Discussion:
Magic Square Wanted
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nigel
2008-10-01 18:06:25 UTC
Permalink
An idea for a lottery system just struck me which is so barkingly mad
that it might be fun to try. The problem is that it needs a very large
magic square as a driver, at least 100x100 but the bigger the better up
to 256x256 (the maximum number of columns per page in my spreadsheet
software).

Does anyone know where I could obtain such a magic square? I'd like to
be able to load it straight into the spreadsheet so comma delimited
format would be ideal.

Thanks for your help,

NigelH
Stephan Bird
2008-10-01 20:22:03 UTC
Permalink
On Wed, 01 Oct 2008 19:06:25 +0100 in
Post by nigel
An idea for a lottery system just struck me which is so barkingly mad
that it might be fun to try. The problem is that it needs a very large
magic square as a driver, at least 100x100 but the bigger the better up
to 256x256 (the maximum number of columns per page in my spreadsheet
software).
Does anyone know where I could obtain such a magic square? I'd like to
be able to load it straight into the spreadsheet so comma delimited
format would be ideal.
The easiest way IMO for something like 255 x 255 would be what Wikipedia
calls the Siamese method <URL:http://en.wikipedia.org/w/index.php?
title=Siamese_method&oldid=233054987> . There may be some stuff you can
use at <URL:http://en.wikipedia.org/w/index.php?
title=Magic_square&oldid=239292292> as well.

Stephan
--
Stephan Bird MChem(Hons) AMRSC
***@mad.scientist.com
Currently in Macclesfield, Cheshire
nigel
2008-10-02 10:57:15 UTC
Permalink
Post by Stephan Bird
On Wed, 01 Oct 2008 19:06:25 +0100 in
Post by nigel
An idea for a lottery system just struck me which is so barkingly mad
that it might be fun to try. The problem is that it needs a very large
magic square as a driver, at least 100x100 but the bigger the better up
to 256x256 (the maximum number of columns per page in my spreadsheet
software).
Does anyone know where I could obtain such a magic square? I'd like to
be able to load it straight into the spreadsheet so comma delimited
format would be ideal.
The easiest way IMO for something like 255 x 255 would be what Wikipedia
calls the Siamese method <URL:http://en.wikipedia.org/w/index.php?
title=Siamese_method&oldid=233054987> . There may be some stuff you can
use at <URL:http://en.wikipedia.org/w/index.php?
title=Magic_square&oldid=239292292> as well.
Stephan
Thanks for the links. 255x255 lol, that would certainly tax the
concentration.

NigelH
Carl G.
2008-10-02 00:50:59 UTC
Permalink
An idea for a lottery system just struck me which is so barkingly mad that
it might be fun to try. The problem is that it needs a very large magic
square as a driver, at least 100x100 but the bigger the better up to
256x256 (the maximum number of columns per page in my spreadsheet
software).
Does anyone know where I could obtain such a magic square? I'd like to be
able to load it straight into the spreadsheet so comma delimited format
would be ideal.
Thanks for your help,
NigelH
If you know someone with the MatLab program, the magic() function creates
magic squares of a specified size. Below is the result from magic(128),
which creates a 128 by 128 magic square. You will have to undo the
reformatting created by the newsreader. I apologize for the size of this
response (at least it is in plain text format).

- Carl G.

16384 2 3 16381 16380 6 7 16377 16376 10 11 16373 16372 14 15 16369 16368 18
19 16365 16364 22 23 16361 16360 26 27 16357 16356 30 31 16353 16352 34 35
16349 16348 38 39 16345 16344 42 43 16341 16340 46 47 16337 16336 50 51
16333 16332 54 55 16329 16328 58 59 16325 16324 62 63 16321 16320 66 67
16317 16316 70 71 16313 16312 74 75 16309 16308 78 79 16305 16304 82 83
16301 16300 86 87 16297 16296 90 91 16293 16292 94 95 16289 16288 98 99
16285 16284 102 103 16281 16280 106 107 16277 16276 110 111 16273 16272 114
115 16269 16268 118 119 16265 16264 122 123 16261 16260 126 127 16257
129 16255 16254 132 133 16251 16250 136 137 16247 16246 140 141 16243 16242
144 145 16239 16238 148 149 16235 16234 152 153 16231 16230 156 157 16227
16226 160 161 16223 16222 164 165 16219 16218 168 169 16215 16214 172 173
16211 16210 176 177 16207 16206 180 181 16203 16202 184 185 16199 16198 188
189 16195 16194 192 193 16191 16190 196 197 16187 16186 200 201 16183 16182
204 205 16179 16178 208 209 16175 16174 212 213 16171 16170 216 217 16167
16166 220 221 16163 16162 224 225 16159 16158 228 229 16155 16154 232 233
16151 16150 236 237 16147 16146 240 241 16143 16142 244 245 16139 16138 248
249 16135 16134 252 253 16131 16130 256
257 16127 16126 260 261 16123 16122 264 265 16119 16118 268 269 16115 16114
272 273 16111 16110 276 277 16107 16106 280 281 16103 16102 284 285 16099
16098 288 289 16095 16094 292 293 16091 16090 296 297 16087 16086 300 301
16083 16082 304 305 16079 16078 308 309 16075 16074 312 313 16071 16070 316
317 16067 16066 320 321 16063 16062 324 325 16059 16058 328 329 16055 16054
332 333 16051 16050 336 337 16047 16046 340 341 16043 16042 344 345 16039
16038 348 349 16035 16034 352 353 16031 16030 356 357 16027 16026 360 361
16023 16022 364 365 16019 16018 368 369 16015 16014 372 373 16011 16010 376
377 16007 16006 380 381 16003 16002 384
16000 386 387 15997 15996 390 391 15993 15992 394 395 15989 15988 398 399
15985 15984 402 403 15981 15980 406 407 15977 15976 410 411 15973 15972 414
415 15969 15968 418 419 15965 15964 422 423 15961 15960 426 427 15957 15956
430 431 15953 15952 434 435 15949 15948 438 439 15945 15944 442 443 15941
15940 446 447 15937 15936 450 451 15933 15932 454 455 15929 15928 458 459
15925 15924 462 463 15921 15920 466 467 15917 15916 470 471 15913 15912 474
475 15909 15908 478 479 15905 15904 482 483 15901 15900 486 487 15897 15896
490 491 15893 15892 494 495 15889 15888 498 499 15885 15884 502 503 15881
15880 506 507 15877 15876 510 511 15873
15872 514 515 15869 15868 518 519 15865 15864 522 523 15861 15860 526 527
15857 15856 530 531 15853 15852 534 535 15849 15848 538 539 15845 15844 542
543 15841 15840 546 547 15837 15836 550 551 15833 15832 554 555 15829 15828
558 559 15825 15824 562 563 15821 15820 566 567 15817 15816 570 571 15813
15812 574 575 15809 15808 578 579 15805 15804 582 583 15801 15800 586 587
15797 15796 590 591 15793 15792 594 595 15789 15788 598 599 15785 15784 602
603 15781 15780 606 607 15777 15776 610 611 15773 15772 614 615 15769 15768
618 619 15765 15764 622 623 15761 15760 626 627 15757 15756 630 631 15753
15752 634 635 15749 15748 638 639 15745
641 15743 15742 644 645 15739 15738 648 649 15735 15734 652 653 15731 15730
656 657 15727 15726 660 661 15723 15722 664 665 15719 15718 668 669 15715
15714 672 673 15711 15710 676 677 15707 15706 680 681 15703 15702 684 685
15699 15698 688 689 15695 15694 692 693 15691 15690 696 697 15687 15686 700
701 15683 15682 704 705 15679 15678 708 709 15675 15674 712 713 15671 15670
716 717 15667 15666 720 721 15663 15662 724 725 15659 15658 728 729 15655
15654 732 733 15651 15650 736 737 15647 15646 740 741 15643 15642 744 745
15639 15638 748 749 15635 15634 752 753 15631 15630 756 757 15627 15626 760
761 15623 15622 764 765 15619 15618 768
769 15615 15614 772 773 15611 15610 776 777 15607 15606 780 781 15603 15602
784 785 15599 15598 788 789 15595 15594 792 793 15591 15590 796 797 15587
