a := (1,2334)( 2,4909)(   3,4617)(   4,5003)(   5,1709)(   6,3846)(   7, 251)
(   8,4316)(   9,1044)(  10,1103)(  11, 742)(  12, 213)(  13,1543)(  14, 859)
(  15, 774)(  16,4656)(  17, 446)(  18,3717)(  19,3383)(  20,1439)(  22,2586)
(  23,2288)(  24,5202)(  25, 205)(  26,1170)(  27,3247)(  28,2255)(  29, 635)
(  30,3791)(  31, 600)(  32,4065)(  33,2701)(  34,3153)(  35,1684)(  36,4881)
(  37, 889)(  38,3417)(  39,3985)(  40,2229)(  41, 388)(  42,3048)(  43,2202)
(  44, 595)(  45,5012)(  46,4051)(  47, 405)(  48, 936)(  49,4828)(  50, 906)
(  51,2536)(  52,2771)(  53,2169)(  54,4513)(  55,3092)(  56, 759)(  57, 536)
(  58, 102)(  59,3754)(  60,1736)(  61,3196)(  62,3006)(  63,1324)(  64,3920)
(  65,1822)(  66,2136)(  67, 110)(  68,4806)(  69,4406)(  70,3690)(  71,2322)
(  72,3726)(  73,3589)(  74,2931)(  75,2389)(  76,1366)(  77,2875)(  78, 415)
(  79,4865)(  80,1021)(  81,3767)(  82,2012)(  83,1808)(  84,1886)(  85, 786)
(  86,4913)(  87, 644)(  88,3991)(  89,1269)(  90,2454)(  91,2973)(  92,4514)
(  93,1362)(  94,2640)(  95,1138)(  96,4363)(  97,4437)(  98, 160)(  99, 902)
( 100, 650)( 101,3364)( 103, 478)( 104,1476)( 105, 960)( 106,1372)( 107,4328)
( 108,3983)( 109,3769)( 111,2128)( 112,3523)( 113,2240)( 114,1802)( 115,1434)
( 116,3331)( 117, 716)( 118,3298)( 119,3966)( 120,4734)( 121,1821)( 122,2849)
( 123,4215)( 124, 687)( 125, 914)( 126,3937)( 127,1420)( 128,1135)( 129, 553)
( 130, 436)( 131,4485)( 132,3786)( 133,4152)( 134,2046)( 135,1502)( 136, 843)
( 137,5204)( 138,2106)( 139,3555)( 140,5142)( 141,4550)( 142,2124)( 143,3785)
( 144,4699)( 145, 897)( 146,3495)( 147,2185)( 148,4492)( 149, 354)( 150,1028)
( 151,4402)( 152, 677)( 153,3942)( 154,2305)( 155,1223)( 156, 586)( 157,2377)
( 158,2161)( 159,3995)( 161,3389)( 162,3640)( 163,4254)( 164,1940)( 165,2810)
( 166,5209)( 167,3654)( 168,1626)( 169,2068)( 170,2122)( 171,2261)( 172,2035)
( 173,4140)( 174,4336)( 175,4693)( 176, 277)( 177,3546)( 178,4507)( 179,4421)
( 180,3931)( 181,2386)( 182,3576)( 183,3249)( 184,3558)( 185, 699)( 186,4276)
( 187,2534)( 188,3435)( 189,3634)( 190,1401)( 191, 887)( 192,4011)( 193, 837)
( 194,3301)( 195,4069)( 196,4774)( 197,2513)( 198,3427)( 199,1567)( 200,4113)
( 201,2872)( 202,3045)( 203,4975)( 204, 622)( 206,4309)( 207,4312)( 208,4310)
( 209,4305)( 210,4308)( 211,4311)( 212,4307)( 214,4318)( 215,4320)( 216,4317)
( 217,4314)( 218,4319)( 219,4304)( 220,4315)( 221,4313)( 222,4306)( 223,3082)
( 224,3332)( 225,3295)( 226,2571)( 227,4601)( 228,4138)( 229,2455)( 230,4874)
( 231,3488)( 232,2248)( 233,2506)( 234,4490)( 235,2832)( 236,2439)( 237, 425)
