bin1 := (1,1088,2635)(2,72,441)(3,870,2997)(4,645,401)(5,3282,1243)(6,2208,103)
     (7,3260,594)(8,1967,3609)(9,1562,223)(10,2859,247)(11,3070,3816)(12,577,
     2502)(13,2871,3676)(14,2340,1315)(15,1048,1779)(16,2245,729)(17,3436,
     1558)(18,1585,410)(19,3042,2651)(20,1292,1019)(21,1046,1216)(22,512,1774)
     (23,2764,3900)(24,3028,836)(25,775,715)(26,283,2471)(27,3525,791)(28,377,
     3603)(29,3731,2568)(30,412,3491)(31,3690,1247)(32,2119,1871)(33,3554,
     1772)(34,2235,329)(35,556,3267)(36,808,1254)(37,1006,1420)(38,493,2416)
     (39,3162,2136)(40,3668,987)(41,188,896)(42,1740,1796)(43,235,1903)(44,
     1812,2706)(45,861,2801)(46,1713,2623)(47,2740,3596)(48,3796,3879)(49,
     2474,2758)(50,827,3506)(51,252,388)(52,3552,1070)(53,2413,3520)(54,2906,
     903)(55,603,3764)(56,3858,1795)(57,1110,1004)(58,1956,1387)(59,239,1532)
     (60,3613,454)(61,2345,2830)(62,241,1396)(63,1109,2761)(64,2723,1829)(65,
     2787,1032)(66,727,810)(67,581,3719)(68,1572,2922)(69,3048,1785)(70,864,
     1847)(71,1474,1263)(73,1150,1904)(74,545,381)(75,3698,3769)(76,753,3868)
     (77,817,160)(78,3841,613)(79,3229,1111)(80,3064,1791)(81,2324,2451)(82,
     275,700)(83,1296,518)(84,3717,2889)(85,1215,1951)(86,1794,2989)(87,131,
     3712)(88,2218,539)(89,1475,602)(90,3029,942)(91,466,3460)(92,2614,2627)
     (93,424,570)(94,3723,3353)(95,142,2453)(96,2785,2216)(97,435,3423)(98,
     2847,460)(99,453,1066)(100,1997,1402)(101,3546,1976)(102,3220,476)(104,
     2508,232)(105,3061,1287)(106,2047,151)(107,3053,349)(108,1052,1291)(109,
     2093,862)(110,3567,1702)(111,1188,3580)(112,3743,2426)(113,2618,2512)
     (114,657,2456)(115,1637,1323)(116,428,2126)(117,605,3221)(118,3356,2385)
     (119,935,3680)(120,3209,1229)(121,3126,2886)(122,1957,268)(123,1686,2370)
     (124,1937,1556)(125,842,563)(126,2532,2087)(127,2788,1798)(128,2304,1047)
     (129,801,766)(130,2055,1224)(132,1842,3757)(133,3379,1836)(134,337,952)
     (135,3640,1939)(136,3295,2673)(137,2800,363)(138,907,2082)(139,3449,3795)
     (140,2944,3812)(141,667,492)(143,3778,2964)(144,2402,1314)(145,1053,1194)
     (146,2941,1331)(147,1716,274)(148,359,1825)(149,2237,1153)(150,874,3536)
     (152,347,850)(153,1878,2217)(154,3669,2418)(155,2520,269)(156,843,625)
     (157,3009,1022)(158,1379,3794)(159,375,2388)(161,2536,3333)(162,1681,
     1883)(163,3141,3222)(164,2664,3261)(165,3123,1605)(166,3642,3033)(167,
     523,1078)(168,2911,3085)(169,3888,590)(170,2865,254)(171,1961,3524)(172,
     1583,3235)(173,3318,1933)(174,1515,1769)(175,1025,3898)(176,694,2407)
     (177,3098,1325)(178,2927,2681)(179,310,3217)(180,430,417)(181,3602,3482)
     (182,3131,357)(183,549,898)(184,2686,1367)(185,1204,2837)(186,2878,1266)
     (187,2976,3775)(189,1486,2187)(190,1750,1856)(191,1731,548)(192,2068,
     1838)(193,3663,3807)(194,829,2797)(195,2511,1942)(196,2176,2933)(197,
     2447,229)(198,3388,1590)(199,799,2858)(200,2815,743)(201,2338,1874)(202,
     3629,2518)(203,597,206)(204,2612,3544)(205,3730,2448)(207,1557,2184)(208,
     344,3371)(209,1478,2855)(210,1757,1200)(211,1849,540)(212,2097,2843)(213,
