a := (1, 473)( 2,2670)(   3,3760)(   4,2042)(   5, 910)(   6, 836)(   7,1217)
(   8,3148)(   9,1795)(  10,1848)(  11,2112)(  12,4754)(  13,2569)(  14,2926)
(  15,1839)(  16,2673)(  17,3106)(  18, 401)(  19, 447)(  20, 145)(  21,3780)
(  22,1436)(  23,3952)(  24,3239)(  25,3562)(  26,3724)(  27,4563)(  28,1609)
(  29,2011)(  30,1325)(  31,3289)(  32,  74)(  33, 959)(  34,3420)(  35, 783)
(  36, 158)(  37,3814)(  38, 739)(  39,2161)(  40, 921)(  41,1913)(  42, 982)
(  43,4370)(  44,2365)(  45,1703)(  46,4011)(  47,2583)(  48, 441)(  49,1448)
(  50,4483)(  51,2789)(  52,4132)(  53, 127)(  54,3959)(  55,3246)(  56, 716)
(  57,2416)(  58,3017)(  60,3404)(  61,1799)(  62,1142)(  63,1843)(  64,1033)
(  65,2886)(  66,4289)(  67, 892)(  68,1485)(  69,4614)(  70,3960)(  71,4267)
(  72,4570)(  73,1393)(  75,2020)(  76,2463)(  77, 895)(  78,2193)(  79,2530)
(  80,1516)(  81,1505)(  82,2489)(  83,4100)(  84, 444)(  85,2954)(  86, 618)
(  87,1063)(  88, 645)(  89,2686)(  90,1608)(  91,3651)(  92, 164)(  93,2854)
(  94, 764)(  95,3440)(  96,4030)(  97,3099)(  98, 992)(  99,4501)( 100,4756)
( 101, 162)( 102,2018)( 103,3921)( 104,1322)( 105,2740)( 106,4202)( 107, 748)
( 108,3208)( 109,3317)( 110,2957)( 111,2748)( 112,3078)( 113,3436)( 114,2420)
( 115,1940)( 116,4668)( 117,2782)( 118,2441)( 119,3572)( 121,3080)( 122,3364)
( 123,3503)( 124, 918)( 125, 587)( 126,1016)( 128, 985)( 129,3388)( 130,2972)
( 131,1807)( 132,4636)( 133,4071)( 134,3817)( 135,1431)( 136,1533)( 137,4170)
( 138,1350)( 139,3965)( 140,1337)( 141,2334)( 142,2012)( 143, 960)( 144,3117)
( 146,4705)( 147,3464)( 148,3387)( 149,1566)( 150,4337)( 151,3027)( 152,2623)
( 153,4283)( 154,4657)( 155,4340)( 156,1689)( 157, 822)( 159,4325)( 160,1787)
( 161, 937)( 163, 790)( 165,2397)( 166,1866)( 167,3335)( 168,1113)( 169,4750)
( 170,2474)( 171,2792)( 172,1284)( 173, 745)( 174,1123)( 175,3687)( 176,3257)
( 177,3333)( 178,4236)( 179, 720)( 180,2675)( 181,2090)( 182,2607)( 183,1988)
( 184,1985)( 185,1563)( 186,4239)( 187,3107)( 188,3033)( 189,3414)( 190, 951)
( 191,3992)( 192,4045)( 193,4309)( 194,2557)( 195, 372)( 196, 729)( 197,4036)
( 198, 476)( 199, 909)( 200,2598)( 201,2644)( 202, 327)( 203,1583)( 204,3633)
( 205,1755)( 206,1042)( 207,1365)( 208,1527)( 209,2366)( 210,3806)( 211,4208)
( 212,3522)( 213,1092)( 214, 256)( 215,3156)( 216,1223)( 217,2980)( 218, 340)
( 219,1617)( 220,2936)( 221,4358)( 222,3118)( 223,4110)( 224,3179)( 225,2173)
( 226,4562)( 227,3900)( 228,1814)( 229, 386)( 230,2638)( 231,3645)( 232,2286)
( 233, 592)( 234,1935)( 235, 309)( 236,1762)( 237,1049)( 238,2913)( 239,4613)
