b := (1, 130, 121)( 2,2053,6348)(   3,4958,1539)(   4,5558,4903)
(   5,4534,3993)(   6,2935,6540)(   7,5857,4622)(   8,1818,5573)
(   9, 665,2781)(  10,5151,3580)(  11,3469,2479)(  12, 747, 865)
(  13,2601,3716)(  14,4279,6016)(  15,3789, 488)(  16,7132,3073)
(  17,6495,1459)(  18,2503,5127)(  19,6653,7218)(  20,1212,2089)
(  21,4945, 869)(  22,5164,5116)(  23,2938,1462)(  24,4283,5578)
(  25,1213,6552)(  26,2037,3725)(  27, 743,4636)(  28,5866,3582)
(  29,2498,2079)(  30,4542,4898)(  31, 653,7210)(  32,1816, 487)
(  33,6489,3994)(  34,3800,2476)(  35,5565,6349)(  36,7131,1537)
(  37,6668,3066)(  38,3461,2787)(  39,2597,6006)(  40,4289,3997)
(  41,4957,2486)(  42,6486,3583)(  43,5865,7205)(  44,2586,1453)
(  45,2038,6549)(  46,4540,5123)(  47,2500,1523)(  48,3474,3724)
(  49,7145, 483)(  50,1216, 875)(  51,6660,5572)(  52,5157,3074)
(  53,1820,4900)(  54,3790,6360)(  55, 658,6014)(  56, 745,2792)
(  57,5554,2077)(  58,2929,4619)(  59,2499,2785)(  60,5868, 495)
(  61,4955,6019)(  62,3464,3998)(  63,6483,1533)(  64,2044,3589)
(  65, 651,4899)(  66,5556,4624)(  67,3799,1449)(  68,1217,7213)
(  69,2943,3065)(  70,4535, 864)(  71,4278,2090)(  72, 750,5570)
(  73,6652,6364)(  74,2603,5125)(  75,7139,3709)(  76,1812,6546)
(  77,5161,2472)(  78,5153,7204)(  79,6498,4629)(  80,2590,6543)
(  81,4950, 493)(  82, 655,3710)(  83,2051,2080)(  84,6666,6012)
(  85,4280,1461)(  86,5869,2789)(  87, 761,2474)(  88,7137,5583)
(  89,3795,4902)(  90,2937, 866)(  91,5555,5124)(  92,3473,6356)
(  93,4525,3578)(  94,1807,4004)(  95,2502,3079)(  96,1205,1522)
(  97,5561,3720)(  98,3476,7207)(  99,5861,5130)( 100,3788,2786)
( 101,4954,4634)( 102,2041,6007)( 103,2595,5587)( 104,1808,2481)
( 105,6655,1529)( 106,2946,4006)( 107,5165,2081)( 108, 652,3072)
( 109,2501,6541)( 110,7127, 862)( 111,4526,6350)( 112,6496,4901)
( 113,1207,1452)( 114, 756,3586)( 115,4294, 477)( 116, 134, 125)
( 117, 122, 128)( 118, 129, 124)( 119, 131, 126)( 120, 127, 133)
( 135, 748,1525)( 136,6661,2788)( 137,3785,5576)( 138,4531,1464)
( 139,3471, 482)( 140,2045,4894)( 141,4943,3069)( 142,7144,7220)
( 143, 654,2487)( 144,4295,3711)( 145,2494,3590)( 146,6494,6539)
( 147,1822,6017)( 148,2940,2086)( 149,2594,6358)( 150,5870, 863)
( 151,5155,4633)( 152,1199,5115)( 153,5564,3992)( 154,6497,5577)
( 155,2933,6023)( 156,1200,3719)( 157,5160,4890)( 158,7142,2083)
( 159,2035,2790)( 160,1814,1535)( 161,4944,6542)( 162,4290,3063)
( 163,6670,5122)( 164,4528, 480)( 165,5553,2478)( 166,2598,7219)
( 167,3470,4637)( 168,2508,6363)( 169, 754,1457)( 170,3797, 858)
( 171,5860,3999)( 172, 656,3574)( 173,2928, 492)( 174,2596,1528)
( 175, 659,2074)( 176,6493,2484)( 177,4537,2793)( 178,2049,3064)
( 179,3798,3576)( 180,5167,3718)( 181,4959,4001)( 182,1825,4635)
( 183, 744,4895)( 184,3462,5126)( 185,1202,5574)( 186,2495,6013)
( 187,5859,6352)( 188,6658,6556)( 189,5557,7211)( 190,4285, 871)
( 191,7136,1446)( 192,6662,3584)( 193,1819,3062)( 194,5566, 491)
