bin1 := (1,2)(3,4)(5,6)(7,9)(8,10)(11,14)(12,15)(13,16)(17,20)(18,21)(19,23)(22,
     27)(24,29)(25,30)(26,32)(28,35)(31,39)(33,41)(34,42)(36,43)(37,44)(38,46)
     (40,49)(45,55)(47,56)(48,57)(50,58)(51,59)(52,61)(53,63)(54,65)(60,72)
     (62,74)(64,76)(66,78)(67,79)(68,80)(69,82)(70,84)(71,86)(73,89)(75,92)
     (77,95)(81,100)(83,102)(85,104)(87,106)(88,107)(90,108)(91,109)(93,112)
     (94,113)(96,114)(97,115)(98,117)(99,119)(101,122)(103,125)(105,128)(110,
     111)(116,139)(118,141)(120,143)(121,144)(123,145)(124,146)(126,149)(127,
     150)(129,151)(130,152)(131,154)(132,156)(133,158)(134,160)(135,161)(136,
     163)(137,165)(138,167)(140,170)(142,173)(147,148)(153,184)(155,186)(157,
     188)(159,190)(162,193)(164,195)(166,197)(168,199)(169,200)(171,201)(172,
     202)(174,203)(175,204)(176,206)(177,208)(178,210)(179,212)(180,213)(181,
     215)(182,217)(183,219)(185,222)(187,225)(189,228)(191,231)(192,233)(194,
     236)(196,239)(198,242)(205,250)(207,252)(209,254)(211,256)(214,259)(216,
     261)(218,263)(221,265)(223,266)(224,267)(226,270)(227,271)(229,272)(230,
     273)(232,276)(234,278)(235,279)(237,280)(238,281)(240,284)(241,285)(243,
     286)(245,288)(246,290)(247,292)(248,294)(249,296)(251,299)(253,302)(255,
     305)(257,308)(258,310)(260,313)(262,316)(264,319)(268,269)(274,329)(275,
     330)(277,333)(282,283)(287,343)(289,345)(291,347)(293,349)(295,351)(297,
     353)(298,354)(300,355)(301,356)(303,359)(304,360)(306,361)(307,362)(309,
     365)(311,367)(312,368)(314,369)(315,370)(317,373)(318,374)(320,375)(321,
     376)(322,378)(323,380)(324,382)(325,383)(326,385)(327,387)(328,389)(331,
     392)(332,393)(334,394)(335,395)(336,397)(337,399)(338,401)(339,403)(340,
     404)(341,406)(342,408)(344,411)(346,414)(348,417)(350,420)(352,423)(357,
     358)(363,434)(364,435)(366,438)(371,372)(377,448)(379,450)(381,452)(384,
     455)(386,457)(388,459)(390,461)(391,462)(396,467)(398,469)(400,471)(402,
     473)(405,476)(407,478)(409,480)(410,481)(412,482)(413,483)(415,486)(416,
     487)(418,488)(419,489)(421,492)(422,493)(424,494)(426,496)(427,498)(428,
     500)(429,502)(430,503)(431,505)(432,507)(433,509)(436,512)(437,513)(439,
     514)(440,515)(441,517)(442,519)(443,521)(444,523)(445,524)(446,526)(447,
     528)(449,530)(451,533)(453,536)(454,538)(456,541)(458,544)(460,547)(463,
     551)(464,553)(465,555)(466,557)(468,560)(470,562)(472,565)(474,568)(475,
     570)(477,573)(479,576)(484,485)(490,491)(495,590)(497,592)(499,594)(501,
     596)(504,599)(506,601)(508,603)(511,605)(516,610)(518,612)(520,614)(522,
     616)(525,619)(527,621)(529,623)(531,626)(532,627)(534,628)(535,629)(537,
