Program to construct Golomb rulers from projective planes

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c Program to construct Golomb rulers from projective planes
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c IBM SOFTWARE DISCLAIMER
c
c conpp.f (version 1.1)
c Copyright (1998,1986)
c International Business Machines Corporation
c
c Permission to use, copy, modify and distribute this software for
c any purpose and without fee is hereby granted, provided that this
c copyright and permission notice appear on all copies of the software.
c The name of the IBM corporation may not be used in any advertising or
c publicity pertaining to the use of the software. IBM makes no
c warranty or representations about the suitability of the software
c for any purpose. It is provided "AS IS" without any express or
c implied warranty, including the implied warranties of merchantability,
c fitness for a particular purpose and non-infringement. IBM shall not
c be liable for any direct, indirect, special or consequential damages
c resulting from the loss of use, data or projects, whether in action
c of contract or tort, arising out or in the connection with the use or
c performance of this software.
c
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c Author: James B. Shearer
c email: jbs@watson.ibm.com
c website: http://www.research.ibm.com/people/s/shearer/
c date: 1998 (based on code written in 1986)
c
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c Version 1.1 (12/11/98) - Renamed variables to conform with
c exhaustive search routines.
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c Requires: ESSL library or portable versions of ESSL routines
c durand, isort (see essl.f)
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c This program constructs good but not necessarily optimal
c Golomb rulers from finte projective planes.
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c Theory
c
c Suppose p is a prime power. Consider the Galois field GF(p) and
c the extension field GF(p**3). Let x be a generator of the cyclic
c multiplicative group of GF(p**3). Then the elements GF(p**3) can
c be represented in the form a+b*x+c*x**2 where a,b,c are elements of
c GF(p). (Note in particular x**3 can be so written, so we may take
c x to be the root of a cubic polynomial over GF(p).) Let two non-
c zero elements, {y,z}, of GF(p**3) be equivalent if one is a scalar
c of the other (ie y/z is an element of the base field GF(p)). This
c partitions the p**3-1 nonzero elements of GF(p**3) into p**2+p+1
c classes (of size p-1). As is well known these classes can be
c thought of as the points of a finite projective plane. Consider
c such a point consisting of the class {y1, y2 ...}. Let y1=x**n1,
c y2=x**n2 ... . We claim n1=n2 mod (p**2+p+1). (Because the
c elements of the base field are generated by x**(p**2+p+1).) Hence
c it is easy to see that we can associate each point of the plane
c with an unique residue mod p**2+p+1. Consider the residues
c associated with the p+1 points on a line in the projective plane.
c We claim these p+1 residues form a distinct difference set mod
c p**2+p+1. Consider for example the points (a+b*x+c*x**2) with
c third coordinate (c) zero. There are p+1 such points which we
c can take to be a+x (a in GF(p)) and 1. Suppose the associated
c residues are not a modular distinct difference set. Then we
c would have for example (a+x)/(b+x)=e*(c+x)/(d+x) (a,b,c,d,e in
c GF(p)). But then x**2+(a+d)*x+a*d=e*(x**2+(b+c)*x+b*c). Or
c equating powers of x, e=1, a+d=b+c, a*d=b*c. So {a,d}={b,c}
c (since they are roots of the same quadratic polynomial). The
c claim follows by contradiction. The other cases involving the
c point 1 are similar.
c Modular distinct difference sets can be unwound and truncated
c to form Golomb rulers. Note we may multiply a modular distinct
c difference set by anything prime to the modulus to obtain another
c modular distinct difference set. The program below tests all
c possibilities to obtain the shortest Golomb rulers.
c The modular difference set construction is due to Singer [2],
c the application to Golomb rulers to Robinson and Bernstein [1].
c The program below finds the best Golomb rulers using this
c construction for prime powers up to maxn-1. It will start to
c fail as maxn**4 overflows integer*4 arithmetic (loop 230). A
c program which just handled primes and not prime powers would be
c simpler.
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c References
c
c 1. J. P. Robinson and A. J. Bernstein, "A class of binary recurrent
c codes with limited error propagation", IEEE Transactions on
c Information Theory, IT-13(1967), p. 106-113.
c 2. J. Singer, "A theorem in finite projective geometry and some
c applications to number theory", Transactions American
c Mathematical Society, 43(1938), p.377-385.
c
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Parameter (maxn=160,maxpow=10)
integer*4 len(maxn),nval(maxn),mrec(maxn,maxn)
integer*4 ids(maxn)
integer*4 mw(2*maxn)
integer*4 ipc(3*maxpow),iit(3*maxpow),itemp(3*maxpow)
real*8 buf(3*maxpow)
integer*4 ibase(3*maxpow,2*maxpow),iperp(3*maxpow,maxpow)
integer*4 irep(maxn),ipiv(maxn)
c initialize best rulers so far
do 5 j=2,maxn
len(j)=maxn*maxn
nval(j)=0
5 continue
c loop over n
do 10 n=2,maxn-1
c check if n is a prime power
c first find smallest prime divisor
do 20 j=2,n
if(mod(n,j).eq.0)go to 30
20 continue
stop "error 20"
30 np=j
npow=1
nprod=j
c next check if n is a power of the smallest prime divisor
40 if(nprod.eq.n)go to 50
nprod=nprod*np
npow=npow+1
if(nprod.le.n)go to 40
c n is not a prime power, go to next n
go to 10
c n is a prime power, construct GF(n**3)=GF(np**ndeg)
50 ndeg=3*npow
c generate random coefficients for monic polynomial P,
c with degree ndeg over GF(np)
60 call irand(ipc,np,ndeg,buf)
c check if constant term is 0, if so generate another polynomial
if(ipc(1).eq.0)go to 60
c check if x is a multiplicative generator mod P
c initialize iit (x**0) to the unit vector
do 70 j=1,ndeg
iit(j)=0
70 continue
iit(1)=1
c generate powers of x
do 80 j=1,n*n*n-2
c multiply iit by x
itemp(1)=ipc(1)*iit(ndeg)
do 90 i=2,ndeg
itemp(i)=iit(i-1)+ipc(i)*iit(ndeg)
90 continue
do 100 i=1,ndeg
iit(i)=mod(itemp(i),np)
100 continue
c check if power of x is 1 prematurely
if(iit(1).ne.1)go to 80
do 110 i=2,ndeg
if(iit(i).ne.0)go to 80
110 continue
c this polynomial no good, go generate another
go to 60
80 continue
c All powers of x ok. We now have a representation of GF(n**3) as
c arithmetic mod a polynomial over GF(np)
c The field GF(n**3) is an extension of the field GF(n). We need
c a way of identifying elements of the subspace generated by GF(n)
c and x. This is easy when n is a prime rather than a prime power,
c these are the elements with x**2 term 0. The prime power case is
c more complicated, we find a linear basis for the space and then
c for the perpendicular space. We can then test by looking at
c inner products with the basis of the perpendicular space.
c First npow powers of x**(n**2+n+1) span GF(n)
c Set first element of GF(n) basis to 1
do 85 j=1,ndeg
ibase(j,1)=0
85 continue
ibase(1,1)=1
c find remaining elements of basis
ibp=n**2+n+1
c initialize iit (x**0) to the unit vector
do 120 j=1,ndeg
iit(j)=0
120 continue
iit(1)=1
c generate powers of x
do 125 ja=2,npow
do 130 j=1,ibp
c multiply iit by x
itemp(1)=ipc(1)*iit(ndeg)
do 140 i=2,ndeg
itemp(i)=iit(i-1)+ipc(i)*iit(ndeg)
140 continue
do 150 i=1,ndeg
iit(i)=mod(itemp(i),np)
150 continue
130 continue
c add to basis vectors
do 160 j=1,ndeg
ibase(j,ja)=iit(j)
160 continue
125 continue
c now find basis of space generated by GF(n) and x.
c generate n additional basis vectors by multiplying first n vectors by x
do 170 ja=1,npow
itemp(1)=ipc(1)*ibase(ndeg,ja)
do 180 i=2,ndeg
itemp(i)=ibase(i-1,ja)+ipc(i)*ibase(ndeg,ja)
180 continue
do 190 i=1,ndeg
ibase(i,npow+ja)=mod(itemp(i),np)
190 continue
170 continue
c we now generate a table of inverses to help us do arithmetic in GF(np)
do 200 j=1,np-1
do 210 i=1,np-1
if(mod(i*j,np).ne.1)go to 210
irep(j)=i
go to 200
210 continue
stop "error 210"
200 continue
c put basis in a normal form.
