bin1 := (2,4,6)(5,10,12)(8,15,17)(9,18,13)(11,22,20)(16,29,31)(21,28,32)(23,40, 38)(25,34,43)(26,45,46)(27,48,50)(30,54,52)(37,51,62)(41,68,66)(44,72,73) (47,74,76)(49,80,82)(53,79,83)(55,89,87)(57,92,93)(58,95,97)(63,102,103) (65,106,86)(69,112,110)(75,118,119)(77,122,123)(78,124,126)(81,129,127) (90,140,138)(94,144,147)(96,150,152)(99,154,155)(101,143,145)(104,160, 161)(107,163,164)(120,176,179)(121,175,177)(125,186,188)(128,185,189) (130,194,192)(135,200,201)(137,204,191)(141,210,208)(146,214,215)(148, 218,219)(149,221,223)(151,226,224)(153,220,229)(156,231,233)(165,242,243) (167,246,205)(172,251,253)(173,254,255)(178,260,261)(180,264,265)(181, 267,259)(184,271,273)(187,276,274)(195,286,284)(197,289,290)(202,295,298) (216,311,313)(217,310,312)(222,320,322)(225,319,323)(227,327,325)(230, 317,331)(232,333,334)(236,314,338)(241,294,296)(244,345,346)(247,349,350) (252,356,358)(256,359,361)(262,367,369)(263,366,368)(266,374,375)(268, 378,377)(270,371,382)(272,384,386)(275,383,387)(277,392,390)(283,399,389) (287,341,403)(291,407,410)(292,347,412)(297,416,417)(299,420,421)(301, 424,425)(303,428,400)(308,433,435)(318,441,443)(321,446,444)(328,454,452) (330,456,457)(332,460,461)(335,463,466)(336,462,464)(337,422,469)(339, 471,472)(348,480,393)(351,484,485)(352,487,489)(353,490,429)(355,493,495) (357,498,496)(360,502,503)(362,506,507)(363,509,511)(370,516,517)(376, 524,525)(379,474,528)(381,530,532)(385,521,533)(397,544,545)(406,554,408) (409,557,558)(411,561,562)(413,565,470)(414,555,566)(418,569,571)(419, 568,570)(423,575,577)(426,579,582)(427,584,586)(430,588,590)(434,594,596) (436,563,597)(440,602,603)(442,607,609)(445,606,610)(447,615,613)(451, 620,612)(458,626,629)(459,625,627)(465,636,637)(467,640,641)(468,643,635) (473,646,648)(477,572,652)(481,656,540)(483,578,580)(486,660,661)(488, 663,665)(491,666,667)(494,671,673)(497,651,674)(499,678,676)(504,681,684) (505,680,682)(508,689,690)(510,692,693)(518,698,550)(519,700,702)(526, 707,708)(531,714,712)(542,724,725)(543,727,729)(546,731,734)(547,736,738) (549,740,742)(551,744,746)(553,747,598)(559,752,754)(560,751,753)(564, 758,759)(576,771,650)(581,775,776)(583,779,780)(585,783,785)(587,787,788) (589,791,793)(591,699,743)(593,797,799)(595,802,800)(600,808,809)(601, 811,813)(604,814,816)(605,818,820)(608,823,821)(616,762,829)(628,839,840) (630,843,844)(631,846,838)(638,853,854)(639,852,794)(642,858,859)(644, 768,861)(645,863,864)(647,866,867)(649,870,871)(653,873,874)(655,877,879) (662,886,888)(664,891,889)(668,894,895)(669,896,795)(670,898,900)(672, 903,901)(683,912,913)(685,916,917)(686,919,713)(691,924,926)(695,929,931) (701,936,938)(715,948,946)(720,953,955)(722,957,959)(723,960,962)(726, 964,967)(728,971,763)(730,973,732)(733,976,977)(735,980,981)(737,984,986) (739,988,989)(741,993,995)(745,998,1000)(755,1008,905)(760,1012,1014) (761,1016,1018)(766,1009,1022)(767,1023,1024)(769,1027,1029)(770,1030, 772)(773,974,1034)(777,1037,1039)(778,1036,1038)(781,1043,1045)(782,1046, 