bin1 := (1,2,7,4)(3,8,19,11)(5,9,20,13)(6,14,28,16)(10,21,39,22)(12,24,44,25)
     (15,29,53,32)(17,30,54,34)(18,35,62,37)(23,41,72,42)(26,45,78,47)(27,48,
     83,50)(31,55,94,56)(33,58,99,59)(36,63,108,66)(38,64,109,68)(40,69,117,
     70)(43,74,125,75)(46,79,133,80)(49,84,142,87)(51,85,143,89)(52,90,151,92)
     (57,96,161,97)(60,100,167,102)(61,103,172,105)(65,110,181,111)(67,113,
     186,114)(71,119,196,120)(73,122,201,123)(76,126,207,128)(77,129,212,130)
     (81,134,220,136)(82,137,225,139)(86,144,236,145)(88,147,241,148)(91,152,
     249,155)(93,153,250,157)(95,158,258,159)(98,163,266,164)(101,168,274,169)
     (104,173,283,176)(106,174,284,178)(112,183,295,184)(115,187,301,189)(116,
     190,306,191)(118,193,311,194)(121,198,319,199)(124,203,273,204)(127,208,
     334,209)(131,213,341,215)(132,216,346,217)(135,221,353,222)(138,226,362,
     229)(140,227,363,231)(141,232,371,234)(146,238,381,239)(149,242,387,244)
     (150,245,391,247)(154,251,398,252)(156,254,403,255)(160,260,413,261)(162,
     263,418,264)(165,267,424,269)(166,270,429,271)(170,275,434,277)(171,278,
     439,280)(175,285,450,286)(177,288,455,289)(182,292,460,293)(185,297,468,
     298)(188,302,476,303)(192,308,486,309)(195,313,417,314)(197,316,498,317)
     (200,321,505,322)(202,324,509,325)(205,327,432,329)(206,330,518,331)(210,
     335,526,337)(211,338,531,339)(214,342,536,343)(218,347,544,349)(219,350,
     549,351)(223,354,554,356)(224,357,559,359)(228,364,570,365)(230,367,575,
     368)(233,372,583,375)(235,373,584,377)(237,378,592,379)(240,383,599,384)
     (243,388,607,389)(246,392,611,395)(248,393,612,397)(253,400,622,401)(256,
     404,626,406)(257,407,631,408)(259,410,636,411)(262,415,644,416)(265,420,
     647,421)(268,425,655,426)(272,430,662,431)(276,435,525,436)(279,440,671,
     443)(281,441,672,445)(282,446,677,448)(287,452,687,453)(290,456,693,458)
     (294,462,703,463)(296,465,708,466)(299,469,714,471)(300,472,719,473)(304,
     477,727,479)(305,480,635,481)(307,483,736,484)(310,488,743,489)(312,491,
     747,492)(315,495,754,496)(318,500,761,501)(320,502,764,503)(323,507,772,
     508)(326,511,778,512)(328,514,782,515)(332,519,788,521)(333,522,793,523)
     (336,527,798,528)(340,532,806,534)(344,537,814,539)(345,540,742,541)(348,
     545,822,546)(352,550,828,552)(355,555,836,556)(358,560,844,563)(360,561,
     845,565)(361,566,853,568)(366,572,863,573)(369,576,869,578)(370,579,873,
     581)(374,585,880,586)(376,588,885,589)(380,594,894,595)(382,597,676,444)
     (385,600,903,602)(386,603,908,604)(390,608,915,609)(394,613,792,614)(396,
     616,921,617)(399,619,925,620)(402,624,646,419)(405,627,935,628)(409,633,
     943,634)(412,638,946,639)(414,641,913,642)(422,648,438,650)(423,651,960,
     652)(427,656,898,658)(428,659,968,660)(433,663,972,664)(437,666,797,668)
     (442,673,983,674)(447,678,986,681)(449,679,987,683)(451,684,995,685)(454,
     689,1002,690)(457,694,1009,695)(459,697,1013,698)(461,700,1018,701)(464,
     705,1025,706)(467,710,1033,711)(470,715,1014,716)(474,720,1043,722)(475,