do 220 j=1,2*npow
c find first non-zero in column j
do 230 i=1,ndeg
if(ibase(i,j).ne.0)go to 240
230 continue
stop "error 230"
c record position of first non-zero
240 ipiv(j)=i
c multiply column so non-zero becomes 1
imult=irep(ibase(i,j))
do 250 i=1,ndeg
ibase(i,j)=mod(ibase(i,j)*imult,np)
250 continue
c zero remaining elements in row
do 260 ja=1,2*npow
if(ja.eq.j)go to 260
imult=ibase(ipiv(j),ja)
do 270 i=1,ndeg
ibase(i,ja)=mod(ibase(i,ja)-imult*ibase(i,j),np)
if(ibase(i,ja).lt.0)ibase(i,ja)=ibase(i,ja)+np
270 continue
260 continue
220 continue
c now construct perpendicular basis
jp=0
do 280 j=1,ndeg
c look for row not among the 2*npow recorded in ipiv
do 290 i=1,2*npow
if(ipiv(i).eq.j)go to 280
290 continue
jp=jp+1
c zero jp'th vector in perpendicular basis
do 300 i=1,ndeg
iperp(i,jp)=0
300 continue
c fill in elements in ipiv rows so as to make inner products 0
do 310 ja=1,2*npow
iperp(ipiv(ja),jp)=ibase(j,ja)
310 continue
c note -1 = np - 1 mod np
iperp(j,jp)=np-1
280 continue
c construct perfect difference set mod n**2+n+1
c look for powers of x in space spanned by GF(n), x
c put 0 in set
ids(1)=0
nc=1
c initialize iit
do 320 j=1,ndeg
iit(j)=0
320 continue
iit(1)=1
c look for powers of x in space spanned by GF(n), x
do 330 j=1,n*n+n
c multiply by x
itemp(1)=ipc(1)*iit(ndeg)
do 340 i=2,ndeg
itemp(i)=iit(i-1)+ipc(i)*iit(ndeg)
340 continue
do 350 i=1,ndeg
iit(i)=mod(itemp(i),np)
350 continue
c check inner products
do 360 ja=1,npow
iip=0
do 370 i=1,ndeg
iip=iip+iperp(i,ja)*iit(i)
370 continue
iip=mod(iip,np)
if(iip.ne.0)go to 330
360 continue
nc=nc+1
ids(nc)=j
330 continue
c check that difference set is right size
if(nc.ne.n+1)stop "error 330"
c output difference set
c write(6,1000)n,(ids(j),j=1,n+1)
c1000 format(1x,i5,5x,(10i5))
c check for better rulers
c cycle over multipliers, don't need to try j and -j mod (n*n+n+1)
c do 420 j=1,n*n+n
do 420 j=1,(n*n+n+1)/2
c check if multiplier prime to modulus
if(igcd(j,n*n+n+1).ne.1)go to 420
c multiply difference set
do 430 i=1,n+1
mw(i)=mod(ids(i)*j,n*n+n+1)
430 continue
c sort new difference set
call isort(mw,1,n+1)
c unwrap difference set
do 440 i=1,n+1
mw(i+n+1)=mw(i)+n*n+n+1
440 continue
c check for new records
do 450 ia=1,n+1
do 460 ib=1,n
if(mw(ia+ib)-mw(ia).ge.len(ib+1))go to 460
c new record ruler
len(ib+1)=mw(ia+ib)-mw(ia)
nval(ib+1)=n
do 470 ja=1,ib+1
mrec(ja,ib+1)=mw(ia+ja-1)-mw(ia)
470 continue
460 continue
450 continue
420 continue
10 continue
c output maximum rulers
do 500 j=2,maxn
if(nval(j).eq.0)go to 500
c put ruler in standard form (flip if needed)
if(mrec((j+1)/2,j)+mrec((j+2)/2,j).lt.len(j))go to 520
c flip ruler
do 510 i=1,(j+1)/2
mtemp=mrec(i,j)
mrec(i,j)=len(j)-mrec(j+1-i,j)
mrec(j+1-i,j)=len(j)-mtemp
510 continue
520 continue
c
c write results for j marks
c
c j,length and prime power to unit 6 (terminal)
c j,length and prime power to unit 1 (disk)
c ruler to unit 1 (disk)
c
write(6,1010)j,len(j),nval(j)
write(1,1020)j,len(j),nval(j)
write(1,1030)(mrec(i,j),i=1,j)
1010 format(1x,3i10)
1020 format(3i10)
1030 format(10i6)
500 continue
c mark end of disk file
write(1,1020)0,0,0
stop
end
c generate random vector of n integers 0,...,np-1
subroutine irand(l,np,n,x)
integer*4 l(*)
real*8 x(*)
real*8 dseed/1.d0/
save dseed
c generate random 0-1 real*8 vector
call durand(dseed,n,x)
c convert to integer 0,...,np-1
do 10 j=1,n
l(j)=np*x(j)
10 continue
return
end
c find gcd of ia,ib using Euler's method
function igcd(ia,ib)
ja=ia
jb=ib
1 jc=mod(ja,jb)
ja=jb
jb=jc
if(jb.ne.0)go to 1
igcd=ja
return
end

Here's output from the program. There are alternating lines; first the number of marks, length and prime power are given, then the modular ruler.

So we have 3 3 2, meaning 3 notes making up 3 scale steps, using
p=2 (which implies n=2^2+2+1=7, the 7-et.) Before that is the truncated ruler of 2 marks on a ruler of length 1 obtained from it.
We have a {0,1,4,6} ruler with p=3 and n=13, a {0,3,4,9,11} ruler
with p=4 and n=21, a {0,1,4,10,12,17} ruler with p=5 and n=31,
and so forth.

2 1 2
0 1
3 3 2
0 1 3
4 6 3
0 1 4 6
5 11 4
0 3 4 9 11
6 17 5
0 1 4 10 12 17
7 28 7
0 3 9 11 23 24 28
8 35 7
0 7 10 16 18 30 31 35
9 45 8
0 3 9 16 20 21 35 43 45
10 55 9
0 1 6 10 23 26 34 41 53 55
11 72 11
0 1 9 19 24 31 52 56 58 69
72
12 85 11
0 2 6 24 29 40 43 55 68 75
76 85
13 114 13
0 3 7 18 20 39 51 61 77 85
86 91 114
14 127 13
0 5 28 38 41 49 50 68 75 92
107 121 123 127
15 155 17
0 7 13 16 30 38 50 77 96 98
122 140 150 151 155
16 179 17
0 9 21 43 47 61 66 67 96 103
135 151 166 168 176 179
17 201 16
0 5 15 34 35 42 73 75 86 89
98 134 151 155 177 183 201
18 216 17
0 2 10 22 53 56 82 83 89 98
130 148 153 167 188 192 205 216
19 246 19
0 4 13 15 42 56 59 77 93 116
126 138 146 174 214 221 240 245 246
20 283 19
0 24 30 43 55 71 75 89 104 125
127 162 167 189 206 215 272 275 282 283
21 333 23
0 4 23 37 40 48 68 78 138 147
154 189 204 238 250 251 256 277 309 331
333
22 358 23
0 2 25 32 58 69 121 130 140 148
152 176 216 233 254 293 307 308 313 342
355 358
23 372 23
0 6 22 24 43 56 95 126 137 146
172 173 201 213 258 273 281 306 311 355
365 369 372
24 425 23
0 9 33 37 38 97 122 129 140 142
152 191 205 208 252 278 286 326 332 353
368 384 403 425
25 480 25
0 12 29 39 72 91 146 157 160 161
166 191 207 214 258 290 316 354 372 394
396 431 459 467 480
26 492 25
0 5 17 28 36 52 62 106 136 149
174 178 234 241 243 289 292 307 329 368
382 388 409 459 491 492
27 553 27
0 3 15 41 66 95 97 106 142 152
220 221 225 242 295 330 338 354 382 388
402 415 486 504 523 546 553
28 585 27
0 3 15 41 66 95 97 106 142 152
220 221 225 242 295 330 338 354 382 388
402 415 486 504 523 546 553 585
29 623 29
0 7 11 31 43 53 100 121 144 150
202 220 229 268 284 285 356 371 390 416
430 465 467 528 582 590 595 620 623
30 680 29
0 12 32 39 49 82 85 100 147 166
206 207 211 286 302 310 316 344 388 399
462 475 500 529 531 552 623 645 671 680
31 747 31
0 17 22 46 72 78 146 176 186 187
245 273 281 288 308 361 365 384 398 436
521 542 555 586 602 604 668 693 735 738
747
32 784 31
0 7 15 26 28 57 112 118 136 176
177 181 211 214 258 309 318 341 389 403
456 476 512 528 582 628 671 696 745 762
772 784
33 859 32
0 22 38 47 91 108 123 136 141 229
256 263 293 319 329 358 360 400 406 505
516 524 559 573 633 684 685 705 708 763
767 847 859
34 938 37
0 4 19 35 77 99 125 148 162 236
249 282 290 366 387 404 431 459 470 506
540 585 679 685 703 746 771 849 869 878
879 881 931 938
35 997 37
0 46 58 64 98 109 114 139 147 221
276 293 364 387 429 431 466 490 509 556
563 625 673 712 733 743 765 769 864 884
893 969 970 984 997
36 1032 37
0 19 54 67 101 112 140 234 290 322
332 362 368 382 419 437 452 481 533 576
607 656 678 739 763 816 839 842 880 905
907 1011 1015 1016 1023 1032
37 1099 37
0 14 63 87 113 169 220 286 289 328
361 363 381 439 464 475 507 519 529 535
566 700 717 746 798 832 839 862 877 962
981 1002 1029 1086 1090 1091 1099
38 1146 37
0 7 57 59 60 69 89 167 192 235
253 259 353 398 432 468 479 507 534 551
572 648 656 689 702 776 790 813 839 861
903 919 934 938 1050 1090 1141 1146
39 1252 41
0 36 51 94 121 125 126 147 186 257
339 350 391 394 441 509 521 539 585 587
593 622 699 762 802 819 918 941 960 974
1041 1069 1079 1103 1128 1148 1236 1245 1252
40 1288 41
0 4 26 38 65 146 169 174 182 206
261 308 333 411 427 446 517 523 532 599
606 639 690 736 739 837 891 893 922 936
966 986 1054 1111 1177 1225 1235 1246 1287 1288
41 1305 41
0 4 26 38 65 146 169 174 182 206
261 308 333 411 427 446 517 523 532 599
606 639 690 736 739 837 891 893 922 936
