509, 1021, 3, 515, 259, 771, 131, 643, 387, 899, 67, 579, 323, 835, 195,   707, 451, 963, 35, 547, 291, 803, 163, 675, 419, 931, 99, 611, 355, 867,   227, 739, 483, 995, 19, 531, 275, 787, 147, 659, 403, 915, 83, 595, 339,   851, 211, 723, 467, 979, 51, 563, 307, 819, 179, 691, 435, 947, 115, 627,   371, 883, 243, 755, 499, 1011, 11, 523, 267, 779, 139, 651, 395, 907, 75,   587, 331, 843, 203, 715, 459, 971, 43, 555, 299, 811, 171, 683, 427, 939,   107, 619, 363, 875, 235, 747, 491, 1003, 27, 539, 283, 795, 155, 667, 411,   923, 91, 603, 347, 859, 219, 731, 475, 987, 59, 571, 315, 827, 187, 699,   443, 955, 123, 635, 379, 891, 251, 763, 507, 1019, 7, 519, 263, 775, 135,   647, 391, 903, 71, 583, 327, 839, 199, 711, 455, 967, 39, 551, 295, 807,   167, 679, 423, 935, 103, 615, 359, 871, 231, 743, 487, 999, 23, 535, 279,   791, 151, 663, 407, 919, 87, 599, 343, 855, 215, 727, 471, 983, 55, 567,   311, 823, 183, 695, 439, 951, 119, 631, 375, 887, 247, 759, 503, 1015, 15,   527, 271, 783, 143, 655, 399, 911, 79, 591, 335, 847, 207, 719, 463, 975,   47, 559, 303, 815, 175, 687, 431, 943, 111, 623, 367, 879, 239, 751, 495,   1007, 31, 543, 287, 799, 159, 671, 415, 927, 95, 607, 351, 863, 223, 735,   479, 991, 63, 575, 319, 831, 191, 703, 447, 959, 127, 639, 383, 895, 255,   767, 511, 1023}; static const int  p2048[2048] =  {0, 1024, 512, 1536, 256, 1280, 768, 1792, 128, 1152, 640, 1664, 384, 1408,   896, 1920, 64, 1088, 576, 1600, 320, 1344, 832, 1856, 192, 1216, 704, 1728,   448, 1472, 960, 1984, 32, 1056, 544, 1568, 288, 1312, 800, 1824, 160, 1184,   672, 1696, 416, 1440, 928, 1952, 96, 1120, 608, 1632, 352, 1376, 864, 1888,   224, 1248, 736, 1760, 480, 1504, 992, 2016, 16, 1040, 528, 1552, 272, 1296,   784, 1808, 144, 1168, 656, 1680, 400, 1424, 912, 1936, 80, 1104, 592, 1616,   336, 1360, 848, 1872, 208, 1232, 720, 1744, 464, 1488, 976, 2000, 48, 1072,   560, 1584, 304, 1328, 816, 1840, 176, 1200, 688, 1712, 432, 1456, 944,   1968, 112, 1136, 624, 1648, 368, 1392, 880, 1904, 240, 1264, 752, 1776,   496, 1520, 1008, 2032, 8, 1032, 520, 1544, 264, 1288, 776, 1800, 136, 1160,   648, 1672, 392, 1416, 904, 1928, 72, 1096, 584, 1608, 328, 1352, 840, 1864,   200, 1224, 712, 1736, 456, 1480, 968, 1992, 40, 1064, 552, 1576, 296, 1320,   808, 1832, 168, 1192, 680, 1704, 424, 1448, 936, 1960, 104, 1128, 616,   1640, 360, 1384, 872, 1896, 232, 1256, 744, 1768, 488, 1512, 1000, 2024,   24, 1048, 536, 1560, 280, 1304, 792, 1816, 152, 1176, 664, 1688, 408, 1432,   920, 1944, 88, 1112, 600, 1624, 344, 1368, 856, 1880, 216, 1240, 728, 1752,   472, 1496, 984, 2008, 56, 1080, 568, 1592, 312, 1336, 824, 1848, 184, 1208,   