     723,1048,724)(478,728,1056,729)(482,733,1065,734)(485,738,1071,739)(487,
     740,1073,741)(490,745,1079,746)(493,749,1085,750)(494,751,1087,752)(497,
     756,1092,757)(499,758,1094,759)(504,766,542,767)(506,769,1108,770)(510,
     775,1116,776)(513,779,1122,780)(516,783,1127,785)(517,771,1110,786)(520,
     789,1133,790)(524,794,1138,796)(529,799,1143,801)(530,802,1148,803)(533,
     807,1156,808)(535,810,1161,811)(543,818,1171,819)(547,823,1179,825)(548,
     826,1131,787)(551,829,1186,830)(553,832,1191,833)(557,837,1199,839)(558,
     838,1200,841)(562,846,1210,847)(564,849,1215,850)(567,854,1223,857)(569,
     855,1224,859)(571,860,1232,861)(574,865,1238,866)(577,870,1233,871)(580,
     874,1246,877)(582,875,1247,879)(587,882,1257,883)(590,886,1263,888)(591,
     889,1268,890)(593,892,984,675)(596,896,1278,897)(598,899,1281,900)(601,
     904,1217,905)(605,909,1294,911)(606,657,632,912)(610,916,1067,735)(615,
     918,1305,919)(618,922,1311,924)(621,927,945,637)(623,929,1320,930)(625,
     931,1323,932)(629,936,1330,938)(630,939,669,940)(640,948,1344,949)(643,
     951,1348,952)(645,953,1350,954)(649,956,1354,957)(653,961,1360,963)(654,
     964,1362,965)(661,969,1368,971)(665,973,1370,975)(667,976,1375,977)(670,
     979,1379,981)(680,988,1388,989)(682,991,1393,992)(686,997,1400,998)(688,
     1000,1404,1001)(691,959,1358,1004)(692,1005,1410,1006)(696,1010,1416,
     1012)(699,1015,1422,1016)(702,1020,1363,966)(704,1022,717,1023)(707,1027,
     1438,1028)(709,1030,1442,1031)(712,1034,1346,950)(713,1035,1448,1036)
     (718,1040,1457,1041)(721,1044,1461,1045)(725,1049,1468,1051)(726,1052,
     1472,1053)(730,1057,1480,1059)(731,1060,1485,1061)(732,1062,1487,1063)
     (737,1068,1491,1069)(744,1076,1178,1077)(748,1082,1508,1083)(753,1078,
     1503,1089)(755,1090,1518,1091)(760,1096,1525,1097)(762,1099,1529,1100)
     (763,1101,1411,1007)(768,1105,1539,1106)(773,1111,1547,1112)(774,1113,
     1549,1114)(777,1118,1555,1119)(781,1123,1563,1124)(784,1128)(791,1134,
     1575,1136)(795,1139,1314,1140)(800,1144,1587,1145)(804,1149,1595,1151)
     (805,1152,1599,1153)(809,1157,1607,1159)(812,1162,1402,999)(813,1163,
     1615,1164)(816,1166,1620,1167)(817,1168,1622,1169)(820,1172,1626,1174)
     (821,1175,1630,1176)(824,1180,1635,1181)(827,1184,1488,1064)(831,1187,
     1646,1189)(834,1192,1650,1194)(835,1195,1507,1196)(840,1117,1554,1203)
     (842,1201,1660,1205)(843,1206,1663,1208)(848,1212,1673,1213)(851,1216,
     1679,1218)(852,1219,1682,1221)(856,1225,1689,1226)(858,1228,1694,1229)
     (862,1234,1369,970)(864,1236,872,1237)(867,1150,1596,1239)(868,1240,1705,
     1241)(876,1248,1717,1249)(878,1251,1722,1252)(881,1254,1727,1255)(884,
     1259,1735,1260)(887,1264,1743,1265)(891,1270,1752,1271)(893,1272,1755,
     1273)(895,1275,1674,1276)(901,1282,1767,1284)(902,1285,1312,923)(906,
     1288,1680,1290)(907,1291,1775,1292)(910,1295,1778,1296)(914,1298,1782,
     1299)(917,1302,1788,1303)(920,1307,1795,1308)(926,1315,1803,1316)(928,
