bin1 := (1,3,6)(2,4,8)(5,9,14)(7,11,17)(10,15,22)(12,18,26)(13,19,28)(16,23,33) (20,29,40)(21,30,42)(24,34,47)(25,35,49)(27,37,52)(31,43,59)(32,44,60) (36,50,51)(38,53,68)(39,54,70)(41,56,73)(45,61,78)(46,62,80)(48,64,83) (55,71,72)(57,74,93)(58,75,95)(63,81,82)(65,84,104)(66,85,106)(67,86,108) (69,88,111)(76,96,120)(77,97,122)(79,99,125)(87,109,110)(89,112,137)(90, 113,139)(91,114,141)(92,115,143)(94,117,146)(98,123,124)(100,126,155) (101,127,157)(102,128,103)(105,130,161)(107,132,164)(116,144,145)(118, 147,179)(119,148,181)(121,150,184)(129,159,194)(131,162,163)(133,165,200) (134,166,202)(135,167,204)(136,168,206)(138,170,209)(140,172,212)(142, 174,215)(149,182,183)(151,185,225)(152,186,227)(153,187,229)(154,188,231) (156,190,234)(158,192,237)(160,195,239)(169,207,208)(171,210,254)(173, 213,214)(175,216,259)(176,217,261)(177,218,263)(178,219,265)(180,220,266) (189,232,233)(191,235,281)(193,238,285)(196,240,288)(197,241,290)(198, 242,292)(199,243,294)(201,245,297)(203,247,300)(205,249,303)(211,255,308) (221,267,321)(222,268,323)(223,269,325)(224,270,327)(226,272,330)(228, 274,333)(230,276,336)(236,282,341)(244,295,296)(246,298,356)(248,301,302) (250,304,362)(251,305,364)(252,306,366)(253,307,368)(256,309,371)(257, 310,373)(258,311,375)(260,313,378)(262,315,381)(264,317,384)(271,328,329) (273,331,398)(275,334,335)(277,337,404)(278,338,406)(279,339,408)(280, 340,410)(283,342,413)(284,343,414)(286,345,417)(287,346,419)(289,348,421) (291,349,422)(293,351,425)(299,357,430)(312,376,377)(314,379,451)(316, 382,383)(318,385,457)(319,386,459)(320,387,461)(322,389,464)(324,391,467) (326,393,469)(332,399,473)(344,415,489)(347,397,420)(350,423,424)(352, 426,498)(353,427,500)(354,428,502)(355,429,504)(358,431,507)(359,432,509) (360,433,511)(361,434,513)(363,436,516)(365,438,519)(367,440,522)(369, 442,370)(372,444,527)(374,446,530)(380,452,535)(388,462,463)(390,465,547) (392,453,468)(394,470,551)(395,471,553)(396,472,494)(400,474,557)(401, 475,559)(402,476,561)(403,477,563)(405,479,566)(407,481,569)(409,483,572) (411,485,575)(412,486,577)(416,490,582)(418,492,585)(435,514,515)(437, 517,609)(439,520,521)(441,523,615)(443,525,618)(445,528,529)(447,531,624) (448,532,626)(449,533,628)(450,534,630)(454,536,632)(455,537,634)(456, 538,636)(458,540,639)(460,542,642)(466,548,647)(478,564,565)(480,567,666) (482,570,571)(484,573,671)(487,578,677)(488,579,679)(491,583,584)(493, 586,685)(495,587,686)(496,588,688)(497,589,690)(499,591,693)(501,593,696) (503,595,699)(505,597,702)(506,598,704)(508,600,707)(510,602,710)(512, 604,713)(518,610,718)(524,616,725)(526,619,727)(539,637,638)(541,640,641) (543,643,750)(544,644,752)(545,645,754)(546,646,756)(549,648,759)(550, 649,761)(552,651,764)(554,653,766)(555,654,767)(556,655,769)(558,657,772) (560,659,775)(562,661,778)(568,667,783)(574,672,789)(576,674,792)(580, 680,581)(590,691,692)(592,694,808)(594,697,698)(596,700,814)(599,705,706) (601,708,822)(603,711,712)(605,714,828)(606,715,830)(607,716,832)(608, 