// // APPROXIMATE LIMITS // int frac[10000]={ 0, -499, -249, -333, -166, -399, -132, -294, -207, -452, -97, -197, -131, -525, -277, -295, -64, -302, -42, -253, -269, -565, -181, -278, -206, -532, -169, -139, 107, -130, 29, -290, -363, -737, -406, -418, -263, -591, -214, -144, 129, -86, 124, -153, -201, -517, -112, -201, -124, -472, -222, -285, -120, -442, -264, -450, -424, -710, -273, -333, -255, -664, -354, -329, -54, -146, 217, 85, 188, -27, 272, 83, 54, -464, -255, -314, -131, -344, -89, -331, -376, -749, -391, -530, -522, -893, -531, -490, -224, -455, -280, -503, -486, -796, -363, -316, -100, -377, -15, 42, 303, 70, 306, 46, 18, -238, 240, 225, 374, 27, 230, 105, 194, -214, -145, -458, -529, -913, -553, -600, -513, -880, -514, -469, -178, -296, 19, -159, -91, -345, -50, -248, -299, -751, -465, -446, -190, -433, -198, -456, -551, -963, -637, -740, -665, -974, -550, -416, -29, -145, 144, -72, -46, -334, -33, -125, -66, -495, -188, -217, -33, -258, 12, -216, -204, -427, 92, 110, 271, -31, 237, 183, 369, 69, 249, 84, 145, -114, 363, 345, 455, 68, 277, 161, 281, 10, 224, 16, 46, -210, 107, -77, -93, -608, -374, -392, -195, -496, -342, -685, -828, -1302, -1029, -1176, -1158, -1531, -1169, -1124, -843, -999, -806, -1111, -1172, -1563, -1216, -1254, -1121, -1407, -953, -825, -513, -640, -277, -414, -331, -522, 39, 92, 306, 25, 317, 345, 623, 394, 631, 480, 566, 329, 699, 568, 568, 74, 264, 114, 210, -35, 212, 17, 63, -218, 104, -73, -116, -577, -309, -288, -19, -243, 20, -138, -101, -393, 60, 14, 121, -165, 151, 152, 391, 132, 270, -85, -204, -594, -235, -238, -86, -430, -27, 51, 302, 62, 297, 42, 32, -235, 135, 82, 200, -156, 60, -47, 99, -268, -189, -511, -594, -973, -606, -689, -640, -1000, -612, -568, -282, -385, -19, -157, -93, -366, -52, -238, -271, -806, -586, -604, -368, -636, -412, -623, -643, -983, -711, -892, -901, -1277, -913, -871, -596, -730, -510, -778, -807, -1162, -770, -762, -620, -971, -632, -631, -432, -678, -451, -647, -607, -810, -281, -238, -48, -342, -132, -225, -89, -459, -333, -604, -622, -918, -456, -505, -404, -795, -431, -368, -120, -253, 101, -42, 49, -180, 175, 109, 206, -203, 31, 3, 226, -13, 189, -109, -220, -660, -359, -553, -578, -924, -515, -434, -102, -272, -75, -330, -357, -725, -344, -367, -229, -590, -213, -96, 214, 29, 335, 195, 305, 144, 602, 619, 794, 474, 732, 662, 843, 602, 840, 678, 747, 488, 880, 768, 765, 272, 520, 437, 609, 403, 694, 555, 662, 498, 907, 833, 916, 495, 711, 663, 862, 605, 842, 586, 502, 144, 431, 222, 166, -275, 27, -1, 181, -130, -42, -402, -514, -953, -649, -649, -511, -863, -455, -382, -108, -332, -172, -506, -605, -953, -547, -659, -610, -976, -768, -884, -754, -1073, -891, -1086, -1084, -1414, -984, -1066, -1012, -1403, -1048, -969, -664, -750, -338, -427, -265, -434, -94, -248, -249, -701, -487, -524, -318, -530, -260, -482, -501, -846, -450, -564, -518, -873, -580, -605, -365, -633, -508, -823, -887, -1255, -890, -914, -779, -1085, -757, -772, -603, -935, -778, -1124, -1216, -1540, -1111, -1151, -1031, -1390, -1159, -1260, -1154, -1502, -1357, -1603, -1605, -1931, -1518, -1494, -1327, -1684, -1275, -1191, -885, -973, -655, -850, -794, -1056, -786, -965, -982, -1435, -1127, -1082, -798, -1002, -728, -903, -901, -1199, -739, -777, -651, -928, -447, -262, 