
% To test an example, the following goal can be called: 
% "example(N,X), cA(B,L,X).", or 

% where X is the list to be tested, N is numerical identifier of the sequence,
% B is a discrepancy bound, L is the length of the list X.
% For two concrete examples reported in the paper use
% example(1160,X),cA(2,1160,X). 
% example(13000,X),cA(3,13000,X).

% If discrepancy is indeed bounded by B, the value of X will be returned; 
% If discrepancy is not bounded "false" will be returned.   


% computes signum of the list of integers 

signify([],[]).
signify([H|X],[HH|XX]):-HH is sign(H),signify(X,XX).


% Given a list X and a positive integer N produces a list Y with every Nth  
% element of X

filter(N,X,Y):-everyN(N,N,X,Y),!.

everyN(N,1,[H|X],[H|Y]):-everyN(N,N,X,Y).
everyN(N,K,[H|X],Y):-KK is K - 1,everyN(N,KK,X,Y). 
everyN(N,K,[],[]):-!.


% Given a list of integers X checks whether the absolute value of 
% partial sums is bounded by a positive integer N 

sb(N,X):-sum_bound(N,X,0). 
sum_bound(N,[],K):- abs(K) =< N. 
sum_bound(N,[H|X],K):- abs(K) =< N,KK is K + H, sum_bound(N,X,KK). 


% Given a bound B and a number N (lenght of the list to be tested)  produces the list of lengths of periods 
% to be tested

gen(B,N,X):-genN(B,N,1,X). 
genN(B,N,K,[]):-K * B >  N,!.
genN(B,N,K,[K|X]):- KK is K + 1, genN(B,N,KK,X).  


% For a given bound B, the list of integers X and the list of lengths of periods,
%checks whether all partial sums are bounded by B on all periods from the third argument 

check(B,X,[]). 
check(B,X,[H|T]):-filter(H,X,Y),sb(B,Y),check(B,X,T). 

% Given a bound B, the lenght of the list of integers N and the list of integers X check whether all partial sums are bounded
%on all periods generated by gen.     
c(B,N,X):-gen(B,N,Y),check(B,X,Y).


% The same as above but first,  the list  is "signified" (signum is computed)  
cA(B,N,X):-signify(X,Y),c(B,N,Y).