     787,2704)(214,1724,2472)(215,2144,2934)(216,967,3658)(217,1170,1777)(218,
     2784,851)(219,2954,1984)(220,2060,1654)(221,2430,2752)(222,1568,437)(224,
     1045,3027)(225,3142,1991)(226,756,674)(227,939,3308)(228,1259,1219)(230,
     3350,1284)(231,3262,2270)(233,2438,3071)(234,1954,714)(236,712,1345)(237,
     3378,1784)(238,1594,1518)(240,1563,3032)(242,806,408)(243,2170,3372)(244,
     3173,2488)(245,2877,3014)(246,1129,3535)(248,3715,3278)(249,1734,1821)
     (250,3441,298)(251,2071,1380)(253,2152,2377)(255,1180,1122)(256,1964,
     3811)(257,2275,1043)(258,1481,3561)(259,2994,3665)(260,1803,2383)(261,
     2039,3030)(262,3749,687)(263,2024,953)(264,3859,504)(265,2148,3298)(266,
     2254,1642)(267,3736,2610)(270,2953,885)(271,1814,2744)(272,3277,1202)
     (273,3090,2579)(276,2201,2077)(277,1007,1220)(278,2151,1451)(279,912,
     3637)(280,1487,3376)(281,852,1694)(282,2478,2317)(284,2108,1352)(285,418,
     2839)(286,2728,3737)(287,2429,1971)(288,3225,2286)(289,957,3100)(290,
     1294,1217)(291,3606,2000)(292,690,1684)(293,2727,3334)(294,749,814)(295,
     1363,3316)(296,2072,2937)(297,2657,1921)(299,350,2756)(300,1124,1457)
     (301,945,2174)(302,346,3729)(303,2864,3113)(304,3395,785)(305,1174,1543)
     (306,1859,2656)(307,2298,2882)(308,3444,928)(309,3155,2981)(311,1343,691)
     (312,3564,1440)(313,2971,2543)(314,1588,3655)(315,1084,3017)(316,1881,
     3442)(317,3317,3230)(318,3288,858)(319,2203,3025)(320,2493,1213)(321,
     3555,1739)(322,3847,2375)(323,3489,807)(324,2255,2132)(325,718,1571)(326,
     705,1441)(327,1947,1632)(328,489,1265)(330,1421,3179)(331,1737,621)(332,
     1319,2827)(333,3397,741)(334,3905,2332)(335,3259,2226)(336,3559,2186)
     (338,1005,3878)(339,1745,1450)(340,2346,2122)(341,2051,908)(342,2990,
     2268)(343,487,3756)(345,1990,442)(348,3592,1626)(351,2834,1695)(352,2759,
     3013)(353,3024,3725)(354,2264,3368)(355,3341,3351)(356,2084,2733)(358,
     1103,595)(360,3693,2726)(361,3666,770)(362,2907,696)(364,1603,1056)(365,
     3635,3265)(366,2925,2371)(367,1553,3007)(368,2320,3252)(369,3619,2498)
     (370,2194,2625)(371,899,2891)(372,2378,2197)(373,1255,940)(374,1260,2607)
     (376,1497,2697)(378,1893,2078)(379,2959,1398)(380,2240,3611)(382,3570,
     731)(383,958,1317)(384,941,3623)(385,3246,2589)(386,1852,3667)(387,2368,
     660)(389,2973,1535)(390,1182,1611)(391,2902,3870)(392,841,3305)(393,438,
     1128)(394,1581,3254)(395,1351,3595)(396,2027,2888)(397,1680,3373)(398,
     1132,2586)(399,1438,2956)(400,3550,1014)(402,3813,2032)(403,3336,797)
     (404,1126,2284)(405,2396,3740)(406,1560,2181)(407,2545,3289)(409,2224,
     3625)(411,3792,1823)(413,1690,2156)(414,649,3158)(415,950,2999)(416,3021,
     3104)(419,1365,3820)(420,3578,3534)(421,1304,1415)(422,2969,1754)(423,
     793,3835)(425,2477,3851)(426,3128,1273)(427,3821,3651)(429,1526,2798)
     (431,1638,1591)(432,1049,3591)(433,3077,516)(434,1123,2339)(436,3565,
     2528)(439,3067,1385)(440,1117,3673)(443,1076,1009)(444,3149,2491)(445,
     1412,2587)(446,560,2867)(447,2897,3355)(448,2437,3705)(449,2799,2300)
