SPOJ 10232. Distinct Primes

Arithmancy is Draco Malfoy's favorite subject, but what spoils it for him is that Hermione Granger is in his class, and she is better than him at it. Prime numbers are of mystical importance in Arithmancy, and Lucky Numbers even more so. Lucky Numbers are those positive integers that have at least three distinct prime factors; 30 and 42 are the first two. Malfoy's teacher has given them a positive integer n, and has asked them to find the nth lucky number. Malfoy would like to beat Hermione at this exercise, so although he is an evil git, please help him, just this once. After all, the know-it-all Hermione does need a lesson.

Input (STDIN):

The first line contains the number of test cases T. Each of the next T lines contains one integer n.

Output (STDOUT):

Output T lines, containing the corresponding lucky number for that test case.

Constraints:

1 <= T <= 20

1 <= n <= 1000

Sample Input:

2

1

2

540,
546,
550,
552,
555,
558,
560,
561,
564,
570,
572,
574,
580,
582,
585,
588,
590,
594,
595,
598,
600,
602,
606,
609,
610,
612,
615,
616,
618,
620,
624,
627,
630,
636,
638,
642,
644,
645,
646,
650,
651,
654,
658,
660,
663,
665,
666,
670,
672,
678,
680,
682,
684,
690,
693,
696,
700,
702,
705,
708,
710,
714,
715,
720,
726,
728,
730,
732,
735,
738,
740,
741,
742,
744,
748,
750,
754,
756,
759,
760,
762,
765,
770,
774,
777,
780,
782,
786,
790,
792,
795,
798,
804,
805,
806,
810,
812,
814,
816,
819,
820,
822,
825,
826,
828,
830,
834,
836,
840,
846,
850,
852,
854,
855,
858,
860,
861,
868,
870,
874,
876,
880,
882,
884,
885,
888,
890,
894,
897,
900,
902,
903,
906,
910,
912,
915,
918,
920,
924,
930,
935,
936,
938,
940,
942,
945,
946,
948,
950,
952,
954,
957,
960,
962,
966,
969,
970,
975,
978,
980,
984,
986,
987,
988,
990,
994,
996,
1001,
1002,
1005,
1008,
1010,
1012,
1014,
1015,
1020,
1022,
1023,
1026,
1030,
1032,
1034,
1035,
1036,
1038,
1040,
1044,
1045,
1050,
1054,
1056,
1060,
1062,
1064,
1065,
1066,
1068,
1070,
1071,
1074,
1078,
1080,
1085,
1086,
1090,
1092,
1095,
1098,
1100,
1102,
1104,
1105,
1106,
1110,
1113,
1116,
1118,
1120,
1122,
1128,
1130,
1131,
1134,
1140,
1144,
1146,
1148,
1150,
1155,
1158,
1160,
1162,
1164,
1166,
1170,
1173,
1176,
1178,
1180,
1182,
1185,
1188,
1190,
1194,
1196,
1197,
1200,
1204,
1206,
1209,
1210,
1212,
1218,
1220,
1221,
1222,
1224,
1230,
1232,
1235,
1236,
1239,
1240,
1242,
1245,
1246,
1248,
1254,
1258,
1260,
1265,
1266,
1270,
1272,
1274,
1275,
1276,
1278,
1281,
1284,
1287,
1288,
1290,
1292,
1295,
1298,
1300,
1302,
1305,
1308,
1309,
1310,
1311,
1314,
1316,
1320,
1326,
1330,
1332,
1334,
1335,
1338,
1340,
1342,
1344,
1350,
1353,
1356,
1358,
1360,
1362,
1364,
1365,
1368,
1370,
1374,
1378,
1380,
1386,
1390,
1392,
1394,
1395,
1398,
1400,
1404,
1406,
1407,
1410,
1414,
1416,
1419,
1420,
1422,
1425,
1426,
1428,
1430,
1434,
1435,
1440,
1442,
1443,
1446,
1449,
1450,
1452,
1455,
1456,
1460,
1462,
1463,
1464,
1470,
1474,
1476,
1479,
1480,
1482,
1484,
1485,
1488,
1490,
1491,
1494,
1495,
1496,
1498,
1500,
1505,
1506,
1508,
1510,
1512,
1515,
