bin1 := (1,3,6)(2,4,8)(5,9,13)(7,10,15)(11,16,22)(12,17,24)(14,19,18)(20,25,31)
     (21,26,33)(23,28,36)(27,34,35)(29,37,45)(30,38,46)(32,40,49)(39,47,48)
     (41,50,58)(42,51,60)(43,52,62)(44,53,64)(54,65,77)(55,66,79)(56,67,81)
     (57,68,83)(59,70,86)(61,72,89)(63,74,92)(69,84,85)(71,87,105)(73,90,91)
     (75,93,111)(76,94,113)(78,96,116)(80,98,119)(82,100,122)(88,106,127)(95,
     114,115)(97,117,137)(99,120,121)(101,123,143)(102,124,145)(103,125,147)
     (104,126,149)(107,128,152)(108,129,154)(109,130,156)(110,131,158)(112,
     132,159)(118,138,164)(133,160,187)(134,161,189)(135,162,191)(136,163,193)
     (139,165,196)(140,166,198)(141,167,200)(142,168,202)(144,170,205)(146,
     172,208)(148,174,211)(150,176,214)(151,177,216)(153,179,219)(155,181,222)
     (157,183,225)(169,203,204)(171,206,248)(173,209,210)(175,212,253)(178,
     217,218)(180,220,261)(182,223,224)(184,226,267)(185,227,269)(186,228,271)
     (188,230,274)(190,232,277)(192,234,280)(194,236,283)(195,237,285)(197,
     239,288)(199,241,291)(201,243,294)(207,249,299)(213,254,305)(215,256,308)
     (221,262,313)(229,272,273)(231,275,325)(233,278,279)(235,281,331)(238,
     286,287)(240,289,339)(242,292,293)(244,295,345)(245,296,347)(246,297,349)
     (247,298,351)(250,300,354)(251,301,356)(252,302,358)(255,306,307)(257,
     309,364)(258,310,366)(259,311,368)(260,312,370)(263,314,373)(264,315,375)
     (265,316,377)(266,317,379)(268,319,382)(270,321,385)(276,326,389)(282,
     332,396)(284,334,399)(290,340,404)(303,359,304)(318,380,381)(320,383,384)
     (322,386,449)(323,387,451)(324,388,453)(327,390,456)(328,391,458)(329,
     392,460)(330,393,462)(333,397,398)(335,400,468)(336,401,470)(337,402,472)
     (338,403,474)(341,405,477)(342,406,479)(343,407,481)(344,408,483)(346,
     410,486)(348,412,489)(350,414,492)(352,416,495)(353,417,497)(355,419,500)
     (357,421,503)(360,424,505)(361,425,507)(362,426,509)(363,427,443)(365,
     429,513)(367,431,516)(369,433,519)(371,435,522)(372,436,524)(374,438,527)
     (376,440,530)(378,442,533)(394,463,395)(409,484,485)(411,487,574)(413,
     490,491)(415,493,580)(418,498,499)(420,501,588)(422,504,423)(428,511,512)
     (430,514,599)(432,517,518)(434,520,605)(437,525,526)(439,528,613)(441,
     531,532)(444,534,619)(445,535,621)(446,536,623)(447,537,448)(450,539,626)
     (452,541,629)(454,543,632)(455,544,634)(457,546,637)(459,548,640)(461,
     550,643)(464,552,646)(465,553,648)(466,554,650)(467,555,652)(469,557,655)
     (471,559,658)(473,561,661)(475,563,664)(476,564,666)(478,566,669)(480,
     568,672)(482,570,675)(488,575,679)(494,581,686)(496,583,689)(502,589,694)
     (506,591,697)(508,593,700)(510,595,703)(515,600,707)(521,606,714)(523,
     608,717)(529,614,722)(538,624,731)(540,627,628)(542,630,737)(545,635,636)
     (547,638,745)(549,641,642)(551,644,751)(556,653,654)(558,656,763)(560,
     659,660)(562,662,769)(565,667,668)(567,670,777)(569,673,674)(571,676,783)
     (572,677,785)(573,678,787)(576,680,790)(577,681,792)(578,682,794)(579,
     683,796)(582,687,688)(584,690,801)(585,691,803)(586,692,805)(587,693,807)
     (590,695,696)(592,698,812)(594,701,702)(596,704,817)(597,705,819)(598,