     (450,3545,915)(451,2464,976)(452,2092,1459)(455,575,2141)(456,2735,2221)
     (457,1028,3551)(458,3793,3706)(459,1793,2246)(461,2730,3806)(462,515,
     1113)(463,3380,3337)(464,2542,2978)(465,1886,2314)(467,2400,994)(468,
     1880,1130)(469,1258,3772)(470,3503,2560)(471,742,3814)(472,1501,1877)
     (473,1092,3639)(474,1463,2279)(475,2975,1020)(477,739,1306)(478,2399,
     1665)(479,1688,1700)(480,3154,1513)(481,1388,3416)(482,1483,1662)(483,
     1356,884)(484,564,1609)(485,2998,1432)(486,3342,3377)(488,2205,3186)(490,
     3169,3244)(491,2038,3434)(494,3906,820)(495,1409,2168)(496,821,1246)(497,
     2804,3849)(498,2863,1262)(499,2507,1206)(500,2845,2770)(501,2783,2233)
     (502,2792,3704)(503,3508,1922)(505,544,1131)(506,3135,3827)(507,1776,
     3638)(508,2473,2095)(509,2331,865)(510,1330,826)(511,3151,881)(513,1155,
     3710)(514,2960,1408)(517,1033,2670)(519,2749,1023)(520,1955,1376)(521,
     2534,2290)(522,3874,3018)(524,848,3057)(525,1349,1819)(526,1401,3078)
     (527,1275,3005)(528,1735,2446)(529,3788,2807)(530,724,3615)(531,3511,918)
     (532,3306,1816)(533,3608,1381)(534,758,2204)(535,3363,1467)(536,2062,
     2280)(537,3720,1303)(538,3107,2004)(541,2127,3002)(542,2501,1479)(543,
     2966,2600)(546,3133,3563)(547,1169,585)(550,1545,978)(551,2466,2504)(552,
     2803,3164)(553,2687,1949)(554,3109,1729)(555,3137,3068)(557,1267,1426)
     (558,2809,1144)(559,2522,1801)(561,3344,1298)(562,2987,3864)(565,1929,
     2816)(566,2241,1335)(567,2718,3402)(568,1728,3887)(569,1017,3745)(571,
     2209,1312)(572,1884,3513)(573,3038,1360)(574,2713,783)(576,2044,2272)
     (578,2374,2893)(579,2495,2334)(580,3152,2585)(582,2469,930)(583,983,2945)
     (584,2630,1105)(586,2100,866)(587,1176,2955)(588,3660,2303)(589,2895,
     1302)(591,971,3391)(592,1714,2242)(593,3583,3132)(596,2930,1075)(598,
     1551,1154)(599,986,772)(600,3258,2159)(601,1373,1648)(604,1199,2862)(606,
     2690,2905)(607,2101,811)(608,970,1278)(609,853,1276)(610,3445,1703)(611,
     3707,3398)(612,1357,3574)(614,3256,2980)(615,2408,1930)(616,3831,2913)
     (617,3366,3188)(618,3842,3466)(619,3409,3597)(620,2774,3614)(622,1905,
     1464)(623,1507,2008)(624,2323,2276)(626,3901,895)(627,2434,647)(628,1488,
     1297)(629,831,3201)(630,1425,2900)(631,2848,1531)(632,1494,3716)(633,
     3774,2701)(634,3281,1850)(635,2214,1347)(636,927,2963)(637,2694,2671)
     (638,1272,2373)(639,2696,1835)(640,3446,2779)(641,3401,698)(642,3329,
     2352)(643,1270,2229)(644,3359,3427)(646,1809,1993)(648,2178,3653)(650,
     2025,2200)(651,1973,3389)(652,1435,3884)(653,1448,2624)(654,3012,1492)
     (655,3819,1372)(656,3174,1498)(658,673,2793)(659,3124,2984)(661,1975,
     1913)(662,1350,1411)(663,1616,2269)(664,774,3381)(665,3641,1911)(666,
     2439,1080)(668,3375,3314)(669,3869,3271)(670,916,1641)(671,2659,1633)
     (672,3050,2505)(675,2180,2643)(676,2161,879)(677,3496,3176)(678,2164,
     2257)(679,3518,1462)(680,1171,2333)(681,1235,2876)(682,689,3697)(683,
     2405,3243)(684,1469,3172)(685,1340,1143)(686,3060,3765)(688,2668,2714)
     (692,3789,2315)(693,767,2824)(695,1413,3686)(697,1016,1817)(699,1940,