     632)(539,634)(540,635)(542,636)(543,637)(545,640)(546,641)(548,642)(550,
     644)(552,647)(554,649)(556,651)(559,653)(561,654)(563,656)(564,657)(566,
     658)(567,659)(569,662)(571,664)(572,665)(574,666)(575,667)(577,670)(578,
     671)(579,672)(580,673)(581,675)(582,676)(583,678)(584,680)(585,682)(586,
     684)(587,685)(588,687)(589,689)(591,692)(593,695)(595,698)(597,701)(598,
     703)(600,706)(602,709)(604,712)(606,715)(607,717)(608,719)(609,721)(611,
     724)(613,727)(615,730)(617,733)(618,735)(620,655)(622,738)(624,625)(630,
     746)(631,747)(633,750)(638,639)(643,758)(645,760)(646,761)(648,764)(650,
     767)(652,770)(660,778)(661,779)(663,782)(668,669)(674,792)(677,795)(679,
     797)(681,799)(683,801)(686,804)(688,806)(690,808)(691,809)(693,810)(694,
     811)(696,814)(697,815)(699,816)(700,817)(702,820)(704,822)(705,823)(707,
     824)(708,825)(710,828)(711,829)(713,830)(714,831)(716,834)(718,836)(720,
     838)(722,840)(723,841)(725,842)(726,843)(728,846)(729,781)(731,847)(732,
     848)(734,851)(736,853)(737,854)(739,857)(740,858)(741,860)(742,861)(743,
     863)(744,865)(745,867)(748,870)(749,871)(751,872)(752,873)(753,875)(754,
     877)(755,879)(756,881)(757,883)(759,886)(762,890)(763,891)(765,892)(766,
     893)(768,896)(769,897)(771,898)(772,899)(773,901)(774,903)(775,905)(776,
     907)(777,909)(780,912)(783,913)(784,914)(785,916)(786,918)(787,920)(788,
     922)(789,923)(790,925)(791,927)(793,930)(794,932)(796,935)(798,937)(800,
     940)(802,943)(803,945)(805,948)(807,951)(812,813)(818,961)(819,962)(821,
     965)(826,827)(832,975)(833,976)(835,979)(837,982)(839,985)(844,845)(849,
     994)(850,995)(852,998)(855,856)(859,1005)(862,1008)(864,1010)(866,1011)
     (868,1013)(869,1014)(874,1018)(876,1020)(878,1022)(880,1024)(882,983)
     (884,1027)(885,1028)(887,1029)(888,1030)(889,1031)(894,895)(900,1041)
     (902,1001)(904,1044)(906,1046)(908,1048)(910,1050)(911,1051)(915,1055)
     (917,1057)(919,1058)(921,1060)(924,1063)(926,1065)(928,1025)(929,1066)
     (931,1069)(933,1071)(934,1072)(936,1073)(938,1076)(939,1077)(941,1078)
     (942,1079)(944,1082)(946,1084)(947,1085)(949,1086)(950,1087)(952,1090)
     (953,1091)(954,1092)(955,1094)(956,1096)(957,1097)(958,1099)(959,1101)
     (960,1103)(963,1106)(964,1107)(966,1108)(967,1109)(968,1111)(969,1113)
     (970,1115)(971,1117)(972,1118)(973,1120)(974,1122)(977,1125)(978,1126)
     (980,1127)(981,1128)(984,1131)(986,1132)(987,1133)(988,1135)(989,1137)
     (990,1139)(991,1140)(992,1142)(993,1144)(996,1147)(997,1148)(999,1149)
