Mathematics:
Cohomology
→Theory
→Implementation
Jena:
External links:
Mod-2-Cohomology of Normalizer(G2(5),Centre(SylowSubgroup(G2(5),2))), a group of order 14400
| About the group | Ring generators | Ring relations | Completion information | Restriction maps |
General information on the group
- Normalizer(G2(5),Centre(SylowSubgroup(G2(5),2))) is a group of order 14400.
- The group order factors as
26 · 32 · 52 . - The group is defined by Group([(1,865)(2,3214)(3,2805)(4,3418)(5,2490)(6,1742)(7,193)(8,1948)(9,3679)(11,2920)(12,1967)(13,2309)(14,3326)(15,1924)(16,101)(18,1247)(19,2066)(21,90)(22,1027)(23,2675)(24,3844)(25,1936)(26,3567)(27,1570)(28,2875)(29,1010)(30,2145)(31,93)(32,3740)(33,826)(34,357)(35,3386)(36,277)(37,2010)(38,1899)(39,3812)(40,790)(41,3149)(42,1577)(43,2539)(44,3712)(45,3473)(46,2068)(47,2992)(48,2938)(49,260)(50,2847)(51,343)(52,3574)(53,330)(54,1237)(55,174)(56,372)(57,3256)(58,1762)(59,3819)(60,125)(61,3021)(62,2306)(63,2902)(64,1880)(65,1349)(66,1371)(67,3163)(68,706)(69,3234)(70,3258)(71,1900)(72,1896)(73,940)(74,2345)(75,318)(76,2748)(77,3610)(78,94)(79,1888)(80,1688)(81,1347)(82,2753)(83,2390)(84,1252)(85,3395)(86,1828)(87,2986)(88,614)(89,2126)(91,1850)(92,2352)(95,3318)(96,3715)(97,757)(98,2401)(99,3900)(100,2074)(102,110)(103,3145)(104,942)(105,3025)(106,3300)(107,448)(108,2348)(109,3564)(111,3719)(112,2622)(113,2187)(114,2101)(115,3876)(116,943)(117,1342)(118,404)(119,904)(120,494)(121,2964)(122,376)(123,2176)(124,1584)(126,1642)(127,793)(128,3601)(129,750)(130,1180)(131,2966)(132,1437)(133,1057)(134,1422)(135,3708)(136,2568)(137,142)(138,762)(139,3851)(140,1972)(141,3120)(143,433)(144,3362)(145,1624)(146,572)(147,2454)(148,3881)(149,3270)(150,2037)(151,1609)(152,1127)(153,3817)(154,3408)(155,2579)(156,171)(157,2837)(158,2879)(159,3313)(160,3269)(161,659)(162,3106)(163,1898)(164,3843)(165,2582)(166,2471)(167,3704)(168,3439)(169,1103)(170,1974)(172,3748)(173,2923)(175,1206)(176,1730)(177,3315)(178,3381)(179,2726)(180,3260)(181,3472)(182,293)(183,2118)(184,1072)(185,3382)(186,3783)(187,3184)(188,592)(189,2804)(190,3613)(191,755)(192,1862)(194,2038)(195,1424)(196,2928)(197,1181)(198,1120)(199,601)(200,3338)(201,1582)(202,3034)(203,269)(204,767)(205,556)(206,634)(207,2706)(208,1650)(209,1705)(210,2156)(211,1146)(212,555)(213,3837)(214,2930)(215,360)(216,1511)(217,3159)(218,564)(219,2554)(220,419)(221,2460)(222,2807)(223,1795)(224,2053)(225,2506)(226,863)(227,2398)(228,3781)(229,272)(230,2831)(231,3393)(232,3018)(233,2970)(234,3345)(235,3399)(236,1220)(237,441)(238,2588)(239,3228)(240,3650)(241,548)(242,3888)(243,2228)(244,3200)(245,3542)(246,3532)(247,2919)(248,859)(249,3404)(250,2867)(251,349)(252,1395)(253,1064)(254,1082)(255,418)(256,2323)(257,3183)(258,1461)(259,2230)(261,2680)(262,2232)(263,423)(264,1085)(265,3512)(266,1623)(267,2219)(268,3839)(270,2028)(271,2585)(273,2669)(274,836)(275,2357)(276,1113)(278,1169)(279,3803)(281,3673)(282,3608)(283,3622)(284,1676)(286,3718)(287,2713)(288,2814)(289,758)(290,1810)(291,2278)(292,1060)(294,3135)(295,3434)(296,3772)(297,2375)(298,579)(299,2152)(300,1887)(301,713)(302,2478)(303,2825)(304,2956)(305,1769)(306,337)(307,3865)(308,391)(309,3332)(310,366)(311,1837)(312,2070)(313,3303)(314,2584)(315,2503)(316,1670)(317,2654)(319,2769)(320,2775)(321,2358)(322,1782)(323,2553)(324,1157)(325,1075)(326,1378)(327,1453)(328,2258)(329,2581)(331,3046)(332,2124)(333,2791)(334,742)(335,1363)(336,447)(338,487)(339,2541)(340,3250)(341,1242)(342,2130)(344,3443)(345,1844)(346,2892)(347,2626)(348,1836)(350,2404)(351,3454)(352,3030)(353,3620)(354,1429)(355,1853)(356,1729)(358,2172)(359,444)(361,1993)(362,2484)(363,1460)(364,3785)(365,1204)(367,2809)(368,2580)(369,508)(370,2524)(371,1520)(373,458)(374,3082)(375,3140)(377,718)(378,608)(379,1586)(380,2695)(381,2236)(382,1581)(383,3660)(384,3557)(385,1374)(386,3230)(387,1882)(388,721)(389,1998)(390,1099)(392,1446)(393,768)(394,3801)(395,1070)(396,3896)(397,2030)(398,2927)(399,3116)(400,2333)(401,1606)(402,1659)(403,1561)(405,1838)(406,3668)(407,849)(408,1253)(409,3361)(410,3670)(411,3666)(412,1435)(413,2052)(414,2670)(415,3682)(416,3084)(417,2925)(420,1038)(421,3178)(422,1019)(424,1601)(425,3892)(426,2968)(427,480)(428,3087)(429,957)(430,1535)(431,1638)(432,3513)(434,2059)(435,1755)(436,3499)(437,3341)(438,3446)(439,2815)(440,798)(442,1665)(443,2297)(445,2001)(446,2859)(449,1191)(450,609)(451,709)(452,1110)(453,2613)(454,1209)(455,3780)(456,3112)(457,2903)(459,753)(460,3702)(461,2274)(462,3868)(463,1094)(464,1629)(465,1968)(466,3538)(467,1154)(468,2891)(469,3049)(470,1915)(471,1822)(472,1232)(473,3153)(474,1227)(475,3219)(476,786)(477,1417)(478,2822)(479,3852)(481,1477)(482,2873)(483,976)(484,2157)(485,1641)(486,1764)(488,3170)(489,3208)(490,877)(491,3233)(492,3333)(493,3826)(495,1748)(496,2559)(497,1852)(498,1929)(499,3220)(500,3540)(501,3901)(502,3492)(503,3215)(504,2430)(505,1000)(506,717)(507,2885)(509,1904)(510,1564)(511,1137)(512,1744)(513,1132)(514,2442)(515,2780)(516,3412)(517,2556)(518,3639)(519,574)(520,1149)(521,2979)(522,2508)(523,2650)(524,1264)(525,892)(526,1568)(527,1684)(528,969)(530,1918)(531,3372)(532,3762)(533,3858)(534,1667)(535,2160)(536,3506)(537,772)(538,3237)(539,1030)(540,1723)(541,1248)(542,2062)(543,3560)(544,723)(545,2717)(546,2590)(547,833)(549,1572)(550,763)(551,1960)(552,1812)(553,3079)(554,693)(557,2684)(558,810)(559,2179)(560,1002)(561,2221)(562,1022)(563,3167)(565,2935)(566,643)(567,3449)(568,1563)(569,1640)(570,1449)(571,1319)(573,1653)(575,3342)(576,1420)(577,2888)(578,1966)(580,1669)(581,2270)(582,1849)(583,1854)(584,2386)(585,1035)(586,3235)(587,1604)(588,3022)(589,3387)(590,3591)(591,891)(593,3693)(594,672)(595,1992)(596,995)(597,1897)(598,3758)(599,3731)(600,2096)(602,1916)(603,1646)(604,803)(605,3471)(606,3158)(607,3241)(610,2434)(611,2712)(612,2953)(613,1536)(615,1990)(616,3543)(617,2784)(618,1306)(619,3391)(620,2073)(621,2710)(622,1907)(623,2024)(624,1711)(625,3377)(626,2295)(627,3093)(628,2509)(630,979)(631,2257)(632,3249)(633,1425)(635,2929)(636,1879)(637,1775)(638,1175)(639,1934)(640,2075)(641,1767)(642,1526)(644,2608)(645,3017)(646,3447)(647,1098)(648,2220)(649,3004)(650,2465)(651,2973)(652,1616)(653,1841)(654,2842)(655,3685)(656,2916)(657,2820)(658,1495)(660,812)(661,1079)(662,1315)(663,2146)(664,1496)(665,2208)(666,1680)(667,3261)(668,3312)(669,1167)(670,2349)(671,1671)(673,3522)(674,1533)(675,3280)(676,3886)(677,1005)(678,3479)(679,827)(680,1043)(681,3813)(683,1147)(684,3551)(685,2406)(686,1956)(687,3788)(688,2555)(689,3695)(690,1275)(691,2248)(692,701)(694,3480)(695,3488)(696,3824)(697,3209)(698,1884)(699,2321)(700,1545)(702,3687)(704,3489)(705,1346)(707,3157)(708,1063)(710,1505)(711,3462)(712,1645)(714,2604)(715,1021)(716,1387)(719,3277)(720,2884)(722,1894)(724,3407)(725,2196)(726,1835)(727,2936)(728,903)(729,3703)(730,3497)(731,3067)(732,2379)(733,1330)(734,1863)(735,1105)(736,1480)(737,3052)(738,3450)(739,1550)(740,2511)(741,1633)(743,2419)(744,1380)(745,3530)(746,1411)(747,1725)(748,1668)(749,1281)(751,3838)(752,982)(754,3456)(756,817)(760,2849)(761,3629)(764,3509)(765,1268)(766,2098)(769,3809)(770,3463)(771,1662)(773,3667)(774,1866)(775,3895)(776,3743)(777,1136)(778,1213)(779,3402)(780,2240)(781,1532)(782,1293)(783,2808)(784,1263)(785,2998)(787,1379)(788,3768)(789,3337)(791,3147)(792,3525)(794,2537)(795,1567)(796,2417)(797,1770)(799,3797)(800,3202)(801,1101)(802,2777)(804,870)(805,1768)(806,1273)(807,2949)(808,3757)(809,2828)(813,1126)(814,2952)(815,3690)(816,1660)(818,1013)(819,2450)(820,1855)(821,1697)(822,3245)(823,2774)(824,3353)(825,2737)(828,1056)(829,1981)(830,2724)(831,3661)(832,2252)(834,2542)(835,2009)(837,2948)(838,2227)(839,1187)(840,1766)(841,1445)(842,3097)(843,1073)(844,2711)(845,1037)(846,3110)(847,3517)(848,2818)(850,2334)(851,3121)(852,2094)(853,1462)(854,1785)(855,3848)(856,2108)(857,1872)(858,3057)(860,3807)(861,2498)(862,1223)(864,3487)(866,1592)(868,1977)(869,3229)(871,3470)(872,2502)(873,1328)(874,1320)(875,3035)(876,3400)(878,2548)(879,2083)(880,2776)(881,1870)(882,2451)(883,2267)(884,2985)(885,2336)(886,1454)(887,1961)(888,3514)(889,3089)(890,1297)(893,3902)(894,2373)(895,3709)(896,2149)(897,3699)(898,1969)(899,1826)(901,3605)(902,3820)(905,1405)(906,2729)(907,3024)(908,3068)(909,1949)(910,2499)(911,2004)(912,3321)(913,1677)(914,2164)(915,1467)(916,1367)(917,1971)(918,3539)(919,1617)(920,2947)(921,2200)(922,3672)(923,3481)(924,3175)(925,1087)(926,2210)(927,1044)(928,1803)(929,2365)(930,1513)(931,2763)(932,2690)(933,3045)(934,2368)(935,1542)(936,3413)(937,1987)(938,1947)(939,2727)(941,2981)(944,1529)(945,3107)(946,2237)(947,1199)(948,2607)(949,2198)(950,3630)(951,1255)(952,3276)(953,3599)(954,2692)(955,3026)(956,3397)(958,1226)(959,1970)(960,3722)(961,1234)(962,2587)(963,3095)(964,1017)(965,3181)(966,2997)(967,1614)(968,1622)(970,2456)(971,3406)(972,2601)(973,3572)(974,1751)(975,2778)(977,3756)(978,3491)(980,2630)(981,3763)(983,1153)(984,1318)(985,3460)(986,2839)(987,2531)(988,2420)(990,1540)(991,3545)(992,2002)(993,1574)(994,2673)(996,2995)(997,1090)(998,2427)(999,3194)(1001,2121)(1003,2749)(1004,3483)(1006,2374)(1007,1240)(1008,2264)(1009,2546)(1011,2790)(1012,3212)(1014,1792)(1015,3262)(1016,3614)(1018,3248)(1020,1720)(1023,2289)(1024,3113)(1025,1410)(1026,3821)(1028,2277)(1029,1061)(1031,2016)(1032,3549)(1033,3451)(1034,1815)(1036,3188)(1039,2975)(1040,3548)(1041,1937)(1042,3582)(1045,3727)(1046,3465)(1047,1666)(1048,2635)(1049,1442)(1050,1630)(1051,3348)(1052,3136)(1053,1092)(1055,2253)(1058,1355)(1059,3432)(1062,3822)(1065,2184)(1066,3071)(1067,1385)(1068,2507)(1069,2519)(1071,3299)(1074,2861)(1076,1772)(1077,3431)(1078,2242)(1080,1713)(1081,2637)(1083,2276)(1084,2407)(1086,2173)(1088,1271)(1089,2758)(1091,3544)(1093,1151)(1095,3427)(1096,2167)(1097,1902)(1100,2862)(1102,1182)(1104,2234)(1106,3721)(1107,3433)(1108,1491)(1109,3027)(1111,1173)(1112,1316)(1114,3686)(1115,2473)(1116,3565)(1117,1798)(1118,3285)(1119,3665)(1121,1249)(1122,1860)(1123,3466)(1124,1402)(1125,2523)(1128,3019)(1129,2178)(1130,1708)(1131,2532)(1133,2976)(1134,1791)(1135,2792)(1138,1952)(1139,2213)(1140,3267)(1141,1681)(1142,2388)(1143,2709)(1144,2609)(1145,3579)(1148,3864)(1150,1481)(1152,3415)(1155,2100)(1156,1170)(1158,3301)(1159,1851)(1160,3186)(1161,1602)(1162,3389)(1163,1859)(1164,1539)(1165,2127)(1166,2678)(1168,1706)(1171,1360)(1172,3584)(1174,3317)(1176,1391)(1177,2514)(1178,2691)(1179,2045)(1183,1722)(1184,2134)(1185,2351)(1186,2954)(1188,3700)(1189,3766)(1190,2315)(1192,3231)(1193,3828)(1194,2080)(1195,2781)(1196,1414)(1197,3528)(1198,3099)(1200,3638)(1201,2103)(1202,3360)(1203,1307)(1205,3394)(1207,1478)(1208,1986)(1210,2209)(1211,3689)(1212,2371)(1214,2810)(1215,2899)(1216,3043)(1217,1398)(1218,3375)(1219,3398)(1221,2771)(1222,3906)(1224,1361)(1225,2265)(1228,1585)(1229,1959)(1230,1522)(1231,2122)(1233,2182)(1235,3659)(1236,2381)(1238,2078)(1239,3527)(1241,2447)(1243,2597)(1244,1510)(1245,2565)(1246,3505)(1250,3725)(1251,2863)(1254,1603)(1256,1999)(1257,2036)(1258,1712)(1259,3566)(1260,1576)(1261,2119)(1262,3376)(1265,2311)(1266,1941)(1267,3726)(1269,2740)(1270,2273)(1272,3674)(1274,1501)(1276,1401)(1277,2893)(1278,1817)(1280,3508)(1282,3880)(1283,3835)(1284,2564)(1285,3384)(1286,3445)(1287,2603)(1288,3056)(1289,2829)(1291,1475)(1292,1707)(1294,3882)(1295,2155)(1296,2833)(1298,3677)(1299,3287)(1300,2492)(1301,3633)(1302,2483)(1303,1911)(1304,2516)(1305,2596)(1308,3207)(1309,3467)(1311,2180)(1312,2339)(1313,2034)(1314,2376)(1317,2570)(1321,2097)(1322,1334)(1323,2558)(1324,3474)(1325,2562)(1326,3778)(1327,2069)(1329,1482)(1331,3475)(1332,2786)(1333,2330)(1335,3597)(1336,3606)(1337,2347)(1338,3316)(1339,2262)(1340,1619)(1341,3461)(1343,1874)(1344,1839)(1345,2756)(1348,3552)(1350,2620)(1351,3274)(1352,2676)(1353,3636)(1354,2019)(1356,3486)(1357,1906)(1358,3570)(1359,2493)(1362,2611)(1364,1506)(1365,3354)(1366,3122)(1368,3015)(1369,1419)(1370,2296)(1372,3325)(1373,3247)(1375,2667)(1376,1759)(1377,2496)(1381,1996)(1382,1649)(1383,2415)(1384,1406)(1386,2428)(1388,3494)(1389,2754)(1390,2372)(1392,3195)(1393,2202)(1394,2882)(1396,2470)(1397,3874)(1399,2940)(1400,3476)(1403,3224)(1404,2612)(1407,2750)(1408,3180)(1409,2367)(1412,3752)(1413,3320)(1415,1503)(1416,2715)(1418,1594)(1421,1430)(1423,3442)(1426,3611)(1427,2092)(1428,1552)(1431,3374)(1432,1805)(1433,3547)(1434,1701)(1436,3761)(1438,3799)(1439,1925)(1440,2785)(1441,3253)(1444,3401)(1447,2455)(1448,3265)(1450,1893)(1451,2868)(1452,3063)(1455,2263)(1456,2015)(1457,2661)(1458,3037)(1459,2793)(1463,2648)(1464,1678)(1465,3074)(1466,2848)(1468,2020)(1469,3083)(1470,1806)(1471,2955)(1472,3156)(1473,2549)(1474,2249)(1476,3379)(1479,3363)(1483,3899)(1484,3294)(1485,1843)(1486,3100)(1487,2850)(1488,3507)(1489,2195)(1490,1917)(1492,3164)(1493,2989)(1494,1588)(1497,2106)(1498,2061)(1499,2217)(1500,3307)(1502,2827)(1504,2688)(1507,2032)(1508,2461)(1509,3367)(1512,2551)(1514,3904)(1515,2204)(1516,3064)(1518,2250)(1519,3281)(1521,1596)(1523,2606)(1524,2983)(1525,3663)(1527,3103)(1528,3292)(1530,2672)(1531,1820)(1534,2008)(1537,2912)(1538,2627)(1541,3028)(1543,2282)(1544,1737)(1546,3304)(1547,2572)(1548,1555)(1549,3336)(1551,1719)(1553,2421)(1554,2414)(1556,3684)(1557,3707)(1558,2950)(1559,3646)(1560,3448)(1562,2666)(1565,3810)(1566,1831)(1569,3275)(1571,1940)(1573,1702)(1575,2567)(1578,3096)(1579,3076)(1580,3108)(1583,2592)(1587,3168)(1589,2642)(1590,2212)(1591,3840)(1593,2605)(1595,2344)(1597,3744)(1598,2284)(1599,2977)(1600,1736)(1605,2772)(1607,2147)(1608,3283)(1610,2765)(1611,2865)(1612,2331)(1613,2624)(1615,2054)(1618,3344)(1620,2881)(1621,2674)(1625,2243)(1626,2342)(1627,2538)(1628,2138)(1631,2102)(1632,3586)(1634,2571)(1635,2645)(1636,2353)(1637,3750)(1639,2699)(1643,3042)(1644,1747)(1647,3152)(1648,2959)(1651,3732)(1652,3585)(1654,1819)(1655,2110)(1656,3137)(1657,1700)(1658,1921)(1663,2628)(1664,3519)(1672,2136)(1673,2625)(1674,2640)(1675,2908)(1679,3735)(1682,1761)(1683,2937)(1685,2651)(1686,3373)(1687,2870)(1689,2958)(1691,3879)(1692,2239)(1693,3441)(1694,2768)(1695,2602)(1696,1740)(1698,2109)(1699,2324)(1703,3680)(1704,3221)(1709,2064)(1710,3378)(1714,2720)(1715,3745)(1716,3117)(1718,2797)(1721,2960)(1724,2961)(1726,3873)(1728,3711)(1731,3020)(1732,2757)(1733,2389)(1734,3003)(1735,3739)(1738,1752)(1739,2082)(1741,2206)(1743,1914)(1745,2652)(1746,2290)(1749,1796)(1750,3429)(1753,2067)(1754,2292)(1756,2285)(1757,3829)(1758,2099)(1760,2340)(1763,2337)(1765,2782)(1771,3751)(1773,3634)(1774,2683)(1776,3846)(1777,3133)(1778,3273)(1779,2063)(1780,2536)(1781,1814)(1783,2972)(1784,3478)(1786,3500)(1787,2046)(1788,2996)(1789,3054)(1790,3425)(1793,2504)(1794,2279)(1797,2382)(1799,3278)(1800,2364)(1801,3172)(1802,1881)(1804,3138)(1807,3119)(1808,3805)(1809,3452)(1811,3282)(1813,3477)(1816,3148)(1818,2435)(1821,1878)(1823,2747)(1824,3856)(1825,2826)(1827,3798)(1829,3066)(1830,2071)(1832,2770)(1833,2799)(1834,3516)(1840,3279)(1842,3339)(1845,2877)(1846,1931)(1847,3385)(1848,3734)(1856,3568)(1857,3546)(1858,2703)(1861,2488)(1864,2025)(1865,3123)(1867,2043)(1868,3130)(1869,2534)(1871,2736)(1873,3697)(1875,2883)(1876,2485)(1877,2346)(1883,3747)(1885,2741)(1886,2197)(1889,3366)(1890,3815)(1891,3350)(1892,3535)(1895,1928)(1901,1942)(1903,2380)(1905,3255)(1908,2457)(1909,2802)(1910,3240)(1912,3832)(1913,2773)(1919,3365)(1922,2133)(1923,3490)(1926,3842)(1927,2332)(1930,3185)(1932,2647)(1933,2318)(1935,2621)(1938,3428)(1939,3055)(1943,2231)(1944,3569)(1945,3648)(1946,2693)(1950,3421)(1951,2410)(1953,3218)(1954,2432)(1955,3322)(1957,2801)(1958,3635)(1962,3694)(1963,3073)(1964,3259)(1965,2003)(1973,2090)(1975,3098)(1976,2533)(1978