     706,821)(601,708,824)(602,709,826)(603,710,828)(604,711,830)(607,715,716)
     (609,718,836)(610,719,838)(611,720,840)(612,721,842)(615,723,845)(616,
     724,847)(617,725,816)(618,726,849)(620,728,852)(622,730,855)(625,732,856)
     (631,738,863)(633,740,866)(639,746,871)(645,752,877)(647,754,880)(649,
     756,883)(651,758,886)(657,764,890)(663,770,896)(665,772,899)(671,778,904)
     (684,797,685)(699,813,936)(712,831,713)(727,850,973)(729,853,854)(733,
     857,980)(734,858,982)(735,859,984)(736,860,986)(739,864,865)(741,867,991)
     (742,868,993)(743,869,995)(744,870,997)(747,872,1000)(748,873,1002)(749,
     874,782)(750,781,906)(753,878,879)(755,881,1010)(757,884,885)(759,835,
     957)(760,887,1016)(761,888,1017)(762,889,1019)(765,891,1022)(766,892,780)
     (767,779,905)(768,893,952)(771,897,898)(773,900,1030)(774,901,1032)(775,
     902,1034)(776,903,1036)(784,908,1041)(786,910,1044)(788,912,1047)(789,
     913,1048)(791,915,1051)(793,917,1054)(795,919,1057)(798,922,1060)(799,
     923,1062)(800,924,1064)(802,926,1067)(804,928,1070)(806,930,1073)(808,
     932,1076)(809,933,1078)(810,934,1080)(811,935,1082)(814,937,1085)(815,
     938,1087)(818,940,1090)(820,942,1093)(822,944,1096)(823,945,1098)(825,
     947,1101)(827,949,1104)(829,951,1107)(832,954,1110)(833,955,1112)(834,
     956,1114)(837,959,1118)(839,961,1121)(841,963,1124)(843,965,1127)(844,
     966,1129)(846,968,1132)(848,970,1135)(851,974,1138)(861,987,862)(875,
     1004,1165)(876,1005,1166)(882,1011,1171)(894,1025,895)(907,1039,1199)
     (909,1042,1043)(911,1045,1204)(914,1049,1050)(916,1052,1211)(918,1055,
     1056)(920,1058,1216)(921,1059,1218)(925,1065,1066)(927,1068,1227)(929,
     1071,1072)(931,1074,1231)(939,1088,1245)(941,1091,1092)(943,1094,1251)
     (946,1099,1100)(948,1102,1258)(950,1105,1106)(953,1108,1264)(958,1116,
     1117)(960,1119,1275)(962,1122,1123)(964,1125,1281)(967,1130,1131)(969,
     1133,1289)(971,1136,1293)(972,1137,1295)(975,1139,1297)(976,1140,1299)
     (977,1141,1301)(978,1142,1303)(979,1143,1305)(981,1145,1307)(983,1146,
     1309)(985,1148,1312)(988,1150,1315)(989,1151,1316)(990,1152,1318)(992,
     1154,1321)(994,1156,1324)(996,1158,1327)(998,1160,1330)(999,1081,1237)
     (1001,1162,1333)(1003,1164,1336)(1006,1167,1339)(1007,1168,1341)(1008,
     1169,1343)(1009,1170,1345)(1012,1172,1347)(1013,1173,1349)(1014,1174,
     1351)(1015,1175,1353)(1018,1177,1356)(1020,1179,1359)(1021,1180,1361)
     (1023,1182,1364)(1024,1183,1366)(1026,1185,1369)(1027,1186,1371)(1028,
     1187,1283)(1029,1188,1373)(1031,1190,1376)(1033,1192,1378)(1035,1194,
     1381)(1037,1196,1384)(1038,1197,1365)(1040,1200,1387)(1046,1205,1391)
     (1053,1212,1395)(1061,1220,1403)(1063,1222,1406)(1069,1228,1308)(1075,
     1232,1414)(1077,1233,1415)(1079,1235,1418)(1083,1239,1423)(1084,1240,
     1425)(1086,1242,1428)(1089,1246,1431)(1095,1252,1346)(1097,1254,1439)
     (1103,1259,1443)(1109,1265,1210)(1111,1267,1452)(1113,1269,1448)(1115,
     1271,1352)(1120,1276,1460)(1126,1282,1372)(1128,1284,1466)(1134,1290,
     1471)(1144,1280,1306)(1147,1310,1311)(1149,1313,1489)(1153,1319,1320)