% Examples to be tested 

% 1. The sequence of discrepancy 2 and the lenght 1160 given at the page 
% cgi.csc.liv.ac.uk/~konev/SAT14
example(1160,
[1,-2,-3,4,-5, 6,7,
-8,-9,10,-11,-12,13,-14,15,
 16,-17,18,19,-20,-21,22,-23,
 24,25, -26,27,28,-29,-30,31,
 -32,33,34,-35, -36,37,-38,-39,
 40,-41,42,43,-44,45, 46,-47,
 -48,49,-50,51,52,-53,-54,55,
 -56,-57,58,-59,60,61,-62,63,
 64,-65, -66,-67,-68,69,70,-71,
 72,73,-74,-75, 76,-77,78,79,
 -80,-81,82,83,-84,85, -86,87,
 88,-89,-90,91,-92,-93,94,-95,
 96,-97,-98,99,100,-101,-102,103,
 -104,105, 106,-107,108,109,-110,-111,
 112,-113,114,115, -116,-117,118,-119,
 -120,121,-122,123,124,-125, -126,127,
 -128,129,130,-131,132,133,134,-135,
 136,-137,-138,139,-140,141,142,-143,
 -144,145, -146,-147,148,149,150,-151,
 -152,153,154,-155, -156,157,-158,-159,
 160,-161,162,163,-164,-165, -166,167,
 168,169,-170,-171,172,-173,-174,175,
 -176,177,178,179,180,-181,-182,-183,
 184,-185, 186,187,-188,189,190,-191,
 -192,-193,194,195, 196,-197,-198,199,
 -200,-201,202,-203,204,205, -206,207,
 208,-209,-210,211,-212,213,214,-215,
 -216,217,-218,219,220,-221,222,-223,
 -224,-225, 226,-227,-228,229,-230,231,
 232,-233,234,235, -236,-237,238,-239,
 240,241,-242,-243,244,-245, -246,247,
 -248,249,250,-251,252,253,-254,-255,
 256,257,-258,-259,-260,261,262,263,
 -264,265, -266,267,-268,-269,270,271,
 -272,-273,274,-275, 276,277,-278,-279,
 280,281,-282,283,-284,285, 286,-287,
 288,-289,-290,-291,292,-293,294,295,
 -296,-297,298,-299,-300,301,-302,303,
 304,-305, -306,307,-308,309,310,-311,
 312,313,-314,-315, 316,-317,318,319,
 -320,-321,322,323,-324,325, -326,-327,
 328,-329,330,-331,332,333,-334,335,
 -336,337,-338,-339,340,-341,342,343,
 -344,-345, 346,-347,348,349,-350,351,
 352,-353,-354,355, -356,357,-358,359,
 -360,-361,362,-363,364,-365, 366,-367,
 -368,369,370,371,-372,373,-374,375,
 376,-377,-378,379,-380,-381,382,-383,
 384,385, 386,-387,-388,389,-390,391,
 -392,393,394,-395, 396,-397,-398,-399,
 400,-401,402,403,-404,405, 406,-407,
 -408,409,-410,411,412,-413,-414,-415,
 -416,417,418,419,420,-421,422,-423,
 424,-425, -426,-427,-428,429,430,431,
 432,-433,-434,-435, 436,-437,-438,439,
 -440,441,442,443,-444,445, -446,-447,
 448,-449,450,451,-452,453,454,-455,
 456,-457,-458,-459,460,461,-462,-463,
 -464,465, 466,-467,-468,469,-470,471,
 472,-473,474,475, -476,-477,478,-479,
 -480,481,-482,483,484,485, 486,-487,
 -488,-489,490,-491,492,493,-494,-495,
 496,-497,-498,499,-500,501,502,503,
 -504,505, -506,-507,508,-509,510,511,
 -512,513,-514,-515, 516,517,518,-519,
 520,-521,-522,523,-524,-525, 526,-527,
 528,529,-530,531,532,-533,-534,535,
 536,-537,-538,-539,-540,541,-542,543,
 544,-545, 546,-547,-548,549,550,-551,
 -552,553,-554,555, 556,-557,558,559,
 -560,-561,-562,563,564,565, -566,-567,
 568,569,-570,-571,-572,573,574,-575,
 -576,577,578,-579,580,-581,582,583,
 -584,585, 586,-587,-588,589,-590,-591,
 592,-593,594,595, -596,597,598,-599,
 600,-601,-602,-603,604,-605, -606,607,
 -608,609,610,-611,612,613,-614,-615,
 616,617,-618,619,-620,-621,622,-623,
 -624,625, -626,627,628,-629,630,631,
 -632,-633,634,-635, -636,637,-638,639,
 640,641,642,-643,-644,-645, -646,647,
 648,649,-650,-651,652,-653,654,655,
 -656,-657,658,659,-660,-661,662,663,
 -664,-665, -666,667,668,669,-670,-671,
 672,-673,-674,675, 676,677,678,-679,
 -680,-681,682,683,-684,685, -686,-687,
 688,-689,690,691,-692,693,694,-695,
 -696,697,-698,699,700,-701,-702,703,
 -704,-705, 706,-707,708,709,-710,-711,
 712,-713,-714,715, 716,717,-718,-719,
 720,721,722,-723,-724,-725, 726,727,
 -728,729,730,-731,-732,-733,734,735,
 736,-737,-738,739,-740,-741,-742,743,
 744,-745, -746,747,748,749,-750,-751,
 -752,753,754,755, 756,-757,758,-759,
 760,-761,-762,763,-764,-765, 766,-767,
 -768,769,-770,771,-772,773,774,775,
 776,-777,-778,-779,780,781,-782,-783,
 784,-785, 786,787,-788,-789,790,-791,
 -792,793,-794,795, 796,-797,798,799,
 -800,801,802,-803,-804,805, -806,807,
 808,-809,-810,-811,-812,813,814,-815,
 816,817,-818,-819,820,821,-822,-823,
 -824,825, 826,827,828,-829,830,-831,
 832,-833,-834,-835, -836,837,-838,839,
 -840,841,842,843,-844,-845, 846,847,
 -848,-849,850,-851,852,-853,854,-855,
 856,857,-858,-859,-860,861,-862,863,
 -864,865, 866,-867,868,-869,870,871,
 -872,873,874,-875, 876,-877,-878,-879,
 880,881,-882,883,-884,-885, -886,887,
 888,889,-890,-891,892,-893,894,895,
 -896,897,898,-899,-900,901,-902,-903,
 904,905, -906,-907,-908,909,910,-911,
 -912,913,914,915, 916,-917,918,-919,
 -920,-921,922,-923,924,925, -926,-927,
 928,-929,-930,931,-932,933,934,-935,
 936,-937,-938,939,940,-941,-942,943,
 -944,945, 946,947,-948,949,-950,951,
 952,-953,954,-955, -956,-957,958,-959,
 960,961,-962,-963,964,965, -966,967,
 -968,969,-970,-971,-972,973,974,-975,
 976,-977,978,979,-980,-981,982,983,
 -984,985, -986,987,988,-989,990,-991,
 -992,993,-994,-995, 996,997,998,-999,
 1000,-1001,-1002,1003,-1004,1005, -1006,-1007,
 1008,1009,-1010,-1011,1012,-1013,1014,1015,
 -1016,-1017,-1018,1019,-1020,1021,1022,1023,
 1024,-1025, -1026,1027,1028,-1029,1030,-1031,
 -1032,1033,-1034,1035, -1036,-1037,1038,1039,
 -1040,-1041,1042,-1043,1044,1045, -1046,-1047,
 1048,1049,1050,-1051,-1052,1053,1054,-1055,
 -1056,1057,-1058,1059,1060,-1061,-1062,1063,
 -1064,-1065, 1066,-1067,1068,1069,-1070,-1071,
 -1072,1073,1074,1075, 1076,-1077,1078,-1079,
 1080,-1081,-1082,1083,1084,-1085, -1086,1087,
 -1088,1089,1090,-1091,-1092,-1093,1094,-1095,
 1096,-1097,-1098,1099,-1100,1101,1102,-1103,
 1104,1105, -1106,1107,1108,-1109,-1110,-1111,
 -1112,1113,-1114,1115, -1116,1117,1118,1119,
 1120,-1121,1122,-1123,-1124,-1125, 1126,1127,
 -1128,1129,-1130,-1131,1132,-1133,1134,1135,
 1136,-1137,-1138,1139,1140,-1141,-1142,1143,
 1144,-1145, -1146,1147,-1148,1149,-1150,1151,
 1152,-1153,1154,-1155, -1156,-1157,-1158,1159,
 -1160]
).
% sequence of discepancy 3 and the lenght 10000
example(10000,
[-1,2,-3,4,5,6,7
,-8,9,-10,-11,12,-13,-14,-15
,-16,17,-18,19,-20,21,22,-23
,-24,25,26,-27,-28,29,30,-31
,32,33,34,-35,-36,37,-38,39
,40,-41,-42,43,44,-45,46,-47
,-48,49,-50,51,-52,-53,54,55
,56,-57,-58,59,60,-61,-62,-63
,64,-65,-66,67,-68,69,70,-71
,72,73,-74,-75,76,-77,78,-79
,80,81,-82,-83,84,85,-86,-87