966 986 1054 1111 1177 1225 1235 1246 1287 1288
1305
42 1397 41
0 34 49 75 88 91 143 160 272 312
318 402 410 420 431 440 517 582 610 635
642 705 706 756 838 861 883 897 941 1014
1047 1090 1095 1114 1151 1230 1234 1261 1296 1308
1395 1397
43 1513 43
0 15 20 84 128 187 287 288 316 397
443 462 485 494 496 518 581 620 732 738
742 745 799 815 836 881 931 967 1081 1107
1121 1159 1251 1292 1322 1340 1371 1398 1433 1445
1488 1505 1513
44 1596 43
0 58 72 133 190 193 214 319 344 351
353 382 438 553 554 590 608 636 655 678
698 728 795 805 821 874 978 986 1027 1127
1133 1207 1211 1222 1255 1321 1389 1434 1485 1498
1520 1525 1537 1596
45 1687 47
0 42 47 54 83 139 148 165 167 279
319 365 426 500 501 521 531 581 599 650
689 714 741 776 898 920 987 1030 1036 1044
1089 1206 1279 1283 1294 1327 1457 1480 1512 1550
1584 1608 1621 1684 1687
46 1703 47
0 2 10 23 54 115 153 237 255 295
311 338 341 457 519 544 551 617 668 685
705 738 780 877 927 936 1005 1050 1054 1131
1143 1157 1179 1198 1288 1348 1456 1503 1527 1532
1538 1566 1623 1638 1702 1703
47 1830 47
0 11 12 116 157 191 224 231 253 290
326 391 396 419 445 513 566 623 702 715
750 813 822 873 900 931 961 976 986 1117
1138 1194 1278 1347 1390 1429 1437 1461 1475 1479
1481 1605 1730 1747 1811 1827 1830
48 1887 49
0 23 36 93 110 161 177 227 252 409
412 433 473 488 536 580 619 651 688 716
770 817 860 905 913 919 954 965 1118 1127
1239 1301 1319 1320 1433 1459 1489 1531 1589 1609
1754 1764 1776 1849 1853 1880 1882 1887
49 1958 49
0 17 20 86 119 140 166 227 240 255
353 430 520 559 564 565 602 675 724 781
817 833 905 929 961 970 980 1131 1162 1189
1212 1319 1403 1433 1437 1451 1462 1497 1504 1589
1601 1680 1763 1785 1825 1880 1888 1956 1958
50 2094 49
0 51 83 110 191 224 226 271 313 413
468 514 591 619 640 683 767 790 796 865
878 887 950 980 990 1046 1199 1211 1225 1285
1329 1391 1525 1536 1540 1543 1577 1593 1601 1671
1672 1710 1809 1829 1834 1973 2027 2046 2063 2094
51 2190 53
0 1 8 26 39 149 223 247 355 384
419 439 485 506 508 548 585 644 650 761
900 936 950 1018 1035 1040 1110 1168 1217 1244
1289 1322 1337 1480 1489 1492 1508 1670 1732 1785
1815 1826 1858 1912 1983 2043 2095 2099 2146 2156
2190
52 2270 53
0 80 81 88 106 119 229 303 327 435
464 499 519 565 586 588 628 665 724 730
841 980 1016 1030 1098 1115 1120 1190 1248 1297
1324 1369 1402 1417 1560 1569 1572 1588 1750 1812
1865 1895 1906 1938 1992 2063 2123 2175 2179 2226
2236 2270
53 2347 53
0 1 9 30 107 211 248 273 297 330
372 386 452 528 572 587 600 655 708 778
809 940 960 962 967 1003 1014 1054 1072 1132
1211 1249 1358 1423 1469 1473 1619 1636 1707 1788
1804 1807 1852 1937 1947 2081 2120 2154 2245 2257
2280 2341 2347
54 2373 53
0 1 9 30 107 211 248 273 297 330
372 386 452 528 572 587 600 655 708 778
809 940 960 962 967 1003 1014 1054 1072 1132
1211 1249 1358 1423 1469 1473 1619 1636 1707 1788
1804 1807 1852 1937 1947 2081 2120 2154 2245 2257
2280 2341 2347 2373
55 2598 59
0 20 86 112 126 141 215 242 284 355
361 525 561 606 703 734 782 842 936 953
957 992 1016 1035 1088 1139 1140 1149 1224 1379
1387 1425 1489 1547 1642 1759 1827 1849 1903 1936
1947 2054 2127 2215 2265 2272 2306 2399 2431 2531
2568 2580 2593 2596 2598
56 2725 59
0 45 52 110 134 169 190 247 298 316
434 489 661 727 757 759 800 838 884 901
1000 1034 1054 1067 1094 1213 1235 1303 1306 1356
1398 1554 1563 1582 1686 1730 1734 1837 2012 2048
2087 2095 2118 2124 2209 2273 2408 2433 2494 2495
2505 2510 2625 2699 2713 2725
57 2773 59
0 16 137 227 231 245 301 373 405 439
534 545 631 686 699 817 829 866 908 929
962 1010 1163 1194 1199 1216 1277 1350 1365 1412
1472 1570 1629 1669 1808 1832 1852 1890 1909 1917
1919 2022 2246 2281 2405 2428 2431 2456 2520 2604
2647 2656 2697 2727 2766 2772 2773
58 2851 59
0 24 87 106 158 270 343 381 446 459
464 471 481 620 636 711 725 755 907 953
968 1015 1052 1094 1122 1128 1148 1314 1357 1386
1443 1528 1536 1567 1659 1668 1852 1856 1892 1966
2019 2060 2083 2128 2178 2395 2397 2446 2548 2645
2646 2678 2705 2726 2782 2793 2848 2851
59 2911 59
0 4 14 133 162 218 400 415 435 440
473 517 576 671 684 805 879 930 980 1056
1073 1122 1154 1200 1242 1261 1272 1313 1347 1412
1577 1599 1608 1688 1691 1840 1897 1936 2006 2100
2162 2163 2169 2190 2216 2300 2397 2542 2550 2587
2610 2674 2710 2722 2765 2789 2893 2895 2911
60 3019 59
0 15 123 168 171 203 208 227 284 386
446 546 584 595 623 656 774 790 840 852
904 910 1016 1143 1157 1241 1250 1315 1332 1378
1407 1461 1502 1592 1732 1734 1757 1843 1851 1939
2006 2042 2131 2141 2175 2228 2246 2372 2504 2511
2654 2658 2684 2685 2705 2727 2806 2951 3006 3019
61 3184 61
0 2 22 71 103 153 187 282 375 408
415 488 555 567 584 625 644 689 744 862
983 1092 1107 1115 1145 1253 1315 1339 1340 1383
1497 1511 1694 1704 1760 1819 1858 1909 1946 1994
2000 2003 2021 2144 2287 2292 2318 2334 2370 2538
2637 2729 2757 2792 2803 2864 2868 2970 3067 3080
3184
62 3215 61
0 16 21 38 63 71 74 81 200 251
291 310 418 462 497 569 593 608 683 729
752 766 872 967 997 1029 1095 1097 1179 1273
1302 1351 1382 1436 1500 1506 1702 1722 1815 1819
1867 1876 2014 2147 2175 2262 2263 2339 2366 2471
2505 2627 2640 2729 2821 2877 2922 2963 2989 3062
3203 3215
63 3391 64
0 22 126 143 172 187 272 278 395 429
487 517 598 654 687 699 736 738 846 933
976 1001 1117 1177 1244 1339 1438 1451 1470 1510
1517 1541 1615 1619 1624 1835 2009 2020 2072 2095
2145 2148 2308 2336 2377 2378 2432 2497 2631 2728
2744 2764 2821 3019 3045 3083 3163 3177 3198 3225
3373 3381 3391
64 3527 64
0 8 44 210 231 247 318 319 510 524
626 651 693 706 725 867 869 878 998 1156
1234 1251 1279 1398 1422 1468 1483 1533 1536 1617
1643 1648 1681 1965 1969 1987 2070 2124 2220 2227
2278 2318 2404 2464 2543 2582 2664 2676 2699 2733
2789 3000 3027 3075 3104 3124 3167 3197 3256 3297
3303 3465 3517 3527
65 3593 64
0 8 44 210 231 247 318 319 510 524
626 651 693 706 725 867 869 878 998 1156
1234 1251 1279 1398 1422 1468 1483 1533 1536 1617
1643 1648 1681 1965 1969 1987 2070 2124 2220 2227
2278 2318 2404 2464 2543 2582 2664 2676 2699 2733
2789 3000 3027 3075 3104 3124 3167 3197 3256 3297
3303 3465 3517 3527 3593
66 3757 67
0 17 25 44 135 180 223 276 345 391
426 440 505 609 675 709 732 894 899 905
909 925 972 1002 1026 1247 1337 1429 1462 1484
1513 1545 1573 1615 1671 1739 1859 1868 2007 2020
2106 2240 2278 2281 2462 2483 2590 2602 2654 2661
2791 2933 2934 3039 3079 3291 3293 3341 3378 3450
3532 3606 3645 3681 3739 3757
67 3819 67
0 17 25 44 135 180 223 276 345 391
426 440 505 609 675 709 732 894 899 905
909 925 972 1002 1026 1247 1337 1429 1462 1484
1513 1545 1573 1615 1671 1739 1859 1868 2007 2020
2106 2240 2278 2281 2462 2483 2590 2602 2654 2661
2791 2933 2934 3039 3079 3291 3293 3341 3378 3450
3532 3606 3645 3681 3739 3757 3819
68 3956 67
0 23 70 137 142 178 241 332 342 350
372 564 629 654 693 697 713 820 853 881
964 1112 1131 1197 1229 1310 1354 1425 1446 1598
1693 1694 1720 1749 1751 1799 1879 1896 1931 2105
2156 2339 2345 2457 2526 2600 2603 2615 2703 2741
2765 2819 2994 3031 3040 3133 3294 3369 3376 3418
3429 3463 3539 3736 3749 3822 3942 3956
69 4145 71
0 41 55 111 171 191 276 322 442 450
495 517 697 751 763 769 853 939 996 1013
1046 1117 1128 1155 1324 1356 1420 1462 1478 1554
1555 1758 1872 1990 2027 2219 2244 2280 2327 2332
2342 2371 2405 2504 2517 2552 2662 2801 2810 2950
3015 3019 3172 3198 3301 3395 3398 3438 3539 3562
3851 3902 3930 3932 3951 4019 4114 4138 4145
70 4217 71
0 18 24 47 99 103 143 176 252 369
431 489 519 591 625 718 757 779 798 810
869 1043 1052 1112 1150 1233 1234 1254 1328 1443
