bin1 := (1,2)(3,4)(5,7)(6,9)(10,14)(11,16)(12,17)(13,19)(15,22)(18,27)(20,30)
     (21,32)(23,35)(24,37)(25,38)(26,40)(28,43)(29,45)(31,48)(33,51)(34,53)
     (36,56)(39,61)(41,64)(42,66)(44,69)(46,72)(47,74)(49,77)(52,80)(54,83)
     (55,85)(57,88)(58,90)(59,91)(60,93)(62,96)(63,98)(65,101)(68,104)(70,107)
     (71,109)(73,111)(75,114)(76,116)(78,119)(79,120)(81,121)(82,123)(84,126)
     (86,129)(87,130)(89,133)(92,138)(94,141)(95,143)(97,146)(99,142)(100,115)
     (102,150)(103,151)(105,154)(106,155)(108,158)(110,160)(112,163)(113,165)
     (117,170)(118,172)(122,177)(124,178)(125,180)(127,183)(128,185)(131,168)
     (132,191)(134,194)(135,196)(136,197)(137,199)(139,202)(140,204)(144,209)
     (145,211)(147,214)(148,216)(149,217)(152,222)(153,224)(156,228)(157,230)
     (159,233)(161,236)(162,238)(164,241)(166,244)(167,246)(169,248)(171,251)
     (173,254)(174,256)(175,257)(176,259)(179,264)(181,266)(182,268)(184,271)
     (186,274)(187,276)(188,277)(189,279)(190,280)(192,283)(193,285)(195,288)
     (198,293)(200,296)(201,298)(203,301)(205,303)(206,305)(207,306)(208,308)
     (210,311)(212,314)(213,316)(215,318)(218,321)(219,323)(220,324)(221,326)
     (223,329)(225,332)(226,333)(227,335)(229,338)(231,341)(232,343)(234,346)
     (235,348)(237,351)(239,354)(240,356)(242,359)(243,361)(245,364)(247,367)
     (249,370)(250,372)(252,374)(253,376)(255,379)(258,384)(260,387)(261,388)
     (262,389)(263,391)(265,394)(267,395)(269,397)(270,399)(272,402)(273,404)
     (275,407)(278,410)(281,415)(282,416)(284,419)(286,422)(287,424)(289,427)
     (290,291)(292,430)(294,433)(295,435)(297,438)(299,441)(300,442)(302,444)
     (304,447)(307,450)(309,453)(310,455)(312,458)(313,460)(315,462)(317,465)
     (319,468)(320,470)(322,473)(325,478)(327,481)(328,483)(330,485)(331,487)
     (334,492)(336,495)(337,497)(339,500)(340,414)(342,504)(344,505)(345,507)
     (347,510)(349,513)(350,514)(352,517)(353,519)(355,520)(357,523)(358,525)
     (360,528)(362,531)(363,479)(365,534)(366,536)(368,539)(369,541)(371,544)
     (373,545)(375,547)(377,550)(378,493)(380,554)(381,556)(382,557)(383,559)
     (385,562)(386,564)(390,570)(392,573)(393,575)(396,461)(398,581)(400,584)
     (401,586)(403,589)(405,592)(406,594)(408,597)(409,599)(411,601)(412,603)
     (413,604)(417,608)(418,610)(420,613)(421,615)(423,618)(425,621)(426,622)
     (428,625)(429,626)(431,629)(432,631)(434,634)(436,636)(437,638)(439,639)
     (440,641)(443,644)(445,647)(446,649)(448,617)(449,652)(451,655)(452,657)
     (454,660)(456,663)(457,665)(459,668)(463,669)(464,670)(466,672)(467,674)
     (469,677)(471,680)(472,682)(474,685)(475,687)(476,688)(477,690)(480,692)
     (482,695)(484,697)(486,698)(488,701)(489,703)(490,704)(491,706)(494,527)
     (496,711)(498,713)(499,715)(501,718)(502,605)(503,630)(506,722)(508,725)
     (509,727)(511,730)(512,732)(515,533)(516,737)(518,738)(521,741)(522,743)