,-88,-89,90,91,92,93,94,-95
,-96,97,-98,99,-100,101,-102,103
,-104,105,106,107,-108,-109,110,-111
,-112,113,-114,-115,116,-117,118,-119
,-120,-121,122,123,124,-125,126,127
,128,-129,-130,131,-132,-133,-134,135
,-136,137,138,139,140,-141,-142,143
,144,145,-146,-147,-148,-149,150,-151
,152,-153,154,155,156,-157,-158,159
,-160,161,-162,163,164,-165,166,-167
,168,169,-170,171,-172,-173,-174,-175
,176,177,178,-179,-180,-181,-182,183
,-184,185,186,-187,188,189,-190,191
,-192,193,194,-195,-196,197,-198,-199
,200,201,202,-203,204,205,-206,-207
,208,-209,-210,211,-212,-213,214,215
,216,217,-218,-219,-220,221,222,-223
,224,225,-226,-227,228,-229,230,231
,-232,-233,-234,-235,-236,-237,238,239
,240,-241,242,-243,244,245,-246,247
,-248,249,-250,251,-252,253,254,-255
,-256,-257,258,-259,260,261,-262,263
,264,-265,266,-267,268,-269,270,-271
,-272,-273,274,275,-276,-277,-278,279
,-280,281,282,-283,284,285,-286,287
,-288,289,290,-291,-292,-293,-294,295
,296,-297,298,-299,-300,301,302,303
,-304,-305,-306,307,308,309,-310,-311
,312,-313,314,-315,316,-317,318,-319
,-320,321,-322,323,324,325,-326,327
,328,329,-330,-331,-332,333,334,-335
,-336,337,-338,339,340,341,-342,-343
,-344,345,346,-347,-348,-349,350,-351
,352,353,-354,-355,-356,357,358,-359
,360,361,362,-363,-364,-365,366,367
,368,-369,-370,-371,-372,373,-374,375
,-376,377,378,379,380,-381,382,-383
,384,-385,386,-387,-388,389,-390,-391
,392,-393,-394,395,396,397,-398,-399
,-400,401,-402,403,-404,405,-406,407
,408,-409,410,-411,-412,413,414,415
,416,-417,418,-419,420,-421,-422,423
,424,-425,426,-427,-428,-429,430,431
,-432,433,-434,-435,436,437,438,-439
,-440,441,-442,-443,-444,445,446,447
,448,449,-450,-451,-452,453,454,455
,-456,457,-458,459,-460,-461,462,-463
,464,-465,-466,467,468,-469,-470,471
,-472,473,-474,-475,476,-477,478,479
,480,-481,482,-483,-484,485,-486,-487
,-488,489,490,-491,-492,493,494,495
,496,497,-498,-499,500,501,-502,503
,-504,-505,-506,-507,508,-509,510,-511
,-512,513,-514,-515,516,517,518,-519
,-520,521,522,523,524,-525,526,-527
,528,-529,-530,-531,-532,533,-534,535
,536,537,-538,-539,-540,541,542,543
,-544,-545,546,-547,548,-549,550,-551
,-552,553,-554,555,556,557,558,559
,-560,-561,-562,563,-564,-565,-566,-567
,568,569,570,-571,-572,573,-574,575
,576,-577,578,-579,580,-581,-582,583
,584,585,-586,-587,588,-589,590,591
,592,-593,-594,595,-596,597,598,599
,-600,-601,-602,-603,604,-605,606,607
,-608,609,-610,-611,-612,-613,614,615
,-616,617,-618,-619,620,621,622,623
,-624,625,626,-627,-628,-629,-630,-631
,632,633,-634,-635,636,-637,638,639
,640,641,-642,643,644,-645,-646,647
,648,-649,650,-651,-652,653,-654,-655
,-656,-657,658,659,660,-661,662,-663
,-664,665,666,-667,-668,669,-670,671
,-672,673,674,-675,676,-677,-678,679
,680,-681,-682,683,684,-685,686,687
,688,-689,-690,691,-692,693,-694,-695
,696,697,698,-699,-700,701,702,-703
,-704,705,706,-707,708,-709,-710,711
,-712,713,-714,715,-716,-717,718,719
,-720,-721,-722,-723,724,725,726,727
,728,-729,730,-731,-732,-733,-734,735
,736,737,738,-739,740,741,-742,-743
,744,-745,-746,-747,748,749,750,751
,-752,-753,-754,-755,-756,757,758,-759
,760,761,-762,763,-764,765,-766,-767
,768,769,-770,771,772,-773,774,-775
,-776,-777,778,-779,-780,781,782,-783
,784,-785,786,787,-788,-789,790,-791
,-792,793,-794,795,-796,-797,798,799
,800,801,-802,803,804,805,-806,-807
,808,-809,-810,811,812,813,-814,815
,-816,817,-818,819,-820,-821,822,-823
,824,-825,-826,-827,-828,829,830,831
,-832,-833,834,835,-836,-837,838,839
,-840,-841,842,-843,844,-845,-846,847
,-848,849,-850,-851,852,853,854,-855
,-856,857,858,859,-860,861,-862,863
,864,865,-866,-867,868,-869,-870,-871
,872,-873,-874,-875,876,-877,878,879
,880,-881,882,-883,884,-885,-886,887
,-888,889,890,891,-892,893,-894,895
,-896,897,-898,-899,900,901,902,-903
,904,905,-906,-907,-908,-909,910,-911
,912,913,-914,-915,916,917,918,-919
,-920,921,922,-923,-924,925,926,927
,-928,-929,930,-931,932,-933,934,-935
,-936,937,938,-939,-940,941,-942,-943
,944,945,-946,947,-948,949,-950,951
,-952,-953,-954,-955,956,957,-958,-959
,960,961,962,-963,964,-965,966,-967
,968,969,-970,-971,972,973,974,975
,-976,-977,-978,-979,-980,981,982,-983
,-984,985,986,-987,-988,989,990,991
,-992,-993,-994,995,996,-997,998,-999
,1000,-1001,-1002,1003,1004,1005,-1006,1007
,1008,-1009,-1010,-1011,-1012,1013,-1014,-1015
,1016,1017,1018,-1019,-1020,1021,-1022,1023
,1024,-1025,-1026,1027,1028,1029,1030,-1031
,-1032,1033,-1034,-1035,-1036,1037,1038,-1039
,-1040,1041,1042,1043,1044,-1045,-1046,-1047
,-1048,-1049,1050,1051,-1052,1053,1054,1055
,-1056,1057,1058,-1059,1060,1061,-1062,-1063
,1064,-1065,1066,1067,-1068,-1069,1070,-1071
,-1072,1073,1074,-1075,1076,1077,-1078,-1079
,1080,-1081,1082,-1083,-1084,-1085,-1086,1087
,1088,-1089,-1090,1091,1092,-1093,-1094,1095
,-1096,1097,-1098,1099,1100,1101,1102,-1103
,1104,-1105,-1106,1107,-1108,-1109,-1110,1111
,1112,-1113,-1114,1115,-1116,1117,-1118,1119
,1120,1121,1122,-1123,-1124,-1125,1126,1127
,1128,-1129,1130,-1131,1132,-1133,-1134,1135
,-1136,1137,-1138,-1139,-1140,-1141,1142,1143
,1144,-1145,1146,1147,1148,1149,-1150,-1151
,-1152,1153,1154,1155,-1156,1157,-1158,-1159
,-1160,-1161,-1162,1163,1164,1165,1166,-1167
,-1168,1169,1170,1171,-1172,-1173,1174,1175
,-1176,-1177,1178,1179,-1180,-1181,-1182,-1183
,1184,-1185,1186,-1187,1188,-1189,-1190,1191
,-1192,1193,-1194,-1195,1196,1197,1198,-1199
,1200,-1201,-1202,1203,1204,1205,1206,1207
,-1208,-1209,-1210,-1211,-1212,1213,1214,-1215
,-1216,-1217,1218,1219,1220,-1221,-1222,1223
,1224,1225,-1226,-1227,-1228,1229,1230,-1231
,1232,-1233,-1234,-1235,1236,1237,1238,1239
,1240,-1241,1242,-1243,-1244,-1245,-1246,1247
,-1248,1249,-1250,-1251,1252,-1253,1254,1255
,1256,1257,-1258,1259,-1260,1261,-1262,1263
,-1264,1265,-1266,-1267,1268,-1269,-1270,-1271
,1272,-1273,1274,1275,-1276,1277,1278,1279
,-1280,1281,1282,1283,-1284,-1285,1286,-1287
,-1288,-1289,1290,-1291,1292,-1293,1294,1295
,-1296,-1297,1298,1299,-1300,-1301,-1302,-1303
,1304,1305,-1306,1307,-1308,1309,1310,1311
,1312,1313,-1314,-1315,1316,-1317,1318,1319
,-1320,1321,-1322,-1323,-1324,-1325,1326,1327
,1328,-1329,1330,-1331,1332,-1333,-1334,1335
,-1336,-1337,-1338,1339,1340,1341,1342,-1343
,1344,1345,-1346,-1347,-1348,-1349,-1350,1351