     1317,1141,1318)(933,1324,1093,1325)(934,1326,1811,1327)(937,1331,1819,
     1332)(941,1335,1823,1336)(942,1337,1825,1338)(944,1339,1826,1340)(947,
     1342,1829,1343)(955,1352,1837,1353)(958,1355,1839,1357)(962,985,1387,
     1361)(967,1364,1846,1365)(974,1371,1852,1372)(978,1376,1858,1377)(980,
     1380,1613,1383)(982,1381,1531,1385)(990,1390,1867,1391)(993,1394,1873,
     1396)(994,1359,1844,1397)(996,1398,1878,1399)(1003,1407,1890,1408)(1008,
     1412,1892,1413)(1011,1417,1900,1418)(1017,1424,1908,1425)(1019,1427,1912,
     1428)(1021,1430,1917,1431)(1024,1434,1768,1283)(1026,1435,1924,1436)
     (1029,1439,1929,1440)(1032,1444,1845,1445)(1037,1449,1940,1451)(1038,
     1452,1944,1453)(1039,1454,1947,1455)(1042,1458,1952,1459)(1046,1462,1955,
     1464)(1047,1465)(1050,1293,1776,1469)(1054,1473,1969,1475)(1055,1476,
     1974,1477)(1058,1481,1982,1482)(1066,1489,1992,1490)(1070,1493,1998,1494)
     (1072,1496,2002,1497)(1075,1499,2005,1500)(1080,1504,1562,1188)(1081,
     1505,2014,1506)(1084,1510,2017,1511)(1086,1513,2021,1514)(1088,1129)
     (1095,1522,2033,1523)(1098,1526,2039,1527)(1102,1532,2046,1533)(1103,
     1534,1582,1535)(1104,1536,1322,1537)(1107,1541,2053,1542)(1109,1543,2056,
     1544)(1115,1551,1197,1552)(1120,1556,2072,1558)(1121,1559,2077,1560)
     (1125,1564,2081,1566)(1126,1567,2084,1568)(1130,1570,2082,1571)(1132,
     1515,2023,1573)(1135,1576,2094,1577)(1137,1579,2098,1580)(1142,1583,2102,
     1584)(1146,1588,2109,1590)(1147,1591,2114,1592)(1154,1600,2124,1602)
     (1155,1603,2129,1604)(1158,1608,2134,1609)(1160,1611,1382,1612)(1165,
     1616,2138,1618)(1170,1623,2144,1624)(1173,1627,2148,1628)(1177,1631,2153,
     1633)(1182,1636,2160,1638)(1183,1639,2163,1640)(1185,1642,2168,1643)
     (1190,1647,2174,1648)(1193,1651,2179,1652)(1198,1656,1367,1657)(1202,
     1509,1661,1204)(1207,1664,2199,1667)(1209,1665,2200,1669)(1211,1670,2208,
     1671)(1214,1675,1766,1676)(1220,1683,2224,1686)(1222,1684,2225,1688)
     (1227,1691,2232,1692)(1230,1695,2238,1697)(1231,1597,1703,1349)(1235,
     1699,2244,1700)(1242,1706,2251,1708)(1243,1709,2256,1710)(1244,1711,2257,
     1712)(1245,1713,2259,1715)(1250,1719,2267,1720)(1253,1723,2271,1725)
     (1256,1729,2281,1730)(1258,1732,2286,1733)(1261,1736,2292,1738)(1262,
     1739,2297,1740)(1266,1744,2305,1746)(1267,1747,2310,1748)(1269,1750,1774,
     1289)(1274,1757,1793,1306)(1277,1759,2147,1760)(1279,1761,2324,1762)
     (1280,1763,2326,1764)(1286,1770,1801,1313)(1287,1771,2336,1772)(1297,
     1779,2343,1780)(1300,1783,2345,1784)(1301,1785,2346,1786)(1304,1790,2353,
     1791)(1309,1796,2360,1798)(1310,1799)(1319,1805,2370,1806)(1321,1808,
     2375,1809)(1328,1812,2380,1814)(1329,1815,2385,1816)(1333,1820,1859,1378)
     (1334,1821,2393,1822)(1341,1827,2399,1828)(1345,1386,1862,1831)(1347,
     1832,2403,1833)(1351,1835,2146,1625)(1356,1840,2411,1841)(1366,1847,2419,
     1849)(1373,1853,2050,1538)(1374,1854,2428,1855)(1384,1861,2100,1581)