1518,
1520,
1524,
1526,
1530,
1533,
1534,
1540,
1542,
1545,
1547,
1548,
1550,
1551,
1554,
1558,
1560,
1562,
1564,
1566,
1570,
1572,
1575,
1578,
1580,
1581,
1582,
1584,
1586,
1590,
1595,
1596,
1598,
1599,
1602,
1605,
1606,
1608,
1610,
1612,
1614,
1615,
1617,
1620,
1624,
1626,
1628,
1630,
1632,
1634,
1635,
1638,
1640,
1644,
1645,
1650,
1652,
1653,
1656,
1659,
1660,
1662,
1665,
1666,
1668,
1670,
1672,
1674,
1677,
1680,
1683,
1686,
1690,
1692,
1694,
1695,
1698,
1700,
1702,
1704,
1705,
1708,
1710,
1716,
1720,
1722,
1725,
1729,
1730,
1734,
1736,
1738,
1740,
1742,
1743,
1746,
1748,
1749,
1750,
1752,
1755,
1758,
1760,
1764,
1767,
1768,
1770,
1771,
1776,
1778,
1780,
1782,
1785,
1786,
1788,
1790,
1794,
1798,
1800,
1802,
1804,
1806,
1810,
1812,
1815,
1818,
1820,
1824,
1826,
1827,
1830,
1833,
1834,
1836,
1840,
1842,
1845,
1846,
1848,
1850,
1854,
1855,
1860,
1862,
1866,
1869,
1870,
1872,
1876,
1878,
1880,
1881,
1884,
1885,
1886,
1887,
1890,
1892,
1896,
1898,
1900,
1902,
1904,
1905,
1908,
1910,
1911,
1914,
1918,
1920,
1924,
1925,
1926,
1930,
1932,
1935,
1938,
1940,
1946,
1947,
1950,
1953,
1955,
1956,
1958,
1960,
1962,
1965,
1968,
1970,
1972,
1974,
1976,
1978,
1980,
1986,
1988,
1989,
1990,
1992,
1995,
1998,
2001,
2002,
2004,
2006,
2010,
2013,
2014,
2015,
2016,
2020,
2022,
2024,
2028,
2030,
2034,
2035,
2037,
2040,
2044,
2046,
2050,
2052,
2054,
2055,
2058,
2060,
2064,
2065,
2067,
2068,
2070,
2072,
2074,
2076,
2079,
2080,
2082,
2085,
2086,
2088,
2090,
2091,
2093,
2094,
2100,
2106,
2108,
2109,
2110,
2112,
2114,
2115,
2118,
2120,
2121,
2124,
2128,
2130,
2132,
2134,
2135,
2136,
2139,
2140,
2142,
2145,
2146,
2148,
2150,
2154,
2156,
2158,
2160,
2162,
2163,
2166,
2170,
2172,
2175,
2178,
2180,
2184,
2185,
2190,
2193,
2196,
2198,
2200,
2202,
2204,
2205,
2208,
2210,
2211,
2212,
2214,
2220,
2222,
2223,
2226,
2230,
2232,
2233,
2235,
2236,
2238,
2240,
2242,
2244,
2247,
2250,
2254,
2255,
2256,
2260,
2261,
2262,
2265,
2266,
2268,
2270,
2274,
2275,
2277,
2278,
2280,
2282,
2286,
2288,
2289,
2290,
2292,
2294,
2295,
2296,
2298,
2300,
2301,
2310,
2314,
2316,
2318,
2320,
2322,
2324,
2325,
2328,
2330,
2331,
2332,
2334,
2337,
2338,
2340,
2343,
2345,
2346,
2350,
2352,
2354,
2355,
2356,
2358,
2360,
2364,
2365,
2366,
2370,
2373,
2376,
2378,
2379,
2380,
2382,
2385,
2387,
2388,
2390,
2392,
2394,
2397,
2398,
2400,
2405,
2406,
2408,
2409,
2410,
2412,
2414,
2415,
2418,
2420,
2422,
2424,
2430,
2431,
2436,
2438,
2440,
2442,
2444,
2445,
2448,
2450,
2451,
2454,
2457,
2460,
2464,
2465,
2466,
2470,
2472,
2475,
2478,
2480,
2482,
2484,
2485,
2486,
2490,
2492,
2494,
2496,
2499,
2502,
2505,
2506,
2508,
2510,
2514,
2516,
2520,
2522,
2526,
2530,
2532,
2534,
2535,
2538,
2540,
2541,
2542,
2544,
2546,
2548,
2550,
2552,
2553,
2555,
2556,
2562,
2565,
2568,
2570,
2574,
2576,
2580,
2583,
2584,
2585,
2586,
2590,
2595,
2596,
2598,
2600,
2604,
2607,
2610,
2613,
2616,
2618,
2620,
2622,
2625,
2626,
2628,
2630,
2632,
2634,
2635,
2639,
2640,
2646,
2650,
2652,
2655,
2658,
2660,
2664,
2665,
2666,
2667,
2668,
2670,
2674,
2676,
2678,
2679};
/*int main()
{