( 195, 758,6545)( 196,2497,4897)( 197,2039,2488)( 198,5162,4007)
( 199,4529,5575)( 200,7135,5117)( 201,4960,2084)( 202,5856,1451)
( 203,2945,3715)( 204,3796,1540)( 205,2589,2778)( 206,1208,6365)
( 207,4277,7216)( 208,6482,6009)( 209, 662,4628)( 210,3467, 857)
( 211,3784,6544)( 212,5552, 872)( 213,2505,2482)( 214,1824,2076)
( 215,4286,5121)( 216,2046,4631)( 217,2936,7214)( 218,6656,4887)
( 219, 755,6024)( 220,6499,3068)( 221,4942,3708)( 222,1209,2780)
( 223,3465,1460)( 224, 664,4008)( 225,7130,6361)( 226,5158, 486)
( 227,2592,3591)( 228,4539,1527)( 229,5867,5569)( 230,7140,4626)
( 231,4530,3723)( 232,6664, 868)( 233, 648,1526)( 234,3787,7212)
( 235,2052,5582)( 236,5864,2085)( 237,1214,3995)( 238,2587, 478)
( 239,2509,1454)( 240,5559,6008)( 241,4949,3579)( 242, 757,5128)
( 243,5159,6555)( 244,6492,6362)( 245,3463,3071)( 246,4282,2490)
( 247,2930,4891)( 248,1823,2776)( 249,5863,3077)( 250,4284,4892)
( 251,5168,1524)( 252,2492, 870)( 253,2944,3592)( 254,2047,1450)
( 255,7129,2475)( 256,3468,6018)( 257,5550,6548)( 258, 666,5586)
( 259,2599,4003)( 260, 749,7217)( 261,4953,2782)( 262,6667, 485)
( 263,1821,6353)( 264,1204,4620)( 265,4527,2082)( 266,3793,3722)
( 267,6485,5113)( 268, 663,5131)( 269,7138,6547)( 270, 752,3996)
( 271,1215,6021)( 272,1817, 859)( 273,2048,7209)( 274,2496,3712)
( 275,2593,3075)( 276,2932,5581)( 277,3478,3575)( 278,3791,4632)
( 279,4291,1538)( 280,4524,2480)( 281,4948,1456)( 282,5152,6355)
( 283,5562,2779)( 284,5871,4896)( 285,6484, 494)( 286,6654,2073)
( 287,1206,2483)( 288, 649,1448)( 289,4532,3076)( 290,2588,4627)
( 291,6657,4005)( 292,2050, 874)( 293,3477,6554)( 294,2942,2783)
( 295,6491,7208)( 296,5568,1534)( 297,1813,5119)( 298,5854,6015)
( 299,7143,4886)( 300,4288,3577)( 301,4946,6366)( 302,3792,2087)
( 303,2504, 481)( 304,5163,5579)( 305, 746,3707)( 306,1811,1463)
( 307,3786,4000)( 308,3460,4888)( 309,6665,3721)( 310,5862,2473)
( 311,2036,5118)( 312,6487, 861)( 313, 753, 490)( 314,4533,4630)
( 315,5169,2794)( 316,4293,6550)( 317,2591,2088)( 318,5567,3581)
( 319,1201,3070)( 320, 660,6354)( 321,4956,5571)( 322,2939,1532)
( 323,7134,6022)( 324,2506,7203)( 325,4541,6020)( 326, 751,2078)
( 327,1810,7221)( 328,7141,3585)( 329,5551,5585)( 330,2040, 479)
( 331,4281,2777)( 332, 661, 867)( 333,1210,4893)( 334,5872,6553)
( 335,3472,1531)( 336,5166,1458)( 337,6659,4623)( 338,6490,3713)
( 339,2934,6351)( 340,2493,4009)( 341,4952,5120)( 342,2602,2485)
( 343,3783,3061)( 344,2600,4889)( 345,1203,3587)( 346,7133,2784)
( 347,2931,5114)( 348, 760,3067)( 349,2042,4002)( 350,5563,1455)
( 351,6481,2091)( 352,5156, 873)( 353,3801,6011)( 354,6663,2489)
( 355,2507,4621)( 356, 650, 489)( 357,5855,1536)( 358,4287,6359)
( 359,1815,3714)( 360,3475,5584)( 361,4951,7206)( 362,4536,6538)
( 363,3466,2075)( 364,2491,5580)( 365,4292,4625)( 366,5560,3078)
( 367,5154,6010)( 368,2043,1530)( 369,1211, 484)( 370,3794,5129)
( 371,1809,3588)( 372,2604, 860)( 373,6488,2791)( 374,7128,4010)