     (524,746)(526,749)(529,753)(530,755)(532,757)(535,760)(537,763)(538,765)
     (540,656)(542,770)(543,772)(546,777)(548,745)(549,781)(551,784)(552,707)
     (553,785)(555,788)(558,793)(560,796)(561,798)(563,801)(565,804)(566,797)
     (567,806)(568,606)(569,808)(571,811)(572,813)(574,816)(576,819)(577,764)
     (578,650)(580,820)(582,823)(583,825)(585,828)(587,831)(588,833)(590,835)
     (591,837)(593,702)(595,841)(596,842)(598,845)(600,612)(602,849)(607,827)
     (609,856)(611,859)(614,861)(616,864)(619,868)(620,870)(623,874)(624,876)
     (627,769)(628,881)(632,885)(633,887)(635,890)(637,893)(640,897)(642,900)
     (643,679)(645,903)(646,904)(648,907)(651,910)(653,913)(654,914)(658,918)
     (659,920)(661,923)(662,925)(664,928)(666,930)(667,921)(671,938)(673,941)
     (675,944)(676,946)(678,947)(681,951)(683,954)(684,955)(686,958)(689,963)
     (691,966)(693,969)(694,971)(696,974)(699,979)(700,877)(705,986)(708,989)
     (709,990)(710,992)(712,995)(714,998)(716,1000)(717,1002)(719,1005)(720,
     1006)(721,1008)(723,1011)(724,1013)(726,1015)(728,1018)(729,1019)(731,
     1022)(733,1025)(734,1027)(735,1028)(736,1030)(739,1031)(742,1035)(744,
     1038)(747,1040)(748,1042)(750,1044)(751,1045)(752,1047)(754,1050)(756,
     1053)(758,1055)(759,1057)(761,1060)(762,949)(766,1066)(767,1068)(768,
     1069)(771,1072)(773,1074)(774,1076)(775,1077)(776,1078)(778,1081)(779,
     1083)(780,1084)(782,1087)(783,1089)(786,1092)(787,1094)(789,1097)(790,
     791)(792,959)(794,1102)(795,1104)(799,1108)(800,1110)(802,1113)(803,984)
     (805,1117)(807,1118)(809,1121)(810,1122)(812,1125)(814,1128)(815,1130)
     (817,836)(818,1134)(821,1138)(822,1140)(824,1142)(826,1145)(829,1148)
     (830,1150)(832,1152)(834,1155)(838,1160)(839,1161)(840,1163)(843,1168)
     (844,1170)(846,1173)(847,1174)(848,1176)(850,1178)(851,1180)(852,1181)
     (853,1183)(854,1184)(855,1186)(857,1189)(858,1191)(860,1192)(862,1090)
     (863,1196)(865,1199)(866,1200)(867,1202)(869,1205)(871,1208)(872,1209)
     (873,1210)(875,1211)(878,1214)(879,1215)(880,1216)(882,1219)(883,1221)
     (884,1220)(886,1223)(888,1226)(889,1228)(891,1231)(892,1233)(894,1236)
     (895,1206)(896,1238)(898,1241)(899,1243)(901,1245)(902,1247)(905,1250)
     (906,1252)(908,1254)(909,1256)(911,1259)(912,1261)(915,1264)(916,1265)
     (917,1162)(919,940)(922,1271)(924,1274)(926,1276)(927,1277)(929,1278)
     (931,1279)(932,1280)(933,1282)(934,1283)(935,1285)(936,1286)(937,1288)
     (939,1291)(942,1293)(943,1295)(945,1244)(948,1149)(950,1303)(952,1306)
     (953,1308)(956,1312)(957,1314)(960,961)(962,1319)(964,1322)(965,1324)
     (967,1326)(968,1328)(970,1331)(972,1333)(973,1335)(975,1338)(976,1339)
     (977,1340)(978,1342)(980,1344)(981,1345)(982,1346)(983,1348)(985,1350)
     (987,1352)(988,1354)(991,1358)(993,1058)(994,1362)(996,1364)(997,1366)