717,834)(611,719,837)(612,720,839)(613,721,841)(614,722,843)(617,726,847) (620,728,850)(621,729,852)(622,730,854)(623,731,856)(625,733,859)(627, 735,862)(629,737,865)(631,739,868)(633,741,871)(635,743,874)(650,762,763) (652,765,800)(656,770,771)(658,773,902)(660,776,777)(662,779,908)(663, 780,910)(664,781,912)(665,782,914)(668,784,917)(669,785,919)(670,786,921) (673,790,791)(675,793,927)(676,794,929)(681,796,932)(682,797,934)(683, 798,936)(684,799,938)(687,801,940)(689,803,943)(695,809,948)(701,815,955) (703,817,958)(709,823,963)(723,844,724)(732,857,858)(734,860,1000)(736, 863,864)(738,866,1006)(740,869,1009)(742,872,873)(744,875,1015)(745,876, 1017)(746,877,1019)(747,878,1021)(748,879,1023)(749,880,1025)(751,882, 1028)(753,884,1031)(755,886,1034)(757,888,1037)(758,889,1038)(760,891, 1041)(768,897,1048)(774,903,1053)(787,922,788)(795,930,1080)(802,941,942) (804,944,1093)(805,945,1095)(806,946,1097)(807,947,1099)(810,949,1102) (811,950,1104)(812,951,1106)(813,952,1108)(816,956,957)(818,959,1114) (819,960,1116)(820,961,1118)(821,962,1120)(824,964,1123)(825,965,1125) (826,966,1127)(827,967,1129)(829,969,1132)(831,971,1135)(833,973,1138) (835,975,1141)(836,976,1143)(838,978,1146)(840,980,1149)(842,982,1152) (845,985,1156)(846,986,1157)(848,988,1160)(849,989,1162)(851,991,1165) (853,993,1168)(855,995,1171)(861,1001,1175)(867,1007,1182)(870,1010,1184) (881,1026,1027)(883,1029,1202)(885,1032,1033)(887,1035,1208)(890,1039, 1040)(892,1042,1215)(893,1043,1217)(894,1044,1219)(895,1045,939)(896, 1046,1047)(898,1049,1224)(899,1050,1226)(900,1051,1228)(901,1052,1230) (904,1054,1233)(905,1055,1235)(906,1056,1237)(907,1057,1239)(909,1059, 1242)(911,1061,1245)(913,1063,1248)(915,1065,1251)(916,1066,1253)(918, 1068,1256)(920,1070,1259)(923,1073,1261)(924,1074,1263)(925,1075,1265) (926,1076,1267)(928,1077,1268)(931,1081,1272)(933,1083,1275)(935,1085, 1278)(937,1087,1281)(953,1109,954)(968,1130,1131)(970,1133,1325)(972, 1136,1137)(974,1139,1331)(977,1144,1145)(979,1147,1339)(981,1150,1151) (983,1153,1345)(984,1154,1347)(987,1158,1351)(990,1163,1164)(992,1166, 1359)(994,1169,1170)(996,1172,1365)(997,1142,1334)(998,1173,1367)(999, 1174,1369)(1002,1176,1372)(1003,1177,1374)(1004,1178,1110)(1005,1179, 1376)(1008,1183,1380)(1011,1185,1383)(1012,1186,1385)(1013,1187,1387) (1014,1188,1389)(1016,1190,1392)(1018,1192,1395)(1020,1194,1398)(1022, 1196,1401)(1024,1198,1404)(1030,1203,1408)(1036,1209,1414)(1058,1240, 1241)(1060,1243,1448)(1062,1246,1247)(1064,1249,1454)(1067,1254,1255) (1069,1257,1462)(1071,1204,1072)(1078,1269,1079)(1082,1273,1274)(1084, 1276,1480)(1086,1279,1280)(1088,1282,1486)(1089,1283,1488)(1090,1284, 1490)(1091,1285,1492)(1092,1286,1494)(1094,1288,1497)(1096,1290,1500) (1098,1292,1503)(1100,1294,1506)(1101,1295,1508)(1103,1297,1511)(1105, 1299,1514)(1107,1301,1517)(1111,1303,1520)(1112,1304,1522)(1113,1305, 