696, 1720, 440, 1464, 952, 1976, 120, 1144, 632, 1656, 376, 1400, 888,   1912, 248, 1272, 760, 1784, 504, 1528, 1016, 2040, 4, 1028, 516, 1540, 260,   1284, 772, 1796, 132, 1156, 644, 1668, 388, 1412, 900, 1924, 68, 1092, 580,   1604, 324, 1348, 836, 1860, 196, 1220, 708, 1732, 452, 1476, 964, 1988, 36,   1060, 548, 1572, 292, 1316, 804, 1828, 164, 1188, 676, 1700, 420, 1444,   932, 1956, 100, 1124, 612, 1636, 356, 1380, 868, 1892, 228, 1252, 740,   1764, 484, 1508, 996, 2020, 20, 1044, 532, 1556, 276, 1300, 788, 1812, 148,   1172, 660, 1684, 404, 1428, 916, 1940, 84, 1108, 596, 1620, 340, 1364, 852,   1876, 212, 1236, 724, 1748, 468, 1492, 980, 2004, 52, 1076, 564, 1588, 308,   1332, 820, 1844, 180, 1204, 692, 1716, 436, 1460, 948, 1972, 116, 1140,   628, 1652, 372, 1396, 884, 1908, 244, 1268, 756, 1780, 500, 1524, 1012,   2036, 12, 1036, 524, 1548, 268, 1292, 780, 1804, 140, 1164, 652, 1676, 396,   1420, 908, 1932, 76, 1100, 588, 1612, 332, 1356, 844, 1868, 204, 1228, 716,   1740, 460, 1484, 972, 1996, 44, 1068, 556, 1580, 300, 1324, 812, 1836, 172,   1196, 684, 1708, 428, 1452, 940, 1964, 108, 1132, 620, 1644, 364, 1388,   876, 1900, 236, 1260, 748, 1772, 492, 1516, 1004, 2028, 28, 1052, 540,   1564, 284, 1308, 796, 1820, 156, 1180, 668, 1692, 412, 1436, 924, 1948, 92,   1116, 604, 1628, 348, 1372, 860, 1884, 220, 1244, 732, 1756, 476, 1500,   988, 2012, 60, 1084, 572, 1596, 316, 1340, 828, 1852, 188, 1212, 700, 1724,   444, 1468, 956, 1980, 124, 1148, 636, 1660, 380, 1404, 892, 1916, 252,   1276, 764, 1788, 508, 1532, 1020, 2044, 2, 1026, 514, 1538, 258, 1282, 770,   1794, 130, 1154, 642, 1666, 386, 1410, 898, 1922, 66, 1090, 578, 1602, 322,   1346, 834, 1858, 194, 1218, 706, 1730, 450, 1474, 962, 1986, 34, 1058, 546,   1570, 290, 1314, 802, 1826, 162, 1186, 674, 1698, 418, 1442, 930, 1954, 98,   1122, 610, 1634, 354, 1378, 866, 1890, 226, 1250, 738, 1762, 482, 1506,   994, 2018, 18, 1042, 530, 1554, 274, 1298, 786, 1810, 146, 1170, 658, 1682,   402, 1426, 914, 1938, 82, 1106, 594, 1618, 338, 1362, 850, 1874, 210, 1234,   722, 1746, 466, 1490, 978, 2002, 50, 1074, 562, 1586, 306, 1330, 818, 1842,   178, 1202, 690, 1714, 434, 1458, 946, 1970, 114, 1138, 626, 1650, 370,   1394, 882, 1906, 242, 1266, 754, 1778, 498, 1522, 1010, 2034, 10, 1034,   522, 1546, 266, 1290, 778, 1802, 138, 1162, 650, 1674, 394, 1418, 906,   1930, 74, 1098, 586, 1610, 330, 1354, 842, 1866, 202, 1226, 714, 1738, 458,   1482, 970, 1994, 42, 1066, 554, 1578, 298, 1322, 810, 1834, 170, 1194, 682,   1706, 426, 1450, 938, 1962, 106, 1130, 618, 1642, 362, 1386, 874, 1898,   234, 1258, 746, 1770, 490, 1514, 1002, 2026, 26, 1050, 