( 238,3258)( 239, 574)( 240, 739)( 241, 738)( 242, 744)( 243, 734)( 244, 749)
( 245, 736)( 246, 741)( 247, 743)( 248, 746)( 249, 747)( 250, 733)( 252, 737)
( 253, 748)( 254, 745)( 255, 735)( 256, 740)( 257,3121)( 258,2740)( 259,4081)
( 260,3491)( 261,3671)( 262,2551)( 263,3516)( 264,4442)( 265,4246)( 266, 951)
( 267,2487)( 268, 288)( 269,4580)( 270,3504)( 271,1055)( 272,2058)( 273,2148)
( 274,4231)( 275,3918)( 276,3923)( 278,3176)( 279,4265)( 280,1648)( 281,2835)
( 282,2996)( 283,5069)( 284,4355)( 285,4165)( 286,3271)( 287, 848)( 289,4088)
( 290,1801)( 291,3169)( 292, 312)( 293,1424)( 294,3630)( 295,2660)( 296,2956)
( 297, 731)( 298,1185)( 299,3613)( 300,1215)( 301, 662)( 302,3826)( 303,1564)
( 304,2180)( 305,1590)( 306,1368)( 307,2042)( 308,4928)( 309,2113)( 310,1864)
( 311,4758)( 313,4454)( 314,2447)( 315, 471)( 316,4291)( 317,2727)( 318,1338)
( 319,2672)( 320,1407)( 321,3535)( 322,4389)( 323,1512)( 324, 871)( 325, 521)
( 326,3481)( 327,4823)( 328,2393)( 329,1089)( 330,2910)( 331,5033)( 332,2474)
( 333, 551)( 334,3799)( 335,5141)( 336,3293)( 337,3334)( 338,3745)( 339, 701)
( 340,3866)( 341,2880)( 342,4525)( 343,2425)( 344,1149)( 345,1121)( 346,2569)
( 347,1386)( 348,5174)( 349,1243)( 350,3455)( 351,1570)( 352,2969)( 353,1947)
( 355,3890)( 356,3440)( 357,3928)( 358, 679)( 359,3299)( 360,4392)( 361,4579)
( 362, 979)( 363,2715)( 364,2324)( 365,2287)( 366, 544)( 367, 396)( 368,1010)
( 369,3336)( 370,4352)( 371,1419)( 372,4427)( 373,2595)( 374,1952)( 375,3948)
( 376,4001)( 377,1054)( 378,2616)( 379,1294)( 380,2086)( 381,1597)( 382,3543)
( 383,4063)( 384,4504)( 385,3011)( 386,3808)( 387,2315)( 389,4024)( 390, 916)
( 391,2564)( 392,1484)( 393,2866)( 394,1381)( 395,1228)( 397,3562)( 398,4882)
( 399,4349)( 400, 730)( 401,2726)( 402,1643)( 403,4238)( 404,1314)( 406,2398)
( 407,1279)( 408,5165)( 409,2695)( 410,1211)( 411,3941)( 412,4880)( 413,4397)
( 414,4071)( 416,1365)( 417, 964)( 418,5056)( 419,4128)( 420,1692)( 421,3656)
( 422,3004)( 423,1457)( 424,4999)( 426,4223)( 427,2004)( 428,3465)( 429,3075)
( 430,1369)( 431, 901)( 432,2816)( 433,4759)( 434,1177)( 435,2853)( 437,3468)
( 438,3014)( 439, 729)( 440,4422)( 441,2493)( 442,1667)( 443,3001)( 444,1105)
( 445,1104)( 447,1113)( 448,1107)( 449,1108)( 450,1109)( 451,1110)( 452,1102)
( 453,1100)( 454,1099)( 455, 989)( 456,1106)( 457,1114)( 458,1111)( 459,1101)
( 460,1112)( 461,1748)( 462,4557)( 463,2423)( 464,2499)( 465,4652)( 466, 953)
( 467, 515)( 468,4060)( 469,4217)( 470,1333)( 472,4356)( 473,1390)( 474,3310)