1454 1551 1629 1684 1880 1923 2041 2092 2127 2141
2289 2376 2430 2433 2446 2601 2647 2692 2729 2757
2793 2916 2924 3029 3260 3286 3349 3397 3463 3513
3647 3771 3910 3977 4045 4175 4185 4190 4192 4217
71 4330 71
0 13 14 31 132 212 218 316 376 526
628 655 667 670 696 705 781 847 891 921
953 1147 1367 1374 1421 1458 1651 1655 1745 1764
1785 1833 1884 1920 1987 1992 2152 2233 2267 2340
2395 2478 2543 2571 2668 2739 2876 2928 2939 3003
3028 3061 3085 3177 3298 3300 3320 3343 3467 3650
3729 3745 3841 3890 3900 3946 4063 4199 4269 4277
4330
72 4473 73
0 51 118 140 211 264 283 425 502 618
635 655 666 762 843 945 960 1021 1176 1225
1238 1419 1453 1507 1553 1576 1658 1728 1865 1957
1964 2014 2047 2089 2092 2133 2201 2281 2387 2482
2620 2730 2734 2735 2793 2996 3048 3056 3080 3219
3298 3364 3465 3477 3493 3495 3520 3661 3667 3765
3852 3873 3887 4144 4217 4314 4343 4353 4379 4417
4464 4473
73 4513 73
0 40 91 158 180 251 304 323 465 542
658 675 695 706 802 883 985 1000 1061 1216
1265 1278 1459 1493 1547 1593 1616 1698 1768 1905
1997 2004 2054 2087 2129 2132 2173 2241 2321 2427
2522 2660 2770 2774 2775 2833 3036 3088 3096 3120
3259 3338 3404 3505 3517 3533 3535 3560 3701 3707
3805 3892 3913 3927 4184 4257 4354 4383 4393 4419
4457 4504 4513
74 4753 73
0 40 91 158 180 251 304 323 465 542
658 675 695 706 802 883 985 1000 1061 1216
1265 1278 1459 1493 1547 1593 1616 1698 1768 1905
1997 2004 2054 2087 2129 2132 2173 2241 2321 2427
2522 2660 2770 2774 2775 2833 3036 3088 3096 3120
3259 3338 3404 3505 3517 3533 3535 3560 3701 3707
3805 3892 3913 3927 4184 4257 4354 4383 4393 4419
4457 4504 4513 4753
75 4982 79
0 12 79 82 166 171 209 348 359 423
485 491 629 735 883 1006 1053 1086 1125 1243
1271 1312 1454 1467 1475 1558 1931 1949 1953 1979
2034 2100 2151 2165 2174 2209 2262 2462 2472 2535
2640 2762 2764 2796 2898 3201 3294 3313 3353 3390
3414 3598 3652 3669 3698 3747 3797 3833 3962 4038
4069 4163 4179 4355 4370 4412 4468 4528 4707 4708
4822 4930 4955 4975 4982
76 5089 79
0 21 68 74 82 104 265 382 409 593
655 657 781 851 1044 1125 1134 1213 1279 1355
1384 1422 1455 1468 1686 1807 1818 1819 1905 1946
2045 2052 2212 2313 2361 2364 2420 2483 2538 2697
2800 2860 2895 2929 3052 3101 3146 3198 3276 3308
3348 3601 3618 3805 3907 3987 4018 4044 4062 4072
4230 4267 4272 4420 4445 4554 4774 4790 4794 4867
4886 4910 4925 4975 5066 5089
77 5204 79
0 21 68 74 82 104 265 382 409 593
655 657 781 851 1044 1125 1134 1213 1279 1355
1384 1422 1455 1468 1686 1807 1818 1819 1905 1946
2045 2052 2212 2313 2361 2364 2420 2483 2538 2697
2800 2860 2895 2929 3052 3101 3146 3198 3276 3308
3348 3601 3618 3805 3907 3987 4018 4044 4062 4072
4230 4267 4272 4420 4445 4554 4774 4790 4794 4867
4886 4910 4925 4975 5066 5089 5204
78 5299 79
0 9 33 160 205 331 395 443 523 608
817 818 875 890 937 951 979 1004 1020 1177
1199 1211 1352 1457 1477 1568 1665 1749 1815 1915
1918 1953 1970 2154 2204 2214 2260 2445 2515 2541
2580 2673 2678 2825 2856 3024 3098 3246 3328 3341
3347 3368 3565 3653 3696 3745 3747 3777 3921 4080
4229 4247 4337 4458 4526 4601 4612 4866 4965 5036
5043 5072 5080 5159 5182 5236 5295 5299
79 5408 79
0 109 118 142 269 314 440 504 552 632
717 926 927 984 999 1046 1060 1088 1113 1129
1286 1308 1320 1461 1566 1586 1677 1774 1858 1924
2024 2027 2062 2079 2263 2313 2323 2369 2554 2624
2650 2689 2782 2787 2934 2965 3133 3207 3355 3437
3450 3456 3477 3674 3762 3805 3854 3856 3886 4030
4189 4338 4356 4446 4567 4635 4710 4721 4975 5074
5145 5152 5181 5189 5268 5291 5345 5404 5408
80 5563 79
0 9 23 48 131 157 190 212 335 425
449 585 621 695 770 814 857 935 975 1067
1114 1163 1166 1193 1290 1309 1322 1506 1541 1613
1641 1782 1839 1843 1897 1912 1983 2025 2294 2300
2494 2582 2662 2861 2877 2911 2923 2928 3048 3086
3150 3333 3364 3417 3424 3571 3641 3744 3861 3924
3965 4157 4225 4246 4323 4331 4761 4790 4855 4856
4866 4967 5100 5118 5120 5270 5425 5481 5518 5563
81 5717 83
0 19 27 30 95 111 157 265 433 492
561 593 732 867 907 1017 1083 1090 1114 1139
1308 1391 1427 1512 1693 1721 1763 1907 2000 2063
2113 2152 2165 2200 2212 2318 2332 2355 2396 2652
2658 2748 2882 2936 3011 3015 3097 3115 3336 3462
3523 3659 3805 3850 3879 4027 4136 4169 4174 4189
4191 4314 4417 4568 4612 4692 4726 4797 4885 4928
5145 5239 5346 5355 5356 5413 5528 5554 5605 5626
5717
82 5814 83
0 24 52 66 106 142 192 235 396 428
616 667 754 803 924 969 1054 1113 1202 1260
1276 1329 1339 1409 1679 1740 1778 1834 1859 1898
2012 2043 2072 2077 2089 2335 2406 2718 2719 2741
2842 2850 2917 2985 3098 3170 3232 3258 3262 3273
3444 3463 3541 3703 3810 3932 3967 4164 4212 4219
4310 4414 4461 4586 4698 4782 4800 4803 4809 4959
5003 5098 5263 5265 5380 5417 5490 5590 5698 5718
5731 5814
83 6020 83
0 59 148 159 231 324 334 351 525 740
885 947 952 1029 1049 1157 1186 1317 1325 1483
1506 1541 1615 1639 1646 1725 1793 1836 1874 1920
1989 1991 2036 2245 2549 2563 2564 2582 2603 2833
2849 2945 2967 3066 3096 3190 3378 3412 3468 3582
3614 3618 3705 3843 3949 3962 4012 4037 4092 4285
4350 4398 4697 4757 4823 4849 5036 5140 5177 5218
5262 5313 5319 5480 5533 5718 5760 5788 5895 5959
5968 5971 6020
84 6159 83
0 42 77 124 288 339 368 407 434 494
495 644 682 765 784 788 936 1005 1209 1254
1257 1300 1414 1477 1518 1531 1713 1763 1878 1904
1998 2256 2309 2340 2441 2448 2485 2503 2537 2559
2675 2878 2888 2899 3077 3205 3286 3310 3385 3444
3461 3551 3553 3686 3833 3986 4140 4165 4170 4237
4243 4301 4366 4503 4539 4625 4725 4823 4837 4894
5004 5037 5053 5443 5528 5536 5556 5568 5698 5872
5881 5951 6144 6159
85 6477 89
0 45 75 208 219 228 392 398 449 453
465 511 547 596 610 809 852 1164 1204 1228
1282 1497 1550 1651 1741 1767 1827 1877 1929 1947
2176 2310 2341 2354 2369 2425 2462 2491 2621 2798
2930 3037 3102 3240 3287 3288 3368 3391 3560 3601
3757 3796 3892 3925 3997 4016 4251 4276 4483 4552
4594 4677 4694 4783 4817 4958 4965 5104 5125 5399
5487 5525 5599 5601 5604 5696 5862 5939 5949 5971
6187 6255 6442 6469 6477
86 6584 89
0 22 83 129 211 248 295 300 316 348
650 683 868 930 933 1075 1109 1132 1160 1295
1324 1479 1570 1577 1636 1647 1667 1837 1875 2011
2066 2183 2322 2335 2365 2380 2444 2453 2695 2766
2853 2961 3001 3075 3076 3111 3235 3289 3415 3487
3526 3620 3823 3916 4063 4112 4179 4356 4383 4469
4486 4592 4642 4754 4835 4960 5293 5349 5425 5444
5524 5565 5625 5786 5849 6018 6043 6087 6297 6438
6440 6446 6450 6464 6542 6584
87 6708 89
0 33 36 81 91 109 156 186 497 593
639 784 821 835 852 923 945 1120 1252 1260
1326 1367 1618 1629 1679 1746 1805 1844 1867 1923
1957 2198 2200 2333 2368 2525 2729 2735 2843 2872
2929 3051 3103 3163 3252 3301 3386 3533 3751 3772
3804 3876 3920 4020 4039 4150 4166 4193 4371 4383
4564 4590 4628 4731 4830 5013 5033 5164 5242 5322
5326 5506 5521 5546 5758 5782 6068 6122 6131 6223
6228 6387 6394 6481 6523 6695 6708
88 6745 89
0 3 48 58 76 123 153 464 560 606
751 788 802 819 890 912 1087 1219 1227 1293
1334 1585 1596 1646 1713 1772 1811 1834 1890 1924
2165 2167 2300 2335 2492 2696 2702 2810 2839 2896
3018 3070 3130 3219 3268 3353 3500 3718 3739 3771
3843 3887 3987 4006 4117 4133 4160 4338 4350 4531
4557 4595 4698 4797 4980 5000 5131 5209 5289 5293
5473 5488 5513 5725 5749 6035 6089 6098 6190 6195
6354 6361 6448 6490 6662 6675 6744 6745
89 6778 89
0 33 36 81 91 109 156 186 497 593
639 784 821 835 852 923 945 1120 1252 1260
1326 1367 1618 1629 1679 1746 1805 1844 1867 1923
1957 2198 2200 2333 2368 2525 2729 2735 2843 2872
2929 3051 3103 3163 3252 3301 3386 3533 3751 3772
3804 3876 3920 4020 4039 4150 4166 4193 4371 4383
4564 4590 4628 4731 4830 5013 5033 5164 5242 5322
