bin1 := (1,2)(3,4)(5,6)(7,9)(8,10)(11,14)(12,15)(13,17)(16,21)(18,22)(19,23)(20,
     25)(24,30)(26,32)(27,33)(28,34)(29,36)(31,39)(35,44)(37,46)(38,47)(40,50)
     (41,51)(42,53)(43,55)(45,58)(48,49)(52,65)(54,67)(56,69)(57,70)(59,73)
     (60,74)(61,76)(63,78)(64,80)(66,83)(68,86)(71,72)(75,93)(77,95)(79,97)
     (81,99)(82,100)(84,103)(85,104)(87,107)(88,108)(89,110)(90,112)(91,113)
     (92,115)(94,118)(96,121)(98,124)(101,102)(105,106)(109,134)(111,136)(114,
     139)(116,141)(117,142)(119,145)(120,146)(122,147)(123,148)(125,151)(126,
     152)(127,154)(128,156)(129,157)(130,159)(131,161)(132,162)(133,164)(135,
     167)(137,170)(138,172)(140,175)(143,144)(149,150)(153,187)(155,189)(158,
     192)(160,194)(163,197)(165,199)(166,200)(168,203)(169,204)(171,207)(173,
     209)(174,210)(176,213)(177,214)(178,216)(179,218)(180,219)(181,221)(182,
     223)(183,225)(184,227)(185,228)(186,230)(188,233)(190,236)(191,238)(193,
     241)(195,244)(196,246)(198,249)(201,202)(205,256)(206,257)(208,260)(211,
     212)(215,267)(217,269)(220,272)(222,274)(224,276)(226,278)(229,281)(231,
     283)(232,284)(234,287)(235,288)(237,291)(239,293)(240,294)(242,297)(243,
     298)(245,301)(247,303)(248,304)(250,307)(251,308)(252,310)(253,312)(254,
     313)(255,315)(258,319)(259,320)(261,323)(262,324)(263,326)(264,328)(265,
     329)(266,331)(268,334)(270,337)(271,339)(273,342)(275,345)(277,348)(279,
     351)(280,353)(282,356)(285,286)(289,363)(290,364)(292,367)(295,296)(299,
     374)(300,375)(302,378)(305,306)(309,385)(311,387)(314,390)(316,392)(317,
     393)(318,394)(321,322)(325,401)(327,403)(330,406)(332,408)(333,409)(335,
     412)(336,413)(338,416)(340,418)(341,419)(343,422)(344,423)(346,426)(347,
     427)(349,430)(350,431)(352,434)(354,436)(355,437)(357,440)(358,441)(359,
     443)(360,445)(361,446)(362,448)(365,452)(366,453)(368,456)(369,457)(370,
     459)(371,461)(372,462)(373,464)(376,468)(377,469)(379,472)(380,473)(381,
     475)(382,477)(383,478)(384,480)(386,483)(388,486)(389,488)(391,491)(395,
     495)(396,496)(397,498)(398,500)(399,501)(400,503)(402,506)(404,509)(405,
     511)(407,514)(410,411)(414,521)(415,522)(417,525)(420,421)(424,532)(425,
     533)(428,429)(432,540)(433,541)(435,544)(438,439)(442,551)(444,553)(447,
     556)(449,558)(450,559)(451,560)(454,455)(458,567)(460,569)(463,572)(465,
     574)(466,575)(467,576)(470,471)(474,583)(476,585)(479,588)(481,590)(482,
     591)(484,594)(485,595)(487,598)(489,600)(490,601)(492,604)(493,605)(494,
     607)(497,611)(499,613)(502,616)(504,618)(505,619)(507,622)(508,623)(510,
     626)(512,628)(513,629)(515,632)(516,633)(517,635)(518,637)(519,638)(520,
     640)(523,644)(524,645)(526,648)(527,649)(528,651)(529,653)(530,654)(531,
     656)(534,659)(535,660)(536,662)(537,664)(538,652)(539,666)(542,670)(543,
     671)(545,674)(546,675)(547,677)(548,679)(549,680)(550,682)(552,685)(554,
     688)(555,690)(557,693)(561,697)(562,698)(563,700)(564,702)(565,703)(566,
     705)(568,708)(570,711)(571,713)(573,716)(577,720)(578,721)(579,723)(580,
     725)(581,726)(582,728)(584,731)(586,734)(587,736)(589,739)(592,593)(596,