,3649)(1979,2411)(1980,2641)(1982,3669)(1983,3742)(1984,3616)(1985,2464)(1988,2905)(1989,2409)(1991,2060)(1994,3814)(1995,3223)(1997,3008)(2000,3094)(2005,3349)(2006,3675)(2007,2766)(2011,3040)(2012,3272)(2013,3201)(2014,3870)(2017,3534)(2018,3161)(2021,3225)(2022,3190)(2023,2967)(2026,2112)(2027,2245)(2029,2436)(2031,3331)(2033,3836)(2035,3717)(2039,2328)(2040,2830)(2041,3775)(2042,3118)(2044,2901)(2047,3688)(2048,3420)(2049,2275)(2050,2734)(2051,3293)(2055,3501)(2056,2439)(2057,2871)(2058,2835)(2065,2089)(2072,3165)(2076,2789)(2077,3571)(2079,2665)(2081,2313)(2084,2836)(2085,2214)(2086,3041)(2087,2216)(2088,2343)(2091,3182)(2093,2576)(2095,3520)(2104,3006)(2105,3662)(2107,3769)(2111,3867)(2113,3355)(2114,2682)(2115,3109)(2116,2857)(2117,3598)(2120,2762)(2123,2162)(2125,3894)(2128,3323)(2129,3724)(2131,3587)(2132,3039)(2135,3714)(2137,2723)(2139,2312)(2140,3784)(2141,3243)(2142,2520)(2143,2535)(2144,2662)(2148,3242)(2150,2897)(2151,3419)(2153,2974)(2154,2440)(2158,2163)(2159,3774)(2161,2733)(2165,3804)(2166,2418)(2168,2702)(2169,3368)(2170,3204)(2171,3550)(2174,3036)(2175,3128)(2177,3771)(2181,2540)(2183,2764)(2185,3891)(2186,2653)(2188,2266)(2189,3236)(2190,2405)(2191,2969)(2192,2887)(2193,3645)(2194,3065)(2199,2945)(2201,2431)(2203,2821)(2205,2751)(2207,2853)(2211,2911)(2215,2350)(2218,2634)(2222,2384)(2223,3889)(2224,3647)(2225,2356)(2226,3289)(2229,3357)(2233,2942)(2235,3730)(2238,3134)(2241,3086)(2244,3678)(2246,3139)(2251,3713)(2254,2472)(2255,3607)(2256,3101)(2259,2817)(2260,3594)(2261,3166)(2268,3196)(2269,3199)(2271,3210)(2272,3723)(2280,2922)(2281,3749)(2283,2980)(2286,2325)(2287,2391)(2288,3286)(2291,3213)(2293,2593)(2294,2718)(2298,2921)(2299,3222)(2300,2994)(2301,3309)(2302,3787)(2303,3612)(2304,3335)(2305,2707)(2307,3091)(2308,3244)(2310,2965)(2314,2445)(2316,3179)(2317,2329)(2319,3811)(2322,3297)(2326,2444)(2327,2854)(2335,3853)(2338,2566)(2341,2412)(2354,2915)(2355,2598)(2359,3346)(2360,3696)(2361,3081)(2362,2687)(2363,2649)(2366,3738)(2369,2393)(2370,2466)(2377,2798)(2378,2527)(2383,2988)(2385,3061)(2387,3818)(2392,3559)(2394,2685)(2395,3641)(2396,2844)(2397,3720)(2399,3847)(2400,3059)(2402,3575)(2408,3554)(2413,3631)(2416,3356)(2422,3653)(2423,3710)(2424,3573)(2425,2552)(2426,2500)(2429,3206)(2433,3691)(2437,3580)(2438,2468)(2441,3831)(2443,3211)(2446,2544)(2448,3887)(2449,3603)(2452,2469)(2453,2512)(2458,3031)(2459,3760)(2462,2716)(2463,3232)(2467,3624)(2474,3878)(2475,3643)(2476,2840)(2477,3656)(2479,2644)(2480,3871)(2481,2632)(2482,2557)(2486,3092)(2487,3417)(2489,3609)(2491,3314)(2494,2583)(2495,3388)(2497,2745)(2505,3132)(2510,3869)(2513,3410)(2515,2906)(2517,3324)(2518,2738)(2521,2719)(2522,2696)(2525,3877)(2526,3588)(2528,3369)(2529,3642)(2543,2987)(2545,3854)(2547,2618)(2550,2686)(2560,3403)(2561,2744)(2563,3029)(2573,3578)(2574,3589)(2575,3150)(2577,3014)(2578,3833)(2586,3796)(2589,3484)(2591,2931)(2595,3380)(2599,3154)(2600,3531)(2610,3482)(2614,3741)(2615,3102)(2616,2697)(2617,3044)(2619,3370)(2623,2963)(2629,2914)(2631,2813)(2633,3782)(2636,2779)(2638,3764)(2639,2841)(2643,3002)(2646,3602)(2655,3701)(2656,2742)(2657,3863)(2658,3526)(2659,2800)(2660,3705)(2663,3600)(2664,3683)(2668,3405)(2671,3060)(2677,2704)(2679,2932)(2681,3171)(2689,3080)(2694,3016)(2698,3371)(2700,3652)(2701,3129)(2705,2876)(2708,3125)(2714,2918)(2721,3310)(2722,2880)(2725,2803)(2728,3291)(2730,2787)(2731,3062)(2732,2834)(2735,3625)(2739,3779)(2743,3197)(2746,3295)(2752,3422)(2759,3423)(2760,3626)(2761,2889)(2767,3592)(2783,2943)(2788,3692)(2794,3655)(2795,2990)(2796,3075)(2806,3676)(2811,3596)(2812,3755)(2816,3033)(2819,3806)(2823,3834)(2832,3884)(2838,3627)(2843,3558)(2845,3364)(2846,3861)(2851,3802)(2852,3453)(2855,3187)(2856,3823)(2858,3753)(2860,2878)(2864,3561)(2866,3875)(2869,2872)(2874,3264)(2886,3903)(2890,3296)(2894,3111)(2895,3792)(2896,3816)(2898,3905)(2900,3593)(2904,3890)(2907,3830)(2909,3162)(2910,3343)(2913,2933)(2917,3257)(2924,3238)(2926,3077)(2934,3754)(2939,3226)(2941,3007)(2944,3251)(2946,3464)(2951,3032)(2957,3085)(2962,3290)(2971,3302)(2978,3144)(2982,3637)(2984,3651)(2991,3733)(2993,3706)(2999,3664)(3000,3115)(3001,3529)(3005,3555)(3009,3671)(3010,3615)(3011,3409)(3012,3617)(3013,3305)(3023,3893)(3038,3855)(3047,3048)(3051,3124)(3053,3458)(3058,3334)(3069,3457)(3070,3793)(3072,3177)(3078,3577)(3088,3424)(3090,3632)(3104,3469)(3105,3654)(3114,3860)(3126,3770)(3127,3736)(3131,3504)(3141,3510)(3142,3444)(3143,3563)(3146,3306)(3151,3825)(3155,3537)(3160,3308)(3169,3729)(3173,3416)(3174,3866)(3176,3595)(3189,3640)(3191,3841)(3192,3268)(3193,3288)(3198,3897)(3203,3794)(3205,3556)(3216,3581)(3217,3765)(3227,3759)(3246,3644)(3252,3430)(3254,3777)(3263,3716)(3266,3435)(3271,3786)(3284,3767)(3298,3518)(3311,3808)(3319,3859)(3328,3827)(3329,3340)(3330,3850)(3347,3383)(3351,3872)(3352,3623)(3358,3536)(3359,3390)(3392,3728)(3396,3790)(3411,3857)(3414,3498)(3426,3515)(3437,3628)(3438,3621)(3440,3459)(3455,3862)(3468,3795)(3485,3698)(3493,3576)(3495,3604)(3496,3898)(3502,3523)(3503,3562)(3511,3618)(3521,3883)(3524,3583)(3533,3885)(3541,3590)(3553,3773)(3619,3789)(3657,3845)(3658,3776)(3746,3800),(2,230)(3,2882)(4,40)(5,1055)(6,207)(7,2985)(8,483)(9,2324)(10,1443)(11,1129)(12,422)(13,2376)(14,115)(15,327)(16,1013)(17,3681)(18,2899)(19,1418)(20,3327)(21,2690)(22,2128)(23,3652)(24,3844)(25,2261)(26,3735)(27,2760)(28,2711)(29,2312)(30,3426)(31,1189)(32,566)(33,1748)(34,1537)(35,1698)(36,1682)(37,2010)(38,3025)(39,2373)(41,3432)(42,1105)(43,1715)(44,3466)(45,1296)(46,2566)(47,1554)(48,899)(49,1741)(50,3184)(51,276)(52,3821)(53,1258)(54,65)(55,1467)(56,2820)(57,702)(58,3826)(59,1856)(60,425)(61,1404)(62,3204)(63,2851)(64,3325)(66,997)(67,1603)(68,486)(69,2384)(70,1737)(71,1568)(72,1545)(73,2827)(74,3174)(75,1677)(76,2962)(77,3230)(78,1584)(79,1869)(80,961)(81,3689)(82,1442)(83,3695)(84,3317)(85,166)(86,3457)(87,3486)(88,3657)(89,3009)(90,932)(91,1168)(92,256)(93,3766)(94,124)(95,840)(96,3371)(97,3342)(98,403)(99,2075)(100,863)(101,818)(102,3781)(103,203)(104,3106)(105,1899)(106,895)(107,1227)(108,1122)(109,822)(110,228)(111,1535)(112,1705)(113,447)(114,1808)(116,943)(117,2316)(118,3554)(119,3717)(120,1221)(121,191)(122,1321)(123,1485)(125,3892)(126,549)(127,2673)(128,2377)(129,835)(130,3875)(131,2385)(132,717)(133,1615)(134,3137)(135,1597)(136,1495)(137,2951)(138,227)(139,194)(140,1102)(141,910)(142,3032)(143,3580)(144,834)(145,1735)(146,236)(147,2454)(148,1926)(149,320)(150,1251)(151,3649)(152,1952)(153,3451)(154,1190)(155,164)(156,3216)(157,2671)(158,1489)(159,1457)(160,3110)(161,821)(162,942)(163,2397)(165,3543)(167,3857)(168,3483)(169,1067)(170,3116)(171,3581)(172,2660)(173,1772)(174,915)(175,347)(176,2169)(177,3760)(178,1249)(179,2240)(180,3676)(181,2413)(182,3289)(183,814)(184,3788)(185,2786)(186,1481)(187,2847)(188,1883)(189,2883)(190,2662)(192,326)(193,884)(195,3475)(196,2480)(197,1062)(198,435)(199,3304)(200,2745)(201,1848)(202,3035)(204,3271)(205,1774)(206,2137)(208,3732)(209,2622)(210,3839)(211,3394)(212,2040)(213,2905)(214,2735)(215,3010)(216,1692)(217,3793)(218,532)(219,595)(220,2173)(221,3177)(222,675)(223,1947)(224,3322)(225,2079)(226,2074)(229,272)(231,452)(232,3104)(233,722)(234,3611)(235,411)(237,1565)(238,3262)(239,3782)(240,2631)(241,2263)(242,2825)(243,3880)(244,1696)(245,647)(246,2737)(247,3502)(248,2192)(249,670)(250,1639)(251,3233)(252,1463)(253,2651)(254,666)(255,1573)(257,2456)(258,588)(259,3646)(260,2206)(261,476)(262,3352)(263,1759)(264,797)(265,2832)(266,325)(267,1791)(268,2156)(269,3145)(270,484)(271,2635)(273,453)(274,3150)(275,3036)(277,1761)(278,2623)(279,1124)(280,2247)(281,338)(282,872)(283,2089)(284,763)(285,900)(286,2780)(287,768)(288,3249)(289,1961)(290,2216)(291,1281)(292,1053)(293,2226)(294,2496)(295,2207)(296,2366)(297,2558)(298,3823)(299,1666)(300,324)(301,956)(302,3538)(303,3888)(304,2668)(305,1932)(306,2931)(307,2557)(308,2512)(309,2096)(310,3510)(311,2835)(312,705)(313,2664)(314,893)(315,1632)(316,853)(317,1595)(318,913)(319,1449)(321,3096)(322,712)(323,1673)(328,3142)(329,604)(330,1712)(331,2407)(332,3868)(333,3040)(334,2056)(335,2610)(336,2187)(337,2591)(339,2332)(340,3665)(341,3628)(342,1884)(343,1113)(344,878)(345,3604)(346,1654)(348,350)(349,491)(351,686)(352,3834)(353,1338)(354,3170)(355,2343)(356,553)(357,2912)(358,499)(359,3243)(360,3615)(361,3749)(362,3656)(363,2829)(364,455)(365,3275)(366,3141)(367,382)(368,3123)(369,2563)(371,1520)(372,657)(373,3769)(374,794)(375,2347)(376,2097)(377,718)(378,1277)(379,2201)(380,1809)(381,3045)(383,2849)(384,2165)(385,1387)(386,3610)(387,1159)(388,3485)(389,2785)(390,2595)(391,2453)(392,2730)(393,2713)(394,968)(395,998)(396,2296)(397,439)(398,3489)(399,1974)(400,2599)(401,1312)(402,2267)(404,2408)(405,1604)(406,3155)(407,823)(408,3830)(409,561)(410,1871)(412,3057)(413,1886)(414,3587)(415,1718)(417,2999)(418,1702)(419,1086)(420,1427)(421,2262)(423,1376)(424,3191)(426,3011)(427,1152)(428,2653)(429,2082)(430,3719)(431,788)(432,927)(433,2437)(434,3886)(436,3878)(437,3314)(438,2684)(440,848)(441,3810)(442,988)(443,1267)(444,2141)(445,1095)(446,607)(448,474)(449,2722)(450,1471)(451,3189)(454,1763)(457,2025)(458,2107)(459,1957)(460,2528)(461,3206)(462,2124)(463,2855)(464,839)(465,1556)(466,2478)(467,3333)(468,3263)(469,1855)(470,1746)(471,936)(472,3547)(473,3603)(475,3224)(477,3242)(478,3477)(479,3111)(480,3415)(481,2342)(482,715)(485,2546)(487,3673)(488,1429)(489,1917)(490,1904)(492,1154)(493,1762)(494,2771)(495,826)(496,2556)(497,1193)(498,2525)(500,1823)(501,3903)(502,1910)(503,2265)(504,959)(505,1436)(506,1437)(507,1108)(508,3029)(509,877)(510,1269)(511,1496)(512,2026)(513,1528)(514,565)(515,3718)(516,791)(517,2559)(518,1313)(519,787)(520,1793)(521,1096)(522,2472)(523,1940)(524,1608)(525,854)(526,1900)(527,2781)(528,1023)(529,1661)(530,3306)(531,2271)(533,590)(534,800)(535,605)(536,908)(537,637)(538,982)(539,2752)(540,2202)(541,3129)(542,681)(543,857)(544,2438)(545,593)(547,3348)(548,1455)(550,1676)(551,2895)(552,1897)(554,2494)(555,2830)(556,2683)(557,3446)(558,1357)(559,804)(560,939)(562,966)(563,953)(564,3762)(567,3887)(568,1401)(569,3006)(570,2769)(571,1153)(572,1220)(573,1516)(574,1379)(575,757)(576,2567)(577,2194)(578,1738)(579,2856)(580,2691)(581,2511)(582,2900)(583,3308)(584,886)(585,967)(586,995)(587,1838)(589,1895)(591,3089)(592,3747)(594,2884)(596,3235)(597,1812)(598,1198)(599,1500)(600,3332)(601,1546)(602,2812)(603,3535)(606,1768)(608,2893)(609,2955)(610,2731)(611,615)(612,773)(613,917)(614,3845)(616,2582)(617,885)(618,674)(619,2617)(620,3585)(621,1633)(622,2399)(623,2864)(624,3614)(625,3285)(626,3118)(627,1798)(628,1637)(629,682)(630,1969)(631,3753)(632,2814)(633,1294)(634,2723)(635,3619)(636,1788)(638,3582)(639,2020)(640,3900)(641,2031)(642,888)(643,3740)(644,3566)(645,778)(646,3592)(648,1445)(649,1100)(650,2551)(651,1328)(652,1001)(653,1316)(654,1141)(655,3838)(656,2686)(658,2568)(659,1697)(660,965)(661,1736)(662,3773)(663,3598)(664,1137)(665,2763)(667,2314)(668,1531)(669,1949)(671,1771)(672,720)(673,2044)(676,2059)(677,3756)(678,1466)(679,3007)(680,2932)(683,2388)(684,3161)(685,2340)(687,1072)(688,2283)(689,2390)(690,2768)(691,2958)(692,2987)(693,2583)(694,1111)(695,2602)(696,3824)(697,2304)(698,2130)(699,1631)(700,1896)(701,2543)(703,3849)(704,2927)(706,1764)(707,2245)(708,2881)(709,3640)(710,2129)(711,2487)(713,3397)(714,955)(716,1374)(719,1716)(721,3698)(723,2468)(724,2538)(725,3703)(726,3831)(727,2064)(728,1324)(729,2196)(730,3311)(731,2519)(732,1617)(733,3894)(734,2120)(735,1577)(736,2461)(737,1827)(738,2640)(739,1745)(740,2270)(741,2710)(742,2439)(743,813)(744,920)(745,3530)(746,2410)(747,2305)(748,3376)(749,2278)(750,2009)(751,3685)(752,3237)(753,2801)(754,3862)(755,2964)(756,3076)(758,887)(759,1920)(760,3660)(761,3846)(762,2398)(764,3711)(765,3487)(766,1779)(767,3786)(770,1217)(771,1382)(772,1775)(774,1052)(775,3453)(776,2301)(777,1231)(779,2235)(780,2726)(781,1532)(782,2389)(783,1065)(784,1529)(785,3571)(786,2680)(789,2372)(790,3418)(792,2696)(793,994)(795,2091)(796,1663)(798,2818)(799,973)(801,843)(802,949)(803,2581)(805,3158)(806,1200)(807,2393)(808,3833)(809,1636)(810,1906)(811,1054)(812,3181)(815,2153)(816,1714)(817,1579)(819,1203)(820,3049)(824,1008)(825,3532)(827,2941)(828,1933)(829,2981)(830,2331)(831,1107)(832,2984)(833,1051)(836,2575)(837,3354)(838,1983)(841,2220)(842,1130)(844,2875)(845,1610)(846,3269)(847,2209)(849,2774)(850,2826)(851,2310)(852,1292)(855,2515)(856,3578)(858,1435)(859,2887)(860,2223)(861,2994)(862,2048)(864,1268)(866,2614)(867,3239)(868,2359)(869,2607)(870,2179)(871,2350)(873,2973)(874,1799)(875,3034)(879,1912)(880,2877)(881,1962)(882,3825)(883,1659)(889,891)(890,1297)(892,1785)(894,3812)(896,1143)(897,1050)(898,979)(901,3440)(902,3328)(903,3474)(904,2035)(905,2224)(906,2416)(907,1602)(909,1167)(911,3644)(912,3173)(914,2007)(916,3701)(918,3539)(919,2379)(921,2205)(922,3119)(923,1800)(924,3526)(925,2571)(926,1036)(928,3501)(929,1334)(930,3014)(931,2208)(933,2236)(934,3019)(935,3194)(937,2535)(938,1795)(940,1502)(941,1981)(944,1263)(945,2307)(946,1672)(947,3869)(948,3229)(950,2299)(951,3363)(952,1389)(954,3655)(957,1739)(958,1954)(960,3108)(962,1786)(963,3247)(964,2942)(969,2289)(970,3183)(971,2298)(972,2067)(974,3000)(975,1540)(976,1948)(977,1005)(978,2904)(980,1901)(981,1815)(983,1319)(984,1272)(985,3056)(986,1842)(987,3853)(989,3737)(990,2778)(991,2545)(992,2249)(993,3232)(996,2783)(999,1542)(1000,3761)(1002,2727)(1003,1011)(1004,3439)(1006,1384)(1007,2933)(1009,1641)(1010,2139)(1012,3226)(1015,2588)(1016,1711)(1017,2233)(1018,3752)(1019,1967)(1020,3360)(1021,2873)(1022,2997)(1024,2212)(1025,1325)(1026,3574)(1027,3323)(1028,1946)(1029,3213)(1030,3422)(1031,1081)(1032,2659)(1033,3817)(1034,3763)(1035,1614)(1037,2765)(1038,2092)(1039,2189)(1040,1194)(1041,3707)(1042,1175)(1043,2679)(1044,3513)(1045,1071)(1046,1765)(1047,2152)(1048,2585)(1049,2753)(1056,2318)(1057,2054)(1058,2924)(1059,3149)(1060,1092)(1061,2291)(1063,1620)(1064,1685)(1066,2017)(1068,1452)(1069,3067)(1070,2427)(1073,1101)(1074,3164)(1075,1623)(1076,2923)(1077,2308)(1078,2166)(1079,1600)(1080,1270)(1082,1680)(1083,1618)(1084,3046)(1085,1770)(1087,1634)(1088,3310)(1090,1371)(1091,3305)(1093,2911)(1094,3187)(1097,1787)(1098,3542)(1099,3380)(1103,1385)(1104,2757)(1106,1360)(1109,3037)(1110,3393)(1112,1841)(1114,1686)(1115,2772)(1116,3001)(1117,3093)(1118,3377)(1119,3250)(1120,1755)(1121,3381)(1123,3712)(1125,1291)(1126,2419)(1127,1138)(1128,2368)(1131,1351)(1132,3292)(1133,2119)(1134,2219)(1135,1868)(1136,2122)(1139,1867)(1140,1348)(1142,1147)(1144,3282)(1145,1796)(1146,1205)(1148,1415)(1149,2504)(1150,3783)(1151,2211)(1155,3171)(1156,2158)(1157,1887)(1158,3425)(1160,1830)(1161,3024)(1162,1353)(1163,1941)(1164,3774)(1165,2589)(1166,3094)(1169,2963)(1170,2163)(1171,3721)(1172,3365)(1173,3480)(1174,1252)(1176,2666)(1177,2744)(1178,1669)(1179,2326)(1180,2866)(1181,3822)(1182,1972)(1183,2457)(1184,2284)(1185,2356)(1186,1780)(1187,1629)(1188,2714)(1191,2880)(1192,2708)(1195,1684)(1196,1777)(1197,2600)(1199,2510)(1201,3272)(1202,1720)(1204,1569)(1206,2626)(1207,2204)(1208,2177)(1209,2337)(1210,3517)(1211,1347)(1212,1284)(1213,3017)(1214,2810)(1215,1247)(1216,2593)(1218,2106)(1219,1392)(1222,3127)(1223,3420)(1224,1469)(1225,3215)(1226,2432)(1228,1721)(1229,2193)(1230,3430)(1232,1433)(1233,2945)(1234,1688)(1235,2694)(1236,3775)(1237,1349)(1238,2367)(1239,2090)(1240,2913)(1241,2363)(1242,3437)(1243,3589)(1244,3725)(1245,2033)(1246,3109)(1248,2701)(1250,1510)(1253,2907)(1254,3163)(1255,1479)(1256,1909)(1257,2485)(1259,2608)(1260,1432)(1261,2976)(1262,1668)(1264,3283)(1265,2993)(1266,1859)(1271,2721)(1273,3638)(1274,1431)