15586 800 801 15583 15582 804 805 15579 15578 808 809 15575 15574 812 813
15571 15570 816 817 15567 15566 820 821 15563 15562 824 825 15559 15558 828
829 15555 15554 832 833 15551 15550 836 837 15547 15546 840 841 15543 15542
844 845 15539 15538 848 849 15535 15534 852 853 15531 15530 856 857 15527
15526 860 861 15523 15522 864 865 15519 15518 868 869 15515 15514 872 873
15511 15510 876 877 15507 15506 880 881 15503 15502 884 885 15499 15498 888
889 15495 15494 892 893 15491 15490 896
15488 898 899 15485 15484 902 903 15481 15480 906 907 15477 15476 910 911
15473 15472 914 915 15469 15468 918 919 15465 15464 922 923 15461 15460 926
927 15457 15456 930 931 15453 15452 934 935 15449 15448 938 939 15445 15444
942 943 15441 15440 946 947 15437 15436 950 951 15433 15432 954 955 15429
15428 958 959 15425 15424 962 963 15421 15420 966 967 15417 15416 970 971
15413 15412 974 975 15409 15408 978 979 15405 15404 982 983 15401 15400 986
987 15397 15396 990 991 15393 15392 994 995 15389 15388 998 999 15385 15384
1002 1003 15381 15380 1006 1007 15377 15376 1010 1011 15373 15372 1014 1015
15369 15368 1018 1019 15365 15364 1022 1023 15361
15360 1026 1027 15357 15356 1030 1031 15353 15352 1034 1035 15349 15348 1038
1039 15345 15344 1042 1043 15341 15340 1046 1047 15337 15336 1050 1051 15333
15332 1054 1055 15329 15328 1058 1059 15325 15324 1062 1063 15321 15320 1066
1067 15317 15316 1070 1071 15313 15312 1074 1075 15309 15308 1078 1079 15305
15304 1082 1083 15301 15300 1086 1087 15297 15296 1090 1091 15293 15292 1094
1095 15289 15288 1098 1099 15285 15284 1102 1103 15281 15280 1106 1107 15277
15276 1110 1111 15273 15272 1114 1115 15269 15268 1118 1119 15265 15264 1122
1123 15261 15260 1126 1127 15257 15256 1130 1131 15253 15252 1134 1135 15249
15248 1138 1139 15245 15244 1142 1143 15241 15240 1146 1147 15237 15236 1150
1151 15233
1153 15231 15230 1156 1157 15227 15226 1160 1161 15223 15222 1164 1165 15219
15218 1168 1169 15215 15214 1172 1173 15211 15210 1176 1177 15207 15206 1180
1181 15203 15202 1184 1185 15199 15198 1188 1189 15195 15194 1192 1193 15191
15190 1196 1197 15187 15186 1200 1201 15183 15182 1204 1205 15179 15178 1208
1209 15175 15174 1212 1213 15171 15170 1216 1217 15167 15166 1220 1221 15163
15162 1224 1225 15159 15158 1228 1229 15155 15154 1232 1233 15151 15150 1236
1237 15147 15146 1240 1241 15143 15142 1244 1245 15139 15138 1248 1249 15135
15134 1252 1253 15131 15130 1256 1257 15127 15126 1260 1261 15123 15122 1264
1265 15119 15118 1268 1269 15115 15114 1272 1273 15111 15110 1276 1277 15107
15106 1280
1281 15103 15102 1284 1285 15099 15098 1288 1289 15095 15094 1292 1293 15091
15090 1296 1297 15087 15086 1300 1301 15083 15082 1304 1305 15079 15078 1308
1309 15075 15074 1312 1313 15071 15070 1316 1317 15067 15066 1320 1321 15063
15062 1324 1325 15059 15058 1328 1329 15055 15054 1332 1333 15051 15050 1336
1337 15047 15046 1340 1341 15043 15042 1344 1345 15039 15038 1348 1349 15035
15034 1352 1353 15031 15030 1356 1357 15027 15026 1360 1361 15023 15022 1364
1365 15019 15018 1368 1369 15015 15014 1372 1373 15011 15010 1376 1377 15007
15006 1380 1381 15003 15002 1384 1385 14999 14998 1388 1389 14995 14994 1392
1393 14991 14990 1396 1397 14987 14986 1400 1401 14983 14982 1404 1405 14979
14978 1408
14976 1410 1411 14973 14972 1414 1415 14969 14968 1418 1419 14965 14964 1422
1423 14961 14960 1426 1427 14957 14956 1430 1431 14953 14952 1434 1435 14949
14948 1438 1439 14945 14944 1442 1443 14941 14940 1446 1447 14937 14936 1450
1451 14933 14932 1454 1455 14929 14928 1458 1459 14925 14924 1462 1463 14921
14920 1466 1467 14917 14916 1470 1471 14913 14912 1474 1475 14909 14908 1478
1479 14905 14904 1482 1483 14901 14900 1486 1487 14897 14896 1490 1491 14893
14892 1494 1495 14889 14888 1498 1499 14885 14884 1502 1503 14881 14880 1506
1507 14877 14876 1510 1511 14873 14872 1514 1515 14869 14868 1518 1519 14865
14864 1522 1523 14861 14860 1526 1527 14857 14856 1530 1531 14853 14852 1534
1535 14849
14848 1538 1539 14845 14844 1542 1543 14841 14840 1546 1547 14837 14836 1550
1551 14833 14832 1554 1555 14829 14828 1558 1559 14825 14824 1562 1563 14821
14820 1566 1567 14817 14816 1570 1571 14813 14812 1574 1575 14809 14808 1578
1579 14805 14804 1582 1583 14801 14800 1586 1587 14797 14796 1590 1591 14793
14792 1594 1595 14789 14788 1598 1599 14785 14784 1602 1603 14781 14780 1606
1607 14777 14776 1610 1611 14773 14772 1614 1615 14769 14768 1618 1619 14765
14764 1622 1623 14761 14760 1626 1627 14757 14756 1630 1631 14753 14752 1634
1635 14749 14748 1638 1639 14745 14744 1642 1643 14741 14740 1646 1647 14737
14736 1650 1651 14733 14732 1654 1655 14729 14728 1658 1659 14725 14724 1662
1663 14721
1665 14719 14718 1668 1669 14715 14714 1672 1673 14711 14710 1676 1677 14707
14706 1680 1681 14703 14702 1684 1685 14699 14698 1688 1689 14695 14694 1692
1693 14691 14690 1696 1697 14687 14686 1700 1701 14683 14682 1704 1705 14679
14678 1708 1709 14675 14674 1712 1713 14671 14670 1716 1717 14667 14666 1720
1721 14663 14662 1724 1725 14659 14658 1728 1729 14655 14654 1732 1733 14651
14650 1736 1737 14647 14646 1740 1741 14643 14642 1744 1745 14639 14638 1748
1749 14635 14634 1752 1753 14631 14630 1756 1757 14627 14626 1760 1761 14623
14622 1764 1765 14619 14618 1768 1769 14615 14614 1772 1773 14611 14610 1776
1777 14607 14606 1780 1781 14603 14602 1784 1785 14599 14598 1788 1789 14595
14594 1792
1793 14591 14590 1796 1797 14587 14586 1800 1801 14583 14582 1804 1805 14579
14578 1808 1809 14575 14574 1812 1813 14571 14570 1816 1817 14567 14566 1820
1821 14563 14562 1824 1825 14559 14558 1828 1829 14555 14554 1832 1833 14551
14550 1836 1837 14547 14546 1840 1841 14543 14542 1844 1845 14539 14538 1848
1849 14535 14534 1852 1853 14531 14530 1856 1857 14527 14526 1860 1861 14523
14522 1864 1865 14519 14518 1868 1869 14515 14514 1872 1873 14511 14510 1876
1877 14507 14506 1880 1881 14503 14502 1884 1885 14499 14498 1888 1889 14495
14494 1892 1893 14491 14490 1896 1897 14487 14486 1900 1901 14483 14482 1904
1905 14479 14478 1908 1909 14475 14474 1912 1913 14471 14470 1916 1917 14467
14466 1920
14464 1922 1923 14461 14460 1926 1927 14457 14456 1930 1931 14453 14452 1934
1935 14449 14448 1938 1939 14445 14444 1942 1943 14441 14440 1946 1947 14437
14436 1950 1951 14433 14432 1954 1955 14429 14428 1958 1959 14425 14424 1962
1963 14421 14420 1966 1967 14417 14416 1970 1971 14413 14412 1974 1975 14409
14408 1978 1979 14405 14404 1982 1983 14401 14400 1986 1987 14397 14396 1990
1991 14393 14392 1994 1995 14389 14388 1998 1999 14385 14384 2002 2003 14381
14380 2006 2007 14377 14376 2010 2011 14373 14372 2014 2015 14369 14368 2018
2019 14365 14364 2022 2023 14361 14360 2026 2027 14357 14356 2030 2031 14353
14352 2034 2035 14349 14348 2038 2039 14345 14344 2042 2043 14341 14340 2046
2047 14337
14336 2050 2051 14333 14332 2054 2055 14329 14328 2058 2059 14325 14324 2062
2063 14321 14320 2066 2067 14317 14316 2070 2071 14313 14312 2074 2075 14309
14308 2078 2079 14305 14304 2082 2083 14301 14300 2086 2087 14297 14296 2090
2091 14293 14292 2094 2095 14289 14288 2098 2099 14285 14284 2102 2103 14281
14280 2106 2107 14277 14276 2110 2111 14273 14272 2114 2115 14269 14268 2118
2119 14265 14264 2122 2123 14261 14260 2126 2127 14257 14256 2130 2131 14253
14252 2134 2135 14249 14248 2138 2139 14245 14244 2142 2143 14241 14240 2146
2147 14237 14236 2150 2151 14233 14232 2154 2155 14229 14228 2158 2159 14225
