bin1 := (1,3,10,5)(2,7,17,8)(4,11,24,13)(6,12,25,15)(9,19,32,21)(14,27,18,26)
     (16,28,43,29)(20,33,51,35)(22,34,52,37)(23,38,58,40)(30,45,69,46)(31,47,
     72,49)(36,54,81,55)(39,59,89,61)(41,60,90,63)(42,64,96,65)(44,66,99,67)
     (48,73,110,75)(50,74,111,77)(53,78,117,79)(56,82,122,83)(57,84,124,86)
     (62,92,137,93)(68,100,150,101)(70,103,153,104)(71,105,156,107)(76,113,
     169,114)(80,118,177,119)(85,125,189,127)(87,126,190,129)(88,130,102,132)
     (91,134,200,135)(94,138,206,140)(95,141,211,142)(97,144,216,145)(98,146,
     219,147)(106,157,237,159)(108,158,238,161)(109,162,244,164)(112,166,251,
     167)(115,170,257,172)(116,173,262,174)(120,178,270,180)(121,181,275,182)
     (123,184,280,186)(128,192,292,193)(131,196,133,197)(136,202,308,203)(139,
     207,316,208)(143,213,325,214)(148,221,338,222)(149,223,341,224)(151,226,
     345,227)(152,228,348,229)(154,231,353,232)(155,233)(160,240,362,241)(163,
     245,370,247)(165,246,371,249)(168,253,382,254)(171,258,390,259)(175,264,
     399,265)(176,266,402,267)(179,271,408,272)(183,276,415,278)(185,281,424,
     283)(187,282,425,285)(188,286,431,288)(191,290,437,291)(194,293,440,295)
     (195,296,445,298)(198,300,452,301)(199,302,455,303)(201,305,460,306)(204,
     309,465,311)(205,312,470,313)(209,317,478,319)(210,320)(212,322,482,323)
     (215,327,487,328)(217,330,492,331)(218,332,495,333)(220,335,381,336)(225,
     343,509,344)(230,350,520,351)(234,318)(235,354)(236,355,526,357)(239,359,
     533,360)(242,363,537,365)(243,366,540,368)(248,373,549,374)(250,376,554,
     377)(252,379,559,380)(255,383,562,385)(256,386,567,387)(260,391,575,393)
     (261,394,580,395)(263,364,538,397)(268,403,592,405)(269,406)(273,409,553,
     411)(274,412,602,413)(277,416,607,417)(279,419,612,421)(284,427,625,428)
     (287,432,633,434)(289,433,634,436)(294,441,646,442)(297,446,654,448)(299,
     447,655,450)(304,457,671,458)(307,461,677,462)(310,466,685,467)(314,471,
     692,473)(315,474,697,475)(321,479,705,480)(324,483,710,484)(326,485,713,
     486)(329,489,719,490)(334,497)(337,499,735,500)(339,501,738,502)(340,503,
     741,504)(342,506,746,507)(346,512,755,513)(347,514,757,515)(349,517,762,
     518)(352,522,769,523)(356,527,777,529)(358,528,778,531)(361,534,786,535)
     (367,541,795,543)(369,542,796,545)(372,546,802,547)(375,550,808,552)(378,
     556,816,557)(384,563,728,564)(388,568,832,570)(389,571,836,572)(392,576,
     844,577)(396,582)(398,584,857,585)(400,586,860,587)(401,588,863,589)(404,
     593,868,594)(407,597)(410,598,876,599)(414,603,884,605)(418,608,892,610)
     (420,613,899,615)(422,614,900,617)(423,618,906,620)(426,622,913,623)(429,
     626,919,628)(430,629,924,631)(435,636,933,637)(438,640,940,641)(439,642,
     942,643)(443,647,948,648)(444,649,950,651)(449,657,962,658)(451,660,967,
     661)(453,663,971,664)(454,665,974,666)(456,668,978,669)(459,673,985,674)
     (463,678,993,680)(464,681,997,682)(468,686,1005,688)(469,689,1010,690)