     (999,1367)(1001,1370)(1004,1374)(1007,1377)(1009,1380)(1010,1381)(1012,
     1382)(1014,1384)(1016,1387)(1017,1388)(1020,1389)(1021,1391)(1023,1394)
     (1024,1396)(1026,1399)(1029,1403)(1032,1407)(1033,1408)(1034,1410)(1036,
     1369)(1037,1414)(1041,1365)(1043,1235)(1046,1425)(1048,1427)(1049,1429)
     (1051,1432)(1052,1434)(1054,1437)(1056,1440)(1059,1444)(1061,1447)(1062,
     1448)(1063,1449)(1064,1450)(1065,1343)(1067,1454)(1070,1458)(1071,1459)
     (1073,1248)(1075,1464)(1079,1469)(1080,1471)(1082,1474)(1085,1479)(1086,
     1481)(1088,1484)(1091,1486)(1093,1489)(1095,1492)(1096,1493)(1098,1496)
     (1099,1497)(1100,1498)(1101,1500)(1103,1503)(1105,1505)(1106,1506)(1107,
     1508)(1109,1511)(1111,1512)(1112,1514)(1114,1516)(1115,1517)(1116,1519)
     (1119,1521)(1120,1523)(1123,1266)(1124,1528)(1126,1529)(1127,1531)(1129,
     1532)(1131,1535)(1132,1536)(1133,1537)(1135,1540)(1136,1153)(1137,1477)
     (1139,1544)(1141,1547)(1143,1548)(1144,1549)(1146,1552)(1147,1553)(1151,
     1263)(1156,1560)(1157,1562)(1158,1563)(1159,1299)(1164,1275)(1165,1426)
     (1166,1567)(1167,1568)(1169,1569)(1171,1572)(1172,1574)(1175,1579)(1177,
     1581)(1179,1584)(1182,1589)(1185,1594)(1187,1597)(1188,1598)(1190,1600)
     (1193,1363)(1194,1604)(1195,1605)(1197,1608)(1198,1610)(1201,1615)(1203,
     1618)(1204,1619)(1207,1622)(1212,1629)(1213,1412)(1217,1634)(1218,1635)
     (1222,1640)(1224,1642)(1225,1643)(1227,1411)(1229,1648)(1230,1504)(1232,
     1652)(1234,1653)(1237,1656)(1239,1658)(1240,1659)(1242,1662)(1246,1667)
     (1249,1573)(1251,1673)(1253,1676)(1255,1678)(1257,1463)(1258,1680)(1260,
     1683)(1262,1443)(1267,1687)(1268,1688)(1269,1690)(1270,1691)(1273,1289)
     (1281,1699)(1284,1704)(1287,1386)(1290,1711)(1292,1714)(1294,1717)(1296,
     1424)(1297,1719)(1298,1720)(1300,1721)(1301,1393)(1302,1723)(1304,1725)
     (1305,1727)(1307,1728)(1309,1730)(1310,1731)(1311,1732)(1313,1733)(1315,
     1736)(1316,1738)(1317,1739)(1318,1740)(1320,1743)(1321,1507)(1323,1746)
     (1325,1749)(1327,1751)(1329,1754)(1330,1510)(1334,1756)(1336,1759)(1337,
     1577)(1341,1765)(1347,1392)(1349,1772)(1351,1773)(1353,1776)(1355,1779)
     (1356,1780)(1357,1782)(1359,1785)(1360,1787)(1361,1788)(1368,1794)(1371,
     1796)(1372,1695)(1373,1798)(1375,1800)(1376,1802)(1378,1803)(1379,1805)
     (1383,1807)(1385,1762)(1390,1814)(1395,1818)(1397,1821)(1398,1823)(1400,
     1826)(1401,1827)(1402,1557)(1404,1829)(1405,1831)(1406,1832)(1409,1836)
     (1413,1840)(1415,1583)(1416,1843)(1417,1815)(1418,1844)(1419,1845)(1420,
     1847)(1421,1848)(1422,1850)(1423,1851)(1428,1857)(1430,1860)(1431,1862)
     (1433,1864)(1435,1866)(1436,1868)(1438,1871)(1439,1873)(1441,1875)(1442,
     1877)(1445,1880)(1446,1881)(1451,1886)(1452,1887)(1453,1889)(1455,1891)
     (1456,1892)(1457,1893)(1461,1897)(1462,1898)(1465,1900)(1466,1901)(1467,
