b := (1,1481,2307)( 2,5075,1083)(   3, 729,3259)(   4,2945,1695)
(   5,2827,4483)(   6, 960,4177)(   7,3788,2001)(   8,3768,2613)
(   9,1424,2647)(  10,2012, 318)(  11,2160,2953)(  12, 373,3871)
(  13,2509,4789)(  14,3400, 189)(  15,4228,5095)(  16, 294, 777)
(  17,4440,1389)(  18,4869,3565)(  19,5153,4261)(  20,4847, 162)
(  21, 835,3356)(  22,3011,1057)(  23,2705,3984)(  24,1141,2407)
(  25,3929, 654)(  26,3623,3133)(  27,1447, 439)(  28,1787,1862)
(  29,2093,1429)(  30, 308,1749)(  31,2399,3515)(  32,3317,2635)
(  33,4235,4679)(  34, 257,5031)(  35,4541,4490)(  36,5011, 788)
(  37,4030,2564)(  38,3670,4770)(  39,1343,1002)(  40,1965,4308)
(  41,2233,3759)(  42, 429, 328)(  43,2479,4367)(  44,3252,1513)
(  45,4351,1261)(  46, 281,3056)(  47,4461, 224)(  48,4907,3938)
(  49, 598,3384)(  50,3000,1963)(  51,2661,2690)(  52,1117,4990)
(  53,5094,1659)(  54,3134,3809)(  55,2693,1182)(  56,1166, 926)
(  57,3977, 393)(  58,3498,4202)(  59,1239, 211)(  60,1895,2785)
(  61,2248,2512)(  62, 409,4560)(  63,2579,5004)(  64,3233,3553)
(  65,4196, 823)(  66,  75,1881)(  67,4612,3024)(  68,4820,4884)
(  69, 714,3484)(  70,5046,3969)(  71,1084,1464)(  72,3998,2667)
(  73,3535, 987)(  74,1446,3626)(  76,2319,4222)(  77, 447,1350)
(  78,2429, 808)(  79,3372,4726)(  80,4284,1818)(  81, 180, 537)
(  82,4513,2452)(  83,4704,5035)(  84, 667,3445)(  85,3154,4637)
(  86,2628,2938)(  87,5176,1365)(  88,4125,2763)(  90,4591,1050)
(  91,4919,1936)(  92, 694,3414)(  93,2978,2982)(  94,2758,4124)
(  95,1044,4576)(  96,3889,3622)(  97,3614,3880)(  98,1372,5170)
(  99,1926,4921)( 100,2312,1495)( 101, 355,2335)( 102,2338, 351)
( 103,3416, 697)( 104,5054,3686)( 105,2122, 361)( 106, 573,5169)
( 107,2386,1010)( 108,3430,2448)( 109,4173,1713)( 110, 136,4055)
( 111,4503,1771)( 112,4882,4071)( 113, 810,3236)( 114,3093,4741)
( 115,2907, 747)( 116, 888, 277)( 117,3818,4510)( 118,3679,2790)
( 119,1267,3121)( 120,1922,1252)( 121,5189,4548)( 122,1351,4822)
( 123,1853,3705)( 124,2172, 967)( 125, 555,2961)( 126,2555,1976)
( 127,3208,5066)( 128,4206, 426)( 129, 254,2862)( 130,4417,4340)
( 131,4693, 622)( 132, 758,3209)( 133,3109,1209)( 134,2736,2421)
( 135,1091,3924)( 137,3559,1623)( 138,5149,3112)( 139, 872,3269)
( 140,2968,2391)( 141,2816,1107)( 142, 932,1305)( 143,3948,4749)
( 144,3723,4606)( 145,1312, 871)( 146,1865,4962)( 147,2048,3784)
( 148, 465,4111)( 149,2600,2711)( 150,3441,1904)( 151,4149, 184)
( 152, 232,3641)( 153,4480,1641)( 154,4739, 517)( 155,4954,2531)