5326 5506 5521 5546 5758 5782 6068 6122 6131 6223
6228 6387 6394 6481 6523 6695 6708 6777 6778
90 6967 89
0 189 222 225 270 280 298 345 375 686
782 828 973 1010 1024 1041 1112 1134 1309 1441
1449 1515 1556 1807 1818 1868 1935 1994 2033 2056
2112 2146 2387 2389 2522 2557 2714 2918 2924 3032
3061 3118 3240 3292 3352 3441 3490 3575 3722 3940
3961 3993 4065 4109 4209 4228 4339 4355 4382 4560
4572 4753 4779 4817 4920 5019 5202 5222 5353 5431
5511 5515 5695 5710 5735 5947 5971 6257 6311 6320
6412 6417 6576 6583 6670 6712 6884 6897 6966 6967
91 7570 97
0 36 52 79 105 142 165 187 356 452
599 648 677 683 702 856 977 1221 1232 1294
1422 1517 1616 1626 1628 1674 1823 1884 2051 2065
2310 2344 2437 2528 2556 2622 2626 2788 2925 2964
3123 3136 3352 3353 3420 3475 3834 3885 4026 4033
4204 4306 4314 4356 4439 4444 4519 4578 4619 4663
4693 4780 5018 5021 5161 5287 5319 5451 5469 5637
5977 5997 6054 6069 6078 6224 6340 6380 6444 6500
6533 6733 6864 7101 7208 7225 7246 7322 7434 7499
7570
92 7617 97
0 36 52 79 105 142 165 187 356 452
599 648 677 683 702 856 977 1221 1232 1294
1422 1517 1616 1626 1628 1674 1823 1884 2051 2065
2310 2344 2437 2528 2556 2622 2626 2788 2925 2964
3123 3136 3352 3353 3420 3475 3834 3885 4026 4033
4204 4306 4314 4356 4439 4444 4519 4578 4619 4663
4693 4780 5018 5021 5161 5287 5319 5451 5469 5637
5977 5997 6054 6069 6078 6224 6340 6380 6444 6500
6533 6733 6864 7101 7208 7225 7246 7322 7434 7499
7570 7617
93 7726 97
0 17 97 139 192 211 315 379 550 692
699 704 762 840 950 1183 1288 1342 1353 1535
1587 1621 1656 1740 1811 1905 1978 2301 2319 2328
2404 2445 2453 2588 2590 2746 2750 2779 2959 2987
3209 3212 3308 3318 3324 3503 3528 3585 3758 3813
3839 4039 4254 4255 4278 4322 4405 4452 4683 4758
4860 5140 5160 5280 5572 5604 5634 5670 5836 5936
5982 5997 6224 6245 6337 6468 6596 6743 6924 7015
7123 7280 7319 7359 7396 7409 7452 7483 7497 7615
7666 7704 7726
94 7884 97
0 36 52 79 105 142 165 187 356 452
599 648 677 683 702 856 977 1221 1232 1294
1422 1517 1616 1626 1628 1674 1823 1884 2051 2065
2310 2344 2437 2528 2556 2622 2626 2788 2925 2964
3123 3136 3352 3353 3420 3475 3834 3885 4026 4033
4204 4306 4314 4356 4439 4444 4519 4578 4619 4663
4693 4780 5018 5021 5161 5287 5319 5451 5469 5637
5977 5997 6054 6069 6078 6224 6340 6380 6444 6500
6533 6733 6864 7101 7208 7225 7246 7322 7434 7499
7570 7617 7853 7884
95 7967 97
0 22 28 270 280 295 329 433 574 610
626 666 864 926 1047 1066 1286 1319 1414 1415
1432 1548 1574 1637 1867 1943 1954 2051 2153 2246
2317 2377 2424 2428 2492 2497 2766 2875 2889 3093
3174 3198 3343 3389 3556 3657 3700 3847 3868 3876
3921 3959 3982 4047 4383 4571 4610 4737 4827 4854
5035 5070 5090 5242 5284 5296 5445 5454 5646 5732
5883 6037 6040 6159 6226 6558 6571 6602 6643 6701
6767 6799 7088 7322 7401 7458 7495 7632 7735 7742
7817 7819 7867 7897 7967
96 8150 97
0 40 57 205 295 361 579 581 612 789
886 961 1026 1087 1146 1267 1329 1377 1435 1445
1482 1689 1887 2011 2034 2112 2225 2246 2257 2342
2513 2612 2656 2682 2694 2695 2745 2831 2884 3209
3227 3318 3385 3571 3644 3814 3848 3936 3960 4036
4064 4260 4275 4522 4571 4673 4788 4823 4852 4868
4955 4975 4982 5117 5607 5667 5736 5761 5880 5935
6046 6138 6144 6365 6529 6538 6610 6656 6816 6979
7136 7179 7320 7372 7376 7633 7647 7652 7655 7726
7881 7989 8019 8073 8114 8150
97 8357 97
0 61 134 184 233 274 312 340 544 628
744 747 767 974 983 1020 1036 1103 1245 1349
1367 1499 1504 1525 1818 1852 1915 1985 2060 2100
2102 2156 2367 2439 2443 2491 2521 2622 2711 2816
2885 3028 3257 3263 3349 3691 3789 3802 3821 3889
3948 3991 4036 4117 4188 4479 4486 4812 4836 4837
4847 4998 5029 5217 5250 5416 5431 5511 5525 5674
5721 5831 5896 6097 6133 6141 6419 6650 6910 6927
6984 7048 7075 7087 7228 7372 7484 7577 7702 7940
8025 8054 8076 8131 8189 8249 8357
98 8462 101
0 47 60 115 161 194 231 290 403 524
711 796 951 978 996 1050 1082 1131 1581 1634
1656 1676 1822 1833 1895 2091 2093 2143 2223 2329
2393 2487 2609 2709 2882 2916 3041 3097 3179 3286
3455 3552 3578 3592 3617 3661 3829 3983 4086 4107
4197 4330 4333 4551 4690 4741 4830 4868 5100 5163
5192 5304 5409 5467 5497 5722 5732 5809 5850 6058
6124 6406 6407 6422 6571 6747 6855 6867 6890 6898
7046 7050 7274 7279 7476 7661 7732 7874 8077 8084
8101 8175 8194 8203 8251 8395 8456 8462
99 8540 101
0 47 60 115 161 194 231 290 403 524
711 796 951 978 996 1050 1082 1131 1581 1634
1656 1676 1822 1833 1895 2091 2093 2143 2223 2329
2393 2487 2609 2709 2882 2916 3041 3097 3179 3286
3455 3552 3578 3592 3617 3661 3829 3983 4086 4107
4197 4330 4333 4551 4690 4741 4830 4868 5100 5163
5192 5304 5409 5467 5497 5722 5732 5809 5850 6058
6124 6406 6407 6422 6571 6747 6855 6867 6890 6898
7046 7050 7274 7279 7476 7661 7732 7874 8077 8084
8101 8175 8194 8203 8251 8395 8456 8462 8540
100 8831 101
0 291 338 351 406 452 485 522 581 694
815 1002 1087 1242 1269 1287 1341 1373 1422 1872
1925 1947 1967 2113 2124 2186 2382 2384 2434 2514
2620 2684 2778 2900 3000 3173 3207 3332 3388 3470
3577 3746 3843 3869 3883 3908 3952 4120 4274 4377
4398 4488 4621 4624 4842 4981 5032 5121 5159 5391
5454 5483 5595 5700 5758 5788 6013 6023 6100 6141
6349 6415 6697 6698 6713 6862 7038 7146 7158 7181
7189 7337 7341 7565 7570 7767 7952 8023 8165 8368
8375 8392 8466 8485 8494 8542 8686 8747 8753 8831
101 8897 101
0 20 43 44 99 106 231 244 302 433
562 592 883 1066 1103 1213 1251 1302 1311 1392
1497 1563 1597 1609 1624 1720 1777 2122 2191 2219
2250 2462 2527 2696 2826 2894 3067 3243 3264 3293
3346 3483 3596 3602 3618 3650 3690 3883 4053 4098
4234 4308 4319 4327 4576 4581 4896 4991 5005 5040
5131 5428 5432 5505 5508 5592 5670 5819 5886 5993
6032 6171 6223 6241 6365 6375 6547 6731 6814 6847
6968 7143 7207 7309 7413 7460 7688 7729 7843 7951
7976 7993 8068 8094 8286 8463 8578 8739 8741 8861
8897
102 9218 101
0 104 120 373 412 453 551 624 646 688
861 889 1027 1088 1221 1258 1371 1385 1610 1648
1769 1894 1964 1975 2288 2315 2323 2455 2505 2573
2665 2777 2940 2960 2984 2986 3071 3228 3285 3295
3364 3487 3642 3671 3678 3787 3850 4110 4116 4206
4284 4406 4436 4453 4742 4824 4968 5044 5110 5220
5225 5229 5285 5474 5677 5692 5695 5778 6272 6273
6372 6421 6469 6528 6634 7172 7265 7298 7323 7400
7412 7452 7484 7503 7546 7782 7837 7912 7925 8053
8327 8358 8381 8645 8753 8798 8915 8986 9020 9144
9197 9218
103 9408 103
0 111 246 266 373 453 455 534 585 807
871 912 1009 1013 1187 1418 1454 1508 1516 1668
1708 1854 2115 2180 2342 2508 2540 2593 2712 2737
2804 2972 3152 3166 3208 3280 3329 3445 3629 3690
3717 3785 3932 3960 3961 4352 4359 4510 4540 4555
4639 4644 4663 4896 4922 5130 5232 5506 5615 5670
5701 5841 5880 5917 5990 6000 6023 6034 6523 6545
6728 6744 6929 6967 7025 7042 7274 7280 7326 7419
7493 7543 7556 7643 7713 7784 7861 8109 8156 8433
8490 8499 8511 8559 8602 8925 8960 9019 9150 9272
9275 9390 9408
104 9581 103
0 111 246 266 373 453 455 534 585 807
871 912 1009 1013 1187 1418 1454 1508 1516 1668
1708 1854 2115 2180 2342 2508 2540 2593 2712 2737
2804 2972 3152 3166 3208 3280 3329 3445 3629 3690
3717 3785 3932 3960 3961 4352 4359 4510 4540 4555
4639 4644 4663 4896 4922 5130 5232 5506 5615 5670
5701 5841 5880 5917 5990 6000 6023 6034 6523 6545
6728 6744 6929 6967 7025 7042 7274 7280 7326 7419
7493 7543 7556 7643 7713 7784 7861 8109 8156 8433
8490 8499 8511 8559 8602 8925 8960 9019 9150 9272
9275 9390 9408 9581
105 9893 107
0 5 85 182 241 263 276 283 354 386
470 614 660 811 1198 1335 1404 1422 1437 1494
1554 1647 1702 1739 1747 2026 2162 2173 2189 2293