( 475,3390)( 476,3319)( 477,3561)( 479,2441)( 480,1698)( 481,4789)( 482,1681)
( 483,4572)( 484,3751)( 485,1578)( 486,1313)( 487,2476)( 488,4367)( 489,2192)
( 490, 694)( 491,3534)( 492,4728)( 493, 799)( 494,5051)( 495,4064)( 496,4720)
( 497,1815)( 498,1777)( 499,2953)( 500, 529)( 501,4986)( 502, 898)( 503,2367)
( 504,1788)( 505,2643)( 506,4944)( 507,1632)( 508,4694)( 509,1241)( 510,2395)
( 511,1858)( 512,3016)( 513,4057)( 514,4333)( 516,2968)( 517,2071)( 518,4575)
( 519,2482)( 520, 844)( 522,4919)( 523,2096)( 524,4872)( 525,1616)( 526,4896)
( 527,3164)( 528,2882)( 530,1262)( 531,4022)( 532,1852)( 533,2505)( 534,2345)
( 535,1615)( 537,4194)( 538,3224)( 539,2804)( 540,1923)( 541,4551)( 542,4690)
( 543,5059)( 545, 689)( 546,1903)( 547,1141)( 548,1764)( 549,3220)( 550,1739)
( 552,4771)( 554,1787)( 555,1492)( 556,3841)( 557,4141)( 558,1914)( 559,4680)
( 560, 954)( 561,3953)( 562,1226)( 563,3394)( 564,4735)( 565,4634)( 566,2366)
( 567,3321)( 568,2708)( 569,1271)( 570, 975)( 571,4377)( 572,2613)( 573,2270)
( 575,3354)( 576,2857)( 578, 628)( 579,2104)( 580,3681)( 581,2605)( 582,2435)
( 583,3601)( 584,4709)( 585,4125)( 587,3876)( 588,5037)( 589,1622)( 590,2525)
( 591,4210)( 592,4335)( 593,4599)( 594, 811)( 596,3072)( 597,1312)( 598,4682)
( 599,3620)( 601,5026)( 602,2075)( 603,3588)( 604,2856)( 605,4293)( 606, 937)
( 607,4491)( 608,2462)( 609, 955)( 610,4467)( 611,3081)( 612,3686)( 613,4532)
( 614,4169)( 615,1503)( 616,1603)( 617,4120)( 618, 952)( 619,1785)( 620,2914)
( 621,1640)( 623,2942)( 624,1005)( 625,4178)( 626,3697)( 627,4778)( 629,4815)
( 630,2009)( 631,2560)( 632,3174)( 633,3221)( 634,1343)( 636,4232)( 637,2607)
( 638,2303)( 639,3355)( 640,3311)( 641,2241)( 642,3510)( 643,4631)( 645,2644)
( 646,2539)( 647,2347)( 648,3675)( 649,4101)( 651,3248)( 652,2056)( 653,3891)
( 654,2205)( 655,4350)( 656,2879)( 657,2621)( 658,4085)( 659,1783)( 660, 834)
( 661,2502)( 664,4857)( 665,4939)( 666,1773)( 667,3312)( 668, 751)( 669,2282)
( 670,3736)( 671,4604)( 672,4073)( 673,4959)( 674,1656)( 675,3615)( 676, 913)
( 678,3237)( 680,1267)( 681,4326)( 682,3653)( 683,2419)( 684,1506)( 685,2228)
( 686,3485)( 688,4015)( 690,2026)( 691,5127)( 692,2784)( 693,3162)( 695,1305)
( 696,3149)( 697,1387)( 698,4369)( 700,1504)( 702,3800)( 703,3058)( 704,4719)
( 705,3673)( 706,2358)( 707,2827)( 708,4049)( 709,1682)( 710,5219)( 711,3967)
( 712,1953)( 713,1274)( 714,1881)( 715,4415)( 717,2752)( 718,2978)( 719,3774)
( 720,3229)( 721,4498)( 722,3480)( 723,4119)( 724,3399)( 725,2648)( 726,1900)
( 727,2698)( 728,3421)( 732,3326)( 750,3541)( 752,3642)( 753,5018)( 754, 999)