14224 2162 2163 14221 14220 2166 2167 14217 14216 2170 2171 14213 14212 2174
2175 14209
2177 14207 14206 2180 2181 14203 14202 2184 2185 14199 14198 2188 2189 14195
14194 2192 2193 14191 14190 2196 2197 14187 14186 2200 2201 14183 14182 2204
2205 14179 14178 2208 2209 14175 14174 2212 2213 14171 14170 2216 2217 14167
14166 2220 2221 14163 14162 2224 2225 14159 14158 2228 2229 14155 14154 2232
2233 14151 14150 2236 2237 14147 14146 2240 2241 14143 14142 2244 2245 14139
14138 2248 2249 14135 14134 2252 2253 14131 14130 2256 2257 14127 14126 2260
2261 14123 14122 2264 2265 14119 14118 2268 2269 14115 14114 2272 2273 14111
14110 2276 2277 14107 14106 2280 2281 14103 14102 2284 2285 14099 14098 2288
2289 14095 14094 2292 2293 14091 14090 2296 2297 14087 14086 2300 2301 14083
14082 2304
2305 14079 14078 2308 2309 14075 14074 2312 2313 14071 14070 2316 2317 14067
14066 2320 2321 14063 14062 2324 2325 14059 14058 2328 2329 14055 14054 2332
2333 14051 14050 2336 2337 14047 14046 2340 2341 14043 14042 2344 2345 14039
14038 2348 2349 14035 14034 2352 2353 14031 14030 2356 2357 14027 14026 2360
2361 14023 14022 2364 2365 14019 14018 2368 2369 14015 14014 2372 2373 14011
14010 2376 2377 14007 14006 2380 2381 14003 14002 2384 2385 13999 13998 2388
2389 13995 13994 2392 2393 13991 13990 2396 2397 13987 13986 2400 2401 13983
13982 2404 2405 13979 13978 2408 2409 13975 13974 2412 2413 13971 13970 2416
2417 13967 13966 2420 2421 13963 13962 2424 2425 13959 13958 2428 2429 13955
13954 2432
13952 2434 2435 13949 13948 2438 2439 13945 13944 2442 2443 13941 13940 2446
2447 13937 13936 2450 2451 13933 13932 2454 2455 13929 13928 2458 2459 13925
13924 2462 2463 13921 13920 2466 2467 13917 13916 2470 2471 13913 13912 2474
2475 13909 13908 2478 2479 13905 13904 2482 2483 13901 13900 2486 2487 13897
13896 2490 2491 13893 13892 2494 2495 13889 13888 2498 2499 13885 13884 2502
2503 13881 13880 2506 2507 13877 13876 2510 2511 13873 13872 2514 2515 13869
13868 2518 2519 13865 13864 2522 2523 13861 13860 2526 2527 13857 13856 2530
2531 13853 13852 2534 2535 13849 13848 2538 2539 13845 13844 2542 2543 13841
13840 2546 2547 13837 13836 2550 2551 13833 13832 2554 2555 13829 13828 2558
2559 13825
13824 2562 2563 13821 13820 2566 2567 13817 13816 2570 2571 13813 13812 2574
2575 13809 13808 2578 2579 13805 13804 2582 2583 13801 13800 2586 2587 13797
13796 2590 2591 13793 13792 2594 2595 13789 13788 2598 2599 13785 13784 2602
2603 13781 13780 2606 2607 13777 13776 2610 2611 13773 13772 2614 2615 13769
13768 2618 2619 13765 13764 2622 2623 13761 13760 2626 2627 13757 13756 2630
2631 13753 13752 2634 2635 13749 13748 2638 2639 13745 13744 2642 2643 13741
13740 2646 2647 13737 13736 2650 2651 13733 13732 2654 2655 13729 13728 2658
2659 13725 13724 2662 2663 13721 13720 2666 2667 13717 13716 2670 2671 13713
13712 2674 2675 13709 13708 2678 2679 13705 13704 2682 2683 13701 13700 2686
2687 13697
2689 13695 13694 2692 2693 13691 13690 2696 2697 13687 13686 2700 2701 13683
13682 2704 2705 13679 13678 2708 2709 13675 13674 2712 2713 13671 13670 2716
2717 13667 13666 2720 2721 13663 13662 2724 2725 13659 13658 2728 2729 13655
13654 2732 2733 13651 13650 2736 2737 13647 13646 2740 2741 13643 13642 2744
2745 13639 13638 2748 2749 13635 13634 2752 2753 13631 13630 2756 2757 13627
13626 2760 2761 13623 13622 2764 2765 13619 13618 2768 2769 13615 13614 2772
2773 13611 13610 2776 2777 13607 13606 2780 2781 13603 13602 2784 2785 13599
13598 2788 2789 13595 13594 2792 2793 13591 13590 2796 2797 13587 13586 2800
2801 13583 13582 2804 2805 13579 13578 2808 2809 13575 13574 2812 2813 13571
13570 2816
2817 13567 13566 2820 2821 13563 13562 2824 2825 13559 13558 2828 2829 13555
13554 2832 2833 13551 13550 2836 2837 13547 13546 2840 2841 13543 13542 2844
2845 13539 13538 2848 2849 13535 13534 2852 2853 13531 13530 2856 2857 13527
13526 2860 2861 13523 13522 2864 2865 13519 13518 2868 2869 13515 13514 2872
2873 13511 13510 2876 2877 13507 13506 2880 2881 13503 13502 2884 2885 13499
13498 2888 2889 13495 13494 2892 2893 13491 13490 2896 2897 13487 13486 2900
2901 13483 13482 2904 2905 13479 13478 2908 2909 13475 13474 2912 2913 13471
13470 2916 2917 13467 13466 2920 2921 13463 13462 2924 2925 13459 13458 2928
2929 13455 13454 2932 2933 13451 13450 2936 2937 13447 13446 2940 2941 13443
13442 2944
13440 2946 2947 13437 13436 2950 2951 13433 13432 2954 2955 13429 13428 2958
2959 13425 13424 2962 2963 13421 13420 2966 2967 13417 13416 2970 2971 13413
13412 2974 2975 13409 13408 2978 2979 13405 13404 2982 2983 13401 13400 2986
2987 13397 13396 2990 2991 13393 13392 2994 2995 13389 13388 2998 2999 13385
13384 3002 3003 13381 13380 3006 3007 13377 13376 3010 3011 13373 13372 3014
3015 13369 13368 3018 3019 13365 13364 3022 3023 13361 13360 3026 3027 13357
13356 3030 3031 13353 13352 3034 3035 13349 13348 3038 3039 13345 13344 3042
3043 13341 13340 3046 3047 13337 13336 3050 3051 13333 13332 3054 3055 13329
13328 3058 3059 13325 13324 3062 3063 13321 13320 3066 3067 13317 13316 3070
3071 13313
13312 3074 3075 13309 13308 3078 3079 13305 13304 3082 3083 13301 13300 3086
3087 13297 13296 3090 3091 13293 13292 3094 3095 13289 13288 3098 3099 13285
13284 3102 3103 13281 13280 3106 3107 13277 13276 3110 3111 13273 13272 3114
3115 13269 13268 3118 3119 13265 13264 3122 3123 13261 13260 3126 3127 13257
13256 3130 3131 13253 13252 3134 3135 13249 13248 3138 3139 13245 13244 3142
3143 13241 13240 3146 3147 13237 13236 3150 3151 13233 13232 3154 3155 13229
13228 3158 3159 13225 13224 3162 3163 13221 13220 3166 3167 13217 13216 3170
3171 13213 13212 3174 3175 13209 13208 3178 3179 13205 13204 3182 3183 13201
13200 3186 3187 13197 13196 3190 3191 13193 13192 3194 3195 13189 13188 3198
3199 13185
3201 13183 13182 3204 3205 13179 13178 3208 3209 13175 13174 3212 3213 13171
13170 3216 3217 13167 13166 3220 3221 13163 13162 3224 3225 13159 13158 3228
3229 13155 13154 3232 3233 13151 13150 3236 3237 13147 13146 3240 3241 13143
13142 3244 3245 13139 13138 3248 3249 13135 13134 3252 3253 13131 13130 3256
3257 13127 13126 3260 3261 13123 13122 3264 3265 13119 13118 3268 3269 13115
13114 3272 3273 13111 13110 3276 3277 13107 13106 3280 3281 13103 13102 3284
3285 13099 13098 3288 3289 13095 13094 3292 3293 13091 13090 3296 3297 13087
13086 3300 3301 13083 13082 3304 3305 13079 13078 3308 3309 13075 13074 3312
3313 13071 13070 3316 3317 13067 13066 3320 3321 13063 13062 3324 3325 13059
13058 3328
3329 13055 13054 3332 3333 13051 13050 3336 3337 13047 13046 3340 3341 13043
13042 3344 3345 13039 13038 3348 3349 13035 13034 3352 3353 13031 13030 3356
3357 13027 13026 3360 3361 13023 13022 3364 3365 13019 13018 3368 3369 13015
13014 3372 3373 13011 13010 3376 3377 13007 13006 3380 3381 13003 13002 3384
3385 12999 12998 3388 3389 12995 12994 3392 3393 12991 12990 3396 3397 12987
12986 3400 3401 12983 12982 3404 3405 12979 12978 3408 3409 12975 12974 3412
3413 12971 12970 3416 3417 12967 12966 3420 3421 12963 12962 3424 3425 12959
12958 3428 3429 12955 12954 3432 3433 12951 12950 3436 3437 12947 12946 3440
3441 12943 12942 3444 3445 12939 12938 3448 3449 12935 12934 3452 3453 12931
12930 3456
12928 3458 3459 12925 12924 3462 3463 12921 12920 3466 3467 12917 12916 3470
3471 12913 12912 3474 3475 12909 12908 3478 3479 12905 12904 3482 3483 12901
12900 3486 3487 12897 12896 3490 3491 12893 12892 3494 3495 12889 12888 3498