2435 2466 2658 2896 2930 2949 3133 3150 3359 3483
3731 3733 3780 3794 4046 4155 4176 4288 4338 4437
4686 4726 4727 4756 4794 4800 5247 5303 5368 5464
5589 5695 5784 5870 5965 5989 6100 6154 6177 6311
6409 6555 6567 6643 6694 6769 6907 6969 7074 7140
7314 7443 7469 7790 7942 8025 8189 8193 8241 8359
8369 8555 8677 8892 9007 9032 9035 9071 9114 9371
9525 9666 9724 9884 9893
106 10135 107
0 178 252 339 349 554 674 703 733 966
1002 1066 1123 1126 1138 1192 1340 1347 1439 1608
1625 1766 1818 1995 2170 2362 2364 2506 2584 2600
2646 2686 2719 2975 2983 3063 3166 3229 3478 3563
3673 3696 4139 4171 4197 4248 4293 4298 4382 4654
4821 4929 4950 4968 4977 5180 5248 5318 5379 5422
5568 5684 5847 6087 6255 6331 6353 6378 6459 6496
6515 6696 6749 6763 6791 7036 7049 7237 7342 7558
7599 7690 7797 7909 8020 8085 8091 8255 8400 8525
8655 8842 8932 8981 9015 9240 9446 9753 9757 9777
9788 9832 9870 9984 9985 10135
107 10241 109
0 44 123 224 343 372 479 593 620 657
765 845 955 1218 1230 1376 1430 1647 1721 1725
1853 1889 1920 1978 2271 2295 2506 2842 2944 2962
3240 3256 3288 3369 3422 3516 3521 3562 3577 3760
3780 3902 3957 3964 3965 4014 4369 4465 4661 4680
4752 4927 4995 5106 5149 5236 5319 5336 5452 5800
5842 5918 5963 6080 6132 6450 6606 6617 6631 6889
6936 7236 7320 7360 7425 7446 7455 7552 7775 7788
7814 7865 8015 8153 8188 8222 8297 8379 8382 8649
8894 8900 9043 9065 9131 9202 9204 9581 9783 9842
9934 9957 10110 10143 10203 10213 10241
108 10415 109
0 28 146 148 208 281 293 374 394 446
772 859 1022 1134 1181 1288 1377 1725 1728 1736
1754 1880 1959 2273 2286 2290 2389 2479 2547 2563
2618 2677 2788 2815 3153 3158 3322 3368 3483 3493
3525 3589 3765 3780 3843 3947 3953 4337 4480 4499
4536 4550 4616 4851 4970 4991 4992 5067 5120 5262
5303 5312 5606 5790 6001 6039 6263 6303 6386 6440
6463 6507 6682 6863 6912 6945 7231 7362 7584 7620
7678 7925 8158 8201 8249 8481 8538 8583 8842 8867
8991 9079 9230 9269 9299 9330 9364 9486 9713 9799
9907 9931 10109 10116 10214 10288 10323 10415
109 10583 109
0 28 146 148 208 281 293 374 394 446
772 859 1022 1134 1181 1288 1377 1725 1728 1736
1754 1880 1959 2273 2286 2290 2389 2479 2547 2563
2618 2677 2788 2815 3153 3158 3322 3368 3483 3493
3525 3589 3765 3780 3843 3947 3953 4337 4480 4499
4536 4550 4616 4851 4970 4991 4992 5067 5120 5262
5303 5312 5606 5790 6001 6039 6263 6303 6386 6440
6463 6507 6682 6863 6912 6945 7231 7362 7584 7620
7678 7925 8158 8201 8249 8481 8538 8583 8842 8867
8991 9079 9230 9269 9299 9330 9364 9486 9713 9799
9907 9931 10109 10116 10214 10288 10323 10415 10583
110 10767 109
0 13 47 97 183 257 299 411 517 619
673 712 812 897 906 941 1023 1257 1358 1515
1530 1859 1861 1884 1921 2109 2135 2249 2628 2632
2783 2926 2932 3024 3185 3197 3214 3215 3304 3360
3540 3567 3663 3746 4102 4211 4260 4341 4393 4398
4412 4579 4856 4966 5079 5087 5103 5279 5343 5384
5546 5597 5645 6006 6086 6156 6233 6401 6479 6566
6606 6627 6638 6836 7035 7057 7102 7177 7374 7540
7872 7967 7987 8025 8091 8156 8199 8202 8209 8334
8624 8655 8683 8746 8962 8995 9031 9337 9416 9471
9612 9740 9816 9904 10124 10197 10341 10596 10699 10767
111 11108 113
0 77 109 297 371 560 603 700 704 790
817 975 1023 1032 1044 1603 1616 1632 1773 1783
1856 1919 2114 2168 2201 2384 2419 2466 2468 2557
2601 2667 2767 2974 3177 3288 3289 3436 3544 3744
3866 3871 3921 4267 4395 4545 4569 4633 4792 4829
4907 4982 5013 5021 5150 5184 5509 5526 5571 5629
5860 6041 6246 6287 6367 6439 6491 6531 6703 6821
6881 6900 7340 7358 7549 7577 7653 7675 7818 7829
7888 7914 8122 8267 8282 8320 8548 8690 8821 8824
8926 9112 9362 9487 9709 9755 9848 9871 9878 10027
10157 10252 10351 10562 10882 10976 11001 11037 11043 11057
11108
112 11292 113
0 76 79 145 181 206 451 462 483 495
542 663 998 1003 1153 1195 1226 1235 1393 1508
1660 1860 1887 2065 2128 2181 2236 2446 2563 2577
2625 2724 2725 2860 2878 3048 3152 3171 3217 3391
3481 3756 3785 3866 3998 4000 4004 4194 4424 4565
4635 4648 4685 4749 4772 4794 4824 4957 5015 5323
5495 5733 5793 5906 6009 6093 6191 6211 6297 6462
6604 6628 7016 7088 7105 7173 7489 7698 7752 7809
7847 8042 8268 8278 8375 8624 8632 8720 8849 8884
8923 9371 9564 9683 9690 9724 9739 9970 9986 10098
10126 10169 10220 10312 10598 10675 10852 10930 11074 11199
11225 11292
113 11423 113
0 57 81 209 228 396 438 490 550 576
578 809 821 867 888 942 1065 1088 1251 1477
1814 1864 1988 2079 2114 2122 2132 2236 2425 2458
2676 2785 3077 3143 3170 3192 3206 3309 3417 3476
3586 3611 3899 3960 4060 4138 4233 4346 4384 4416
4586 4601 4691 4929 4976 5082 5126 5166 5171 5258
5605 5703 6023 6062 6091 6211 6275 6416 6423 6657
6677 6739 6876 7019 7374 7492 7566 7575 7789 7862
7865 7896 7992 8368 8398 8453 8469 8470 8628 8634
8897 9093 9192 9248 9317 9328 9600 9731 9779 9876
9995 10032 10036 10330 10537 10550 10741 10947 11119 11196
11261 11312 11423
114 11764 113
0 77 109 297 371 560 603 700 704 790
817 975 1023 1032 1044 1603 1616 1632 1773 1783
1856 1919 2114 2168 2201 2384 2419 2466 2468 2557
2601 2667 2767 2974 3177 3288 3289 3436 3544 3744
3866 3871 3921 4267 4395 4545 4569 4633 4792 4829
4907 4982 5013 5021 5150 5184 5509 5526 5571 5629
5860 6041 6246 6287 6367 6439 6491 6531 6703 6821
6881 6900 7340 7358 7549 7577 7653 7675 7818 7829
7888 7914 8122 8267 8282 8320 8548 8690 8821 8824
8926 9112 9362 9487 9709 9755 9848 9871 9878 10027
10157 10252 10351 10562 10882 10976 11001 11037 11043 11057
11108 11400 11468 11764
115 12212 121
0 118 132 189 209 443 467 527 724 880
1028 1287 1534 1608 1650 1656 1771 1896 2006 2022
2031 2081 2168 2176 2189 2379 2382 2383 2803 2835
2931 3023 3239 3413 3439 3468 3515 3649 4111 4177
4280 4451 4482 4523 4635 4779 4852 5260 5282 5345
5396 5442 5569 5597 5710 5737 5861 5876 5965 6143
6188 6250 6308 6521 6817 6827 7066 7287 7327 7420
7506 7714 7744 7823 8027 8203 8297 8302 8493 8529
8688 8741 8852 9004 9027 9245 9346 9475 9518 9740
9807 9809 9863 9897 10040 10339 10404 10422 10439 10868
11060 11112 11190 11337 11443 11763 11827 12013 12025 12032
12093 12130 12163 12174 12212
116 12412 121
0 180 261 291 305 418 451 553 607 741
788 932 1179 1230 1326 1541 1715 1734 1771 1797
1956 1974 2023 2274 2291 2327 2555 2713 2737 3056
3467 3551 3566 3582 3593 3902 3954 4162 4171 4226
4231 4266 4367 4444 4519 4611 4650 4845 4917 4951
5175 5329 5639 5722 5862 5864 5971 6056 6064 6076
6285 6531 6569 6572 6692 6928 6935 6978 7394 7404
7426 7523 7754 8029 8057 8406 8557 8578 8603 8651
8721 8727 8835 8925 9327 9393 9464 9493 9538 9603
9626 9758 9845 9995 10008 10125 10469 10581 10585 10642
10764 10912 10980 11151 11509 11571 11674 11772 11850 11971
12057 12146 12225 12226 12284 12412
117 12517 121
0 102 145 361 397 509 681 703 719 769
928 1321 1501 1513 1541 1555 1637 1638 1745 1752
1912 1983 2101 2247 2286 2413 2662 2792 2867 2890
2931 3000 3060 3336 3340 3493 3625 3655 3756 3933
3952 4009 4087 4460 4508 4563 4598 4989 5000 5219
5256 5369 5390 5414 5513 5542 5569 5716 5879 5894
6112 6177 6254 6516 6565 6830 7044 7053 7193 7344
7362 7436 7527 7579 7649 7930 8014 8034 8382 8714
8795 8912 8915 8959 9021 9205 9236 9427 9478 9654
9726 9912 9925 9998 10093 10204 10640 10642 10648 10727
11199 11232 11299 11487 11699 11716 11953 12069 12094 12128
12174 12330 12335 12398 12424 12456 12517
118 12741 125
0 123 257 271 330 353 382 406 485 757
776 840 866 1025 1065 1268 1367 1698 1758 1826
1836 1842 1996 2005 2275 2324 2710 2756 2939 3025
3037 3386 3442 3503 3609 3679 3783 3974 4088 4089
4092 4127 4234 4354 4556 4618 4749 4796 4807 4968
5081 5132 5221 5488 5887 5912 5987 6109 6204 6443