( 755,1916)( 756,2511)( 757,2371)( 758,1199)( 760,3313)( 761,3276)( 762,2703)
( 763,2050)( 764,3098)( 765,2814)( 766,3086)( 767,2337)( 768,2328)( 769,2342)
( 770,2333)( 771,2335)( 772,2331)( 773,2340)( 775,2332)( 776,2336)( 777,2338)
( 778,2341)( 779,2329)( 780,2339)( 781,2330)( 782,2327)( 783,2343)( 784,3958)
( 785,3560)( 787,5035)( 788,4168)( 789,3108)( 790,4047)( 791,2647)( 792,4032)
( 793,1675)( 794,4114)( 795,5190)( 796,4609)( 797,2947)( 798,1526)( 800,2092)
( 801,1331)( 802,3908)( 803,3422)( 804,4613)( 805,4794)( 806,3515)( 807,1613)
( 808,3781)( 809,1195)( 810,5162)( 812,2684)( 813,4994)( 814,3798)( 815,5124)
( 816,3843)( 817,4740)( 818,5046)( 819,2839)( 820,3453)( 821,1876)( 822,2460)
( 823,3036)( 824,3787)( 825,2540)( 826,1231)( 827,3598)( 828,3231)( 829,3099)
( 830,4388)( 831,4374)( 832,3127)( 833,3752)( 835,2186)( 836,3041)( 838,2317)
( 839,2800)( 840,4600)( 841, 879)( 842,1462)( 845,1803)( 846,5010)( 847,4808)
( 849,3684)( 850,2979)( 851,2275)( 852,5005)( 853,5101)( 854,5102)( 855,4537)
( 856,5098)( 857,5100)( 858,2217)( 860,5097)( 861,1389)( 862,3919)( 863,5096)
( 864,5099)( 865,5103)( 866,5105)( 867,5106)( 868,5104)( 869,2692)( 870, 973)
( 872,4404)( 873,4691)( 874,3896)( 875,2792)( 876,5129)( 877,4786)( 878,2720)
( 880,3213)( 881,2919)( 882, 992)( 883,1449)( 884,2087)( 885,1086)( 886,3905)
( 888,2102)( 890,2824)( 891, 921)( 892,3300)( 893,5028)( 894,3112)( 895,1361)
( 896,4452)( 899,2957)( 900,1750)( 903,1857)( 904,3728)( 905,4436)( 907,2936)
( 908,4727)( 909,1094)( 910,3238)( 911,2131)( 912,1416)( 915,4227)( 917,2074)
( 918,3257)( 919,3254)( 920,2676)( 922,4802)( 923,1156)( 924,4370)( 925, 938)
( 926,1991)( 927,2388)( 928,4162)( 929,3216)( 930,4189)( 931,2284)( 932,3971)
( 933,3279)( 934,2878)( 935,1204)( 939,4516)( 940,4212)( 941,3641)( 942,1077)
( 943,3974)( 944,3239)( 945,3502)( 946,2184)( 947,1489)( 948,4527)( 949,4341)
( 950,2924)( 956,3990)( 957,3685)( 958,4953)( 959,1679)( 961,4438)( 962,1154)
( 963,2704)( 965, 984)( 966,4448)( 967,2043)( 968,2298)( 969,4010)( 970,4991)
( 971,1948)( 972,1594)( 976,3327)( 977,3742)( 978,1720)( 980,4982)( 981,1394)
( 982,4640)( 983,2928)( 985,3879)( 986,2158)( 987,1612)( 988,3089)( 990,3139)
( 991,3904)( 993,1688)( 994,4958)( 995,4569)( 996,1561)( 997,2224)( 998,2384)
(1000,3464)(1001,5217)(1002,2937)(1003,4066)(1004,4457)(1006,2242)(1007,2060)
(1008,4675)(1009,2778)(1011,5071)(1012,1456)(1013,4706)(1014,3989)(1015,1627)
(1016,4240)(1017,2798)(1018,4920)(1019,2181)(1020,1290)(1022,2834)(1023,1510)
(1024,1917)(1025,4204)(1026,4971)(1027,3477)(1029,4624)(1030,3251)(1031,3180)