     (1155,1322,1497)(1157,1325,1326)(1159,1328,1502)(1161,1331,1332)(1163,
     1334,1504)(1176,1354,1355)(1178,1357,1523)(1181,1362,1363)(1184,1367,
     1530)(1189,1374,1375)(1191,1377,1537)(1193,1379,1380)(1195,1382,1542)
     (1198,1386,1547)(1201,1388,1550)(1202,1389,1436)(1203,1390,1298)(1206,
     1392,1207)(1208,1393,1555)(1209,1394,1557)(1213,1396,1560)(1214,1397,
     1562)(1215,1398,1564)(1217,1400,1567)(1219,1401,1402)(1221,1404,1571)
     (1223,1407,1224)(1225,1408,1576)(1226,1409,1578)(1229,1410,1580)(1230,
     1411,1582)(1234,1416,1587)(1236,1419,1420)(1238,1421,1590)(1241,1426,
     1427)(1243,1429,1598)(1244,1430,1600)(1247,1432,1603)(1248,1433,1605)
     (1249,1434,1607)(1250,1435,1551)(1253,1437,1438)(1255,1440,1611)(1256,
     1441,1612)(1257,1442,1614)(1260,1444,1617)(1261,1445,1619)(1262,1446,
     1529)(1263,1447,1621)(1266,1450,1451)(1268,1453,1623)(1270,1455,1456)
     (1272,1457,1626)(1273,1458,1628)(1274,1459,1629)(1277,1461,1632)(1278,
     1462,1634)(1279,1463,1636)(1285,1467,1638)(1286,1468,1640)(1287,1469,
     1642)(1288,1470,1644)(1291,1472,1647)(1292,1473,1648)(1294,1475,1651)
     (1296,1477,1654)(1300,1479,1657)(1302,1480,1658)(1304,1482,1661)(1314,
     1490,1669)(1317,1493,1673)(1323,1498,1558)(1329,1501,1678)(1335,1505,
     1680)(1337,1507,1683)(1338,1508,1685)(1340,1510,1687)(1342,1512,1689)
     (1344,1514,1692)(1348,1517,1696)(1350,1519,1699)(1358,1524,1704)(1360,
     1526,1707)(1368,1531,1711)(1370,1533,1714)(1383,1543,1723)(1385,1545,
     1726)(1399,1565,1566)(1405,1572,1747)(1412,1583,1413)(1417,1588,1527)
     (1422,1591,1762)(1424,1593,1765)(1449,1454,1624)(1464,1637,1465)(1474,
     1649,1650)(1476,1652,1815)(1478,1655,1819)(1481,1659,1660)(1483,1662,
     1825)(1484,1663,1579)(1485,1664,1827)(1486,1665,1829)(1487,1666,1488)
     (1491,1670,1568)(1492,1671,1672)(1494,1674,1838)(1495,1675,1840)(1496,
     1676,1842)(1499,1622,1790)(1500,1677,1844)(1503,1679,1847)(1506,1681,
     1850)(1509,1540,1686)(1511,1688,1856)(1513,1690,1691)(1515,1693,1609)
     (1516,1694,1695)(1518,1697,1863)(1520,1700,1867)(1521,1701,1869)(1522,
     1656,1820)(1525,1705,1706)(1528,1708,1875)(1532,1712,1713)(1534,1715,
     1881)(1535,1716,1883)(1536,1717,1885)(1538,1718,1887)(1539,1719,1889)
     (1541,1720,1890)(1544,1724,1725)(1546,1727,1895)(1548,1729,1898)(1549,
     1730,1900)(1552,1732,1903)(1553,1733,1905)(1554,1734,1906)(1556,1736,
     1909)(1559,1737,1910)(1561,1739,1911)(1563,1741,1914)(1569,1745,1918)
     (1570,1746,1920)(1573,1748,1923)(1574,1749,1925)(1575,1750,1926)(1577,
     1752,1929)(1581,1610,1780)(1584,1756,1933)(1585,1757,1935)(1586,1758,
     1874)(1589,1759,1938)(1592,1763,1764)(1594,1766,1944)(1595,1767,1946)
     (1596,1768,1947)(1597,1769,1949)(1599,1770,1950)(1601,1772,1953)(1602,
     1773,1738)(1604,1775,1956)(1606,1777,1959)(1608,1779,1962)(1613,1783,
     1966)(1615,1785,1969)(1616,1786,1618)(1620,1788,1972)(1625,1791,1976)
     (1627,1793,1978)(1630,1796,1981)(1631,1797,1983)(1633,1799,1985)(1635,
     1800,1986)(1639,1803,1990)(1641,1805,1992)(1643,1807,1995)(1645,1809,
     1997)(1646,1810,1999)(1653,1816,2006)(1667,1831,2018)(1668,1832,2019)
