bin1 := (1,2,5,11,23,41,69,77,47,26,14,7,3)(4,8,16,30,55,90,141,156,99,60,35,19,
     9)(6,12,24,42,70,113,171,117,74,45,44,25,13)(10,20,36,61,100,157,234,231,
     154,104,63,37,21)(15,27,49,81,130,195,287,292,198,133,84,51,28)(17,31,56,
     91,142,211,307,317,220,148,94,57,32)(18,33,58,96,151,227,328,332,230,153,
     98,59,34)(22,38,64,105,162,239,341,347,244,165,107,65,39)(29,52,85,134,
     199,293,413,422,299,202,135,86,53)(40,66,108,166,245,348,481,486,351,247,
     167,109,67)(43,71,114,172,252,357,499,508,362,256,173,115,72)(46,73,116,
     174,257,363,510,526,376,266,180,120,75)(48,78,125,187,277,393,540,475,
     342,240,163,106,79)(50,82,131,196,288,405,553,563,411,291,197,132,83)(54,
     87,136,203,300,423,576,583,426,301,205,137,88)(62,101,95,149,222,321,447,
     616,470,337,235,158,102)(68,110,168,248,352,488,664,668,491,353,249,169,
     111)(76,121,181,268,379,511,693,711,529,380,269,182,122)(80,127,190,280,
     396,543,728,735,546,397,281,191,128)(89,138,206,302,427,585,784,789,587,
     429,303,207,139)(92,143,212,308,434,595,803,806,598,436,309,213,144)(93,
     145,97,152,228,329,455,624,501,359,254,216,146)(103,159,236,251,355,494,
     672,872,649,473,339,237,160)(112,123,183,270,381,531,715,897,669,492,354,
     250,170)(118,175,215,312,338,253,358,500,679,512,364,258,176)(119,177,
     259,365,513,694,928,896,699,518,370,262,178)(124,184,272,385,489,665,881,
     657,482,349,246,204,185)(126,188,278,394,541,723,961,968,726,542,395,279,
     189)(129,192,282,398,547,737,985,990,739,548,400,283,193)(140,208,304,
     430,589,792,1061,1063,795,591,431,305,209)(147,217,314,439,601,812,1089,
     1098,817,604,440,315,218)(150,224,324,449,618,832,646,471,418,297,201,
     296,225)(155,161,238,340,474,509,691,925,860,642,467,335,232)(164,241,
     319,221,318,442,608,772,577,650,476,343,242)(179,263,371,519,701,937,
     1231,1233,939,703,520,372,264)(186,274,388,536,720,954,1254,1259,956,721,
     537,389,275)(194,284,401,549,741,994,1316,1319,997,743,550,402,285)(200,
     294,414,433,593,798,1066,972,729,763,567,415,295)(210,233,336,468,644,
     862,927,692,708,796,592,432,306)(214,310,437,599,807,1079,1412,1422,1086,
     810,600,438,311)(219,316,378,528,710,944,1240,1129,845,630,458,330,229)
     (223,322,448,617,831,1091,814,602,559,409,290,408,323)(226,325,450,619,
     833,1113,873,777,581,425,580,451,326)(243,344,477,651,493,670,899,1192,
     1164,875,653,478,345)(255,313,267,377,527,709,943,1238,1214,918,685,504,
     360)(260,366,514,695,930,1222,1080,1413,1224,932,696,515,367)(261,368,
     382,532,716,949,892,666,490,428,399,383,271)(265,373,521,487,662,887,
     1180,1526,1234,940,704,522,374)(273,386,534,718,951,1248,1592,1597,1250,
     952,719,535,387)(276,390,538,722,958,1263,1619,1567,1226,934,698,517,391)
     (286,403,551,745,999,1322,1236,942,707,525,706,552,404)(289,406,555,749,
     1004,1329,1628,1269,962,1005,750,556,407)(298,419,572,766,811,1087,1424,
     1728,1353,1025,767,573,420)(320,444,611,826,1107,1350,1023,978,733,545,