6524 6654 6661 6797 6862 7013 7018 7033 7195 7208
7449 7649 7743 7815 7836 8067 8111 8276 8343 8664
9040 9067 9141 9159 9351 9353 9385 9537 9663 9897
9945 10002 10030 10318 10553 10608 10641 10814 10856 11114
11157 11377 11413 11454 11504 11534 11956 11978 12136 12202
12233 12304 12341 12349 12537 12591 12678 12741
119 12911 121
0 53 394 496 539 755 791 903 1075 1097
1113 1163 1322 1715 1895 1907 1935 1949 2031 2032
2139 2146 2306 2377 2495 2641 2680 2807 3056 3186
3261 3284 3325 3394 3454 3730 3734 3887 4019 4049
4150 4327 4346 4403 4481 4854 4902 4957 4992 5383
5394 5613 5650 5763 5784 5808 5907 5936 5963 6110
6273 6288 6506 6571 6648 6910 6959 7224 7438 7447
7587 7738 7756 7830 7921 7973 8043 8324 8408 8428
8776 9108 9189 9306 9309 9353 9415 9599 9630 9821
9872 10048 10120 10306 10319 10392 10487 10598 11034 11036
11042 11121 11593 11626 11693 11881 12093 12110 12347 12463
12488 12522 12568 12724 12729 12792 12818 12850 12911
120 13089 121
0 6 44 86 191 241 297 379 425 621
625 648 1075 1116 1169 1311 1429 1733 1985 2022
2093 2209 2216 2249 2307 2308 2359 2448 2705 2768
2782 2844 3145 3153 3313 3362 3489 3506 3515 3679
3783 3794 3814 3986 4112 4281 4355 4745 4857 4966
4994 5173 5256 5334 5377 5445 5597 5783 6028 6241
6276 6295 6606 6696 6781 6783 6999 7011 7332 7489
7554 7590 7651 7773 7902 7932 7998 8027 8161 8176
8208 8416 8708 8730 8775 8854 8875 8878 8888 9008
9125 9290 9617 9642 9690 10033 10378 10447 10583 10653
10734 11106 11181 11199 11238 11464 11548 11828 11930 11994
12101 12232 12433 12488 12493 12607 12819 13001 13017 13089
121 13280 121
0 6 46 97 252 256 297 333 555 608
619 992 999 1024 1025 1187 1211 1504 1634 1776
1969 2070 2174 2176 2315 2401 2404 2499 2538 2557
2665 2674 2708 2758 2889 3034 3086 3232 3352 3375
3746 3763 3896 3995 4107 4173 4369 4452 4494 4613
4693 4748 4919 4995 5022 5174 5619 5649 5721 5759
5796 5888 5961 6079 6360 6445 6864 6879 6923 7036
7180 7194 7318 7374 7688 7770 7877 7955 7973 7986
8190 8404 8527 8790 8811 8819 8880 9158 9252 9272
9326 9426 9674 9823 10133 10212 10561 10626 10790 10795
10916 11003 11406 11441 11453 11469 11706 11854 11924 11986
12046 12114 12162 12219 12229 12450 12538 13098 13209 13258
13280
122 13521 125
0 1 225 301 418 423 612 629 975 1070
1252 1317 1339 1496 1543 1554 1651 1923 1939 1975
2057 2204 2306 2316 2445 2482 2508 2533 2601 2619
2829 3189 3317 3330 3478 3563 3730 3931 4249 4276
4310 4322 4376 4414 4481 4485 4529 4630 4940 4949
4979 5019 5293 5476 5740 5768 5912 6047 6217 6277
6516 6547 6678 6680 6737 7003 7072 7092 7113 7312
7520 7817 7895 7898 8001 8133 8188 8391 8406 8549
8673 8825 8921 9367 9412 9562 9581 9762 9856 10033
10113 10229 10264 10293 10355 10515 10703 10871 10946 11132
11438 11470 11661 11924 11948 11998 12047 12281 12643 12785
12828 12905 12958 13041 13083 13155 13367 13400 13423 13507
13513 13521
123 13802 127
0 65 109 122 154 213 309 450 502 527
621 857 880 950 1048 1081 1122 1468 1505 1526
1568 1650 2106 2185 2310 2321 2548 2587 2614 2753
2893 3006 3025 3028 3277 3279 3327 3500 3535 3730
3916 3963 4065 4329 4412 4568 4597 4993 5219 5365
5382 5499 5559 5579 5628 5666 5709 5804 5916 6258
6573 6626 6911 6912 7110 7114 7140 7427 7434 7489
7505 7701 7737 7920 7984 8089 8095 8246 8254 8698
8765 8816 8850 8862 8976 9347 9375 9474 9528 9616
9708 9836 9851 10248 10272 10464 10570 10579 10654 10740
10946 11429 11485 11490 11669 11745 11785 12104 12135 12478
12568 12640 12829 12937 13038 13111 13255 13269 13392 13402
13512 13580 13802
124 13991 125
0 23 193 323 347 458 465 537 548 1045
1050 1058 1064 1210 1338 1429 1477 1829 1922 2038
2039 2071 2324 2475 2542 2699 2753 2757 2882 2898
2994 3082 3230 3232 3565 3602 3678 3833 4008 4144
4229 4350 4620 4640 5192 5265 5345 5387 5444 5519
5578 5808 5825 6068 6083 6265 6429 6606 6618 6627
6721 6882 6923 7005 7015 7249 7312 7571 7948 8134
8168 8194 8221 8239 8341 8397 8537 8680 8709 8865
8896 8931 9245 9291 9343 9346 9453 9514 9719 9763
9998 10020 10082 10129 10179 10248 10487 10593 10895 11349
11387 11575 11664 11788 11831 11856 11896 11926 12000 12318
12357 12605 12656 12742 12959 12987 13296 13377 13557 13751
13828 13877 13955 13991
125 14055 125
0 23 193 323 347 458 465 537 548 1045
1050 1058 1064 1210 1338 1429 1477 1829 1922 2038
2039 2071 2324 2475 2542 2699 2753 2757 2882 2898
2994 3082 3230 3232 3565 3602 3678 3833 4008 4144
4229 4350 4620 4640 5192 5265 5345 5387 5444 5519
5578 5808 5825 6068 6083 6265 6429 6606 6618 6627
6721 6882 6923 7005 7015 7249 7312 7571 7948 8134
8168 8194 8221 8239 8341 8397 8537 8680 8709 8865
8896 8931 9245 9291 9343 9346 9453 9514 9719 9763
9998 10020 10082 10129 10179 10248 10487 10593 10895 11349
11387 11575 11664 11788 11831 11856 11896 11926 12000 12318
12357 12605 12656 12742 12959 12987 13296 13377 13557 13751
13828 13877 13955 13991 14055
126 14348 127
0 25 113 243 438 492 564 577 578 582
588 638 891 989 1188 1367 1559 1726 1902 2018
2254 2256 2285 2300 2323 2391 2544 2574 2772 2998
3098 3110 3207 3327 3330 3408 3478 3956 4138 4239
4302 4343 4350 4416 4499 4606 4658 4779 4922 4939
5275 5311 5413 5453 5660 5719 5777 5822 5932 6056
6431 6513 6546 6679 6916 7107 7162 7201 7281 7309
7346 7577 7793 7846 7921 7968 8086 8148 8536 8794
8837 8858 9051 9144 9379 9399 9456 9585 9872 9959
10043 10373 10405 10504 10638 10795 10922 10949 10998 11090
11222 11430 11588 11850 12031 12192 12281 12417 12433 12468
12678 12687 12850 12872 13149 13191 13360 13379 13549 13575
13583 13654 13906 14031 14253 14348
127 14460 128
0 92 108 250 347 380 531 542 563 847
1016 1041 1107 1370 1390 1409 1431 1473 1772 1774
1808 1982 2012 2041 2244 2379 2429 2518 2561 3087
3127 3165 3209 3293 3338 3568 3868 3891 3895 3963
4122 4311 4320 4371 4429 4760 4835 4948 5058 5105
5205 5348 5383 5469 5698 5920 6060 6306 6404 6521
6601 6677 6734 6762 6765 6933 6986 7010 7023 7320
7483 8083 8129 8137 8208 8273 8354 8591 8768 8778
8969 8970 8987 9074 9089 9205 9342 9752 9867 10017
10144 10243 10463 10557 10612 10757 10932 11043 11113 11236
11285 11450 11464 11576 11588 11743 12187 12260 12467 12472
12568 12620 12754 12959 13155 13389 13549 13701 13808 13815
13871 13877 14213 14319 14367 14393 14460
128 14821 128
0 136 312 427 446 526 698 699 810 1051
1060 1076 1178 1281 1319 1394 1479 1823 1825 2047
2498 2529 2547 2579 2783 2852 2936 2989 3065 3215
3320 3385 3528 3808 3842 3886 4073 4077 4521 4542
4638 4690 4760 4998 5130 5288 5423 5485 5521 5585
5906 5920 5966 5993 6131 6299 6405 6460 6557 6650
6708 6852 6857 7067 7108 7114 7197 7483 8043 8111
8199 8266 8306 8392 8448 8573 8581 8632 8740 9292
9469 9511 9703 9807 9947 9964 9986 10314 10362 10388
10423 10542 10608 10687 10996 11003 11026 11273 11368 11397
11469 11597 11600 12176 12196 12239 12267 12359 12413 12689
13025 13036 13200 13224 13237 13314 13347 13541 13556 13727
13843 14131 14141 14561 14643 14655 14700 14821
129 15075 128
0 42 110 186 202 267 308 351 487 639
671 801 883 954 969 1112 1228 1241 1545 1609
1620 1869 1984 2033 2092 2175 2205 2402 2491 2576
2654 2723 2749 2756 2996 3357 3485 3507 3928 4005
4206 4235 4333 4424 4451 4572 4617 4677 4910 5034
5071 5249 5284 5419 5424 5575 5713 5765 5779 5964
5982 5984 6078 6259 6588 6878 6981 7140 7237 7281
7348 7354 7404 8123 8144 8178 8216 8224 8277 8600
8679 8737 8933 9115 9169 9324 9411 9450 9501 9621
10087 10226 10335 10409 10578 10640 10765 10835 11105 11114
11115 11162 11417 11562 11693 11797 11800 11825 12195 12212
12231 12235 12423 12785 12848 13236 13412 13443 13680 13704