538, 1562, 282,   1306, 794, 1818, 154, 1178, 666, 1690, 410, 1434, 922, 1946, 90, 1114, 602,   1626, 346, 1370, 858, 1882, 218, 1242, 730, 1754, 474, 1498, 986, 2010, 58,   1082, 570, 1594, 314, 1338, 826, 1850, 186, 1210, 698, 1722, 442, 1466,   954, 1978, 122, 1146, 634, 1658, 378, 1402, 890, 1914, 250, 1274, 762,   1786, 506, 1530, 1018, 2042, 6, 1030, 518, 1542, 262, 1286, 774, 1798, 134,   1158, 646, 1670, 390, 1414, 902, 1926, 70, 1094, 582, 1606, 326, 1350, 838,   1862, 198, 1222, 710, 1734, 454, 1478, 966, 1990, 38, 1062, 550, 1574, 294,   1318, 806, 1830, 166, 1190, 678, 1702, 422, 1446, 934, 1958, 102, 1126,   614, 1638, 358, 1382, 870, 1894, 230, 1254, 742, 1766, 486, 1510, 998,   2022, 22, 1046, 534, 1558, 278, 1302, 790, 1814, 150, 1174, 662, 1686, 406,   1430, 918, 1942, 86, 1110, 598, 1622, 342, 1366, 854, 1878, 214, 1238, 726,   1750, 470, 1494, 982, 2006, 54, 1078, 566, 1590, 310, 1334, 822, 1846, 182,   1206, 694, 1718, 438, 1462, 950, 1974, 118, 1142, 630, 1654, 374, 1398,   886, 1910, 246, 1270, 758, 1782, 502, 1526, 1014, 2038, 14, 1038, 526,   1550, 270, 1294, 782, 1806, 142, 1166, 654, 1678, 398, 1422, 910, 1934, 78,   1102, 590, 1614, 334, 1358, 846, 1870, 206, 1230, 718, 1742, 462, 1486,   974, 1998, 46, 1070, 558, 1582, 302, 1326, 814, 1838, 174, 1198, 686, 1710,   430, 1454, 942, 1966, 110, 1134, 622, 1646, 366, 1390, 878, 1902, 238,   1262, 750, 1774, 494, 1518, 1006, 2030, 30, 1054, 542, 1566, 286, 1310,   798, 1822, 158, 1182, 670, 1694, 414, 1438, 926, 1950, 94, 1118, 606, 1630,   350, 1374, 862, 1886, 222, 1246, 734, 1758, 478, 1502, 990, 2014, 62, 1086,   574, 1598, 318, 1342, 830, 1854, 190, 1214, 702, 1726, 446, 1470, 958,   1982, 126, 1150, 638, 1662, 382, 1406, 894, 1918, 254, 1278, 766, 1790,   510, 1534, 1022, 2046, 1, 1025, 513, 1537, 257, 1281, 769, 1793, 129, 1153,   641, 1665, 385, 1409, 897, 1921, 65, 1089, 577, 1601, 321, 1345, 833, 1857,   193, 1217, 705, 1729, 449, 1473, 961, 1985, 33, 1057, 545, 1569, 289, 1313,   801, 1825, 161, 1185, 673, 1697, 417, 1441, 929, 1953, 97, 1121, 609, 1633,   353, 1377, 865, 1889, 225, 1249, 737, 1761, 481, 1505, 993, 2017, 17, 1041,   529, 1553, 273, 1297, 785, 1809, 145, 1169, 657, 1681, 401, 1425, 913,   1937, 81, 1105, 593, 1617, 337, 1361, 849, 1873, 209, 1233, 721, 1745, 465,   1489, 977, 2001, 49, 1073, 561, 1585, 305, 1329, 817, 1841, 177, 1201, 689,   1713, 433, 1457, 945, 1969, 113, 1137, 625, 1649, 369, 1393, 881, 1905,   241, 1265, 753, 1777, 497, 1521, 1009, 2033, 9, 1033, 521, 1545, 265, 1289,   777, 1801, 137, 1161, 649, 1673, 393, 1417, 905, 1929, 73, 1097, 585, 1609,   329, 1353, 841, 1865, 201, 1225, 