,1352,1353,1354,-1355,1356,-1357,-1358,1359
,1360,-1361,1362,1363,-1364,-1365,-1366,1367
,-1368,1369,-1370,-1371,-1372,-1373,1374,1375
,1376,1377,-1378,-1379,1380,1381,1382,-1383
,-1384,-1385,-1386,1387,1388,-1389,1390,1391
,-1392,-1393,-1394,1395,1396,-1397,1398,1399
,1400,-1401,1402,1403,-1404,-1405,-1406,1407
,-1408,1409,-1410,1411,-1412,-1413,1414,-1415
,1416,-1417,-1418,1419,1420,-1421,1422,-1423
,1424,1425,-1426,-1427,-1428,1429,1430,1431
,-1432,-1433,1434,1435,1436,-1437,-1438,1439
,-1440,-1441,1442,1443,1444,-1445,-1446,1447
,1448,-1449,-1450,-1451,1452,-1453,-1454,1455
,-1456,1457,1458,-1459,-1460,1461,1462,1463
,-1464,1465,-1466,1467,1468,-1469,-1470,1471
,-1472,-1473,1474,-1475,-1476,-1477,1478,1479
,-1480,1481,-1482,1483,1484,-1485,-1486,-1487
,1488,-1489,1490,-1491,1492,-1493,1494,1495
,-1496,-1497,1498,-1499,1500,1501,-1502,1503
,1504,-1505,-1506,1507,-1508,1509,1510,1511
,1512,-1513,-1514,-1515,-1516,1517,-1518,1519
,1520,1521,-1522,-1523,1524,1525,1526,-1527
,-1528,1529,-1530,-1531,1532,1533,1534,1535
,-1536,1537,-1538,-1539,-1540,1541,1542,-1543
,-1544,-1545,1546,1547,-1548,-1549,1550,1551
,1552,-1553,1554,-1555,1556,1557,-1558,-1559
,1560,-1561,-1562,-1563,-1564,1565,-1566,1567
,-1568,-1569,1570,1571,-1572,1573,1574,1575
,1576,-1577,1578,-1579,-1580,1581,1582,-1583
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,-9144,9145,9146,-9147,9148,-9149,-9150,9151
,-9152,-9153,-9154,9155,9156,-9157,-9158,9159
,-9160,9161,9162,-9163,9164,-9165,9166,-9167
,-9168,9169,-9170,9171,-9172,9173,-9174,-9175
,9176,9177,-9178,-9179,9180,-9181,9182,9183
,9184,9185,9186,9187,-9188,-9189,-9190,-9191
,-9192,9193,9194,-9195,9196,-9197,-9198,9199
,9200,-9201,-9202,9203,9204,9205,-9206,9207
,-9208,9209,9210,-9211,9212,-9213,9214,-9215
,9216,9217,-9218,-9219,-9220,9221,-9222,9223
,9224,9225,-9226,-9227,9228,-9229,9230,-9231
,-9232,9233,9234,-9235,-9236,-9237,-9238,-9239
,9240,-9241,9242,9243,9244,9245,9246,9247
,-9248,9249,-9250,-9251,-9252,-9253,9254,9255
,-9256,9257,-9258,-9259,-9260,-9261,9262,-9263
,9264,9265,9266,9267,-9268,9269,-9270,9271
,9272,-9273,-9274,9275,-9276,9277,-9278,-9279
,9280,-9281,9282,9283,9284,-9285,9286,-9287
,9288,-9289,-9290,9291,-9292,9293,-9294,-9295
,-9296,-9297,9298,9299,9300,9301,9302,-9303
,-9304,-9305,9306,9307,-9308,9309,9310,-9311
,-9312,9313,9314,9315,-9316,9317,-9318,-9319
,9320,9321,-9322,-9323,9324,9325,-9326,-9327
,9328,-9329,-9330,-9331,9332,9333,9334,-9335
,-9336,-9337,-9338,9339,9340,-9341,-9342,9343
,-9344,-9345,9346,9347,9348,-9349,-9350,-9351
,9352,-9353,9354,9355,9356,9357,-9358,9359
,-9360,-9361,-9362,9363,9364,9365,9366,9367
,-9368,-9369,9370,-9371,-9372,9373,-9374,9375
,9376,-9377,-9378,9379,-9380,-9381,9382,9383
,9384,-9385,-9386,9387,9388,-9389,9390,9391
,-9392,-9393,-9394,9395,-9396,9397,9398,-9399
,-9400,-9401,9402,9403,-9404,-9405,9406,-9407
,-9408,-9409,9410,9411,9412,9413,9414,-9415
,-9416,-9417,9418,-9419,-9420,-9421,9422,9423
,9424,-9425,9426,9427,-9428,-9429,-9430,9431
,9432,9433,-9434,9435,9436,-9437,-9438,-9439
,9440,9441,-9442,9443,-9444,-9445,-9446,-9447
,9448,9449,-9450,9451,-9452,9453,9454,-9455
,-9456,9457,9458,9459,9460,-9461,-9462,-9463
,-9464,9465,-9466,-9467,9468,-9469,9470,-9471
,9472,-9473,9474,9475,9476,-9477,-9478,9479
,9480,9481,9482,9483,-9484,-9485,-9486,9487
,-9488,-9489,-9490,9491,9492,-9493,9494,-9495
,9496,9497,9498,9499,-9500,9501,-9502,-9503
,-9504,9505,-9506,-9507,-9508,9509,9510,9511
,-9512,9513,-9514,-9515,9516,-9517,-9518,9519
,9520,9521,-9522,9523,9524,-9525,9526,-9527
,-9528,-9529,9530,-9531,-9532,9533,9534,9535
,-9536,9537,-9538,-9539,9540,-9541,9542,-9543
,9544,-9545,9546,9547,9548,-9549,-9550,-9551
,-9552,9553,9554,9555,9556,-9557,9558,-9559
,-9560,9561,9562,-9563,-9564,9565,-9566,9567
,9568,9569,-9570,9571,-9572,-9573,9574,-9575
,-9576,9577,-9578,9579,-9580,9581,-9582,-9583
,9584,9585,9586,-9587,-9588,-9589,9590,9591
,9592,-9593,9594,-9595,9596,-9597,-9598,9599
,9600,-9601,9602,9603,-9604,-9605,-9606,9607
,9608,-9609,9610,9611,-9612,9613,-9614,9615
,-9616,-9617,-9618,9619,-9620,-9621,-9622,9623
,9624,9625,9626,-9627,9628,-9629,-9630,-9631
,-9632,-9633,9634,9635,9636,9637,-9638,9639
,-9640,-9641,-9642,-9643,9644,9645,-9646,-9647
,9648,9649,9650,9651,9652,-9653,9654,-9655
,-9656,9657,9658,9659,-9660,-9661,-9662,-9663
,9664,9665,9666,-9667,9668,-9669,9670,-9671
,-9672,9673,9674,-9675,-9676,9677,-9678,-9679
,-9680,9681,-9682,-9683,9684,9685,-9686,-9687
,9688,9689,9690,9691,-9692,-9693,9694,-9695
,-9696,9697,-9698,-9699,9700,-9701,9702,9703
,9704,-9705,-9706,9707,9708,9709,-9710,-9711
,9712,-9713,9714,9715,-9716,9717,9718,9719
,-9720,-9721,9722,9723,-9724,9725,-9726,-9727
,-9728,-9729,-9730,-9731,9732,9733,-9734,9735
,9736,9737,-9738,9739,9740,-9741,9742,-9743
,9744,-9745,-9746,9747,9748,9749,-9750,-9751
,-9752,9753,-9754,-9755,-9756,9757,-9758,9759
,9760,9761,9762,-9763,-9764,9765,9766,-9767
,-9768,-9769,9770,-9771,9772,-9773,9774,-9775
,9776,9777,9778,-9779,-9780,9781,-9782,-9783
,-9784,9785,-9786,9787,-9788,9789,9790,-9791
,9792,9793,9794,-9795,-9796,-9797,9798,9799
,9800,-9801,9802,-9803,-9804,-9805,-9806,9807
,-9808,-9809,9810,9811,9812,-9813,-9814,-9815
,9816,9817,-9818,9819,9820,9821,-9822,9823
,-9824,9825,9826,9827,-9828,9829,-9830,-9831
,-9832,-9833,9834,-9835,9836,9837,-9838,-9839
,9840,9841,9842,-9843,9844,-9845,-9846,-9847
,-9848,-9849,9850,-9851,9852,9853,-9854,9855
,-9856,9857,9858,9859,-9860,-9861,9862,9863
,-9864,-9865,9866,-9867,-9868,9869,-9870,-9871
,9872,9873,-9874,9875,9876,9877,-9878,9879
,9880,-9881,9882,-9883,9884,-9885,-9886,-9887
,9888,9889,9890,-9891,-9892,9893,-9894,-9895
,9896,9897,9898,-9899,-9900,-9901,-9902,9903
,-9904,9905,9906,-9907,9908,-9909,9910,9911
,-9912,9913,-9914,-9915,9916,9917,-9918,-9919
,-9920,9921,9922,-9923,9924,-9925,9926,-9927
,-9928,9929,-9930,9931,9932,9933,-9934,9935
,9936,-9937,9938,9939,-9940,9941,-9942,-9943
,-9944,9945,-9946,-9947,9948,9949,-9950,-9951
,9952,9953,9954,9955,-9956,-9957,-9958,9959
,9960,-9961,9962,-9963,-9964,9965,-9966,-9967
,9968,-9969,9970,-9971,-9972,-9973,9974,9975
,-9976,-9977,9978,9979,-9980,9981,-9982,9983
,-9984,9985,-9986,-9987,9988,9989,-9990,-9991
,9992,9993,9994,-9995,-9996,9997,9998,9999
,-10000]).