     732,612,445)(327,452,621,834,1114,1450,1380,1053,788,1052,835,622,453)
     (331,459,631,847,1131,1221,926,1220,1468,1132,848,632,460)(333,462,417,
     570,652,497,356,496,675,906,850,634,463)(334,464,635,851,1135,948,1188,
     1531,1476,1140,855,638,465)(346,479,654,876,1165,924,1218,1562,1342,1015,
     760,564,412)(350,483,620,606,441,605,819,786,586,785,882,658,484)(361,
     505,686,700,935,1227,1241,1581,1559,1215,920,687,506)(369,384,533,717,
     950,1245,1586,1941,1566,1225,933,697,516)(375,523,539,392,480,655,878,
     1169,1513,1235,941,705,524)(410,560,755,1009,1333,1703,2088,2096,1707,
     1336,1010,756,561)(416,568,764,1020,1078,1410,1792,2108,1721,1349,1021,
     765,569)(421,574,768,1026,1354,1239,1579,1878,1488,1150,865,645,469)(424,
     578,773,1033,797,1064,1303,987,738,986,1035,774,579)(435,596,804,1073,
     1404,1415,1082,808,1081,1003,748,554,566)(443,609,824,1106,1445,1704,
     1334,1275,966,725,965,825,610)(446,613,827,1108,1446,1743,1673,1307,989,
     1306,1110,828,614)(454,461,633,849,1133,1470,1520,1392,1772,1452,1116,
     836,623)(456,625,558,753,905,674,495,673,904,1198,1117,837,626)(457,627,
     838,947,714,946,1243,1583,1851,1460,1123,841,628)(466,639,588,790,1056,
     1384,1768,1571,1558,1477,1141,856,640)(472,571,643,861,1146,1230,1237,
     1578,1890,1497,1156,868,647)(485,659,883,1173,1190,898,1189,1532,1840,
     1451,1175,884,660)(498,676,907,1199,1337,1012,758,744,776,1038,1174,908,
     677)(502,680,910,929,1008,1022,813,1090,1429,1542,1202,911,681)(503,682,
     713,530,712,945,1242,1582,1572,1551,1208,914,683)(507,688,921,1178,886,
     1177,1521,1909,1933,1560,1216,922,689)(544,730,974,1286,1328,1696,1606,
     1256,955,1255,1287,975,731)(557,751,1006,1331,1699,2080,2430,2438,2086,
     1702,1332,1007,752)(562,757,1011,1228,1568,1944,2300,2176,1789,1408,1076,
     805,597)(565,761,1017,1344,1715,1577,1564,1219,1145,1480,1346,1019,762)
     (575,769,1028,1358,1734,1575,1867,1479,1144,859,1143,1031,770)(582,778,
     1040,1365,1741,1423,1809,2198,2137,1745,1366,1041,779)(584,781,1044,1370,
     1752,1573,1866,1478,1142,858,641,857,782)(590,793,1062,1186,894,667,893,
     1115,1109,1099,818,637,794)(594,800,1069,1400,1779,1717,1347,1716,1649,
     1285,973,1034,801)(603,754,846,1130,936,1229,1569,1945,2218,1824,1435,
     1094,815)(607,821,1103,1443,1833,2038,1989,1610,1258,1609,1444,1104,822)
     (615,829,1111,1447,1836,2138,1746,1688,2071,1838,1448,1112,830)(629,842,
     1124,1461,1852,1953,2157,1948,2241,1854,1462,1125,843)(636,852,1136,1472,
     1861,2132,1795,1411,1794,1863,1473,1137,853)(648,869,1157,1055,1382,1764,
     1951,1580,1467,1858,1498,1158,870)(656,661,885,1176,1519,1576,1934,1561,
     1546,1907,1517,1172,880)(663,889,1183,1529,1902,1574,1925,1547,1206,913,
     1205,1184,890)(671,901,1195,1538,1481,1147,863,1016,977,1290,1539,1196,
     902)(678,690,923,1217,1509,1167,877,1166,1508,1899,1541,1200,909)(684,
     915,1209,1552,1244,1584,1954,2302,2294,1930,1553,1210,916)(702,938,1232,
     1570,1946,1939,2193,1803,1418,1084,809,1083,919)(724,963,1271,1631,2016,