     746)(597,747)(599,750)(602,603)(606,757)(608,759)(609,760)(610,762)(612,
     765)(614,768)(615,770)(617,773)(620,621)(624,780)(625,781)(627,784)(630,
     631)(634,791)(636,793)(639,796)(641,798)(642,799)(643,800)(646,647)(650,
     807)(655,811)(657,813)(658,814)(661,817)(663,819)(665,821)(667,823)(668,
     824)(669,825)(672,673)(676,832)(678,834)(681,837)(683,839)(684,840)(686,
     843)(687,844)(689,847)(691,849)(692,850)(694,853)(695,854)(696,856)(699,
     860)(701,862)(704,865)(706,867)(707,868)(709,871)(710,872)(712,875)(714,
     877)(715,878)(717,881)(718,882)(719,884)(722,888)(724,890)(727,892)(729,
     894)(730,895)(732,898)(733,899)(735,902)(737,904)(738,905)(740,908)(741,
     909)(742,911)(743,913)(744,914)(745,916)(748,920)(749,921)(751,924)(752,
     925)(753,927)(754,929)(755,930)(756,932)(758,935)(761,939)(763,941)(764,
     942)(766,945)(767,946)(769,949)(771,951)(772,952)(774,955)(775,956)(776,
     958)(777,960)(778,961)(779,963)(782,967)(783,968)(785,971)(786,972)(787,
     974)(788,976)(789,977)(790,979)(792,982)(794,985)(795,987)(797,990)(801,
     994)(802,995)(803,997)(804,999)(805,1000)(806,1002)(808,1005)(809,1007)
     (810,1009)(812,1012)(815,1016)(816,1018)(818,1021)(820,1024)(822,1026)
     (826,1030)(827,1031)(828,1033)(829,1035)(830,1036)(831,1038)(833,1041)
     (835,1044)(836,1046)(838,1049)(841,842)(845,1055)(846,1056)(848,1059)
     (851,852)(855,1066)(857,1068)(858,1069)(859,1071)(861,1074)(863,1077)
     (864,1079)(866,1082)(869,870)(873,1089)(874,1090)(876,1093)(879,880)(883,
     1100)(885,1102)(886,1103)(887,1105)(889,1108)(891,1111)(893,1113)(896,
     897)(900,1120)(901,1121)(903,1124)(906,907)(910,1131)(912,1133)(915,1136)
     (917,1138)(918,1139)(919,1140)(922,923)(926,1147)(928,1149)(931,1152)
     (933,1154)(934,1155)(936,1158)(937,1159)(938,1161)(940,1164)(943,944)
     (947,1171)(948,1172)(950,1175)(953,954)(957,1182)(959,1184)(962,1187)
     (964,1189)(965,1190)(966,1191)(969,970)(973,1198)(975,1200)(978,1202)
     (980,1204)(981,1205)(983,1208)(984,1209)(986,1212)(988,1214)(989,1215)
     (991,1218)(992,1219)(993,1221)(996,1225)(998,1227)(1001,1230)(1003,1232)
     (1004,1233)(1006,1236)(1008,1237)(1010,1239)(1011,1240)(1013,1243)(1014,
     1244)(1015,1246)(1017,1249)(1019,1251)(1020,1252)(1022,1255)(1023,1256)
     (1025,1259)(1027,1262)(1028,1263)(1029,1265)(1032,1269)(1034,1271)(1037,
     1274)(1039,1276)(1040,1277)(1042,1280)(1043,1281)(1045,1284)(1047,1286)
     (1048,1287)(1050,1290)(1051,1291)(1052,1293)(1053,1295)(1054,1297)(1057,
     1301)(1058,1302)(1060,1305)(1061,1306)(1062,1308)(1063,1310)(1064,1311)
     (1065,1313)(1067,1316)(1070,1320)(1072,1322)(1073,1323)(1075,1326)(1076,
     1327)(1078,1330)(1080,1332)(1081,1333)(1083,1336)(1084,1337)(1085,1339)
     (1086,1341)(1087,1342)(1088,1344)(1091,1348)(1092,1349)(1094,1352)(1095,
     1353)(1096,1355)(1097,1357)(1098,1358)(1099,1360)(1101,1363)(1104,1367)
     (1106,1369)(1107,1370)(1109,1373)(1110,1374)(1112,1377)(1114,1380)(1115,
     1381)(1116,1383)(1117,1385)(1118,1386)(1119,1388)(1122,1392)(1123,1393)
