b := (1,3680,1282)( 2,3492,1312)(   3,1863,2730)(   4,4831,3563)
(   5,1564, 371)(   6, 140,4250)(   7,5156,5170)(   8,3024,  52)
(   9, 691,3850)(  10,1319,1231)(  11,2700,2690)(  12, 263,4877)
(  13, 237,1837)(  14, 982, 724)(  15,4538,2393)(  16,2016,2870)
(  17,2388,4337)(  18,1706,1649)(  19,2658, 909)(  20,4654,4330)
(  21,3458,3738)(  22,4620,4934)(  23,3995,3622)(  24,5064,2291)
(  25,3555, 142)(  26,1660,4074)(  27,3298, 343)(  28,2742,5114)
(  29,2132,1380)(  30,3275,4956)(  31,3840,1785)(  32,1810, 754)
(  33, 471,3316)(  34,4780,3238)(  35,2580,4609)(  36,3681, 447)
(  37,3686,3841)(  38,3684,4093)(  39,3679, 953)(  40,3687,1628)
(  41,3674, 106)(  42,3683,1409)(  43,3677,2561)(  44,3682,4552)
(  45,3177, 789)(  46,3678, 706)(  47,2762,1454)(  48,3685,1425)
(  49,3673,1437)(  50,3676, 921)(  51,3675,3096)(  53,4798,3338)
(  54,2321,  92)(  55, 280,4391)(  56,1456,4179)(  57,1798,1256)
(  58, 189, 130)(  59,2803,3286)(  60, 877,3531)(  61,2270,4709)
(  62,2184, 253)(  63,4605,4854)(  64, 135,2908)(  65, 525,4474)
(  66,2971,3432)(  67,3045,2094)(  68,3844,1559)(  69,5009, 549)
(  70,4019,4660)(  71,1675, 812)(  72,2303,3122)(  73, 986, 591)
(  74,4965, 977)(  75,3976,1917)(  76,1158,4429)(  77, 117, 878)
(  78, 558,3196)(  79,2036,3779)(  80,4440,4052)(  81, 411,3270)
(  82, 737,4529)(  83, 607,1206)(  84,4986,4113)(  85,2712,2304)
(  86,1230, 690)(  87,4867,3408)(  88,1697,3136)(  89,1428,2676)
(  90,1645,3356)(  91,2490,1748)(  93,1163, 578)(  94,1286,3925)
(  95,1739,4413)(  96,3570, 734)(  97,2171,3236)(  98,2648,1629)
(  99, 805,2022)( 100,4471,5075)( 101, 468,3516)( 102,3029,1174)
( 103,3865,4109)( 104,2479, 975)( 105,1813,2158)( 107, 489,5045)
( 108, 621,4507)( 109,3899,2281)( 110,3949,2572)( 111,1602,4840)
( 112,2542,4968)( 113,2146,1752)( 114,4566,4745)( 115,1694, 846)
( 116, 458, 852)( 118,3472,1194)( 119,3143, 376)( 120,3085,3775)
( 121, 871,2766)( 122,1042,4659)( 123,2552,1245)( 124,4948,3741)
( 125,4497,2532)( 126,4340,4772)( 127,3700,2999)( 128,4992,4853)
( 129,2777,4089)( 131,3761,1030)( 132,2439,2674)( 133,2661,2715)
( 134,3213,2078)( 136,1982,5220)( 137, 703,1526)( 138,2966,3560)
( 139, 863,2484)( 141,3647,3556)( 143,4565,3561)( 144,2667,3559)
( 145,3880,3549)( 146,1873,3553)( 147,4736,3552)( 148,2091,3562)
( 149,2174,3557)( 150,4417,3550)( 151,4541,3558)( 152,1774,3551)
( 153,4487,3554)( 154,4454,1719)( 155,1723,1781)( 156,2914,3511)
( 157,1169,4002)( 158,3273,1103)( 159, 277,3131)( 160,2352, 796)