713, 1737, 457, 1481, 969, 1993, 41, 1065,   553, 1577, 297, 1321, 809, 1833, 169, 1193, 681, 1705, 425, 1449, 937,   1961, 105, 1129, 617, 1641, 361, 1385, 873, 1897, 233, 1257, 745, 1769,   489, 1513, 1001, 2025, 25, 1049, 537, 1561, 281, 1305, 793, 1817, 153,   1177, 665, 1689, 409, 1433, 921, 1945, 89, 1113, 601, 1625, 345, 1369, 857,   1881, 217, 1241, 729, 1753, 473, 1497, 985, 2009, 57, 1081, 569, 1593, 313,   1337, 825, 1849, 185, 1209, 697, 1721, 441, 1465, 953, 1977, 121, 1145,   633, 1657, 377, 1401, 889, 1913, 249, 1273, 761, 1785, 505, 1529, 1017,   2041, 5, 1029, 517, 1541, 261, 1285, 773, 1797, 133, 1157, 645, 1669, 389,   1413, 901, 1925, 69, 1093, 581, 1605, 325, 1349, 837, 1861, 197, 1221, 709,   1733, 453, 1477, 965, 1989, 37, 1061, 549, 1573, 293, 1317, 805, 1829, 165,   1189, 677, 1701, 421, 1445, 933, 1957, 101, 1125, 613, 1637, 357, 1381,   869, 1893, 229, 1253, 741, 1765, 485, 1509, 997, 2021, 21, 1045, 533, 1557,   277, 1301, 789, 1813, 149, 1173, 661, 1685, 405, 1429, 917, 1941, 85, 1109,   597, 1621, 341, 1365, 853, 1877, 213, 1237, 725, 1749, 469, 1493, 981,   2005, 53, 1077, 565, 1589, 309, 1333, 821, 1845, 181, 1205, 693, 1717, 437,   1461, 949, 1973, 117, 1141, 629, 1653, 373, 1397, 885, 1909, 245, 1269,   757, 1781, 501, 1525, 1013, 2037, 13, 1037, 525, 1549, 269, 1293, 781,   1805, 141, 1165, 653, 1677, 397, 1421, 909, 1933, 77, 1101, 589, 1613, 333,   1357, 845, 1869, 205, 1229, 717, 1741, 461, 1485, 973, 1997, 45, 1069, 557,   1581, 301, 1325, 813, 1837, 173, 1197, 685, 1709, 429, 1453, 941, 1965,   109, 1133, 621, 1645, 365, 1389, 877, 1901, 237, 1261, 749, 1773, 493,   1517, 1005, 2029, 29, 1053, 541, 1565, 285, 1309, 797, 1821, 157, 1181,   669, 1693, 413, 1437, 925, 1949, 93, 1117, 605, 1629, 349, 1373, 861, 1885,   221, 1245, 733, 1757, 477, 1501, 989, 2013, 61, 1085, 573, 1597, 317, 1341,   829, 1853, 189, 1213, 701, 1725, 445, 1469, 957, 1981, 125, 1149, 637,   1661, 381, 1405, 893, 1917, 253, 1277, 765, 1789, 509, 1533, 1021, 2045, 3,   1027, 515, 1539, 259, 1283, 771, 1795, 131, 1155, 643, 1667, 387, 1411,   899, 1923, 67, 1091, 579, 1603, 323, 1347, 835, 1859, 195, 1219, 707, 1731,   451, 1475, 963, 1987, 35, 1059, 547, 1571, 291, 1315, 803, 1827, 163, 1187,   675, 1699, 419, 1443, 931, 1955, 99, 1123, 611, 1635, 355, 1379, 867, 1891,   227, 1251, 739, 1763, 483, 1507, 995, 2019, 19, 1043, 531, 1555, 275, 1299,   787, 1811, 147, 1171, 659, 1683, 403, 1427, 915, 1939, 83, 1107, 595, 1619,   339, 1363, 851, 1875, 211, 1235, 723, 1747, 467, 1491, 979, 2003, 51, 1075,   563, 1587, 307, 1331, 819, 1843, 179, 1203, 691, 1715, 435, 1459, 947,   1971, 115, 1139, 