( 240, 820)( 242,1207)( 243,3996)( 244,3339)( 245,4040)( 246,3230)( 247, 689)
( 248,2092)( 249,3089)( 250,3682)( 251,2417)( 252,1763)( 253,2070)( 254,2373)
( 255,3590)( 257,4217)( 258,4660)( 259,3092)( 260,4390)( 261,4727)( 262,3713)
( 263,3702)( 264,4686)( 265,1903)( 266,2641)( 267, 757)( 268,2815)( 269,3260)
( 270,2842)( 271, 489)( 272,3805)( 273,1454)( 274, 346)( 275, 657)( 276,2961)
( 277,1243)( 278,1833)( 279, 902)( 280,3189)( 281,2304)( 282,2559)( 283, 344)
( 284,4215)( 285,1724)( 286,3519)( 287, 543)( 288,2005)( 289,2945)( 290,1011)
( 291,1120)( 292, 760)( 293, 551)( 294, 881)( 295,1239)( 296,4617)( 297,4137)
( 298,2471)( 299, 585)( 300,4638)( 301,1375)( 303, 883)( 304,1167)( 305,1306)
( 306,3115)( 307,2784)( 308,3213)( 310,3182)( 311,1191)( 312, 775)( 313,4004)
( 314,2439)( 315,1874)( 316,1620)( 317,3628)( 318,3730)( 319,1973)( 320,3547)
( 321,1768)( 322,3534)( 323,4531)( 324,4209)( 325,3157)( 326, 920)( 328,2508)
( 329,1267)( 330,1190)( 331,3763)( 332,2140)( 333, 830)( 334, 426)( 335,2086)
( 336,2460)( 337,2143)( 338,3886)( 339,3019)( 341,2128)( 342,3984)( 343,3134)
( 345,2987)( 347,4594)( 348,4063)( 349,1138)( 350,3310)( 351,2553)( 352,4671)
( 353, 595)( 354,3481)( 355,2942)( 356,3320)( 357,1490)( 358,1060)( 359,1136)
( 360,2039)( 361,2917)( 362, 478)( 363,4287)( 364, 410)( 365,4185)( 366,4182)
( 367,3745)( 368,2184)( 369,1457)( 370,2109)( 371, 503)( 373,2204)( 374,4305)
( 375,4321)( 376,1536)( 377, 610)( 378,3094)( 379,1998)( 380,4535)( 381,1429)
( 382, 844)( 383,2107)( 384,1927)( 385,2810)( 387,1844)( 388,2185)( 389,1453)
( 391,4318)( 392,3459)( 393, 996)( 394, 924)( 395,3079)( 396,1425)( 397,2166)
( 398,3575)( 399,2900)( 400,2375)( 402,3789)( 403,1607)( 404,3357)( 405, 867)
( 406,3884)( 407,2156)( 408,4367)( 409,3119)( 411, 693)( 412, 507)( 413,2848)
( 414,1072)( 415,3413)( 416,3054)( 417,1459)( 418,2730)( 419,1131)( 420,4092)
( 421,3242)( 422,2044)( 423,2701)( 424,2985)( 425, 517)( 427,3721)( 428,3537)
( 429,4252)( 430,3832)( 431, 884)( 432,3393)( 433,3593)( 434,4486)( 435,2639)
( 436,2138)( 437,3641)( 438,3097)( 439,1166)( 440,1663)( 442,2632)( 443, 812)
( 445, 594)( 446,1018)( 448,3051)( 449,2275)( 450,3989)( 451,1499)( 452,4167)
( 453,2541)( 454,3252)( 455,1888)( 456, 684)( 457,2139)( 458, 813)( 459,3867)
( 460,2183)( 461,2835)( 462,2758)( 463,4424)( 464,1737)( 465,1540)( 467,1277)
( 468,1766)( 469, 781)( 470,3561)( 471,2908)( 472,1463)( 474,2713)( 475,4297)
( 477, 885)( 479,3983)( 480,2323)( 481,3583)( 482,4533)( 483,3800)( 484,1451)