( 375,5858,3717)( 376,4538,7215)( 377, 759,6357)( 378,2941,2477)
( 379, 657,6551)( 380,6669,1447)( 381,4947,4885)( 382, 739,6651)
( 383,4986,3595)( 384,5304,1566)( 385,5467,5441)( 386,6061,1042)
( 387,6465,2389)( 388,6673,1884)( 389,7081,5240)( 390, 885,4597)
( 391,1177,7097)( 392,1684,4762)( 393,2162,6146)( 394,2192,3045)
( 395,2726,3661)( 396,2989,2641)( 397,3573,1370)( 398,3677,4305)
( 399,4120,6409)( 400,4448, 568)( 401,1244,5106)( 402,4098,4804)
( 403,5003, 628)( 404,3963,2185)( 405,2466,6527)( 406,5277,4188)
( 407,1088,5905)( 408, 497,1054)( 409,4361,6947)( 410,2854,3766)
( 411,6733,3027)( 412,1917,5722)( 413,3458,3532)( 414,3170,4396)
( 415,6396,1742)( 416,5511,2510)( 417,1490,1278)( 418,5949,6383)
( 419,6934,2709)( 420,3080,7159)( 421,2210,4216)( 422,6106,3214)
( 423,6753,1521)( 424,5481,4381)( 425,4152,6716)( 426,6889, 548)
( 427,2900,3924)( 428, 640,2008)( 429,6284,6028)( 430,4575,1185)
( 431,2125,2664)( 432,3912,2260)( 433,5186,5765)( 434,4788,4859)
( 435,1673, 990)( 436, 820,5079)( 437,3405,6270)( 438,1430,3622)
( 439,7045,3426)( 440,5330,5803)( 441,6245,4686)( 442,3311, 980)
( 443,4168,3022)( 444,2968, 588)( 445,1595,6790)( 446,4663,4978)
( 447,6873,2265)( 448, 667,4042)( 449,3844,5621)( 450,1862,5143)
( 451,5940,1947)( 452,1119,1423)( 453,2872,3976)( 454,2433,1750)
( 455,5540,2770)( 456,4911,6185)( 457,1023,7014)( 458,5343, 787)
( 459,5517,3183)( 460,3397,2617)( 461,4411,6093)( 462,1788,5419)
( 463,2331,1312)( 464,1357,5671)( 465,6175,6691)( 466,2647,3730)
( 467,5064,4614)( 468, 598,3305)( 469,2146,1839)( 470,6571,4932)
( 471,4014,7011)( 472,6002, 710)( 473, 913,4068)( 474,7175,2354)
( 475,3814,6301)( 476,3146,1772)( 496,2518,2534)( 498,6519,5694)
( 499,2717,3945)( 500,6949,1257)( 501,1736,3116)( 502,5104,4492)
( 503,5906,4067)( 504,4803, 955)( 505,3521,6855)( 506,6369,2563)
( 507,2177,7063)( 508, 613,1549)( 509,5727,5376)( 510,3780,5839)
( 511,1293,4828)( 512,3038,3379)( 513,4402,6433)( 514,4183,2056)
( 515,4484,5647)( 516,6338, 804)( 517,3238,4342)( 518,2284,3543)
( 519,4724,5889)( 520,2849,3835)( 521,3821,4717)( 522, 808,1879)
( 523,1620,2851)( 524,7122,1627)( 525,5646,6778)( 526,1869,3241)
( 527,4338,5384)( 529,1134,2283)( 530,5891,7108)( 531,3548,4478)
( 532,5394,6335)( 533,6773,1140)( 534, 938,3090)( 535,2921,2123)
( 536,2575,3913)( 537,6079,5185)( 538,5212,4777)( 539,1332,1659)
( 540,5754, 830)( 541,6813,3408)( 542,3747,1435)( 543,4436,2224)
( 544,3490,6103)( 545,1931,6764)( 546,4867,5487)( 547,7239,4147)
( 549,4333,2890)( 550,2437, 630)( 551,6228,6286)( 552,1651,4569)
( 553,5825,6052)( 554,6591,5313)( 555,1612,2201)( 556,1223,2998)
( 557,4641,2153)( 558,3888,7072)( 559,6200,3564)( 560,4265,5458)
( 561,5415, 730)( 562,2359,2735)( 563,3134, 894)( 564,1990,4995)
( 565,6958,6682)( 566,3506,1675)( 567,5778,1168)( 569,2751,3686)
( 570, 844,6474)( 571,5029,4111)( 572,4812,1115)( 573,3876,1592)
( 574,5603,5947)( 575,7188,7048)( 576,6611,4170)( 577,3271,4909)