% Sequence of length 13000 and discrepancy 3 
example(13000, [-1, -2, 3, -4, 5, 6, 7
, 8, -9, 10, -11, -12, 13, 14, 15
, -16, -17, -18, 19, -20, -21, 22, 23
, 24, 25, -26, -27, 28, -29, -30, -31
, -32, 33, 34, -35, 36, -37, 38, 39
, 40, -41, -42, 43, -44, -45, 46, 47
, 48, 49, -50, -51, 52, -53, 54, -55
, -56, -57, -58, 59, 60, 61, 62, 63
, -64, -65, -66, -67, 68, 69, -70, -71
, -72, 73, -74, 75, -76, 77, -78, 79
, 80, -81, 82, 83, -84, 85, -86, -87
, 88, 89, 90, -91, -92, 93, -94, -95
, 96, -97, 98, -99, 100, 101, -102, -103
, -104, -105, 106, 107, 108, -109, -110, 111
, 112, -113, 114, 115, 116, -117, -118, -119
, -120, 121, -122, 123, -124, -125, 126, 127
, 128, -129, 130, -131, 132, -133, 134, 135
, -136, -137, -138, -139, 140, 141, 142, 143
, -144, 145, -146, 147, 148, -149, -150, 151
, -152, 153, -154, 155, -156, 157, 158, -159
, -160, -161, 162, 163, 164, -165, 166, -167
, 168, 169, -170, -171, -172, 173, -174, -175
, -176, 177, 178, -179, -180, 181, -182, -183
, 184, -185, 186, 187, 188, 189, 190, 191
, -192, -193, 194, -195, -196, -197, 198, -199
, 200, 201, -202, 203, -204, -205, -206, 207
, 208, 209, 210, 211, -212, 213, -214, -215
, -216, -217, -218, -219, 220, 221, 222, -223
, 224, 225, -226, -227, 228, 229, -230, -231
, -232, -233, 234, 235, 236, -237, 238, 239
, -240, 241, -242, -243, -244, 245, 246, 247
, 248, -249, 250, -251, -252, -253, -254, 255
, 256, -257, 258, 259, -260, 261, 262, -263
, 264, 265, -266, -267, -268, -269, -270, 271
, -272, 273, 274, -275, 276, 277, 278, -279
, -280, -281, -282, 283, 284, 285, 286, -287
, 288, -289, 290, -291, -292, 293, -294, -295
, 296, 297, -298, -299, 300, 301, -302, -303
, 304, 305, 306, -307, -308, 309, -310, 311
, -312, 313, -314, -315, 316, 317, -318, -319
, 320, -321, 322, 323, -324, -325, 326, 327
, -328, -329, 330, 331, 332, -333, -334, 335
, 336, 337, -338, -339, -340, -341, -342, 343
, 344, 345, -346, 347, 348, -349, 350, 351
, -352, -353, -354, -355, -356, 357, 358, -359
, 360, -361, 362, 363, 364, -365, -366, 367
, -368, 369, -370, -371, -372, 373, 374, -375
, -376, 377, -378, 379, 380, -381, 382, -383
, -384, 385, 386, 387, 388, -389, 390, -391
, -392, -393, 394, -395, -396, 397, -398, 399
, -400, 401, 402, -403, 404, 405, -406, 407
, 408, -409, 410, -411, 412, -413, -414, -415
, 416, 417, -418, 419, -420, 421, -422, -423
, 424, -425, 426, 427, -428, -429, 430, 431
, 432, -433, 434, -435, -436, -437, 438, 439
, -440, -441, -442, 443, -444, 445, 446, 447
, -448, -449, -450, 451, 452, 453, -454, 455
, -456, 457, -458, -459, 460, 461, 462, -463
, -464, -465, 466, -467, 468, -469, -470, 471
, -472, -473, 474, -475, 476, 477, -478, 479
, 480, -481, 482, -483, 484, 485, -486, -487
, 488, 489, -490, -491, -492, 493, 494, 495
, 496, 497, -498, -499, 500, -501, 502, -503
, -504, -505, -506, 507, -508, -509, 510, 511
, 512, 513, -514, 515, 516, 517, -518, -519
, -520, -521, 522, -523, -524, 525, 526, 527
, -528, 529, -530, -531, 532, 533, 534, -535
, 536, -537, 538, -539, -540, -541, 542, -543
, -544, 545, -546, 547, -548, 549, 550, 551
, 552, 553, -554, 555, -556, -557, -558, -559
, 560, -561, 562, -563, 564, 565, 566, 567
, -568, 569, -570, 571, -572, -573, -574, -575
, 576, -577, -578, 579, -580, 581, -582, 583
, 584, 585, 586, -587, 588, -589, 590, -591
, -592, 593, 594, -595, -596, 597, 598, 599
, -600, 601, -602, -603, 604, -605, -606, 607
, -608, -609, -610, -611, 612, 613, 614, -615
, 616, 617, -618, 619, 620, -621, -622, -623
, 624, 625, -626, -627, -628, 629, 630, 631
, -632, 633, 634, -635, 636, -637, -638, -639
, 640, -641, 642, 643, -644, 645, -646, -647
, -648, 649, 650, 651, -652, 653, 654, -655
, -656, -657, 658, -659, -660, -661, 662, -663
, 664, 665, 666, 667, 668, 669, -670, -671
, -672, -673, 674, -675, -676, 677, -678, -679
, 680, 681, 682, -683, 684, 685, 686, 687
, -688, -689, -690, -691, 692, 693, -694, 695
, 696, -697, 698, 699, -700, 701, -702, -703
, 704, -705, 706, -707, -708, 709, -710, -711
, -712, 713, -714, 715, -716, 717, 718, -719
, 720, -721, -722, 723, -724, 725, -726, -727
, 728, 729, -730, 731, 732, 733, 734, -735
, 736, -737, -738, -739, -740, -741, 742, 743
, -744, 745, -746, 747, 748, 749, 750, -751
, 752, -753, 754, -755, 756, 757, -758, -759
, 760, -761, 762, -763, -764, -765, -766, 767
, -768, 769, 770, 771, 772, -773, -774, 775
, -776, -777, -778, 779, 780, 781, 782, -783
, -784, -785, 786, -787, 788, 789, 790, 791
, -792, 793, -794, -795, 796, -797, 798, -799
, -800, 801, -802, -803, -804, 805, -806, -807
, 808, 809, 810, 811, -812, -813, 814, -815
, 816, 817, -818, -819, -820, -821, 822, -823
, 824, 825, 826, 827, -828, -829, -830, 831
, -832, 833, -834, 835, 836, 837, -838, 839
, 840, -841, 842, 843, -844, -845, 846, -847
, 848, 849, -850, -851, -852, 853, -854, -855
, -856, 857, -858, 859, 860, -861, 862, 863
, -864, 865, 866, 867, -868, -869, -870, 871
, 872, 873, -874, -875, 876, -877, 878, -879
, -880, -881, 882, -883, -884, 885, -886, -887
, 888, 889, 890, -891, 892, 893, -894, 895
, 896, 897, -898, -899, -900, 901, 902, -903
, -904, 905, 906, -907, 908, 909, -910, 911
, -912, -913, 914, -915, 916, 917, -918, -919
, -920, -921, -922, -923, 924, 925, -926, 927
, 928, -929, 930, -931, 932, -933, -934, 935
, 936, 937, -938, -939, -940, -941, 942, 943
, 944, 945, 946, 947, -948, -949, 950, -951
, -952, 953, -954, -955, 956, 957, -958, 959
, -960, 961, 962, 963, -964, -965, 966, -967
, -968, -969, 970, -971, 972, -973, -974, 975
, 976, -977, -978, 979, 980, 981, 982, -983
, 984, -985, 986, 987, -988, -989, -990, 991
, -992, -993, 994, 995, -996, 997, -998, -999
, -1000, 1001, 1002, -1003, 1004, 1005, -1006, 1007
, -1008, -1009, 1010, -1011, 1012, -1013, -1014, -1015
, 1016, 1017, -1018, -1019, 1020, -1021, 1022, 1023
, -1024, 1025, 1026, 1027, 1028, -1029, -1030, 1031
, -1032, 1033, -1034, -1035, -1036, 1037, 1038, -1039
, 1040, 1041, -1042, 1043, -1044, -1045, -1046, -1047
, 1048, 1049, -1050, -1051, 1052, 1053, 1054, -1055
, 1056, -1057, 1058, -1059, -1060, 1061, 1062, 1063
, 1064, 1065, -1066, -1067, -1068, 1069, 1070, -1071
, -1072, 1073, 1074, -1075, -1076, -1077, -1078, 1079
, 1080, -1081, 1082, 1083, -1084, -1085, -1086, 1087
, -1088, 1089, 1090, -1091, 1092, -1093, -1094, 1095
, -1096, 1097, -1098, 1099, 1100, -1101, 1102, 1103
, -1104, -1105, -1106, -1107, 1108, 1109, -1110, -1111
, 1112, 1113, 1114, -1115, 1116, -1117, 1118, 1119
, 1120, -1121, -1122, 1123, -1124, -1125, -1126, 1127
, 1128, 1129, 1130, -1131, -1132, 1133, -1134, 1135
, -1136, 1137, 1138, -1139, -1140, 1141, 1142, 1143
, -1144, -1145, 1146, -1147, 1148, -1149, 1150, -1151
, 1152, 1153, -1154, -1155, 1156, -1157, -1158, -1159
, -1160, 1161, 1162, -1163, 1164, 1165, -1166, -1167
, 1168, 1169, -1170, 1171, -1172, 1173, 1174, 1175
, -1176, 1177, -1178, -1179, -1180, 1181, 1182, -1183
, 1184, 1185, -1186, 1187, -1188, -1189, -1190, -1191
, 1192, 1193, 1194, -1195, 1196, -1197, -1198, -1199
, 1200, 1201, -1202, -1203, -1204, -1205, 1206, 1207
, -1208, 1209, 1210, -1211, 1212, 1213, -1214, -1215
, 1216, -1217, 1218, -1219, 1220, 1221, 1222, -1223
, -1224, 1225, 1226, -1227, -1228, -1229, -1230, 1231