( 485,3076)( 486,3927)( 487,1519)( 488,1392)( 490,3508)( 491,4002)( 492,1581)
( 493,2394)( 495,3735)( 496, 853)( 497,1650)( 498,1348)( 499, 791)( 500,3315)
( 501,4255)( 502,1496)( 504,2620)( 505,1474)( 506, 805)( 508,3691)( 509,4674)
( 510,4488)( 511, 906)( 512,4296)( 513,4246)( 514,4702)( 515,4347)( 516,2671)
( 518,3253)( 519,1801)( 520,2094)( 521,2956)( 522,4500)( 523,1610)( 524,1915)
( 525,4448)( 526,2461)( 527,3264)( 528,3437)( 529,1862)( 530,1571)( 531,4013)
( 532, 542)( 533,2615)( 534,1887)( 535,1705)( 536,2351)( 537,1878)( 538,3374)
( 539,2995)( 540, 736)( 541,3776)( 544,4010)( 545,2533)( 546,1185)( 547,1952)
( 548,3008)( 549,1335)( 550, 578)( 552,4469)( 553,3544)( 554,2910)( 555,2082)
( 556,2953)( 557,4258)( 558,1013)( 559,1906)( 560,1012)( 561,2659)( 562,1572)
( 563,1206)( 564,3149)( 565,3476)( 566,4588)( 567,4512)( 568,3225)( 569,2482)
( 570,1101)( 571,4035)( 572,1949)( 573,2178)( 574,1008)( 575,2048)( 576,2218)
( 577,3275)( 579,1201)( 580,1726)( 581,3556)( 582,2374)( 583,4302)( 584,3798)
( 586,1645)( 588,1091)( 589,4459)( 590,4055)( 591, 861)( 593,4147)( 596,3273)
( 597,1005)( 598,1918)( 599,4579)( 600,1169)( 601,1525)( 602,1189)( 603,4054)
( 604,1589)( 605, 674)( 606,1699)( 607,3715)( 608,1487)( 609,3318)( 611,1261)
( 612,1417)( 613,2582)( 614,1164)( 615,3449)( 616,3543)( 617,2437)( 619,2472)
( 620,1514)( 621,3523)( 622,3433)( 623,4479)( 624,1399)( 625,1556)( 626,1529)
( 627, 821)( 628,1266)( 629,2142)( 630,1299)( 631,4524)( 632,2907)( 633, 663)
( 634,1567)( 635,3355)( 636,1465)( 637,2912)( 638,2658)( 639,2216)( 640,4265)
( 641,3147)( 642,4229)( 643,4373)( 644,1517)( 646,3834)( 647,3951)( 648,4095)
( 649,2989)( 650,3794)( 651,2610)( 652, 896)( 653,4326)( 654,1677)( 655, 661)
( 656,2928)( 658,1842)( 659,4576)( 660,1468)( 662, 955)( 664,3689)( 665,2225)
( 666,1156)( 667,3184)( 668,3337)( 669,3367)( 670,1847)( 671,3155)( 672,3243)
( 673,3531)( 675, 697)( 676,3922)( 677,3153)( 678,3174)( 679,2491)( 680,4387)
( 681,2440)( 682,1088)( 683,1707)( 685,3432)( 686,3062)( 687,3132)( 688,3681)
( 690,3698)( 691,2113)( 692,2506)( 694,3271)( 695,3878)( 696,2135)( 698, 928)
( 699,2194)( 700,1661)( 701,4355)( 702,4261)( 703,2596)( 704,1443)( 705,3075)
( 706,4278)( 707,2376)( 708,3311)( 709,1770)( 710,2829)( 711,2668)( 712,1520)
( 713,2751)( 714,3571)( 715,2834)( 717,4514)( 718,2009)( 719,2353)( 721,3324)
( 722, 763)( 723,1157)( 724,3991)( 725,2497)( 726,3712)( 727,2525)( 728, 864)
( 730,1181)( 731,2853)( 732,3810)( 733,1905)( 734,1093)( 735,2537)( 737,2110)
( 738,2301)( 740,3025)( 741,1462)( 742,3912)( 743,4393)( 744,1700)( 746,4489)