( 156,1772, 632)( 157,2073,4451)( 158, 337,1031)( 159,2354, 249)
( 160,3228, 476)( 161,4090,3665)( 163,4386,3858)( 164,4663,2682)
( 165, 625,3425)( 166,2942,4191)( 167,2638,1569)( 168, 907,3149)
( 169,3803,5209)( 170,3511,1196)( 171,1201,1769)( 172,4984, 506)
( 173,2786,3738)( 174,1021,2029)( 175,3986, 910)( 176,3592, 606)
( 177,1214,3815)( 178,2005,1551)( 179,2188,5074)( 181,2520,3062)
( 182,3275,4539)( 183,4154,2538)( 185,4535,4706)( 186,4658,1410)
( 187, 859,3318)( 188,3193,2730)( 190,1588,3034)( 191,1468, 710)
( 192,1705,1132)( 193,1619,2908)( 194,1737,4380)( 195,1650,4644)
( 196,1615,2379)( 197,1546,1841)( 198,1698,1605)( 199,1731, 261)
( 200,1679,1330)( 201,1508,5114)( 202,1558,4282)( 203,1574, 383)
( 204,1658,3827)( 205,1521,3712)( 206,5214,5121)( 207, 411,1914)
( 208,2495,3949)( 209,3285,1105)( 210,4078,4428)( 212,4562,2850)
( 213,4787,1587)( 214, 800,3300)( 215,3169, 847)( 216,2847, 581)
( 217,1065,4665)( 218,3842,2923)( 219,3737,3528)( 220,1308,4161)
( 221,1828,2483)( 222,2079, 307)( 223,5117,4844)( 225,4397, 552)
( 226,4724,1170)( 227, 653,3217)( 228,3123,4935)( 229,2886,1798)
( 230,1036,3581)( 231,3899,1319)( 233,1178,2491)( 234,1986,3083)
( 235,2135,2825)( 236, 501, 665)( 237,2619,1531)( 238,3307,4301)
( 239,4305,3908)( 240,5127,1940)( 241,3582,5147)( 242,1391,1533)
( 243,1758, 940)( 244,2213,4871)( 245, 391,2753)( 246,2442,1289)
( 247,3350,4029)( 248,4110,3190)( 250,4628,3492)( 251,4768,4404)
( 252, 832,3291)( 253,3065, 448)( 255, 944, 763)( 256,4044,4237)
( 258,2380,4334)( 259,3476,3179)( 260,4321,1145)( 262,4600, 868)
( 263,4842,2586)( 264, 737,3460)( 265,2918,3744)( 266,2749,5196)
( 267,1001,2878)( 268,3847,4032)( 269,3707, 576)( 270,1398,1436)
( 271,1815,4617)( 272,2202,2013)( 273, 483,4909)( 274,4948,2812)
( 275,3461,1462)( 276,4255,4082)( 278,4432,4974)( 279,4810,3001)
( 280, 637,3347)( 282,2802,4812)( 283,1139, 492)( 284,3866,1677)
( 285,3540,1833)( 286,1281,4409)( 287,2038,4008)( 288,2272, 719)
( 289, 519,3595)( 290,2451,2570)( 291,4970,2230)( 292,4368,2131)
( 293,4747,2180)( 295,3043,2209)( 296,2687,2218)( 297, 974,2262)
( 298,3921,2121)( 299,3748,2098)( 300,1251,2276)( 301,1941,2161)
( 302,2293,2153)( 303, 591,2287)( 304,2540,2322)( 305,3363,2074)
( 306,4293,2054)( 309,1517,2589)( 310,1717,3454)( 311,1584,3755)
( 312,1542,5193)( 313,1504,2883)( 314,1570,4036)( 315,1631, 574)
( 316,1554,1444)( 317,1480,4624)( 319,1675,4910)( 320,1611,4336)
