bin1 := (1,2,5,3)(4,7,13,8)(6,10,17,11)(9,15,23,16)(12,18,26,19)(14,20,29,21) (22,31,46,32)(24,33,49,34)(25,35,52,36)(27,38,57,39)(28,40,60,41)(30,43, 65,44)(37,54,83,55)(42,62,96,63)(45,67,104,68)(47,70,109,71)(48,72,112, 73)(50,75,117,76)(51,77,120,78)(53,80,125,81)(56,85,133,86)(58,88,138,89) (59,90,141,91)(61,93,146,94)(64,98,153,99)(66,101,158,102)(69,106,166, 107)(74,114,178,115)(79,122,190,123)(82,127,165,128)(84,130,167,131)(87, 135,208,136)(92,143,197,144)(95,148,228,149)(97,151,232,152)(100,155,201, 156)(103,160,245,161)(105,163,250,164)(108,168,253,169)(110,171,185,119) (111,172,259,173)(113,175,264,176)(116,180,270,181)(118,183,275,184)(121, 187,281,188)(124,192,289,193)(126,195,294,196)(129,199,230,150)(132,202, 297,203)(134,205,302,206)(137,210,310,211)(139,213,315,214)(140,215,318, 216)(142,218,298,219)(145,222,329,223)(147,225,334,226)(154,235,349,236) (157,239,354,240)(159,242,359,243)(162,247,367,248)(170,255,380,256)(174, 261,198,262)(177,265,394,266)(179,267,397,268)(182,272,200,273)(186,278, 412,279)(189,283,420,284)(191,286,425,287)(194,291,433,292)(204,299,444, 300)(207,304,452,305)(209,307,457,308)(212,312,465,313)(217,320,477,321) (220,324,482,325)(221,326,484,327)(224,331,492,332)(227,336,499,337)(229, 339,503,340)(231,341,506,342)(233,344,510,345)(234,346,513,347)(237,351, 478,322)(238,352,522,353)(241,356,527,357)(244,361,534,362)(246,364,539, 365)(249,369,547,370)(251,372,552,373)(252,374,555,375)(254,377,560,378) (257,382,568,383)(258,384,570,385)(260,355,525,387)(263,390,580,391)(269, 399,494,333)(271,401,598,402)(274,405,551,406)(276,408,472,317)(277,409, 608,410)(280,414,616,415)(282,417,621,418)(285,422,543,423)(288,427,633, 428)(290,430,638,431)(293,435,646,436)(295,438,651,439)(296,440,653,441) (301,446,663,447)(303,449,668,450)(306,454,564,455)(309,459,682,460)(311, 462,686,463)(314,467,694,468)(316,470,699,471)(319,474,704,475)(323,479, 424,480)(328,486,720,487)(330,489,725,490)(335,496,736,497)(338,501,508, 343)(348,515,760,516)(350,518,765,519)(358,529,783,530)(360,532,788,533) (363,536,793,537)(366,541,800,542)(368,544,803,545)(371,549,811,550)(376, 557,822,558)(379,562,830,563)(381,565,833,566)(386,572,844,573)(388,575, 848,576)(389,577,850,578)(392,582,856,583)(393,584,740,585)(395,587,860, 588)(396,589,863,590)(398,592,751,593)(400,595,870,596)(403,600,846,574) (404,601,879,602)(407,604,883,605)(411,610,893,611)(413,613,898,614)(416, 618,906,619)(419,623,913,624)(421,626,917,627)(426,630,922,631)(429,635, 930,636)(432,640,938,641)(434,643,943,644)(437,648,950,649)(442,655,961, 656)(443,657,964,658)(445,660,969,661)(448,665,975,666)(451,670,981,671) (453,673,985,674)(456,676,987,677)(458,679,991,680)(461,683,997,684)(464, 688,1004,689)(466,691,1009,692)(469,696,1016,697)(473,701,1024,702)(476, 706,869,707)(481,711,1039,712)(483,714,1044,715)(485,717,1049,718)(488, 722,1055,723)(491,727,1061,728)(493,730,884,731)(495,733,1070,734)(498, 