     (472,693,1015,694)(476,698,1022,700)(477,701,1027,702)(481,707,1036,708)
     (488,716,591,717)(491,721,1054,722)(493,724,1059,725)(494,726,1062,727)
     (496,729,1064,730)(498,732,1069,733)(505,743,1085,744)(508,748,1092,749)
     (510,750,1095,751)(511,752,1098,753)(516,759,1107,760)(519,764,1115,765)
     (521,766,1118,767)(524,771,1125,772)(525,773,1128,775)(530,780,1137,781)
     (532,783,1142,784)(536,787,1148,789)(539,790,1153,792)(544,798,1166,799)
     (548,804,1176,805)(551,809,1184,810)(555,813,866,814)(558,818,1194,819)
     (560,821,1199,822)(561,823,1202,824)(565,827,850,828)(566,829,1208,830)
     (569,833,1213,834)(573,837,1218,839)(574,840,1223,841)(578,845,1231,847)
     (579,848,1235,849)(581,851,1237,852)(583,854,1242,855)(590,864,1255,865)
     (595,869,1260,871)(596,872,1265,873)(600,877,1273,879)(601,880,1278,881)
     (604,885,1284,886)(606,888,1289,889)(609,893,896,611)(616,902,1308,903)
     (619,907,1316,909)(621,908,1317,911)(624,915,1327,916)(627,920,1334,921)
     (630,925,1342,927)(632,926,1343,929)(635,930,1349,931)(638,934,1354,936)
     (639,937,1359,938)(644,943,1366,945)(645,812,1188,946)(650,951,1377,953)
     (652,952,1378,954)(653,955,1380,957)(656,959,1387,960)(659,963,1393,965)
     (662,968,1400,969)(667,975,1411,976)(670,980,1419,981)(672,982,1422,983)
     (675,987,1428,988)(676,989,1431,990)(679,994,1336,922)(683,998,1441,1000)
     (684,1001,1446,1002)(687,1006,1452,1007)(691,1011,1459,1013)(695,1016,
     1467,1018)(696,1019,1471,1020)(699,1023,1476,1024)(703,1028,1481,1030)
     (704,1031,1486,1032)(706,1033,1489,1034)(709,1038,1497,1039)(711,1041,
     1502,1042)(712,1043,1505,1044)(714,1046,1510,1047)(715,1048,1361,939)
     (718,1050,1515,1051)(720,1052,1518,1053)(723,1056,1524,1057)(731,1066,
     1535,1067)(734,1071,1543,1072)(736,1074,1547,1075)(737,1076,1550,1077)
     (739,1079,1080,740)(742,1082,1559,1083)(745,1087,1566,1088)(747,995,1437,
     1090)(754,825,1203,1100)(756,1102,1587,1103)(758,1105,1325,914)(761,1109,
     1595,1110)(763,1112,1597,1113)(768,1120,1608,1121)(770,1122,1610,1123)
     (774,1129,1619,1131)(776,1130,1620,1133)(779,1134,1626,1135)(782,1138,
     1632,1140)(785,1144,1642,1145)(788,1149,1649,1150)(791,1154,1658,1156)
     (793,1155,1659,1158)(794,1159,1665,1161)(797,1163,1672,1164)(800,1167,
     1678,1169)(801,1170,1683,1171)(803,1173,1688,1174)(806,1177,1694,1179)
     (807,1180,1698,1181)(811,1185,1703,1187)(815,1190,1711,1191)(817,1192,
     1714,1193)(820,1196,1370,1197)(826,1204,1728,1205)(831,1209,1735,1211)
     (835,1214,1743,1216)(838,1219,1749,1220)(842,1224,1584,1226)(843,1227,
     1760,1228)(846,1232,1530,1061)(853,1239,1777,1240)(856,1244,1480,1026)
     (858,1246,1785,1247)(859,1248,1787,1249)(861,1251,1298,895)(862,1060,
     1529,1252)(867,1256,1063,1257)(870,1261,1800,1262)(874,1266,1807,1268)
     (875,1269,1810,1270)(878,1274,1815,1275)(882,1279,1612,1124)(883,1280,
     1823,1281)(887,1285,1831,1287)(890,1290,1836,1292)(891,1293,1840,1294)