     2316,1967,1594,1249,1593,1632,1272,964)(727,969,1280,1643,2028,2373,2246,
     1924,1935,1713,1647,1283,970)(734,979,1292,1654,2037,2087,2439,2690,2390,
     2040,1655,1293,980)(736,982,1296,1660,2048,2292,1928,1550,1927,1712,1341,
     1299,983)(740,991,1310,1678,2065,1932,1557,1213,1556,1711,1340,1014,992)
     (742,995,1317,1378,1051,787,1050,1377,1759,1773,1393,1318,996)(746,1000,
     1323,1691,1390,1391,1771,2158,2100,1710,1339,1013,759)(747,1001,1325,
     1693,2074,2296,1937,1563,1936,2076,1695,1327,1002)(771,780,1042,1321,
     1690,2072,2304,1949,2262,2130,1738,1362,1032)(775,1036,1363,1739,2131,
     1791,2179,2530,2491,2135,1740,1364,1037)(783,1047,1374,1512,1901,2279,
     2574,2263,1883,1492,1757,1375,1048)(791,1058,1387,1525,1912,2285,2267,
     1885,1493,1154,867,1153,1059)(799,1067,1398,1778,2162,2082,1700,2081,
     2014,1629,1270,1399,1068)(802,1070,1401,1780,2163,2133,2419,2408,2056,
     1669,1760,1402,1071)(816,1095,1436,1826,2219,2559,2305,1950,2258,2220,
     1827,1437,1096)(820,1101,1441,1831,2225,2366,2320,1971,1596,1970,1832,
     1442,1102)(823,1030,1361,1736,2125,2391,2041,1943,2245,1865,1475,1139,
     1105)(839,1118,1453,1841,2231,1960,2182,1793,2181,2233,1842,1454,1119)
     (840,1120,1134,1471,1185,891,895,1187,1530,1915,1845,1456,1121)(844,1126,
     1463,1449,1839,1992,1612,1991,2342,2242,1855,1464,1127)(854,1100,1046,
     1373,1755,2148,2504,2297,1940,2244,1864,1474,1138)(864,1018,1345,1389,
     1060,1388,1770,1952,2306,2253,1873,1484,1148)(866,1151,1489,1860,1653,
     1742,1427,1088,1426,1813,1880,1490,1152)(871,1159,1499,1368,1043,1367,
     1747,2139,2239,1850,1891,1500,1160)(874,1039,998,1320,1689,1767,2156,
     1947,2303,2278,1897,1504,1162)(879,1170,1514,1903,1686,1687,2070,2426,
     2188,2281,1905,1515,1171)(888,1181,1527,1913,2001,1942,2299,2189,1801,
     1417,1800,1528,1182)(900,1193,1536,1918,1782,1405,1074,1324,1274,1635,
     1919,1537,1194)(903,1161,1501,1892,1730,1356,1027,1355,1729,2120,1920,
     1540,1197)(912,1203,1543,1590,1247,1589,1961,2310,2597,2289,1921,1544,
     1204)(917,1211,1554,1516,1261,957,1260,1613,1994,2295,1931,1555,1212)
     (931,1223,1565,1938,1969,1595,1968,2318,2535,2184,1797,1414,1201)(953,
     1251,1599,1976,2328,2291,1926,1549,1207,1548,1906,1602,1252)(959,1264,
     1620,1671,1305,988,1304,1670,2057,2348,2002,1621,1265)(960,1266,1623,
     2006,2354,2598,2290,1923,1545,1922,2011,1626,1267)(967,1276,1637,2020,
     2365,2659,2796,2895,2661,2368,2021,1638,1277)(971,981,1294,1656,1765,
     2154,2509,2602,2680,2384,2033,1648,1284)(976,1288,1651,2035,2309,2429,
     2725,2917,2685,2387,2036,1652,1289)(984,1300,1665,1733,2062,2414,2715,
     2840,2589,2273,2053,1666,1301)(993,1313,1682,1751,2143,2498,2793,2591,
     2274,1895,1503,1683,1314)(1024,1291,1343,1714,1383,1766,2155,2301,2604,
     2474,2114,1724,1351)(1029,1359,1685,1315,1684,2069,2424,2605,2762,2485,
     2123,1735,1360)(1045,1371,1753,1618,2000,2347,2641,2763,2458,2103,2146,
     1754,1372)(1049,1054,1381,1763,2153,2507,2249,1871,1483,1870,1837,1758,