(1275,1694)(1276,1563)(1278,3077)(1279,1690)(1280,1758)(1282,2228)(1283,2549)(1286,1984)(1287,2006)(1288,3460)(1289,1460)(1290,2824)(1293,1733)(1295,2634)(1298,3162)(1299,1343)(1300,1783)(1301,1350)(1302,1488)(1303,2725)(1304,1784)(1305,2914)(1306,1533)(1307,2450)(1308,2330)(1309,2286)(1310,3436)(1311,3273)(1314,2309)(1315,3553)(1317,3617)(1318,3674)(1320,3278)(1322,2365)(1323,2375)(1326,1553)(1327,1336)(1329,3863)(1330,2125)(1331,1424)(1332,3382)(1333,3207)(1335,2788)(1337,3140)(1339,3178)(1340,1397)(1341,2716)(1342,3179)(1344,3424)(1345,1430)(1346,2070)(1352,3905)(1354,2544)(1355,3238)(1356,2986)(1358,1905)(1359,3559)(1361,3083)(1362,2049)(1363,3482)(1364,3080)(1365,2948)(1366,1963)(1367,2655)(1368,1599)(1369,2360)(1370,3896)(1372,1880)(1373,3095)(1375,2260)(1377,3135)(1378,1862)(1380,2947)(1381,1797)(1383,2846)(1386,3403)(1388,2685)(1390,3337)(1391,1562)(1393,1723)(1394,2805)(1395,2648)(1396,2643)(1398,3463)(1399,2409)(1400,3590)(1402,3803)(1403,3219)(1405,3647)(1406,2374)(1407,2191)(1408,2961)(1409,2078)(1410,2562)(1411,1951)(1412,3248)(1413,1470)(1414,3133)(1416,1448)(1417,2148)(1419,3696)(1420,1575)(1421,2756)(1422,1656)(1423,3055)(1425,3882)(1426,3345)(1428,2282)(1434,2317)(1438,2086)(1439,3468)(1440,1998)(1441,3458)(1444,3419)(1446,2787)(1447,2656)(1450,3319)(1451,3005)(1453,1924)(1454,2386)(1456,2834)(1458,3027)(1459,3343)(1461,3022)(1462,1670)(1464,3042)(1465,2819)(1468,1934)(1472,3448)(1473,3835)(1474,2002)(1475,2523)(1476,1831)(1477,1626)(1478,1515)(1480,1508)(1482,2657)(1483,1726)(1484,2816)(1486,2412)(1487,2188)(1490,3208)(1491,2885)(1492,2861)(1493,1965)(1494,2241)(1497,3375)(1498,2872)(1499,1976)(1501,3374)(1503,3864)(1504,1687)(1505,3724)(1506,2689)(1509,3221)(1511,2239)(1512,2465)(1513,2577)(1514,2014)(1517,2403)(1518,1914)(1519,2464)(1521,3621)(1522,3252)(1523,2605)(1524,1647)(1525,2123)(1526,3514)(1527,2405)(1530,3197)(1534,2728)(1536,1971)(1538,2214)(1539,2159)(1541,2280)(1543,1552)(1544,3258)(1547,2433)(1548,2114)(1549,2978)(1550,2652)(1551,3286)(1555,2682)(1557,1937)(1558,1750)(1559,2230)(1560,3156)(1561,2401)(1564,2740)(1566,3379)(1567,3182)(1570,3626)(1571,2650)(1572,1642)(1574,2463)(1576,1805)(1578,2358)(1580,3722)(1581,2809)(1582,3734)(1583,1950)(1585,2960)(1586,2431)(1587,3251)(1588,3086)(1589,2400)(1590,3113)(1591,2840)(1592,3741)(1593,2606)(1594,2066)(1596,3438)(1598,2134)(1601,3841)(1605,2473)(1606,2339)(1607,2436)(1609,1978)(1611,2255)(1612,2724)(1613,2621)(1616,2121)(1619,3874)(1621,2878)(1622,3801)(1624,3739)(1625,1840)(1627,3407)(1628,3414)(1630,3699)(1635,3669)(1638,3768)(1640,2104)(1643,1678)(1644,1834)(1645,1782)(1646,1892)(1648,2327)(1649,1662)(1650,1651)(1652,2073)(1653,3064)(1655,3562)(1657,3298)(1658,3860)(1660,2720)(1664,2917)(1665,2420)(1667,3202)(1671,3751)(1674,3450)(1675,3297)(1679,3567)(1681,2842)(1683,3392)(1689,2248)(1691,3577)(1695,3488)(1699,3679)(1700,3518)(1701,2329)(1703,2618)(1704,3367)(1706,1850)(1707,2094)(1708,3097)(1709,2936)(1710,2380)(1713,2273)(1717,1727)(1719,2288)(1722,1908)(1724,3180)(1725,2707)(1728,3509)(1729,3079)(1730,3368)(1731,2039)(1732,2234)(1734,1944)(1740,3200)(1742,2706)(1743,2250)(1744,2112)(1747,3516)(1749,3579)(1751,3115)(1752,1966)(1753,2601)(1754,2738)(1756,2481)(1757,3829)(1760,2406)(1766,3318)(1767,3331)(1769,2647)(1773,2526)(1776,3629)(1778,2180)(1781,2175)(1790,3301)(1794,3524)(1801,3090)(1803,2055)(1804,3784)(1806,3320)(1807,3672)(1810,2087)(1811,2609)(1813,2822)(1814,3128)(1816,2302)(1817,2926)(1818,2229)(1819,2892)(1820,3312)(1821,3818)(1822,3413)(1824,3211)(1825,2334)(1826,2938)(1828,3069)(1829,2354)(1832,2639)(1833,3521)(1835,2441)(1836,2404)(1837,2058)(1839,3088)(1843,2176)(1844,3495)(1845,2776)(1846,2836)(1847,3385)(1849,3593)(1851,1882)(1852,3828)(1853,2088)(1854,3160)(1857,3520)(1858,2838)(1860,2348)(1861,2489)(1863,2762)(1864,2903)(1865,2580)(1866,3136)(1870,3694)(1872,3560)(1873,3039)(1874,3287)(1875,2804)(1876,2036)(1877,3351)(1878,2387)(1879,2996)(1885,2185)(1888,2534)(1889,3366)(1890,3198)(1891,2615)(1893,3859)(1894,2970)(1898,3720)(1902,2046)(1903,3378)(1907,3847)(1911,2803)(1913,2619)(1915,2290)(1916,3755)(1918,3146)(1919,3584)(1921,3114)(1922,2817)(1923,3410)(1925,3795)(1927,2541)(1928,3387)(1929,3877)(1930,2505)(1931,2084)(1935,2624)(1936,3166)(1938,2150)(1939,3442)(1942,2630)(1943,3031)(1945,2013)(1953,2734)(1955,2053)(1956,3454)(1958,3556)(1959,3645)(1960,3792)(1964,2424)(1968,3684)(1970,2430)(1973,3527)(1975,2957)(1977,3346)(1979,3563)(1980,2452)(1982,2645)(1985,3281)(1986,3771)(1987,2143)(1988,3837)(1989,2940)(1990,2712)(1991,2093)(1992,2554)(1993,2281)(1994,2946)(1995,3193)(1996,2382)(1997,3855)(1999,2802)(2000,2678)(2001,3427)(2003,2989)(2004,3246)(2005,2889)(2008,3291)(2011,2791)(2012,2103)(2015,2732)(2016,2637)(2018,3551)(2019,2446)(2021,2718)(2022,2636)(2023,3637)(2024,3561)(2027,3157)(2028,2157)(2029,2147)(2030,2815)(2034,3639)(2037,2863)(2038,3851)(2041,2381)(2042,2295)(2043,2213)(2045,2444)(2047,2990)(2050,3218)(2051,3536)(2052,2197)(2057,2251)(2060,2576)(2061,2869)(2062,3813)(2063,2098)(2065,3622)(2068,2338)(2069,3606)(2071,3186)(2072,3867)(2076,3658)(2077,2998)(2080,3548)(2081,3575)(2083,3832)(2085,2627)(2095,3546)(2099,3508)(2100,2681)(2101,3805)(2102,2321)(2105,3533)(2108,2573)(2109,3386)(2110,3503)(2111,3165)(2113,3850)(2115,3505)(2116,3759)(2117,2146)(2118,2952)(2126,3671)(2127,3484)(2131,2670)(2132,3697)(2133,2259)(2135,3048)(2136,2237)(2138,3498)(2140,3138)(2144,3613)(2145,3515)(2149,2709)(2151,3401)(2154,3624)(2155,2218)(2160,3471)(2161,2821)(2162,3663)(2164,2766)(2167,2979)(2168,2383)(2170,2306)(2171,3092)(2172,3220)(2174,2357)(2178,2920)(2181,3347)(2182,2199)(2184,2808)(2186,3087)(2190,3103)(2195,2879)(2198,2777)(2200,2751)(2203,2733)(2210,3188)(2215,3470)(2217,2533)(2221,3361)(2222,3234)(2225,2351)(2227,3742)(2231,2458)(2232,3623)(2238,3134)(2242,2418)(2243,3279)(2244,2874)(2246,3254)(2252,3651)(2253,2490)(2254,2508)(2256,3396)(2257,2858)(2258,3444)(2264,3353)(2266,2850)(2268,3764)(2269,3596)(2272,3051)(2274,2429)(2275,2611)(2276,3344)(2277,2693)(2279,3583)(2285,2632)(2292,2518)(2293,3043)(2294,3225)(2297,3726)(2300,2498)(2303,2426)(2311,3706)(2313,2402)(2315,3408)(2319,3296)(2320,2569)(2322,2908)(2323,2352)(2325,3467)(2328,3020)(2333,3154)(2335,2531)(2336,2784)(2341,3100)(2344,2654)(2345,3866)(2346,3872)(2349,3404)(2353,2828)(2355,2529)(2361,3816)(2364,3481)(2369,2949)(2370,3329)(2371,2564)(2392,2493)(2394,3494)(2395,3746)(2396,3770)(2411,3143)(2414,2992)(2415,3861)(2417,2628)(2421,3778)(2422,3324)(2423,3796)(2425,3558)(2428,2560)(2434,3062)(2435,3357)(2440,2467)(2442,2935)(2443,3856)(2445,3261)(2447,2649)(2448,3449)(2449,3153)(2451,3151)(2455,2742)(2459,3315)(2460,3072)(2462,3461)(2466,3340)(2469,2641)(2470,3002)(2471,3395)(2474,3499)(2475,3729)(2476,3840)(2477,2484)(2479,3217)(2482,3865)(2483,3507)(2486,3550)(2488,3609)(2491,3341)(2492,2972)(2495,3268)(2497,3338)(2499,3120)(2500,3612)(2501,3050)(2502,3608)(2503,3586)(2506,2665)(2507,3063)(2509,3750)(2513,3490)(2514,2561)(2516,3478)(2517,3653)(2521,3295)(2522,3525)(2530,3791)(2532,3274)(2536,2954)(2537,3082)(2539,3745)(2540,3383)(2542,3362)(2547,3680)(2548,3443)(2550,2916)(2552,2843)(2553,2625)(2555,2980)(2565,3836)(2570,3012)(2572,3691)(2574,2597)(2578,3757)(2579,3843)(2584,3902)(2586,3710)(2587,3500)(2592,3421)(2594,2755)(2596,2629)(2598,3642)(2603,3675)(2604,3026)(2612,3021)(2613,2669)(2616,3595)(2620,3633)(2633,3228)(2638,3196)(2642,3059)(2644,3765)(2646,3302)(2658,3175)(2661,3313)(2663,2705)(2667,3594)(2672,2743)(2674,2860)(2675,2700)(2676,2898)(2677,3794)(2688,2870)(2692,2794)(2695,3452)(2697,3176)(2698,3715)(2699,2867)(2702,2988)(2703,3627)(2704,3203)(2715,3265)(2717,3693)(2719,2746)(2729,3356)(2736,3670)(2739,3131)(2741,3891)(2747,3540)(2748,3290)(2749,2790)(2750,2969)(2754,3276)(2759,3423)(2761,3349)(2767,3447)(2770,2841)(2773,3370)(2775,3270)(2779,3190)(2782,3465)(2789,3776)(2792,3130)(2793,2910)(2795,3688)(2796,3075)(2797,3682)(2798,3601)(2799,3883)(2800,3549)(2806,3260)(2807,3280)(2811,3199)(2813,3650)(2823,3030)(2831,3214)(2833,3473)(2837,3060)(2839,3339)(2844,3126)(2848,3479)(2852,3895)(2853,3434)(2854,2959)(2857,3227)(2859,3241)(2862,3004)(2865,3607)(2868,3555)(2871,3713)(2876,3600)(2886,3901)(2888,3065)(2890,3811)(2891,3716)(2894,3852)(2896,3081)(2897,3428)(2901,3522)(2902,3802)(2906,3848)(2909,3677)(2915,3066)(2918,3700)(2919,3523)(2921,3406)(2922,3028)(2925,3664)(2928,3871)(2929,3789)(2930,3625)(2934,3754)(2937,3728)(2939,3212)(2943,2995)(2944,3168)(2950,3429)(2953,3667)(2956,3405)(2965,3121)(2966,3061)(2967,2982)(2968,3409)(2971,3602)(2974,3690)(2975,3236)(2977,3015)(2983,3152)(3003,3569)(3008,3038)(3013,3544)(3016,3659)(3018,3469)(3023,3893)(3033,3294)(3041,3799)(3044,3391)(3047,3714)(3052,3798)(3053,3253)(3058,3493)(3068,3506)(3070,3159)(3071,3534)(3073,3122)(3074,3806)(3078,3879)(3085,3098)(3091,3107)(3099,3758)(3101,3790)(3102,3350)(3105,3496)(3117,3277)(3124,3723)(3125,3231)(3132,3185)(3139,3777)(3144,3336)(3147,3412)(3148,3787)(3167,3599)(3169,3643)(3172,3632)(3192,3388)(3195,3398)(3201,3648)(3205,3635)(3209,3335)(3210,3372)(3222,3630)(3223,3288)(3240,3492)(3244,3431)(3245,3564)(3255,3570)(3256,3687)(3257,3519)(3259,3573)(3264,3678)(3266,3767)(3267,3552)(3284,3435)(3293,3358)(3299,3727)(3300,3709)(3303,3683)(3307,3731)(3309,3743)(3316,3620)(3321,3416)(3326,3876)(3330,3355)(3334,3576)(3359,3511)(3369,3702)(3373,3686)(3389,3636)(3390,3618)(3399,3666)(3402,3730)(3411,3704)(3417,3462)(3433,3661)(3445,3616)(3455,3456)(3459,3605)(3464,3814)(3472,3631)(3476,3541)(3491,3890)(3497,3808)(3504,3779)(3512,3884)(3528,3531)(3529,3565)(3537,3668)(3545,3854)(3557,3804)(3568,3819)(3572,3797)(3588,3634)(3591,3858)(3597,3692)(3641,3800)(3654,3898)(3662,3885)(3705,3748)(3708,3744)(3736,3906)(3738,3772)(3780,3785)(3807,3889)(3815,3897)(3820,3827)(3842,3881)(3870,3904)(3873,3899),(2,385)(3,2805)(4,1163)(5,156)(6,3878)(7,3586)(8,2279)(9,314)(11,2718)(12,3312)(13,3182)(14,530)(15,1964)(16,2359)(17,3737)(18,2162)(19,2363)(20,3436)(21,2401)(22,1576)(23,993)(24,3366)(25,2517)(26,3029)(27,3319)(28,2923)(29,2084)(30,764)(31,1546)(32,1578)(33,602)(34,539)(35,1588)(36,2272)(38,433)(39,3061)(40,1941)(41,690)(42,2635)(43,2085)(44,3115)(45,1852)(46,1075)(47,2477)(48,2925)(49,3412)(50,1097)(51,2715)(52,1678)(53,3143)(54,589)(55,2620)(56,2228)(57,1616)(58,1635)(59,1510)(60,2140)(61,793)(62,1283)(63,307)(64,1832)(65,1895)(66,997)(67,800)(68,177)(69,3003)(70,1151)(71,2880)(72,225)(73,477)(74,2494)(75,2256)(76,1313)(77,527)(78,1853)(79,2215)(80,1996)(81,2107)(82,2485)(83,3695)(84,1845)(85,3171)(86,402)(88,3620)(89,1819)(90,98)(91,3272)(92,3517)(93,3304)(94,355)(95,1222)(96,717)(97,1961)(99,640)(100,3353)(101,3346)(102,3197)(103,1617)(104,3810)(105,3580)(106,2647)(107,1259)(108,2094)(109,1085)(110,2743)(111,2738)(112,2393)(113,1173)(114,1424)(115,3306)(116,3023)(117,1891)(118,1861)(119,2467)(120,2838)(121,2498)(122,3453)(123,3444)(124,2343)(125,3784)(126,3039)(127,3021)(128,2252)(129,3211)(130,935)(131,894)(132,3371)(133,3263)(134,3059)(135,3406)(136,169)(137,1842)(138,1987)(139,3131)(140,215)(141,1202)(142,3339)(143,1899)(144,1740)(145,2769)(146,3700)(148,1926)(149,992)(150,1274)(151,1978)(152,231)(153,2058)(154,1006)(155,1611)(157,1636)(158,2048)(159,1898)(160,3237)(161,906)(162,237)(163,3313)(164,2255)(165,597)(166,1155)(167,3731)(168,2218)(170,709)(171,2490)(172,2116)(173,2875)(174,1350)(175,2736)(176,2519)(178,3593)(179,3015)(180,1307)(181,3863)(182,466)(183,2952)(184,3674)(185,1466)(186,241)(187,2046)(188,2023)(189,1536)(190,3161)(191,2300)(192,3901)(193,1632)(194,2739)(195,2101)(196,3625)(197,3334)(198,313)(199,3766)(200,1566)(201,3431)(202,1529)(203,732)(204,1319)(205,2774)(206,1410)(207,436)(208,334)(209,2949)(210,3119)(211,828)(212,1560)(213,3662)(214,3871)(216,2846)(217,1043)(218,1065)(219,663)(220,2780)(221,1716)(222,2055)(223,1795)(224,3518)(226,1008)(227,2143)(228,2672)(229,781)(230,1387)(232,2405)(233,1738)(234,1662)(235,587)(236,2918)(238,1305)(239,2047)(240,3172)(242,1022)(243,372)(244,2542)(245,1444)(246,3532)(247,2244)(248,3305)(249,3698)(250,3556)(251,2452)(252,773)(253,553)(254,2060)(255,3335)(256,1210)(257,2674)(258,1140)(259,2050)(260,516)(261,424)(262,2523)(263,2742)(264,3564)(265,3286)(266,2338)(267,3122)(268,3672)(269,2379)(270,3776)(271,1105)(272,1532)(273,3169)(274,1552)(275,3309)(276,3265)(277,3723)(278,2963)(279,3162)(280,2320)(281,968)(282,888)(283,1909)(284,881)(285,3050)(286,2173)(287,1412)(288,3299)(289,3342)(290,2721)(291,2458)(292,1009)(293,3538)(294,2370)(295,2207)(296,1496)(297,2331)(298,2915)(299,1435)(300,3753)(301,3173)(302,2226)(303,966)(304,2161)(305,3709)(306,907)(308,677)(309,985)(310,2765)(311,1033)(312,3369)(315,884)(316,673)(317,856)(318,3101)(319,1624)(320,2249)(321,643)(322,1409)(323,3181)(324,631)(325,2068)(326,2886)(327,2424)(328,1843)(329,3834)(330,3563)(331,1493)(332,2120)(333,2924)(335,2547)(336,694)(337,3024)(338,394)(339,3813)(340,3665)(341,1781)(342,785)(343,1416)(344,2604)(345,2556)(346,3671)(347,3670)(348,3852)(349,2469)(350,2894)(351,2941)(352,604)(353,614)(354,2922)(356,2651)(357,1030)(358,857)(359,1672)(360,1972)(361,3409)(362,2414)(363,2072)(364,1144)(365,2884)(366,1610)(367,1581)(368,1765)(369,1679)(370,769)(371,377)(373,1211)(374,2537)(375,598)(376,2852)(378,608)(379,1164)(380,3873)(381,2022)(382,2809)(383,3043)(384,3389)(386,1195)(387,2341)(388,2349)(389,2336)(390,2396)(391,1005)(392,3570)(393,1018)(395,1468)(396,3347)(397,1618)(398,2710)(399,3189)(400,2599)(401,1878)(403,932)(404,2488)(405,3666)(406,1217)(407,2683)(408,1583)(409,688)(410,2626)(411,1838)(412,2152)(413,1261)(414,1439)(415,3800)(416,546)(417,2938)(418,2304)(419,515)(420,2122)(421,1362)(422,1820)(423,2656)(425,3138)(426,2281)(427,903)(428,1627)(429,908)(430,2292)(431,2254)(432,2792)(435,2664)(437,1425)(438,2470)(439,1083)(440,806)(441,3106)(442,1949)(443,2297)(444,2136)(445,2973)(446,1519)(447,3480)(448,3566)(449,526)(450,2564)(451,1974)(452,1952)(453,3643)(454,2196)(455,3282)(456,2378)(457,2495)(458,3689)(459,2433)(460,1346)(461,482)(462,1863)(463,1908)(464,925)(465,3398)(467,882)(468,1615)(469,3428)(470,1512)(471,3572)(472,3478)(473,3417)(474,644)(475,3337)(476,3191)(478,1806)(479,1836)(480,728)(481,3796)(483,3583)(484,2789)(485,1092)(486,3760)(487,3801)(488,1541)(489,2179)(490,1704)(491,2641)(492,3151)(493,1982)(494,3627)(495,3755)(496,3604)(497,3473)(498,3771)(499,543)(500,1126)(501,1862)(502,1012)(503,1359)(504,2638)(505,1389)(506,3715)(507,3125)(508,3735)(509,1509)(510,949)(511,2366)(512,519)(513,3292)(514,3359)(517,1844)(518,2962)(520,1724)(521,2271)(522,3768)(523,1499)(524,2328)(525,2163)(528,3561)(529,3849)(531,1096)(532,783)(533,1749)(534,1603)(535,1743)(536,2082)(537,829)(538,3269)(540,1041)(541,3129)(542,1927)(544,3864)(545,3832)(547,1034)(548,3783)(549,1873)(550,3694)(551,3505)(552,616)(554,3174)(555,3448)(556,823)(557,2643)(558,3164)(559,3208)(560,1562)(561,2283)(562,3888)(563,1930)(564,2184)(565,3511)(566,2358)(567,591)(568,3235)(569,665)(570,1735)(571,767)(572,1188)(573,2842)(574,1744)(575,758)(576,2565)(577,2689)(578,722)(579,2354)(580,2993)(581,2166)(582,1121)(583,606)(584,738)(585,2719)(586,1563)(588,1348)(590,3579)(592,2967)(593,2083)(594,3275)(595,3598)(596,1401)(599,3704)(600,1288)(601,1189)(603,2114)(605,2250)(607,2464)(609,1284)(610,3550)(611,2090)(612,1463)(613,2804)(615,1239)(617,1440)(618,3778)(619,1315)(620,2598)(621,2927)(622,2182)(623,2289)(624,2302)(625,1131)(626,692)(627,649)(628,2164)(629,811)(630,2577)(632,1045)(633,3341)(634,1025)(635,1147)(636,3186)(637,2981)(638,2942)(639,2427)(641,3279)(642,872)(645,1207)(646,3254)(647,3419)(648,3217)(650,2290)(651,2001)(652,3256)(654,1653)(655,2677)