     (894,1297,1300,897)(898,1301,1851,1303)(901,1305,1857,1306)(904,1309,
     1863,1311)(905,1312,1868,1314)(910,1319,1875,1320)(912,1322,1878,1323)
     (917,1328,1886,1330)(918,1331,1890,1332)(923,1337,1898,1339)(928,1345,
     1911,1346)(932,1111,1596,1351)(935,1355,1924,1356)(941,1363,1933,1364)
     (944,1367,1938,1368)(947,1371)(949,1373,1945,1375)(956,1381,1955,1383)
     (958,1382,1956,1385)(961,1389,1215,1390)(964,1394,1973,1395)(966,1397,
     1978,1398)(970,1402,1519,1403)(972,1405,1988,1406)(973,1407,1991,1408)
     (977,1413,1998,1414)(979,1416,2000,1417)(984,1424,2010,1425)(986,1426,
     2012,1427)(991,1432,2017,1433)(992,1434,2019,1435)(996,1438,2023,1439)
     (999,1442,2027,1443)(1003,1447,2034,1449)(1004,1450,1576,1094)(1008,1453,
     2039,1455)(1009,1456)(1012,1460,2046,1461)(1014,1463,2051,1464)(1017,
     1468,2059,1469)(1021,1472,2064,1474)(1025,1477,2070,1479)(1029,1482,2073,
     1483)(1035,1491,2084,1492)(1037,1494,2087,1495)(1040,1499,2094,1500)
     (1045,1507,2105,1508)(1049,1513,2035,1448)(1055,1521,2122,1522)(1058,
     1526,2128,1527)(1065,1473,2065,1533)(1068,1537,2140,1538)(1070,1540,2143,
     1541)(1073,1544,2149,1545)(1078,1552,2159,1553)(1081,1556,2165,1557)
     (1084,1561,2172,1562)(1086,1563,2174,1564)(1089,1568,2179,1569)(1091,
     1571,2184,1572)(1093,1574,2189,1575)(1096,1578,2193,1579)(1097,1580,2196,
     1581)(1099,1582,2199,1583)(1101,1585)(1104,1588,1919,1589)(1106,1590,
     2205,1591)(1108,1592,2208,1593)(1114,1599)(1116,1601,2218,1602)(1117,
     1603,2220,1604)(1119,1606,2225,1607)(1126,1613,2232,1614)(1127,1615,1832,
     1286)(1132,1622,2242,1623)(1136,1628,1488,1629)(1139,1633,2255,1634)
     (1141,1636,2259,1637)(1143,1639,2260,1640)(1146,1643,2266,1645)(1147,
     1646,1779,1647)(1151,1650,2271,1652)(1152,1653,2275,1655)(1157,1661,2285,
     1662)(1160,1666,2289,1668)(1162,1667,2290,1670)(1165,1674,2297,1675)
     (1168,1679,2303,1680)(1172,1685,2311,1686)(1175,1690,2316,1691)(1178,
     1695,2323,1696)(1182,1644,2267,1700)(1183,1687,1509,1701)(1186,1704,2332,
     1705)(1189,1708,2336,1709)(1195,1717,2347,1718)(1198,1721,2353,1722)
     (1200,1724,1793,1253)(1201,1725,1887,1329)(1206,1729,2361,1730)(1207,
     1731,2363,1732)(1210,1736,2371,1737)(1212,1739,2376,1740)(1217,1745,2381,
     1746)(1221,1750,2389,1752)(1222,1753,2392,1754)(1225,1756,2396,1757)
     (1229,1761,2403,1763)(1230,1764,2406,1765)(1233,1768,1769,1234)(1236,
     1771,1258,1772)(1238,1774,2415,1775)(1241,1778,1834,1288)(1243,1611,1669,
     1780)(1245,1782,2422,1783)(1250,1789,2431,1790)(1254,1794,2437,1795)
     (1259,1797,2441,1798)(1263,1801,2445,1803)(1264,1804,2447,1805)(1267,
     1808,2278,1656)(1271,1811,2155,1549)(1272,1812,1648,1813)(1276,1478,2071,
     1817)(1277,1818,2458,1819)(1282,1824,2467,1826)(1283,1827,2471,1828)
     (1291,1837)(1295,1841,2487,1842)(1296,1843,2488,1844)(1299,1847,2494,
     1848)(1302,1852,2502,1854)(1304,1853,2503,1855)(1307,1859,2509,1860)
     (1310,1864,2516,1865)(1313,1869,2380,1742)(1315,1870,2524,1871)(1318,