, 1232, 1233, -1234, 1235, -1236, -1237, -1238, 1239
, -1240, 1241, 1242, -1243, 1244, 1245, -1246, -1247
, -1248, 1249, -1250, 1251, 1252, -1253, 1254, 1255
, 1256, -1257, 1258, -1259, 1260, -1261, -1262, -1263
, -1264, -1265, 1266, 1267, -1268, -1269, 1270, 1271
, -1272, 1273, 1274, -1275, 1276, -1277, -1278, 1279
, -1280, 1281, 1282, -1283, 1284, 1285, 1286, -1287
, -1288, -1289, -1290, 1291, -1292, 1293, 1294, 1295
, 1296, 1297, -1298, -1299, -1300, 1301, -1302, -1303
, 1304, 1305, -1306, -1307, -1308, 1309, 1310, 1311
, 1312, -1313, -1314, -1315, -1316, -1317, 1318, -1319
, 1320, 1321, -1322, -1323, 1324, 1325, 1326, -1327
, -1328, 1329, -1330, 1331, -1332, 1333, 1334, -1335
, -1336, 1337, 1338, -1339, 1340, 1341, 1342, -1343
, -1344, -1345, -1346, 1347, -1348, 1349, 1350, -1351
, 1352, 1353, -1354, -1355, 1356, -1357, 1358, -1359
, 1360, -1361, -1362, 1363, -1364, 1365, -1366, -1367
, 1368, -1369, 1370, -1371, 1372, 1373, -1374, 1375
, 1376, 1377, 1378, 1379, -1380, 1381, -1382, 1383
, -1384, -1385, -1386, -1387, 1388, 1389, 1390, 1391
, -1392, -1393, -1394, -1395, 1396, 1397, -1398, 1399
, -1400, -1401, -1402, -1403, 1404, 1405, 1406, 1407
, -1408, -1409, 1410, -1411, 1412, -1413, 1414, 1415
, 1416, 1417, -1418, -1419, -1420, -1421, 1422, -1423
, 1424, 1425, -1426, -1427, -1428, 1429, -1430, 1431
, 1432, 1433, 1434, -1435, 1436, -1437, -1438, 1439
, -1440, 1441, 1442, 1443, -1444, -1445, 1446, -1447
, 1448, 1449, -1450, -1451, -1452, 1453, 1454, 1455
, -1456, -1457, -1458, 1459, -1460, -1461, 1462, -1463
, -1464, 1465, -1466, -1467, 1468, -1469, 1470, -1471
, 1472, 1473, 1474, -1475, -1476, 1477, -1478, 1479
, 1480, -1481, -1482, 1483, -1484, -1485, 1486, 1487
, 1488, 1489, -1490, -1491, 1492, 1493, 1494, 1495
, -1496, -1497, -1498, 1499, 1500, -1501, 1502, 1503
, -1504, 1505, -1506, -1507, -1508, 1509, -1510, 1511
, 1512, -1513, 1514, -1515, -1516, -1517, 1518, 1519
, -1520, -1521, 1522, 1523, -1524, -1525, -1526, 1527
, 1528, -1529, 1530, -1531, 1532, -1533, 1534, 1535
, 1536, 1537, -1538, -1539, 1540, -1541, -1542, -1543
, -1544, -1545, 1546, 1547, 1548, -1549, -1550, 1551
, -1552, 1553, -1554, 1555, 1556, -1557, 1558, 1559
, -1560, -1561, 1562, 1563, -1564, 1565, -1566, 1567
, 1568, 1569, -1570, -1571, -1572, -1573, 1574, 1575
, -1576, -1577, -1578, 1579, 1580, -1581, 1582, -1583
, 1584, -1585, 1586, 1587, -1588, -1589, 1590, 1591
, -1592, 1593, -1594, 1595, 1596, -1597, 1598, -1599
, 1600, 1601, -1602, -1603, -1604, -1605, 1606, 1607
, -1608, 1609, -1610, -1611, 1612, 1613, 1614, 1615
, -1616, 1617, -1618, -1619, 1620, 1621, -1622, -1623
, 1624, -1625, -1626, 1627, -1628, 1629, 1630, -1631
, 1632, -1633, -1634, -1635, 1636, 1637, 1638, -1639
, 1640, 1641, -1642, -1643, -1644, -1645, 1646, -1647
, 1648, 1649, -1650, -1651, -1652, 1653, 1654, -1655
, -1656, 1657, 1658, -1659, -1660, 1661, 1662, -1663
, -1664, 1665, -1666, -1667, 1668, -1669, 1670, 1671
, 1672, 1673, 1674, -1675, -1676, 1677, 1678, -1679
, -1680, 1681, -1682, -1683, -1684, 1685, -1686, 1687
, 1688, -1689, 1690, 1691, -1692, -1693, -1694, 1695
, 1696, -1697, -1698, -1699, 1700, 1701, 1702, 1703
, 1704, 1705, -1706, -1707, 1708, 1709, -1710, 1711
, -1712, -1713, -1714, -1715, 1716, 1717, -1718, 1719
, -1720, 1721, 1722, 1723, -1724, -1725, 1726, -1727
, -1728, -1729, 1730, -1731, -1732, -1733, 1734, -1735
, 1736, 1737, -1738, 1739, 1740, 1741, -1742, -1743
, 1744, 1745, -1746, 1747, 1748, -1749, 1750, -1751
, 1752, -1753, -1754, -1755, -1756, 1757, 1758, 1759
, -1760, 1761, -1762, -1763, -1764, 1765, -1766, 1767
, 1768, -1769, -1770, 1771, 1772, 1773, 1774, 1775
, -1776, -1777, 1778, -1779, -1780, -1781, 1782, -1783
, -1784, 1785, 1786, -1787, 1788, -1789, -1790, 1791
, -1792, 1793, -1794, 1795, 1796, -1797, 1798, -1799
, 1800, 1801, -1802, -1803, -1804, -1805, 1806, 1807
, 1808, 1809, -1810, -1811, 1812, -1813, 1814, -1815
, 1816, 1817, -1818, -1819, 1820, 1821, -1822, 1823
, -1824, 1825, 1826, -1827, 1828, -1829, 1830, 1831
, -1832, -1833, -1834, -1835, -1836, 1837, -1838, 1839
, 1840, -1841, 1842, 1843, -1844, 1845, -1846, -1847
, -1848, 1849, -1850, -1851, 1852, 1853, 1854, 1855
, 1856, 1857, -1858, 1859, -1860, -1861, 1862, -1863
, -1864, -1865, 1866, 1867, 1868, 1869, -1870, -1871
, -1872, -1873, 1874, -1875, 1876, -1877, 1878, -1879
, 1880, 1881, 1882, 1883, -1884, -1885, -1886, -1887
, -1888, 1889, -1890, 1891, -1892, -1893, 1894, 1895
, 1896, -1897, 1898, -1899, -1900, -1901, 1902, -1903
, 1904, 1905, -1906, 1907, 1908, -1909, -1910, 1911
, -1912, 1913, -1914, 1915, 1916, 1917, -1918, 1919
, 1920, -1921, 1922, 1923, -1924, -1925, -1926, -1927
, -1928, -1929, 1930, -1931, 1932, -1933, 1934, -1935
, 1936, 1937, -1938, 1939, -1940, 1941, 1942, -1943
, 1944, -1945, -1946, -1947, 1948, 1949, 1950, -1951
, -1952, -1953, 1954, 1955, -1956, 1957, 1958, -1959
, -1960, 1961, -1962, -1963, 1964, 1965, -1966, 1967
, 1968, 1969, 1970, 1971, -1972, -1973, -1974, 1975
, -1976, -1977, -1978, -1979, 1980, 1981, 1982, 1983
, -1984, -1985, 1986, -1987, -1988, 1989, 1990, -1991
, -1992, 1993, 1994, -1995, 1996, 1997, -1998, 1999
, -2000, 2001, -2002, -2003, -2004, -2005, 2006, -2007
, 2008, 2009, -2010, -2011, 2012, 2013, -2014, 2015
, 2016, -2017, -2018, 2019, -2020, 2021, 2022, -2023
, 2024, -2025, -2026, 2027, 2028, 2029, 2030, -2031
, -2032, -2033, 2034, 2035, 2036, 2037, -2038, -2039
, -2040, 2041, 2042, -2043, -2044, -2045, -2046, 2047
, 2048, 2049, 2050, -2051, -2052, 2053, -2054, 2055
, -2056, 2057, -2058, -2059, 2060, -2061, 2062, 2063
, -2064, -2065, 2066, -2067, -2068, -2069, 2070, -2071
, 2072, 2073, -2074, 2075, -2076, 2077, -2078, 2079
, 2080, 2081, -2082, -2083, 2084, -2085, 2086, -2087
, 2088, -2089, 2090, 2091, 2092, -2093, 2094, -2095
, -2096, -2097, 2098, 2099, -2100, -2101, 2102, 2103
, -2104, -2105, -2106, -2107, 2108, 2109, -2110, 2111
, 2112, -2113, 2114, 2115, -2116, 2117, -2118, 2119
, 2120, 2121, -2122, -2123, 2124, 2125, -2126, -2127
, -2128, 2129, -2130, 2131, -2132, -2133, -2134, 2135
, 2136, 2137, -2138, -2139, 2140, 2141, 2142, -2143
, 2144, 2145, -2146, -2147, 2148, 2149, -2150, -2151
, -2152, 2153, -2154, -2155, 2156, 2157, 2158, -2159
, -2160, 2161, 2162, -2163, -2164, 2165, 2166, -2167
, 2168, -2169, -2170, 2171, -2172, -2173, 2174, -2175
, -2176, 2177, 2178, -2179, 2180, 2181, -2182, -2183
, -2184, 2185, -2186, -2187, 2188, 2189, 2190, 2191
, 2192, -2193, 2194, -2195, 2196, -2197, 2198, 2199
, -2200, -2201, -2202, 2203, -2204, 2205, 2206, 2207
, -2208, -2209, -2210, -2211, -2212, 2213, 2214, -2215
, -2216, 2217, -2218, -2219, 2220, -2221, 2222, 2223
, 2224, 2225, 2226, -2227, -2228, -2229, -2230, 2231
, -2232, -2233, 2234, -2235, 2236, 2237, -2238, -2239
, 2240, 2241, 2242, 2243, 2244, -2245, -2246, -2247
, -2248, 2249, 2250, 2251, 2252, -2253, -2254, 2255
, 2256, -2257, -2258, 2259, -2260, 2261, 2262, 2263
, -2264, -2265, -2266, -2267, -2268, -2269, 2270, 2271
, 2272, 2273, -2274, -2275, -2276, -2277, 2278, -2279
, 2280, 2281, -2282, 2283, 2284, -2285, -2286, 2287
, 2288, -2289, 2290, 2291, -2292, -2293, 2294, 2295
, 2296, -2297, -2298, -2299, -2300, 2301, 2302, -2303