( 161,1389,3979)( 162,1293,4795)( 163,5167, 227)( 164,1138, 671)
( 165, 925,4028)( 166,2468, 840)( 167,4562,1844)( 168, 759,2757)
( 169,2711,2473)( 170,2434, 804)( 171,4619,5218)( 172, 729,3027)
( 173,3876,4938)( 174,2892,4492)( 175,3047,2349)( 176,4400, 206)
( 177, 248,1195)( 178,1651, 614)( 179,2719,1354)( 180, 633,4485)
( 181,2946, 540)( 182,1349,3521)( 183, 787, 814)( 184, 504,3247)
( 185,3927,1517)( 186,3031,1125)( 187,2147,4781)( 188,1904, 524)
( 190,5163, 224)( 191,4116,4789)( 192,2287,3957)( 193,2173,3657)
( 194, 308,3424)( 195, 626,1631)( 196,2198, 604)( 197, 741,1872)
( 198,1480,2996)( 199,5021,1592)( 200,1014,2423)( 201,2835, 755)
( 202,3997,2894)( 203,4715,3264)( 204,1347,5002)( 205, 699,4750)
( 207,4863,2902)( 208,2810,2621)( 209, 385,1284)( 210, 320,1487)
( 211,3292,2322)( 212,2370,2567)( 213,4247,1714)( 214, 762,2759)
( 215, 492, 917)( 216,5193,4005)( 217,2308,3798)( 218,4289,3002)
( 219,3600,1058)( 220,1483,2088)( 221,4319,4014)( 222,3940,1586)
( 223,1763,5148)( 225,3282,5171)( 226,3173,5174)( 228,4547,5164)
( 229, 306,5172)( 230,3805,5169)( 231,3937,4949)( 232, 627,5161)
( 233,3267,5173)( 234,4944,4946)( 235,3589,5168)( 236,2544,5162)
( 238,3982,5166)( 239,4616,5165)( 240,1908,3265)( 241,3334,4640)
( 242,1004,3463)( 243,3281,2597)( 244, 667,2154)( 245,3318,4151)
( 246,5006, 710)( 247,2827,3345)( 249, 748,2685)( 250,2376,4473)
( 251,3543,1352)( 252,3100,4893)( 254,3093,3716)( 255,2059,1787)
( 256,2519,4024)( 257,3114,1279)( 258,1569,1277)( 259,5201,1280)
( 260,1545,1268)( 261,1373,1275)( 262,4551,1267)( 264,1143,1270)
( 265, 541,1276)( 266,3482,1278)( 267,3315,1273)( 268,1069,1283)
( 269,2948,1271)( 270,4264,1274)( 271,1716,1272)( 272,1589,1269)
( 273,1479,1281)( 274,4728,4442)( 275, 893,2453)( 276, 764, 637)
( 278,1926, 482)( 279,1636,3366)( 281,2931, 899)( 282,3441,2628)
( 283,1519,4902)( 284,1062,4510)( 285, 442,1353)( 286,2258,3999)
( 287, 770,4361)( 288,1920,1148)( 289, 711,2964)( 290,3165, 656)
( 291,1764,4626)( 292,4062,2716)( 293,3692,3564)( 294,4038,3343)
( 295, 499,2109)( 296,1418,4370)( 297,1960,2273)( 298,2534,2610)
( 299,3646,3402)( 300,3341,4733)( 301, 352,2849)( 302,2981, 574)
( 303,3528, 616)( 304,4311,2372)( 305,2455,2330)( 307,4981,1974)
( 309,1026,3642)( 310,3104,4291)( 311,4563,3723)( 312, 569, 827)
( 313, 632,2655)( 314,1124, 839)( 315,2961,4202)( 316,4159,3454)
( 317,4226,1054)( 318,5087,3954)( 319,4580,3409)( 321,5107,2035)