3499 12885 12884 3502 3503 12881 12880 3506 3507 12877 12876 3510 3511 12873
12872 3514 3515 12869 12868 3518 3519 12865 12864 3522 3523 12861 12860 3526
3527 12857 12856 3530 3531 12853 12852 3534 3535 12849 12848 3538 3539 12845
12844 3542 3543 12841 12840 3546 3547 12837 12836 3550 3551 12833 12832 3554
3555 12829 12828 3558 3559 12825 12824 3562 3563 12821 12820 3566 3567 12817
12816 3570 3571 12813 12812 3574 3575 12809 12808 3578 3579 12805 12804 3582
3583 12801
12800 3586 3587 12797 12796 3590 3591 12793 12792 3594 3595 12789 12788 3598
3599 12785 12784 3602 3603 12781 12780 3606 3607 12777 12776 3610 3611 12773
12772 3614 3615 12769 12768 3618 3619 12765 12764 3622 3623 12761 12760 3626
3627 12757 12756 3630 3631 12753 12752 3634 3635 12749 12748 3638 3639 12745
12744 3642 3643 12741 12740 3646 3647 12737 12736 3650 3651 12733 12732 3654
3655 12729 12728 3658 3659 12725 12724 3662 3663 12721 12720 3666 3667 12717
12716 3670 3671 12713 12712 3674 3675 12709 12708 3678 3679 12705 12704 3682
3683 12701 12700 3686 3687 12697 12696 3690 3691 12693 12692 3694 3695 12689
12688 3698 3699 12685 12684 3702 3703 12681 12680 3706 3707 12677 12676 3710
3711 12673
3713 12671 12670 3716 3717 12667 12666 3720 3721 12663 12662 3724 3725 12659
12658 3728 3729 12655 12654 3732 3733 12651 12650 3736 3737 12647 12646 3740
3741 12643 12642 3744 3745 12639 12638 3748 3749 12635 12634 3752 3753 12631
12630 3756 3757 12627 12626 3760 3761 12623 12622 3764 3765 12619 12618 3768
3769 12615 12614 3772 3773 12611 12610 3776 3777 12607 12606 3780 3781 12603
12602 3784 3785 12599 12598 3788 3789 12595 12594 3792 3793 12591 12590 3796
3797 12587 12586 3800 3801 12583 12582 3804 3805 12579 12578 3808 3809 12575
12574 3812 3813 12571 12570 3816 3817 12567 12566 3820 3821 12563 12562 3824
3825 12559 12558 3828 3829 12555 12554 3832 3833 12551 12550 3836 3837 12547
12546 3840
3841 12543 12542 3844 3845 12539 12538 3848 3849 12535 12534 3852 3853 12531
12530 3856 3857 12527 12526 3860 3861 12523 12522 3864 3865 12519 12518 3868
3869 12515 12514 3872 3873 12511 12510 3876 3877 12507 12506 3880 3881 12503
12502 3884 3885 12499 12498 3888 3889 12495 12494 3892 3893 12491 12490 3896
3897 12487 12486 3900 3901 12483 12482 3904 3905 12479 12478 3908 3909 12475
12474 3912 3913 12471 12470 3916 3917 12467 12466 3920 3921 12463 12462 3924
3925 12459 12458 3928 3929 12455 12454 3932 3933 12451 12450 3936 3937 12447
12446 3940 3941 12443 12442 3944 3945 12439 12438 3948 3949 12435 12434 3952
3953 12431 12430 3956 3957 12427 12426 3960 3961 12423 12422 3964 3965 12419
12418 3968
12416 3970 3971 12413 12412 3974 3975 12409 12408 3978 3979 12405 12404 3982
3983 12401 12400 3986 3987 12397 12396 3990 3991 12393 12392 3994 3995 12389
12388 3998 3999 12385 12384 4002 4003 12381 12380 4006 4007 12377 12376 4010
4011 12373 12372 4014 4015 12369 12368 4018 4019 12365 12364 4022 4023 12361
12360 4026 4027 12357 12356 4030 4031 12353 12352 4034 4035 12349 12348 4038
4039 12345 12344 4042 4043 12341 12340 4046 4047 12337 12336 4050 4051 12333
12332 4054 4055 12329 12328 4058 4059 12325 12324 4062 4063 12321 12320 4066
4067 12317 12316 4070 4071 12313 12312 4074 4075 12309 12308 4078 4079 12305
12304 4082 4083 12301 12300 4086 4087 12297 12296 4090 4091 12293 12292 4094
4095 12289
12288 4098 4099 12285 12284 4102 4103 12281 12280 4106 4107 12277 12276 4110
4111 12273 12272 4114 4115 12269 12268 4118 4119 12265 12264 4122 4123 12261
12260 4126 4127 12257 12256 4130 4131 12253 12252 4134 4135 12249 12248 4138
4139 12245 12244 4142 4143 12241 12240 4146 4147 12237 12236 4150 4151 12233
12232 4154 4155 12229 12228 4158 4159 12225 12224 4162 4163 12221 12220 4166
4167 12217 12216 4170 4171 12213 12212 4174 4175 12209 12208 4178 4179 12205
12204 4182 4183 12201 12200 4186 4187 12197 12196 4190 4191 12193 12192 4194
4195 12189 12188 4198 4199 12185 12184 4202 4203 12181 12180 4206 4207 12177
12176 4210 4211 12173 12172 4214 4215 12169 12168 4218 4219 12165 12164 4222
4223 12161
4225 12159 12158 4228 4229 12155 12154 4232 4233 12151 12150 4236 4237 12147
12146 4240 4241 12143 12142 4244 4245 12139 12138 4248 4249 12135 12134 4252
4253 12131 12130 4256 4257 12127 12126 4260 4261 12123 12122 4264 4265 12119
12118 4268 4269 12115 12114 4272 4273 12111 12110 4276 4277 12107 12106 4280
4281 12103 12102 4284 4285 12099 12098 4288 4289 12095 12094 4292 4293 12091
12090 4296 4297 12087 12086 4300 4301 12083 12082 4304 4305 12079 12078 4308
4309 12075 12074 4312 4313 12071 12070 4316 4317 12067 12066 4320 4321 12063
12062 4324 4325 12059 12058 4328 4329 12055 12054 4332 4333 12051 12050 4336
4337 12047 12046 4340 4341 12043 12042 4344 4345 12039 12038 4348 4349 12035
12034 4352
4353 12031 12030 4356 4357 12027 12026 4360 4361 12023 12022 4364 4365 12019
12018 4368 4369 12015 12014 4372 4373 12011 12010 4376 4377 12007 12006 4380
4381 12003 12002 4384 4385 11999 11998 4388 4389 11995 11994 4392 4393 11991
11990 4396 4397 11987 11986 4400 4401 11983 11982 4404 4405 11979 11978 4408
4409 11975 11974 4412 4413 11971 11970 4416 4417 11967 11966 4420 4421 11963
11962 4424 4425 11959 11958 4428 4429 11955 11954 4432 4433 11951 11950 4436
4437 11947 11946 4440 4441 11943 11942 4444 4445 11939 11938 4448 4449 11935
11934 4452 4453 11931 11930 4456 4457 11927 11926 4460 4461 11923 11922 4464
4465 11919 11918 4468 4469 11915 11914 4472 4473 11911 11910 4476 4477 11907
11906 4480
11904 4482 4483 11901 11900 4486 4487 11897 11896 4490 4491 11893 11892 4494
4495 11889 11888 4498 4499 11885 11884 4502 4503 11881 11880 4506 4507 11877
11876 4510 4511 11873 11872 4514 4515 11869 11868 4518 4519 11865 11864 4522
4523 11861 11860 4526 4527 11857 11856 4530 4531 11853 11852 4534 4535 11849
11848 4538 4539 11845 11844 4542 4543 11841 11840 4546 4547 11837 11836 4550
4551 11833 11832 4554 4555 11829 11828 4558 4559 11825 11824 4562 4563 11821
11820 4566 4567 11817 11816 4570 4571 11813 11812 4574 4575 11809 11808 4578
4579 11805 11804 4582 4583 11801 11800 4586 4587 11797 11796 4590 4591 11793
11792 4594 4595 11789 11788 4598 4599 11785 11784 4602 4603 11781 11780 4606
4607 11777
11776 4610 4611 11773 11772 4614 4615 11769 11768 4618 4619 11765 11764 4622
4623 11761 11760 4626 4627 11757 11756 4630 4631 11753 11752 4634 4635 11749
11748 4638 4639 11745 11744 4642 4643 11741 11740 4646 4647 11737 11736 4650
4651 11733 11732 4654 4655 11729 11728 4658 4659 11725 11724 4662 4663 11721
11720 4666 4667 11717 11716 4670 4671 11713 11712 4674 4675 11709 11708 4678
4679 11705 11704 4682 4683 11701 11700 4686 4687 11697 11696 4690 4691 11693
11692 4694 4695 11689 11688 4698 4699 11685 11684 4702 4703 11681 11680 4706
4707 11677 11676 4710 4711 11673 11672 4714 4715 11669 11668 4718 4719 11665
11664 4722 4723 11661 11660 4726 4727 11657 11656 4730 4731 11653 11652 4734
4735 11649
4737 11647 11646 4740 4741 11643 11642 4744 4745 11639 11638 4748 4749 11635
11634 4752 4753 11631 11630 4756 4757 11627 11626 4760 4761 11623 11622 4764
4765 11619 11618 4768 4769 11615 11614 4772 4773 11611 11610 4776 4777 11607
11606 4780 4781 11603 11602 4784 4785 11599 11598 4788 4789 11595 11594 4792
4793 11591 11590 4796 4797 11587 11586 4800 4801 11583 11582 4804 4805 11579
11578 4808 4809 11575 11574 4812 4813 11571 11570 4816 4817 11567 11566 4820
4821 11563 11562 4824 4825 11559 11558 4828 4829 11555 11554 4832 4833 11551