( 321,1654,3164)( 322,1727,1148)( 323,1694,1721)( 324,1646, 861)
( 325,3118,4258)( 326,4316, 662)( 327,4719,3138)( 329,3910,1856)
( 330,2130,1422)( 331,2614,1747)( 332, 664,3516)( 333, 496,2620)
( 334,4392,4690)( 335,5112,5033)( 336,1981,4493)( 338,3302,3355)
( 339,1189,1061)( 340,3652,3987)( 341,2881,2414)( 342, 691,1370)
( 343,3413,2981)( 344,4588,4131)( 345,4122,4580)( 346,1041,3615)
( 347,1939,3891)( 348, 352,5173)( 349,4916,4929)( 350,2309,1497)
( 353,1369, 682)( 354,2771,2757)( 356,3611,1051)( 357,3886,1934)
( 358,2991,3404)( 359,4799,2234)( 360,2456,2255)( 362,3466,2097)
( 363,2791,2274)( 364,1286,2164)( 365,2277,2150)( 366,4437,2281)
( 367,2027,2329)( 368,4260,2059)( 369,4937,2044)( 370,3545,2084)
( 371,3061,2134)( 372, 524,2191)( 374,1128,2211)( 375, 642,2226)
( 376,4604,2529)( 377, 487,3672)( 378,4325,4850)( 379,2368,3860)
( 380,2922,2683)( 381,3695,3433)( 382,1819,4185)( 384,1402,3160)
( 385,3480,5208)( 386,5019,1199)( 387,3851,1762)( 388, 741, 636)
( 389,2206,4441)( 390, 989,1028)( 392,4846, 461)( 394,2077,4225)
( 395,3299,1349)( 396, 425, 802)( 397, 798,4711)( 398,3840,1820)
( 399,1306, 544)( 400,4076,2463)( 401,3735,5039)( 402,2493,3442)
( 403,5212,4638)( 404,1063,2928)( 405,4785,1467)( 406,1826,2665)
( 407,2845, 980)( 408,3167,3631)( 410,4181,1666)( 412,2394,2775)
( 413,2114,2513)( 414,4890,4571)( 415, 896,5007)( 416,3687,3538)
( 417,3422, 822)( 418,3826,1878)( 419, 565,3022)( 420,5062,4889)
( 421,2899,3486)( 422,4495,3802)( 423,1275,1176)( 424,3085, 934)
( 427,3219,2811)( 428,1208,3345)( 430,1779,4805)( 431,4377, 494)
( 432,2645,1674)( 433,3794,1823)( 434,2361,4412)( 435, 914,4009)
( 436,2064, 724)( 437,4961,3603)( 438,2933,2574)( 440,3518,4085)
( 441, 616, 899)( 442,4670,4981)( 443,4097,2995)( 444,2554, 507)
( 445,3558,1562)( 446,2171,5082)( 449,3108,4524)( 450,1106,2543)
( 451, 554,4142)( 452,2735,4696)( 453,1852,1412)( 454,5188,3322)
( 455, 757,2737)( 456,4205,3736)( 457,4054,2032)( 458,4692, 904)
( 459,4416, 603)( 460,3207,3814)( 462,4045,1799)( 463,1759,3578)
( 464,3583,1326)( 466, 833,2485)( 467,2863,3086)( 468,2214,2829)
( 469,3066, 668)( 470,1392,1524)( 471,5128,4286)( 472,4769,3906)
( 473,3335,4460)( 474, 945, 560)( 475,4629,1160)( 477,2443,4940)
( 478,2235,3385)( 479,1119,4648)( 480,1329,2381)( 481,4016,1846)
( 482,3254,1604)( 484,3002,1341)( 485,1967,5104)( 486, 600,4280)
( 488,5013,3830)( 489,4463,3715)( 490,2481,3042)( 491,2663, 711)
( 493,4353,2901)( 495,1872, 791)( 497,3521,4365)( 498,1073,1498)