( 322,2774,1469)( 323,2726,1320)( 324,4204,2441)( 325,2424,2752)
( 326, 797,2523)( 327,2638,3863)( 328,3914,1936)( 329,1168,2065)
( 330,4133,3924)( 331,1088,3218)( 332,2126,3938)( 333,1002,2202)
( 334,1394, 412)( 335,4237,1699)( 336, 907,3910)( 337,1212,2188)
( 338,3757,4029)( 339,1253,4744)( 340,3717, 544)( 341, 623,3379)
( 342,3083,1073)( 344,4051,4807)( 345,2066,1722)( 346,4905,2425)
( 347,3615, 733)( 348,1311,4836)( 349, 961,4235)( 350,4286,4597)
( 351,5024,2152)( 353,4523,3818)( 354,4684,1525)( 355,4504,1295)
( 356, 944,4691)( 357,2458,3701)( 358,3594,3784)( 359,3496, 582)
( 360,3489,2045)( 361,3494,2833)( 362,3499,4796)( 363,3490,1043)
( 364,3487,4326)( 365,3485,3448)( 366,3495,4298)( 367,3498,2717)
( 368,3497,1968)( 369,3500,2589)( 370,3491,4546)( 372,3493,1357)
( 373,3501,2646)( 374,3488,4755)( 375,3486,1495)( 377,4727,2851)
( 378,2811, 646)( 379,4873,1858)( 380,3462,3665)( 381, 638,2486)
( 382,1102,2194)( 383,3223,3753)( 384,4724,2079)( 386,4215,3303)
( 387,2990,4118)( 388,4112,4281)( 389,1010,1755)( 390,3592, 580)
( 391,4932,1149)( 392,3328,3290)( 393,4868,4255)( 394,2729,1327)
( 395,2530, 477)( 396,1896,3106)( 397,2860,1112)( 398,3972,2320)
( 399,1448,3381)( 400,4366, 897)( 401,2582,3895)( 402,3257,3614)
( 403, 536,2356)( 404,3882,1962)( 405,1254,3268)( 406,1064,4675)
( 407,5145,1987)( 408,3637, 547)( 409, 747,4125)( 410,1467,4891)
( 413,5123,4034)( 414,3740,3102)( 415,1392,1678)( 416,1165,5030)
( 417,2058, 478)( 418,1166,5205)( 419,4035,2082)( 420,2960,4603)
( 421,4498,2941)( 422,4622,2336)( 423, 457,4104)( 424,4509,1523)
( 425,4385,3960)( 426,2876,5036)( 427,2808,3182)( 428,1536,1983)
( 429, 836,3789)( 430,4347,4773)( 431,4702,2137)( 432, 570,2499)
( 433,3801,3860)( 434,1989,3048)( 435,2743,1007)( 436,1666,3172)
( 437,1433,2080)( 438,2536,4953)( 439,2168,1476)( 440,3617,1356)
( 441,2410,1627)( 443,1906,4314)( 444,4465,1670)( 445,1849,2028)
( 446,3690, 603)( 448,2832,4460)( 449,1131,4962)( 450,2114, 745)
( 451,1134,4009)( 452,2741,4444)( 453,3749,2707)( 454,4271,1150)
( 455, 609, 552)( 456,3160,2300)( 459,2364,4989)( 460,1461,3978)
( 461,2957,2602)( 462,3453,2239)( 463,1979,2650)( 464, 601,3309)
( 465,1410,1336)( 466,1635,3369)( 467,3794,4222)( 469,3883,3162)
( 470,2792,2571)( 472,2072,3222)( 473,4139,2305)( 474,4797,3504)
( 475,5106,2351)( 476, 483,4633)( 479,3897,4418)( 480,2761,4604)
( 481,3641,2420)( 484,1642,3368)( 485, 988,2789)( 486,1841,1017)
( 487,2477,5199)( 488, 635,3352)( 490,3200, 964)( 491,1031,3634)