1524)(1115,1307,1527)(1117,1309,1529)(1119,1311,1532)(1121,1313,1535) (1122,1314,1537)(1124,1316,1540)(1126,1318,1543)(1128,1320,1546)(1134, 1326,1551)(1140,1332,1558)(1148,1340,1565)(1155,1348,1574)(1159,1352, 1579)(1161,1354,1582)(1167,1360,1587)(1180,1377,1181)(1189,1390,1391) (1191,1393,1618)(1193,1396,1397)(1195,1399,1624)(1197,1402,1403)(1199, 1405,1630)(1200,1406,1632)(1201,1407,1634)(1205,1409,1635)(1206,1410, 1637)(1207,1411,1639)(1210,1415,1379)(1211,1416,1644)(1212,1417,1646) (1213,1418,1648)(1214,1419,1650)(1216,1421,1653)(1218,1423,1656)(1220, 1425,1659)(1221,1426,1661)(1222,1427,1663)(1223,1428,1665)(1225,1430, 1668)(1227,1432,1671)(1229,1434,1674)(1231,1436,1677)(1232,1437,1679) (1234,1439,1682)(1236,1441,1685)(1238,1443,1688)(1244,1449,1693)(1250, 1455,1700)(1252,1457,1703)(1258,1463,1708)(1260,1464,1709)(1262,1466, 1712)(1264,1468,1715)(1266,1470,1718)(1270,1474,1723)(1271,1475,1724) (1277,1481,1729)(1287,1495,1496)(1289,1498,1745)(1291,1501,1502)(1293, 1504,1751)(1296,1509,1510)(1298,1512,1758)(1300,1515,1516)(1302,1518, 1763)(1306,1525,1526)(1308,1528,1773)(1310,1530,1531)(1312,1533,1777) (1315,1538,1539)(1317,1541,1785)(1319,1544,1545)(1321,1547,1791)(1322, 1548,1793)(1323,1549,1795)(1324,1550,1797)(1327,1552,1800)(1328,1553, 1802)(1329,1554,1804)(1330,1555,1806)(1333,1559,1560)(1335,1561,1810) (1336,1562,1812)(1337,1563,1814)(1338,1564,1816)(1341,1566,1819)(1342, 1567,1821)(1343,1568,1823)(1344,1569,1825)(1346,1571,1828)(1349,1575, 1833)(1350,1576,1835)(1353,1580,1581)(1355,1583,1841)(1356,1584,1843) (1357,1585,1845)(1358,1586,1847)(1361,1588,1850)(1362,1589,1851)(1363, 1590,1853)(1364,1591,1855)(1366,1592,1857)(1368,1594,1860)(1370,1596, 1863)(1371,1597,1865)(1373,1599,1868)(1375,1601,1871)(1378,1604,1875) (1381,1606,1878)(1382,1607,1880)(1384,1609,1883)(1386,1611,1886)(1388, 1613,1889)(1394,1619,1894)(1400,1625,1899)(1412,1640,1413)(1420,1651, 1652)(1422,1654,1926)(1424,1657,1658)(1429,1666,1667)(1431,1669,1939) (1433,1672,1673)(1435,1675,1945)(1438,1680,1681)(1440,1683,1953)(1442, 1686,1687)(1444,1689,1959)(1445,1690,1961)(1446,1691,1963)(1447,1692, 1965)(1450,1694,1968)(1451,1695,1970)(1452,1696,1972)(1453,1697,1974) (1456,1701,1702)(1458,1704,1980)(1459,1705,1982)(1460,1706,1984)(1461, 1707,1986)(1465,1710,1711)(1467,1713,1992)(1469,1716,1717)(1471,1719, 1997)(1472,1720,1999)(1473,1721,2001)(1476,1725,2005)(1477,1726,2007) (1478,1727,2009)(1479,1728,2011)(1482,1730,2014)(1483,1731,2016)(1484, 1732,2018)(1485,1733,2020)(1487,1662,1932)(1489,1736,1798)(1491,1738, 2026)(1493,1740,2029)(1499,1746,2034)(1505,1750,2037)(1507,1753,2040) (1513,1759,2043)(1519,1764,2048)(1521,1766,2051)(1523,1768,2054)(1534, 1778,1756)(1536,1780,2066)(1542,1786,2071)(1556,1807,1557)(1570,1826, 1827)(1572,1829,2109)(1573,1830,2110)(1577,1836,1578)(1593,1858,1859) (1595,1861,2139)(1598,1866,1867)(1600,1869,2147)(1602,1872,2150)(1603, 1873,2152)(1605,1876,2156)(1608,1881,1882)(1610,1884,2164)(1612,1887, 