     (1000,1150)(1002,1153)(1003,1154)(1004,1155)(1006,1158)(1007,1160)(1009,
     1163)(1012,1165)(1015,1169)(1016,1171)(1017,1173)(1019,1175)(1021,1178)
     (1023,1181)(1026,1185)(1032,1190)(1033,1191)(1034,1193)(1035,1195)(1036,
     1197)(1037,1199)(1038,1200)(1039,1202)(1040,1204)(1042,1083)(1043,1151)
     (1045,1208)(1047,1211)(1049,1214)(1052,1217)(1053,1141)(1054,1219)(1056,
     1222)(1059,1224)(1061,1227)(1062,1229)(1064,1232)(1067,1236)(1068,1237)
     (1070,1240)(1074,1075)(1080,1250)(1081,1251)(1088,1089)(1093,1262)(1095,
     1264)(1098,1267)(1100,1269)(1102,1271)(1104,1273)(1105,1274)(1110,1279)
     (1112,1281)(1114,1283)(1116,1285)(1119,1288)(1121,1290)(1123,1292)(1124,
     1293)(1129,1130)(1134,1302)(1136,1304)(1138,1306)(1143,1309)(1146,1311)
     (1152,1316)(1156,1319)(1157,1320)(1159,1323)(1161,1325)(1162,1326)(1164,
     1327)(1166,1328)(1167,1329)(1168,1331)(1170,1333)(1172,1335)(1174,1337)
     (1176,1338)(1177,1339)(1179,1342)(1180,1343)(1182,1344)(1183,1345)(1184,
     1347)(1186,1348)(1187,1349)(1188,1350)(1189,1352)(1192,1356)(1194,1358)
     (1196,1360)(1198,1362)(1201,1365)(1203,1367)(1205,1369)(1206,1371)(1207,
     1372)(1209,1373)(1210,1374)(1212,1377)(1213,1378)(1215,1379)(1216,1380)
     (1218,1383)(1220,1385)(1221,1386)(1223,1387)(1225,1388)(1226,1389)(1228,
     1392)(1230,1394)(1231,1395)(1233,1396)(1234,1397)(1235,1346)(1238,1400)
     (1239,1401)(1241,1402)(1243,1404)(1244,1332)(1245,1406)(1246,1407)(1247,
     1409)(1248,1411)(1249,1413)(1252,1415)(1253,1370)(1254,1416)(1255,1418)
     (1256,1420)(1257,1422)(1258,1424)(1259,1425)(1260,1427)(1261,1429)(1263,
     1432)(1265,1435)(1266,1437)(1268,1440)(1270,1443)(1272,1446)(1275,1449)
     (1276,1451)(1277,1453)(1278,1455)(1280,1457)(1282,1460)(1284,1463)(1286,
     1466)(1287,1468)(1289,1471)(1291,1474)(1294,1477)(1295,1478)(1296,1480)
     (1297,1482)(1298,1484)(1299,1486)(1300,1488)(1301,1490)(1303,1493)(1305,
     1496)(1307,1499)(1308,1501)(1310,1504)(1312,1507)(1313,1509)(1314,1511)
     (1315,1513)(1317,1516)(1318,1518)(1321,1522)(1322,1523)(1324,1526)(1330,
     1533)(1334,1536)(1336,1539)(1340,1341)(1351,1552)(1353,1554)(1354,1555)
     (1355,1557)(1357,1560)(1359,1563)(1361,1566)(1363,1569)(1364,1571)(1366,
     1574)(1368,1577)(1375,1376)(1381,1589)(1382,1590)(1384,1593)(1390,1599)
     (1391,1600)(1393,1603)(1398,1609)(1399,1610)(1403,1614)(1405,1616)(1408,
     1619)(1410,1621)(1412,1623)(1414,1625)(1417,1628)(1419,1630)(1421,1632)
     (1423,1634)(1426,1636)(1428,1638)(1430,1639)(1431,1640)(1433,1641)(1434,
     1642)(1436,1645)(1438,1647)(1439,1648)(1441,1649)(1442,1650)(1444,1653)