738,1078,739)(500,741,1081,742)(502,645,945,743)(504,744,1084,745)(505, 746,1087,747)(507,748,798,540)(509,749,1091,750)(511,752,1094,753)(512, 754,843,755)(514,757,1100,758)(517,762,1101,763)(520,767,1111,768)(521, 769,1008,770)(523,772,1116,773)(524,774,1118,775)(526,777,1122,778)(528, 780,857,781)(531,785,1133,786)(535,790,1141,791)(538,795,968,796)(546, 805,1159,806)(548,808,1164,809)(553,814,1173,815)(554,816,1175,817)(556, 819,1180,820)(559,824,1188,825)(561,827,1193,828)(567,835,1203,836)(569, 838,1207,839)(571,841,1212,842)(579,852,1227,853)(581,854,1230,855)(586, 628,675,591)(594,867,1245,868)(597,872,1251,873)(599,875,1256,876)(603, 881,831,882)(606,885,1267,886)(607,887,1269,888)(609,890,1271,891)(612, 895,1184,896)(615,900,1285,901)(617,903,1289,904)(620,802,759,908)(622, 910,1297,911)(625,915,1114,771)(629,919,1309,920)(632,924,1316,925)(634, 927,721,928)(637,932,1325,933)(639,935,1324,936)(642,940,889,941)(647, 947,939,948)(650,952,1350,953)(652,955,1355,956)(654,958,1357,959)(659, 966,1145,967)(662,971,1373,972)(664,951,1348,974)(667,764,1106,976)(669, 978,1383,979)(672,983,1334,984)(678,988,1277,989)(681,993,1399,994)(685, 862,1238,999)(687,1001,1409,1002)(690,1006,1167,1007)(693,1011,1304,916) (695,1013,1422,1014)(698,1018,1430,1019)(700,1021,957,1022)(703,1026, 1438,1027)(705,1028,1441,1029)(708,1032,1247,1033)(709,1034,1449,1035) (710,1036,1452,1037)(713,1041,1459,1042)(716,1046,1465,1047)(719,1051, 1471,1052)(724,1056,1477,1057)(726,1059,1482,1060)(729,1063,1265,1064) (732,1067,1062,1068)(735,1072,1494,1073)(737,1075,1499,1076)(756,1098, 1214,1099)(761,1103,1538,1104)(766,1108,1545,1109)(776,1120,1560,1121) (779,1124,1231,1125)(782,1043,1460,1128)(784,1130,1571,1131)(787,1135, 1576,1136)(789,1138,1581,1139)(792,1143,1589,1144)(794,1146,1592,1147) (797,1149,1597,1150)(799,1152,1602,1153)(801,894,1276,1154)(804,1156, 1608,1157)(807,1161,1613,1162)(810,1166,1408,1000)(812,1168,1621,1169) (813,1170,1624,1171)(818,1177,1632,1178)(821,1182,1639,1183)(823,1185, 1642,1186)(826,1190,1650,1191)(829,1194,1549,1195)(832,1197,1658,1198) (834,1200,1660,1201)(837,1204,1666,1205)(840,1209,1123,1210)(845,1215, 1679,1216)(847,1218,1683,1219)(849,1221,1590,1222)(851,1224,1313,1225) (858,1232,1697,1233)(859,1234,1700,1235)(861,1236,1703,1237)(864,1239, 1637,1181)(865,1240,1708,1241)(866,1242,1711,1243)(871,1248,1718,1249) (874,1253,1719,1254)(877,1258,1729,1259)(878,1260,1732,1261)(880,1262, 1734,1263)(892,1273,1749,1274)(897,1279,1753,1280)(899,1282,1758,1283) (902,1287,1323,931)(905,1291,1333,1115)(907,1292,1765,1293)(909,1294, 1768,1295)(912,1299,1776,1300)(914,1302,1781,1303)(918,1306,1787,1307) (921,1311,1794,1312)(923,1314,1796,1315)(926,1252,1723,1318)(929,1320, 1537,1321)(934,1327,1811,1328)(937,1331,1818,1332)(942,1335,1821,1336) (944,1338,1825,1339)(946,1341,1830,1342)(949,1345,1833,1346)(954,1352, 1841,1353)(960,1359,1851,1360)(962,1362,1856,1363)(963,1364,1859,1365) (965,1367,1863,1368)(970,1371,1867,1372)(973,1375,1871,1376)(977,1380, 