     1806)(1468,1903)(1470,1905)(1472,1485)(1473,1908)(1475,1909)(1476,1649)
     (1478,1910)(1480,1912)(1482,1915)(1483,1811)(1487,1921)(1488,1923)(1490,
     1925)(1491,1927)(1494,1930)(1495,1932)(1499,1939)(1501,1942)(1502,1944)
     (1509,1951)(1513,1929)(1515,1957)(1518,1962)(1520,1965)(1522,1710)(1524,
     1888)(1525,1969)(1526,1970)(1527,1972)(1530,1977)(1533,1981)(1534,1983)
     (1538,1986)(1539,1988)(1541,1722)(1542,1991)(1543,1993)(1545,1996)(1546,
     1998)(1550,2005)(1551,2006)(1554,2007)(1555,1856)(1556,2008)(1558,2009)
     (1559,1679)(1561,2012)(1564,2017)(1565,2018)(1566,2019)(1570,2024)(1571,
     2026)(1575,2027)(1576,2029)(1578,1692)(1580,2033)(1582,2034)(1585,2038)
     (1586,1593)(1587,2040)(1588,2042)(1590,1617)(1591,2046)(1592,1974)(1595,
     2049)(1596,2051)(1599,2054)(1601,2055)(1602,2056)(1603,2037)(1606,2060)
     (1607,2062)(1609,1631)(1611,2065)(1612,2066)(1613,2067)(1614,2069)(1616,
     2070)(1620,2076)(1621,2077)(1623,2080)(1624,2082)(1625,2083)(1626,2085)
     (1627,2086)(1628,2088)(1630,2089)(1632,2090)(1633,2092)(1636,2096)(1637,
     1933)(1638,2098)(1639,2099)(1641,2101)(1644,1666)(1645,2107)(1646,2108)
     (1647,2110)(1650,2113)(1651,2115)(1654,2117)(1655,2119)(1657,2122)(1660,
     2127)(1661,2129)(1663,1671)(1664,2130)(1665,2131)(1668,2135)(1669,2137)
     (1670,2138)(1672,2140)(1674,1763)(1675,2143)(1677,2144)(1681,2147)(1682,
     2149)(1684,2151)(1685,2152)(1686,2153)(1689,2158)(1693,2160)(1694,1709)
     (1696,2162)(1697,2163)(1698,2165)(1700,2166)(1701,2168)(1702,2169)(1703,
     2171)(1705,2174)(1706,2175)(1707,2176)(1708,2178)(1712,2181)(1713,2183)
     (1715,2185)(1716,2187)(1718,2190)(1724,2196)(1726,2116)(1729,2201)(1734,
     2206)(1735,2208)(1737,1928)(1741,2079)(1742,2217)(1744,2218)(1745,2220)
     (1747,2222)(1748,2224)(1750,1758)(1752,2094)(1753,2226)(1755,1899)(1757,
     2028)(1760,2229)(1761,2230)(1764,2232)(1766,2233)(1767,2234)(1768,2235)
     (1769,2236)(1770,2237)(1771,2238)(1774,2243)(1775,2245)(1777,2247)(1778,
     2249)(1781,2253)(1783,2023)(1784,2256)(1786,2259)(1789,2081)(1790,2260)
     (1791,2262)(1792,2011)(1793,2263)(1795,1984)(1797,2268)(1799,2269)(1801,
     2170)(1804,1822)(1808,1853)(1809,2048)(1810,2275)(1812,2276)(1813,2278)
     (1816,2280)(1817,1834)(1819,2281)(1820,2283)(1824,2286)(1825,2287)(1828,
     1833)(1830,2293)(1835,2182)(1837,2298)(1838,2300)(1839,2301)(1841,2303)
     (1842,2305)(1846,2309)(1849,2311)(1852,1917)(1854,1890)(1855,2313)(1858,
     1934)(1859,1879)(1861,2296)(1863,2318)(1865,2320)(1867,2295)(1869,2323)
     (1870,2192)(1872,2325)(1874,2328)(1876,2330)(1878,2331)(1882,2335)(1883,
     2337)(1884,2338)(1885,2340)(1894,2347)(1895,2288)(1896,2348)(1902,2350)
     (1904,2351)(1906,2353)(1907,2058)(1911,2356)(1913,2357)(1914,2358)(1916,
     2022)(1918,2043)(1919,2073)(1920,2360)(1922,2363)(1924,2125)(1926,2366)