     1376)(1057,1385,1769,1958,2298,2601,2767,2460,2104,1719,1348,1718,1386)
     (1065,1395,1775,2160,2512,2385,2681,2629,2336,1985,2161,1776,1396)(1072,
     1077,1409,1790,2177,2529,2810,2722,2425,2510,2164,1781,1403)(1075,1326,
     1694,2075,1859,1522,1910,2283,2595,2520,2170,1785,1406)(1085,1419,1804,
     1929,2293,2599,2800,2603,2527,2542,2194,1805,1420)(1092,1430,1815,2204,
     2019,2202,1812,1425,1811,2201,2206,1816,1431)(1093,1432,1817,1469,1524,
     1179,1523,1911,2284,2554,2212,1820,1433)(1097,1438,1828,2221,2230,2569,
     2638,2496,2606,2560,2223,1829,1439)(1122,1457,1846,2236,2324,1974,1598,
     1973,2322,2572,2237,1847,1458)(1128,1465,1856,1506,1163,1505,1676,1309,
     1675,2061,2243,1857,1466)(1149,1485,1835,2229,2567,2719,2417,2586,2270,
     1889,2254,1874,1486)(1155,1494,1756,2150,2147,2502,2718,2823,2558,2217,
     2268,1886,1495)(1168,1510,1900,2064,2416,2550,2210,1819,2209,2222,1908,
     1518,1511)(1191,1533,1916,2287,2024,1641,1279,1640,2023,2370,2288,1917,
     1534)(1246,1587,1959,1987,1608,1257,1607,1986,2338,2534,2286,1914,1588)
     (1253,1603,1981,2027,2372,2665,2897,2986,2865,2627,2333,1982,1604)(1262,
     1616,1998,2047,2397,2697,2731,2433,2730,2594,2282,1999,1617)(1268,1278,
     1639,2022,2369,2662,2799,2963,2888,2654,2360,2012,1627)(1273,1633,2017,
     1962,2311,2608,2846,2978,2894,2658,2363,2018,1634)(1281,1644,2029,2141,
     1748,2140,2497,2792,2905,2672,2377,2030,1645)(1282,1646,2031,2379,2675,
     2908,2832,2576,2539,2454,2099,1777,1397)(1295,1657,2042,2392,2238,1849,
     1459,1848,1535,1507,1898,2044,1658)(1297,1661,2049,2394,2043,2393,2692,
     2924,2929,2705,2401,2050,1662)(1298,1663,2051,2403,2708,2930,2815,2541,
     2192,2453,2098,1709,1664)(1302,1308,1674,2060,2413,2714,2782,2483,2122,
     2482,2126,2054,1667)(1311,1679,2066,2418,2323,2614,2746,2944,2787,2489,
     2134,2067,1680)(1312,1681,2068,2422,2721,2532,2183,1796,1808,2197,2097,
     1708,1338)(1330,1698,2079,2428,2724,2812,2533,2596,2315,2362,2015,1630,
     1650)(1335,1636,1692,2073,2240,1955,2307,2607,2845,2751,2447,2092,1705)
     (1352,1725,2115,2476,2374,2666,2575,2581,2257,1877,2256,2116,1726)(1357,
     1731,1677,2063,2415,2717,2774,2469,2773,2494,2136,1744,1732)(1369,1749,
     1993,2343,2635,2776,2470,2112,1723,2111,2467,2142,1750)(1379,1761,2151,
     2505,2798,2516,2168,1784,2167,2178,2506,2152,1762)(1394,1668,2055,2407,
     2711,2656,2890,2847,2609,2317,2511,2159,1774)(1407,1786,2171,2521,2619,
     2858,2971,2820,2549,2593,2522,2172,1787)(1416,1798,2185,1963,2312,2364,
     2388,2089,2441,2741,2536,2186,1799)(1421,1806,2195,1904,1615,1997,2346,
     2639,2842,2807,2543,2196,1807)(1428,1440,1830,2224,1894,1502,1893,2271,
     2421,2412,2508,2203,1814)(1434,1821,2213,2555,2332,2625,2622,2860,2844,
     2780,2556,2214,1822)(1455,1843,2234,2570,2350,2004,1622,2003,2349,2642,
     2571,2235,1844)(1482,1868,2247,2577,2833,2967,2811,2531,2180,2464,2578,
     2248,1869)(1487,1875,2228,1834,2227,2565,2699,2398,2698,2573,2266,2255,
     1876)(1491,1881,2259,2582,2561,2824,2973,2935,2726,2738,2583,2260,1882)