     (1445,1654)(1447,1655)(1448,1656)(1450,1659)(1452,1661)(1454,1663)(1456,
     1665)(1458,1666)(1459,1667)(1461,1670)(1462,1671)(1464,1672)(1465,1673)
     (1467,1676)(1469,1678)(1470,1679)(1472,1680)(1473,1681)(1475,1684)(1476,
     1685)(1479,1689)(1481,1691)(1483,1693)(1485,1695)(1487,1696)(1489,1540)
     (1491,1698)(1492,1699)(1494,1702)(1495,1703)(1497,1704)(1498,1705)(1500,
     1708)(1502,1710)(1503,1711)(1505,1712)(1506,1713)(1508,1716)(1510,1718)
     (1512,1720)(1514,1722)(1515,1723)(1517,1726)(1519,1728)(1520,1729)(1521,
     1731)(1524,1734)(1525,1735)(1527,1736)(1528,1737)(1529,1739)(1530,1741)
     (1531,1743)(1532,1745)(1534,1747)(1535,1749)(1537,1752)(1538,1753)(1541,
     1755)(1542,1757)(1543,1759)(1544,1760)(1546,1763)(1547,1765)(1548,1767)
     (1549,1768)(1550,1770)(1551,1772)(1553,1775)(1556,1779)(1558,1781)(1559,
     1592)(1561,1782)(1562,1783)(1564,1786)(1565,1787)(1567,1748)(1568,1788)
     (1570,1791)(1572,1793)(1573,1794)(1575,1795)(1576,1796)(1578,1799)(1579,
     1800)(1580,1802)(1581,1804)(1582,1806)(1583,1808)(1584,1810)(1585,1811)
     (1586,1813)(1587,1815)(1588,1817)(1591,1821)(1594,1822)(1595,1823)(1596,
     1825)(1597,1827)(1598,1829)(1601,1832)(1602,1833)(1604,1834)(1605,1835)
     (1606,1837)(1607,1839)(1608,1841)(1611,1845)(1612,1847)(1613,1849)(1615,
     1852)(1617,1855)(1618,1857)(1620,1860)(1622,1863)(1624,1866)(1626,1868)
     (1627,1869)(1629,1872)(1631,1875)(1633,1878)(1635,1881)(1637,1884)(1643,
     1891)(1644,1892)(1646,1895)(1651,1652)(1657,1906)(1658,1907)(1660,1910)
     (1662,1913)(1664,1916)(1668,1669)(1674,1926)(1675,1927)(1677,1930)(1682,
     1683)(1686,1938)(1687,1939)(1688,1697)(1690,1943)(1692,1946)(1694,1949)
     (1700,1701)(1706,1960)(1707,1961)(1709,1964)(1714,1969)(1715,1970)(1717,
     1973)(1719,1976)(1721,1979)(1724,1981)(1725,1982)(1727,1985)(1730,1989)
     (1732,1991)(1733,1992)(1738,1997)(1740,1999)(1742,2000)(1744,2002)(1746,
     2004)(1750,1751)(1754,2009)(1756,2011)(1758,2013)(1761,2016)(1762,2017)
     (1764,2019)(1766,2021)(1769,2024)(1771,2026)(1773,2027)(1774,2028)(1776,
     2029)(1777,2030)(1778,2032)(1780,2034)(1784,1785)(1789,2041)(1790,2042)
     (1792,2045)(1797,1798)(1801,2054)(1803,2056)(1805,2058)(1809,2060)(1812,
     2063)(1814,2065)(1816,1867)(1818,2067)(1819,2068)(1820,2069)(1824,2074)
     (1826,2076)(1828,2077)(1830,2079)(1831,2080)(1836,2085)(1838,2087)(1840,
     2089)(1842,2091)(1843,2092)(1844,2094)(1846,2097)(1848,2099)(1850,2101)
     (1851,2102)(1853,2103)(1854,2104)(1856,2107)(1858,2044)(1859,2109)(1861,
     2110)(1862,2111)(1864,2114)(1865,2115)(1870,2118)(1871,2119)(1873,2120)