( 747,2083)( 749, 972)( 750,4675)( 751,4026)( 752,1790)( 753,4395)( 754,2457)
( 755,2480)( 756,2753)( 758,4188)( 759,2718)( 761,1414)( 762,1003)( 765,1452)
( 766,2285)( 767,1965)( 768,2540)( 769, 776)( 770,1182)( 771,2024)( 772,1212)
( 773,1562)( 774,1034)( 777,1052)( 778, 964)( 779,1053)( 780,4224)( 782,3304)
( 784,1821)( 785,2079)( 786,4739)( 787,4093)( 788,2621)( 789,2398)( 792,2846)
( 793,1388)( 794,3201)( 795,1070)( 796,4154)( 797,1728)( 798,2736)( 799,3349)
( 800,1486)( 801,3340)( 802,3942)( 803,3988)( 804,1400)( 806,4556)( 807,3053)
( 808,4656)( 809,2312)( 810,1440)( 811,2745)( 814,1654)( 815,3223)( 816,1837)
( 817,4379)( 818,2502)( 819,3447)( 823,1729)( 824,2201)( 825,4701)( 826,1662)
( 827,4290)( 828,2937)( 829,1694)( 831,3823)( 832,1959)( 833,1331)( 834,1194)
( 835,1419)( 837,1889)( 838,4693)( 839,3808)( 840,1269)( 841,3334)( 842,1493)
( 843,3316)( 845,1543)( 846,1968)( 847,1251)( 848,3410)( 849,1634)( 850,2162)
( 851,3787)( 852,1929)( 854,2645)( 855,4166)( 856,3004)( 857,2613)( 858,1919)
( 859,3512)( 860,3706)( 862,4474)( 863,1658)( 865,2883)( 866,4672)( 868,1537)
( 869,2514)( 870, 939)( 871,3513)( 872,4523)( 873,1615)( 874,1469)( 875,4735)
( 876,3471)( 877,1937)( 878,2902)( 879,2682)( 880,4109)( 882,2592)( 886,2384)
( 887,3377)( 888,1554)( 889,1784)( 890,1521)( 891,1068)( 893,4716)( 894,4471)
( 897,2575)( 898,1946)( 899,3581)( 900,2635)( 901,1778)( 903,4136)( 904,3826)
( 905,3893)( 907,4140)( 908,4518)( 911,2337)( 912,1456)( 913,1122)( 914,2203)
( 915,4454)( 916,1780)( 917,2554)( 919,3610)( 922,2606)( 923,2008)( 925,1586)
( 926,3818)( 927,3372)( 929,1652)( 930,4277)( 931,4099)( 932,4247)( 933,3601)
( 934,3748)( 935,2884)( 936,1234)( 938,1684)( 940,2562)( 941,1576)( 942,3756)
( 943,3221)( 944,4420)( 945,3957)( 946,3844)( 947,4411)( 948,2076)( 949,1914)
( 950,2838)( 952,2761)( 953,3609)( 954,1997)( 956,2874)( 957,1047)( 958,2868)
( 961,1255)( 962,4416)( 963,1911)( 965,3997)( 966,4718)( 967,4640)( 968,4286)
( 969,1415)( 970,2226)( 971,4159)( 973,3336)( 974,1187)( 975,1077)( 976,4742)
( 977,2875)( 978,3351)( 979,1211)( 980,1678)( 981,3813)( 983,4142)( 984,4598)
( 986,3802)( 987,2864)( 988,4697)( 989,1872)( 990,3638)( 991,1907)( 993,3226)
( 994,3982)( 995,2402)( 997,3578)( 998,3497)( 999,4620)(1000,1679)(1001,1594)
(1002,3632)(1004,2991)(1006,2199)(1007,3438)(1009,4707)(1010,3422)(1014,1781)
(1015,4731)(1017,2280)(1019,2001)(1020,4567)(1021,3390)(1022,3862)(1023,2133)
(1024,3140)(1025,2000)(1026,3012)(1027,4749)(1028,2765)(1029,3190)(1030,4728)