     (1496,1887,2128,1737,2127,2124,2486,2695,2843,2600,2553,2269,1888)(1585,
     1956,2308,2327,2616,2733,2434,2084,1701,2083,1825,1853,1957)(1591,1964,
     2313,2353,2643,2875,2989,2936,2727,2431,2205,2232,1965)(1600,1977,2329,
     2618,2857,2982,2892,2657,2891,2752,2621,2330,1978)(1601,1979,2331,2623,
     2862,2950,2814,2540,2191,1802,2190,2280,1980)(1605,1611,1990,2341,2634,
     2870,2797,2501,2145,2500,2149,2334,1983)(1614,1995,2344,2636,2874,2747,
     2445,2091,2444,2744,2528,2345,1996)(1624,2007,2355,2637,2830,2640,2791,
     2962,2991,2880,2647,2356,2008)(1625,2009,2357,2649,2883,2992,2968,2813,
     2538,2187,2537,2358,2010)(1642,2025,2371,2664,2716,2861,2977,2960,2920,
     2688,2389,2039,2026)(1659,2045,2395,2694,2871,2913,2961,2789,2493,2566,
     2696,2396,2046)(1672,2058,2410,2713,2932,2901,2670,2376,2669,2380,2676,
     2411,2059)(1697,2013,2361,2655,2889,2951,2795,2953,2867,2630,2337,2409,
     2078)(1706,2093,2448,2753,2644,2876,2837,2584,2261,2488,2754,2449,2094)
     (1720,2105,2144,2499,2794,2896,2934,2809,2526,2175,2525,2461,2106)(1722,
     2109,2465,2769,2633,2818,2546,2200,1810,2119,2479,2466,2110)(1727,2117,
     2477,2492,2564,2828,2923,2691,2835,2580,2252,2478,2118)(1783,2165,2513,
     2801,2645,2877,2964,2804,2515,2803,2802,2514,2166)(1788,2173,2523,2490,
     2701,2399,2700,2927,2926,2938,2808,2524,2174)(1818,2207,2547,2652,2359,
     2651,2648,2881,2900,2970,2819,2548,2208)(1823,2215,2276,1896,2275,2052,
     2405,2402,2706,2872,2822,2557,2216)(1862,2034,2314,1966,1972,2321,2613,
     2851,2952,2758,2455,2101,1879)(1872,2250,2495,2790,2918,2686,2825,2974,
     2945,2831,2766,2579,2251)(1884,2264,2129,2487,2563,2226,2562,2826,2855,
     2617,2838,2585,2265)(1975,2325,2615,2853,2914,2683,2386,2682,2475,2568,
     2663,2503,2326)(1984,2335,2628,2866,2988,2985,2887,2979,2848,2610,2723,
     2427,2077)(1988,2339,2631,2868,2990,2882,2703,2400,2702,2404,2709,2632,
     2340)(2005,2351,2620,2859,2624,2863,2983,2911,2770,2834,2660,2367,2352)
     (2032,2381,2378,2673,2854,2972,2821,2552,2211,2551,2277,2592,2382)(2085,
     2435,2734,2626,2864,2984,2987,2966,2839,2679,2910,2735,2436)(2090,2442,
     2742,2879,2850,2969,2817,2545,2199,2544,2816,2743,2443)(2095,2450,2755,
     2786,2704,2928,2995,3003,2954,2761,2784,2756,2451)(2102,2456,2759,2836,
     2976,2869,2933,2740,2440,2452,2757,2760,2457)(2107,2462,2481,2121,2480,
     2781,2958,2925,2965,2806,2519,2768,2463)(2113,2471,2777,2957,2919,2981,
     2999,2956,2775,2779,2473,2778,2472)(2169,2517,2788,2899,2668,2375,2667,
     2898,2943,2745,2942,2805,2518)(2272,2406,2710,2931,2893,2994,2996,2904,
     2940,2737,2437,2736,2588)(2319,2611,2646,2878,2650,2884,2720,2420,2587,
     2423,2712,2849,2612)(2383,2677,2909,2684,2915,2959,3000,3002,2939,2732,
     2841,2590,2678)(2432,2728,2886,2653,2885,2980,2993,2941,2739,2922,3001,
     2937,2729)(2446,2748,2946,2903,2671,2902,2916,2955,2772,2468,2771,2947,
     2749)(2459,2764,2484,2783,2689,2921,2998,2912,2997,2949,2750,2948,2765)
     (2674,2856,2829,2785,2693,2707,2873,2975,2906,2852,2687,2827,2907);