     (1935,2372)(1936,2345)(1937,2374)(1938,2376)(1940,2377)(1941,2379)(1943,
     2382)(1945,2383)(1946,2385)(1947,2103)(1948,2386)(1949,2112)(1950,2093)
     (1952,2388)(1953,2389)(1954,2390)(1955,2373)(1956,2392)(1958,2395)(1959,
     2397)(1960,2398)(1961,2013)(1963,2157)(1964,2327)(1966,2403)(1967,2404)
     (1968,2405)(1971,2406)(1973,2407)(1975,2250)(1976,2410)(1978,2202)(1979,
     2412)(1980,2414)(1982,2417)(1985,2421)(1987,2161)(1989,2424)(1990,2426)
     (1992,2429)(1994,2420)(1995,2431)(1997,2433)(1999,2302)(2000,2413)(2001,
     2435)(2002,2437)(2003,2438)(2004,2440)(2010,2449)(2014,2156)(2015,2452)
     (2016,2454)(2020,2457)(2021,2459)(2025,2461)(2030,2466)(2031,2467)(2032,
     2468)(2035,2471)(2036,2472)(2039,2474)(2041,2475)(2044,2332)(2045,2477)
     (2047,2063)(2050,2479)(2052,2480)(2053,2221)(2057,2487)(2059,2436)(2061,
     2489)(2064,2442)(2068,2387)(2071,2342)(2072,2499)(2074,2120)(2075,2501)
     (2078,2506)(2084,2511)(2095,2517)(2097,2409)(2100,2521)(2102,2423)(2104,
     2123)(2105,2523)(2106,2524)(2109,2529)(2111,2441)(2114,2481)(2118,2533)
     (2121,2394)(2124,2537)(2126,2371)(2128,2291)(2132,2540)(2133,2541)(2134,
     2203)(2136,2543)(2139,2546)(2141,2548)(2142,2549)(2145,2553)(2146,2554)
     (2148,2557)(2150,2225)(2154,2558)(2155,2560)(2159,2564)(2164,2343)(2167,
     2568)(2172,2572)(2173,2573)(2177,2577)(2179,2579)(2180,2509)(2184,2582)
     (2186,2299)(2188,2324)(2189,2583)(2191,2584)(2193,2585)(2194,2586)(2195,
     2588)(2197,2362)(2198,2589)(2199,2384)(2200,2447)(2204,2591)(2205,2592)
     (2207,2593)(2209,2527)(2210,2279)(2211,2597)(2212,2599)(2213,2600)(2214,
     2601)(2215,2258)(2219,2605)(2223,2608)(2227,2460)(2228,2610)(2231,2612)
     (2239,2618)(2240,2620)(2241,2257)(2242,2621)(2244,2622)(2246,2624)(2248,
     2625)(2251,2626)(2252,2627)(2254,2629)(2255,2630)(2261,2617)(2264,2633)
     (2265,2635)(2266,2636)(2267,2637)(2270,2639)(2271,2641)(2272,2550)(2273,
     2400)(2274,2643)(2277,2648)(2282,2653)(2284,2655)(2289,2349)(2290,2659)
     (2292,2339)(2294,2662)(2297,2664)(2304,2669)(2306,2561)(2307,2427)(2308,
     2672)(2310,2673)(2312,2321)(2314,2675)(2315,2676)(2316,2677)(2317,2678)
     (2319,2681)(2322,2684)(2329,2689)(2333,2694)(2334,2695)(2336,2448)(2341,
     2702)(2344,2703)(2346,2478)(2352,2710)(2354,2552)(2355,2469)(2359,2539)
     (2361,2717)(2364,2720)(2365,2721)(2367,2723)(2368,2670)(2369,2725)(2370,
     2530)(2375,2646)(2378,2730)(2380,2504)(2381,2733)(2391,2737)(2393,2739)
     (2396,2741)(2399,2744)(2401,2745)(2402,2649)(2408,2751)(2411,2753)(2415,
     2754)(2416,2542)(2418,2755)(2419,2756)(2422,2759)(2425,2580)(2428,2762)
     (2430,2763)(2432,2764)(2434,2765)(2439,2770)(2443,2771)(2444,2772)(2445,
     2773)(2446,2774)(2450,2777)(2451,2614)(2453,2778)(2455,2780)(2456,2476)
     (2458,2578)(2462,2783)(2463,2679)(2464,2785)(2465,2699)(2470,2747)(2473,