     (1874,2121)(1876,2124)(1877,2125)(1879,2126)(1880,2117)(1882,1883)(1885,
     2129)(1886,2130)(1887,2131)(1888,2133)(1889,2135)(1890,2137)(1893,2139)
     (1894,2140)(1896,2141)(1897,2142)(1898,2082)(1899,2145)(1900,2147)(1901,
     2149)(1902,2150)(1903,2152)(1904,2154)(1905,2156)(1908,2160)(1909,2161)
     (1911,2162)(1912,2163)(1914,2166)(1915,2167)(1917,2073)(1918,2168)(1919,
     2062)(1920,2171)(1921,2173)(1922,2174)(1924,2177)(1925,2179)(1928,2182)
     (1929,2183)(1931,2048)(1932,2184)(1933,2186)(1934,2188)(1935,2190)(1936,
     2191)(1937,2192)(1940,2193)(1941,2194)(1942,2195)(1944,2196)(1945,2197)
     (1947,2200)(1948,2201)(1950,2202)(1951,2203)(1952,2205)(1953,2206)(1954,
     2207)(1955,2209)(1956,2211)(1957,2212)(1958,2214)(1959,2215)(1962,2218)
     (1963,2219)(1965,2220)(1966,2221)(1967,2222)(1968,2224)(1971,2227)(1972,
     2228)(1974,2229)(1975,2230)(1977,2233)(1978,2234)(1980,2235)(1983,2237)
     (1984,2238)(1986,2239)(1987,2240)(1988,2242)(1990,2245)(1993,2249)(1994,
     2251)(1995,2253)(1996,2072)(1998,2256)(2001,2260)(2003,2263)(2005,2265)
     (2006,2267)(2007,2268)(2008,2270)(2010,2273)(2012,2276)(2014,2279)(2015,
     2281)(2018,2284)(2020,2287)(2022,2289)(2023,2204)(2025,2293)(2031,2299)
     (2033,2216)(2035,2300)(2036,2084)(2037,2302)(2038,2303)(2039,2305)(2040,
     2306)(2043,2308)(2046,2309)(2047,2310)(2049,2312)(2050,2314)(2051,2316)
     (2052,2317)(2053,2318)(2055,2321)(2057,2323)(2059,2326)(2061,2328)(2064,
     2332)(2066,2334)(2070,2274)(2071,2338)(2075,2342)(2078,2345)(2081,2347)
     (2083,2350)(2086,2354)(2088,2357)(2090,2360)(2093,2364)(2095,2366)(2096,
     2367)(2098,2370)(2100,2373)(2105,2377)(2106,2378)(2108,2381)(2112,2113)
     (2116,2387)(2122,2123)(2127,2394)(2128,2395)(2132,2400)(2134,2402)(2136,
     2404)(2138,2406)(2143,2411)(2144,2412)(2148,2414)(2151,2417)(2153,2419)
     (2155,2264)(2157,2421)(2158,2422)(2159,2423)(2164,2165)(2169,2254)(2170,
     2432)(2172,2434)(2175,2437)(2176,2438)(2178,2250)(2180,2440)(2181,2441)
     (2185,2445)(2187,2447)(2189,2449)(2198,2199)(2208,2463)(2210,2465)(2213,
     2468)(2217,2470)(2223,2476)(2225,2478)(2226,2479)(2231,2232)(2236,2488)
     (2241,2492)(2243,2493)(2244,2494)(2246,2495)(2247,2496)(2248,2498)(2252,
     2501)(2255,2503)(2257,2358)(2258,2504)(2259,2505)(2261,2508)(2262,2509)
     (2266,2511)(2269,2514)(2271,2516)(2272,2517)(2275,2520)(2277,2521)(2278,
     2522)(2280,2523)(2282,2525)(2283,2526)(2285,2527)(2286,2528)(2288,2529)
     (2290,2530)(2291,2531)(2292,2532)(2294,2533)(2295,2534)(2296,2535)(2297,
     2537)(2298,2539)(2301,2542)(2304,2497)(2307,2545)(2311,2549)(2313,2551)