1888)(1614,1890,2170)(1615,1891,2172)(1616,1892,2174)(1617,1893,2176) (1620,1895,2179)(1621,1896,2181)(1622,1897,2183)(1623,1898,1837)(1626, 1900,2187)(1627,1901,2189)(1628,1902,1629)(1631,1904,2193)(1633,1906, 2196)(1636,1649,1921)(1638,1910,2201)(1641,1913,2205)(1642,1914,2207) (1643,1915,2209)(1645,1917,2212)(1647,1919,2215)(1655,1927,2221)(1660, 1734,2021)(1664,1934,2227)(1670,1940,2231)(1676,1946,2238)(1678,1948, 2241)(1684,1954,2246)(1698,1975,1699)(1714,1993,2284)(1722,2002,2294) (1735,2022,2023)(1737,2024,2315)(1739,2027,2028)(1741,2030,2321)(1742, 2031,1754)(1743,2032,2324)(1744,2033,2325)(1747,1967,2259)(1748,2035, 2328)(1749,2036,2330)(1752,2038,2039)(1755,2041,2335)(1757,2042,2337) (1760,2044,2340)(1761,2045,2341)(1762,2046,2343)(1765,2049,2347)(1767, 2052,2053)(1769,2055,2353)(1770,2056,2355)(1771,2057,2357)(1772,2058, 2359)(1774,2059,2361)(1775,2060,2363)(1776,2061,2365)(1779,2064,2065) (1781,2067,2370)(1782,2068,2372)(1783,2069,2374)(1784,2070,2376)(1787, 2072,2379)(1788,2073,2381)(1789,2074,2383)(1790,2075,2385)(1792,2077, 2388)(1794,2079,2391)(1796,2081,2394)(1799,2083,2397)(1801,2085,2399) (1803,2087,2402)(1808,1969,2261)(1809,2089,1856)(1811,2091,2407)(1813, 2093,2410)(1815,2095,2413)(1817,2097,2416)(1818,2098,2418)(1820,2100, 2420)(1822,2102,2423)(1824,2104,2426)(1831,2111,2433)(1832,2112,2435) (1834,2114,2438)(1838,2117,2442)(1839,2118,2444)(1840,2119,2446)(1842, 2121,2449)(1844,2123,2452)(1846,2125,2455)(1848,2127,2458)(1849,2128, 2460)(1852,2131,2463)(1854,2133,2466)(1862,2140,2474)(1864,2142,2477) (1870,2148,2480)(1874,2153,2485)(1877,2157,2490)(1879,2159,2493)(1885, 2165,2498)(1903,2191,2525)(1905,2194,2195)(1907,2197,2531)(1908,2198, 1922)(1909,2199,2200)(1911,2202,2535)(1912,2203,2537)(1916,2210,2211) (1918,2213,2546)(1920,2216,2217)(1923,2218,2550)(1924,2219,2552)(1925, 2220,2292)(1928,2222,2556)(1929,2223,1935)(1930,2224,1933)(1931,2225, 2559)(1936,2228,2562)(1937,2229,2564)(1938,2230,2566)(1941,2232,2569) (1942,2233,2571)(1943,2234,2573)(1944,2235,2575)(1947,2239,2240)(1949, 2242,2580)(1950,2243,2582)(1951,2244,2584)(1952,2245,2586)(1955,2247, 2589)(1956,2248,2591)(1957,2249,2592)(1958,2250,2594)(1960,2252,2597) (1962,2254,2600)(1964,2256,2603)(1966,2258,2606)(1971,2263,2612)(1973, 2265,2615)(1976,2268,2619)(1977,2269,2621)(1978,2270,2623)(1979,2271, 2625)(1981,2273,2628)(1983,2275,2631)(1985,2277,2634)(1987,2279,2637) (1988,2280,2639)(1989,2281,2641)(1990,2282,2643)(1991,2283,2645)(1994, 2285,2648)(1995,2286,2650)(1996,2287,2652)(1998,2289,2655)(2000,2291, 2658)(2003,2295,2661)(2004,2296,2663)(2006,2298,2666)(2008,2300,2669) (2010,2302,2672)(2012,2303,2674)(2013,2304,2676)(2015,2306,2679)(2017, 2308,2682)(2019,2310,2685)(2025,2316,2689)(2047,2344,2149)(2050,2348, 2716)(2062,2366,2063)(2076,2386,2387)(2078,2389,2754)(2080,2392,2393) (2082,2395,2314)(2084,2146,2398)(2086,2400,2763)(2088,2403,2767)(2090, 2405,2406)(2092,2408,2772)(2094,2411,2412)(2096,2414,2778)(2099,2317, 