     (1125,1396)(1126,1397)(1127,1399)(1128,1401)(1129,1402)(1130,1404)(1132,
     1407)(1134,1410)(1135,1412)(1137,1415)(1141,1419)(1142,1420)(1143,1422)
     (1144,1424)(1145,1425)(1146,1427)(1148,1430)(1150,1433)(1151,1435)(1153,
     1438)(1156,1157)(1160,1445)(1162,1447)(1163,1448)(1165,1451)(1166,1452)
     (1167,1454)(1168,1456)(1169,1457)(1170,1459)(1173,1463)(1174,1464)(1176,
     1467)(1177,1468)(1178,1470)(1179,1472)(1180,1473)(1181,1475)(1183,1478)
     (1185,1481)(1186,1483)(1188,1486)(1192,1490)(1193,1491)(1194,1493)(1195,
     1495)(1196,1496)(1197,1498)(1199,1501)(1201,1504)(1203,1507)(1206,1207)
     (1210,1514)(1211,1515)(1213,1518)(1216,1217)(1220,1525)(1222,1527)(1223,
     1528)(1224,1530)(1226,1533)(1228,1536)(1229,1538)(1231,1541)(1234,1235)
     (1238,1548)(1241,1242)(1245,1555)(1247,1557)(1248,1558)(1250,1561)(1253,
     1254)(1257,1568)(1258,1569)(1260,1261)(1264,1575)(1266,1577)(1267,1578)
     (1268,1580)(1270,1583)(1272,1586)(1273,1588)(1275,1591)(1278,1279)(1282,
     1598)(1283,1599)(1285,1602)(1288,1289)(1292,1609)(1294,1611)(1296,1613)
     (1298,1615)(1299,1616)(1300,1617)(1303,1304)(1307,1624)(1309,1626)(1312,
     1629)(1314,1631)(1315,1632)(1317,1635)(1318,1636)(1319,1637)(1321,1640)
     (1324,1325)(1328,1647)(1329,1648)(1331,1651)(1334,1335)(1338,1658)(1340,
     1660)(1343,1663)(1345,1665)(1346,1666)(1347,1667)(1350,1351)(1354,1674)
     (1356,1676)(1359,1679)(1361,1681)(1362,1682)(1364,1685)(1365,1686)(1366,
     1688)(1368,1691)(1371,1372)(1375,1698)(1376,1699)(1378,1379)(1382,1705)
     (1384,1707)(1387,1710)(1389,1712)(1390,1713)(1391,1714)(1394,1395)(1398,
     1721)(1400,1723)(1403,1726)(1405,1728)(1406,1729)(1408,1732)(1409,1733)
     (1411,1736)(1413,1738)(1414,1739)(1416,1742)(1417,1743)(1418,1745)(1421,
     1749)(1423,1751)(1426,1754)(1428,1756)(1429,1757)(1431,1760)(1432,1761)
     (1434,1764)(1436,1766)(1437,1767)(1439,1770)(1440,1771)(1441,1773)(1442,
     1775)(1443,1776)(1444,1778)(1446,1781)(1449,1450)(1453,1788)(1455,1790)
     (1458,1793)(1460,1795)(1461,1796)(1462,1797)(1465,1466)(1469,1802)(1471,
     1804)(1474,1807)(1476,1809)(1477,1810)(1479,1813)(1480,1814)(1482,1817)
     (1484,1819)(1485,1820)(1487,1823)(1488,1824)(1489,1826)(1492,1830)(1494,
     1832)(1497,1835)(1499,1837)(1500,1838)(1502,1841)(1503,1842)(1505,1844)
     (1506,1845)(1508,1848)(1509,1849)(1510,1851)(1511,1853)(1512,1854)(1513,
     1856)(1516,1860)(1517,1861)(1519,1864)(1520,1865)(1521,1867)(1522,1869)
     (1523,1870)(1524,1872)(1526,1875)(1529,1879)(1531,1881)(1532,1882)(1534,
     1885)(1535,1886)(1537,1889)(1539,1891)(1540,1892)(1542,1895)(1543,1896)
     (1544,1898)(1545,1900)(1546,1901)(1547,1903)(1549,1906)(1550,1907)(1551,
     1909)(1552,1911)(1553,1912)(1554,1914)(1556,1917)(1559,1921)(1560,1922)
     (1562,1925)(1563,1926)(1564,1928)(1565,1930)(1566,1931)(1567,1933)(1570,
     1937)(1571,1938)(1572,1940)(1573,1941)(1574,1943)(1576,1946)(1579,1950)
     (1581,1952)(1582,1953)(1584,1956)(1585,1957)(1587,1960)(1589,1962)(1590,
     1963)(1592,1966)(1593,1967)(1594,1969)(1595,1971)(1596,1972)(1597,1974)