     (1389,1864,2438,1865)(1392,1869,2446,1870)(1395,1874,2454,1875)(1401,
     1881,2101,1610)(1403,1882,2463,1883)(1405,1885,2468,1886)(1406,1887,2470,
     1888)(1409,1891,2044,1530)(1414,1893,2475,1895)(1415,1896,2480,1897)
     (1419,1901,2484,1902)(1420,1903,2486,1904)(1421,1905,2319,1756)(1423,
     1721,2269,1906)(1426,1909,2492,1910)(1429,1914,1446,1915)(1432,1919,2501,
     1920)(1433,1921,2503,1922)(1437,1926)(1441,1931,2514,1932)(1443,1934,
     2519,1935)(1447,1937,2522,1938)(1450,1941)(1456,1948,2533,1949)(1460,
     1953,2266,1718)(1463,1956,2545,1957)(1466,1960)(1467,1961,2551,1962)
     (1470,1751,2313,1965)(1471,1966,2556,1967)(1474,1970,2561,1971)(1478,
     1975,2566,1977)(1479,1978,2569,1979)(1483,1983,2577,1984)(1484,1985,2578,
     1986)(1486,1645,2172,1988)(1492,1995,2590,1996)(1495,1999,2596,2000)
     (1498,2003,2601,2004)(1501,2007,2603,2008)(1502,2009,2605,2010)(1512,
     2019,2089,2020)(1516,2024,1565,1899)(1517,1989,2583,2025)(1519,2027,2626,
     2028)(1520,2029,2628,2030)(1521,2031,2344,1781)(1524,2035,2635,2036)
     (1528,2041,2643,2042)(1540,2051,2652,2052)(1545,2058,2660,2059)(1546,
     2060,2662,2061)(1548,2062,2665,2063)(1550,2064,2668,2065)(1553,2068,1834,
     2069)(1557,2073,2680,2074)(1561,2078,2687,2080)(1569,2085,2584,1991)
     (1572,2087,2582,2088)(1574,2090,2695,2091)(1578,2095,2703,2097)(1585,
     2103,2435,2104)(1586,2105,2708,2106)(1589,2110,2714,2111)(1593,2115,2721,
     2117)(1594,2118,2726,2119)(1598,2121,2731,2122)(1601,2125,2513,2126)
     (1605,2130,2740,2132)(1606,1927,2509,2133)(1614,2135,2746,2136)(1617,
     2139,2141,1619)(1621,2142,2753,2143)(1629,2149,2759,2151)(1632,2154,2766,
     2155)(1634,2157,2769,2158)(1637,1880,2461,2161)(1641,2164,2775,2166)
     (1644,2169,2781,2171)(1649,2175,2789,2177)(1653,2180,2797,2182)(1654,
     2183,2802,2184)(1655,2185,2805,2186)(1658,2188,1850,2190)(1659,2191,2814,
     2192)(1662,2195,2821,2197)(1666,2201,2828,2202)(1668,2204,2833,2205)
     (1672,2209,2318,2210)(1677,2213,2330,2215)(1678,2216,2851,2217)(1681,
     2219,2856,2221)(1685,2226,2867,2227)(1687,1702,2248,2228)(1690,2229,2870,
     2230)(1693,2234,2878,2235)(1696,2239,2885,2240)(1698,2242,2889,2243)
     (1701,2246,2891,2247)(1704,2249,2167,2159)(1707,2252,2894,2253)(1714,
     2260,2902,2263)(1716,2261,2903,2265)(1724,2272,2917,2273)(1726,2275,2328,
     2276)(1728,2278,2923,2279)(1731,2283,2929,2284)(1734,2288,2935,2289)
     (1737,2293,2938,2294)(1741,2298,2944,2300)(1742,2301,2947,2302)(1745,
     2306,2953,2307)(1749,2311,2351,1789)(1753,2314,2962,2315)(1754,2316,2964,
     2317)(1758,2321,2969,2322)(1765,2327,2975,2329)(1769,2332,2979,2333)
     (1773,2337,2987,2338)(1777,2339,2989,2340)(1787,2348,2997,2349)(1792,
     2355)(1794,2356,3006,2357)(1797,2361)(1800,2364)(1802,2365,3019,2366)
     (1804,2368,2434,1860)(1807,2372,3030,2373)(1810,2376,3036,2377)(1813,
     2381,3043,2382)(1817,2386,1857,2388)(1818,2389,3051,2390)(1824,2395,2720,
     2396)(1830,2401,3063,2402)(1836,2406,3070,2407)(1838,2408)(1842,2412,