(1032,4902)(1033,4906)(1034,4911)(1035,4903)(1036,4901)(1037,4905)(1038,4904)
(1039,4898)(1040,4907)(1041,4042)(1042,4899)(1043,4900)(1045,4908)(1046,4910)
(1047,4912)(1048,3219)(1049,2041)(1050,2818)(1051,1820)(1052,2253)(1053,3746)
(1056,1391)(1057,2609)(1058,4547)(1059,2418)(1060,3030)(1061,3525)(1062,4890)
(1063,2735)(1064,4117)(1065,3056)(1066,3741)(1067,3463)(1068,2446)(1069,4264)
(1070,5159)(1071,1260)(1072,3136)(1073,2510)(1074,2756)(1075,4992)(1076,3770)
(1078,1483)(1079,2107)(1080,3821)(1081,2165)(1082,1959)(1083,3337)(1084,3594)
(1085,4846)(1087,3302)(1088,2945)(1090,3512)(1091,2179)(1092,2037)(1093,4381)
(1095,1929)(1096,1631)(1097,1123)(1098,2688)(1115,4627)(1116,4775)(1117,4456)
(1118,1602)(1119,1592)(1120,3778)(1122,4338)(1124,3065)(1125,3111)(1126,4474)
(1127,2246)(1128,4800)(1129,4354)(1130,4723)(1131,3927)(1132,3274)(1133,3527)
(1134,4394)(1136,4712)(1137,1265)(1139,1555)(1140,3431)(1142,2083)(1143,5201)
(1144,1278)(1145,4914)(1146,4469)(1147,4851)(1148,4175)(1150,1641)(1151,3250)
(1152,4756)(1153,5178)(1155,2600)(1157,1807)(1158,1322)(1159,2544)(1160,2805)
(1161,2082)(1162,5093)(1163,4373)(1164,2634)(1165,1566)(1166,1395)(1167,4170)
(1168,2938)(1169,5089)(1171,4330)(1172,3404)(1173,1842)(1174,2189)(1175,3284)
(1176,1217)(1178,2410)(1179,3002)(1180,5095)(1181,4869)(1182,1982)(1183,3186)
(1184,2845)(1186,2323)(1187,1571)(1188,1445)(1189,3046)(1190,1604)(1191,3650)
(1192,2830)(1193,5032)(1194,3214)(1196,3554)(1197,2951)(1198,4841)(1200,4639)
(1201,2364)(1202,4426)(1203,3522)(1205,3997)(1206,4766)(1207,4196)(1208,1686)
(1209,3622)(1210,3763)(1212,2933)(1213,5135)(1214,3448)(1216,5128)(1218,2983)
(1219,2188)(1220,1606)(1221,2736)(1222,3120)(1224,2172)(1225,2574)(1227,1530)
(1229,2387)(1230,1661)(1232,2361)(1233,4977)(1234,3339)(1235,4025)(1236,3700)
(1237,3645)(1238,2762)(1239,3526)(1240,2445)(1242,4052)(1244,1417)(1245,1963)
(1246,2990)(1247,2017)(1248,5173)(1249,1759)(1250,3674)(1251,1466)(1252,2682)
(1253,2943)(1254,3117)(1255,3567)(1256,1588)(1257,4545)(1258,3316)(1259,5193)
(1261,3472)(1263,1580)(1264,4262)(1266,4876)(1268,3959)(1270,4744)(1272,3820)
(1273,3042)(1275,4957)(1276,4058)(1277,5131)(1280,5183)(1281,3582)(1282,4241)
(1283,4947)(1284,1325)(1285,4139)(1286,4935)(1287,3819)(1288,2021)(1289,4020)
(1291,2967)(1292,3123)(1293,4038)(1295,2847)(1296,4824)(1297,4346)(1298,1617)
(1299,1695)(1300,3280)(1301,3466)(1302,3318)(1303,2962)(1304,1405)(1306,1725)
(1307,4137)(1308,4805)(1309,3528)(1310,3802)(1311,2065)(1315,1985)(1316,3880)