     1872,2526,1873)(1321,1876,2531,1877)(1324,1880,2534,1881)(1326,1883,2394,
     1755)(1333,1891,2546,1893)(1335,1894,2551,1895)(1338,1899,2560,1901)
     (1340,1900,2561,1903)(1341,1904,2567,1906)(1344,1908,2574,1909)(1347,
     1912,2579,1914)(1348,1451,2037,1915)(1350,1917,2584,1918)(1352,1415,1999,
     1920)(1353,1921,2587,1922)(1357,1762,2404,1926)(1358,1927,2596,1928)
     (1360,1929,2599,1930)(1362,1931)(1365,1934,2606,1936)(1369,1939,2613,
     1941)(1372,1943)(1374,1946,2622,1948)(1376,1947,2623,1950)(1379,1951,
     2625,1953)(1384,1958,2633,1959)(1386,1961,1715,1962)(1388,1964,2640,1965)
     (1391,1967,1744,1969)(1392,1970,1430,1971)(1396,1974,2651,1976)(1399,
     1980,2659,1981)(1401,1982,2661,1983)(1404,1986,1586,1987)(1409,1992,2586,
     1993)(1410,1458,2044,1994)(1412,1995,2672,1996)(1418,2002)(1420,2003,
     2680,2004)(1421,2005,2682,2006)(1423,2008,2687,2009)(1429,2013,2692,2014)
     (1436,2020,2582,2022)(1440,1600,2216,2025)(1444,2028,2704,2030)(1445,
     2031,2709,2032)(1454,2040,2718,2041)(1457,2043)(1462,2047,2724,2049)
     (1465,2052,2730,2054)(1466,2055,2670,2056)(1470,2060,2740,2062)(1475,
     2066,2744,2067)(1484,2074,2753,2075)(1485,2076,2154,1548)(1487,2078,2757,
     2079)(1490,2081,2759,2082)(1493,2085,1814,2086)(1496,1809,2451,2089)
     (1498,2091,2770,2092)(1501,2095,2773,2096)(1503,2098,2777,2099)(1504,
     2100,2780,2101)(1506,2103,2784,2104)(1511,2108,2790,2109)(1512,2110,2177,
     1567)(1514,2112,2795,2113)(1516,2115,2799,2116)(1517,2117,2666,2118)
     (1520,2119,2803,2120)(1523,1884,2539,2124)(1525,2125,2811,2126)(1528,
     2129,2816,2130)(1531,2133,2821,2134)(1532,2048,2725,2135)(1534,2137,2671,
     2138)(1536,2139,2276,1654)(1539,2141,1638,2142)(1542,2145,2829,2146)
     (1546,2151,2836,2152)(1551,2157)(1554,2160,2845,2161)(1555,2162,2848,
     2163)(1558,2166,2851,2167)(1560,2169,2855,2170)(1565,2175,2349,1719)
     (1570,2181,2869,2182)(1573,2186,2877,2187)(1577,2191,2882,2192)(1594,
     2210,2906,2211)(1598,2214,2911,2215)(1605,2222,2702,2223)(1609,2228,2927,
     2229)(1616,2234,2427,1786)(1617,2235,2478,1833)(1618,2236,2896,2201)
     (1621,2239,2937,2240)(1624,2243,2943,2245)(1625,2246,1630,2247)(1627,
     1949,2624,2249)(1631,2252,2952,2253)(1635,1979,2657,2257)(1641,2262,2963,
     2263)(1651,2272,2972,2273)(1657,2279,2980,2281)(1660,2283,2985,2284)
     (1663,2286,2987,2287)(1664,2288,2333,1706)(1671,2291,2989,2292)(1673,
     2294,2470,2295)(1676,2298,2970,2270)(1677,2299,2999,2300)(1681,2304,2835,
     2306)(1682,2307,3009,2308)(1684,2217,2914,2310)(1689,2093,2771,2314)
     (1692,2317,3020,2319)(1693,2320,3025,2321)(1697,2045,2723,2325)(1699,
     2326,3034,2327)(1702,2329,3038,2330)(1707,2334,2131,1879)(1710,2337,3046,
     2338)(1712,2340,3048,2341)(1713,2342,3051,2343)(1716,2344,3052,2345)
     (1720,2350,3059,2351)(1723,2354,3064,2355)(1726,2357,1767,1888)(1727,
     2358,3070,2359)(1733,2364,3077,2366)(1734,2367,2520,2368)(1738,2372,3084,
