = 0.     Total = 281468546805538
ngtr_digits(40) = 0.     Total = 281468546805538
ngtr_digits(41) = 0.     Total = 281468546805538
ngtr_digits(42) = 0.     Total = 281468546805538
ngtr_digits(43) = 0.     Total = 281468546805538
ngtr_digits(44) = 0.     Total = 281468546805538
ngtr_digits(45) = 0.     Total = 281468546805538
ngtr_digits(46) = 0.     Total = 281468546805538
ngtr_digits(47) = 0.     Total = 281468546805538
neq_digits(0) = 314457495.     Total = 281468861263033
neq_digits(1) = 208611211.     Total = 281469069874244
neq_digits(2) = 215553195.     Total = 281469285427439
neq_digits(3) = 177232627.     Total = 281469462660066
neq_digits(4) = 0.     Total = 281469462660066
neq_digits(5) = 118030185.     Total = 281469580690251
neq_digits(6) = 66368826.     Total = 281469647059077
neq_digits(7) = 0.     Total = 281469647059077
neq_digits(8) = 0.     Total = 281469647059077
neq_digits(9) = 35105010.     Total = 281469682164087
neq_digits(10) = 0.     Total = 281469682164087
neq_digits(11) = 0.     Total = 281469682164087
neq_digits(12) = 23535820.     Total = 281469705699907
neq_digits(13) = 18156204.     Total = 281469723856111
neq_digits(14) = 0.     Total = 281469723856111
neq_digits(15) = 0.     Total = 281469723856111
neq_digits(16) = 0.     Total = 281469723856111
neq_digits(17) = 5852925.     Total = 281469729709036
neq_digits(18) = 0.     Total = 281469729709036
neq_digits(19) = 0.     Total = 281469729709036
neq_digits(20) = 0.     Total = 281469729709036
neq_digits(21) = 776092.     Total = 281469730485128
neq_digits(22) = 1081575.     Total = 281469731566703
neq_digits(23) = 0.     Total = 281469731566703
neq_digits(24) = 0.     Total = 281469731566703
neq_digits(25) = 0.     Total = 281469731566703
neq_digits(26) = 203490.     Total = 281469731770193
neq_digits(27) = 125970.     Total = 281469731896163
neq_digits(28) = 0.     Total = 281469731896163
neq_digits(29) = 0.     Total = 281469731896163
neq_digits(30) = 0.     Total = 281469731896163
neq_digits(31) = 0.     Total = 281469731896163
neq_digits(32) = 0.     Total = 281469731896163
neq_digits(33) = 3003.     Total = 281469731899166
neq_digits(34) = 0.     Total = 281469731899166
neq_digits(35) = 495.     Total = 281469731899661
neq_digits(36) = 0.     Total = 281469731899661
neq_digits(37) = 45.     Total = 281469731899706
neq_digits(38) = 9.     Total = 281469731899715
neq_digits(39) = 1.     Total = 281469731899716
neq_digits(40) = 0.     Total = 281469731899716
neq_digits(41) = 0.     Total = 281469731899716
neq_digits(42) = 0.     Total = 281469731899716
neq_digits(43) = 0.     Total = 281469731899716
neq_digits(44) = 0.     Total = 281469731899716
neq_digits(45) = 0.     Total = 281469731899716
neq_digits(46) = 0.     Total = 281469731899716
neq_digits(47) = 0.     Total = 281469731899716
S=957837542544882028114572037810101728066730780324    X=536624519    Answer=281469731899716
UNIX>