786)(784,1049,1047)(789,1051,1054)(790,1055,1057)(792,1060,1058)(798, 1065,1067)(801,1033,1068)(803,1072,1070)(805,1074,1075)(806,1002,1077) (807,1078,1080)(810,1082,1085)(812,1088,1090)(815,1092,1093)(817,1096, 1097)(819,1100,1101)(822,1099,1102)(828,1109,1104)(835,1115,1110)(841, 1119,1122)(842,1118,1120)(845,1127,1128)(847,1011,1130)(849,1124,1134) (855,1138,1139)(860,1144,1145)(862,876,1026)(865,1147,1149)(868,1152, 1155)(869,1151,1153)(872,1160,1161)(875,1113,1163)(878,1168,1170)(880, 1167,1171)(883,1040,1174)(887,1179,1181)(890,1178,1182)(893,1050,1052) (897,928,1188)(899,1191,1193)(902,1190,1194)(908,1173,1196)(910,1003, 1201)(914,1204,1207)(915,1203,1205)(918,1212,1213)(921,1209,1184)(925, 1219,1220)(927,1165,1221)(930,1006,1223)(935,1131,1228)(937,1230,1229) (943,1237,1231)(944,1239,1241)(950,1244,1246)(951,1247,1249)(954,1253, 1255)(956,1257,1258)(958,1262,1264)(961,1268,1005)(963,1270,965)(966, 1273,1274)(968,1277,1278)(969,1279,1281)(970,1282,972)(978,1289,1291) (979,1288,1290)(982,1295,1297)(983,1298,987)(985,1302,1300)(990,1305, 1308)(991,1309,1311)(992,1312,996)(994,1315,1313)(999,1321,1320)(1001, 1324,1326)(1004,1328,1330)(1010,1334,1335)(1013,1338,1318)(1015,1340, 1341)(1017,1343,1345)(1020,1331,1222)(1021,1347,1348)(1025,1350,1352) (1028,1357,1359)(1032,1356,1360)(1044,1369,1371)(1048,1368,1372)(1053, 1379,1166)(1056,1383,1385)(1059,1157,1386)(1061,1390,1388)(1063,1391, 1392)(1064,1393,1394)(1066,1397,1395)(1076,1405,1407)(1079,1411,1413) (1081,1414,1083)(1084,1416,1417)(1086,1420,1421)(1087,1423,1425)(1089, 1428,1426)(1094,1431,1434)(1095,1430,1432)(1098,1439,1440)(1114,1449, 1451)(1121,1455,1189)(1123,1458,1459)(1129,1466,1467)(1133,1469,1471) (1140,1475,1448)(1148,1482,1483)(1150,1486,1487)(1154,1491,1492)(1156, 1495,1496)(1162,1502,1503)(1164,1506,1507)(1169,1512,1510)(1172,1509, 1516)(1175,1450,1518)(1177,1520,1522)(1180,1525,1523)(1192,1535,1533) (1206,1545,1546)(1208,1549,1550)(1214,1557,1558)(1218,1561,1563)(1227, 1354,1568)(1233,1238,1571)(1234,1572,1573)(1235,1574,1575)(1236,1576, 1577)(1240,1580,1581)(1245,1585,1587)(1248,1591,1593)(1250,1595,1596) (1251,1598,1600)(1252,1601,1256)(1254,1605,1603)(1259,1608,1611)(1260, 1612,1614)(1261,1615,1265)(1263,1618,1616)(1266,1622,1624)(1267,1625, 1269)(1271,1630,1399)(1275,1634,1636)(1276,1633,1635)(1280,1642,1644) (1284,1641,1645)(1286,1631,1650)(1292,1653,1539)(1296,1659,1661)(1301, 1658,1662)(1303,1664,1668)(1304,1669,1306)(1307,1672,1355)(1310,1677, 1679)(1314,1676,1680)(1316,1686,1684)(1319,1687,1688)(1322,1519,1690) (1325,1692,1694)(1329,1697,1698)(1332,1700,1701)(1336,1704,1706)(1339, 1708,1709)(1342,1712,1713)(1344,1656,1714)(1349,1717,1720)(1351,1722, 1723)(1353,1726,1727)(1358,1733,1731)(1362,1730,1737)(1365,1654,1742) (1366,1743,1744)(1367,1746,1748)(1370,1751,1749)(1375,1499,1756)(1377, 1670,1760)(1380,1762,1511)(1381,1761,1508)(1382,1715,1765)(1384,1767, 1766)(1396,1773,1774)(1402,1759,1776)(1406,1783,1784)(1408,1787,1788) (1410,1791,1793)(1412,1796,1794)(1418,1799,1802)(1419,1798,1800)(1422, 