( 578,2825,3852)( 579,5259,2421)( 580,2957,5331)( 581,4131,1010)
( 582,1327, 670)( 583,2018,4675)( 584, 762,2885)( 585,6132,6865)
( 586,2308,1855)( 587,4713,3308)( 589,1721,6249)( 590,6451,5539)
( 591,5675,1708)( 592,6994,4522)( 593,4602,5192)( 594,6306,4241)
( 595,1302,2692)( 596, 794,5635)( 597,4085,1158)( 599,6089,4746)
( 600,3731,3199)( 601,4935,6982)( 602,1832,2400)( 603,2614,3649)
( 604,1770,3335)( 605,6693,6837)( 606,3193,5968)( 607,5431,2098)
( 608, 709,6501)( 609,2349,1078)( 610,2562,3961)( 611,5836,1246)
( 612,4059,3454)( 614,3380,6921)( 615,4837,5266)( 616,4498,2860)
( 617,1260,4355)( 618,7057,5954)( 619,3102,5508)( 620, 969,2470)
( 621,2061,1498)( 622,5696,4097)( 623,6424,1920)( 624,5365,3162)
( 625,3953,6728)( 626,6853,1101)( 627,2545,6397)( 629,3917,4430)
( 631,7149,4873)( 632,5082,2573)( 633,2668,3760)( 634,4387, 946)
( 635,6038,1638)( 636,5761,7236)( 637,2258,5757)( 638,1520,1930)
( 639,4210,4326)( 641,3221,1336)( 642,6713,6075)( 643,1002,3497)
( 644,6271,5208)( 645,4847,6814)( 646,1190,6220)( 647,3617,2925)
( 668,1763,7195)( 669,3980, 777)( 671, 973,1717)( 672,5611,2019)
( 673,3005,2311)( 674,4976,2818)( 675,6182,2954)( 676,5808,3287)
( 677,2757,3860)( 678,1943,4141)( 679,4692,4707)( 680,2272,4811)
( 681,3436,5254)( 682,7031,5588)( 683,1425,6138)( 684,6793,6456)
( 685,5138,6601)( 686,3352,1973)( 687,4557,6630)( 688, 930,1391)
( 689,3264,5038)( 690, 695,5712)( 691,6631,4551)( 692,5042,3266)
( 693,2225,5920)( 694,4235,1477)( 696,5287,5290)( 697,1967,3349)
( 698,1401, 931)( 699,3699,2802)( 700,1467,4233)( 701,2813,3688)
( 702,6317,6904)( 703,6900,6328)( 704,5915,2236)( 705,6833,2646)
( 706,2684,3807)( 707,1151,6566)( 708,4239,2328)( 711,3334,4015)
( 712,1705,1804)( 713,5642,3385)( 714,1081,5067)( 715,2402,4423)
( 716,2096,1361)( 717,5200,7171)( 718,4510,3151)( 719,6983, 897)
( 720,4751,2130)( 721,5970,5524)( 722,3211,6165)( 723,3644,5359)
( 724,6421,5034)( 725,3603,5796)( 726,2394,6960)( 727,1039,6579)
( 728,3664,3510)( 729,6145,2748)( 731,3047,3129)( 732,1371,4272)
( 733,5236,1224)( 734,7104,1986)( 735,1883, 843)( 736,1567,5817)
( 737,4754,2367)( 738,4309,4653)( 740,4585,1605)( 741,5439,6198)
( 742,2636,3891)( 763,3323,5133)( 764,4913,5622)( 765,4669,5802)
( 766,1108,6188)( 767,7038,6785)( 768,2969,7016)( 769,1026, 987)
( 770,1852,1417)( 771,5544,1764)( 772,6234,1958)( 773,5327,2280)
( 774,3858,2765)( 775,6872,3010)( 776,2431,3435)( 778,5931,4040)
( 779,4173,4678)( 780,1587,4965)( 781,6988,5998)( 782,4244,1369)
( 783,3196,4424)( 784,1709,3806)( 785,4511,6168)( 786,6835,4011)
( 788,3635,2335)( 789,2109,3145)( 790,5978,2143)( 791,1157,7182)
( 792,2682,3400)( 793,2414,5519)( 795,4740,2655)( 796,1080, 901)
( 797,5197,5065)( 798,6511,6558)( 799,3330,1791)( 800,1130,3831)
( 801,2295,3249)( 802,5391,6779)( 805,4475,4714)( 806,2835,1124)
( 807,6771,3550)( 809,3553,7120)( 810,3246,5395)( 811,6339,2848)
( 812,5663,4473)( 813,1623,5877)( 814,5873,5656)( 815,7124,2287)