     2374)(1741,2377,3090,2379)(1747,2382,3094,2384)(1748,2385,3099,2386)
     (1751,2390,2468,1825)(1758,2397,3113,2399)(1759,2365,3078,2400)(1766,
     2407,3125,2409)(1770,2411,3132,2412)(1773,2413,3134,2414)(1776,2227,2026,
     2417)(1781,2419,3140,2420)(1784,2424,3143,2425)(1788,2429)(1791,2251,
     2951,2432)(1792,2433,3151,2434)(1796,2438,3158,2440)(1799,2442,3161,2444)
     (1802,2446,2136,2416)(1806,2063,2207,2449)(1816,2454,3172,2455)(1820,
     2459,3179,2461)(1821,2462,3182,2463)(1822,2464,3183,2465)(1829,2472,3189,
     2474)(1830,2475,3194,2476)(1835,2479,3198,2480)(1838,2483)(1839,2484,
     2542,2485)(1845,2250,2950,2490)(1846,2491,3207,2492)(1849,2495,3211,2497)
     (1850,2498,2482,2500)(1856,2504,2717,2505)(1858,2507,3220,2508)(1861,
     2510,2910,2512)(1862,2513,3204,2514)(1866,2517,3227,2518)(1867,2519,2369,
     2521)(1874,2527,3237,2528)(1882,2536,3248,2537)(1885,2540,2430,2541)
     (1889,2543,3253,2544)(1892,2547,3258,2548)(1896,2552,3264,2554)(1897,
     2555,3269,2557)(1902,2563,3280,2564)(1905,2568,3286,2570)(1907,2569,3287,
     2572)(1910,2576)(1913,2256,2955,2580)(1916,2538,3250,2583)(1923,2588,
     3303,2590)(1925,2592,3309,2593)(1932,2602,3322,2603)(1935,2607,3328,2608)
     (1937,2610,3331,2611)(1940,2614,3334,2615)(1942,2077,2755,2617)(1944,
     2439,3159,2620)(1952,2626,2204,2628)(1954,2627,2021,2630)(1957,2631,3346,
     2632)(1960,2634,3348,2635)(1963,2638,1990,2639)(1966,2642,3357,2643)
     (1968,2645)(1972,2648,2015,2650)(1975,2652,2038,2653)(1977,2655,3366,
     2656)(1984,2662,3372,2663)(1985,2664)(1989,2667,2213,2649)(1997,2674,
     3383,2675)(2001,2678,3387,2679)(2007,2684,2206,2685)(2011,2689,3399,2690)
     (2016,2693,3402,2694)(2018,2696,3406,2697)(2024,2700,2057,2701)(2029,
     2705,2277,2706)(2033,2710,3424,2712)(2036,2713,3428,2714)(2042,2719,3431,
     2721)(2050,2726,2946,2727)(2053,2731,3444,2732)(2058,2736,3453,2737)
     (2061,2741,3414,2703)(2068,2745,3466,2747)(2069,2233,2933,2748)(2072,
     2750,3469,2751)(2080,2658,3212,2496)(2083,2761,3476,2762)(2088,2766,3481,
     2767)(2090,2769,3082,2370)(2097,2774,3487,2775)(2102,2782,3493,2783)
     (2106,2786,3498,2787)(2107,2788,3500,2789)(2111,2792,3505,2793)(2114,
     2797,2522,2798)(2121,2805,3520,2806)(2123,2808,2834,2150)(2127,2796,3509,
     2813)(2132,2818,3536,2819)(2144,2826,3545,2827)(2147,2831,3548,2832)
     (2148,2453,3170,2833)(2153,2838,3554,2839)(2156,2840,3555,2841)(2158,
     2843,2532,2844)(2164,2849,2842,2850)(2168,2853,3558,2854)(2171,2856,2339,
     2857)(2173,2859,3569,2860)(2176,2862,2486,2863)(2178,2864,3575,2865)
     (2180,2866,3578,2867)(2183,2871,3584,2872)(2185,2874,3588,2875)(2188,
     2879)(2190,2760,3474,2881)(2194,2885,3599,2886)(2195,2887,3602,2888)
     (2197,2890,3604,2891)(2198,2892,3605,2893)(2200,2894,3607,2895)(2202,
     2897,3610,2898)(2203,2899,3612,2900)(2209,2903,2768,2904)(2212,2908,3624,
     2909)(2219,2915,2938,2916)(2221,2918,3633,2919)(2224,2922,3640,2923)
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