1807,1808)(1424,1810,1811)(1427,1741,1812)(1433,1818,1819)(1435,1822, 1823)(1436,1825,1817)(1446,1834,1745)(1447,1835,1837)(1452,1476,1838) (1456,1844,1534)(1457,1843,1532)(1460,1849,1850)(1461,1826,1853)(1463, 1846,1840)(1470,1859,1524)(1472,1860,1862)(1484,1869,1872)(1485,1868, 1870)(1488,1876,1877)(1489,1649,1879)(1493,1882,1884)(1494,1881,1757) (1497,1888,1889)(1504,1894,1896)(1505,1893,1683)(1513,1902,1901)(1515, 1904,1621)(1517,1554,1906)(1521,1770,1910)(1526,1582,1912)(1528,1804, 1914)(1530,1763,1899)(1531,1771,1772)(1540,1845,1917)(1541,1915,1920) (1547,1923,1924)(1548,1922,1907)(1551,1928,1866)(1552,1929,1588)(1562, 1935,1936)(1564,1934,1937)(1566,1939,1940)(1567,1942,1943)(1578,1947, 1948)(1579,1949,1950)(1583,1952,1909)(1584,1953,1955)(1586,1958,1956) (1589,1960,1962)(1590,1963,1594)(1592,1966,1964)(1597,1969,1972)(1599, 1975,1977)(1604,1974,1978)(1606,1980,1984)(1607,1985,1609)(1610,1988, 1640)(1613,1993,1995)(1617,1992,1996)(1619,2001,2000)(1623,2005,2007) (1627,2004,2008)(1628,2010,2013)(1637,2019,1919)(1643,2027,2025)(1648, 2024,2032)(1651,2034,1861)(1655,2038,2039)(1657,2041,2043)(1660,2047, 2045)(1666,2044,2052)(1673,2059,1732)(1674,2058,1729)(1675,1734,2062) (1678,2064,2063)(1693,2022,2073)(1696,2002,2077)(1702,2082,2085)(1703, 2087,2089)(1705,2090,2091)(1707,2094,2095)(1710,2098,2099)(1716,2101, 1718)(1719,2102,2103)(1721,2106,2107)(1724,2110,2113)(1725,2109,2111) (1728,2118,2119)(1735,2121,2122)(1736,2124,2126)(1738,2128,2129)(1739, 2035,2132)(1740,2133,2134)(1747,2069,2140)(1750,2138,2141)(1752,2143, 1991)(1754,2144,2145)(1755,2147,2149)(1758,1836,2142)(1764,2072,2154) (1768,2156,2157)(1785,2166,2169)(1786,2165,2167)(1789,2174,2175)(1790, 2171,2178)(1792,2180,2181)(1795,2131,2182)(1801,2187,2188)(1803,2191, 2192)(1809,1871,2199)(1815,2014,2205)(1820,2208,2211)(1821,2207,2209) (1824,2216,2217)(1828,2213,2222)(1833,2226,2040)(1839,2230,1999)(1841, 2204,2232)(1851,2239,1933)(1852,2240,1957)(1867,1925,2246)(1873,2251, 2252)(1878,2257,2258)(1883,2261,2262)(1885,2265,2266)(1890,2270,2241) (1895,2272,2273)(1897,2276,2277)(1905,2195,2280)(1908,2221,2282)(1941, 1946,2298)(1945,2301,2302)(1951,2304,2305)(1954,2155,2307)(1961,2309, 2311)(1965,2231,2017)(1967,2185,2315)(1968,2317,1970)(1971,2319,2003) (1973,2297,2323)(1976,2327,2325)(1982,2324,2332)(1986,2337,2161)(1989, 2340,2026)(1990,2339,2023)(1994,2284,2343)(2006,2353,2351)(2012,2350, 2359)(2020,2364,2202)(2021,2366,2367)(2028,2372,2374)(2030,2375,2376) (2031,2378,2380)(2033,2382,2383)(2036,2385,2386)(2037,2365,2388)(2042, 2347,2393)(2046,2391,2394)(2048,2397,2398)(2050,2399,2400)(2051,2402, 2404)(2053,2275,2406)(2054,2125,2396)(2057,2338,2409)(2060,2412,2120) (2061,2279,2414)(2065,2416,2417)(2067,2419,2420)(2068,2421,2423)(2070, 2425,2071)(2074,2369,2219)(2078,2348,2427)(2080,2429,2310)(2081,2431, 2083)(2084,2432,2433)(2086,2436,2437)(2088,2440,2441)(2092,2443,2446) (2093,2442,2444)(2096,2451,2452)(2100,2454,2164)(2104,2457,2459)(2105, 2456,2146)(2108,2463,2464)(2112,2468,2469)(2114,2472,2473)(2115,2475, 