     (1600,1978)(1601,1979)(1603,1982)(1604,1983)(1605,1985)(1606,1987)(1607,
     1988)(1608,1990)(1610,1993)(1612,1843)(1614,1998)(1618,2002)(1619,2003)
     (1620,2005)(1621,2007)(1622,2008)(1623,2010)(1625,2013)(1627,2016)(1628,
     2018)(1630,2021)(1633,1634)(1638,2028)(1639,2029)(1641,2032)(1642,2033)
     (1643,2035)(1644,2037)(1645,2038)(1646,2040)(1649,2044)(1650,2045)(1652,
     2048)(1653,2049)(1654,2051)(1655,2053)(1656,2054)(1657,2056)(1659,2059)
     (1661,2062)(1662,2064)(1664,2067)(1668,2071)(1669,2072)(1670,2074)(1671,
     2076)(1672,2077)(1673,2079)(1675,2082)(1677,2085)(1678,2087)(1680,2090)
     (1683,1684)(1687,2097)(1689,2099)(1690,2100)(1692,2103)(1693,2104)(1694,
     2106)(1695,2108)(1696,2109)(1697,2111)(1700,2115)(1701,2116)(1702,2118)
     (1703,2119)(1704,2121)(1706,2124)(1708,2127)(1709,2129)(1711,2132)(1715,
     2136)(1716,2137)(1717,2139)(1718,2141)(1719,2142)(1720,2144)(1722,2147)
     (1724,2150)(1725,2152)(1727,2155)(1730,1731)(1734,2162)(1735,2163)(1737,
     2166)(1740,1741)(1744,2173)(1746,2175)(1747,2176)(1748,2178)(1750,2181)
     (1752,2184)(1753,2186)(1755,2189)(1758,1759)(1762,2196)(1763,2197)(1765,
     2200)(1768,1769)(1772,2207)(1774,2209)(1777,2212)(1779,2214)(1780,2215)
     (1782,2216)(1783,2217)(1784,2219)(1785,2221)(1786,2222)(1787,2224)(1789,
     2227)(1791,2230)(1792,2232)(1794,2235)(1798,2239)(1799,2240)(1800,2242)
     (1801,2244)(1803,2247)(1805,2250)(1806,2252)(1808,2255)(1811,1812)(1815,
     2262)(1816,2263)(1818,2266)(1821,1822)(1825,2273)(1827,2275)(1828,2276)
     (1829,2278)(1831,2281)(1833,2284)(1834,2286)(1836,2289)(1839,1840)(1846,
     1847)(1850,2301)(1852,2303)(1855,2306)(1857,2308)(1858,2309)(1859,2310)
     (1862,1863)(1866,2317)(1868,2319)(1871,2322)(1873,2324)(1874,2325)(1876,
     2328)(1877,2329)(1878,2331)(1880,2334)(1883,1884)(1887,2341)(1888,2342)
     (1890,2345)(1893,1894)(1897,2352)(1899,2354)(1902,2357)(1904,1905)(1908,
     2362)(1910,2364)(1913,2367)(1915,2369)(1916,2370)(1918,2373)(1919,2374)
     (1920,2376)(1923,1924)(1927,2382)(1929,2384)(1932,2387)(1934,2389)(1935,
     2390)(1936,2391)(1939,2395)(1942,2398)(1944,2400)(1945,2401)(1947,2404)
     (1948,2405)(1949,2407)(1951,2410)(1954,1955)(1958,2417)(1959,2418)(1961,
     2421)(1964,1965)(1968,2428)(1970,2430)(1973,2433)(1975,2435)(1976,2436)
     (1977,2437)(1980,1981)(1984,2443)(1986,2445)(1989,2448)(1991,2450)(1992,
     2451)(1994,2454)(1995,2455)(1996,2456)(1997,2457)(1999,2460)(2000,2461)
     (2001,2463)(2004,2467)(2006,2469)(2009,2472)(2011,2474)(2012,2475)(2014,
     2478)(2015,2479)(2017,2482)(2019,2484)(2020,2485)(2022,2488)(2023,2489)
     (2024,2491)(2025,2493)(2026,2494)(2027,2496)(2030,2031)(2034,2503)(2036,
     2505)(2039,2508)(2041,2510)(2042,2511)(2043,2512)(2046,2047)(2050,2519)
     (2052,2521)(2055,2524)(2057,2526)(2058,2527)(2060,2530)(2061,2531)(2063,
     2534)(2065,2536)(2066,2537)(2068,2540)(2069,2541)(2070,2543)(2073,2547)
     (2075,2549)(2078,2552)(2080,2554)(2081,2555)(2083,2558)(2084,2559)(2086,
     2562)(2088,2564)(2089,2565)(2091,2568)(2092,2569)(2093,2571)(2094,2573)
     (2095,2574)(2096,2576)(2098,2579)(2101,2102)(2105,2586)(2107,2588)(2110,