( 499,2416,1265)( 500,4507,3057)( 502,1430,3935)( 503,4694,3377)
( 504,3997,1971)( 505,5034,2701)( 508,3147,4777)( 509,4269,1004)
( 510,3368,4307)( 511,2314,3762)( 512,1217,3676)( 513,3196,4049)
( 514,3989,1775)( 515,2789,4079)( 516, 540,3239)( 518,4645, 749)
( 520,4538,4515)( 521,1008,2793)( 522,4987,3128)( 523,4157,1249)
( 525, 862,5162)( 526,3278,1009)( 527,2523,2433)( 528,1992,1714)
( 529,3488,3105)( 530, 704,4608)( 531,1172, 882)( 532,3140,4960)
( 533,2254,3791)( 534,4186,4101)( 535,4618,2719)( 536,3967,1889)
( 538,2699,3645)( 539,5100,1635)( 541,1901,3274)( 542,4826,2388)
( 543,2585,1110)( 545,1229,4752)( 546,3957,1943)( 547,4732,1279)
( 548,2809,4014)( 549, 881,3187)( 550,1858,2362)( 551,3450,3491)
( 553, 925,3298)( 556,5142, 761)( 557,2593,4248)( 558,1321,5148)
( 559,4489,1537)( 561,2057,4865)( 562,3716,2755)( 563,1156,4542)
( 564,4551,5051)( 566,4861,2865)( 567,1451,4345)( 568,2400, 629)
( 569,4238,3210)( 570,2717,1212)( 571,3325,2420)( 572, 841,3914)
( 575,3625,4819)( 577,2102, 965)( 578,1800,2965)( 579,3934,1987)
( 580,2681,5132)( 582, 771,1590)( 583,4362,3303)( 584,3758, 837)
( 586,3357,4664)( 587,3037,2925)( 588,2550,3522)( 589,4757,4162)
( 590,4980,2476)( 592,3915,1921)( 593,4287,3954)( 594,1951,1090)
( 595,1245,4436)( 596, 984,1237)( 597, 679,2820)( 599,4509,4811)
( 601,1080,1668)( 602,1877,1835)( 604,4700,4003)( 605,2315, 723)
( 607,5042,2571)( 608,1442,1452)( 609,2624,4086)( 610,2425, 902)
( 611,3531,4967)( 612,4010,3006)( 613,3150,3343)( 614,3690,4252)
( 615, 805,3137)( 617,3088,1867)( 618,2117,1428)( 619,4168,1745)
( 620,4498,3510)( 621,3813,2625)( 623,2902,5025)( 624,5065,4494)
( 626,1917,3364)( 627,4893,1058)( 628,2397,3991)( 630,1262, 651)
( 631,2859,3688)( 633, 829,4068)( 634,4641,3243)( 635,3579,4737)
( 638,3078,4514)( 639,2439,2794)( 640,4765,3114)( 641,5124,1243)
( 643,4041,5168)( 644,4107,1018)( 645,1755,2438)( 646,1388,1708)
( 647, 941,4060)( 648,3808, 795)( 649,4668,4363)( 650,2643,1503)
( 652,1777,3051)( 655, 912,3383)( 656,4095,1960)( 657,2931,2704)
( 658,4959,4995)( 659,2359,2566)( 660,1206,4763)( 661,4375, 996)
( 663,2062,3763)( 666,2052,5071)( 669, 876,4529)( 670,3952,2542)
( 671,1316,4148)( 672,4137,4708)( 673,3711,1404)( 674,2588,3319)
( 675,5137,2723)( 676, 936,3734)( 677,4743,2036)( 678,1869, 915)
( 680,2972,3823)( 681,4484,1565)( 683,3887,4117)( 684,1924,4577)
( 685,3612,3621)( 686,4123,3894)( 687, 692,5174)( 688,2772,4918)
( 689,2310,1489)( 690,2992,2342)( 693,4917,2768)( 695,1042,1045)
