//
// 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,
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