(656,1224)(657,3880)(658,1385)(659,2729)(660,2625)(661,2476)(662,3391)(664,3772)(666,2576)(667,1989)(668,1967)(669,988)(670,721)(671,2064)(672,1569)(674,2421)(675,1803)(678,2786)(679,1956)(680,3159)(681,2541)(682,1054)(683,2929)(684,2662)(686,827)(687,984)(689,2390)(691,3157)(693,3866)(695,2619)(696,1757)(697,1702)(698,2077)(699,774)(700,2665)(701,2295)(702,2121)(703,1661)(704,1633)(705,3702)(706,3315)(707,2248)(708,3041)(710,1488)(711,2449)(712,2078)(713,3416)(714,3443)(715,3206)(716,2831)(718,1520)(719,3177)(720,1204)(723,1148)(724,2186)(725,1209)(726,2552)(727,1771)(729,1763)(730,2269)(731,2169)(733,3617)(734,3868)(735,2585)(736,1758)(737,3612)(739,3378)(740,2242)(741,3489)(742,1650)(743,2747)(744,1648)(745,2759)(746,1101)(747,3113)(748,2606)(749,1943)(750,2443)(751,3203)(752,3110)(753,3691)(754,2974)(755,2994)(756,2834)(757,887)(760,2593)(761,3236)(762,937)(763,1962)(765,1783)(766,1104)(768,3248)(770,3155)(771,3345)(772,1981)(775,1321)(776,2174)(777,2092)(778,2204)(779,3546)(780,1599)(782,2693)(784,3035)(786,3841)(787,2026)(788,2508)(789,3219)(790,1266)(791,2206)(792,1107)(794,3082)(795,1314)(796,3301)(797,3245)(798,1273)(799,3413)(801,1411)(802,1269)(803,3030)(804,1490)(805,3160)(807,1705)(808,3098)(809,2671)(810,1492)(812,1673)(813,3540)(814,2118)(815,3455)(816,3108)(817,2732)(818,1977)(819,2806)(820,2150)(821,2416)(822,1770)(824,2074)(825,2737)(826,1916)(830,2558)(831,2696)(832,3601)(833,1815)(834,3200)(835,1824)(836,1428)(837,1340)(838,3144)(839,2571)(840,3127)(841,2644)(842,3590)(843,1951)(844,1772)(845,3141)(846,982)(847,2352)(848,1200)(849,1774)(850,2313)(851,855)(852,2348)(853,2044)(854,1170)(858,1666)(859,3013)(860,2361)(861,2964)(862,1489)(863,2264)(864,2492)(866,2871)(867,1717)(868,1013)(869,2127)(870,1917)(871,2534)(873,1095)(874,2029)(875,1263)(876,3733)(877,3221)(878,3026)(879,3693)(880,1174)(883,3069)(885,1998)(886,2640)(889,2448)(890,2796)(891,3449)(892,2158)(893,2324)(895,1769)(896,2751)(897,1630)(898,930)(899,3664)(900,2501)(901,3440)(902,3820)(904,3624)(905,1199)(909,1665)(910,1720)(911,2193)(912,956)(913,3790)(914,2509)(915,1301)(916,2561)(917,1875)(918,3134)(919,3145)(920,2327)(921,2709)(922,3839)(923,3562)(924,1753)(926,1747)(927,3130)(928,3280)(929,1336)(931,2104)(933,2779)(934,1080)(936,3797)(938,1947)(939,1391)(940,1417)(941,1775)(942,1565)(943,3893)(944,3034)(945,3251)(946,3243)(947,1405)(948,2589)(950,3519)(951,1997)(952,1436)(953,2505)(954,3055)(955,2548)(957,3068)(958,1226)(959,3196)(960,1714)(961,2382)(962,3288)(963,2322)(964,3582)(965,2553)(967,2746)(969,2864)(970,2878)(971,3708)(972,2658)(973,1822)(974,1123)(975,3588)(976,3524)(977,2453)(978,2904)(979,3014)(980,1343)(981,1051)(983,3271)(986,2951)(987,2667)(989,3681)(990,1773)(991,3424)(994,1404)(995,1276)(996,2346)(998,1934)(999,2866)(1000,2754)(1001,3687)(1002,2666)(1003,3904)(1004,1295)(1007,3094)(1010,2836)(1011,3870)(1014,2391)(1015,2629)(1016,3148)(1017,1042)(1019,1531)(1020,2499)(1021,2429)(1023,2024)(1024,1725)(1026,3042)(1027,1260)(1028,1733)(1031,1596)(1032,2138)(1035,2521)(1036,3516)(1037,3510)(1038,1231)(1039,1776)(1040,1922)(1044,1868)(1046,3123)(1047,3057)(1048,1577)(1049,2036)(1050,3699)(1052,1631)(1053,1641)(1055,3216)(1056,1146)(1057,3716)(1058,3040)(1059,1694)(1060,2546)(1062,3576)(1063,2086)(1064,3079)(1066,2188)(1067,1495)(1068,1994)(1069,1730)(1070,2020)(1071,2814)(1072,1272)(1073,2410)(1074,1357)(1076,2711)(1077,1582)(1078,2511)(1079,2840)(1081,3438)(1082,1991)(1084,2003)(1086,3718)(1087,1629)(1088,2087)(1090,1371)(1091,2192)(1093,3258)(1094,2457)(1098,2151)(1099,2844)(1100,1798)(1102,3010)(1103,2568)(1106,3403)(1108,3231)(1109,1691)(1110,1138)(1111,2187)(1113,1448)(1114,3343)(1115,1921)(1116,2394)(1117,2862)(1118,3274)(1119,3250)(1120,3303)(1122,1707)(1124,1298)(1125,2232)(1127,3393)(1128,2273)(1129,2021)(1130,1400)(1132,1528)(1133,2197)(1134,1963)(1135,3513)(1136,1427)(1137,3738)(1139,1522)(1141,3064)(1142,3619)(1143,2200)(1145,3591)(1149,2961)(1150,1455)(1152,3474)(1153,3786)(1154,2451)(1156,1785)(1157,2257)(1158,2417)(1159,3100)(1160,1879)(1161,2591)(1162,3557)(1165,3229)(1166,2933)(1167,2420)(1168,1201)(1169,2623)(1171,2428)(1172,2351)(1175,2233)(1176,2727)(1177,2655)(1178,2311)(1179,3458)(1180,1542)(1181,3058)(1182,3615)(1183,3187)(1184,2134)(1185,3584)(1186,1984)(1187,1634)(1190,1384)(1191,1568)(1192,1491)(1193,2833)(1194,2817)(1196,2702)(1197,2816)(1198,2347)(1203,3260)(1205,2318)(1206,1871)(1208,3877)(1212,2955)(1213,1515)(1215,1525)(1216,3660)(1218,3375)(1219,1968)(1220,2714)(1221,1858)(1223,2195)(1225,2392)(1227,2608)(1228,1421)(1229,3644)(1230,2213)(1232,1784)(1233,1907)(1234,1797)(1235,2330)(1236,3714)(1237,3387)(1238,1645)(1240,2000)(1241,1418)(1242,1814)(1243,3555)(1244,3819)(1245,1420)(1246,1960)(1247,2123)(1248,2701)(1249,1849)(1250,1856)(1251,1431)(1252,2877)(1253,2592)(1254,1667)(1255,3008)(1256,2089)(1257,1442)(1258,2411)(1262,2605)(1264,2039)(1265,2691)(1267,3726)(1268,2972)(1270,3019)(1271,2216)(1275,3149)(1277,2893)(1278,3291)(1279,1517)(1280,2461)(1281,2231)(1282,2820)(1285,1802)(1286,1780)(1287,1465)(1289,2111)(1290,2530)(1291,3623)(1292,1860)(1293,1946)(1294,2491)(1296,3828)(1297,3075)(1299,1901)(1300,3487)(1302,2129)(1304,1433)(1306,1326)(1308,2694)(1309,3429)(1310,3327)(1311,2890)(1312,2387)(1317,3894)(1318,3788)(1320,2436)(1322,2069)(1323,2724)(1324,3415)(1325,2723)(1327,1334)(1328,3427)(1329,2413)(1330,3012)(1331,1808)(1332,3479)(1333,3659)(1335,3410)(1337,3099)(1338,3845)(1339,2275)(1341,3883)(1342,3350)(1344,2545)(1345,2960)(1347,3769)(1349,1928)(1351,3285)(1352,1701)(1353,3804)(1354,2113)(1355,2011)(1358,1446)(1360,1386)(1361,2916)(1363,2618)(1364,3065)(1365,3874)(1366,2219)(1367,2744)(1368,2726)(1369,3815)(1370,2540)(1372,2841)(1373,1675)(1374,3214)(1375,2531)(1376,1447)(1377,3340)(1378,3903)(1379,2112)(1380,2959)(1381,1688)(1382,1426)(1383,1692)(1388,3529)(1390,3224)(1392,3684)(1393,1557)(1394,2882)(1395,3667)(1396,3446)(1397,3354)(1398,3668)(1399,2445)(1402,3677)(1403,2372)(1406,2315)(1407,3435)(1408,2504)(1413,1813)(1414,2168)(1415,2468)(1419,1890)(1422,2400)(1423,3655)(1429,2280)(1430,1585)(1432,3323)(1434,2676)(1437,2698)(1438,1620)(1441,2326)(1445,2479)(1449,3739)(1450,2760)(1451,2574)(1452,2946)(1453,3573)(1454,1674)(1456,3076)(1457,3720)(1458,3078)(1459,1686)(1460,3165)(1461,3267)(1462,2901)(1464,3574)(1467,3633)(1469,2686)(1470,2822)(1471,2371)(1472,2830)(1473,2170)(1474,2775)(1475,3352)(1476,2497)(1477,2586)(1478,3017)(1479,3038)(1480,2099)(1481,2263)(1482,3631)(1483,3452)(1484,2600)(1485,2258)(1486,1851)(1487,2017)(1494,3386)(1497,2106)(1498,2616)(1500,3411)(1501,2037)(1502,2148)(1503,2438)(1504,3357)(1505,3507)(1506,2194)(1507,3441)(1508,3508)(1511,3861)(1513,1969)(1514,2749)(1516,1681)(1518,3471)(1521,2016)(1523,1668)(1524,1613)(1526,2502)(1527,3104)(1530,3781)(1533,1553)(1534,2926)(1535,1754)(1537,2752)(1538,3745)(1539,1586)(1540,3634)(1543,3150)(1544,2911)(1545,2079)(1547,1957)(1548,3535)(1549,3742)(1550,1710)(1551,2832)(1554,2484)(1555,1892)(1556,3195)(1558,2325)(1559,1953)(1561,2690)(1564,2198)(1567,2376)(1570,3859)(1571,2533)(1572,3697)(1573,3209)(1574,2675)(1575,2033)(1579,2015)(1580,1660)(1584,2088)(1587,2307)(1589,1656)(1590,2305)(1591,1600)(1592,2057)(1593,3376)(1594,2447)(1595,3578)(1597,2921)(1598,2284)(1601,2680)(1602,2931)(1604,3399)(1605,3860)(1606,1821)(1607,3278)(1608,3020)(1609,3649)(1612,2375)(1614,3295)(1619,2948)(1621,3183)(1622,3673)(1623,2566)(1625,3331)(1626,3710)(1628,3549)(1637,2766)(1638,2472)(1639,1958)(1640,2208)(1642,2132)(1643,3821)(1644,2210)(1646,2682)(1647,2621)(1649,3611)(1651,2439)(1652,2529)(1654,2126)(1655,1800)(1657,1955)(1658,2473)(1659,1828)(1663,1790)(1664,3630)(1669,3706)(1670,3522)(1671,1709)(1676,1870)(1677,3396)(1680,2093)(1682,3051)(1683,2971)(1684,3610)(1685,1729)(1687,2435)(1689,2245)(1690,2403)(1693,2032)(1695,2773)(1696,3362)(1697,3356)(1698,3086)(1699,3902)(1700,3322)(1703,3482)(1706,2103)(1708,3476)(1711,3787)(1712,1979)(1713,2368)(1715,2627)(1718,3641)(1719,3884)(1721,2756)(1722,2855)(1723,1937)(1726,2695)(1727,3239)(1728,3515)(1731,3283)(1732,2063)(1734,3234)(1736,3840)(1737,2211)(1739,3506)(1741,3147)(1742,2474)(1745,1903)(1746,2465)(1748,2812)(1750,3467)(1751,3466)(1752,2970)(1755,3683)(1756,3536)(1759,2455)(1761,3124)(1762,2645)(1764,2459)(1766,3736)(1767,1840)(1768,3308)(1777,2988)(1778,2319)(1779,2757)(1782,2367)(1786,3223)(1787,3184)(1788,2071)(1791,3073)(1792,2287)(1793,3180)(1794,1948)(1796,3858)(1799,2147)(1801,3650)(1804,3892)(1805,2128)(1807,2156)(1809,3899)(1810,3310)(1811,3780)(1812,3543)(1816,3614)(1817,2728)(1818,2870)(1823,2419)(1825,3575)(1826,2999)(1827,2500)(1829,2856)(1830,2996)(1831,3338)(1833,2462)(1834,3188)(1835,2425)(1837,3451)(1839,3854)(1846,2139)(1847,3754)(1848,3244)(1850,2012)(1854,3158)(1855,2897)(1857,3402)(1859,3418)(1864,3192)(1865,3465)(1866,2321)(1867,3252)(1869,3470)(1872,2172)(1874,2630)(1876,2753)(1877,2995)(1880,2770)(1881,3384)(1882,2412)(1883,3637)(1884,3571)(1885,2005)(1886,2976)(1887,2858)(1888,2350)(1889,3844)(1893,3626)(1894,1966)(1896,2506)(1897,2582)(1900,2722)(1902,2847)(1904,3367)(1905,2787)(1906,2861)(1910,3226)(1912,2717)(1913,2602)(1914,2160)(1915,2551)(1918,3326)(1919,2356)(1923,2788)(1924,3259)(1925,2670)(1929,2177)(1931,2312)(1932,3300)(1933,3394)(1935,3152)(1936,3324)(1938,3049)(1939,2692)(1940,1976)(1942,3287)(1944,2222)(1945,3654)(1950,3830)(1954,2432)(1959,3246)(1965,2407)(1970,2268)(1971,2883)(1973,2712)(1975,3757)(1980,3233)(1983,3336)(1985,3241)(1986,2525)(1988,3533)(1990,3527)(1992,2117)(1993,3011)(1995,3500)(1999,2065)(2002,3270)(2004,3645)(2006,2819)(2007,3750)(2008,3077)(2009,3856)(2013,3898)(2014,2790)(2018,3613)(2019,3355)(2025,3268)(2027,2958)(2028,3658)(2030,3344)(2031,2243)(2034,2748)(2035,2154)(2038,3779)(2040,3156)(2041,3048)(2042,2543)(2043,3430)(2045,3053)(2049,2262)(2051,2481)(2052,2119)(2053,3298)(2054,2891)(2056,3732)(2061,2697)(2062,2332)(2066,2649)(2067,3175)(2070,2528)(2073,2355)(2075,3900)(2076,2157)(2080,2259)(2081,2334)(2091,2309)(2095,2235)(2096,3056)(2097,3895)(2098,2234)(2100,2471)(2102,3136)(2105,3837)(2108,2654)(2109,2241)(2110,2364)(2115,2895)(2124,2762)(2125,2570)(2130,2998)(2131,3795)(2133,3548)(2135,2381)(2137,2562)(2141,2237)(2142,3364)(2144,3551)(2145,3509)(2146,2554)(2149,2205)(2153,3456)(2155,3483)(2159,2431)(2165,3636)(2167,3372)(2171,2434)(2175,3628)(2176,3142)(2178,3225)(2180,3296)(2181,2296)(2183,2687)(2185,2889)(2189,3629)(2190,3018)(2191,3284)(2199,2399)(2201,3774)(2202,3707)(2203,3405)(2209,2323)(2212,2707)(2214,2539)(2217,2650)(2220,3765)(2221,2980)(2223,3816)(2224,2510)(2225,3365)(2227,2978)(2229,2688)(2230,2734)(2236,3190)(2238,3539)(2239,2415)(2240,2977)(2246,3592)(2247,2569)(2251,3741)(2253,3581)(2260,2335)(2261,3653)(2265,3559)(2266,3071)(2267,3457)(2270,2418)(2274,2873)(2276,2815)(2277,2389)(2278,3031)(2282,2575)(2285,3358)(2286,2950)(2288,3512)(2293,2849)(2294,2920)(2298,3744)(2299,3257)(2301,2357)(2303,3052)(2306,3835)(2308,3734)(2310,2515)(2314,2940)(2316,2615)(2317,2898)(2329,3905)(2333,3154)(2337,3703)(2339,3818)(2342,2423)(2344,2573)(2345,2583)(2353,2837)(2360,3897)(2362,2764)(2365,3606)(2369,2622)(2373,2966)(2374,3408)(2377,3651)(2380,2652)(2383,3133)(2384,3569)(2385,3812)(2386,3450)(2388,3789)(2395,2797)(2397,2661)(2398,2535)(2402,2826)(2404,3111)(2408,3609)(2409,3261)(2422,3166)(2426,3798)(2430,3764)(2437,3025)(2440,3717)(2441,3558)(2442,3390)(2444,3253)(2446,3330)(2450,3676)(2456,2860)(2460,3117)(2463,2700)(2466,3135)(2475,2613)(2478,3289)(2480,2930)(2482,3802)(2483,3724)(2486,2731)(2487,3153)(2489,3554)(2493,3215)(2496,3329)(2503,2985)(2507,3814)(2512,3756)(2513,3597)(2514,3701)(2516,3547)(2518,3719)(2520,2845)(2522,3661)(2524,3809)(2526,2778)(2527,3112)(2532,3377)(2536,3445)(2538,3087)(2544,3850)(2549,3204)(2550,3083)(2555,3361)(2557,2851)(2559,3495)(2560,3721)(2563,3567)(2567,3836)(2572,2801)(2578,2957)(2579,2865)(2580,2782)(2581,2823)(2584,3679)(2587,3193)(2588,2596)(2590,3084)(2595,3770)(2597,3005)(2601,3526)(2603,3074)(2607,3484)(2609,3785)(2610,3680)(2611,3178)(2612,2673)(2614,3713)(2617,3553)(2624,2983)(2628,3425)(2631,3632)(2632,3293)(2633,2795)(2634,3439)(2636,3045)(2637,3621)(2639,3325)(2642,3137)(2646,3728)(2648,2953)(2653,3407)(2657,3472)(2659,3498)(2660,3759)(2663,2876)(2668,2821)(2669,3729)(2678,2913)(2679,3793)(2681,3395)(2684,3002)(2685,3565)(2699,3635)(2703,2771)(2704,3685)(2705,3600)(2706,3499)(2708,2885)(2713,3752)(2716,2799)(2720,3722)(2730,3255)(2733,2956)(2735,2928)(2740,2777)(2741,3349)(2745,3379)(2750,3266)(2761,3891)(2763,3006)(2767,3139)(2768,3432)(2772,3114)(2776,3317)(2781,3230)(2783,3872)(2784,2785)(2791,3238)(2793,3373)(2794,3442)(2798,2984)(2800,3414)(2802,3622)(2807,3501)(2808,3762)(2811,3808)(2813,3090)(2818,3638)(2824,3791)(2825,2997)(2827,3242)(2828,3060)(2829,3867)(2835,3817)(2839,3032)(2843,3831)(2848,3382)(2850,3534)(2853,3434)(2854,2947)(2857,3748)(2859,3281)(2863,3374)(2867,3205)(2868,3589)(2869,3176)(2872,3595)(2874,3502)(2879,3420)(2881,3799)(2887,3544)(2888,3080)(2892,3009)(2896,3889)(2899,3663)(2900,3381)(2902,3865)(2903,3388)(2905,3885)(2906,2965)(2907,3421)(2908,3247)(2909,3803)(2910,3686)(2912,3422)(2914,3262)(2917,3222)(2919,3678)(2932,3070)(2934,3385)(2935,3618)(2936,3751)(2937,3302)(2939,3240)(2943,3351)(2944,3107)(2945,3847)(2954,3616)(2968,3749)(2969,3767)(2975,3846)(2979,3210)(2982,3747)(2987,3118)(2989,3046)(2990,3782)(2991,3400)(2992,3656)(3000,3712)(3001,3494)(3004,3093)(3007,3454)(3016,3207)(3022,3552)(3027,3879)(3028,3170)(3033,3528)(3036,3743)(3037,3577)(3044,3773)(3047,3775)(3062,3092)(3063,3464)(3066,3823)(3067,3368)(3072,3277)(3081,3807)(3085,3833)(3088,3545)(3089,3887)(3091,3168)(3095,3297)(3096,3740)(3097,3541)(3102,3179)(3103,3469)(3105,3648)(3109,3792)(3116,3640)(3120,3360)(3121,3848)(3126,3380)(3128,3437)(3132,3599)(3140,3758)(3146,3876)(3163,3202)(3167,3185)(3194,3875)(3198,3696)(3199,3497)(3201,3496)(3212,3492)(3218,3646)(3220,3560)(3227,3705)(3228,3688)(3232,3652)(3249,3727)(3264,3523)(3273,3811)(3276,3761)(3290,3639)(3294,3531)(3307,3857)(3311,3596)(3314,3882)(3316,3657)(3318,3906)(3320,3477)(3321,3397)(3328,3827)(3332,3460)(3333,3825)(3348,3763)(3363,3855)(3370,3488)(3383,3896)(3392,3602)(3401,3542)(3404,3485)(3423,3530)(3426,3711)(3433,3525)(3447,3777)(3459,3605)(3461,3521)(3462,3603)(3463,3537)(3468,3587)(3475,3805)(3481,3503)(3490,3692)(3491,3890)(3493,3822)(3504,3851)(3514,3608)(3520,3730)(3568,3725)(3585,3642)(3594,3853)(3607,3843)(3647,3869)(3669,3826)(3675,3806)(3682,3746)(3690,3862)(3794,3838)(3824,3829)(3842,3881),(2,1564)(3,2882)(4,3669)(5,3707)(6,2209)(7,3455)(8,2150)(9,3401)(10,1443)(11,2748)(12,1967)(13,1463)(14,2779)(15,1175)(16,3768)(17,529)(18,1611)(19,104)(20,1310)(21,3033)(22,3797)(23,3208)(24,2399)(25,2478)(26,1337)(27,1792)(28,1535)(29,2217)(30,2570)(31,954)(32,2164)(33,1694)(34,2880)(35,470)(36,1685)(37,3600)(38,3346)(39,525)(40,2735)(41,3755)(42,2662)(43,2539)(44,2658)(45,2481)(46,664)(47,2375)(48,3210)(49,1481)(50,492)(51,2326)(52,2614)(53,1689)(54,506)(55,1097)(56,2132)(57,3488)(58,1941)(59,128)(60,1952)(61,2955)(62,701)(63,133)(64,3715)(65,1832)(66,1248)(67,680)(68,547)(69,2695)(70,3805)(71,2525)(72,3351)(73,2556)(74,3174)(75,2713)(76,2920)(77,413)(78,1056)(79,875)(80,3217)(81,579)(82,1856)(83,1926)(84,118)(85,576)(86,1590)(87,401)(88,770)(89,3694)(90,2816)(91,210)(92,3499)(93,2692)(94,828)(95,1009)(96,1880)(97,479)(98,1683)(99,3649)(100,1671)(101,788)(102,1763)(105,522)(106,3875)(107,2094)(108,1922)(109,822)(110,2337)(111,2729)(112,681)(113,304)(114,1558)(115,387)(116,1025)(117,2659)(119,259)(120,415)(121,316)(122,820)(123,1573)(124,1539)(125,1138)(126,2756)(127,254)(129,3412)(130,2951)(131