( 696,4589,1932)( 698,2336,2990)( 699,1807,3966)( 700,2741,1358)
( 701,3699, 813)( 702, 993,4716)( 703,2372,1812)( 705, 745,2466)
( 706,1406,5036)( 707,4834,3436)( 708,3855,4632)( 709,5023,2940)
( 712,2910, 986)( 713,4329,3630)( 715,2210,4229)( 716,3007,2231)
( 717,4342,2116)( 718,4914,2106)( 720,4021,2165)( 721,2240,2144)
( 722,2470,2292)( 725,4468,2056)( 726,5002,2083)( 727,1972,2138)
( 728,1108,2194)( 730,1334,2203)( 731,3661,2215)( 732,2668,2261)
( 733,2271,3390)( 734,1138,2373)( 735,1280,1845)( 736,3865,1613)
( 738,4809,1344)( 739,3055,5116)( 740,2037,4278)( 742,3539,3831)
( 743,4947,3719)( 744,4431,3031)( 746,2801,1125)( 748,4254,4371)
( 750,1092,1944)( 751,4418,4019)( 752,3110,3181)( 753,4678,2351)
( 754,1352,3500)( 755,2556,4403)( 756,4207,3284)( 760,5190,4251)
( 762,3560,1534)( 764,2173,4876)( 765,1854,2747)( 766,4056,1291)
( 767,1576,5135)( 768,1700,1594)( 769,1510,3304)( 770,1733, 849)
( 772,1739,4673)( 773,1601,2917)( 774,1560,3533)( 775,1636,4156)
( 776,1681,2482)( 778,1621,1907)( 779,1523,3953)( 780,1548,1095)
( 781,1707,4425)( 782,1470,1235)( 783,1660,2841)( 784,2603,1652)
( 785,3640,2787)( 786,2127,2507)( 787,1175,4574)( 789,3113,3543)
( 790,1022, 831)( 792,2875,3020)( 793,1974,4888)( 794,5102,3478)
( 796,4303,1187)( 797,3895, 923)( 799,4388,4203)( 801,4615,4553)
( 803,4199,2869)( 804,2582,4344)( 806,3501,3204)( 807,1898,1213)
( 809,1242,3926)( 811,5097,1620)( 812,3964,4813)( 814,2251, 963)
( 815,1169,2962)( 816,2696,1990)( 817,4823,5056)( 818,1298,2527)
( 819,3175,4851)( 820,3832,3852)( 821,2853,2677)( 824,4793,1573)
( 825,3727,3163)( 826,4568,5217)( 827,1071,1203)( 828,5220,1768)
( 830,2085,4453)( 834,1834,3658)( 836,1244,3465)( 838,1950,5187)
( 839,4361,2882)( 840,2680,4033)( 842,2549,1433)( 843, 983,4610)
( 844,2286,2021)( 845,4979,4904)( 846,3036,4328)( 848,3757,1152)
( 850,4756, 867)( 851,4302,2590)( 852,4247,3111)( 853,1793, 885)
( 854,2409,4958)( 855,2095,3777)( 856,4854,4113)( 857,1149,2708)
( 858,3634,1894)( 860,3943,3642)( 863,2710,3273)( 864,4544,2382)
( 865,1460,1111)( 866,3015,1300)( 869,4652,4838)( 870,2530,3572)
( 873,2780,2496)( 874,1224,3090)( 875,2182,2826)( 877,1999,1530)
( 878,4164,4291)( 879,4994,3904)( 880,3602,4469)( 883,3996,3231)
( 884,1015,4939)( 886,4903,4555)( 887,2475,3920)( 889,3264,1624)
( 890,2657,4817)( 891,1339,3692)( 892,2245, 954)( 893,4457,2976)
( 894,1961,1989)( 895,4347,5064)( 897,3666,2864)( 898,2996,4349)