     (1682,1851,2034)(1684,1853,2037)(1698,1864,2045)(1702,1870,1703)(1709,
     1876,2054)(1710,1877,2055)(1721,1891,1722)(1728,1896,2072)(1731,1901,
     1860)(1735,1907,2080)(1740,1912,2086)(1742,1915,1743)(1744,1916,2091)
     (1751,1927,1928)(1753,1930,2104)(1754,1859,2042)(1755,1931,2106)(1760,
     1939,1761)(1771,1951,2122)(1774,1954,1955)(1776,1957,2128)(1778,1960,
     1961)(1781,1963,2134)(1782,1964,1965)(1784,1967,2136)(1787,1971,2140)
     (1789,1973,1975)(1792,1977,2146)(1794,1979,1795)(1798,1892,1984)(1801,
     1987,2152)(1802,1988,1989)(1804,1888,2065)(1806,1993,1994)(1808,1841,
     2027)(1811,2000,2164)(1812,2001,2165)(1813,2002,2167)(1814,2003,2169)
     (1817,1904,1902)(1818,2007,2173)(1821,2008,2174)(1822,2009,2176)(1823,
     2010,2178)(1824,2011,2180)(1826,2012,2181)(1828,2014,2184)(1830,2016,
     2186)(1833,2020,2190)(1834,2021,2192)(1835,2022,2194)(1836,2023,1837)
     (1839,2025,2198)(1843,2028,2202)(1845,2030,1940)(1846,1880,2058)(1848,
     2032,2207)(1849,2033,2071)(1852,2035,2036)(1854,2038,2130)(1855,2039,
     2213)(1857,2040,2215)(1858,2041,2217)(1861,2043,2220)(1862,2044,2222)
     (1865,2046,2225)(1866,2047,2227)(1868,2048,2228)(1871,2050,2231)(1872,
     2051,2233)(1873,2052,2235)(1878,2056,2239)(1879,2057,2241)(1882,2060,
     2079)(1884,2062,2247)(1886,2063,2248)(1893,2068,2250)(1894,2069,2252)
     (1897,2073,2255)(1899,2075,2258)(1908,2081,2262)(1913,2087,2266)(1917,
     2092,2272)(1919,2094,2275)(1921,2096,2277)(1922,2097,2279)(1924,2099,
     1948)(1932,2107,2289)(1934,2109,2292)(1936,2111,2295)(1937,2112,2296)
     (1941,2114,2299)(1942,2115,2301)(1943,2116,2303)(1945,2118,2306)(1952,
     2123,2311)(1958,2129,2212)(1968,2137,2320)(1970,2139,2323)(1974,2143,
     2327)(1980,2148,2332)(1982,2150,2335)(1991,2155,2064)(1996,2159,2341)
     (1998,2161,2344)(2004,2170,2005)(2013,2182,2183)(2015,2185,2348)(2017,
     2187,2369)(2024,2196,2378)(2026,2199,2200)(2029,2203,2204)(2031,2205,
     2385)(2049,2229,2405)(2053,2236,2412)(2059,2243,2244)(2061,2245,2420)
     (2066,2249,2211)(2067,2210,2390)(2074,2256,2257)(2076,2259,2429)(2077,
     2260,2431)(2078,2261,2419)(2082,2263,2326)(2083,2264,2436)(2084,2124,
     2312)(2085,2265,2438)(2088,2267,2407)(2089,2268,2441)(2090,2269,2443)
     (2093,2273,2274)(2095,2276,2449)(2098,2280,2281)(2100,2282,2454)(2101,
     2283,2456)(2102,2284,2458)(2103,2285,2460)(2105,2286,2462)(2108,2290,
     2291)(2110,2293,2294)(2113,2297,2153)(2117,2304,2305)(2119,2307,2453)
     (2120,2308,2479)(2121,2162,2345)(2125,2313,2483)(2126,2314,2485)(2127,
     2315,2487)(2131,2316,2489)(2132,2317,2172)(2133,2151,2336)(2135,2209,
     2389)(2138,2321,2322)(2141,2324,2496)(2142,2325,2497)(2144,2328,2226)
     (2145,2329,2500)(2147,2330,2331)(2149,2333,2334)(2154,2337,2505)(2156,
     2338,2507)(2157,2339,2508)(2158,2340,2435)(2160,2342,2343)(2163,2346,
     2465)(2166,2349,2517)(2168,2351,2520)(2171,2354,2432)(2175,2357,2238)
     (2177,2359,2529)(2179,2361,2531)(2188,2370,2539)(2189,2371,2541)(2191,
     2373,2544)(2193,2270,2444)(2195,2376,2547)(2197,2379,2548)(2201,2381,
     2549)(2206,2386,2555)(2208,2388,2558)(2214,2391,2560)(2216,2393,2563)