int o=1,flag;
for(int m=1;m<100000;m++)
{
if(
((m%2==0)&&(m%3==0)&&(m%5==0))||
((m%2==0)&&(m%3==0)&&(m%7==0))||
((m%2==0)&&(m%3==0)&&(m%11==0))||
((m%2==0)&&(m%3==0)&&(m%13==0))||
((m%2==0)&&(m%3==0)&&(m%17==0))||
((m%2==0)&&(m%3==0)&&(m%19==0))||
((m%2==0)&&(m%7==0)&&(m%5==0))||
((m%2==0)&&(m%11==0)&&(m%5==0))||
((m%2==0)&&(m%13==0)&&(m%5==0))||
((m%2==0)&&(m%17==0)&&(m%5==0))||
((m%2==0)&&(m%19==0)&&(m%5==0))||
((m%2==0)&&(m%7==0)&&(m%11==0))||
((m%2==0)&&(m%7==0)&&(m%13==0))||
((m%2==0)&&(m%7==0)&&(m%17==0))||
((m%2==0)&&(m%7==0)&&(m%19==0))||
((m%2==0)&&(m%11==0)&&(m%13==0))||
((m%2==0)&&(m%11==0)&&(m%17==0))||
((m%2==0)&&(m%11==0)&&(m%19==0))||
((m%2==0)&&(m%13==0)&&(m%17==0))||
((m%2==0)&&(m%17==0)&&(m%19==0))||
((m%3==0)&&(m%7==0)&&(m%5==0))||
((m%11==0)&&(m%3==0)&&(m%5==0))||
((m%13==0)&&(m%3==0)&&(m%5==0))||
((m%17==0)&&(m%3==0)&&(m%5==0))||
((m%19==0)&&(m%3==0)&&(m%5==0))||
((m%7==0)&&(m%3==0)&&(m%11==0))||
((m%7==0)&&(m%3==0)&&(m%13==0))||
((m%7==0)&&(m%3==0)&&(m%17==0))||
((m%7==0)&&(m%3==0)&&(m%19==0))||
((m%11==0)&&(m%3==0)&&(m%13==0))||
((m%11==0)&&(m%3==0)&&(m%17==0))||
((m%11==0)&&(m%3==0)&&(m%19==0))||
((m%13==0)&&(m%3==0)&&(m%17==0))||
((m%13==0)&&(m%3==0)&&(m%19==0))||
((m%17==0)&&(m%3==0)&&(m%19==0))||
((m%11==0)&&(m%7==0)&&(m%5==0))||
((m%13==0)&&(m%7==0)&&(m%5==0))||
((m%17==0)&&(m%7==0)&&(m%5==0))||
((m%19==0)&&(m%7==0)&&(m%5==0))||
((m%17==0)&&(m%11==0)&&(m%5==0))||
((m%19==0)&&(m%11==0)&&(m%5==0))||
((m%13==0)&&(m%11==0)&&(m%5==0))||
((m%13==0)&&(m%11==0)&&(m%7==0))||
((m%17==0)&&(m%11==0)&&(m%7==0))||
((m%19==0)&&(m%11==0)&&(m%7==0))||
((m%17==0)&&(m%13==0)&&(m%11==0))||
((m%19==0)&&(m%13==0)&&(m%11==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))||
((m%19==0)&&(m%17==0)&&(m%13==0))

)
{
flag=0;
for(int q=m-1;q>0;q--)
{
if(a[q]==m)
flag=1;
}
if(flag==0)
{
a[o]=m;
o=o+1;
}
}
}
int n;
scanf("%d",&n);
FILE *fp;//建立一个文件操作指针
fp=fopen("1.txt","w+");//以追加的方式建立或打开1.txt，默认位置在你程序的目录下面
for(int i=0;i<n;i++)
{

printf("%d\n",a[i]);
fprintf(fp,"%d,\n",a[i]);
}
return 0;
} */
int main()
{
int n;
scanf("%d",&n);
while(n--)
{
int m;
scanf("%d",&m);
printf("%d\n",a[m]);
}
return 0;
}

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