( 900,4026,3201)( 901,1113,1220)( 903,4508,4256)( 905,4279,5018)
( 906,2424,4501)( 908,3530,3360)( 909,1876,1072)( 911,1441,2401)
( 913,5041,3142)( 916,2330,1418)( 917,1079,1736)( 918,2623,3507)
( 919,4699,2633)( 920,3839,4831)( 921,4784,1520)( 922,2844,4299)
( 924,1825,4465)( 927,1062,3230)( 928,4075,4944)( 929,3166,1790)
( 930,5211,3576)( 931,2492,1313)( 933,4559,2498)( 935,2092,2840)
( 937,3098,2518)( 938,4211,5213)( 939,4682,1198)( 942,2177,4447)
( 943,2560,1026)( 946,4406,3659)( 947,5194,4858)( 948,1842,3845)
( 949,1096,2674)( 950,3213,3426)( 951,1356,4198)( 952,3564,1578)
( 953,2725,3162)( 955,4491,2072)( 956,3081,2050)( 957,4886,2088)
( 958,1271,2133)( 959,2390,2193)( 961,2895,2196)( 962,3434,2219)
( 964,5058,2113)( 966,3683,2263)( 968,2126,2148)( 969,1910,2294)
( 970,3822,2316)( 971,4194,5134)( 972,1893,4153)( 973,2577,2472)
( 975,4818,1908)( 976,1164,3958)( 977,3496,1103)( 978,3247,4429)
( 979,3975,1226)( 981,5092,1589)( 982,2691,3311)( 985,3132,4669)
( 988,2143,3398)( 990,1186,3838)( 991,3907,3714)( 992,3315,3035)
( 994,3115,1126)( 995,1978,2897)( 997,3649,4659)( 998,5109,2366)
( 999,4389,1850)(1000,2611,1609)(1003,4313,5110)(1005,1288,3101)
(1006,3047,3656)(1007,3873,1648)(1011,4801,1118)(1012,3547,1297)
(1013,4423,4751)(1014,1130,4593)(1016,4262,4949)(1017,2279,3778)
(1019,3468,2712)(1020,2458,1902)(1023,3349,1964)(1024,4627,2703)
(1025,4109,4997)(1027,1757,4764)(1029,4767,4312)(1030,2228,3770)
(1032,5126,4354)(1033,1390,1511)(1034,2861,1276)(1035,2441,3048)
(1037,4043,3933)(1038,3064,3373)(1039,1927,1374)(1040,2759,2337)
(1043,2339,2770)(1046,1373,1923)(1047,4920,3410)(1048,3890,2986)
(1049,5177,4118)(1052,2979,3893)(1053,4126,5181)(1054,3417,4922)
(1055,2313,1482)(1056,2640,1653)(1059,4372,3471)(1060,3513,3798)
(1064,2356,4217)(1066,4956,2781)(1067,2075,2504)(1068,3805,4573)
(1069,4092,5006)(1070,1774,3551)(1074,1600,1397)(1075,1719,3333)
(1076,1532,2724)(1077,1651,3725)(1078,1702,2031)(1081,1617,3819)
(1082,1685,1564)(1085,1566,3073)(1086,1634,4537)(1087,1583,2547)
(1088,1515,4138)(1089,1549,4702)(1093,3751,4250)(1094,4296,5139)
(1097,2296,4878)(1098,3030,2740)(1099,1254,1285)(1100,4973,4027)
(1101,4750,3185)(1102,3366,2355)(1104,4355,4393)(1109,3281,3596)
(1112,3992,4093)(1114,4160,4968)(1115,3598,3008)(1116,2526,3334)
(1120,1995,1672)(1121,2776,1829)(1122,3183,4411)(1123,4525,4000)
(1124,3700,3682)(1127,2911,1247)(1129,4330,5158)(1131,3856,2446)
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