     3532)(701,3809,1192)(702,2529,2715)(703,2449,3843)(704,3713,3755)(706,
     1346,1378)(707,3396,1442)(708,867,2114)(709,1659,3802)(710,3722,2031)
     (711,2751,2813)(713,2225,2231)(716,1198,1707)(717,1445,2629)(719,3226,
     3247)(720,3095,3456)(721,1241,786)(722,2691,3096)(723,2772,2870)(725,
     3694,728)(726,3157,1965)(730,2576,1286)(732,1524,3766)(733,750,2597)(734,
     2431,2684)(735,1824,1095)(736,2398,2916)(737,1115,1834)(738,1692,1828)
     (740,823,795)(744,1910,3386)(745,1539,2898)(746,3650,3798)(747,1151,860)
     (748,1720,1240)(751,2547,1645)(752,3199,2765)(754,3171,1051)(755,2685,
     1941)(757,2248,1299)(759,3290,2066)(760,3628,3180)(761,3417,1928)(762,
     2198,1938)(763,2124,1841)(764,2115,1316)(765,1804,1854)(768,3759,3015)
     (769,825,1433)(771,973,3505)(773,1460,3584)(776,3654,813)(777,1873,2461)
     (778,3118,3390)(779,2234,3701)(780,1889,1708)(781,3303,2392)(782,1520,
     2583)(784,1307,1091)(788,2724,3216)(789,3624,2232)(790,2330,2594)(792,
     2593,2521)(794,2029,1423)(796,2244,3251)(798,2435,2403)(800,3432,2996)
     (802,3346,3115)(803,985,897)(804,1397,2569)(805,3589,2211)(809,3714,1355)
     (812,913,3618)(815,2182,3572)(816,1417,2363)(818,2460,2282)(819,3332,
     2362)(822,3394,1709)(824,1584,3364)(828,3143,1404)(830,1018,1996)(832,
     1065,2173)(833,2239,3212)(834,2573,3144)(835,1455,2720)(837,3648,1580)
     (838,1900,2463)(839,1800,3768)(840,2011,3447)(844,2553,3106)(845,3454,
     3301)(846,1086,2748)(847,1044,3689)(849,1599,1719)(854,3825,2519)(855,
     3501,3773)(856,894,951)(857,2921,2833)(859,2658,1832)(863,1759,1621)(868,
     1234,2191)(869,3785,3886)(871,2147,1981)(872,2171,3661)(873,2613,1062)
     (875,2702,3605)(876,3121,2605)(877,3566,2452)(878,2311,3493)(880,1081,
     2500)(882,3079,2188)(883,921,3384)(886,3734,997)(887,3045,890)(888,1579,
     1160)(889,3692,2348)(891,2212,2422)(892,2556,3498)(893,1332,1593)(900,
     3486,2481)(901,1418,1108)(902,3136,2831)(904,2924,998)(905,1833,1139)
     (906,2665,2196)(909,3646,3500)(910,3399,2301)(911,3478,3593)(914,3696,
     1830)(917,3134,1992)(919,2030,2190)(920,1797,3530)(922,1607,2985)(923,
     2580,1508)(924,982,2318)(925,2154,2917)(926,2499,1963)(929,2489,3739)
     (931,1196,1098)(932,1392,1179)(933,2541,1424)(934,2818,3411)(936,2149,
     3310)(937,3418,2353)(938,3459,2326)(943,3023,2023)(944,977,2058)(946,
     2230,1059)(947,1891,3599)(948,1223,1390)(949,2250,1723)(954,2557,3081)
     (955,3556,2309)(956,1443,1135)(959,3617,1516)(960,3472,2116)(961,2026,
     1484)(962,3861,2791)(963,1519,3575)(964,2484,1866)(965,1753,3815)(966,
     2523,1885)(968,1493,1744)(969,1250,1512)(972,1116,3086)(974,1696,1578)
     (975,3522,3787)(979,2606,2755)(980,3485,3257)(981,2688,2192)(984,3647,
     1863)(988,2395,3145)(989,2771,3495)(990,1058,3537)(991,2393,1439)(992,
     1699,3343)(993,2965,3004)(995,1748,2546)(996,1471,2719)(999,1141,2811)
     (1000,1914,3001)(1001,2951,1787)(1002,1771,3797)(1003,1251,2977)(1008,
     1383,1840)(1010,1530,3553)(1011,2271,1536)(1012,2619,3319)(1013,3036,
     1118)(1015,2711,3473)(1021,2356,3569)(1024,3810,3761)(1026,3063,1721)