11550 4836 4837 11547 11546 4840 4841 11543 11542 4844 4845 11539 11538 4848
4849 11535 11534 4852 4853 11531 11530 4856 4857 11527 11526 4860 4861 11523
11522 4864
4865 11519 11518 4868 4869 11515 11514 4872 4873 11511 11510 4876 4877 11507
11506 4880 4881 11503 11502 4884 4885 11499 11498 4888 4889 11495 11494 4892
4893 11491 11490 4896 4897 11487 11486 4900 4901 11483 11482 4904 4905 11479
11478 4908 4909 11475 11474 4912 4913 11471 11470 4916 4917 11467 11466 4920
4921 11463 11462 4924 4925 11459 11458 4928 4929 11455 11454 4932 4933 11451
11450 4936 4937 11447 11446 4940 4941 11443 11442 4944 4945 11439 11438 4948
4949 11435 11434 4952 4953 11431 11430 4956 4957 11427 11426 4960 4961 11423
11422 4964 4965 11419 11418 4968 4969 11415 11414 4972 4973 11411 11410 4976
4977 11407 11406 4980 4981 11403 11402 4984 4985 11399 11398 4988 4989 11395
11394 4992
11392 4994 4995 11389 11388 4998 4999 11385 11384 5002 5003 11381 11380 5006
5007 11377 11376 5010 5011 11373 11372 5014 5015 11369 11368 5018 5019 11365
11364 5022 5023 11361 11360 5026 5027 11357 11356 5030 5031 11353 11352 5034
5035 11349 11348 5038 5039 11345 11344 5042 5043 11341 11340 5046 5047 11337
11336 5050 5051 11333 11332 5054 5055 11329 11328 5058 5059 11325 11324 5062
5063 11321 11320 5066 5067 11317 11316 5070 5071 11313 11312 5074 5075 11309
11308 5078 5079 11305 11304 5082 5083 11301 11300 5086 5087 11297 11296 5090
5091 11293 11292 5094 5095 11289 11288 5098 5099 11285 11284 5102 5103 11281
11280 5106 5107 11277 11276 5110 5111 11273 11272 5114 5115 11269 11268 5118
5119 11265
11264 5122 5123 11261 11260 5126 5127 11257 11256 5130 5131 11253 11252 5134
5135 11249 11248 5138 5139 11245 11244 5142 5143 11241 11240 5146 5147 11237
11236 5150 5151 11233 11232 5154 5155 11229 11228 5158 5159 11225 11224 5162
5163 11221 11220 5166 5167 11217 11216 5170 5171 11213 11212 5174 5175 11209
11208 5178 5179 11205 11204 5182 5183 11201 11200 5186 5187 11197 11196 5190
5191 11193 11192 5194 5195 11189 11188 5198 5199 11185 11184 5202 5203 11181
11180 5206 5207 11177 11176 5210 5211 11173 11172 5214 5215 11169 11168 5218
5219 11165 11164 5222 5223 11161 11160 5226 5227 11157 11156 5230 5231 11153
11152 5234 5235 11149 11148 5238 5239 11145 11144 5242 5243 11141 11140 5246
5247 11137
5249 11135 11134 5252 5253 11131 11130 5256 5257 11127 11126 5260 5261 11123
11122 5264 5265 11119 11118 5268 5269 11115 11114 5272 5273 11111 11110 5276
5277 11107 11106 5280 5281 11103 11102 5284 5285 11099 11098 5288 5289 11095
11094 5292 5293 11091 11090 5296 5297 11087 11086 5300 5301 11083 11082 5304
5305 11079 11078 5308 5309 11075 11074 5312 5313 11071 11070 5316 5317 11067
11066 5320 5321 11063 11062 5324 5325 11059 11058 5328 5329 11055 11054 5332
5333 11051 11050 5336 5337 11047 11046 5340 5341 11043 11042 5344 5345 11039
11038 5348 5349 11035 11034 5352 5353 11031 11030 5356 5357 11027 11026 5360
5361 11023 11022 5364 5365 11019 11018 5368 5369 11015 11014 5372 5373 11011
11010 5376
5377 11007 11006 5380 5381 11003 11002 5384 5385 10999 10998 5388 5389 10995
10994 5392 5393 10991 10990 5396 5397 10987 10986 5400 5401 10983 10982 5404
5405 10979 10978 5408 5409 10975 10974 5412 5413 10971 10970 5416 5417 10967
10966 5420 5421 10963 10962 5424 5425 10959 10958 5428 5429 10955 10954 5432
5433 10951 10950 5436 5437 10947 10946 5440 5441 10943 10942 5444 5445 10939
10938 5448 5449 10935 10934 5452 5453 10931 10930 5456 5457 10927 10926 5460
5461 10923 10922 5464 5465 10919 10918 5468 5469 10915 10914 5472 5473 10911
10910 5476 5477 10907 10906 5480 5481 10903 10902 5484 5485 10899 10898 5488
5489 10895 10894 5492 5493 10891 10890 5496 5497 10887 10886 5500 5501 10883
10882 5504
10880 5506 5507 10877 10876 5510 5511 10873 10872 5514 5515 10869 10868 5518
5519 10865 10864 5522 5523 10861 10860 5526 5527 10857 10856 5530 5531 10853
10852 5534 5535 10849 10848 5538 5539 10845 10844 5542 5543 10841 10840 5546
5547 10837 10836 5550 5551 10833 10832 5554 5555 10829 10828 5558 5559 10825
10824 5562 5563 10821 10820 5566 5567 10817 10816 5570 5571 10813 10812 5574
5575 10809 10808 5578 5579 10805 10804 5582 5583 10801 10800 5586 5587 10797
10796 5590 5591 10793 10792 5594 5595 10789 10788 5598 5599 10785 10784 5602
5603 10781 10780 5606 5607 10777 10776 5610 5611 10773 10772 5614 5615 10769
10768 5618 5619 10765 10764 5622 5623 10761 10760 5626 5627 10757 10756 5630
5631 10753
10752 5634 5635 10749 10748 5638 5639 10745 10744 5642 5643 10741 10740 5646
5647 10737 10736 5650 5651 10733 10732 5654 5655 10729 10728 5658 5659 10725
10724 5662 5663 10721 10720 5666 5667 10717 10716 5670 5671 10713 10712 5674
5675 10709 10708 5678 5679 10705 10704 5682 5683 10701 10700 5686 5687 10697
10696 5690 5691 10693 10692 5694 5695 10689 10688 5698 5699 10685 10684 5702
5703 10681 10680 5706 5707 10677 10676 5710 5711 10673 10672 5714 5715 10669
10668 5718 5719 10665 10664 5722 5723 10661 10660 5726 5727 10657 10656 5730
5731 10653 10652 5734 5735 10649 10648 5738 5739 10645 10644 5742 5743 10641
10640 5746 5747 10637 10636 5750 5751 10633 10632 5754 5755 10629 10628 5758
5759 10625
5761 10623 10622 5764 5765 10619 10618 5768 5769 10615 10614 5772 5773 10611
10610 5776 5777 10607 10606 5780 5781 10603 10602 5784 5785 10599 10598 5788
5789 10595 10594 5792 5793 10591 10590 5796 5797 10587 10586 5800 5801 10583
10582 5804 5805 10579 10578 5808 5809 10575 10574 5812 5813 10571 10570 5816
5817 10567 10566 5820 5821 10563 10562 5824 5825 10559 10558 5828 5829 10555
10554 5832 5833 10551 10550 5836 5837 10547 10546 5840 5841 10543 10542 5844
5845 10539 10538 5848 5849 10535 10534 5852 5853 10531 10530 5856 5857 10527
10526 5860 5861 10523 10522 5864 5865 10519 10518 5868 5869 10515 10514 5872
5873 10511 10510 5876 5877 10507 10506 5880 5881 10503 10502 5884 5885 10499
10498 5888
5889 10495 10494 5892 5893 10491 10490 5896 5897 10487 10486 5900 5901 10483
10482 5904 5905 10479 10478 5908 5909 10475 10474 5912 5913 10471 10470 5916
5917 10467 10466 5920 5921 10463 10462 5924 5925 10459 10458 5928 5929 10455
10454 5932 5933 10451 10450 5936 5937 10447 10446 5940 5941 10443 10442 5944
5945 10439 10438 5948 5949 10435 10434 5952 5953 10431 10430 5956 5957 10427
10426 5960 5961 10423 10422 5964 5965 10419 10418 5968 5969 10415 10414 5972
5973 10411 10410 5976 5977 10407 10406 5980 5981 10403 10402 5984 5985 10399
10398 5988 5989 10395 10394 5992 5993 10391 10390 5996 5997 10387 10386 6000
6001 10383 10382 6004 6005 10379 10378 6008 6009 10375 10374 6012 6013 10371
10370 6016
10368 6018 6019 10365 10364 6022 6023 10361 10360 6026 6027 10357 10356 6030
6031 10353 10352 6034 6035 10349 10348 6038 6039 10345 10344 6042 6043 10341
10340 6046 6047 10337 10336 6050 6051 10333 10332 6054 6055 10329 10328 6058
6059 10325 10324 6062 6063 10321 10320 6066 6067 10317 10316 6070 6071 10313
10312 6074 6075 10309 10308 6078 6079 10305 10304 6082 6083 10301 10300 6086
6087 10297 10296 6090 6091 10293 10292 6094 6095 10289 10288 6098 6099 10285
10284 6102 6103 10281 10280 6106 6107 10277 10276 6110 6111 10273 10272 6114
6115 10269 10268 6118 6119 10265 10264 6122 6123 10261 10260 6126 6127 10257
10256 6130 6131 10253 10252 6134 6135 10249 10248 6138 6139 10245 10244 6142
6143 10241
10240 6146 6147 10237 10236 6150 6151 10233 10232 6154 6155 10229 10228 6158
6159 10225 10224 6162 6163 10221 10220 6166 6167 10217 10216 6170 6171 10213
10212 6174 6175 10209 10208 6178 6179 10205 10204 6182 6183 10201 10200 6186