     3075,2414)(1843,2415,3080,2416)(1848,2420,3083,2421)(1851,2423,3088,2424)
     (1856,2429,3097,2431)(1863,1994,2588,2436)(1866,2440,3107,2441)(1868,
     2443,3110,2444)(1871,2447,2861,2449)(1872,2450,2071,2451)(1876,2455,3120,
     2457)(1877,2255,2897,2458)(1879,2460,2520,1936)(1884,2465,2770,2466)
     (1889,2471,3136,2472)(1894,2476,3140,2477)(1898,2481,3143,2482)(1907,
     2410)(1911,2493,3154,2494)(1913,2496,3157,2497)(1916,2498,3159,2499)
     (1918,2500)(1923,2504,2916,2505)(1925,2507,3168,2508)(1928,2510,3170,
     2511)(1930,2512,2896,2254)(1933,2516,2744,2517)(1939,2523,3182,2525)
     (1942,2527)(1943,1973,2563,2127)(1945,2312,2960,2529)(1946,2530,2641,
     2040)(1950,2534,3197,2536)(1951,2537,3200,2538)(1954,2541,3203,2542)
     (1958,2546,3211,2548)(1959,2549,3058,2394)(1963,2552,3215,2553)(1964,
     2554,2602,2006)(1968,2557,3221,2559)(1972,2562,2890,2245)(1976,2323,2970,
     2567)(1980,2570,3236,2572)(1981,2573,3238,2574)(1987,2580,2622,2581)
     (1990,2086,2022,2467)(1993,2586,3250,2587)(1997,2592,2418,2593)(2001,
     2598,3263,2599)(2011,2606,3269,2607)(2012,2608,3271,2609)(2013,2610,3274,
     2611)(2015,2612,3277,2613)(2016,2614,2397,2615)(2018,2617,3280,2618)
     (2026,2623,3288,2624)(2032,2483,3144,2630)(2034,2632,3298,2633)(2037,
     2637,3304,2638)(2038,2639,3307,2640)(2043,2490,3151,2645)(2045,2646,3314,
     2647)(2047,2648,2649,2048)(2049,2140,2751,2650)(2054,2473,3137,2655)
     (2055,2656,3324,2657)(2057,2417,3081,2658)(2066,2670,2445,2671)(2067,
     2672,3342,2673)(2070,2676,3348,2677)(2075,2681,2748,2683)(2076,2684,3353,
     2685)(2079,2688,2813,2689)(2083,2691,3360,2692)(2092,2696,2774,2698)
     (2093,2699,3371,2700)(2096,2704,3378,2705)(2099,2464,3130,2707)(2107,
     2709,3383,2710)(2108,2711)(2112,2715,3389,2717)(2113,2716,3390,2718)
     (2116,2722,3395,2723)(2120,2727,2550,2729)(2123,2732,3405,2734)(2128,
     2736,3412,2737)(2131,2741,3419,2742)(2137,2747,3423,2749)(2145,2756)
     (2150,2760,2971,2761)(2152,2763,2479,2764)(2156,2462,3128,2768)(2162,
     2771,3446,2772)(2165,2776,3450,2777)(2170,2782,3457,2783)(2173,2785,3461,
     2786)(2176,2790,3468,2791)(2178,2793,3473,2794)(2181,2798,3478,2799)
     (2187,2807,3486,2808)(2189,2810,3491,2811)(2193,2815,3493,2817)(2194,
     2818,3498,2819)(2196,2822,3485,2825)(2198,2823,3503,2827)(2203,2830,3513,
     2831)(2206,2834,3519,2836)(2207,2837,2958,2838)(2211,2842,3531,2843)
     (2212,2844,3534,2845)(2214,2847,3539,2848)(2218,2852,3546,2854)(2220,
     2857,3551,2860)(2222,2858,3552,2862)(2223,2863,3556,2865)(2231,2872,3569,
     2873)(2233,2875,3573,2876)(2236,2879,3578,2880)(2237,2881,3580,2882)
     (2241,2886,3437,2888)(2250,2893,2779,2604)(2258,2866,3558,2900)(2262,
     2904,3600,2905)(2264,2907,3605,2908)(2268,2912,3612,2913)(2270,2540)
     (2274,2918,3616,2919)(2277,2922,3237,2571)(2280,2925,3624,2926)(2282,
     2927,3138,2474)(2285,2930,3421,2743)(2287,2932,3630,2933)(2290,2936,3117,
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