170, 105, 417, 238, 257, -52, 273, 217, 320, -85, 227, 208, 385, 136, 377, 174, 222, 19, 564, 617, 804, 530, 846, 840, 1073, 807, 999, 863, 979, 761, 1207, 1150, 1227, 810, 1012, 892, 1023, 788, 1043, 807, 808, 523, 833, 694, 713, 223, 488, 492, 694, 387, 589, 280, 168, -265, 57, -46, -2, -357, 55, 155, 523, 412, 658, 392, 378, 40, 445, 444, 619, 402, 840, 952, 1252, 1057, 1365, 1163, 1169, 916, 1330, 1249, 1332, 971, 1158, 1072, 1244, 903, 1058, 822, 828, 514, 818, 621, 546, -23, 160, 46, 176, -24, 277, 116, 202, -46, 291, 180, 221, -244, 42, 56, 308, 62, 309, 137, 142, -181, 163, -7, -7, -407, -160, -251, -91, -390, -304, -722, -892, -1313, -986, -1070, -981, -1352, -980, -940, -722, -1009, -831, -1116, -1175, -1490, -1057, -1051, -894, -1213, -944, -1020, -837, -1128, -996, -1219, -1187, -1490, -1030, -1082, -998, -1349, -976, -930, -641, -749, -391, -547, -496, -765, -449, -603, -595, -1074, -808, -775, -498, -663, -359, -544, -524, -805, -468, -613, -601, -991, -630, -586, -351, -521, -294, -576, -615, -981, -676, -764, -720, -1163, -867, -871, -669, -968, -772, -1000, -981, -1214, -697, -635, -415, -678, -478, -619, -510, -892, -792, -1072, -1113, -1432, -995, -1024, -932, -1289, -967, -969, -754, -946, -627, -821, -757, -1028, -694, -811, -759, -1164, -817, -746, -418, -584, -347, -564, -584, -948, -557, -608, -500, -722, -260, -144, 225, 90, 359, 114, 108, -250, 49, -28, 24, -368, -16, 61, 360, 141, 413, 199, 234, 24, 442, 358, 423, 3, 183, 17, 80, -242, -81, -311, -333, -689, -280, -367, -349, -817, -522, -569, -364, -537, -209, -278, -102, -255, 150, 104, 211, -173, 65, 57, 309, 41, 191, -146, -287, -712, -388, -563, -564, -980, -641, -604, -385, -599, -416, -705, -728, -1094, -787, -804, -671, -1038, -646, -594, -356, -614, -453, -793, -907, -1292, -926, -1049, -1009, -1408, -1208, -1316, -1172, -1489, -1308, -1531, -1538, -1829, -1385, -1405, -1292, -1635, -1313, -1271, -982, -1096, -706, -825, -688, -886, -607, -826, -887, -1395, -1149, -1183, -958, -1164, -883, -1114, -1155, -1530, -1144, -1222, -1177, -1511, -1093, -1002, -690, -864, -652, -850, -793, -1078, -599, -475, -183, -414, -1, 77, 360, 151, 419, 226, 283, 109, 603, 603, 752, 453, 723, 666, 810, 446, 585, 316, 295, -19, 425, 442, 582, 246, 583, 588, 848, 697, 975, 732, 726, 431, 717, 506, 465, -1, 289, 323, 603, 374, 654, 480, 495, 151, 575, 492, 582, 274, 632, 713, 1025, 851, 1050, 752, 696, 304, 559, 400, 412, -64, 188, 132, 249, 40, 302, 107, 192, -24, 528, 606, 828, 545, 872, 848, 1062, 765, 930, 774, 845, 591, 1097, 1106, 1223, 848, 1115, 1080, 1300, 1130, 1425, 1271, 1367, 1173, 1572, 1479, 1539, 1119, 1358, 1337, 1519, 1242, 1468, 1187, 1090, 662, 987, 892, 946, 663, 1123, 1260, 1626, 1504, 1727, 1451, 1416, 1086, 1435, 1383, 1475, 1153, 1552, 1603, 1864, 1618, 1871, 1608, 1564, 1252, 1611, 1534, 1606, 1189, 1351, 1265, 1411, 1099, 1269, 1056, 1092, 801, 1092, 920, 885, 377, 622, 570, 730, 585, 928, 773, 852, 635, 1014, 878, 894, 381, 647, 630, 864, 610, 846, 651, 637, 289, 622, 469, 472, 114, 421, 371, 595, 289, 400, 53, -47, -443, -63, -85, 28, -334, -32, -48, 