( 493,3827,3057)( 494,1893,5038)( 495,3750,4508)( 496,3142,1850)
( 497,3823,1668)( 498,3451,3375)( 500,1488,3310)( 501, 950,3033)
( 502,2520,4666)( 503,2178,2776)( 505,1261,1370)( 506,3771,2098)
( 507,2448,1051)( 508,3051, 957)( 509,4993,1087)( 510,3859,1549)
( 511,4258,4475)( 512,3714,2362)( 513,4888,3080)( 514,2181,3312)
( 515,1363,3107)( 516,3452, 670)( 517,4157,1190)( 518, 705,1006)
( 519,2675,3280)( 520,2607,3644)( 521,4644,3535)( 522,3256,2055)
( 523,3354,1378)( 526,4008, 738)( 527,2160,2514)( 528,1786,2820)
( 529,5175,4987)( 530,3964,1016)( 531,1952,1746)( 532,4414,3538)
( 533,1878,4488)( 534,1687,2467)( 535,2814,3892)( 537,1045,3071)
( 538,3806,2812)( 539,4282,2575)( 542,3059,3664)( 543,1503,3170)
( 545,4714,4976)( 546,4929,1105)( 548,4674,2500)( 550,3505,3442)
( 551,4639,3609)( 553,2096,2165)( 554,3148,1754)( 555,2901,1083)
( 556,3639,4501)( 557,2084,1388)( 559,2001,2684)( 560,3930,1815)
( 561,2839,2244)( 562,2408,5186)( 563,5105,1534)( 564,4348,4764)
( 565,2891,5066)( 566,2207,2784)( 567,4869,4896)( 568,3890,2316)
( 571,2047,2119)( 572,2026,3241)( 573, 658,3084)( 575,1776,4822)
( 576,2609,3510)( 577,3253,5050)( 579,4102,3879)( 581,2149,1846)
( 583,3778,2541)( 584,1978,4117)( 585,5141,4643)( 586,4518,1489)
( 587,1198,1167)( 588,4843,1581)( 589,1740,2145)( 590,4751,5210)
( 592, 868, 767)( 593,5042,2893)( 594,2286,1183)( 595,2562,2795)
( 596, 841,1801)( 597,4760,2593)( 598,3053,2037)( 599,4695,3387)
( 600,4894,4477)( 602,3994,1252)( 605,5073,3795)( 606,3607, 641)
( 608,4725, 753)( 610,1116,1793)( 611,4343,1385)( 612,1895,3116)
( 613,4972, 680)( 615,1840,1086)( 617,3306,2834)( 618,2101, 886)
( 619,4482,3825)( 620,4661,4558)( 622,1679,1733)( 624,1096,1541)
( 625,2779,3537)( 628,1060,2599)( 629,3030,4859)( 630, 959,4531)
( 631,2525,3928)( 634,5085,5200)( 636,1535,2369)( 639,3586,4858)
( 640,4299,1491)( 642,4003,2301)( 643, 727,3013)( 644,3319,3302)
( 645,4401,4309)( 647,1611,4288)( 648,1248,3000)( 649,1226, 696)
( 650,4100,4942)( 651,4198,2150)( 652,1652,2524)( 653,3808,1901)
( 654,5194,4900)( 655,3719,1800)( 657,2107,5122)( 659,4123, 928)
( 660,2233,1970)( 661,4754,1085)( 662,2924, 820)( 663,4360,1883)
( 664,1415,1156)( 665,4419,5027)( 666,4866,2297)( 668,3211,4325)
( 669,4977,1686)( 672,3111,4090)( 673,2106,1188)( 674,5052,1937)
( 675,5178,3389)( 676,1301,4826)( 677,1474,2315)( 678, 769,2550)
( 679,4176,1082)( 681, 913,1997)( 682,2926,1228)( 683,4719,1224)
( 684, 806,1218)( 685,1902,1227)( 686,4958, 984)( 687,2782,1232)