, -2304, 2305, -2306, -2307, 2308, 2309, 2310, 2311
, 2312, -2313, -2314, -2315, 2316, 2317, 2318, -2319
, -2320, -2321, 2322, 2323, -2324, 2325, -2326, 2327
, 2328, -2329, -2330, 2331, -2332, 2333, 2334, 2335
, -2336, -2337, -2338, 2339, -2340, 2341, 2342, -2343
, -2344, -2345, -2346, -2347, 2348, 2349, -2350, 2351
, 2352, -2353, 2354, 2355, -2356, -2357, 2358, -2359
, 2360, 2361, -2362, -2363, -2364, 2365, 2366, 2367
, -2368, 2369, -2370, -2371, 2372, 2373, 2374, 2375
, -2376, -2377, 2378, -2379, 2380, -2381, 2382, -2383
, 2384, -2385, -2386, 2387, -2388, 2389, -2390, 2391
, 2392, 2393, -2394, 2395, -2396, -2397, -2398, -2399
, 2400, -2401, -2402, -2403, 2404, -2405, 2406, -2407
, 2408, 2409, 2410, 2411, 2412, -2413, 2414, -2415
, -2416, 2417, -2418, 2419, -2420, 2421, 2422, -2423
, -2424, -2425, -2426, -2427, 2428, 2429, 2430, -2431
, 2432, -2433, -2434, -2435, 2436, 2437, 2438, 2439
, -2440, 2441, -2442, -2443, -2444, 2445, 2446, -2447
, -2448, 2449, 2450, 2451, -2452, 2453, 2454, -2455
, 2456, -2457, -2458, -2459, -2460, 2461, -2462, 2463
, -2464, 2465, 2466, -2467, 2468, 2469, 2470, 2471
, -2472, -2473, -2474, -2475, 2476, -2477, -2478, -2479
, 2480, 2481, -2482, -2483, 2484, 2485, 2486, -2487
, -2488, -2489, 2490, 2491, -2492, -2493, 2494, 2495
, 2496, 2497, 2498, 2499, -2500, 2501, -2502, -2503
, -2504, -2505, -2506, 2507, -2508, 2509, -2510, -2511
, 2512, 2513, 2514, 2515, 2516, 2517, -2518, 2519
, -2520, -2521, -2522, -2523, 2524, 2525, 2526, 2527
, -2528, 2529, -2530, -2531, 2532, -2533, 2534, -2535
, 2536, 2537, -2538, -2539, 2540, -2541, -2542, 2543
, -2544, -2545, -2546, 2547, 2548, -2549, -2550, -2551
, 2552, 2553, 2554, 2555, 2556, -2557, 2558, -2559
, -2560, 2561, -2562, 2563, -2564, 2565, -2566, 2567
, 2568, -2569, 2570, -2571, -2572, -2573, 2574, -2575
, -2576, 2577, 2578, 2579, -2580, -2581, 2582, -2583
, 2584, -2585, 2586, -2587, -2588, -2589, 2590, 2591
, 2592, -2593, 2594, 2595, -2596, -2597, -2598, 2599
, 2600, 2601, -2602, 2603, 2604, -2605, 2606, 2607
, -2608, -2609, -2610, -2611, 2612, 2613, 2614, 2615
, -2616, 2617, -2618, -2619, 2620, 2621, -2622, -2623
, -2624, 2625, -2626, 2627, -2628, -2629, 2630, -2631
, 2632, 2633, 2634, -2635, -2636, -2637, -2638, 2639
, 2640, 2641, -2642, -2643, 2644, 2645, 2646, 2647
, -2648, 2649, -2650, -2651, 2652, -2653, -2654, -2655
, 2656, -2657, -2658, 2659, -2660, 2661, 2662, -2663
, 2664, 2665, 2666, -2667, -2668, 2669, -2670, -2671
, 2672, 2673, 2674, 2675, -2676, -2677, -2678, -2679
, -2680, 2681, -2682, -2683, 2684, -2685, 2686, 2687
, 2688, -2689, 2690, -2691, -2692, -2693, 2694, -2695
, 2696, 2697, -2698, -2699, 2700, 2701, 2702, 2703
, -2704, 2705, -2706, 2707, 2708, -2709, 2710, 2711
, -2712, 2713, -2714, 2715, -2716, -2717, -2718, -2719
, -2720, 2721, 2722, 2723, -2724, -2725, 2726, 2727
, 2728, -2729, -2730, -2731, 2732, -2733, 2734, 2735
, 2736, -2737, -2738, -2739, -2740, -2741, 2742, 2743
, -2744, 2745, 2746, 2747, -2748, 2749, 2750, 2751
, -2752, -2753, -2754, -2755, 2756, 2757, -2758, -2759
, 2760, -2761, 2762, 2763, 2764, -2765, 2766, 2767
, -2768, -2769, -2770, -2771, 2772, 2773, -2774, -2775
, 2776, -2777, 2778, 2779, -2780, -2781, 2782, 2783
, -2784, 2785, 2786, 2787, -2788, -2789, 2790, 2791
, -2792, -2793, -2794, -2795, -2796, 2797, -2798, 2799
, 2800, -2801, 2802, -2803, 2804, 2805, 2806, 2807
, -2808, 2809, -2810, -2811, 2812, 2813, -2814, -2815
, 2816, -2817, -2818, -2819, 2820, 2821, 2822, 2823
, -2824, -2825, -2826, 2827, -2828, -2829, -2830, 2831
, 2832, 2833, 2834, -2835, -2836, 2837, -2838, -2839
, 2840, 2841, -2842, -2843, -2844, 2845, 2846, -2847
, 2848, -2849, 2850, -2851, -2852, -2853, 2854, 2855
, 2856, -2857, -2858, 2859, 2860, -2861, 2862, 2863
, -2864, -2865, -2866, 2867, 2868, 2869, -2870, 2871
, 2872, 2873, -2874, -2875, -2876, -2877, -2878, 2879
, -2880, 2881, -2882, -2883, 2884, 2885, 2886, -2887
, -2888, 2889, 2890, 2891, 2892, 2893, -2894, -2895
, 2896, -2897, 2898, -2899, 2900, 2901, -2902, 2903
, -2904, -2905, 2906, -2907, 2908, -2909, -2910, 2911
, -2912, 2913, -2914, -2915, -2916, -2917, 2918, 2919
, 2920, 2921, 2922, -2923, -2924, 2925, 2926, 2927
, -2928, -2929, -2930, 2931, -2932, -2933, 2934, 2935
, 2936, -2937, -2938, 2939, 2940, 2941, -2942, -2943
, 2944, -2945, -2946, -2947, -2948, 2949, 2950, -2951
, 2952, -2953, 2954, 2955, 2956, -2957, -2958, 2959
, -2960, 2961, 2962, -2963, -2964, 2965, 2966, -2967
, -2968, -2969, -2970, 2971, 2972, 2973, -2974, 2975
, -2976, 2977, 2978, -2979, -2980, -2981, 2982, -2983
, 2984, -2985, 2986, 2987, -2988, -2989, -2990, 2991
, 2992, -2993, 2994, 2995, -2996, 2997, -2998, -2999
, -3000, -3001, 3002, 3003, 3004, 3005, 3006, 3007
, -3008, -3009, 3010, -3011, 3012, -3013, -3014, -3015
, -3016, 3017, -3018, 3019, 3020, -3021, -3022, 3023
, -3024, 3025, 3026, 3027, -3028, 3029, 3030, -3031
, 3032, -3033, 3034, -3035, 3036, -3037, -3038, -3039
, 3040, -3041, 3042, 3043, -3044, 3045, -3046, -3047
, 3048, -3049, -3050, 3051, 3052, -3053, -3054, 3055
, 3056, 3057, 3058, 3059, -3060, -3061, 3062, -3063
, -3064, -3065, -3066, 3067, -3068, 3069, -3070, 3071
, -3072, 3073, -3074, -3075, 3076, 3077, 3078, 3079
, -3080, -3081, 3082, 3083, 3084, -3085, -3086, 3087
, -3088, 3089, 3090, -3091, 3092, -3093, -3094, -3095
, 3096, -3097, -3098, -3099, 3100, -3101, 3102, -3103
, 3104, 3105, 3106, 3107, -3108, 3109, -3110, 3111
, -3112, -3113, -3114, 3115, 3116, -3117, -3118, 3119
, 3120, -3121, 3122, -3123, -3124, 3125, -3126, 3127
, -3128, -3129, 3130, -3131, 3132, 3133, 3134, 3135
, 3136, 3137, -3138, 3139, -3140, 3141, -3142, -3143
, 3144, -3145, 3146, -3147, -3148, 3149, -3150, -3151
, 3152, 3153, -3154, -3155, -3156, 3157, 3158, -3159
, 3160, -3161, 3162, 3163, -3164, -3165, 3166, 3167
, -3168, 3169, 3170, 3171, -3172, -3173, -3174, -3175
, -3176, -3177, 3178, -3179, 3180, 3181, -3182, 3183
, 3184, -3185, -3186, 3187, 3188, -3189, 3190, -3191
, 3192, -3193, -3194, 3195, -3196, 3197, 3198, -3199
, -3200, 3201, 3202, -3203, 3204, -3205, 3206, 3207
, -3208, -3209, -3210, 3211, 3212, -3213, -3214, 3215
, -3216, 3217, -3218, -3219, 3220, -3221, 3222, 3223
, 3224, 3225, 3226, -3227, -3228, 3229, -3230, 3231
, 3232, -3233, -3234, 3235, -3236, 3237, 3238, 3239
, -3240, -3241, -3242, -3243, -3244, 3245, -3246, 3247
, 3248, 3249, -3250, -3251, 3252, -3253, 3254, 3255
, -3256, -3257, -3258, 3259, 3260, -3261, 3262, -3263
, 3264, -3265, 3266, -3267, 3268, -3269, 3270, 3271
, -3272, 3273, -3274, -3275, -3276, -3277, 3278, 3279
, -3280, 3281, -3282, 3283, 3284, -3285, 3286, -3287
, 3288, -3289, -3290, 3291, -3292, -3293, 3294, 3295
, -3296, -3297, 3298, 3299, -3300, 3301, -3302, 3303
, -3304, -3305, 3306, 3307, -3308, -3309, 3310, 3311
, 3312, 3313, -3314, -3315, 3316, -3317, 3318, 3319
, 3320, -3321, -3322, 3323, -3324, 3325, -3326, -3327
, 3328, 3329, 3330, 3331, -3332, -3333, 3334, -3335
, -3336, 3337, -3338, 3339, 3340, -3341, -3342, 3343
, -3344, -3345, -3346, -3347, 3348, -3349, 3350, 3351
, 3352, -3353, 3354, -3355, -3356, -3357, 3358, 3359
, -3360, 3361, -3362, -3363, 3364, 3365, 3366, 3367
, 3368, 3369, -3370, -3371, 3372, -3373, -3374, 3375