88, -222, -117, -497, -652, -1050, -716, -796, -696, -1111, -920, -1021, -877, -1190, -1073, -1358, -1387, -1751, -1366, -1448, -1398, -1776, -1408, -1379, -1116, -1274, -935, -1043, -973, -1205, -887, -1056, -1058, -1574, -1330, -1289, -1026, -1204, -891, -1047, -1020, -1300, -953, -1097, -1085, -1479, -1188, -1230, -1048, -1267, -1128, -1482, -1589, -1999, -1661, -1712, -1621, -1980, -1652, -1655, -1457, -1761, -1566, -1777, -1743, -1950, -1444, -1402, -1230, -1515, -1338, -1480, -1373, -1772, -1659, -1953, -2022, -2370, -1967, -2018, -1927, -2341, -2002, -1995, -1782, -1971, -1639, -1824, -1712, -1932, -1585, -1682, -1602, -2020, -1703, -1625, -1329, -1540, -1311, -1580, -1637, -1996, -1656, -1858, -1857, -2244, -1837, -1806, -1482, -1685, -1496, -1799, -1904, -2365, -2049, -2095, -1969, -2356, -1976, -1893, -1606, -1792, -1491, -1641, -1548, -1725, -1239, -1252, -1097, -1456, -1202, -1280, -1113, -1374, -1199, -1420, -1398, -1719, -1324, -1453, -1455, -1926, -1641, -1689, -1477, -1640, -1290, -1362, -1191, -1360, -898, -928, -808, -1136, -883, -864, -647, -927, -694, -980, -1050, -1430, -1018, -1146, -1078, -1438, -1019, -902, -565, -735, -516, -787, -845, -1238, -873, -844, -645, -955, -589, -554, -350, -629, -490, -867, -983, -1372, -988, -1129, -1081, -1411, -1147, -1174, -979, -1223, -988, -1135, -1079, -1362, -879, -911, -810, -1223, -875, -834, -504, -613, -246, -425, -307, -543, -306, -502, -557, -1068, -870, -968, -800, -1076, -830, -1070, -1091, -1440, -1131, -1276, -1291, -1684, -1364, -1350, -1086, -1297, -1103, -1334, -1338, -1645, -1193, -1141, -930, -1184, -793, -748, -513, -765, -535, -766, -784, -1009, -480, -467, -270, -588, -298, -339, -171, -495, -325, -514, -475, -730, -321, -326, -218, -580, -232, -188, 95, -29, 263, 54, 113, -163, 149, 17, 35, -371, -80, -63, 216, 42, 364, 193, 171, -152, 260, 192, 289, -11, 362, 481, 814, 635, 871, 631, 642, 321, 626, 551, 615, 250, 613, 684, 970, 818, 1176, 1026, 1121, 973, 1513, 1562, 1726, 1409, 1592, 1441, 1540, 1151, 1243, 1019, 1011, 712, 1140, 1070, 1141, 738, 1003, 952, 1132, 956, 1256, 1066, 1133, 902, 1276, 1129, 1154, 666, 936, 939, 1146, 862, 1086, 810, 737, 313, 610, 510, 602, 274, 691, 795, 1129, 1023, 1234, 982, 921, 588, 892, 795, 875, 537, 912, 1029, 1305, 1099, 1328, 1057, 994, 703, 1135, 1086, 1193, 797, 1005, 919, 1104, 756, 933, 730, 775, 460, 794, 628, 584, 88, 327, 242, 406, 227, 544, 418, 502, 261, 619, 491, 477, 15, 290, 311, 602, 376, 614, 431, 416, 128, 556, 516, 625, 341, 699, 713, 982, 810, 993, 708, 639, 307, 649, 594, 702, 349, 724, 797, 1034, 788, 1045, 806, 791, 546, 1015, 1147, 1413, 1202, 1553, 1621, 1930, 1735, 1962, 1806, 1867, 1614, 2068, 1998, 2057, 1705, 2006, 1993, 2178, 1990, 2286, 2061, 2055, 1735, 1988, 1760, 1686, 1193, 1453, 1487, 1755, 1579, 1879, 1703, 1709, 1400, 1745, 1595, 1572, 1176, 1439, 1401, 1601, 1378, 1556, 1242, 1202, 806, 1178, 1197, 1325, 999, 1330, 1366, 1628, 1344, 1586, 1397, 1459, 1247, 1715, 1678, 1812, 1442, 1572, 1370, 1376, 878, 901, 560, 464, 105, 511, 393, 422, -53, 217, 189, 322, 116, 397, 165, 168, -160, 