6187 10197 10196 6190 6191 10193 10192 6194 6195 10189 10188 6198 6199 10185
10184 6202 6203 10181 10180 6206 6207 10177 10176 6210 6211 10173 10172 6214
6215 10169 10168 6218 6219 10165 10164 6222 6223 10161 10160 6226 6227 10157
10156 6230 6231 10153 10152 6234 6235 10149 10148 6238 6239 10145 10144 6242
6243 10141 10140 6246 6247 10137 10136 6250 6251 10133 10132 6254 6255 10129
10128 6258 6259 10125 10124 6262 6263 10121 10120 6266 6267 10117 10116 6270
6271 10113
6273 10111 10110 6276 6277 10107 10106 6280 6281 10103 10102 6284 6285 10099
10098 6288 6289 10095 10094 6292 6293 10091 10090 6296 6297 10087 10086 6300
6301 10083 10082 6304 6305 10079 10078 6308 6309 10075 10074 6312 6313 10071
10070 6316 6317 10067 10066 6320 6321 10063 10062 6324 6325 10059 10058 6328
6329 10055 10054 6332 6333 10051 10050 6336 6337 10047 10046 6340 6341 10043
10042 6344 6345 10039 10038 6348 6349 10035 10034 6352 6353 10031 10030 6356
6357 10027 10026 6360 6361 10023 10022 6364 6365 10019 10018 6368 6369 10015
10014 6372 6373 10011 10010 6376 6377 10007 10006 6380 6381 10003 10002 6384
6385 9999 9998 6388 6389 9995 9994 6392 6393 9991 9990 6396 6397 9987 9986
6400
6401 9983 9982 6404 6405 9979 9978 6408 6409 9975 9974 6412 6413 9971 9970
6416 6417 9967 9966 6420 6421 9963 9962 6424 6425 9959 9958 6428 6429 9955
9954 6432 6433 9951 9950 6436 6437 9947 9946 6440 6441 9943 9942 6444 6445
9939 9938 6448 6449 9935 9934 6452 6453 9931 9930 6456 6457 9927 9926 6460
6461 9923 9922 6464 6465 9919 9918 6468 6469 9915 9914 6472 6473 9911 9910
6476 6477 9907 9906 6480 6481 9903 9902 6484 6485 9899 9898 6488 6489 9895
9894 6492 6493 9891 9890 6496 6497 9887 9886 6500 6501 9883 9882 6504 6505
9879 9878 6508 6509 9875 9874 6512 6513 9871 9870 6516 6517 9867 9866 6520
6521 9863 9862 6524 6525 9859 9858 6528
9856 6530 6531 9853 9852 6534 6535 9849 9848 6538 6539 9845 9844 6542 6543
9841 9840 6546 6547 9837 9836 6550 6551 9833 9832 6554 6555 9829 9828 6558
6559 9825 9824 6562 6563 9821 9820 6566 6567 9817 9816 6570 6571 9813 9812
6574 6575 9809 9808 6578 6579 9805 9804 6582 6583 9801 9800 6586 6587 9797
9796 6590 6591 9793 9792 6594 6595 9789 9788 6598 6599 9785 9784 6602 6603
9781 9780 6606 6607 9777 9776 6610 6611 9773 9772 6614 6615 9769 9768 6618
6619 9765 9764 6622 6623 9761 9760 6626 6627 9757 9756 6630 6631 9753 9752
6634 6635 9749 9748 6638 6639 9745 9744 6642 6643 9741 9740 6646 6647 9737
9736 6650 6651 9733 9732 6654 6655 9729
9728 6658 6659 9725 9724 6662 6663 9721 9720 6666 6667 9717 9716 6670 6671
9713 9712 6674 6675 9709 9708 6678 6679 9705 9704 6682 6683 9701 9700 6686
6687 9697 9696 6690 6691 9693 9692 6694 6695 9689 9688 6698 6699 9685 9684
6702 6703 9681 9680 6706 6707 9677 9676 6710 6711 9673 9672 6714 6715 9669
9668 6718 6719 9665 9664 6722 6723 9661 9660 6726 6727 9657 9656 6730 6731
9653 9652 6734 6735 9649 9648 6738 6739 9645 9644 6742 6743 9641 9640 6746
6747 9637 9636 6750 6751 9633 9632 6754 6755 9629 9628 6758 6759 9625 9624
6762 6763 9621 9620 6766 6767 9617 9616 6770 6771 9613 9612 6774 6775 9609
9608 6778 6779 9605 9604 6782 6783 9601
6785 9599 9598 6788 6789 9595 9594 6792 6793 9591 9590 6796 6797 9587 9586
6800 6801 9583 9582 6804 6805 9579 9578 6808 6809 9575 9574 6812 6813 9571
9570 6816 6817 9567 9566 6820 6821 9563 9562 6824 6825 9559 9558 6828 6829
9555 9554 6832 6833 9551 9550 6836 6837 9547 9546 6840 6841 9543 9542 6844
6845 9539 9538 6848 6849 9535 9534 6852 6853 9531 9530 6856 6857 9527 9526
6860 6861 9523 9522 6864 6865 9519 9518 6868 6869 9515 9514 6872 6873 9511
9510 6876 6877 9507 9506 6880 6881 9503 9502 6884 6885 9499 9498 6888 6889
9495 9494 6892 6893 9491 9490 6896 6897 9487 9486 6900 6901 9483 9482 6904
6905 9479 9478 6908 6909 9475 9474 6912
6913 9471 9470 6916 6917 9467 9466 6920 6921 9463 9462 6924 6925 9459 9458
6928 6929 9455 9454 6932 6933 9451 9450 6936 6937 9447 9446 6940 6941 9443
9442 6944 6945 9439 9438 6948 6949 9435 9434 6952 6953 9431 9430 6956 6957
9427 9426 6960 6961 9423 9422 6964 6965 9419 9418 6968 6969 9415 9414 6972
6973 9411 9410 6976 6977 9407 9406 6980 6981 9403 9402 6984 6985 9399 9398
6988 6989 9395 9394 6992 6993 9391 9390 6996 6997 9387 9386 7000 7001 9383
9382 7004 7005 9379 9378 7008 7009 9375 9374 7012 7013 9371 9370 7016 7017
9367 9366 7020 7021 9363 9362 7024 7025 9359 9358 7028 7029 9355 9354 7032
7033 9351 9350 7036 7037 9347 9346 7040
9344 7042 7043 9341 9340 7046 7047 9337 9336 7050 7051 9333 9332 7054 7055
9329 9328 7058 7059 9325 9324 7062 7063 9321 9320 7066 7067 9317 9316 7070
7071 9313 9312 7074 7075 9309 9308 7078 7079 9305 9304 7082 7083 9301 9300
7086 7087 9297 9296 7090 7091 9293 9292 7094 7095 9289 9288 7098 7099 9285
9284 7102 7103 9281 9280 7106 7107 9277 9276 7110 7111 9273 9272 7114 7115
9269 9268 7118 7119 9265 9264 7122 7123 9261 9260 7126 7127 9257 9256 7130
7131 9253 9252 7134 7135 9249 9248 7138 7139 9245 9244 7142 7143 9241 9240
7146 7147 9237 9236 7150 7151 9233 9232 7154 7155 9229 9228 7158 7159 9225
9224 7162 7163 9221 9220 7166 7167 9217
9216 7170 7171 9213 9212 7174 7175 9209 9208 7178 7179 9205 9204 7182 7183
9201 9200 7186 7187 9197 9196 7190 7191 9193 9192 7194 7195 9189 9188 7198
7199 9185 9184 7202 7203 9181 9180 7206 7207 9177 9176 7210 7211 9173 9172
7214 7215 9169 9168 7218 7219 9165 9164 7222 7223 9161 9160 7226 7227 9157
9156 7230 7231 9153 9152 7234 7235 9149 9148 7238 7239 9145 9144 7242 7243
9141 9140 7246 7247 9137 9136 7250 7251 9133 9132 7254 7255 9129 9128 7258
7259 9125 9124 7262 7263 9121 9120 7266 7267 9117 9116 7270 7271 9113 9112
7274 7275 9109 9108 7278 7279 9105 9104 7282 7283 9101 9100 7286 7287 9097
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8848 8849 7535 7534 8852 8853 7531 7530 8856 8857 7527 7526 8860 8861 7523
7522 8864 8865 7519 7518 8868 8869 7515 7514 8872 8873 7511 7510 8876 8877
7507 7506 8880 8881 7503 7502 8884 8885 7499 7498 8888 8889 7495 7494 8892
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8961 7423 7422 8964 8965 7419 7418 8968 8969 7415 7414 8972 8973 7411 7410
8976 8977 7407 7406 8980 8981 7403 7402 8984 8985 7399 7398 8988 8989 7395
7394 8992 8993 7391 7390 8996 8997 7387 7386 9000 9001 7383 7382 9004 9005
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9021 7363 7362 9024 9025 7359 7358 9028 9029 7355 7354 9032 9033 7351 7350
9036 9037 7347 7346 9040 9041 7343 7342 9044 9045 7339 7338 9048 9049 7335
7334 9052 9053 7331 7330 9056 9057 7327 7326 9060 9061 7323 7322 9064 9065
7319 7318 9068 9069 7315 7314 9072 9073 7311 7310 9076 9077 7307 7306 9080
9081 7303 7302 9084 9085 7299 7298 9088
7296 9090 9091 7293 7292 9094 9095 7289 7288 9098 9099 7285 7284 9102 9103
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9119 7265 7264 9122 9123 7261 7260 9126 9127 7257 7256 9130 9131 7253 7252
9134 9135 7249 7248 9138 9139 7245 7244 9142 9143 7241 7240 9146 9147 7237
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7168 9218 9219 7165 7164 9222 9223 7161 7160 9226 9227 7157 7156 9230 9231
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9322 9323 7061 7060 9326 9327 7057 7056 9330 9331 7053 7052 9334 9335 7049
7048 9338 9339 7045 7044 9342 9343 7041
9345 7039 7038 9348 9349 7035 7034 9352 9353 7031 7030 9356 9357 7027 7026
9360 9361 7023 7022 9364 9365 7019 7018 9368 9369 7015 7014 9372 9373 7011
7010 9376 9377 7007 7006 9380 9381 7003 7002 9384 9385 6999 6998 9388 9389