( 688,3299,1220)( 689,1178,1229)( 692,3540,1222)( 693,1998,1223)
( 694,3347,1221)( 695,1386,1225)( 697,4544,1217)( 698,2068,1219)
( 700,2463,2263)( 701,4642,1458)( 702,1440,2312)( 704,1758,1797)
( 707,4408,2193)( 708,4623, 881)( 709,4069,4602)( 712,2039,3040)
( 713,2780,2977)( 714,4268,2478)( 715,4857,4799)( 716,3015,2227)
( 717,3021,2223)( 718,3025,2221)( 719,3019,2219)( 720,3020, 749)
( 721,3017,2222)( 722,3016,2220)( 723,3022,2226)( 725,3028,2224)
( 726,3023,1249)( 728,2898,2228)( 730,3018,2229)( 731,3026, 822)
( 732,3014,2225)( 735,4432,3214)( 736,1287,4365)( 739,2363,2136)
( 740,1931,5090)( 742, 849,3139)( 743,2577,1396)( 744,2770,4589)
( 746,4132,2060)( 750,2333,3623)( 751,1393,2309)( 752,1447,3003)
( 756,2756,1251)( 757,2289,2778)( 758,2579,1397)( 760,2758,1065)
( 761,2254,1741)( 763,1691,4027)( 765,1182,1938)( 766,2755,2885)
( 768,4887,2261)( 771,4481,1993)( 772,2799,4208)( 773,1348,3470)
( 774,3232,1350)( 775,4172,2949)( 776,3862,4783)( 777,2864,5151)
( 778,3812,4792)( 779,2361,5079)( 780,1439,4022)( 781,1114, 962)
( 782,3956,3765)( 783,3001,1966)( 784,3603,4402)( 785,2432,4278)
( 786,4331,1505)( 788,3886,1886)( 790,4591,4743)( 791,4130,3054)
( 792,4219,1942)( 793,1619,2819)( 794,2600,3963)( 795,2327,1695)
( 798,5132,1032)( 799,3063,3803)( 800,4704,4721)( 801,1921,5043)
( 802,3429,3739)( 803,4810,1685)( 807,1544,3185)( 808, 923,4677)
( 809,2853,2191)( 810,3901,4581)( 811,3731,4788)( 813,1009,3545)
( 815,4058,1579)( 816,3737,4318)( 817,1338,4353)( 818,1368,1587)
( 819,2334,4647)( 821,3826,1100)( 823,2956,4435)( 824,3630,2196)
( 825,1185,3874)( 826,2180,2025)( 828,2660, 960)( 829,3613, 883)
( 830,3169,3744)( 831,2042,1953)( 832,1215,4974)( 833,1424,3279)
( 834,1590,2647)( 835,4582,1585)( 837,2942,3217)( 838,2354,4711)
( 842,4466,3340)( 843,4657,1399)( 844,2003,2488)( 845,2866,5155)
( 847,2619,1799)( 848,4137,3727)( 850,4756,1655)( 851,3649,2507)
( 853,5078,3371)( 854,3044,5049)( 855,1262,2888)( 856,2427,4231)
( 857,2280,2272)( 858,1362,2177)( 859,4793,3070)( 860,1372, 998)
( 861,3503,4023)( 862,2073,1140)( 864,1599,2491)( 865,1513,3530)
( 866,1770,5219)( 867,2371,2932)( 869,2967,4049)( 870,3094,2764)
( 872,4369,3907)( 873,3061,4066)( 874,1597,3407)( 875,5118,2927)
( 876,1852,1566)( 879,2872,5158)( 880,1377,5097)( 882,2298,4490)
( 884,4679,2162)( 885,2576,2481)( 887,5211,5198)( 888,2817,4746)
( 889,3598,2243)( 890,1315,4827)( 891,1773,1429)( 892,1446,3800)