1876,1381)(980,1385,1762,1288)(982,1386,1767,1387)(986,1390,1890,1391) (990,1393,1895,1394)(992,1396,1899,1397)(995,1401,1907,1402)(996,1403, 1910,1404)(998,1406,1915,1407)(1003,1411,1839,1351)(1005,1413,1924,1414) (1010,1388,1886,1417)(1012,1419,1931,1420)(1015,1424,1937,1425)(1017, 1427,1942,1428)(1020,1432,1949,1433)(1023,1435,1504,1079)(1025,1436,1954, 1437)(1030,1443,1961,1444)(1031,1445,1964,1446)(1038,1454,1974,1455) (1040,1457,1979,1458)(1045,1462,1984,1463)(1048,1467,1989,1468)(1050, 1132,1573,1469)(1053,1473,1998,1474)(1054,1475,2000,1476)(1058,1479,2004, 1480)(1065,1485,2011,1486)(1066,1487,2014,1488)(1069,1491,1801,1319) (1071,1492,1831,1343)(1074,1496,2027,1497)(1077,1501,2032,1502)(1080, 1505,2037,1506)(1082,1508,2039,1509)(1083,1510,2041,1511)(1085,1513,2044, 1514)(1086,1515,2047,1516)(1088,1495,2025,1518)(1089,1519,2052,1520) (1090,1521,1957,1440)(1092,1523,2057,1524)(1093,1525,2060,1526)(1095, 1528,2065,1529)(1096,1530,1990,1531)(1097,1532,2068,1533)(1102,1535,2073, 1536)(1105,1540,2079,1541)(1107,1542,2081,1543)(1110,1547,2088,1548) (1112,1550,2089,1551)(1113,1552,2092,1553)(1117,1555,2096,1556)(1119, 1557,2099,1558)(1126,1564,2103,1565)(1127,1566,2106,1567)(1129,1568,2109, 1569)(1134,1574,1935,1423)(1137,1578,2121,1579)(1140,1583,2128,1584) (1142,1586,2132,1587)(1148,1594,2143,1595)(1151,1599,2149,1600)(1155, 1605,1278,1606)(1158,1610,2162,1611)(1160,1286,1692,1228)(1163,1614,2168, 1615)(1165,1617,1344,1618)(1172,1626,2184,1627)(1174,1561,2102,1628) (1176,1630,2189,1631)(1179,1634,1641,1635)(1187,1644,2203,1645)(1189, 1647,2208,1648)(1192,1652,1255,1653)(1196,1655,1415,1656)(1199,1220,1369, 1484)(1202,1662,2224,1663)(1206,1668,2229,1669)(1208,1379,1290,1671) (1211,1674,2234,1675)(1213,1677,2238,1678)(1217,1680,1563,1681)(1223, 1686,1447,1687)(1226,1689,2250,1690)(1229,1693,2255,1694)(1244,1713,2283, 1714)(1246,1716,2287,1717)(1250,1720,2289,1721)(1257,1726,2299,1727) (1264,1736,2312,1737)(1266,1738,2315,1739)(1268,1740,2316,1741)(1270, 1743,2321,1744)(1272,1746,2324,1747)(1275,1750,2055,1522)(1281,1755,2337, 1756)(1284,1431,1947,1760)(1296,1770,2351,1771)(1298,1773,2355,1774) (1301,1778,2362,1779)(1305,1784,2368,1785)(1308,1789,1464,1790)(1310, 1791,2377,1792)(1317,1798,2384,1799)(1322,1804,2191,1805)(1326,1808,2388, 1809)(1329,1813,2170,1814)(1330,1815,2020,1816)(1337,1512,1665,1823) (1340,1827,2413,1828)(1347,1834,2210,1835)(1349,1780,2363,1837)(1354, 1843,2431,1844)(1356,1846,2436,1847)(1358,1848,2439,1849)(1361,1853,2166, 1854)(1366,1861,2049,1517)(1370,1865,2462,1866)(1374,1868,2204,1869) (1377,1872,2470,1873)(1378,1874,2180,1875)(1382,1878,2477,1879)(1384, 1881,2481,1882)(1389,1887,1450,1888)(1392,1892,2494,1893)(1395,1896,2499, 1897)(1398,1901,2506,1902)(1400,1904,2511,1905)(1405,1912,2125,1913) (1410,1919,2530,1920)(1412,1922,2473,1923)(1416,1507,2038,1926)(1418, 1928,1962,1929)(1421,1932,2069,1933)(1426,1939,2146,1940)(1429,1944,2072, 