2467)(2123,2481,2484)(2127,2480,2482)(2130,2264,2488)(2135,2163,2490) (2136,2492,2493)(2137,2228,2495)(2139,2424,2496)(2148,2503,2334)(2150, 2499,2500)(2153,2413,2508)(2158,2426,2510)(2168,2515,2179)(2170,2518, 2519)(2176,2526,2527)(2177,2528,2506)(2184,2533,2534)(2189,2538,2539) (2190,2537,2281)(2193,2541,2244)(2198,2250,2544)(2200,2249,2545)(2203, 2507,2546)(2210,2549,2303)(2212,2552,2553)(2218,2558,2294)(2225,2561, 2368)(2227,2564,2566)(2229,2476,2568)(2242,2267,2573)(2243,2574,2575) (2245,2299,2576)(2253,2580,2560)(2263,2584,2581)(2271,2408,2587)(2274, 2588,2590)(2278,2551,2593)(2285,2498,2342)(2286,2596,2316)(2295,2554, 2600)(2300,2602,2603)(2306,2605,2606)(2318,2610,2511)(2320,2612,2352) (2321,2611,2349)(2322,2601,2614)(2326,2504,2418)(2328,2616,2617)(2330, 2619,2620)(2331,2622,2624)(2333,2555,2626)(2341,2633,2370)(2345,2529, 2637)(2346,2638,2640)(2354,2643,2644)(2356,2645,2646)(2357,2648,2650) (2360,2652,2653)(2363,2656,2657)(2371,2663,2567)(2377,2668,2671)(2379, 2674,2676)(2381,2667,2669)(2384,2678,2679)(2387,2512,2684)(2389,2686, 2687)(2390,2563,2689)(2392,2641,2691)(2395,2693,2695)(2401,2701,2704) (2403,2707,2709)(2405,2700,2702)(2410,2712,2422)(2415,2716,2718)(2430, 2726,2597)(2434,2729,2732)(2435,2728,2730)(2438,2737,2738)(2439,2483, 2739)(2445,2745,2746)(2447,2749,2750)(2448,2752,2744)(2458,2761,2762) (2460,2765,2766)(2465,2629,2770)(2470,2772,2775)(2471,2771,2773)(2474, 2779,2780)(2477,2777,2494)(2485,2764,2784)(2486,2699,2785)(2489,2786, 2705)(2491,2523,2788)(2497,2791,2639)(2501,2795,2796)(2502,2719,2664) (2505,2713,2721)(2509,2799,2800)(2516,2804,2531)(2517,2803,2530)(2520, 2806,2807)(2521,2753,2621)(2532,2798,2811)(2535,2812,2723)(2550,2820, 2586)(2559,2662,2599)(2562,2825,2827)(2565,2829,2696)(2569,2810,2830) (2572,2767,2831)(2577,2769,2834)(2582,2836,2661)(2589,2839,2680)(2591, 2841,2808)(2594,2734,2627)(2595,2792,2842)(2604,2774,2844)(2613,2850, 2642)(2615,2852,2854)(2618,2856,2675)(2623,2861,2863)(2625,2858,2859) (2631,2660,2833)(2634,2869,2818)(2635,2871,2872)(2636,2873,2708)(2647, 2801,2879)(2649,2882,2884)(2651,2877,2878)(2654,2886,2887)(2658,2711, 2893)(2665,2896,2666)(2670,2900,2725)(2672,2903,2904)(2673,2855,2906) (2681,2911,2682)(2683,2912,2913)(2685,2909,2916)(2688,2918,2919)(2690, 2783,2922)(2692,2892,2925)(2694,2706,2843)(2697,2926,2698)(2703,2883, 2846)(2714,2870,2933)(2715,2897,2934)(2717,2860,2823)(2731,2938,2793) (2733,2939,2838)(2740,2782,2941)(2742,2847,2880)(2747,2943,2945)(2748, 2942,2944)(2751,2949,2950)(2755,2946,2787)(2758,2951,2797)(2759,2953, 2895)(2763,2954,2835)(2776,2956,2822)(2789,2959,2960)(2809,2840,2966) (2824,2967,2868)(2826,2975,2907)(2828,2908,2857)(2845,2977,2862)(2851, 2980,2969)(2853,2981,2972)(2865,2985,2888)(2866,2987,2989)(2874,2974, 2930)(2875,2984,2876)(2881,2935,2901)(2889,2993,2952)(2890,2991,2891) (2894,2931,2995)(2902,2970,2917)(2905,2929,2996)(2914,2998,2999)(2915, 2997,2961)(2920,2957,3000)(2923,2982,2958)(2924,2994,2965)(2928,2992, 2978)(2932,2990,2973)(2936,2988,2986);