627, 1651, 371, 1395, 883, 1907, 243, 1267, 755, 1779,   499, 1523, 1011, 2035, 11, 1035, 523, 1547, 267, 1291, 779, 1803, 139,   1163, 651, 1675, 395, 1419, 907, 1931, 75, 1099, 587, 1611, 331, 1355, 843,   1867, 203, 1227, 715, 1739, 459, 1483, 971, 1995, 43, 1067, 555, 1579, 299,   1323, 811, 1835, 171, 1195, 683, 1707, 427, 1451, 939, 1963, 107, 1131,   619, 1643, 363, 1387, 875, 1899, 235, 1259, 747, 1771, 491, 1515, 1003,   2027, 27, 1051, 539, 1563, 283, 1307, 795, 1819, 155, 1179, 667, 1691, 411,   1435, 923, 1947, 91, 1115, 603, 1627, 347, 1371, 859, 1883, 219, 1243, 731,   1755, 475, 1499, 987, 2011, 59, 1083, 571, 1595, 315, 1339, 827, 1851, 187,   1211, 699, 1723, 443, 1467, 955, 1979, 123, 1147, 635, 1659, 379, 1403,   891, 1915, 251, 1275, 763, 1787, 507, 1531, 1019, 2043, 7, 1031, 519, 1543,   263, 1287, 775, 1799, 135, 1159, 647, 1671, 391, 1415, 903, 1927, 71, 1095,   583, 1607, 327, 1351, 839, 1863, 199, 1223, 711, 1735, 455, 1479, 967,   1991, 39, 1063, 551, 1575, 295, 1319, 807, 1831, 167, 1191, 679, 1703, 423,   1447, 935, 1959, 103, 1127, 615, 1639, 359, 1383, 871, 1895, 231, 1255,   743, 1767, 487, 1511, 999, 2023, 23, 1047, 535, 1559, 279, 1303, 791, 1815,   151, 1175, 663, 1687, 407, 1431, 919, 1943, 87, 1111, 599, 1623, 343, 1367,   855, 1879, 215, 1239, 727, 1751, 471, 1495, 983, 2007, 55, 1079, 567, 1591,   311, 1335, 823, 1847, 183, 1207, 695, 1719, 439, 1463, 951, 1975, 119,   1143, 631, 1655, 375, 1399, 887, 1911, 247, 1271, 759, 1783, 503, 1527,   1015, 2039, 15, 1039, 527, 1551, 271, 1295, 783, 1807, 143, 1167, 655,   1679, 399, 1423, 911, 1935, 79, 1103, 591, 1615, 335, 1359, 847, 1871, 207,   1231, 719, 1743, 463, 1487, 975, 1999, 47, 1071, 559, 1583, 303, 1327, 815,   1839, 175, 1199, 687, 1711, 431, 1455, 943, 1967, 111, 1135, 623, 1647,   367, 1391, 879, 1903, 239, 1263, 751, 1775, 495, 1519, 1007, 2031, 31,   1055, 543, 1567, 287, 1311, 799, 1823, 159, 1183, 671, 1695, 415, 1439,   927, 1951, 95, 1119, 607, 1631, 351, 1375, 863, 1887, 223, 1247, 735, 1759,   479, 1503, 991, 2015, 63, 1087, 575, 1599, 319, 1343, 831, 1855, 191, 1215,   703, 1727, 447, 1471, 959, 1983, 127, 1151, 639, 1663, 383, 1407, 895,   1919, 255, 1279, 767, 1791, 511, 1535, 1023, 2047}; static const int  p4096[4096] = {0, 2048, 1024, 3072, 512, 2560, 1536, 3584, 256, 2304, 1280, 3328, 768,   2816, 1792, 3840, 128, 2176, 1152, 3200, 640, 2688, 1664, 3712, 384, 2432,   1408, 3456, 896, 2944, 1920, 3968, 64, 2112, 1088, 3136, 576, 2624, 1600,   3648, 320, 2368, 1344, 3392, 832, 2880, 1856, 3904, 192, 2240, 1216, 3264,   704, 2752, 1728, 3776, 448, 2496, 1472, 3520, 960, 3008, 1984, 4032, 32,