     2795)(2482,2491)(2483,2804)(2484,2805)(2485,2595)(2486,2806)(2488,2807)
     (2490,2719)(2492,2507)(2493,2790)(2494,2810)(2495,2811)(2496,2812)(2497,
     2726)(2498,2768)(2500,2815)(2502,2816)(2503,2817)(2505,2818)(2508,2819)
     (2510,2821)(2512,2822)(2513,2823)(2514,2824)(2515,2825)(2516,2826)(2518,
     2829)(2519,2830)(2520,2831)(2522,2832)(2525,2767)(2526,2835)(2528,2837)
     (2531,2536)(2532,2839)(2534,2840)(2535,2779)(2538,2843)(2545,2848)(2547,
     2851)(2551,2705)(2555,2651)(2556,2714)(2559,2858)(2562,2859)(2563,2860)
     (2565,2619)(2566,2863)(2567,2864)(2569,2865)(2570,2613)(2571,2615)(2575,
     2869)(2576,2870)(2581,2872)(2587,2879)(2590,2882)(2594,2885)(2596,2887)
     (2598,2888)(2602,2893)(2603,2895)(2604,2881)(2606,2898)(2607,2899)(2609,
     2897)(2611,2901)(2616,2904)(2623,2911)(2628,2918)(2631,2919)(2632,2920)
     (2634,2921)(2638,2924)(2640,2926)(2642,2927)(2644,2916)(2645,2846)(2647,
     2912)(2650,2657)(2652,2847)(2654,2935)(2656,2936)(2658,2845)(2660,2937)
     (2661,2938)(2663,2674)(2665,2933)(2666,2941)(2667,2942)(2668,2944)(2671,
     2946)(2680,2798)(2682,2715)(2683,2828)(2685,2951)(2686,2945)(2687,2952)
     (2688,2928)(2690,2761)(2691,2954)(2692,2955)(2693,2814)(2696,2957)(2697,
     2959)(2698,2769)(2700,2960)(2701,2961)(2704,2929)(2706,2966)(2707,2808)
     (2708,2849)(2709,2968)(2711,2969)(2712,2970)(2713,2971)(2716,2973)(2718,
     2975)(2722,2977)(2724,2734)(2727,2979)(2728,2980)(2729,2982)(2731,2844)
     (2732,2984)(2735,2985)(2736,2986)(2738,2989)(2740,2990)(2742,2991)(2743,
     2943)(2746,2995)(2748,2800)(2749,2793)(2750,2996)(2752,2856)(2757,3001)
     (2758,3002)(2760,3004)(2766,2789)(2775,3006)(2776,3010)(2781,3011)(2782,
     3012)(2784,2786)(2787,3016)(2788,2797)(2791,2871)(2792,2953)(2794,3019)
     (2799,2827)(2801,2836)(2802,2992)(2803,2949)(2809,2857)(2813,2972)(2820,
     3028)(2833,2907)(2834,3013)(2838,2902)(2841,3027)(2842,3034)(2852,3015)
     (2853,2876)(2854,2867)(2855,3038)(2861,2931)(2862,3005)(2866,2910)(2868,
     3042)(2873,3023)(2874,3035)(2875,3043)(2877,3045)(2878,3046)(2880,3044)
     (2883,2948)(2884,2894)(2886,3047)(2889,3048)(2890,3052)(2891,3031)(2892,
     3053)(2896,3054)(2900,2917)(2903,3056)(2905,3022)(2906,2956)(2908,2974)
     (2909,3003)(2913,3060)(2914,3061)(2915,3040)(2922,3063)(2923,3007)(2925,
     3029)(2930,3065)(2932,3066)(2934,3067)(2939,3017)(2940,2998)(2947,2950)
     (2958,3058)(2962,3025)(2963,3073)(2964,3059)(2965,3039)(2967,2978)(2976,
     3037)(2981,3069)(2983,3081)(2987,3078)(2988,3083)(2993,3085)(2994,3086)
     (3000,3076)(3008,3090)(3009,3091)(3014,3092)(3018,3057)(3020,3055)(3021,
     3093)(3024,3094)(3026,3084)(3030,3062)(3032,3064)(3033,3087)(3036,3095)
     (3049,3096)(3050,3097)(3051,3070)(3068,3071)(3072,3074)(3075,3088)(3077,
     3099)(3080,3100)(3082,3098);