(1031,4549)(1032,1739)(1035,3331)(1036,4234)(1037,1850)(1038,1656)(1039,1064)
(1040,1804)(1041,4352)(1043,2104)(1044,4386)(1045,2618)(1046,2869)(1048,1856)
(1050,2271)(1051,1483)(1054,1810)(1055,2651)(1056,2715)(1057,4160)(1058,1731)
(1059,4600)(1061,1817)(1062,2211)(1065,3973)(1066,2434)(1067,2724)(1069,1569)
(1071,2360)(1073,3872)(1074,2891)(1075,4733)(1076,2793)(1078,2774)(1079,3356)
(1080,3338)(1081,2209)(1082,2221)(1083,4481)(1084,3910)(1085,3974)(1086,3443)
(1087,1921)(1089,4231)(1090,3727)(1094,3515)(1095,1455)(1096,1873)(1097,1809)
(1098,2240)(1099,4212)(1100,2237)(1102,2255)(1103,3990)(1104,4230)(1105,2495)
(1106,3668)(1107,2979)(1108,3890)(1109,4464)(1110,2490)(1111,3953)(1112,3332)
(1114,2905)(1115,2297)(1116,2499)(1117,1162)(1118,2697)(1119,3040)(1121,2806)
(1124,1148)(1125,4138)(1126,2522)(1127,2918)(1128,2031)(1129,3894)(1130,1377)
(1132,1951)(1133,3369)(1134,3232)(1135,3309)(1137,3038)(1139,3170)(1140,2865)
(1141,3277)(1143,2998)(1144,1599)(1145,4227)(1146,1690)(1147,3961)(1149,3488)
(1150,3821)(1151,1522)(1152,2996)(1153,4539)(1154,3175)(1155,1788)(1158,2832)
(1159,3276)(1160,2601)(1161,2103)(1163,4256)(1165,1215)(1168,1596)(1170,2866)
(1171,2154)(1172,3330)(1173,1394)(1174,3375)(1175,3124)(1176,4465)(1177,2735)
(1178,3371)(1179,4470)(1180,3084)(1183,3895)(1184,1901)(1186,2529)(1188,2160)
(1192,1203)(1193,3218)(1195,2526)(1196,2629)(1197,2118)(1198,1535)(1199,2310)
(1200,1565)(1202,1488)(1204,4023)(1205,2131)(1208,4443)(1209,1709)(1210,3506)
(1213,3045)(1214,3820)(1216,2612)(1218,3833)(1219,2073)(1220,3484)(1221,2145)
(1222,4732)(1224,4348)(1225,3207)(1226,3672)(1227,2466)(1228,1290)(1229,1534)
(1230,4585)(1231,4462)(1232,2307)(1233,1272)(1235,2882)(1236,2819)(1237,3816)
(1238,2430)(1240,2725)(1241,3204)(1242,4635)(1244,4350)(1245,1360)(1246,3283)
(1247,1353)(1248,4487)(1249,2144)(1250,3016)(1252,2812)(1253,4569)(1254,2447)
(1256,1928)(1257,2407)(1258,1909)(1259,4516)(1260,1740)(1262,2589)(1263,1502)
(1264,1588)(1268,4259)(1270,4428)(1271,1345)(1273,2091)(1274,3073)(1275,4226)
(1276,2264)(1278,4394)(1279,2762)(1280,4714)(1281,2293)(1282,1368)(1283,4706)
(1285,4622)(1286,4319)(1287,3417)(1288,2501)(1289,1863)(1291,3346)(1292,3588)
(1293,3775)(1294,4046)(1295,1582)(1296,3507)(1297,1367)(1298,2022)(1300,3195)
(1301,1735)(1302,1577)(1303,1411)(1304,4522)(1305,4264)(1307,2125)(1309,3407)
(1310,3493)(1311,2687)(1312,4027)(1313,1446)(1314,2010)(1315,3056)(1316,3068)
(1317,4192)(1318,3291)(1319,1867)(1320,4607)(1321,4748)(1324,2127)(1326,2818)
(1327,2308)(1328,1747)(1329,4199)(1330,1369)(1332,3549)(1333,2157)(1334,2870)