104, -71, -43, -538, -318, -358, -173, -448, -369, -694, -866, -1355, -1085, -1310, -1352, -1745, -1381, -1328, -1058, -1243, -1059, -1339, -1405, -1776, -1376, -1421, -1264, -1631, -1241, -1137, -833, -986, -621, -782, -700, -873, -444, -520, -416, -834, -644, -798, -708, -1071, -930, -1203, -1210, -1535, -1094, -1146, -1050, -1480, -1163, -1120, -854, -989, -599, -657, -448, -594, -170, -223, -112, -480, -310, -357, -175, -501, -326, -629, -794, -1188, -922, -1090, -1114, -1472, -1094, -1050, -788, -1012, -898, -1222, -1305, -1732, -1392, -1417, -1282, -1623, -1221, -1137, -857, -1096, -901, -1204, -1269, -1575, -1136, -1152, -1014, -1236, -866, -831, -537, -736, -489, -627, -548, -820, -432, -469, -409, -855, -602, -627, -435, -620, -311, -513, -480, -728, -487, -699, -751, -1304, -1112, -1150, -965, -1188, -902, -1139, -1185, -1558, -1196, -1298, -1267, -1617, -1240, -1138, -854, -1031, -809, -965, -877, -1104, -601, -489, -196, -438, -3, 70, 366, 185, 481, 246, 272, 92, 598, 611, 771, 454, 721, 666, 821, 529, 652, 417, 402, 61, 429, 352, 421, 0, 254, 198, 329, 114, 302, 20, 13, -335, -99, -348, -425, -945, -688, -682, -431, -657, -375, -553, -604, -957, -582, -712, -660, -1001, -692, -636, -344, -542, -320, -595, -644, -981, -679, -791, -730, -1116, -781, -750, -544, -750, -476, -652, -582, -778, -299, -319, -195, -554, -375, -463, -345, -696, -526, -702, -661, -910, -418, -371, -182, -503, -201, -218, -5, -162, 167, -16, 71, -136, 162, -25, -57, -618, -373, -445, -281, -633, -475, -814, -975, -1404, -1089, -1215, -1148, -1454, -1070, -971, -645, -797, -618, -930, -1003, -1414, -1069, -1121, -1021, -1338, -971, -948, -724, -1006, -782, -1016, -1052, -1349, -904, -940, -828, -1178, -937, -968, -735, -1006, -849, -1068, -1069, -1370, -1041, -1198, -1200, -1669, -1433, -1505, -1372, -1538, -1214, -1374, -1278, -1499, -1162, -1296, -1287, -1803, -1541, -1560, -1353, -1592, -1393, -1613, -1658, -2003, -1614, -1698, -1619, -1942, -1620, -1609, -1333, -1573, -1424, -1784, -1897, -2302, -1923, -1928, -1768, -2070, -1704, -1659, -1452, -1734, -1500, -1730, -1726, -1961, -1468, -1391, -1158, -1379, -978, -942, -645, -879, -668, -862, -844, -1149, -759, -861, -865, -1264, -931, -932, -685, -848, -501, -643, -597, -833, -462, -561, -484, -904, -566, -485, -113, -258, 94, -70, -25, -275, -13, -237, -285, -729, -523, -590, -447, -715, -578, -942, -1079, -1492, -1208, -1284, -1220, -1655, -1340, -1366, -1179, -1473, -1283, -1473, -1478, -1726, -1202, -1237, -1078, -1424, -1274, -1478, -1397, -1803, -1717, -1984, -1991, -2290, -1858, -1888, -1800, -2204, -1846, -1779, -1547, -1704, -1414, -1589, -1540, -1792, -1484, -1584, -1536, -2003, -1750, -1792, -1580, -1776, -1577, -1828, -1885, -2280, -1947, -2065, -2039, -2365, -1935, -1805, -1447, -1606, -1368, -1600, -1607, -1989, -1650, -1698, -1597, -1964, -1582, -1457, -1177, -1363, -1058, -1248, -1206, -1407, -978, -1063, -987, -1372, -1286, -1489, -1437, -1756, -1607, -1829, -1803, -2117, -1700, -1754, -1706, -2106, -1766, -1744, -1486, -1611, -1290, -1393, -1248, -1441, -1001, -1081, -1002, -1432, -1210, -1260, -1077, -1354, -1126, -1391, -1433, -1739, -1349, -1382, -1235, -1496, -970, -816, -442, -569, -296, -540, -538, -872, -531, -532, -378, -684, -269, -183, 136, -49, 139, -147, -182, -453, -9, -34, 82, -212, 85, 47, 241, -35, 184, -28, -31, -349, 13, -113, -83, -562, -331, -397, -208, -410, -150, -351, -269, -540, -325, -549, -625, -1150, -968, -1007, -817, -1068, -851, -1165, -1240, -1656, -1344, -1481, 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