, -3376, 3377, 3378, -3379, -3380, -3381, -3382, 3383
, -3384, 3385, 3386, 3387, 3388, 3389, -3390, -3391
, -3392, -3393, -3394, 3395, 3396, -3397, -3398, -3399
, 3400, 3401, 3402, 3403, -3404, 3405, 3406, 3407
, -3408, -3409, -3410, -3411, 3412, 3413, -3414, -3415
, 3416, 3417, 3418, -3419, -3420, -3421, 3422, 3423
, 3424, -3425, -3426, -3427, -3428, -3429, 3430, -3431
, 3432, 3433, -3434, 3435, 3436, -3437, -3438, 3439
, 3440, -3441, -3442, 3443, 3444, 3445, 3446, 3447
, -3448, -3449, 3450, -3451, -3452, 3453, -3454, 3455
, 3456, -3457, -3458, -3459, -3460, 3461, 3462, 3463
, 3464, -3465, 3466, -3467, -3468, -3469, 3470, 3471
, -3472, -3473, -3474, -3475, 3476, -3477, 3478, 3479
, -3480, -3481, 3482, 3483, 3484, -3485, -3486, -3487
, 3488, 3489, -3490, 3491, -3492, 3493, -3494, 3495
, -3496, 3497, 3498, -3499, -3500, -3501, 3502, 3503
, -3504, 3505, -3506, 3507, 3508, 3509, 3510, 3511
, -3512, -3513, -3514, -3515, 3516, -3517, 3518, 3519
, 3520, -3521, -3522, -3523, 3524, -3525, -3526, 3527
, 3528, 3529, -3530, -3531, 3532, -3533, 3534, 3535
, -3536, -3537, 3538, 3539, 3540, -3541, 3542, 3543
, -3544, -3545, -3546, 3547, -3548, -3549, -3550, 3551
, 3552, -3553, 3554, 3555, 3556, -3557, -3558, -3559
, -3560, 3561, 3562, -3563, -3564, 3565, -3566, 3567
, 3568, -3569, 3570, -3571, 3572, 3573, 3574, 3575
, -3576, -3577, -3578, -3579, 3580, 3581, -3582, 3583
, -3584, -3585, -3586, 3587, -3588, 3589, -3590, 3591
, 3592, 3593, 3594, -3595, -3596, 3597, 3598, -3599
, 3600, -3601, 3602, -3603, -3604, -3605, 3606, 3607
, -3608, -3609, 3610, -3611, -3612, 3613, 3614, -3615
, -3616, 3617, -3618, 3619, -3620, -3621, 3622, -3623
, 3624, 3625, 3626, 3627, -3628, 3629, 3630, -3631
, 3632, 3633, -3634, -3635, 3636, -3637, -3638, -3639
, 3640, 3641, -3642, 3643, -3644, 3645, -3646, -3647
, 3648, -3649, 3650, 3651, 3652, 3653, -3654, -3655
, -3656, 3657, 3658, 3659, -3660, -3661, -3662, -3663
, 3664, 3665, -3666, 3667, -3668, -3669, -3670, 3671
, 3672, 3673, -3674, -3675, 3676, -3677, 3678, -3679
, -3680, 3681, 3682, 3683, -3684, -3685, -3686, -3687
, 3688, 3689, 3690, 3691, 3692, -3693, -3694, 3695
, -3696, -3697, 3698, -3699, 3700, -3701, 3702, 3703
, 3704, -3705, -3706, 3707, 3708, -3709, -3710, 3711
, -3712, -3713, 3714, 3715, 3716, 3717, -3718, -3719
, -3720, -3721, 3722, -3723, -3724, 3725, -3726, -3727
, 3728, 3729, 3730, 3731, 3732, -3733, -3734, -3735
, -3736, 3737, 3738, -3739, 3740, 3741, 3742, 3743
, -3744, 3745, -3746, 3747, -3748, -3749, -3750, -3751
, 3752, -3753, 3754, -3755, -3756, 3757, 3758, 3759
, -3760, 3761, -3762, -3763, 3764, 3765, -3766, -3767
, 3768, -3769, -3770, 3771, 3772, -3773, -3774, 3775
, -3776, 3777, 3778, -3779, -3780, 3781, 3782, -3783
, 3784, -3785, 3786, 3787, -3788, -3789, 3790, 3791
, 3792, -3793, -3794, 3795, 3796, -3797, 3798, 3799
, -3800, -3801, -3802, -3803, -3804, -3805, 3806, 3807
, 3808, 3809, 3810, 3811, -3812, -3813, -3814, 3815
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, -11104, 11105, 11106, -11107, 11108, 11109, -11110, 11111
, -11112, -11113, 11114, 11115, -11116, -11117, 11118, -11119
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, -12488, -12489, 12490, -12491, 12492, 12493, 12494, 12495
, 12496, -12497, -12498, 12499, -12500, 12501, -12502, -12503
, 12504, 12505, -12506, -12507, -12508, 12509, -12510, -12511
, 12512, 12513, 12514, 12515, -12516, -12517, -12518, -12519
, 12520, 12521, 12522, 12523, 12524, -12525, 12526, 12527
, -12528, -12529, 12530, 12531, -12532, -12533, -12534, -12535
, -12536, -12537, 12538, 12539, 12540, 12541, -12542, 12543
, 12544, -12545, -12546, -12547, 12548, -12549, -12550, 12551
, 12552, 12553, -12554, -12555, -12556, 12557, 12558, -12559
, -12560, 12561, -12562, -12563, 12564, -12565, 12566, -12567
, 12568, -12569, 12570, -12571, 12572, 12573, -12574, 12575
, -12576, 12577, 12578, -12579, -12580, 12581, 12582, -12583
, 12584, 12585, -12586, -12587, -12588, 12589, -12590, 12591
, 12592, -12593, 12594, 12595, -12596, 12597, 12598, -12599
, -12600, -12601, 12602, 12603, -12604, 12605, -12606, 12607
, -12608, -12609, 12610, 12611, -12612, 12613, 12614, -12615
, 12616, -12617, -12618, 12619, 12620, -12621, -12622, -12623
, 12624, -12625, 12626, 12627, -12628, 12629, 12630, 12631
, -12632, -12633, 12634, -12635, 12636, -12637, -12638, -12639
, -12640, -12641, 12642, 12643, 12644, 12645, -12646, 12647
, 12648, -12649, 12650, -12651, -12652, 12653, -12654, 12655
, 12656, -12657, -12658, 12659, 12660, -12661, 12662, 12663
, -12664, -12665, -12666, 12667, -12668, -12669, 12670, -12671
, 12672, 12673, -12674, 12675, 12676, -12677, 12678, 12679
, -12680, -12681, 12682, -12683, -12684, -12685, -12686, 12687
, -12688, 12689, -12690, 12691, -12692, 12693, 12694, -12695
, 12696, 12697, 12698, -12699, 12700, 12701, -12702, -12703
, 12704, 12705, -12706, -12707, 12708, -12709, 12710, -12711
, -12712, 12713, -12714, 12715, -12716, 12717, 12718, 12719
, -12720, -12721, -12722, 12723, 12724, -12725, -12726, -12727
, 12728, 12729, -12730, -12731, -12732, -12733, 12734, 12735
, 12736, 12737, 12738, -12739, 12740, -12741, -12742, 12743
, -12744, -12745, 12746, -12747, 12748, 12749, 12750, -12751
, -12752, -12753, -12754, 12755, -12756, 12757, 12758, -12759
, -12760, 12761, 12762, 12763, -12764, -12765, -12766, -12767
, 12768, 12769, -12770, 12771, 12772, -12773, 12774, 12775
, -12776, -12777, -12778, 12779, 12780, -12781, 12782, 12783
, 12784, -12785, -12786, 12787, 12788, -12789, -12790, 12791
, 12792, 12793, -12794, -12795, -12796, -12797, -12798, 12799
, 12800, 12801, -12802, -12803, -12804, -12805, 12806, 12807
, 12808, 12809, 12810, -12811, 12812, -12813, 12814, 12815
, -12816, -12817, -12818, 12819, -12820, -12821, 12822, -12823
, -12824, -12825, 12826, 12827, -12828, 12829, -12830, 12831
, 12832, -12833, 12834, -12835, -12836, 12837, -12838, 12839
, 12840, 12841, 12842, 12843, -12844, 12845, -12846, -12847
, -12848, -12849, -12850, -12851, 12852, -12853, 12854, 12855
, -12856, 12857, -12858, 12859, 12860, 12861, 12862, -12863
, -12864, -12865, 12866, 12867, -12868, 12869, -12870, -12871
, 12872, -12873, 12874, 12875, 12876, -12877, 12878, -12879
, -12880, -12881, 12882, 12883, 12884, 12885, -12886, -12887
, -12888, -12889, 12890, 12891, 12892, 12893, -12894, -12895
, -12896, -12897, -12898, 12899, -12900, 12901, -12902, -12903
, 12904, 12905, -12906, -12907, 12908, -12909, 12910, -12911
, 12912, 12913, -12914, 12915, 12916, -12917, 12918, 12919
, 12920, 12921, -12922, -12923, 12924, -12925, -12926, 12927
, -12928, 12929, -12930, -12931, -12932, -12933, 12934, 12935
, -12936, 12937, 12938, -12939, -12940, 12941, -12942, 12943
, 12944, -12945, 12946, 12947, 12948, 12949, -12950, 12951
, -12952, -12953, 12954, -12955, -12956, -12957, 12958, 12959
, 12960, -12961, -12962, 12963, 12964, 12965, -12966, -12967
, -12968, -12969, -12970, -12971, 12972, -12973, 12974, 12975
, 12976, -12977, 12978, -12979, 12980, -12981, 12982, -12983
, -12984, 12985, -12986, 12987, -12988, 12989, -12990, 12991
, -12992, 12993, 12994, -12995, -12996, 12997, 12998, 12999
, -13000]).