1945)(1434,1710,1953,1951)(1439,1807,1994,1956)(1442,1958,2564,1959) (1448,1966,2573,1967)(1451,1968,2574,1969)(1453,1971,2577,1972)(1456, 1976,2584,1977)(1461,1981,2376,1982)(1466,1986,2595,1987)(1470,1992,2598, 1993)(1472,1995,2600,1996)(1478,2001,2391,2002)(1481,2005,2609,2006) (1483,2008,2610,2009)(1489,2016,2621,2017)(1490,2018,2623,2019)(1493, 2022,2364,2023)(1498,1975,2582,2029)(1500,2030,2633,2031)(1503,2034,2636, 2035)(1527,2062,2666,2063)(1534,2070,1562,2071)(1539,2076,1803,2077) (1544,2083,2662,2058)(1546,2085,2690,2086)(1554,2094,2701,2095)(1559, 2101,2356,2098)(1570,2111,2169,1616)(1572,2113,2546,1936)(1575,2115,2727, 2116)(1577,2118,2731,2119)(1580,2123,2737,2124)(1582,1795,2381,2126) (1585,2130,2742,2131)(1588,2134,2746,2135)(1591,2137,2748,2138)(1593, 2140,1952,2141)(1596,2144,2756,2145)(1598,2147,2415,1829)(1601,2151,2764, 2152)(1603,2153,2765,2154)(1604,2155,2768,2156)(1607,2158,2660,2056) (1609,2159,2773,2160)(1612,2164,2778,2165)(1619,2171,2655,2172)(1620, 2173,2783,2174)(1622,2176,2787,2177)(1623,2178,2789,2179)(1625,2181,2792, 2182)(1629,2187,2798,2188)(1633,1800,2040,2192)(1636,2193,2516,1909) (1638,2195,2806,2196)(1640,2197,2493,2198)(1643,2200,2642,2201)(1646, 2205,2814,2206)(1649,2209,1802,1670)(1651,2211,2256,1761)(1654,1938,2548, 2212)(1657,2215,2824,2216)(1659,2218,2828,2219)(1661,2221,2050,2222) (1664,2226,2835,2227)(1667,1684,2199,2228)(1672,2127,2740,2231)(1673, 1728,2301,2232)(1676,2235,2842,2236)(1682,2241,2848,2242)(1685,2244,2850, 2245)(1688,2248,2028,2249)(1691,2252,2858,2253)(1695,2257,2862,2258) (1696,2104,2710,2259)(1698,2261,2340,2262)(1699,2263,2483,1884)(1701, 2265,2867,2266)(1702,2267,2869,2268)(1704,2270,2871,2271)(1705,1985,2594, 2272)(1706,2273,2399,2274)(1707,2275,2844,2237)(1709,2277,2478,2278) (1712,2280,2876,2281)(1715,2285,2881,2286)(1722,2291,2887,2292)(1724, 2294,2889,2295)(1725,2296,2891,2297)(1730,2302,1991,2303)(1731,2045,2647, 2304)(1733,2306,2899,2307)(1735,2309,2903,2310)(1742,2318,2420,2319) (1745,2264,2385,2323)(1748,2326,2919,2327)(1751,2330,2925,2331)(1752, 2332,2927,2333)(1754,2334,2929,2335)(1757,2339,2446,1855)(1759,2341,2558, 1948)(1763,2343,1883,2344)(1764,2345,2535,2346)(1766,2329,2923,2347) (1769,2349,2353,1772)(1775,2357,2948,2358)(1777,2359,2950,2360)(1782, 2314,2909,2365)(1783,2366,2955,2367)(1786,2370,2959,2371)(1788,2373,2489, 1889)(1793,2379,2854,2380)(1797,2382,2895,2383)(1806,2386,2940,2348) (1810,2389,2970,2390)(1812,2392,2972,2393)(1817,2397,2980,2398)(1819, 2400,2982,2401)(1820,2402,2983,2403)(1822,2404,2985,2405)(1824,2407,2498, 2408)(1826,2410,2993,2411)(1832,2418,2387,2419)(1836,2421,2021,2422) (1838,2424,3008,2425)(1840,2426,3009,2427)(1842,2428,3012,2429)(1845, 2433,3019,2434)(1850,2440,3027,2441)(1852,2443,3030,2444)(1857,2448,3033, 2449)(1858,2450,3036,2451)(1860,2453,3040,2454)(1862,2456,2763,2457) (1864,2459,3046,2460)(1870,2466,3051,2467)(1877,2475,3059,2476)(1880, 2479,3062,2480)(1885,2484,3066,2485)(1891,2491,3074,2492)(1894,2496,3078, 