6995 6994 9392 9393 6991 6990 9396 9397 6987 6986 9400 9401 6983 6982 9404
9405 6979 6978 9408 9409 6975 6974 9412 9413 6971 6970 9416 9417 6967 6966
9420 9421 6963 6962 9424 9425 6959 6958 9428 9429 6955 6954 9432 9433 6951
6950 9436 9437 6947 6946 9440 9441 6943 6942 9444 9445 6939 6938 9448 9449
6935 6934 9452 9453 6931 6930 9456 9457 6927 6926 9460 9461 6923 6922 9464
9465 6919 6918 9468 9469 6915 6914 9472
9473 6911 6910 9476 9477 6907 6906 9480 9481 6903 6902 9484 9485 6899 6898
9488 9489 6895 6894 9492 9493 6891 6890 9496 9497 6887 6886 9500 9501 6883
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6867 6866 9520 9521 6863 6862 9524 9525 6859 6858 9528 9529 6855 6854 9532
9533 6851 6850 9536 9537 6847 6846 9540 9541 6843 6842 9544 9545 6839 6838
9548 9549 6835 6834 9552 9553 6831 6830 9556 9557 6827 6826 9560 9561 6823
6822 9564 9565 6819 6818 9568 9569 6815 6814 9572 9573 6811 6810 9576 9577
6807 6806 9580 9581 6803 6802 9584 9585 6799 6798 9588 9589 6795 6794 9592
9593 6791 6790 9596 9597 6787 6786 9600
6784 9602 9603 6781 6780 9606 9607 6777 6776 9610 9611 6773 6772 9614 9615
6769 6768 9618 9619 6765 6764 9622 9623 6761 6760 9626 9627 6757 6756 9630
9631 6753 6752 9634 9635 6749 6748 9638 9639 6745 6744 9642 9643 6741 6740
9646 9647 6737 6736 9650 9651 6733 6732 9654 9655 6729 6728 9658 9659 6725
6724 9662 9663 6721 6720 9666 9667 6717 6716 9670 9671 6713 6712 9674 9675
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6664 9722 9723 6661 6660 9726 9727 6657
6656 9730 9731 6653 6652 9734 9735 6649 6648 9738 9739 6645 6644 9742 9743
6641 6640 9746 9747 6637 6636 9750 9751 6633 6632 9754 9755 6629 6628 9758
9759 6625 6624 9762 9763 6621 6620 9766 9767 6617 6616 9770 9771 6613 6612
9774 9775 6609 6608 9778 9779 6605 6604 9782 9783 6601 6600 9786 9787 6597
6596 9790 9791 6593 6592 9794 9795 6589 6588 9798 9799 6585 6584 9802 9803
6581 6580 9806 9807 6577 6576 9810 9811 6573 6572 9814 9815 6569 6568 9818
9819 6565 6564 9822 9823 6561 6560 9826 9827 6557 6556 9830 9831 6553 6552
9834 9835 6549 6548 9838 9839 6545 6544 9842 9843 6541 6540 9846 9847 6537
6536 9850 9851 6533 6532 9854 9855 6529
9857 6527 6526 9860 9861 6523 6522 9864 9865 6519 6518 9868 9869 6515 6514
9872 9873 6511 6510 9876 9877 6507 6506 9880 9881 6503 6502 9884 9885 6499
6498 9888 9889 6495 6494 9892 9893 6491 6490 9896 9897 6487 6486 9900 9901
6483 6482 9904 9905 6479 6478 9908 9909 6475 6474 9912 9913 6471 6470 9916
9917 6467 6466 9920 9921 6463 6462 9924 9925 6459 6458 9928 9929 6455 6454
9932 9933 6451 6450 9936 9937 6447 6446 9940 9941 6443 6442 9944 9945 6439
6438 9948 9949 6435 6434 9952 9953 6431 6430 9956 9957 6427 6426 9960 9961
6423 6422 9964 9965 6419 6418 9968 9969 6415 6414 9972 9973 6411 6410 9976
9977 6407 6406 9980 9981 6403 6402 9984
9985 6399 6398 9988 9989 6395 6394 9992 9993 6391 6390 9996 9997 6387 6386
10000 10001 6383 6382 10004 10005 6379 6378 10008 10009 6375 6374 10012
10013 6371 6370 10016 10017 6367 6366 10020 10021 6363 6362 10024 10025 6359
6358 10028 10029 6355 6354 10032 10033 6351 6350 10036 10037 6347 6346 10040
10041 6343 6342 10044 10045 6339 6338 10048 10049 6335 6334 10052 10053 6331
6330 10056 10057 6327 6326 10060 10061 6323 6322 10064 10065 6319 6318 10068
10069 6315 6314 10072 10073 6311 6310 10076 10077 6307 6306 10080 10081 6303
6302 10084 10085 6299 6298 10088 10089 6295 6294 10092 10093 6291 6290 10096
10097 6287 6286 10100 10101 6283 6282 10104 10105 6279 6278 10108 10109 6275
6274 10112
6272 10114 10115 6269 6268 10118 10119 6265 6264 10122 10123 6261 6260 10126
10127 6257 6256 10130 10131 6253 6252 10134 10135 6249 6248 10138 10139 6245
6244 10142 10143 6241 6240 10146 10147 6237 6236 10150 10151 6233 6232 10154
10155 6229 6228 10158 10159 6225 6224 10162 10163 6221 6220 10166 10167 6217
6216 10170 10171 6213 6212 10174 10175 6209 6208 10178 10179 6205 6204 10182
10183 6201 6200 10186 10187 6197 6196 10190 10191 6193 6192 10194 10195 6189
6188 10198 10199 6185 6184 10202 10203 6181 6180 10206 10207 6177 6176 10210
10211 6173 6172 10214 10215 6169 6168 10218 10219 6165 6164 10222 10223 6161
6160 10226 10227 6157 6156 10230 10231 6153 6152 10234 10235 6149 6148 10238
10239 6145
6144 10242 10243 6141 6140 10246 10247 6137 6136 10250 10251 6133 6132 10254
10255 6129 6128 10258 10259 6125 6124 10262 10263 6121 6120 10266 10267 6117
6116 10270 10271 6113 6112 10274 10275 6109 6108 10278 10279 6105 6104 10282
10283 6101 6100 10286 10287 6097 6096 10290 10291 6093 6092 10294 10295 6089
6088 10298 10299 6085 6084 10302 10303 6081 6080 10306 10307 6077 6076 10310
10311 6073 6072 10314 10315 6069 6068 10318 10319 6065 6064 10322 10323 6061
6060 10326 10327 6057 6056 10330 10331 6053 6052 10334 10335 6049 6048 10338
10339 6045 6044 10342 10343 6041 6040 10346 10347 6037 6036 10350 10351 6033
6032 10354 10355 6029 6028 10358 10359 6025 6024 10362 10363 6021 6020 10366
10367 6017
10369 6015 6014 10372 10373 6011 6010 10376 10377 6007 6006 10380 10381 6003
6002 10384 10385 5999 5998 10388 10389 5995 5994 10392 10393 5991 5990 10396
10397 5987 5986 10400 10401 5983 5982 10404 10405 5979 5978 10408 10409 5975
5974 10412 10413 5971 5970 10416 10417 5967 5966 10420 10421 5963 5962 10424
10425 5959 5958 10428 10429 5955 5954 10432 10433 5951 5950 10436 10437 5947
5946 10440 10441 5943 5942 10444 10445 5939 5938 10448 10449 5935 5934 10452
10453 5931 5930 10456 10457 5927 5926 10460 10461 5923 5922 10464 10465 5919
5918 10468 10469 5915 5914 10472 10473 5911 5910 10476 10477 5907 5906 10480
10481 5903 5902 10484 10485 5899 5898 10488 10489 5895 5894 10492 10493 5891
5890 10496
10497 5887 5886 10500 10501 5883 5882 10504 10505 5879 5878 10508 10509 5875
5874 10512 10513 5871 5870 10516 10517 5867 5866 10520 10521 5863 5862 10524
10525 5859 5858 10528 10529 5855 5854 10532 10533 5851 5850 10536 10537 5847
5846 10540 10541 5843 5842 10544 10545 5839 5838 10548 10549 5835 5834 10552
10553 5831 5830 10556 10557 5827 5826 10560 10561 5823 5822 10564 10565 5819
5818 10568 10569 5815 5814 10572 10573 5811 5810 10576 10577 5807 5806 10580
10581 5803 5802 10584 10585 5799 5798 10588 10589 5795 5794 10592 10593 5791
5790 10596 10597 5787 5786 10600 10601 5783 5782 10604 10605 5779 5778 10608
10609 5775 5774 10612 10613 5771 5770 10616 10617 5767 5766 10620 10621 5763
5762 10624
5760 10626 10627 5757 5756 10630 10631 5753 5752 10634 10635 5749 5748 10638
10639 5745 5744 10642 10643 5741 5740 10646 10647 5737 5736 10650 10651 5733
5732 10654 10655 5729 5728 10658 10659 5725 5724 10662 10663 5721 5720 10666
10667 5717 5716 10670 10671 5713 5712 10674 10675 5709 5708 10678 10679 5705
5704 10682 10683 5701 5700 10686 10687 5697 5696 10690 10691 5693 5692 10694
10695 5689 5688 10698 10699 5685 5684 10702 10703 5681 5680 10706 10707 5677
5676 10710 10711 5673 5672 10714 10715 5669 5668 10718 10719 5665 5664 10722
10723 5661 5660 10726 10727 5657 5656 10730 10731 5653 5652 10734 10735 5649
5648 10738 10739 5645 5644 10742 10743 5641 5640 10746 10747 5637 5636 10750
10751 5633
5632 10754 10755 5629 5628 10758 10759 5625 5624 10762 10763 5621 5620 10766
10767 5617 5616 10770 10771 5613 5612 10774 10775 5609 5608 10778 10779 5605
5604 10782 10783 5601 5600 10786 10787 5597 5596 10790 10791 5593 5592 10794
10795 5589 5588 10798 10799 5585 5584 10802 10803 5581 5580 10806 10807 5577
5576 10810 10811 5573 5572 10814 10815 5569 5568 10818 10819 5565 5564 10822