,1156)(132,2841)(134,3708)(135,1422)(137,895)(138,3046)(139,3268)(140,2580)(141,3423)(142,3709)(143,1638)(144,3867)(145,307)(146,1217)(147,1050)(148,3665)(149,1778)(150,1692)(151,2952)(152,3614)(153,2896)(154,2157)(155,1994)(156,2850)(157,1935)(158,3702)(159,2363)(160,1036)(161,173)(162,163)(164,3663)(165,990)(166,1984)(167,3243)(168,1034)(169,456)(170,1359)(171,1487)(172,1174)(174,1902)(175,3133)(176,3506)(177,3483)(178,3116)(179,3789)(180,2467)(181,351)(182,3653)(183,640)(184,2316)(185,2291)(186,3211)(187,1301)(188,2670)(189,2509)(190,2666)(191,3635)(192,2803)(193,3862)(194,2200)(195,2211)(196,493)(197,3212)(198,1086)(199,3442)(200,1802)(201,2369)(202,3246)(203,769)(204,1622)(205,746)(206,634)(207,632)(208,3288)(209,3244)(211,1586)(212,3253)(213,1925)(214,1635)(215,507)(216,2458)(217,728)(218,3577)(219,1231)(220,3177)(221,1755)(222,2216)(223,2171)(224,907)(225,273)(226,1509)(227,2419)(228,738)(229,920)(230,2073)(231,3138)(232,780)(233,1358)(234,722)(235,3409)(236,3657)(237,2447)(238,1619)(239,3460)(240,3391)(241,3147)(242,3134)(243,1421)(244,1460)(245,2083)(246,1379)(247,2160)(248,1300)(249,734)(250,861)(251,356)(252,2643)(253,1980)(255,3285)(256,3727)(257,2049)(258,1262)(260,1150)(261,3298)(262,1178)(263,279)(264,797)(265,3344)(266,2366)(267,3417)(268,3838)(269,3809)(270,391)(271,3161)(272,2947)(274,1226)(275,1625)(276,3448)(277,2651)(278,374)(280,2530)(281,737)(282,386)(283,1999)(284,346)(285,2247)(286,1716)(287,318)(288,3517)(289,2404)(290,1361)(291,1274)(292,1335)(293,2422)(294,3000)(296,3833)(297,2992)(298,1347)(299,580)(300,3293)(301,1679)(302,1936)(303,2825)(305,1542)(306,786)(308,2028)(309,1874)(310,3075)(311,860)(312,862)(313,3277)(314,1912)(315,2974)(317,1308)(319,2054)(320,3281)(321,3750)(322,712)(323,1375)(324,497)(325,808)(326,3901)(327,585)(328,2304)(329,1616)(330,2958)(331,762)(332,721)(333,2836)(334,2024)(335,3806)(336,898)(337,476)(338,1153)(339,1848)(340,3695)(341,1914)(342,3110)(343,2444)(344,878)(345,1172)(347,1302)(348,3158)(349,1729)(350,758)(352,702)(353,1188)(354,3170)(355,2431)(357,2722)(359,1293)(360,2885)(361,1555)(362,830)(363,3200)(364,455)(365,3275)(366,2796)(367,382)(368,1972)(369,598)(370,1617)(371,668)(372,3039)(373,3066)(375,956)(376,1855)(377,422)(378,2607)(379,1146)(380,3234)(381,3146)(383,2822)(384,2718)(385,2529)(388,2124)(389,2910)(390,2595)(392,771)(393,3363)(394,2500)(395,3013)(396,2158)(397,3722)(398,2109)(399,3381)(400,1090)(402,2926)(403,2600)(404,1252)(405,2281)(406,3316)(407,843)(409,472)(410,2702)(411,1892)(412,2523)(414,592)(416,1872)(417,3041)(418,1118)(419,3072)(420,2204)(421,2860)(423,3803)(424,1161)(425,624)(426,603)(427,1603)(428,3835)(429,3067)(430,2875)(431,433)(432,2125)(434,2099)(435,2460)(436,2352)(437,3314)(438,2953)(439,1719)(440,1218)(441,1241)(442,1390)(443,2065)(444,782)(445,1216)(446,3811)(447,1969)(448,852)(449,2177)(450,2060)(451,582)(452,2302)(453,2943)(454,1674)(457,2739)(458,1829)(459,1629)(460,2879)(461,3390)(462,1983)(463,1664)(464,753)(465,1740)(466,3276)(467,1350)(468,2557)(469,3524)(471,1805)(473,3546)(474,3548)(475,669)(477,3365)(478,3660)(480,1254)(481,1663)(482,2515)(483,3453)(484,3408)(485,3490)(486,2218)(487,983)(488,1429)(489,2675)(490,3353)(491,2272)(494,3682)(495,573)(496,2225)(498,539)(499,2590)(500,1987)(501,1378)(502,2061)(503,3593)(504,2104)(505,2226)(508,3758)(509,2064)(510,3214)(511,3098)(512,2737)(513,2537)(514,3848)(515,2664)(516,750)(517,940)(518,3225)(519,2112)(520,685)(521,3799)(523,3040)(524,3020)(526,3422)(527,1526)(528,3732)(530,3100)(531,708)(532,3004)(533,3081)(534,3070)(535,2919)(536,1730)(537,2417)(538,2077)(540,3216)(541,1371)(542,1077)(544,2438)(545,3419)(546,3220)(548,791)(549,3880)(550,2380)(551,1879)(552,3588)(553,3124)(554,2494)(555,1441)(556,1411)(557,3182)(558,1357)(559,2840)(560,1048)(561,850)(562,1022)(563,2771)(564,3078)(565,1021)(566,613)(567,1788)(568,1773)(569,3648)(570,2851)(571,1827)(572,1398)(574,2026)(575,1854)(577,3563)(578,2787)(581,3055)(583,3342)(584,3703)(586,616)(587,2682)(588,3905)(589,3325)(590,3451)(591,1246)(593,1699)(594,2884)(595,1213)(596,2778)(597,1401)(599,2693)(600,2990)(601,1423)(602,1141)(604,3370)(605,3128)(606,1836)(607,2002)(608,948)(609,1991)(610,3092)(611,754)(612,3446)(614,3463)(615,884)(617,1686)(618,3003)(619,3650)(620,2831)(621,1512)(622,1907)(623,742)(625,1485)(626,2653)(627,1458)(628,2804)(629,1054)(630,2668)(631,2285)(633,1294)(635,3104)(636,1960)(637,1626)(638,1924)(639,2192)(641,776)(642,1684)(643,1536)(644,1860)(645,1136)(646,1139)(647,3902)(648,2307)(649,3762)(650,2241)(651,1813)(652,2581)(653,1608)(654,1059)(655,1706)(656,3501)(657,1721)(658,2527)(659,2923)(660,3853)(661,2700)(662,2005)(663,1478)(665,2268)(666,2371)(667,2362)(670,1549)(671,2074)(672,720)(673,2699)(674,1726)(675,3083)(676,2461)(677,1006)(678,1061)(679,1482)(682,1920)(683,2977)(684,2727)(686,2014)(687,3549)(688,2402)(689,3250)(690,1516)(691,2689)(692,2306)(693,2583)(694,2203)(695,3256)(696,3824)(697,2532)(698,2210)(699,1693)(700,2475)(703,989)(704,1746)(705,1596)(706,833)(707,2411)(709,1849)(710,2736)(711,3730)(713,3735)(714,955)(715,2935)(716,802)(717,1237)(718,1019)(719,3303)(723,2468)(724,3204)(725,2672)(726,3088)(727,1008)(729,2386)(730,1124)(731,957)(733,1728)(735,1391)(736,1280)(739,881)(740,3304)(741,1494)(743,2398)(744,1380)(745,1720)(747,2267)(748,2676)(749,2415)(751,3839)(752,1747)(755,1958)(756,3820)(757,3852)(759,811)(760,873)(761,1839)(763,1903)(764,927)(765,1091)(766,3279)(767,968)(768,1479)(772,796)(773,1567)(775,1938)(777,3017)(778,1992)(779,1791)(781,2959)(783,1109)(784,3645)(785,3516)(787,3532)(789,1504)(790,3625)(792,1333)(793,1082)(794,1132)(795,3667)(798,3375)(799,1027)(800,3474)(801,923)(803,2619)(804,3232)(805,887)(806,2818)(807,1927)(809,2983)(810,1906)(812,2335)(813,2407)(814,1609)(815,3527)(816,2276)(817,902)(818,2437)(819,2035)(821,2292)(823,1800)(824,877)(825,1744)(826,2768)(827,1329)(829,2586)(831,3016)(832,1876)(834,3195)(835,2263)(836,958)(837,3775)(838,3485)(839,3114)(840,3410)(841,1797)(842,2674)(844,2416)(845,1297)(846,2130)(847,2814)(848,1273)(849,1073)(851,3206)(853,3205)(854,2540)(855,2442)(856,3433)(857,3084)(858,1265)(859,2492)(863,3367)(864,998)(866,1451)(867,3239)(868,2472)(869,2589)(870,2463)(871,1529)(872,2197)(874,2915)(879,3542)(880,3609)(882,2046)(883,1725)(885,2360)(886,2743)(888,2119)(889,1160)(890,1037)(891,3505)(892,3812)(893,1098)(894,3347)(896,3131)(897,3699)(899,1620)(900,3791)(901,2758)(903,3159)(904,2230)(905,2625)(906,3719)(908,1407)(909,3357)(910,2499)(911,1869)(912,2563)(913,1255)(914,3740)(915,3825)(916,973)(917,2766)(918,966)(919,2524)(921,2038)(922,1201)(924,2370)(925,1115)(926,1884)(928,3310)(929,3406)(930,2733)(931,3898)(932,3602)(933,2341)(934,3675)(935,1769)(936,1177)(937,3540)(938,3062)(939,3551)(941,1790)(942,2066)(943,1410)(944,3470)(945,1996)(946,1028)(947,2531)(949,2598)(950,2322)(951,1677)(952,3538)(953,2797)(959,2013)(960,2030)(961,1587)(962,3561)(963,3187)(964,3573)(965,2510)(967,1042)(969,1651)(970,3476)(971,2365)(972,1377)(974,1753)(975,995)(976,2852)(977,2789)(978,2904)(979,3405)(980,3782)(981,2459)(982,1644)(984,3350)(985,3228)(986,2647)(987,1199)(988,2870)(991,1039)(992,3241)(993,1591)(994,1284)(996,2665)(997,2333)(999,3339)(1000,3289)(1001,1913)(1002,2635)(1003,3007)(1004,3315)(1005,2374)(1007,2678)(1010,1499)(1011,2657)(1012,1181)(1013,3580)(1014,1570)(1015,3047)(1016,1127)(1017,2424)(1018,3396)(1020,3530)(1023,3223)(1024,2008)(1026,3555)(1029,3479)(1030,1929)(1031,1489)(1032,3788)(1033,3591)(1035,1453)(1038,1515)(1040,1227)(1041,3534)(1043,3163)(1044,3509)(1045,2323)(1046,3615)(1047,3352)(1049,2798)(1051,1295)(1052,2032)(1053,3127)(1055,3071)(1057,2902)(1058,2139)(1060,3597)(1062,2616)(1063,3372)(1064,2641)(1065,1117)(1066,2253)(1068,2899)(1069,3435)(1070,3305)(1071,3878)(1072,3179)(1074,3164)(1075,3757)(1076,2738)(1078,3655)(1079,3652)(1080,2610)(1081,3369)(1083,1660)(1084,1126)(1085,1770)(1087,2473)(1088,2686)(1089,3605)(1092,3736)(1093,2325)(1094,3519)(1095,1806)(1096,2999)(1099,3380)(1100,3879)(1101,3481)(1102,3231)(1103,3112)(1104,2301)(1105,1176)(1106,1612)(1107,2108)(1108,2782)(1110,3787)(1111,3014)(1112,2039)(1113,1560)(1114,1369)(1116,3152)(1119,3881)(1120,2173)(1121,2392)(1122,2608)(1123,3329)(1125,1435)(1128,2618)(1129,3636)(1130,2262)(1131,3209)(1133,1195)(1134,3402)(1135,3515)(1137,1975)(1140,1701)(1142,2405)(1143,2025)(1144,3282)(1145,2223)(1147,1599)(1148,1415)(1149,2406)(1151,2286)(1152,2932)(1154,2620)(1155,3836)(1157,1852)(1158,3710)(1159,3190)(1162,2962)(1163,3871)(1164,1584)(1165,1277)(1166,1240)(1167,3219)(1168,3685)(1169,3082)(1170,2966)(1171,3656)(1173,2577)(1179,1472)(1180,3032)(1182,1192)(1183,2299)(1184,2933)(1185,1502)(1186,2565)(1187,3860)(1189,2166)(1190,2512)(1191,3771)(1193,3358)(1194,1707)(1196,3507)(1197,3392)(1198,3173)(1200,1497)(1202,3360)(1203,1559)(1204,1569)(1205,2088)(1206,1777)(1207,2146)(1208,2912)(1209,2640)(1210,1742)(1211,2029)(1212,1680)(1214,2810)(1215,2507)(1219,3165)(1220,3845)(1221,3167)(1222,2788)(1223,2070)(1224,1810)(1225,3189)(1228,1873)(1229,2215)(1230,3521)(1232,3361)(1233,3366)(1234,3168)(1235,3578)(1236,2596)(1238,2367)(1239,3690)(1242,1743)(1243,2251)(1244,2036)(1245,2954)(1247,2865)(1249,3559)(1250,3651)(1251,2231)(1256,3622)(1257,1510)(1258,1364)(1259,2817)(1260,2561)(1261,3514)(1263,2193)(1264,1731)(1266,1762)(1267,1909)(1268,3544)(1269,3585)(1270,3074)(1271,2550)(1272,3414)(1275,3064)(1276,1897)(1278,2707)(1279,1661)(1281,1383)(1282,1572)(1283,3087)(1285,3379)(1286,2567)(1287,1703)(1288,1901)(1289,3684)(1290,3050)(1291,2993)(1292,2080)(1296,2858)(1298,2455)(1299,2047)(1303,3903)(1304,2980)(1305,2381)(1306,1734)(1307,3646)(1309,3475)(1311,2464)(1312,1878)(1313,3804)(1314,2470)(1315,3349)(1316,2328)(1317,2145)(1318,1891)(1319,3798)(1320,2354)(1321,2279)(1322,3059)(1323,1386)(1324,3202)(1325,2562)(1326,1809)(1327,1597)(1328,2849)(1330,3711)(1331,3467)(1332,2848)(1334,2400)(1336,1656)(1338,3668)(1339,1708)(1340,2588)(1341,3592)(1342,2800)(1343,3332)(1344,3629)(1345,1642)(1346,1521)(1348,1523)(1349,2770)(1351,3444)(1352,1668)(1353,2178)(1354,2544)(1355,2312)(1356,3818)(1360,2477)(1362,3590)(1363,2819)(1365,2914)(1366,3520)(1367,3572)(1368,1527)(1370,3061)(1372,3387)(1373,2917)(1374,3642)(1376,3808)(1381,3107)(1382,1752)(1384,3658)(1387,2777)(1388,1613)(1389,3166)(1392,2542)(1393,2188)(1394,2805)(1395,3002)(1396,2376)(1397,3714)(1399,2183)(1400,2456)(1402,3497)(1403,2435)(1404,2093)(1405,1673)(1406,3776)(1408,1760)(1409,2078)(1412,3008)(1413,2293)(1414,1488)(1416,2040)(1417,1919)(1418,3720)(1419,3686)(1420,3395)(1424,2911)(1425,3882)(1426,3255)(1427,2117)(1428,3150)(1430,2228)(1431,2846)(1432,1822)(1433,1825)(1434,3267)(1436,3324)(1437,2639)(1438,2979)(1439,3837)(1440,3815)(1442,2377)(1444,3679)(1445,2382)(1446,1662)(1447,3677)(1448,3053)(1449,3802)(1450,2287)(1452,2255)(1454,3197)(1455,2009)(1456,3328)(1457,3810)(1459,3897)(1461,3376)(1462,3556)(1464,3589)(1465,2273)(1466,2786)(1467,3151)(1468,2972)(1469,3280)(1470,3427)(1471,3021)(1473,3118)(1474,2890)(1475,3706)(1476,3384)(1477,2628)(1480,3508)(1483,3569)(1484,2971)(1486,1918)(1490,1600)(1491,1765)(1492,2861)(1493,2747)(1495,2378)(1496,2068)(1498,3492)(1500,2136)(1501,2278)(1503,3864)(1505,1871)(1506,1712)(1507,3136)(1508,3886)(1511,3031)(1513,2161)(1514,2413)(1517,3737)(1518,2874)(1519,2775)(1520,3312)(1522,3883)(1524,2828)(1525,3843)(1528,2963)(1530,2196)(1531,1820)(1532,1648)(1533,3873)(1534,3113)(1537,1986)(1538,2627)(1540,2582)(1541,2280)(1543,1954)(1544,1750)(1545,3643)(1546,2511)(1547,1634)(1548,1993)(1550,1870)(1551,2815)(1552,2575)(1553,2222)(1554,3403)(1556,2829)(1557,2490)(1561,3531)(1562,3613)(1563,3634)(1565,2661)(1568,2752)(1571,1931)(1574,3840)(1575,3445)(1576,2744)(1577,2144)(1578,1875)(1579,2834)(1580,2288)(1581,2809)(1582,2393)(1583,2520)(1585,3697)(1588,1633)(1589,2921)(1592,2868)(1593,2317)(1594,2397)(1595,2522)(1598,3094)(1601,1602)(1604,2114)(1605,2433)(1606,2986)(1607,2856)(1610,2765)(1614,3582)(1615,2769)(1618,3512)(1621,3097)(1623,3738)(1624,3865)(1627,2987)(1628,3102)(1630,2454)(1632,2090)(1636,3001)(1637,2358)(1639,3522)(1640,1945)(1641,1923)(1643,2871)(1645,1782)(1646,2968)(1647,3565)(1649,1738)(1650,3193)(1652,2740)(1653,1748)(1654,3378)(1655,1951)(1657,2591)(1658,1957)(1659,3077)(1665,2372)(1666,3623)(1667,3793)(1669,2152)(1670,2964)(1672,3307)(1675,1908)(1676,2892)(1678,2574)(1681,1916)(1682,2469)(1687,2420)(1688,3765)(1690,3681)(1691,2862)(1695,3834)(1696,1968)(1697,1754)(1698,2927)(1700,2931)(1702,2176)(1704,3751)(1705,2308)(1709,1904)(1710,1819)(1711,3892)(1713,3482)(1714,2832)(1715,1847)(1717,1727)(1718,3599)(1722,3222)(1723,3581)(1724,1793)(1732,3331)(1733,3857)(1735,3263)(1736,1917)(1737,3429)(1739,3767)(1741,1824)(1745,3671)(1749,2058)(1751,2067)(1756,2257)(1757,3829)(1758,2059)(1759,3311)(1761,2452)(1764,2634)(1766,2513)(1767,3743)(1768,1961)(1771,3221)(1772,2518)(1774,3503)(1775,2342)(1776,2441)(1779,2174)(1780,3171)(1781,3502)(1783,2020)(1784,2081)(1785,2181)(1786,2056)(1787,2451)(1789,2207)(1794,2097)(1795,3550)(1796,2835)(1798,2184)(1799,3769)(1801,2761)(1803,2721)(1804,3393)(1807,2677)(1808,3258)(1811,2609)(1812,2526)(1814,3523)(1815,3439)(1816,2140)(1817,2305)(1818,3224)(1821,2339)(1823,2989)(1826,2881)(1828,2212)(1830,2115)(1833,3777)(1834,2998)(1835,3424)(1837,3807)(1838,3749)(1840,2098)(1841,3283)(1842,3194)(1843,3377)(1844,3584)(1845,3227)(1846,1940)(1850,2156)(1851,2022)(1853,2201)(1857,3153)(1858,3641)(1859,2480)(1861,2857)(1862,2725)(1863,3404)(1864,2709)(1865,3125)(1867,2716)(1868,3617)(1877,3169)(1881,3338)(1882,3876)(1883,3662)(1885,2631)(1886,2502)(1887,2051)(1888,3035)(1889,2182)(1890,2785)(1893,2391)(1894,3345)(1895,2698)(1896,3872)(1898,3106)(1899,2359)(1900,3877)(1905,3611)(1910,3493)(1911,2886)(1915,3386)(1921,2801)(1928,3371)(1930,3746)(1932,2839)(1933,2159)(1934,2887)(1937,2017)(1939,2270)(1942,3056)(1943,2863)(1944,3899)(1946,3731)(1947,2731)(1948,2897)(1949,2229)(1953,2154)(1955,3191)(1956,3870)(1959,2350)(1962,2126)(1963,2449)(1964,2746)(1965,2535)(1966,2730)(1970,3201)(1971,2007)(1973,3586)(1974,2493)(1976,2924)(1977,2254)(1978,3900)(1979,3157)(1981,3796)(1982,3418)(1985,2180)(1988,2967)(1990,2985)(1995,2289)(1997,3752)(1998,3343)(2000,2284)(2001,3043)(2003,2143)(2004,2534)(2006,2368)(2010,2663)(2011,2650)(2012,3794)(2015,3827)(2016,2195)(2018,2585)(2019,2446)(2021,3639)(2023,2905)(2027,2194)(2031,2757)(2033,2100)(2034,2165)(2037,2239)(2041,2948)(2042,2549)(2043,2462)(2044,2300)(2045,3156)(2048,3438)(2050,3676)(2052,3610)(2053,3024)(2055,2916)(2057,3042)(2062,3431)(2063,3036)(2069,3744)(2071,3109)(2072,3398)(2075,2118)(2076,3756)(2079,2995)(2082,3284)(2084,2791)(2085,2934)(2086,2925)(2087,2807)(2089,2297)(2091,2684)(2092,3598)(2095,3122)(2096,2795)(2101,2950)(2103,3672)(2105,3747)(2106,3638)(2107,3278)(2110,2410)(2111,3362)(2113,3850)(2116,2488)(2120,2978)(2121,2773)(2122,2554)(2123,3464)(2127,2893)(2128,2655)(2129,2383)(2131,3885)(2133,2348)(2134,2913)(2135,3874)(2137,3023)(2138,2615)(2141,3704)(2142,2592)(2147,3823)(2148,3495)(2149,3504)(2151,2717)(2153,2503)(2155,3348)(2162,2946)(2163,3896)(2167,3664)(2168,3670)(2169,2969)(2170,3407)(2175,3471)(2179,2476)(2185,3044)(2186,2295)(2187,2956)(2189,2425)(2190,2388)(2191,3368)(2198,2355)(2199,2945)(2202,2266)(2205,3388)(2206,3856)(2208,3196)(2213,3447)(2214,3754)(2219,2487)(2220,3091)(2221,2334)(2224,3594)(2227,3698)(2232,2691)(2233,2719)(2234,3309)(2235,3462)(2236,3306)(2237,2277)(2238,3888)(2240,3018)(2242,2794)(2243,2357)(2244,3628)(2245,3065)(2246,3252)(2248,3080)(2249,3296)(2250,3264)(2252,2485)(2256,3855)(2258,3335)(2259,3566)(2260,3647)(2261,2754)(2264,2936)(2265,3640)(2269,2742)(2271,2938