(1317,1642)(1318,4466)(1319,1693)(1320,4535)(1321,3864)(1323,1425)(1326,2650)
(1327,2166)(1328,1633)(1329,3044)(1330,3489)(1332,1752)(1334,3565)(1335,2653)
(1336,2381)(1337,4586)(1339,3259)(1340,3517)(1341,5013)(1342,4337)(1344,2099)
(1345,1499)(1346,4965)(1347,1568)(1348,3012)(1349,2459)(1350,3830)(1351,1931)
(1352,3888)(1353,4932)(1354,1383)(1355,2471)(1356,2421)(1357,2268)(1358,2690)
(1359,2556)(1360,1415)(1363,1490)(1364,1470)(1367,4271)(1370,2749)(1371,5111)
(1373,3482)(1374,3228)(1375,3428)(1376,2966)(1377,3400)(1378,1902)(1379,4493)
(1380,2646)(1382,4126)(1384,2408)(1385,3607)(1388,3423)(1392,2274)(1393,4093)
(1396,3085)(1397,3867)(1398,3973)(1399,3064)(1400,4929)(1402,1843)(1403,1904)
(1404,3432)(1406,3760)(1408,2563)(1409,4263)(1410,3349)(1411,1814)(1412,4300)
(1413,4435)(1414,3577)(1418,2515)(1421,2668)(1422,3970)(1423,4584)(1426,2985)
(1427,2260)(1428,2480)(1429,2306)(1430,2458)(1431,3744)(1432,1635)(1433,4917)
(1435,2221)(1436,2503)(1437,1969)(1438,3115)(1440,1865)(1441,2770)(1442,3965)
(1443,3946)(1444,3992)(1446,2767)(1447,3936)(1448,3245)(1450,4465)(1451,1657)
(1452,3964)(1453,3396)(1454,4671)(1455,3366)(1458,5166)(1459,3666)(1460,2963)
(1461,3010)(1463,3599)(1464,4549)(1465,2429)(1467,2279)(1468,3508)(1469,2373)
(1471,1509)(1472,3035)(1473,3553)(1474,3899)(1475,1766)(1477,5082)(1478,4836)
(1479,1589)(1480,2076)(1481,5074)(1482,3954)(1485,4109)(1486,3885)(1487,3548)
(1488,5169)(1491,4623)(1493,3759)(1494,1804)(1495,1924)(1496,5177)(1497,3148)
(1498,4721)(1500,3996)(1501,2204)(1505,2831)(1507,2285)(1508,5027)(1511,5168)
(1513,2175)(1514,4122)(1515,3361)(1516,2281)(1517,3815)(1518,3572)(1519,2081)
(1520,3270)(1521,2821)(1522,2781)(1523,4207)(1524,2219)(1525,3441)(1527,1611)
(1528,4297)(1529,1795)(1531,2746)(1532,1538)(1533,1536)(1534,1548)(1535,1539)
(1537,1540)(1542,1546)(1544,1547)(1549,4783)(1550,3129)(1551,2806)(1552,3103)
(1553,2998)(1554,4924)(1556,2239)(1557,3878)(1558,2400)(1559,3350)(1560,3498)
(1562,2289)(1563,4521)(1565,2033)(1569,4877)(1572,4673)(1573,1621)(1574,4419)
(1575,2929)(1576,4155)(1577,5176)(1579,2614)(1581,2747)(1582,2469)(1583,1883)
(1584,3368)(1585,3076)(1586,2003)(1587,3832)(1591,4072)(1593,2719)(1595,1644)
(1596,5208)(1598,4055)(1599,3079)(1600,3013)(1601,3518)(1605,4489)(1607,2350)
(1608,3187)(1609,4785)(1610,4936)(1614,4494)(1618,3146)(1619,3026)(1620,5077)
(1623,1784)(1624,2040)(1625,4385)(1628,1978)(1629,3963)(1630,3078)(1634,1778)
(1636,4948)(1637,2449)(1638,3596)(1639,4927)(1645,4224)(1646,1936)(1647,2822)
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(4993,5206)(5023,5164)(5029,5151);