2419)(2101,2421,2784)(2103,2424,2425)(2105,2427,2790)(2106,2428,2792) (2107,2429,2794)(2108,2430,2796)(2113,2436,2437)(2115,2439,2803)(2116, 2440,2805)(2120,2447,2448)(2122,2450,2814)(2124,2453,2454)(2126,2456, 2820)(2129,2461,2130)(2132,2464,2465)(2134,2467,2829)(2135,2468,2831) (2136,2469,2833)(2137,2470,2835)(2138,2471,2837)(2141,2475,2476)(2143, 2459,2823)(2144,2478,2843)(2145,2479,2845)(2151,2482,2849)(2154,2486, 2208)(2155,2487,2855)(2158,2491,2492)(2160,2494,2861)(2161,2495,2863) (2162,2496,2865)(2163,2497,2867)(2166,2499,2514)(2167,2500,2871)(2168, 2501,2873)(2169,2502,2875)(2171,2504,2878)(2173,2506,2881)(2175,2508, 2884)(2177,2510,2887)(2178,2511,2889)(2180,2513,2870)(2182,2515,2893) (2184,2517,2896)(2185,2518,2897)(2186,2519,2899)(2188,2521,2902)(2190, 2523,2905)(2192,2526,2907)(2204,2538,2920)(2206,2540,2923)(2214,2547, 2929)(2226,2560,2941)(2236,2576,2237)(2251,2595,2596)(2253,2598,2979) (2255,2601,2602)(2257,2604,2985)(2260,2608,2609)(2262,2610,2990)(2264, 2613,2614)(2266,2616,2995)(2267,2617,2997)(2272,2626,2627)(2274,2629, 3009)(2276,2632,2633)(2278,2635,3015)(2288,2653,2654)(2290,2656,2657) (2293,2553,2935)(2297,2664,2665)(2299,2667,3043)(2301,2670,2671)(2305, 2677,2678)(2307,2680,3055)(2309,2683,2684)(2311,2686,3061)(2312,2687, 3063)(2313,2688,2396)(2318,2690,3066)(2319,2691,3068)(2320,2692,3070) (2322,2694,3073)(2323,2333,2704)(2326,2697,3076)(2327,2698,3078)(2329, 2700,3081)(2331,2702,3084)(2332,2703,3086)(2334,2705,3088)(2336,2707, 3090)(2338,2709,3093)(2339,2710,3094)(2342,2712,3097)(2345,2630,3010) (2346,2715,3024)(2349,2717,3102)(2350,2718,3104)(2351,2719,3106)(2352, 2720,3108)(2354,2722,3111)(2356,2724,3114)(2358,2726,3117)(2360,2727, 3118)(2362,2729,3121)(2364,2731,3124)(2367,2706,3089)(2368,2733,3127) (2369,2734,3129)(2371,2736,3132)(2373,2738,3135)(2375,2740,3138)(2377, 2742,3141)(2378,2743,3143)(2380,2745,3146)(2382,2747,3149)(2384,2749, 3152)(2390,2755,3157)(2401,2764,3165)(2404,2768,3168)(2409,2773,3172) (2415,2779,3053)(2417,2781,3181)(2422,2785,3184)(2431,2797,3196)(2432, 2798,2918)(2434,2799,3198)(2441,2806,3204)(2443,2808,3207)(2445,2810, 3210)(2451,2815,3214)(2457,2821,3221)(2462,2825,3225)(2472,2838,2473) (2481,2847,2848)(2483,2850,3247)(2484,2851,3248)(2488,2856,2489)(2503, 2876,2877)(2505,2879,3274)(2507,2882,2883)(2509,2885,3280)(2512,2890, 2891)(2516,2894,2895)(2520,2900,2901)(2522,2903,3294)(2524,2906,3298) (2527,2908,3300)(2528,2909,3302)(2529,2910,3304)(2530,2911,3306)(2532, 2913,3309)(2533,2914,3311)(2534,2915,3313)(2536,2917,3316)(2539,2921, 2922)(2541,2924,3321)(2542,2925,3323)(2543,2926,3325)(2544,2927,3326) (2545,2928,3328)(2548,2930,3330)(2549,2931,3331)(2551,2933,3334)(2554, 2936,3337)(2555,2937,3034)(2557,2939,3340)(2558,2940,3342)(2561,2942, 3344)(2563,2944,2789)(2565,2946,3349)(2567,2948,3352)(2568,2949,3354) (2570,2951,3357)(2572,2953,2972)(2574,2955,3361)(2577,2958,3365)(2578, 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