( 816,4345,1625)( 817,4718,4352)( 818,3830,1866)( 819, 995, 942)
( 821,1180,4327)( 822,5773,2436)( 823,6718,6223)( 824,3918,1636)
( 825,4379,2927)( 826,3623,2580)( 827,2007,6069)( 828,4848,5219)
( 829,7163,1347)( 831,4219,6809)( 832,2247,3748)( 833,6266,4439)
( 834,1518,3483)( 835,3225,1928)( 836,2670,4883)( 837,6041,7223)
( 838,2985,2385)( 839,5462,6154)( 840,4114,4763)( 841,7079,3594)
( 842,2729,6412)( 845,4461,5448)( 846,2163,3655)( 847,3684,1380)
( 848,5319,3056)( 849,4997,4594)( 850,1692,4300)( 851, 877,1030)
( 852,3557,6642)( 853,1164,2627)( 854,2191,7095)( 855,6049,1576)
( 856,6677,5245)( 876,4308,2744)( 878,5440,1987)( 879,3043,5795)
( 880,4767,6201)( 881,6410,5398)( 882,6150,3893)( 883,2624,6586)
( 884,1886,2361)( 886,2386,5828)( 887,3607,4269)( 888,7107,1600)
( 889,1387,3516)( 890,6641,5025)( 891,5233,4639)( 892,1573,1222)
( 893,3657,6970)( 895,6700,5631)( 896,6292,2408)( 898,3296,4521)
( 899,1781,6504)( 900,5680,1142)( 902,2345,4248)( 903,1830,3329)
( 904,5428,5975)( 905,4605,3642)( 906,7002,4743)( 907,4941,2093)
( 908,6084,2698)( 909,3192,1699)( 910,3739,6841)( 911,2608,3197)
( 912,1303,5202)( 914,1469,4547)( 915,3262,3357)( 916,6906,5291)
( 917,2240,6629)( 918,3691,6313)( 919,3346,3251)( 920,6627,2238)
( 921,5919,5045)( 922,1960,2796)( 923,6316,3694)( 925,4552,1474)
( 926,5302,6917)( 927,4236,5718)( 928,2800,1964)( 929,5719,4237)
( 932,5051,5925)( 933,4774,6712)( 934,6763,2672)( 935,3404,1186)
( 936,2901,4215)( 937,5183,6255)( 939,4150,3624)( 940,1441,1510)
( 941,2113,5777)( 943,6113,2253)( 944,2213,2005)( 945,4580,5092)
( 947,1664,7150)( 948,6280,4863)( 949,3914,6026)( 950,5489,3224)
( 951,6884,3929)( 952,6402,4184)( 953,3968,5730)( 954,5955,3028)
( 956,3161,6368)( 957,1238,5892)( 958,5274,2711)( 959,6933,2174)
( 960,1902,4408)( 961,1491,2514)( 962,5001,3525)( 963,4100,6944)
( 964,6746,1291)( 965,4357,6533)( 966,5496,5097)( 967,2864,1746)
( 968,3451,3782)( 970,1096,1059)( 971,2309,4905)( 972,7196,4665)
( 974,5256,1591)( 975,6134,6252)( 976,4822,3840)( 977,3274,5541)
( 978,6445,7037)( 979,2025,6877)( 981,5594,2878)( 982,3875,5328)
( 983,1331,2981)( 984,2962,4176)( 985,4706,1106)( 986,4126,1859)
( 988,6595,5939)( 989,2831,2426)( 991,6080,6754)( 992,6218,6104)
( 993,6806,2122)( 994,7233,6289)( 996,1348,4571)( 997,1646,5174)
( 998,1934,4159)( 999,2439,2892)(1000,2574,5480)(1001,2913,1432)
(1003,3753,4783)(1004,4329,3081)(1005,4429,6893)(1006,4872,2222)
(1007,5209,3905)(1008,5752,3413)(1009,3428,2033)(1011,6802,3861)
(1012,4966,7194)(1013,2263,6459)(1014,4045,2301)(1015,5617,6603)
(1016,5135,1316)(1017,1948,4823)(1018,1420,5589)(1019,3984,4700)
(1020,1752,2951)(1021,2775,6133)(1022,6184,1723)(1024,5801,5258)
(1025,4690,3285)(1027,3017,2823)(1028,5789,7086)(1029,1226,4985)
(1031,4275,5312)(1032,3514,6477)(1033,5823,3555)(1034,3883,4113)
(1035,5030,2987)(1036,1984,1687)(1037,2747,4466)(1038,1599,6675)
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