2497)(1898,2501,2560,1950)(1900,2503,2784,2504)(1903,2508,2455,2509) (1906,2512,3090,2513)(1908,2514,3091,2515)(1911,2518,3094,2519)(1914, 2311,2905,2521)(1916,2523,3098,2524)(1917,2525,2549,2526)(1918,2527,3099, 2528)(1921,2532,3104,2533)(1925,2233,2739,2529)(1927,2537,3108,2538) (1930,2540,3113,2541)(1934,2544,3115,2545)(1941,2550,3119,2551)(1943, 2552,2868,2553)(1946,2555,2718,2556)(1955,2547,3117,2561)(1960,2566,3133, 2567)(1963,2569,3136,2570)(1965,2571,3139,2572)(1970,2576,2630,2026) (1973,2579,3144,2580)(1978,2585,2601,1997)(1980,2587,3151,2588)(1983, 2591,2161,2592)(1988,2597,2794,2183)(1999,2603,3163,2604)(2003,2606,2968, 2607)(2007,2562,2816,2207)(2010,2611,2133,2612)(2012,2614,2372,2615) (2013,2616,2933,2617)(2015,2619,3174,2620)(2024,2627,3179,2628)(2033, 2634,3187,2635)(2036,2638,3191,2639)(2042,2293,2888,2643)(2043,2644,3194, 2645)(2046,2648,3199,2649)(2048,2651,3204,2652)(2051,2653,3206,2654) (2053,2656,3209,2657)(2054,2658,2736,2659)(2059,2663,2912,2320)(2061, 2664,3022,2437)(2064,2668,3219,2669)(2066,2300,2896,2670)(2067,2671,3222, 2672)(2074,2676,3226,2677)(2075,2678,2832,2679)(2078,2680,3229,2681) (2080,2682,2185,2683)(2082,2685,2943,2686)(2084,2688,2557,2689)(2087, 2692,2818,2693)(2090,2695,3239,2696)(2091,2697,3241,2698)(2093,2699,3243, 2700)(2097,2704,3248,2705)(2100,2707,3249,2708)(2105,2711,2129,2712) (2107,2714,3257,2715)(2108,2716,3260,2717)(2110,2719,2543,2720)(2112, 2722,3227,2723)(2114,2724,3265,2725)(2117,2728,2542,2729)(2120,2230,2838, 2732)(2122,2734,2863,2735)(2136,2747,2472,2276)(2139,2749,2445,2750) (2142,2752,3285,2753)(2148,2758,3292,2759)(2150,2761,3295,2762)(2157, 2770,2246,2771)(2163,2640,3193,2776)(2167,2779,2605,2780)(2175,2269,2520, 2785)(2186,2795,3124,2796)(2190,2800,3330,2801)(2194,2803,3334,2804) (2202,2812,2624,2813)(2213,2819,3348,2820)(2214,2821,2240,2822)(2217, 2826,3355,2827)(2220,2618,2596,2829)(2223,2706,2608,2831)(2225,2833,3007, 2834)(2239,2845,3368,2846)(2243,2849,2486,2465)(2247,2852,3374,2853) (2251,2856,3377,2857)(2254,2416,2817,2860)(2260,2864,2939,2865)(2279, 2874,3392,2875)(2282,2877,3393,2878)(2284,2879,2578,2880)(2288,2884,3356, 2885)(2290,2859,3379,2886)(2298,2893,3398,2894)(2305,2897,3349,2898) (2308,2901,2378,2902)(2313,2907,3404,2908)(2317,2790,3207,2910)(2322, 2435,3021,2913)(2325,2916,3413,2917)(2328,2921,3419,2922)(2336,2930,2461, 2836)(2338,2931,3426,2932)(2342,2935,3228,2936)(2350,2941,3112,2942) (2352,2944,3434,2945)(2354,2947,3016,2733)(2361,2952,3224,2674)(2369, 2956,3445,2957)(2374,2961,2505,2962)(2375,2963,2960,2964)(2394,2973,3456, 2974)(2395,2975,3457,2976)(2396,2977,3460,2978)(2406,2987,3410,2914) (2409,2990,3472,2991)(2412,2995,3380,2996)(2414,2997,3481,2998)(2417, 2999,3484,3000)(2423,3005,3488,3006)(2430,3014,3223,3015)(2432,2744,2590, 3017)(2438,3023,2673,3024)(2442,2568,3135,3028)(2447,3031,3503,3032) (2452,3037,3506,3038)(2458,3044,3425,3045)(2463,3047,3512,3048)(2464, 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