)(2274,3359)(2275,3183)(2282,2432)(2283,2516)(2290,3489)(2294,3557)(2296,2385)(2298,2642)(2303,3271)(2309,2648)(2310,3618)(2311,3057)(2313,3478)(2315,2453)(2318,3774)(2319,2859)(2320,2501)(2321,3441)(2324,3693)(2327,2854)(2329,2605)(2330,3525)(2331,3721)(2332,2949)(2336,3696)(2338,3085)(2340,3180)(2343,3394)(2344,2696)(2345,3866)(2346,3729)(2347,3567)(2349,3336)(2351,2827)(2353,3529)(2356,2559)(2361,3858)(2364,2774)(2373,3383)(2384,2421)(2387,3486)(2389,3411)(2390,3842)(2394,2671)(2395,2703)(2396,3770)(2401,2937)(2403,3849)(2408,2660)(2412,3045)(2414,2560)(2418,3766)(2423,3301)(2426,3801)(2427,3487)(2428,2558)(2429,3121)(2430,3006)(2434,2486)(2436,3689)(2439,3500)(2440,3218)(2443,3783)(2448,2895)(2450,3717)(2457,2908)(2465,3086)(2466,3175)(2471,3616)(2474,3299)(2479,3251)(2482,2891)(2483,2626)(2484,2724)(2489,2776)(2491,3341)(2495,2751)(2496,2601)(2498,2867)(2504,2961)(2505,3627)(2506,2669)(2508,3025)(2514,3413)(2517,3761)(2519,3266)(2521,2942)(2528,2637)(2533,3238)(2536,2681)(2538,2543)(2541,3734)(2545,3558)(2546,3318)(2547,3019)(2548,3443)(2551,2710)(2552,3236)(2553,2667)(2555,3575)(2564,2673)(2566,2957)(2569,2824)(2571,2572)(2573,3659)(2576,2612)(2578,3772)(2579,3814)(2584,3832)(2587,2864)(2593,3320)(2594,3327)(2597,3713)(2599,3129)(2602,2823)(2603,3680)(2604,3026)(2606,3552)(2611,3541)(2613,2783)(2617,3891)(2621,2837)(2622,3813)(2623,3292)(2624,3494)(2629,3354)(2630,2633)(2632,3473)(2636,3326)(2638,3654)(2644,2944)(2645,2930)(2646,2690)(2649,3313)(2652,3009)(2654,3207)(2656,3199)(2679,3415)(2680,3518)(2683,3562)(2685,3060)(2687,3261)(2688,3337)(2694,3661)(2697,3822)(2701,3154)(2704,3119)(2705,2876)(2706,3249)(2708,3123)(2711,3356)(2712,3456)(2714,3537)(2715,2830)(2720,3884)(2723,3893)(2726,3619)(2728,3457)(2732,3076)(2734,2806)(2741,2813)(2749,2941)(2750,3068)(2753,3568)(2755,3436)(2759,3120)(2762,3144)(2763,3496)(2764,2940)(2767,3461)(2772,3691)(2780,3683)(2781,2976)(2784,3373)(2790,3863)(2792,3426)(2793,3198)(2799,3254)(2802,3726)(2808,3027)(2811,2909)(2812,3149)(2820,2960)(2821,3480)(2826,3547)(2833,3753)(2838,3132)(2842,3432)(2843,3854)(2844,3126)(2845,3830)(2847,3333)(2853,3054)(2855,3095)(2866,3300)(2869,3058)(2872,3334)(2873,2906)(2877,3759)(2878,3178)(2883,3096)(2888,3143)(2889,3172)(2894,3160)(2898,3022)(2900,3215)(2901,2994)(2903,3779)(2907,3364)(2918,3155)(2922,3028)(2928,3826)(2929,3469)(2939,3595)(2965,3511)(2970,3570)(2973,3477)(2975,3545)(2981,3425)(2982,3468)(2984,3725)(2988,3724)(2996,3449)(2997,3539)(3005,3821)(3010,3465)(3011,3399)(3012,3130)(3015,3103)(3029,3321)(3030,3687)(3034,3644)(3037,3093)(3038,3101)(3048,3262)(3049,3583)(3051,3079)(3052,3673)(3063,3607)(3069,3291)(3073,3603)(3089,3186)(3090,3553)(3099,3416)(3105,3764)(3108,3286)(3111,3308)(3115,3135)(3117,3718)(3137,3606)(3139,3430)(3140,3397)(3141,3510)(3142,3274)(3148,3784)(3162,3596)(3176,3226)(3181,3869)(3184,3633)(3185,3800)(3188,3269)(3192,3851)(3203,3272)(3213,3382)(3229,3484)(3230,3608)(3233,3723)(3235,3543)(3237,3571)(3240,3576)(3242,3604)(3245,3564)(3247,3257)(3248,3790)(3259,3295)(3260,3624)(3265,3458)(3270,3273)(3287,3688)(3290,3389)(3294,3302)(3297,3630)(3317,3748)(3322,3841)(3323,3701)(3330,3355)(3340,3466)(3374,3861)(3385,3745)(3420,3621)(3428,3895)(3437,3678)(3450,3781)(3452,3778)(3454,3472)(3491,3890)(3498,3674)(3513,3894)(3526,3712)(3528,3728)(3533,3587)(3535,3666)(3536,3828)(3554,3705)(3574,3741)(3579,3889)(3601,3819)(3612,3786)(3620,3700)(3631,3904)(3632,3773)(3637,3795)(3692,3906)(3716,3739)(3742,3868)(3760,3763)(3780,3785)(3792,3887)(3816,3817)(3831,3846)(3844,3847),(1,3,865,2805)(2,50,1269,467,2073,3633,3214,2847,2740,1154,620,1301)(4,1091,2645,864,2735,1070,3418,3544,1635,3487,3625,395)(5,3551,1937,1002,3071,2585,2490,684,1041,560,1066,271)(6,3734,3517,2332,632,2393,1742,1848,847,1927,3249,2369)(7,2656,754,3596,1990,3677,193,2742,3456,2811,615,1298)(8,2108,3428,3661,3453,3659,1948,856,1938,831,2852,1235)(9,1380,3419,2947,3693,272,3679,744,2151,920,593,229)(10,1443)(11,2152,2962,2691,3636,3352,2920,299,3290,1178,1353,3623)(12,3761,422,2422,377,3289,1967,1436,1019,3653,718,2226)(13,677,1395,1406,1396,2076,2309,1005,252,1384,2470,2789)(14,839,2022,1658,387,753,3326,1187,3190,1921,1882,459)(15,1028,3582,2136,585,3731,1924,2277,1042,1672,1035,599)(16,2902,431,1615,3580,1449,101,63,1638,2054,2437,570)(17,3737,1661,2403,1690,703)(18,688,3607,2081,1068,2516,1247,2555,2255,2313,2507,1304)(19,421,162,1621,3720,1130,2066,3178,3106,2674,2397,1708)(20,759,3436,1054,2594,682)(21,1422,1484,3744,2646,1336,90,134,3294,1597,3602,3606)(22,2860,973,1339,2655,842,1027,2878,3572,2262,3701,3097)(23,1900,1917,498,1079,3422,2675,71,1490,1929,661,2752)(24,3109,1907,1160,3847,591,3844,2115,622,3186,2399,891)(25,2362,3538,2445,2754,667,1936,2687,466,2314,1389,3261)(26,2172,375,499,713,546,3567,358,3140,3220,301,2590)(27,1138,1014,425,2760,1016,1570,1952,1792,3892,3626,3614)(28,3663,3719,2579,3356,2946,2875,1525,111,155,2416,3464)(29,917,1976,914,1355,566,1010,1971,2533,2164,1058,643)(30,3875,3617,3709,2792,2951,2145,2866,3012,895,1135,3032)(31,3120,2794,2759,2166,910,93,141,3655,3423,2418,2499)(32,3046,2007,2398,613,1126,3740,331,2766,227,1536,813)(33,2286,690,2911,1653,3475,826,2325,1275,2211,573,1331)(34,3738,449,325,1986,2578,357,2366,1191,1075,1208,3833)(35,3778,2290,380,2927,2384,3386,1326,1746,2695,398,2222)(36,3080,253,2958,2469,1258,277,2689,1064,1689,2452,1712)(37,1165,2705,608,2663,869,2010,2127,2876,378,3600,3229)(38,3768,868,818,2508,143,1899,788,1977,1013,522,433)(39,962,1785,623,3383,2056,3812,2587,854,2024,3347,2439)(40,2206,2930,3211,3669,1150,790,1741,214,2443,1982,1481)(41,2950,602,1808,2842,1737,3149,1558,1916,3805,654,1544)(42,3301,3613,2586,1176,941,1577,1158,190,3796,1391,2981)(43,1140,1715,2317,1847,1523,2539,3267,3745,2329,3385,2606)(44,1251,924,3031,3340,1692,3712,2863,3175,2458,3329,2239)(45,3462,2285,3402,2858,267,3473,711,1756,779,3753,2219)(46,1568,511,1030,2957,2525,2068,526,1137,539,3085,3877)(47,2488,2558,3227,3403,880,2992,1861,1323,3759,2560,2776)(48,1595,531,792,1620,1308,2938,2344,3372,3525,2881,3207)(49,2807,3783,290,1824,1469,260,222,186,1810,3856,3083)(51,2442,2045,2906,3448,715,343,514,1179,2515,1560,1021)(52,705,1592,3621,3005,862,3574,1346,866,3438,3555,1223)(53,3482,691,1270,1364,2819,330,2610,2248,2273,1506,3806)(54,113,132,3405,1832,1969,1237,2187,1437,2668,2770,898)(55,646,2046,2043,3151,1341,174,3447,1787,1867,3825,3461)(56,3615,1873,2782,2960,2885,372,3010,3697,1765,1721,507)(57,2720,2602,265,352,1083,3256,1714,1695,3512,3030,2276)(58,2887,1859,2020,2928,2492,1762,2192,1163,1468,196,1300)(59,1773,2798,1276,82,1812,3819,3634,2377,1401,2753,552)(60,1297,1127,2765,624,1037,125,890,152,1610,1711,845)(61,3554,450,172,2093,84,3021,2408,609,3748,2576,1252)(62,328,2987,3209,724,3274,2306,2258,2543,697,3407,1351)(64,2203,3371,1173,589,930,1880,2821,2698,1111,3387,1513)(65,722,2841,1426,506,1358,1349,1894,2639,3611,717,3570)(66,3133,3129,2626,2333,1488,1371,1777,2701,347,400,3507)(67,3279,2679,2063,427,2357,3163,1840,2932,1779,480,275)(68,1487,1051,3216,2218,1393,706,2850,3348,3581,2634,2202)(69,1605,1809,2572,2421,1087,3234,2772,3452,1547,1553,925)(70,1309,114,1424,3429,1151,3258,3467,2101,195,1750,1093)(72,1077,2346,3813,3643,1705,1896,3431,1877,681,2475,209)(73,2680,2559,1657,2351,306,940,261,496,1700,1185,337)(74,365,2345,1204)(75,1865,768,1192,951,140,318,3123,393,3231,1255,1972)(76,3700,1129,1338,1162,3155,2748,1188,2178,3316,3389,3537)(77,3410,2197,3318,3608,1641,3610,2513,1886,95,282,485)(78,163,1933,104,1164,1594,94,1898,2318,942,1539,1418)(79,3469,202,3619,911,2240,1888,3104,3034,3789,2004,780)(80,3014,2644,3480,1587,2733,1688,2577,2479,694,3168,2161)(81,2322,3823,3222,2436,2457,1347,3297,2856,2299,2029,1908)(83,1774,3881,1655,340,746,2390,2683,148,2110,3250,1411)(85,200,1575,1881,1984,2745,3395,3338,2567,1802,3616,2497)(86,414,1024,1883,2728,3533,1828,2670,3113,3747,3291,3885)(87,2000,2339,2134,2387,1007,2986,3094,1312,1184,3818,1240)(88,809,1398,1647,236,3001,614,2828,1217,3152,1220,3529)(89,1535,881,844,2652,2729,2126,430,1870,2711,1745,906)(91,2419,268,762,3685,1084,1850,743,3839,138,655,2407)(92,2308,3878,2622,3727,542,2352,3244,2474,112,1045,2062)(96,1649,3325,1966,1928,1446,3715,1382,1372,578,1895,392)(97,457,2894,3504,583,1143,757,2903,3111,3131,1854,2709)(98,929,3728,2298,2600,2400,2401,2365,3392,2921,3531,3059)(99,2736,1609,3724,2118,2168,3900,1871,151,2129,183,2702)(100,1462,1771,3635,3367,2964,2074,853,3751,1958,1509,121)(102,3730,1209,3417,3450,1134,110,2235,454,2487,738,1791)(103,1189,269,2242,769,954,3145,3766,203,1078,3809,2692)(105,468,2254,3865,2359,1735,3025,2891,2472,307,3346,3739)(106,2028,1180,2453,137,154,3300,270,130,2512,142,3408)(107,2706,1292,2814,1040,1210,448,207,1707,288,3548,2209)(108,3169,2259,3872,2608,1545,2348,3729,2817,3351,644,700)(109,2809,3564,367)(115,2551,1851,1633,2779,2241,3876,1512,1159,741,2636,3086)(116,369,2562,3099,1410,912,943,508,1325,1198,1025,3321)(117,3646,3549,819,184,119,1342,1559,1032,2450,1072,904)(118,3656,1174,1106,3705,830,404,2477,3317,3721,2660,2724)(120,2117,2797,1038,3167,1207,494,3598,1718,420,563,1478)(122,2522,469,2654,2279,2330,376,2696,3049,317,1794,1333)(123,1376,418,730,625,3803,2176,1759,255,3497,3377,279)(124,916,3774,3797,828,3323,1584,1367,2159,799,1056,2128)(126,1835,1430,1839,3880,1776,1642,726,1421,1344,1282,3846)(127,1845,1680,2116,2564,2489,793,2877,666,2857,1284,3609)(128,3036,3568,766,1442,1625,3601,2174,1856,2098,1049,2243)(129,2480,791,1941,2263,493,750,3871,3147,1266,1455,3826)(131,3556,2163,316,2296,755,2966,3205,2158,1670,1370,191)(133,145,3802,2482,2769,3263,1057,1624,2851,2557,319,3716)(135,476,3137,2931,1327,3298,3708,786,1656,2591,2069,3518)(136,1348,658,1593,2378,1701,2568,3552,1495,2605,2527,1434)(139,2404,3388,887,2200,606,3851,350,2495,1961,921,3158)(144,363,3165,1696,3195,1556,3362,1460,2072,1740,1392,3684)(146,1313,3463,384,3657,3225,572,2034,770,3557,3845,2021)(147,2015,3699,902,1630,3076,2454,1456,897,3820,1050,1579)(149,1564,1311,2831,3281,1652,3270,510,2180,230,1519,3585)(150,3007,1511,2790,2231,1482,2037,2941,216,1011,1943,1329)(153,2150,2361,976,590,775,3817,2897,3081,483,3591,3895)(156,1105,2188,1562,540,2662,171,735,2266,2666,1723,2144)(157,1669,1613,1666,2394,262,2837,580,2624,1047,2685,2232)(158,2048,2528,1521,1031,312,2879,3420,3369,1596,2016,2070)(159,355,2447,379,3810,3394,3313,1853,1241,1586,1565,1205)(160,2204,2210,2092,342,2146,3269,1515,926,1427,2130,663)(161,1903,1076,1676,2292,1654,659,2380,1772,284,1754,1819)(164,3361,2123,3547,1994,2334,3843,409,2162,1433,3814,850)(165,3474,975,1667,3235,3159,2582,1324,2778,534,586,217)(166,2997,3445,3539,576,562,2471,966,1286,918,1420,1022)(167,2719,444,964,1733,1964,3704,2521,359,1017,2389,3259)(168,1055,981,2017,177,3707,3439,2253,3763,3534,3315,1557)(169,2676,3112,1262,1067,3022,1103,1352,456,3376,1385,588)(170,532,2392,1100,178,3577,1974,3762,3559,2862,3381,3078)(173,1452,1697,2865,2518,2899,2923,3063,821,1611,2738,1215)(175,640,1196,2952,1302,1978,1206,2075,1414,814,2483,3649)(176,3128,908,2160,2969,3523,1730,2175,3068,535,2191,3502)(179,1113,635,1472,3018,2444,2726,276,2929,3156,232,2326)(180,950,2154,1675,2050,1183,3260,3630,2440,2908,2734,1722)(181,2185,1956,619,1514,2631,3472,3891,686,3391,3904,2813)(182,2183,3324,1989,1000,1399,293,2764,2517,2409,505,2940)(185,610,1029,3550,1466,1947,3382,2434,1061,2171,2848,938)(187,3254,2620,3521,3333,3252,3184,3777,1350,3883,492,3430)(188,2967,3587,213,3662,3468,592,2023,2131,3837,2105,3795)(189,2143,1637,1493,3096,500,2804,2535,3750,2989,1578,3540)(192,2678,1303,2913,3901,2284,1862,1166,1911,2933,501,1598)(194,1526,2205,1195,3268,1261,2038,642,2751,2781,3192,2119)(197,465,3226,244,2616,2829,1181,1968,2939,3200,2697,1289)(198,3303,220,3117,2460,2780,1120,313,419,1716,221,515)(199,919,3055,370,740,2379,601,1617,1939,2524,2511,732)(201,2506,807,453,339,996,1582,225,2949,2613,2541,2995)(204,1874,394,600,2303,3688,767,1343,3801,2096,3612,2047)(205,3082,1951,2623,3503,513,556,374,2410,2963,3562,1132)(206,1337,2137,1679,3023,3397,634,2347,2723,3735,3893,956)(208,1704,1995,671,528,863,1650,3221,3223,1671,969,226)(210,2312,1706,2924,751,2217,2156,2139,1168,3238,3838,1499)(211,936,2201,2561,2343,1805,1146,3413,2431,2744,2088,1432)(212,2310,3458,3359,1416,3206,555,2965,3053,3390,2715,2429)(215,1997,1491,3248,3465,2256,360,3008,1108,1018,1046,3101)(218,2229,3879,1167,3004,3224,564,3357,1691,669,649,1403)(219,2998,1136,1747,1213,538,2554,785,777,1644,778,3237)(223,1149,2486,2340,2731,2961,1795,520,3092,1760,3062,1724)(224,1322,1161,1589,3841,971,2053,1334,1602,2642,3191,3406)(228,2553,1674,2260,2337,905,3781,323,2640,3594,1763,1405)(231,2796,3784,3510,2302,310,3393,3075,2140,3141,3787,366)(233,648,3255,3107,234,2382,2970,2220,1905,945,3345,1797)(235,1360,426,362,1892,1612,3399,1171,2968,2484,3535,2331)(237,1362,2363,3476,2661,257,441,2611,2649,1400,1457,3183)(238,2505,1397,1858,3048,3746,2588,3132,3874,2703,3047,3800)(239,737,3056,487,980,571,3228,3052,1288,338,2630,1319)(240,3135,2617,974,1885,972,3650,294,3044,1751,2741,2601)(241,2055,516,2686,835,2721,548,3501,3412,2550,2009,3310)(242,1245,3134,1780,303,2100,3888,2565,2238,2536,2825,1155)(243,2708,1345,2580,549,1182,2228,3125,2756,368,1572,1102)(245,1052,1912,1507,3902,774,3542,3136,3832,2032,893,1866)(246,2039,519,653,512,1264,3532,2328,574,1841,1744,524)(247,2244,605,1242,1781,1518,2919,3678,3471,341,1814,2250)(248,1271,2972,656,639,1803,859,1088,1783,2916,1934,928)(249,503,2762,582,1549,3640,3404,3215,2120,1849,3336,3189)(250,894,2300,2540,3522,892,2867,2373,2994,2181,673,525)(251,2245,3079,577,3723,2411,349,2027,553,2888,2272,1979)(254,361,994,2114,2371,1838,1082,1993,2673,2682,1212,405)(256,1922,1071,1860,3499,1259,2323,2133,3299,1122,436,3566)(258,2085,748,2934,3905,1538,1461,2214,1668,3754,2898,2627)(259,1373,2035,3519,1307,2855,2230,3247,3717,1664,1203,3187)(263,1632,1402,3527,3311,2974,423,3586,1124,1239,3808,2153)(264,382,1085,1581)(266,2104,3772,1970,808,1945,1623,3006,296,959,3757,3648)(273,2094,2665,474,2943,1194,2669,852,2079,1227,2783,2080)(274,1731,1954,1608,1428,1112,836,3020,2432,3283,1552,1316)(278,1073,2537,823,3292,3481,1169,843,794,2774,1528,923)(280,3050,3791,2824,285,2320)(281,1622,3798,3786,1153,2426,3673,968,1827,3271,983,2500)(283,2291,1909,1332,2297,678,3622,3213,2802,2786,443,3479)(286,1328,3277,3660,3683,1813,3718,873,719,383,2664,3477)(287,3831,1677,3629,1479,3088,2713,2441,913,761,3363,3424)(289,2788,348,3736,1768,292,758,3692,1836,3127,805,1060)(291,2067,3374,3000,1383,1377,2278,1753,1431,3115,2415,2496)(295,3328,2853,2732,1789,817,3434,3827,2207,2834,3054,756)(297,1548,1554,3749,2428,1604,2375,1555,2414,2281,1386,587)(298,2615,3689,3414,2147,1318,579,3102,1211,3498,1607,984)(300,3546,3536,2449,497,3122,1887,1857,3358,3603,1852,1366)(302,1520,2261,1531,952,668,2478,371,3166,1820,3276,3312)(304,3091,336,1445,630,1381,2956,2307,447,841,979,1996)(305,733,3194,764,2839,3513,1769,1330,999,3509,986,432)(308,3182,484,438,1190,773,391,2091,2157,3446,2315,3667)(309,985,1299,3782,2795,1942,3332,3460,3287,2633,2990,1901)(311,2271,3889,899,1796,708,1837,3210,2223,1826,1749,1063)(314,781,2083,2327,1098,1648,2584,1532,879,2854,647,2959)(315,2295,815,428,2090,2549,2503,626,3690,3087,1973,1473)(320,1833,2464,2246,1778,1230,2775,2799,1985,3139,3273,1522)(321,3040,628,1571,2883,2836,2358,2011,2509,1940,1875,2084)(322,1425,1782,633)(324,812,3828,987,3293,3869,1157,660,1193,2531,2051,2510)(326,1497,3903,1273,2803,798,1378,2106,2886,806,2725,440)(327,2581,1614,2121,1175,2619,1453,329,967,1001,638,3370)(332,2493,3485,3116,3742,1121,2124,1359