     (2218,2395,2461)(2219,2396,2565)(2221,2398,2568)(2223,2399,2569)(2224,
     2400,2571)(2230,2406,2440)(2232,2408,2377)(2234,2410,2579)(2237,2413,
     2583)(2240,2415,2586)(2242,2417,2588)(2246,2421,2589)(2251,2302,2473)
     (2253,2425,2254)(2271,2374,2545)(2278,2451,2610)(2287,2463,2618)(2288,
     2464,2619)(2298,2383,2551)(2300,2471,2375)(2309,2480,2310)(2318,2491,
     2319)(2347,2515,2367)(2350,2518,2519)(2352,2521,2660)(2353,2522,2602)
     (2355,2524,2404)(2356,2525,2526)(2358,2527,2528)(2360,2478,2631)(2362,
     2532,2418)(2363,2533,2669)(2364,2506,2649)(2365,2534,2670)(2366,2535,
     2516)(2368,2536,2672)(2372,2542,2543)(2380,2433,2598)(2382,2550,2394)
     (2384,2552,2679)(2387,2556,2557)(2392,2561,2682)(2397,2566,2567)(2401,
     2572,2499)(2402,2573,2691)(2403,2574,2693)(2409,2577,2696)(2411,2580,
     2699)(2414,2584,2585)(2416,2476,2629)(2422,2426,2592)(2423,2590,2488)
     (2424,2591,2474)(2427,2593,2708)(2428,2594,2674)(2430,2596,2658)(2434,
     2599,2439)(2437,2600,2616)(2442,2601,2715)(2445,2604,2718)(2446,2605,
     2720)(2447,2606,2722)(2448,2607,2724)(2450,2608,2609)(2452,2611,2727)
     (2455,2613,2729)(2457,2614,2681)(2459,2486,2484)(2466,2620,2733)(2467,
     2621,2735)(2468,2622,2737)(2469,2623,2738)(2470,2624,2740)(2472,2626,
     2627)(2475,2628,2704)(2477,2630,2744)(2481,2634,2748)(2482,2635,2714)
     (2490,2638,2752)(2492,2640,2755)(2493,2641,2757)(2494,2642,2495)(2498,
     2644,2761)(2501,2645,2762)(2502,2646,2764)(2503,2647,2726)(2504,2648,
     2766)(2509,2652,2768)(2510,2653,2770)(2511,2654,2772)(2512,2655,2774)
     (2513,2656,2776)(2514,2632,2745)(2523,2662,2779)(2530,2666,2783)(2537,
     2639,2753)(2538,2673,2540)(2546,2625,2741)(2553,2680,2554)(2559,2659,
     2778)(2562,2683,2789)(2564,2597,2712)(2570,2687,2792)(2575,2694,2797)
     (2576,2695,2798)(2578,2697,2799)(2581,2700,2802)(2582,2701,2804)(2587,
     2703,2806)(2595,2710,2711)(2603,2716,2813)(2612,2671,2728)(2615,2636,
     2750)(2617,2730,2821)(2633,2746,2831)(2637,2751,2837)(2643,2759,2843)
     (2650,2767,2651)(2657,2777,2684)(2661,2690,2794)(2663,2780,2862)(2664,
     2781,2864)(2665,2782,2866)(2667,2763,2847)(2668,2769,2713)(2675,2707,
     2808)(2676,2786,2868)(2677,2787,2869)(2678,2743,2829)(2685,2702,2805)
     (2686,2790,2791)(2688,2793,2872)(2689,2773,2855)(2692,2795,2874)(2698,
     2800,2878)(2705,2807,2882)(2706,2725,2819)(2709,2810,2809)(2717,2814,
     2865)(2719,2803,2880)(2721,2816,2871)(2723,2818,2885)(2731,2754,2784)
     (2732,2822,2886)(2734,2824,2888)(2736,2825,2858)(2739,2827,2891)(2742,
     2828,2892)(2747,2832,2894)(2749,2834,2820)(2756,2840,2839)(2758,2841,
     2833)(2760,2844,2899)(2765,2849,2848)(2771,2853,2846)(2775,2857,2906)
     (2785,2838,2897)(2788,2870,2817)(2796,2875,2863)(2801,2879,2893)(2811,
     2883,2859)(2812,2873,2910)(2815,2877,2913)(2823,2887,2909)(2826,2890,
     2850)(2830,2889,2914)(2835,2895,2851)(2836,2896,2861)(2842,2898,2916)
     (2845,2900,2918)(2852,2901,2902)(2854,2903,2919)(2856,2904,2905)(2860,
     2907,2881)(2867,2908,2876)(2884,2915,2922)(2911,2920,2925)(2912,2921,
     2924)(2917,2923,2926);