     (2315,2553)(2319,2556)(2320,2557)(2322,2558)(2324,2559)(2325,2560)(2327,
     2563)(2329,2566)(2330,2567)(2331,2568)(2333,2513)(2335,2570)(2336,2571)
     (2337,2573)(2339,2475)(2340,2576)(2341,2577)(2343,2580)(2344,2581)(2346,
     2582)(2348,2584)(2349,2585)(2351,2587)(2352,2588)(2353,2589)(2355,2590)
     (2356,2591)(2359,2594)(2361,2595)(2362,2596)(2363,2597)(2365,2599)(2368,
     2603)(2369,2604)(2371,2456)(2372,2605)(2374,2608)(2375,2609)(2376,2610)
     (2379,2613)(2380,2614)(2382,2615)(2383,2616)(2384,2618)(2385,2619)(2386,
     2621)(2388,2623)(2389,2624)(2390,2626)(2391,2628)(2392,2630)(2393,2632)
     (2396,2633)(2397,2634)(2398,2636)(2399,2638)(2401,2641)(2403,2644)(2405,
     2647)(2407,2649)(2408,2651)(2409,2653)(2410,2655)(2413,2657)(2415,2466)
     (2416,2660)(2418,2663)(2420,2664)(2424,2667)(2425,2668)(2426,2670)(2427,
     2672)(2428,2674)(2429,2676)(2430,2677)(2431,2679)(2433,2681)(2435,2684)
     (2436,2686)(2439,2689)(2442,2691)(2443,2693)(2444,2695)(2446,2698)(2448,
     2701)(2450,2467)(2451,2658)(2452,2706)(2453,2707)(2454,2546)(2455,2709)
     (2457,2711)(2458,2713)(2459,2715)(2460,2717)(2461,2718)(2462,2720)(2464,
     2723)(2469,2729)(2471,2732)(2472,2734)(2473,2736)(2474,2738)(2477,2741)
     (2480,2744)(2481,2745)(2482,2746)(2483,2748)(2484,2750)(2485,2751)(2486,
     2753)(2487,2755)(2489,2758)(2490,2760)(2491,2762)(2499,2769)(2500,2770)
     (2502,2772)(2506,2507)(2510,2611)(2512,2569)(2515,2783)(2518,2519)(2524,
     2790)(2536,2803)(2538,2805)(2540,2806)(2541,2807)(2543,2809)(2544,2811)
     (2547,2813)(2548,2815)(2550,2816)(2552,2819)(2554,2822)(2555,2824)(2561,
     2562)(2564,2833)(2565,2834)(2572,2840)(2574,2786)(2575,2842)(2578,2579)
     (2583,2850)(2586,2853)(2592,2593)(2598,2863)(2600,2864)(2601,2865)(2602,
     2866)(2606,2607)(2612,2875)(2617,2880)(2620,2883)(2622,2885)(2625,2888)
     (2627,2890)(2629,2892)(2631,2893)(2635,2687)(2637,2897)(2639,2899)(2640,
     2900)(2642,2901)(2643,2902)(2645,2905)(2646,2906)(2648,2907)(2650,2908)
     (2652,2910)(2654,2912)(2656,2914)(2659,2917)(2661,2919)(2662,2920)(2665,
     2921)(2666,2923)(2669,2927)(2671,2929)(2673,2930)(2675,2932)(2678,2935)
     (2680,2937)(2682,2938)(2683,2939)(2685,2942)(2688,2944)(2690,2945)(2692,
     2948)(2694,2950)(2696,2792)(2697,2951)(2699,2954)(2700,2955)(2702,2956)
     (2703,2957)(2704,2959)(2705,2960)(2708,2963)(2710,2870)(2712,2966)(2714,
     2968)(2716,2970)(2719,2962)(2721,2973)(2722,2974)(2724,2975)(2725,2976)
     (2726,2978)(2727,2979)(2728,2980)(2730,2886)(2731,2981)(2733,2984)(2735,
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