     (1027,3047,3043)(1029,3703,1845)(1030,3475,3197)(1031,3347,2796)(1034,
     1057,2709)(1035,1268,2427)(1036,1595,2341)(1037,2692,1391)(1038,2636,
     1309)(1039,2458,2227)(1040,2199,2539)(1041,1554,1552)(1042,2680,3791)
     (1050,1666,1208)(1054,1698,2641)(1055,2442,2120)(1060,1622,2588)(1061,
     3529,1395)(1063,1988,1173)(1064,2598,1725)(1067,1896,1222)(1068,1712,
     1505)(1069,3088,2137)(1071,1610,2667)(1072,3111,3523)(1073,2302,2707)
     (1074,3895,3237)(1077,2615,2006)(1079,1326,3571)(1082,1248,2163)(1083,
     3448,2236)(1085,2853,2642)(1087,1882,3836)(1089,2158,3691)(1090,1561,
     3517)(1093,1566,2342)(1094,1853,3872)(1096,1210,2146)(1097,1114,3120)
     (1099,1575,1225)(1100,2251,2669)(1101,1564,1676)(1102,1369,3323)(1104,
     2419,2577)(1106,1675,3205)(1107,3119,1477)(1112,3150,2140)(1119,2574,
     1134)(1120,3499,3477)(1121,1746,1948)(1125,2563,1293)(1127,3891,3082)
     (1133,3476,3601)(1136,1142,1628)(1137,2795,3889)(1138,1851,1660)(1140,
     1167,3163)(1145,2675,2608)(1146,2766,2296)(1147,1185,2979)(1148,3746,
     2708)(1149,1875,1617)(1152,2609,1253)(1156,3838,3232)(1157,2929,1807)
     (1158,3313,1511)(1159,3881,2826)(1161,2860,1646)(1162,2263,1958)(1163,
     2069,1876)(1164,2789,2083)(1165,3404,1640)(1166,2080,2781)(1168,1820,
     3852)(1172,3228,3539)(1175,2297,2091)(1177,2143,3675)(1178,1431,2602)
     (1181,2293,1366)(1183,1943,2061)(1184,1264,1311)(1186,1950,2215)(1187,
     1890,2454)(1189,1635,3804)(1190,1503,3324)(1191,1361,1629)(1193,2457,
     2820)(1195,2814,1570)(1197,2544,2013)(1201,2249,3672)(1203,1762,2575)
     (1205,3352,2649)(1207,3374,1901)(1209,2695,2428)(1211,3354,3479)(1212,
     3382,3558)(1214,2622,1710)(1218,1895,1550)(1221,1277,1837)(1226,1476,
     3008)(1227,3238,1846)(1228,3065,2118)(1230,1313,3474)(1231,1359,3087)
     (1232,1337,3263)(1233,3678,1925)(1236,1652,2177)(1237,1697,3645)(1238,
     2844,1770)(1239,2663,2918)(1242,2409,1416)(1244,3461,3834)(1245,2102,
     2962)(1249,3196,3322)(1252,2538,3621)(1256,1592,3824)(1257,2919,1279)
     (1261,3490,3860)(1269,1305,1831)(1271,3112,2166)(1274,3311,3403)(1280,
     1310,2852)(1281,3250,2601)(1282,2648,3189)(1283,3276,3075)(1285,2455,
     2260)(1288,2064,3166)(1289,2379,3540)(1290,2259,3224)(1295,3659,3470)
     (1300,2193,1972)(1301,2672,3600)(1308,2179,3165)(1318,3066,2802)(1320,
     3455,3662)(1321,2219,3099)(1322,3192,2991)(1324,1969,2079)(1327,2986,
     2337)(1328,2644,2678)(1329,1537,1410)(1333,3056,2040)(1334,3092,3727)
     (1336,3094,3718)(1338,1979,1544)(1339,1589,2485)(1341,3026,1482)(1342,
     3037,2856)(1344,2666,2394)(1348,2938,3882)(1353,2596,1926)(1354,2365,
     2674)(1358,2054,1620)(1362,1374,3760)(1364,1382,2459)(1368,2836,3633)
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     3312)(1931,2070,3684)(1935,3839,2677)(1936,3185,3771)(1945,2736,3400)
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     3292)(1980,2050,2716)(1983,2133,3744)(1985,2868,2942)(1994,3413,3360)
     (1995,2935,2074)(1998,2767,3767)(1999,3040,2915)(2001,2923,3219)(2003,
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