,3698,399,1983,1249)(333,2103,1931,3119,523,3794,2791,1201,1846,1807,2650,3203)(334,1008,2864,1709,1786,877,742,2264,3561,2064,3500,490)(335,1369,1465,3373,1080,885,1363,1419,3074,1686,1713,2336)(344,2078,3443,1238)(345,2937,1919,403,3242,3528,1844,1683,3365,1561,2148,1197)(346,2980,550,3478,3378,3575,2892,2283,763,1784,1710,2402)(351,1501,3631,1281,2014,3861,3454,1274,2413,749,3870,2846)(353,3494,2918,2621,3668,2671,3620,1388,2714,1935,406,3060)(354,1354,1429,2019)(356,2785,491,3897,3124,2910,1729,1440,3233,3198,3051,3343)(364,1757,3785,3829)(373,3179,2354,3788,1799,2800,458,2316,2915,687,3278,2659)(381,2571,530,2433,2412,1115,2236,1634,1918,3691,2341,2473)(385,915,2598,2451,2777,1902,1374,1467,2355,882,802,1097)(386,2149,2502,2739,2052,1864,3230,896,872,3779,413,2025)(388,475,3868,909,838,1818,721,3219,462,1949,2227,2435)(389,2368,1459,2603,1890,2618,1998,934,2793,1287,3815,2547)(390,1294,1099,3882)(396,1023,1170,3193,2385,3732,3896,2289,1156,3288,3061,1651)(397,946,3108,2693,1719,3307,2030,2237,1580,1946,1551,1500)(401,848,1356,1200,1878,1218,1606,2818,3486,3638,1821,3375)(402,2905,1278,2982,747,1925,1659,1988,1817,3637,1725,1439)(407,689,1101,3665,1800,3842,849,3695,801,1119,2364,1926)(408,1788,2907,2448,2845,1960,1253,2996,3830,3887,3364,551)(410,541,2383,997,1505,2599,3670,1248,2988,1090,710,3154)(411,1471,603,1404,3409,2060,3666,2955,1646,2612,3011,1991)(412,2718,1291,3804,2311,3639,1435,2294,1475,2165,1265,518)(415,3775,2771,1365,3599,2596,3682,2041,1221,3354,953,1305)(416,3416,543,598,1872,3029,3084,3173,3560,3758,857,2563)(417,2694,1438,1107,1096,3578,2925,3016,3799,3433,2167,2573)(424,1417,907,1172,1955,3495,1601,477,3024,3584,3322,3604)(429,3437,2519,2874,3284,1743,957,3628,1069,3264,3767,1914)(434,1543,1280,1226,1508,2575,2059,2282,3508,958,2461,3150)(435,3043,3177,1095,1086,1413,1755,1216,3072,3427,2173,3320)(437,1409,3341,2367)(439,604,3286,1913,3722,1616,2815,803,2288,2773,960,652)(442,1863,789,670,2870,3144,1665,734,3337,2349,1687,2978)(445,651,2293,478,1806,2849,2001,2973,2593,2822,1470,760)(446,1387,3296,949,2002,2529,2859,716,2890,2198,992,3642)(451,3037,3593,1798,1225,783,709,1458,2900,1117,2265,2808)(452,3859,3148,1450,3138,2391,1110,3319,1816,1893,1804,2287)(455,876,3780,3400)(460,1464,1489,2597,2637,2057,3702,1678,2195,1243,1081,2871)(461,1959,3511,3470,851,784,2274,1229,3618,871,3121,1263)(463,874,3257,1829,3095,3769,1094,1320,2917,3066,963,2107)(464,1533,1957,1483,3114,1734,1629,674,2801,3899,3860,3003)(470,3146,2109,933,704,1486,1915,3306,1698,3045,3489,3100)(471,970,1260,3590,1177,2275,1822,2456,1576,3541,2514,2049)(472,3694,2221,3671,2826,1550,1232,1962,561,3009,1825,739)(473,725,3520,3197,3073,584,3153,2196,2095,2743,1963,2386)(479,3490,575,1009,3308,1766,3852,1923,3342,2546,3160,840)(481,3161,2417,1048,1775,2727,1477,2018,796,2635,637,939)(482,875,3848,2534,2935,3644,2873,3035,855,1869,565,3246)(486,3710,1295,1790,547,829,1764,2423,2155,3425,833,1981)(488,3028,3170,1541)(489,665,3652,2638,1736,3496,3208,2208,2700,3764,1600,3898)(495,2812,3064,3432,2768,1141,1748,3755,1516,1059,1694,1681)(502,3822,2872,3595,3493,1012,3492,1062,2869,3176,3576,3212)(504,3232,569,2179,2013,1591,2430,2463,1640,559,3201,3840)(509,1639,2936,2044,824,861,1904,2699,727,2901,3353,2498)(517,3033,2827,932,2356,3302,2556,2816,1502,2690,2225,2971)(521,1033,2086,533,2999,3816,2979,3451,3041,3858,3664,2896)(527,1092,888,1222,2976,3597,1684,1053,3514,3906,1133,1335)(529,1279,3681)(536,2082,2169,3266,1407,3067,3506,1739,3368,3435,2750,731)(537,1034,1663,1004,1626,3760,772,1815,2628,3483,2342,2459)(544,554,723,693)(545,2102,3401,699,1699,3441,2717,1631,1444,2321,2324,1693)(557,1317,795,3426,612,1868,2684,2570,1567,3515,2953,3130)(558,2438,810,2468)(567,2945,1879,1233,3792,3366,3449,2199,636,2182,2895,1889)(568,1254,3588,1152,597,1043,1563,1603,2526,3415,1897,680)(581,745,3442,3360,1546,1020,2270,3530,1423,1202,3304,1720)(594,1357,672,1906)(595,3627,645,3185,1231,2395,1992,2838,3017,1930,2122,3641)(596,3651,1540,1244,3543,2485,995,2984,990,1510,616,1876)(607,2462,2249,1139,3811,2767,3241,2716,1474,2213,2319,3592)(611,1627,3455,701,884,2170,2712,2538,3862,692,2985,3204)(617,1685,3686,1761,2360,2641,2784,2651,1114,1682,3696,1980)(618,1588,1944,2710,1726,2465,1306,1494,3569,621,3873,650)(627,988,1109,1504,2184,1390,3093,2420,3027,2688,1065,2372)(629,2755,811,1310,1920,3327)(631,2224,2481,1375,2833,2625,2257,3647,2632,2667,1296,1673)(641,800,3309,728,2757,3070,1767,3202,2301,903,1732,3793)(657,3854,1585,2425,3039,2975,2820,2545,1228,2552,2132,1039)(662,827,2761,2657,3632,2749,1315,679,2889,3863,3090,1003)(664,931,2338,3105,1975,3196,1496,2763,2566,3654,3098,2268)(675,2427,1224,1268,2216,3305,3280,998,1361,765,2087,3013)(676,787,1480,2737,1758,2112,3886,1379,736,825,2099,2026)(683,3265,1368,3253,2190,2830,1147,1448,3015,1441,2405,2040)(685,2089,2504,1267,3180,1999,2406,2065,1793,3726,1408,1256)(695,2233,702,3295,2823,2424,3488,2942,3687,2746,3834,3573)(696,1144,3824,2609)(698,2629,1036,2948,846,1236,1884,2914,3188,837,3110,2381)(707,3680,3563,2006,3065,3019,3157,1703,3143,3675,2194,1128)(712,2604,1645,714)(720,2583,2884,2494)(729,3853,886,3181,1530,1199,3703,2335,1454,965,2672,947)(752,1340,1834,3262,3571,3714,982,1619,3516,1015,2077,2135)(771,3251,2787,3765,1752,961,1662,2944,2730,3217,1738,1234)(776,832,3331,1257,1104,3725,3743,2252,2031,2036,2234,1250)(782,816,3243,1618,3411,2832,1293,1660,2141,3344,3857,3884)(797,978,1770,3491)(804,2880,1574,2912,2840,3771,870,2722,993,1537,2476,2177)(820,2058,2097,1145,3583,3807,1855,2835,1321,3579,3524,860)(822,2904,3245,3890)(834,3240,1219,3058,3867,1498,2542,1910,3398,3334,2111,2061)(858,1524,3706,1636,1125,3565,3057,2983,2993,2353,2523,1116)(878,3770,2548,3126)(883,2008,2305,1590,3077,3069,2267,1534,2707,2212,2926,3457)(889,3421,2071,1583,3505,2142,3089,1950,1830,2592,1246,2520)(900,2247,2530)(901,2589,1089,948,3440,1277,3605,3484,2758,2607,3459,2893)(922,2747,2012,2003,2704,937,3672,1823,3272,1965,2677,1987)(927,2648,1728,2376,2125,3002,1044,1463,3711,1314,3894,2643)(935,3776,1932,1006,1842,977,1542,3658,2647,2374,3339,3756)(944,1527,2350,2977,2193,1142,1529,3103,2215,1599,3645,2388)(955,2595,3026,3380)(989,1517,3849)(991,3855,3236,3790,3558,3752,3545,3038,2189,3396,2843,1412)(1026,1643,1451,2251,3741,2574,3821,3042,2868,3713,2614,3589)(1074,3275,2861,1569)(1118,2186,1573,3118,1843,1283,3285,2653,1702,2042,1485,3835)(1123,3553,2466,3172,3526,3349,3466,3773,2370,1801,2658,2005)(1131,2269,2304,1447,3444,3162,2532,3199,3335,2455,3142,2909)(1148,3174,3864,3866)(1186,3384,2033,1566,3171,1476,2954,1285,3836,1831,2681,3379)(1214,2882,2810,1394)(1272,3676,2138,1953,3350,2467,3674,2806,1628,3218,1891,3624)(1290,2569,2501)(1415,1492,1503,3164)(1727,3239)(1811,3733,3282,2991)(2113,2922,3355,2280)(2396,3314,2844,2491)(2446,3850,2544,3330),(1,8,2565,820)(2,112,2673,1431)(3,3370,814,3417)(4,2203,3555,3469)(5,2636,2347,251)(6,1778,3744,2971)(7,2437,1533,2512)(9,1886,2172,250)(10,1727,867,1443)(11,3793,1107,1313)(12,2181,999,460)(13,2295,121,3084)(14,319,1103,525)(15,346,3579,3126)(16,2976,249,1599)(17,1290,3327,811)(18,2233,1099,3451)(19,2938,960,950)(20,3791,2569,759)(21,3007,3705,294)(22,3134,3565,3309)(23,1571,2362,30)(24,708,1203,3524)(25,77,2010,3593)(26,1070,1473,3480)(27,3694,711,3028)(28,3810,1094,2748)(29,3142,2770,1665)(31,3730,3186,3243)(32,3714,1996,855)(33,3242,3039,2969)(34,1190,357,2315)(35,1317,2163,332)(36,2164,68,3012)(37,2900,1936,3610)(38,486,2792,386)(39,1658,2841,670)(40,945,1641,131)(41,2803,2348,2741)(42,3203,1403,96)(43,621,986,2084)(44,2877,573,2813)(45,1035,3464,3607)(46,3877,2764,1126)(47,3424,1281,3403)(48,3722,3630,2066)(49,2637,1507,2808)(50,56,2053,1522)(51,2040,2717,1376)(52,2218,2880,808)(53,1147,3713,511)(54,1768,1013,3551)(55,1848,2466,1642)(57,1246,2523,3649)(58,2194,1970,80)(59,2036,1530,3450)(60,2681,3154,2440)(61,3638,3252,2580)(62,3738,3140,673)(63,2179,1044,1004)(64,1509,1709,95)(65,459,617,1008)(66,1791,591,1338)(67,3845,2001,3510)(69,2590,2435,3311)(70,1501,1572,1174)(71,3776,1689,2930)(72,3466,726,700)(73,2400,2250,2646)(74,845,1813,2667)(75,2116,1585,786)(76,2875,1565,463)(78,303,228,672)(79,2024,3069,2951)(81,2242,166,2118)(82,89,3753,1238)(83,837,3735,864)(84,3375,230,477)(85,1304,2945,3453)(86,3875,1402,2161)(87,1007,1093,1604)(88,1050,905,1138)(90,2941,2660,3135)(91,1002,2546,253)(92,2817,3558,3248)(93,2235,1160,2141)(94,2825,3781,594)(97,3325,715,2398)(98,602,2046,2323)(99,2033,3138,904)(100,3083,3086,292)(101,1133,3404,2977)(102,1906,1254,384)(103,383,3668,2344)(104,175,1510,2548)(105,3111,1170,371)(106,1698,1631,2048)(107,288,1102,3632)(108,1885,3149,2725)(109,1614,3478,1241)(110,1357,1603,3557)(111,3117,3498,1453)(113,1262,1481,2305)(114,2782,974,2612)(115,2589,3342,374)(116,3709,1393,1682)(117,936,1625,2521)(118,3038,3429,2812)(119,3900,3836,1804)(120,843,2143,2044)(122,1933,1628,1887)(123,2434,3598,563)(124,353,1654,3859)(125,3171,2599,2154)(126,174,3734,2370)(127,1656,2545,2591)(128,2702,2363,714)(129,727,2662,2070)(130,3571,1989,3238)(132,3190,2358,3511)(133,2258,3251,2596)(134,609,201,2475)(135,3891,535,3523)(136,2171,142,2385)(137,3061,2568,3550)(138,2155,2130,789)(139,2104,2838,2752)(140,345,3528,924)(141,1611,2823,3850)(143,2635,3221,2368)(144,204,1744,2026)(145,3619,388,661)(146,1205,3824,3661)(147,3700,1939,2277)(148,859,912,3098)(149,1387,1657,297)(150,932,2133,2249)(151,180,3282,2915)(152,3445,1816,3491)(153,3724,2664,2625)(154,611,1637,1639)(155,3807,1551,1647)(156,1169,537,2324)(157,454,2798,2507)(158,1734,1941,658)(159,3095,3884,521)(160,1769,3092,744)(161,1017,797,2397)(162,3361,1388,1183)(163,1488,1215,3402)(164,2391,1429,3073)(165,2386,3539,1413)(167,558,269,3277)(168,431,3640,1224)(169,892,3326,2769)(170,3479,2585,1419)(171,278,772,1699)(172,2541,2529,3506)(173,3676,1415,2592)(176,1561,3128,1892)(177,1999,583,982)(178,1223,229,3310)(179,894,758,2297)(181,1275,3475,3609)(182,952,794,3707)(183,1347,1078,2471)(184,435,586,1645)(185,2648,1506,1531)(186,2731,1351,226)(187,882,2477,3841)(188,2787,3289,3116)(189,998,1030,1815)(190,1466,1684,3906)(191,2419,3690,2789)(192,1873,1737,3548)(193,3580,674,2453)(194,1365,2883,3745)(195,1839,1292,644)(196,3383,3513,921)(197,1112,2737,3798)(198,2379,2108,2232)(199,3443,2115,858)(200,2640,1812,2780)(202,1121,3885,3852)(203,719,3704,810)(205,3654,316,1971)(206,553,893,645)(207,3363,2428,2620)(208,1229,606,608)(209,1564,3545,2067)(210,2643,2709,1538)(211,365,2196,1831)(212,795,3587,528)(213,252,276,1703)(214,1900,3658,2958)(215,2716,2369,1814)(216,2576,3727,1902)(217,1297,441,473)(218,3456,1451,3193)(219,2482,2153,1005)(220,347,1876,2237)(221,2796,693,947)(222,3756,498,1065)(223,3112,2735,777)(224,1230,2847,372)(225,3604,1003,1122)(227,757,1372,1021)(231,2510,1789,2993)(232,2645,2695,522)(233,2597,635,2227)(234,2961,3503,1766)(235,2484,1251,3391)(236,3792,1001,3129)(237,3153,3159,890)(238,3710,2651,3173)(239,3056,1219,737)(240,3406,2943,996)(241,1389,1426,1534)(242,3344,3041,760)(243,2351,507,3024)(244,676,1954,1901)(245,853,2562,804)(246,3508,3195,1289)(247,2415,1519,1877)(248,3321,1975,3881)(254,1334,446,2106)(255,1735,2289,509)(256,2401,1916,1787)(257,2491,2361,3670)(258,1441,3677,2342)(259,430,756,1826)(260,1081,2032,783)(261,1555,3296,1341)(262,1120,732,856)(263,1958,369,3308)(264,421,3547,2257)(265,3816,2652,2021)(266,788,1019,2245)(267,1594,366,480)(268,3136,650,2870)(270,2085,1499,1038)(271,1369,1974,678)(272,2721,3381,862)(273,3811,1106,1377)(274,281,1968,3283)(275,1575,2031,1214)(277,914,706,3617)(279,1926,2898,2478)(280,989,1310,2594)(282,2105,1918,2850)(283,2683,3132,930)(284,745,2019,1616)(285,1517,682,629)(286,412,534,1610)(287,3749,1077,3777)(289,443,2726,2373)(290,2495,2157,2916)(291,3333,1911,3392)(293,3276,2537,1557)(295,3594,1144,1672)(296,937,3390,3217)(298,3588,902,821)(299,1879,437,425)(300,376,2318,2138)(301,3219,2963,2404)(302,3803,3842,3905)(304,2797,2873,3046)(305,2486,1380,3269)(306,1421,326,915)(307,1340,691,2378)(308,698,734,3563)(309,3271,3332,3786)(310,427,2219,1418)(311,965,2293,1414)(312,750,2936,2144)(313,1891,2595,3664)(314,3835,689,2811)(315,1588,1882,2057)(317,1152,3573,1157)(318,2857,1228,476)(320,411,3008,848)(321,3618,1437,2022)(322,2051,1525,3725)(323,1016,1695,1830)(324,2654,3415,2424)(325,869,3047,340)(327,3719,1716,3414)(328,2944,1305,1057)(329,3784,987,567)(330,683,2251,1137)(331,2956,1718,482)(333,2498,1640,3285)(334,1464,746,1671)(335,784,1932,3077)(336,3871,2388,2065)(337,1430,1378,1467)(338,1319,2061,2630)(339,3642,536,3748)(342,3337,762,1295)(343,2830,545,1759)(344,3109,3057,601)(348,2003,667,926)(349,2490,2779,1337)(350,713,475,2623)(351,2356,802,3499)(352,1394,3546,2333)(354,1963,3843,2287)(355,2760,3063,1666)(356,1728,981,3540)(358,2867,3679,2197)(359,1049,1505,873)(360,2462,2393,1781)(361,2005,1059,1739)(362,2863,619,3399)(363,2990,1062,3176)(364,3646,997,2029)(367,1897,2834,596)(368,3021,1200,3430)(370,2861,2693,1470)(373,1248,1420,2270)(375,3522,2306,2366)(377,3868,2502,3213)(378,1650,1959,3158)(379,1792,3889,3853)(380,2508,3018,1635)(381,2004,3019,1165)(382,2692,2954,1546)(385,2332,603,1808)(387,2871,2503,1494)(389,1930,1797,3686)(390,1033,1247,2942)(391,1884,1863,3143)(392,2762,2405,3180)(393,951,3231,2911)(394,1480,2059,502)(395,2549,694,3567)(396,3103,1026,3045)(397,1353,1333,2583)(398,3188,1187,2513)(399,592,2730,2226)(400,3030,2882,1857)(401,3606,2761,2913)(402,3874,1472,1741)(403,2175,3535,1730)(404,3855,1750,3755)(405,2244,3172,2846)(406,1595,3145,3660)(407,685,1651,3897)(408,2063,1155,2729)(409,3494,1722,3106)(410,3183,3314,3081)(413,3672,2274,1923)(414,1080,1523,2421)(415,2360,2862,1191)(416,2309,626,2964)(417,3827,1232,1953)(418,3739,1023,1904)(419,2626,2485,946)(420,2028,2214,2217)(422,2027,1623,3768)(423,3635,508,3160)(424,2558,2114,2060)(426,2458,2325,2564)(428,1231,2267,2338)(429,2180,474,2413)(432,2200,2928,3347)(433,1048,1704,934)(434,3492,3801,736)(436,3454,2225,2777)(438,1346,1067,1979)(439,1285,3177,2881)(440,1677,3846,2355)(442,1010,3444,1832)(444,1442,710,1328)(445,3141,3163,3657)(447,2480,1142,2089)(448,2814,1182,3090)(449,3682,3696,1100)(450,1582,3643,1422)(451,3267,3014,3795)(452,2450,1110,819)(453,2189,1558,1598)(455,660,897,3857)(456,3625,1136,1795)(457,3455,1793,3262)(458,541,576,581)(461,3490,2052,922)(462,872,2291,718)(464,735,1807,3051)(465,1608,836,3673)(466,3208,1817,1995)(467,1694,2874,681)(468,1486,1895,1573)(469,3170,2917,1636)(470,2934,2007,3146)(471,910,739,3463)(472,3218,2925,3328)(478,1272,3358,2980)(479,3034,1249,3533)(481,639,598,1662)(483,2621,966,2431)(484,656,1810,3388)(485,2966,790,3107)(487,571,1498,980)(488,3257,2353,3049)(489,1278,3223,3538)(490,2638,896,1803)(491,1335,801,1578)(492,1303,3728,2278)(493,1368,1615,1207)(494,1073,2535,2901)(495,1315,3169,1194)(496,1141,2790,1329)(497,3356,970,822)(499,2272,1775,612)(500,1729,3711,3763)(501,3064,2816,2886)(503,2785,1843,2528)(504,2364,1643,630)(505,2193,2628,2656)(506,2788,2479,1221)(510,991,1753,1705)(512,2112,3362,767)(513,2688,3029,2341)(514,3838,3899,2013)(515,3338,1674,552)(516,2317,595,2758)(517,1166,2308,2488)(518,1476,1432,3036)(519,2039,985,1874)(520,3527,3037,2864)(523,2229,3516,1532)(524,2869,2939,1226)(526,2854,1031,2376)(527,1222,3613,2848)(529,3681,1279,2530)(530,1487,3608,3662)(531,2844,2800,1095)(532,846,1330,627)(533,2835,3108,2276)(538,2551,3144,3698)(539,1034,2804,2427)(540,875,3166,2188)(542,2708,1914,2079)(543,618,3419,2641)(544,2035,2081,2845)(546,1818,3808,3234)(547,3501,2547,1909)(548,2754,3611,2008)(549,3317,3258,1274)(550,2252,729,3290)(551,2449,2511,599)(554,1199,2460,3075)(555,1567,2131,969)(556,3105,1670,917)(557,