     2591)(2112,2593)(2113,2594)(2114,2595)(2117,2599)(2120,2602)(2122,2604)
     (2123,2605)(2125,2608)(2126,2609)(2128,2612)(2130,2614)(2131,2615)(2133,
     2618)(2134,2619)(2135,2621)(2138,2625)(2140,2627)(2143,2630)(2145,2632)
     (2146,2633)(2148,2636)(2149,2637)(2151,2640)(2153,2642)(2154,2643)(2156,
     2646)(2157,2647)(2158,2649)(2159,2651)(2160,2652)(2161,2654)(2164,2658)
     (2165,2659)(2167,2662)(2168,2663)(2169,2665)(2170,2667)(2171,2668)(2172,
     2670)(2174,2673)(2177,2677)(2179,2679)(2180,2680)(2182,2683)(2183,2684)
     (2185,2687)(2187,2689)(2188,2690)(2190,2693)(2191,2694)(2192,2696)(2193,
     2698)(2194,2699)(2195,2701)(2198,2705)(2199,2706)(2201,2709)(2202,2710)
     (2203,2712)(2204,2714)(2205,2715)(2206,2717)(2208,2720)(2210,2723)(2211,
     2725)(2213,2728)(2218,2734)(2220,2736)(2223,2739)(2225,2741)(2226,2742)
     (2228,2745)(2229,2746)(2231,2749)(2233,2751)(2234,2752)(2236,2755)(2237,
     2756)(2238,2758)(2241,2762)(2243,2764)(2245,2766)(2246,2767)(2248,2770)
     (2249,2771)(2251,2774)(2253,2776)(2254,2777)(2256,2780)(2257,2781)(2258,
     2783)(2259,2785)(2260,2786)(2261,2788)(2264,2792)(2265,2793)(2267,2796)
     (2268,2797)(2269,2799)(2270,2801)(2271,2802)(2272,2804)(2274,2807)(2277,
     2811)(2279,2813)(2280,2814)(2282,2817)(2283,2818)(2285,2821)(2287,2823)
     (2288,2824)(2290,2827)(2291,2828)(2292,2830)(2293,2832)(2294,2833)(2295,
     2835)(2296,2837)(2297,2839)(2298,2841)(2299,2842)(2300,2844)(2302,2847)
     (2304,2850)(2305,2852)(2307,2855)(2311,2858)(2312,2859)(2313,2861)(2314,
     2863)(2315,2864)(2316,2866)(2318,2869)(2320,2872)(2321,2874)(2323,2877)
     (2326,2327)(2330,2884)(2332,2886)(2333,2887)(2335,2890)(2336,2891)(2337,
     2893)(2338,2895)(2339,2896)(2340,2898)(2343,2902)(2344,2903)(2346,2906)
     (2347,2907)(2348,2909)(2349,2911)(2350,2912)(2351,2914)(2353,2917)(2355,
     2920)(2356,2922)(2358,2925)(2359,2927)(2360,2928)(2361,2930)(2363,2933)
     (2365,2936)(2366,2938)(2368,2941)(2371,2372)(2375,2948)(2377,2949)(2378,
     2951)(2379,2953)(2380,2954)(2381,2956)(2383,2959)(2385,2962)(2386,2964)
     (2388,2967)(2392,2971)(2393,2972)(2394,2974)(2396,2977)(2397,2979)(2399,
     2982)(2402,2403)(2406,2989)(2408,2991)(2409,2992)(2411,2995)(2412,2996)
     (2413,2998)(2414,3000)(2415,3001)(2416,3003)(2419,3007)(2420,3008)(2422,
     3011)(2423,3012)(2424,3014)(2425,3016)(2426,3017)(2427,3019)(2429,3022)
     (2431,3025)(2432,3027)(2434,3030)(2438,3034)(2439,3035)(2440,3037)(2441,
     3039)(2442,3040)(2444,3043)(2446,3046)(2447,3048)(2449,3051)(2452,2453)
     (2458,2459)(2462,3063)(2464,3065)(2465,3066)(2466,3068)(2468,3071)(2470,
     3074)(2471,3076)(2473,3079)(2476,2477)(2480,3086)(2481,3087)(2483,3090)
     (2486,2487)(2490,3097)(2492,3099)(2495,3102)(2497,3104)(2498,3105)(2499,
     3107)(2500,3109)(2501,3110)(2502,3112)(2504,3115)(2506,3118)(2507,3120)
     (2509,3123)(2513,3127)(2514,3128)(2515,3130)(2516,3132)(2517,3133)(2518,
     3135)(2520,3138)(2522,3141)(2523,3143)(2525,3146)(2528,2529)(2532,3153)
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