13904 14023 14229 14547 14741 14829 14963 14975 15075
130 15275 131
0 142 211 227 332 430 501 654 663 845
1045 1096 1282 1527 1645 1838 2012 2056 2095 2365
2571 2637 2650 2652 2686 2987 3226 3342 3359 3620
3624 3652 3754 3878 3883 3943 4029 4124 4284 4371
4956 4977 5059 5120 5121 5445 5567 5796 5816 5819
5864 5936 5991 6044 6145 6321 6339 6398 6605 6697
6705 6901 7084 7467 7473 7525 7551 7767 7863 7890
7999 8196 8355 8380 8494 8557 8707 9204 9316 9353
9629 9636 9726 9755 9767 9802 10265 10375 10479 10503
10533 10743 10783 11086 11100 11330 11566 11727 11884 11894
12019 12353 12459 12552 12622 12774 12930 12997 13138 13232
13270 13343 13417 13632 13688 13731 13777 13948 14169 14347
14633 14652 14683 14740 14820 14831 14853 14895 15087 15275
131 15548 131
0 67 93 115 221 506 571 977 1161 1212
1216 1237 1274 1531 1561 1747 1817 2016 2164 2180
2325 2372 2378 2447 2452 2480 2652 2729 2862 2881
2992 3174 3406 3445 3458 3704 3947 3958 4082 4211
4343 4441 4730 4761 4773 4829 4970 5084 5445 5481
5491 5581 5598 5630 5718 5809 6057 6183 6288 6478
6505 6780 6781 6783 6974 7118 7152 7175 7633 7657
7974 8056 8224 8400 8516 8589 8603 8760 8841 8979
9278 9447 9536 9621 9630 9659 9713 9777 9872 10068
10193 10522 10643 11160 11231 11456 11464 11565 11606 11651
11896 12063 12175 12238 12485 12564 12636 12798 13013 13156
13217 13314 13321 13380 13424 13694 13975 14145 14619 14703
14738 14753 14884 14926 15086 15106 15146 15312 15452 15530
15548
132 15893 131
0 80 195 477 705 775 798 1032 1207 1235
1399 1420 1578 1785 1892 2144 2192 2294 2316 2556
2668 2800 3000 3036 3094 3278 3317 3323 3335 3391
3497 3584 3626 3651 3698 3773 3786 3850 4361 4391
4445 4446 4662 4950 4974 5039 5312 5350 5358 5449
5604 5919 6215 6265 6318 6548 6688 6885 6946 7067
7099 7133 7140 7150 7331 7371 7621 7767 7786 7884
8060 8202 8311 8373 8616 8742 8893 9050 9081 9287
9407 9597 9824 9928 10044 10046 10213 10424 10771 10857
10976 11066 11137 11229 11262 11278 11305 11406 11488 11848
12168 12276 12424 12551 12555 12560 12694 12909 13315 13352
13396 13448 13809 13888 13914 14238 14307 14456 14485 14939
14959 15125 15184 15281 15284 15295 15625 15685 15748 15763
15858 15893
133 16192 137
0 50 56 147 185 222 224 323 579 762
769 953 1154 1195 1205 1206 1375 1610 1618 1703
1712 1736 1928 2000 2428 2440 2673 2752 2826 3352
3509 3592 3628 3717 3748 3770 3790 3963 4055 4070
4252 4269 4627 4736 4802 4847 4963 5084 5247 5586
5654 5672 5716 5903 5985 6275 6471 6501 6549 6767
6848 6851 6912 7015 7156 7227 7361 7629 7808 7954
8216 8263 8303 8457 8597 8622 8734 8799 8951 9074
9090 9385 9483 9737 9804 10082 10292 10473 10624 10883
10988 10993 11007 11083 11115 11143 11243 11286 11544 11573
11887 12352 12411 12415 12559 12900 12954 12980 13086 13113
13324 13675 13721 13744 13978 13991 14048 14197 14311 14426
14677 14698 14794 14907 15065 15269 15357 15552 15683 15741
15969 16157 16192
134 16296 137
0 9 16 38 62 114 178 267 463 744
775 955 1027 1225 1379 1390 1651 1782 1937 2023
2126 2175 2256 2351 2352 2536 2642 2781 2974 3029
3037 3329 3611 3655 3798 4077 4319 4331 4615 4685
4807 4948 4982 5105 5138 5165 5183 5213 5256 5312
5427 5677 5774 5980 5983 6034 6117 6351 6453 6545
6672 6838 6918 7194 7417 7504 7529 7617 7726 7728
7854 7874 8033 8169 8360 8437 8933 8952 8956 9188
9227 9346 9447 9659 9724 9977 10141 10518 10791 10857
10898 10977 11433 11438 11571 11779 11840 11872 11940 11982
12022 12324 12382 12418 12542 12705 12969 13348 13358 13415
13636 13662 13806 13875 14010 14237 14250 14418 14465 14590
15075 15090 15149 15473 15487 15508 15558 15675 15703 15807
15824 16206 16212 16296
135 16622 139
0 35 43 163 301 354 370 453 525 584
650 870 904 922 1013 1139 1387 1489 1814 1860
1914 2178 2295 2370 2373 2449 2507 2891 3089 3410
3461 3491 3635 3750 4048 4132 4189 4408 4493 4512
4532 4777 4806 5056 5103 5192 5217 5531 5932 6024
6239 6240 6262 6276 6440 6444 6472 6629 6725 6906
6966 7073 7205 7407 7837 7854 8030 8178 8205 8220
8624 8753 8786 9015 9046 9056 9392 9441 9489 9552
9576 9692 9698 9864 10272 10581 10679 10686 10750 10844
11281 11348 11434 11507 11690 11751 11839 11901 11945 11957
12144 12687 12757 12797 12936 13018 13039 13044 13252 13475
13617 13712 13750 13863 13990 14221 14366 14368 14377 14489
14554 14845 14913 15140 15241 15647 15702 15875 15920 15994
16230 16452 16532 16545 16622
136 16766 137
0 50 56 147 185 222 224 323 579 762
769 953 1154 1195 1205 1206 1375 1610 1618 1703
1712 1736 1928 2000 2428 2440 2673 2752 2826 3352
3509 3592 3628 3717 3748 3770 3790 3963 4055 4070
4252 4269 4627 4736 4802 4847 4963 5084 5247 5586
5654 5672 5716 5903 5985 6275 6471 6501 6549 6767
6848 6851 6912 7015 7156 7227 7361 7629 7808 7954
8216 8263 8303 8457 8597 8622 8734 8799 8951 9074
9090 9385 9483 9737 9804 10082 10292 10473 10624 10883
10988 10993 11007 11083 11115 11143 11243 11286 11544 11573
11887 12352 12411 12415 12559 12900 12954 12980 13086 13113
13324 13675 13721 13744 13978 13991 14048 14197 14311 14426
14677 14698 14794 14907 15065 15269 15357 15552 15683 15741
15969 16157 16192 16662 16717 16766
137 17031 139
0 48 69 81 303 323 387 570 687 691
725 955 1091 1153 1250 1291 1292 1365 1432 1603
1885 1908 1917 2035 2632 2828 2889 2929 3051 3320
3337 3344 3359 3525 3764 3827 4178 4188 4458 4533
4718 4864 5067 5117 5273 5510 5599 5644 5655 5820
5875 5927 5933 6101 6374 6444 6907 7023 7094 7172
7198 7264 7520 7588 7779 7932 8025 8069 8112 8148
8177 8302 8321 9072 9167 9204 9287 9381 9550 9585
9743 9869 9971 10323 10442 10533 10700 10730 10757 11097
11226 11244 11275 11329 11439 11600 11724 12025 12185 12261
12275 12357 12403 12720 12733 12832 13040 13093 13224 13226
13443 13451 13691 14038 14063 14066 14143 14502 14616 14704
14764 14815 14915 15058 15144 15250 15577 16135 16151 16314
16386 16630 16635 16765 16824 16922 17031
138 17124 139
0 35 43 163 301 354 370 453 525 584
650 870 904 922 1013 1139 1387 1489 1814 1860
1914 2178 2295 2370 2373 2449 2507 2891 3089 3410
3461 3491 3635 3750 4048 4132 4189 4408 4493 4512
4532 4777 4806 5056 5103 5192 5217 5531 5932 6024
6239 6240 6262 6276 6440 6444 6472 6629 6725 6906
6966 7073 7205 7407 7837 7854 8030 8178 8205 8220
8624 8753 8786 9015 9046 9056 9392 9441 9489 9552
9576 9692 9698 9864 10272 10581 10679 10686 10750 10844
11281 11348 11434 11507 11690 11751 11839 11901 11945 11957
12144 12687 12757 12797 12936 13018 13039 13044 13252 13475
13617 13712 13750 13863 13990 14221 14366 14368 14377 14489
14554 14845 14913 15140 15241 15647 15702 15875 15920 15994
16230 16452 16532 16545 16622 16944 17074 17124
139 17587 139
0 27 32 216 269 346 371 633 774 778
809 843 1039 1058 1192 1427 1715 1730 1738 1880
1998 2257 2340 2705 2751 2808 2995 3109 3206 3432
3938 4024 4233 4247 4331 4581 4609 4687 4778 4808
4814 5032 5169 5445 5448 5474 5544 5605 6017 6083
6093 6130 6188 6349 6436 6524 6706 6788 6897 6991
7193 7234 7283 7383 7434 7523 7556 7608 8502 8576
8631 8843 8958 8978 9026 9106 9278 9328 9656 9812
9964 10390 10463 10534 10667 10847 10860 10979 11054 11146
11450 11512 11576 11620 11744 12111 12123 12324 12340 12444
12483 12621 12664 12675 12903 13065 13175 13177 13383 13782
13791 13898 13970 13977 14037 14191 14215 14308 14466 14506
14928 14970 14987 15355 15436 15602 16224 16347 16458 16583
16604 16605 16768 17097 17233 17486 17531 17549 17587
140 17938 139
0 80 83 209 332 404 509 561 671 877
933 991 1115 1302 1751 1867 1915 1934 2042 2198
2253 2288 2351 2561 2740 2887 2931 3083 3182 3271
3382 3735 3759 3900 3961
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