(1336,2164)(1338,1882)(1339,4610)(1340,2625)(1341,1851)(1342,1738)(1343,4580)
(1344,1710)(1346,2813)(1347,2750)(1349,4121)(1351,4511)(1352,3529)(1354,1506)
(1355,3736)(1356,2294)(1357,3909)(1358,2313)(1359,2778)(1361,4736)(1362,1570)
(1363,4331)(1364,2667)(1366,3647)(1370,2492)(1371,1507)(1372,3781)(1373,2393)
(1374,2911)(1376,1510)(1378,2595)(1379,4545)(1380,1964)(1381,3194)(1382,1883)
(1383,3888)(1384,3096)(1385,2072)(1386,2678)(1387,3809)(1389,2485)(1391,3489)
(1395,3661)(1396,2630)(1397,4456)(1398,4251)(1401,4629)(1402,2454)(1403,2287)
(1404,3130)(1405,4662)(1406,1855)(1407,4274)(1408,4378)(1409,4313)(1410,3750)
(1412,3150)(1413,3116)(1416,2247)(1418,1430)(1420,1758)(1421,2332)(1422,4417)
(1423,1933)(1424,4596)(1426,2088)(1428,1555)(1432,2343)(1433,4025)(1434,4740)
(1435,3199)(1437,1980)(1438,2356)(1439,4681)(1441,3187)(1442,2256)(1444,2634)
(1445,1748)(1447,1676)(1449,4376)(1450,3563)(1458,2276)(1460,4365)(1461,1513)
(1464,3592)(1466,1580)(1467,2096)(1470,1552)(1471,3303)(1472,1591)(1473,1984)
(1475,3423)(1476,2395)(1477,1625)(1478,1926)(1479,4254)(1480,4037)(1481,3754)
(1482,2390)(1484,2885)(1489,2435)(1491,4450)(1492,2861)(1494,2705)(1495,1972)
(1497,3930)(1498,1852)(1500,1600)(1501,2887)(1503,2422)(1504,1861)(1508,2281)
(1509,3057)(1511,1877)(1512,4101)(1515,2923)(1518,2804)(1523,4119)(1524,2624)
(1526,3746)(1528,4402)(1530,3287)(1531,4532)(1532,1575)(1538,2692)(1539,3552)
(1541,1893)(1542,4552)(1544,2238)(1545,2341)(1546,3905)(1547,2563)(1548,2564)
(1549,3723)(1550,4741)(1551,3131)(1553,3607)(1557,3678)(1558,1732)(1559,3139)
(1560,2035)(1561,2299)(1564,4066)(1568,2386)(1574,3901)(1578,3490)(1579,2738)
(1584,3569)(1585,2003)(1587,3870)(1590,3048)(1592,2599)(1593,2380)(1595,4144)
(1597,2847)(1598,4493)(1601,2781)(1602,4051)(1603,2680)(1604,4388)(1605,3183)
(1606,1982)(1611,3036)(1612,3584)(1613,2929)(1614,1644)(1616,3178)(1618,3958)
(1619,3434)(1621,3123)(1622,1631)(1623,3411)(1624,3347)(1626,3028)(1627,1975)
(1628,2046)(1629,3101)(1630,4685)(1632,4260)(1633,4312)(1635,2627)(1636,3415)
(1637,2843)(1638,1971)(1639,3931)(1640,2120)(1641,3861)(1642,4043)(1643,2278)
(1646,4612)(1647,3143)(1648,3971)(1649,2056)(1651,1744)(1653,3947)(1655,1769)
(1657,4220)(1659,1987)(1660,4589)(1664,3838)(1665,3219)(1666,4602)(1667,2561)
(1668,2507)(1669,1981)(1670,2656)(1671,4174)(1672,1771)(1673,3784)(1674,4213)
(1675,3270)(1680,4343)(1681,2892)(1682,2239)(1683,1974)(1685,4338)(1686,1818)
(1687,2603)(1688,2448)(1691,3580)(1692,2175)(1693,3305)(1695,4360)(1696,3102)
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