1883,3405,724)(559,927,3483,2902)(560,1009,1064,1850)(561,2536,2234,3421)(562,2561,2468,3286)(564,754,2868,3288)(565,2139,3840,2801)(566,1632,2205,1300)(568,3830,3279,1211)(569,1118,2791,861)(570,2263,649,884)(572,3394,696,831)(574,2328,3460,1343)(575,3082,3876,3484)(577,3775,1760,2240)(578,1092,2515,1536)(579,2526,3820,1697)(580,2514,876,2679)(582,3879,2321,1061)(584,918,3320,2582)(585,2946,2255,3473)(587,2986,1240,1151)(588,3675,1024,2204)(589,3641,3080,1983)(590,1450,828,3647)(593,1600,3440,2092)(597,2732,995,2809)(600,2282,1552,3576)(604,3525,769,3476)(605,2842,1259,1356)(607,2750,1069,1269)(610,2117,3167,2176)(613,1966,1053,2906)(614,1630,1405,1952)(615,2989,1167,704)(616,874,776,2142)(620,1878,3011,1602)(622,2738,1984,1321)(623,3457,3032,1888)(624,2734)(625,1931,1268,1445)(628,3206,1634,3255)(631,1085,3178,1433)(632,1301,3870,2657)(633,842,3133,1796)(634,3079,3902,3017)(636,3341,3892,2152)(637,2953,3220,3723)(638,1732,3701,984)(640,1178,3887,1366)(641,2544,3187,1129)(642,3832,3452,2705)(643,3586,2751,2492)(646,3368,827,3151)(647,1179,2350,2017)(648,665)(651,3102,1409,1773)(652,1676,3530,1354)(653,2072,3688,1731)(654,3566,3486,3471)(655,2018,961,1468)(657,1692,1039,908)(659,964,1770,3720)(662,3729,2080,1748)(663,2987,1783,1410)(664,2444,962,2607)(666,3329,1680,3340)(668,1521,3232,1549)(669,3489,1990,1493)(671,742,1678,1411)(675,1648,1947,791)(677,2554,2557,2974)(679,3825,3447,2169)(680,1613,809,2696)(684,1237,805,818)(687,2173,1772,2481)(688,2015,1540,1829)(690,1331,2489,3472)(692,1668,1348,1119)(695,2262,1302,3009)(697,3800,3205,1976)(699,1029,1849,1691)(701,748,3552,3665)(702,2860,919,1235)(705,1385,2411,3446)(707,3599,3898,1258)(709,1140,2577,3468)(712,1072,1755,3235)(716,1700,2375,3270)(717,3692,2644,2771)(720,2399,1825,2147)(721,1079,1624,3789)(722,2905,1396,1790)(723,3717,2313,3364)(725,1566,1146,1204)(728,1492,1454,3001)(730,941,3497,2981)(731,2756,3067,1345)(733,3093,3762,3110)(738,3819,1257,2672)(740,3731,1960,3603)(741,764)(743,815,2076,755)(747,1752,1066,1542)(749,2560,2992,3088)(751,1483,3201,2442)(752,3315,1256,1854)(753,2784,2264,1349)(761,3010,3752,3322)(763,832,3703,2962)(765,841,3377,1846)(766,2671,2322,2113)(768,1255,1192,2211)(770,1822,2499,1550)(771,1477,1934,3758)(773,2704,2314,2912)(774,3192,3182,1332)(775,2718,2908,2280)(778,2011,2310,1858)(779,1898,3507,2899)(780,2888,2041,2340)(781,2650,3357,1834)(782,3655,3352,2853)(785,3027,2793,2772)(787,3782,2616,2099)(792,3809,1400,803)(793,3137,3854,2931)(796,1236,2212,2476)(798,913,1776,2598)(799,1291,2123,1202)(800,3016,2285,3582)(806,3759,2408,3592)(807,1184,2617,1046)(812,3699,3411,3780)(813,2068,2525,2183)(816,1148,973,2497)(817,899,2230,1535)(823,2614,1649,3114)(824,923,1267,2819)(825,1827,1181,1316)(826,2148,2132,2191)(829,3652,3023,3544)(830,2256,1139,2043)(833,2055,2618,2802)(834,3058,2542,3334)(835,2715,3833,2728)(838,2970,1243,2929)(839,3410,2927,1036)(840,3345,1724,3562)(844,3366,1569,3769)(847,1652,3467,1282)(849,2406,3732,3198)(850,3259,3549,3043)(851,2763,1111,2747)(852,2600,2642,1312)(854,3736,1547,1370)(857,1195,1041,2372)(860,1719,3152,2579)(863,3783,3062,3274)(865,1948,1245,1855)(866,2410,2336,1287)(868,2090,1798,2392)(870,3542,1462,1325)(871,1851,1439,1225)(877,3764,2149,928)(878,942,1206,1244)(879,2586,1869,944)(880,3767,1833,3883)(881,2746,3828,3378)(883,2566,3087,2122)(885,2603,1592,1951)(886,3529,903,3164)(887,2023,3873,2909)(888,2125,2940,1168)(889,3537,2302,3882)(891,3316,1371,1134)(895,2202,1761,943)(898,2455,2420,1198)(901,993,3653,2443)(906,1253,1779,2100)(907,2228,1185,2885)(909,3216,1358,956)(911,1128,2127,2236)(916,2389,3568,1720)(920,2177,2887,1355)(925,3371,1087,2698)(929,1471,972,3553)(931,1173,1823,3121)(933,3896,1527,3821)(935,1725,1738,3071)(938,3147,3280,2959)(939,1115,1917,1489)(940,3059,1518,3602)(948,1496,2326,2587)(949,1943,3628,2387)(953,3496,1712,3157)(954,1186,3304,1581)(955,2418,1217,2996)(957,1311,1227,3631)(958,1264,2872,3226)(959,1688,1762,3065)(963,2832,2979,3313)(967,1784,2447,3564)(968,1696,1556,3212)(971,2783,2995,3650)(975,3197,2457,2674)(976,1935,2997,2201)(977,1929,2184,2807)(978,1127,1286,3148)(979,2430,1800,3042)(983,2303,3150,2461)(988,3099,1969,1447)(990,3066,2555,1456)(992,1071,2960,3115)(994,3374,3214,2622)(1000,3645,1663,2742)(1006,2739,3426,1644)(1011,1482,2559,1681)(1012,1622,1740,3684)(1014,2223,2335,1586)(1015,2903,3862,2504)(1018,2352,2259,2843)(1020,1367,1733,1856)(1022,2744,2438,2288)(1025,2146,2543,2972)(1027,2238,1116,2301)(1028,2454,1188,3055)(1032,1216,2334,1964)(1037,3477,1375,2345)(1040,1862,3697,1544)(1042,3202,2694,1756)(1043,2624,2828,2522)(1045,1097,1511,2093)(1047,1853,3626,1452)(1051,2686,1824,3263)(1052,2465,1687,3839)(1054,3436,1690,3849)(1055,2253)(1056,2224,3591,1893)(1058,2947,3771,2192)(1060,2074,1469,2241)(1063,1307,3583,3844)(1068,2837,1209,2377)(1074,1946,1806,2524)(1075,3229,3048,3250)(1076,2632,3788,1086)(1082,1322,2859,1497)(1083,3858,2058,1580)(1084,1655,3691,2469)(1088,3078,3130,2290)(1089,3412,2329,1992)(1090,2436,3785,1559)(1091,1981,2700,3893)(1096,1233,1938,2467)(1098,2045,2215,3534)(1101,3096,3233,3597)(1104,1950,2221,1780)(1105,3119,3124,1629)(1108,2474,2209,1212)(1109,1459,1605,2998)(1113,3680,3837,1395)(1114,1998,3185,2382)(1117,3559,1977,1973)(1123,1835,1545,1896)(1124,2733,1828,2866)(1125,1978,3256,3505)(1130,2292,3804,3222)(1131,1686,3500,2851)(1132,1504,2563,2412)(1135,3230,1899,1764)(1143,2627,2156,3002)(1145,3770,1924,2892)(1149,1239,1458,3561)(1150,2707,2187,3376)(1153,3612,2575,1508)(1154,2768,3264,3813)(1156,1520,3025,2894)(1158,3292,2517,1593)(1159,1925,2265,3470)(1161,2073,1821,3409)(1162,1794,1539,1881)(1163,1982,1864,1208)(1164,1802,3389,2279)(1171,3298,1865,2552)(1172,1502,3872,3094)(1175,2757,2655,1318)(1176,2254,2610,3343)(1177,3400,2932,1669)(1180,2077,2409,2924)(1189,2856)(1193,1710,1870,3295)(1196,1837,3181,2593)(1197,3175,1972,1844)(1201,3305,3504,1693)(1210,2371,1491,3878)(1213,3040,2965,2703)(1218,2831,1417,1252)(1220,2895,2121,2701)(1234,2020,3685,3161)(1250,1782,3293,3663)(1260,3423,3651,1500)(1261,3761,2439,3637)(1263,2647,2926,1363)(1265,3207,3829,2159)(1266,1495,2879,3003)(1270,2087,2459,3589)(1271,3577,1868,1746)(1273,3227,3554,2767)(1276,2049,1373,2337)(1277,1465,3458,2914)(1280,1392,2829,3532)(1283,3695,3596,2584)(1284,2968,3031,2286)(1288,3398,3052,3228)(1293,2794,3623,2207)(1294,3089,3155,3787)(1296,2316,2088,2150)(1298,1626,1461,3253)(1299,3287)(1306,2151,1980,3560)(1308,1757,3774,2311)(1309,3880,3517,3585)(1314,1568,2327,2016)(1320,3743,2520,3543)(1323,2682,1991,1601)(1324,3733,3323,2918)(1326,3438,3335,3196)(1327,3365,1514,1683)(1336,2889,2933,1606)(1339,2483,3671,3488)(1342,3413,2243,2719)(1344,1707,2608,1424)(1350,2706,1479,1386)(1352,1359,2663,3569)(1360,3518,3123,2425)(1361,3439,1638,3189)(1362,2773,3814,2736)(1364,1820,3382,1463)(1374,1927,1646,3805)(1379,2633,2697,1758)(1381,3848,3740,2135)(1382,3860,2774,3741)(1383,3281,2346,2919)(1384,2222,2012,1847)(1390,1872,2781,1937)(1391,2472,3482,2910)(1397,3156,2206,1659)(1398,1788,3026,2166)(1399,1706,3514,3894)(1401,2275,3247,1763)(1404,2101,1765,1751)(1406,2384,3272,3385)(1407,2519,2740,3241)(1408,1446,2120,2190)(1412,1955,3629,3615)(1416,2578,3291,2009)(1423,1799,3442,3278)(1425,3097,1777,1749)(1427,3693,1736,3459)(1428,3493,2096,1543)(1434,2186,3118,1560)(1435,1667,2765,3718)(1436,2056,2982,2119)(1438,3076,3210,2904)(1440,1485,3369,3215)(1444,3246,3265,2538)(1448,1627,3401,3644)(1449,1455,3004,2985)(1457,3520,2380,2383)(1460,2795,3822,3595)(1474,2037,2690,1922)(1475,2162,3360,3797)(1478,3826,3015,2054)(1484,3435,2441,2921)(1490,2195,2727,2473)(1503,1583,2923,2806)(1512,2978,3485,3237)(1513,3622,1774,2505)(1515,3022,2006,3113)(1516,3033,3903,3901)(1524,3575,3541,1664)(1526,1912,1809,2876)(1528,3324,2605,3301)(1529,2083,3796,2534)(1537,3667,2677,2445)(1541,1570,1962,3462)(1548,2890,3461,2680)(1553,2670,1713,2606)(1554,2246,1985,2658)(1562,3346,3085,2307)(1563,2907,1840,3689)(1574,2422,3211,3605)(1576,2759,2984,3307)(1577,3794,3224,3715)(1579,2271,3890,3799)(1584,3620,1819,3319)(1587,3648,1771,3815)(1589,2339,2094,3531)(1590,2840,2417,2381)(1591,1957,2935,2312)(1596,2463,3336,3312)(1597,3302,1742,3273)(1607,2884,3847,2826)(1609,3260,1811,2354)(1617,3659,3687,2878)(1618,2086,2849,3888)(1619,2248,2527,3865)(1620,2815,3384,3072)(1621,2778,2743,1908)(1633,3509)(1653,2631,3712,1845)(1660,3864,3572,2745)(1661,2501,2755,1920)(1673,3817,2129,3683)(1675,2922,3895,2294)(1679,3487,2390,2948)(1685,3416,2588,2423)(1701,2653,2042,3448)(1702,2891,3100,1928)(1708,1754,2165,2299)(1711,2050)(1714,3174,3578,2685)(1715,2038,3354,1875)(1721,3000,2002,3299)(1723,3035,2261,2266)(1726,3162,1961,2967)(1743,2665,2062,3125)(1745,3225,3512,2896)(1747,2374,3779,3515)(1767,2446,2855,2178)(1785,3127,2572,2296)(1786,3802,2532,3373)(1801,3861,1838,3678)(1805,2174,3639,3379)(1836,1965,3261,2210)(1841,3165,2047,3020)(1842,2723,2300,3199)(1852,2416,2456,3245)(1859,3669,2025,1986)(1860,2506,3495,2749)(1861,2556,2678,3244)(1866,3268,2091,2786)(1867,2724,3101,2213)(1871,2611,1913,1994)(1880,3367,2064,3318)(1889,3275,2107,2711)(1890,3168,1945,3751)(1894,1988,2470,3425)(1903,2988,2661,2095)(1905,2509,2429,2571)(1907,2518,3616,2097)(1910,3240)(1915,3754,2766,3306)(1919,3904,2937,2069)(1921,2639,2349,3812)(1940,2687,2145,2675)(1942,3200,3886,2432)(1944,2676,2493,3600)(1949,3581,3570,3397)(1967,2540,3194,3702)(1987,3359,3765,3772)(1993,3349,3432,2082)(1997,2818,2775,3666)(2000,3584,2827,3351)(2014,3863,3249,3633)(2030,3636,2330,2494)(2034,2920,3070,3433)(2071,2553,3614,2602)(2075,2691,2448,3122)(2078,2753,2126,2858)(2098,3060,3297,3355)(2102,3420,3300,2109)(2103,3013,3131,3441)(2110,2433,2452,2407)(2111,3867)(2124,3386,2570,2158)(2128,2714,3474,2991)(2134,3044,3465,2949)(2136,3434,2260,2609)(2137,2994,2269,3339)(2140,2531,3449,2581)(2160,3502,3708,2185)(2167,2182,3428,3624)(2168,2649,2604,3601)(2170,3204)(2198,2231,3437,3818)(2199,2852,3395,2516)(2208,2220)(2216,3760,2574,2273)(2239,2975,3068,2820)(2268,3778,3621,2304)(2281,3431,3254,2713)(2283,2822,3674,3536)(2284,2613,3236,2950)(2298,3294,3266,3831)(2319,3721,2496,2669)(2320,3737,3050,2824)(2343,2897,2833,3179)(2357,2567,3331,2810)(2359,2957,3091,2666)(2365,2955,2601,3773)(2367,3634,2973,2615)(2394,2720,3866,2573)(2395,2689,3742,3387)(2396,2659,3427,3372)(2402,3590,3519,2983)(2414,3139,2464,3526)(2426,2500)(2451,3656,3191,3184)(2487,2805,2619,2952)(2533,3209,3746,3556)(2539,2710,2839,2836)(2550,3856,3716,3348)(2629,2893,3074,3053)(2634,2722,3757,3574)(2668,3407,2684,3747)(2699,3408,2712,3750)(2776,3284,2799,3521)(2821,3005,3104,3418)(2865,3834,3330,3120)(2999,3303,3350,3380)(3006,3627,3422,3851)(3054,3706,3393,3869)(3353,3481,3726,3806)(3766,3823)]).
- It is non-abelian.
- It has 2-Rank 3.
- The centre of a Sylow 2-subgroup has rank 1.
- Its Sylow 2-subgroup has 5 conjugacy classes of maximal elementary abelian subgroups, which are all of rank 3.
Structure of the cohomology ring
The computation was based on 7 stability conditions for H*(Syl2(M12); GF(2)).General information
- The cohomology ring is of dimension 3 and depth 3.
- The depth exceeds the Duflot bound, which is 1.
- The Poincaré series is
( − 1)·(1 − t + t2) ( − 1 + t)3 · (1 + t + t2) - The a-invariants are -∞,-∞,-∞,-3. They were obtained using the filter regular HSOP of the Hilbert-Poincaré test.
- The filter degree type of any filter regular HSOP is [-1, -2, -3, -3].
| About the group | Ring generators | Ring relations | Completion information | Restriction maps |
Ring generators
The cohomology ring has 5 minimal generators of maximal degree 4:
-
b_1_0 , an element of degree 1 -
b_2_0 , an element of degree 2 -
b_3_1 , an element of degree 3 -
b_3_0 , an element of degree 3 -
c_4_4 , a Duflot element of degree 4
| About the group | Ring generators | Ring relations | Completion information | Restriction maps |
Ring relations
There are 2 minimal relations of maximal degree 6:
-
b_1_0·b_3_1 -
b_3_0·b_3_1 + b_3_02 + b_1_03·b_3_0 + b_2_0·b_1_0·b_3_0 + c_4_4·b_1_02
| About the group | Ring generators | Ring relations | Completion information | Restriction maps |
Data used for the Hilbert-Poincaré test
- We proved completion in degree 6 using the Hilbert-Poincaré criterion.
- The completion test was perfect: It applied in the last degree in which a generator or relation was found.
- The following is a filter regular homogeneous system of parameters:
c_4_4 , an element of degree 4b_1_02 + b_2_0 , an element of degree 2b_3_1 + b_2_0·b_1_0 , an element of degree 3
- A Duflot regular sequence is given by
c_4_4 . - The Raw Filter Degree Type of the filter regular HSOP is [-1, -1, -1, 6].
| About the group | Ring generators | Ring relations | Completion information | Restriction maps |
Restriction maps
Expressing the generators as elements of H*(Syl2(M12); GF(2))
-
b_1_0 →b_1_0 -
b_2_0 →b_1_22 + b_1_1·b_1_2 + b_1_12 + b_2_5 -
b_3_1 →b_1_1·b_1_22 + b_1_12·b_1_2 + b_2_5·b_1_2 -
b_3_0 →b_3_9 + b_2_5·b_1_2 + b_2_4·b_1_1 -
c_4_4 →b_2_4·b_1_1·b_1_2 + b_2_42 + c_4_14
Restriction map to the greatest el. ab. subgp. in the centre of a Sylow subgroup, which is of rank 1
-
b_1_0 →0 , an element of degree 1 -
b_2_0 →0 , an element of degree 2 -
b_3_1 →0 , an element of degree 3 -
b_3_0 →0 , an element of degree 3 -
c_4_4 →c_1_04 , an element of degree 4
Restriction map to a maximal el. ab. subgp. of rank 3 in a Sylow subgroup
-
b_1_0 →c_1_1 , an element of degree 1 -
b_2_0 →c_1_22 + c_1_1·c_1_2 , an element of degree 2 -
b_3_1 →0 , an element of degree 3 -
b_3_0 →c_1_0·c_1_12 + c_1_02·c_1_1 , an element of degree 3 -
c_4_4 →c_1_0·c_1_1·c_1_22 + c_1_0·c_1_12·c_1_2 + c_1_0·c_1_13 + c_1_02·c_1_22
+ c_1_02·c_1_1·c_1_2 + c_1_04 , an element of degree 4
Restriction map to a maximal el. ab. subgp. of rank 3 in a Sylow subgroup
-
b_1_0 →0 , an element of degree 1 -
b_2_0 →c_1_22 + c_1_1·c_1_2 + c_1_12 , an element of degree 2 -
b_3_1 →c_1_1·c_1_22 + c_1_12·c_1_2 , an element of degree 3 -
b_3_0 →0 , an element of degree 3 -
c_4_4 →c_1_0·c_1_1·c_1_22 + c_1_0·c_1_12·c_1_2 + c_1_02·c_1_22 + c_1_02·c_1_1·c_1_2
+ c_1_02·c_1_12 + c_1_04 , an element of degree 4
Restriction map to a maximal el. ab. subgp. of rank 3 in a Sylow subgroup
-
b_1_0 →0 , an element of degree 1 -
b_2_0 →c_1_22 + c_1_1·c_1_2 + c_1_12 , an element of degree 2 -
b_3_1 →c_1_1·c_1_22 + c_1_12·c_1_2 , an element of degree 3 -
b_3_0 →c_1_1·c_1_22 + c_1_12·c_1_2 , an element of degree 3 -
c_4_4 →c_1_0·c_1_1·c_1_22 + c_1_0·c_1_12·c_1_2 + c_1_02·c_1_22 + c_1_02·c_1_1·c_1_2
+ c_1_02·c_1_12 + c_1_04 , an element of degree 4
Restriction map to a maximal el. ab. subgp. of rank 3 in a Sylow subgroup
-
b_1_0 →0 , an element of degree 1 -
b_2_0 →c_1_22 + c_1_1·c_1_2 + c_1_12 , an element of degree 2 -
b_3_1 →c_1_1·c_1_22 + c_1_12·c_1_2 , an element of degree 3 -
b_3_0 →c_1_1·c_1_22 + c_1_12·c_1_2 , an element of degree 3 -
c_4_4 →c_1_0·c_1_1·c_1_22 + c_1_0·c_1_12·c_1_2 + c_1_02·c_1_22 + c_1_02·c_1_1·c_1_2
+ c_1_02·c_1_12 + c_1_04 , an element of degree 4
Restriction map to a maximal el. ab. subgp. of rank 3 in a Sylow subgroup
-
b_1_0 →0 , an element of degree 1 -
b_2_0 →c_1_22 + c_1_1·c_1_2 + c_1_12 , an element of degree 2 -
b_3_1 →c_1_1·c_1_22 + c_1_12·c_1_2 , an element of degree 3 -
b_3_0 →0 , an element of degree 3 -
c_4_4 →c_1_0·c_1_1·c_1_22 + c_1_0·c_1_12·c_1_2 + c_1_02·c_1_22 + c_1_02·c_1_1·c_1_2
+ c_1_02·c_1_12 + c_1_04 , an element of degree 4
| About the group | Ring generators | Ring relations | Completion information | Restriction maps |
|
Simon King Department of Mathematics and Computer Science Friedrich-Schiller-Universität Jena 07737 Jena GERMANY
|