( 894,4658,3705)( 895,1160,1650)( 896,1375,1239)( 898,1923,4129)
( 900,4925,4105)( 901,4227,3079)( 902,1584,4195)( 903,3904,2704)
( 904,4396,1442)( 905,3332,4741)( 906,3572,1076)( 908,4436,4472)
( 910,5013,5082)( 911,5140,1061)( 912,3695,5047)( 914,1630,3912)
( 915,1494,4119)( 916,1829,2385)( 918,1662,1736)( 919,2024,2503)
( 920,2167,2596)( 922,4525,2438)( 924,3706,1623)( 926,1791,4590)
( 927,3430,4217)( 929,3415,4334)( 930,4947,3066)( 931,3313,5128)
( 932,2709,2516)( 933,2256,3881)( 934,5142,4701)( 935,1507,3605)
( 936,2555,2341)( 937,3835,2989)( 938,2211,1416)( 939,3444,4030)
( 940,4941,3520)( 941,3672,2447)( 942,4920,1969)( 943,1546,3348)
( 945,3652,4064)( 946,4358,1761)( 947,1180,3643)( 948,4153,4970)
( 949,1985,4307)( 951,5215,2528)( 952,2306,3699)( 954,4747,4535)
( 955,3829,1676)( 956,3754,4818)( 958,3986,2074)( 963,3748,3661)
( 965,4489,2568)( 966,4720,1792)( 967,4698,4392)( 968,3567,4585)
( 969,2324,1135)( 970,3628,4197)( 971,1038,4963)( 972,2626,4955)
( 973,3669,4954)( 974,2251,4957)( 976,4295,3923)( 978,1080,4966)
( 979,1775,4960)( 980,2111,4959)( 981,3867,4964)( 983,3921,4961)
( 985,2311,1718)( 987,3922,3959)( 989,2366,4037)( 990,3230,2014)
( 991,3011,5203)( 992,1106,1529)( 993,4890,2909)( 994,2874,5152)
( 995,4182,3322)( 996,4357,2938)( 997,1604,3638)( 999,2705,2983)
(1000,1620,4449)(1001,3611,4200)(1003,3207,3004)(1005,4221,1730)
(1008,3967,3308)(1011,2865,4742)(1012,2629,3793)(1013,5180,2634)
(1015,4017,5100)(1018,2769,1809)(1019,1310,4828)(1020,3157,4933)
(1021,1501,4253)(1022,3767,3864)(1023,1108,2573)(1024,4969,1910)
(1025,3174,3065)(1027,4095,4433)(1028,4378,3344)(1029,1656,3431)
(1033,2965,1109)(1034,1963,3648)(1035,3412,4012)(1036,1066,1654)
(1037,3804,1512)(1039,3251,3144)(1040,3215,3167)(1041,4390,2475)
(1044,5031,2781)(1046,2368,4379)(1047,3920,4087)(1048,2723,1325)
(1049,2076,1779)(1050,4111,4662)(1052,1871,1935)(1053,1436,1591)
(1055,4301,2816)(1056,2268,1155)(1057,3437,1445)(1059,3271,4918)
(1063,3473,5204)(1067,4614,1768)(1068,4082,2953)(1070,5115,4931)
(1071,3747,1924)(1072,3191,2006)(1074,4940,1462)(1075,1783,3769)
(1077,2285,4004)(1078,4332,2887)(1079,3183,4186)(1081,3304,1672)
(1084,4274,1734)(1089,4646,4152)(1090,1624,3121)(1091,1643,3358)
(1092,4613,1299)(1093,3776,2249)(1094,4294,5018)(1095,2584,4310)
(1097,3010,3889)(1098,4583,4085)(1099,1387,4013)(1101,2724,1333)
(1104,2987,4821)(1107,2179,1696)(1110,3127,2230)(1111,1179,1625)
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