10823 5561 5560 10826 10827 5557 5556 10830 10831 5553 5552 10834 10835 5549
5548 10838 10839 5545 5544 10842 10843 5541 5540 10846 10847 5537 5536 10850
10851 5533 5532 10854 10855 5529 5528 10858 10859 5525 5524 10862 10863 5521
5520 10866 10867 5517 5516 10870 10871 5513 5512 10874 10875 5509 5508 10878
10879 5505
10881 5503 5502 10884 10885 5499 5498 10888 10889 5495 5494 10892 10893 5491
5490 10896 10897 5487 5486 10900 10901 5483 5482 10904 10905 5479 5478 10908
10909 5475 5474 10912 10913 5471 5470 10916 10917 5467 5466 10920 10921 5463
5462 10924 10925 5459 5458 10928 10929 5455 5454 10932 10933 5451 5450 10936
10937 5447 5446 10940 10941 5443 5442 10944 10945 5439 5438 10948 10949 5435
5434 10952 10953 5431 5430 10956 10957 5427 5426 10960 10961 5423 5422 10964
10965 5419 5418 10968 10969 5415 5414 10972 10973 5411 5410 10976 10977 5407
5406 10980 10981 5403 5402 10984 10985 5399 5398 10988 10989 5395 5394 10992
10993 5391 5390 10996 10997 5387 5386 11000 11001 5383 5382 11004 11005 5379
5378 11008
11009 5375 5374 11012 11013 5371 5370 11016 11017 5367 5366 11020 11021 5363
5362 11024 11025 5359 5358 11028 11029 5355 5354 11032 11033 5351 5350 11036
11037 5347 5346 11040 11041 5343 5342 11044 11045 5339 5338 11048 11049 5335
5334 11052 11053 5331 5330 11056 11057 5327 5326 11060 11061 5323 5322 11064
11065 5319 5318 11068 11069 5315 5314 11072 11073 5311 5310 11076 11077 5307
5306 11080 11081 5303 5302 11084 11085 5299 5298 11088 11089 5295 5294 11092
11093 5291 5290 11096 11097 5287 5286 11100 11101 5283 5282 11104 11105 5279
5278 11108 11109 5275 5274 11112 11113 5271 5270 11116 11117 5267 5266 11120
11121 5263 5262 11124 11125 5259 5258 11128 11129 5255 5254 11132 11133 5251
5250 11136
5248 11138 11139 5245 5244 11142 11143 5241 5240 11146 11147 5237 5236 11150
11151 5233 5232 11154 11155 5229 5228 11158 11159 5225 5224 11162 11163 5221
5220 11166 11167 5217 5216 11170 11171 5213 5212 11174 11175 5209 5208 11178
11179 5205 5204 11182 11183 5201 5200 11186 11187 5197 5196 11190 11191 5193
5192 11194 11195 5189 5188 11198 11199 5185 5184 11202 11203 5181 5180 11206
11207 5177 5176 11210 11211 5173 5172 11214 11215 5169 5168 11218 11219 5165
5164 11222 11223 5161 5160 11226 11227 5157 5156 11230 11231 5153 5152 11234
11235 5149 5148 11238 11239 5145 5144 11242 11243 5141 5140 11246 11247 5137
5136 11250 11251 5133 5132 11254 11255 5129 5128 11258 11259 5125 5124 11262
11263 5121
5120 11266 11267 5117 5116 11270 11271 5113 5112 11274 11275 5109 5108 11278
11279 5105 5104 11282 11283 5101 5100 11286 11287 5097 5096 11290 11291 5093
5092 11294 11295 5089 5088 11298 11299 5085 5084 11302 11303 5081 5080 11306
11307 5077 5076 11310 11311 5073 5072 11314 11315 5069 5068 11318 11319 5065
5064 11322 11323 5061 5060 11326 11327 5057 5056 11330 11331 5053 5052 11334
11335 5049 5048 11338 11339 5045 5044 11342 11343 5041 5040 11346 11347 5037
5036 11350 11351 5033 5032 11354 11355 5029 5028 11358 11359 5025 5024 11362
11363 5021 5020 11366 11367 5017 5016 11370 11371 5013 5012 11374 11375 5009
5008 11378 11379 5005 5004 11382 11383 5001 5000 11386 11387 4997 4996 11390
11391 4993
11393 4991 4990 11396 11397 4987 4986 11400 11401 4983 4982 11404 11405 4979
4978 11408 11409 4975 4974 11412 11413 4971 4970 11416 11417 4967 4966 11420
11421 4963 4962 11424 11425 4959 4958 11428 11429 4955 4954 11432 11433 4951
4950 11436 11437 4947 4946 11440 11441 4943 4942 11444 11445 4939 4938 11448
11449 4935 4934 11452 11453 4931 4930 11456 11457 4927 4926 11460 11461 4923
4922 11464 11465 4919 4918 11468 11469 4915 4914 11472 11473 4911 4910 11476
11477 4907 4906 11480 11481 4903 4902 11484 11485 4899 4898 11488 11489 4895
4894 11492 11493 4891 4890 11496 11497 4887 4886 11500 11501 4883 4882 11504
11505 4879 4878 11508 11509 4875 4874 11512 11513 4871 4870 11516 11517 4867
4866 11520
11521 4863 4862 11524 11525 4859 4858 11528 11529 4855 4854 11532 11533 4851
4850 11536 11537 4847 4846 11540 11541 4843 4842 11544 11545 4839 4838 11548
11549 4835 4834 11552 11553 4831 4830 11556 11557 4827 4826 11560 11561 4823
4822 11564 11565 4819 4818 11568 11569 4815 4814 11572 11573 4811 4810 11576
11577 4807 4806 11580 11581 4803 4802 11584 11585 4799 4798 11588 11589 4795
4794 11592 11593 4791 4790 11596 11597 4787 4786 11600 11601 4783 4782 11604
11605 4779 4778 11608 11609 4775 4774 11612 11613 4771 4770 11616 11617 4767
4766 11620 11621 4763 4762 11624 11625 4759 4758 11628 11629 4755 4754 11632
11633 4751 4750 11636 11637 4747 4746 11640 11641 4743 4742 11644 11645 4739
4738 11648
4736 11650 11651 4733 4732 11654 11655 4729 4728 11658 11659 4725 4724 11662
11663 4721 4720 11666 11667 4717 4716 11670 11671 4713 4712 11674 11675 4709
4708 11678 11679 4705 4704 11682 11683 4701 4700 11686 11687 4697 4696 11690
11691 4693 4692 11694 11695 4689 4688 11698 11699 4685 4684 11702 11703 4681
4680 11706 11707 4677 4676 11710 11711 4673 4672 11714 11715 4669 4668 11718
11719 4665 4664 11722 11723 4661 4660 11726 11727 4657 4656 11730 11731 4653
4652 11734 11735 4649 4648 11738 11739 4645 4644 11742 11743 4641 4640 11746
11747 4637 4636 11750 11751 4633 4632 11754 11755 4629 4628 11758 11759 4625
4624 11762 11763 4621 4620 11766 11767 4617 4616 11770 11771 4613 4612 11774
11775 4609
4608 11778 11779 4605 4604 11782 11783 4601 4600 11786 11787 4597 4596 11790
11791 4593 4592 11794 11795 4589 4588 11798 11799 4585 4584 11802 11803 4581
4580 11806 11807 4577 4576 11810 11811 4573 4572 11814 11815 4569 4568 11818
11819 4565 4564 11822 11823 4561 4560 11826 11827 4557 4556 11830 11831 4553
4552 11834 11835 4549 4548 11838 11839 4545 4544 11842 11843 4541 4540 11846
11847 4537 4536 11850 11851 4533 4532 11854 11855 4529 4528 11858 11859 4525
4524 11862 11863 4521 4520 11866 11867 4517 4516 11870 11871 4513 4512 11874
11875 4509 4508 11878 11879 4505 4504 11882 11883 4501 4500 11886 11887 4497
4496 11890 11891 4493 4492 11894 11895 4489 4488 11898 11899 4485 4484 11902
11903 4481
11905 4479 4478 11908 11909 4475 4474 11912 11913 4471 4470 11916 11917 4467
4466 11920 11921 4463 4462 11924 11925 4459 4458 11928 11929 4455 4454 11932
11933 4451 4450 11936 11937 4447 4446 11940 11941 4443 4442 11944 11945 4439
4438 11948 11949 4435 4434 11952 11953 4431 4430 11956 11957 4427 4426 11960
11961 4423 4422 11964 11965 4419 4418 11968 11969 4415 4414 11972 11973 4411
4410 11976 11977 4407 4406 11980 11981 4403 4402 11984 11985 4399 4398 11988
11989 4395 4394 11992 11993 4391 4390 11996 11997 4387 4386 12000 12001 4383
4382 12004 12005 4379 4378 12008 12009 4375 4374 12012 12013 4371 4370 12016
12017 4367 4366 12020 12021 4363 4362 12024 12025 4359 4358 12028 12029 4355
4354 12032
12033 4351 4350 12036 12037 4347 4346 12040 12041 4343 4342 12044 12045 4339
4338 12048 12049 4335 4334 12052 12053 4331 4330 12056 12057 4327 4326 12060
12061 4323 4322 12064 12065 4319 4318 12068 12069 4315 4314 12072 12073 4311
4310 12076 12077 4307 4306 12080 12081 4303 4302 12084 12085 4299 4298 12088
12089 4295 4294 12092 12093 4291 4290 12096 12097 4287 4286 12100 12101 4283
4282 12104 12105 4279 4278 12108 12109 4275 4274 12112 12113 4271 4270 12116
12117 4267 4266 12120 12121 4263 4262 12124 12125 4259 4258 12128 12129 4255
4254 12132 12133 4251 4250 12136 12137 4247 4246 12140 12141 4243 4242 12144
12145 4239 4238 12148 12149 4235 4234 12152 12153 4231 4230 12156 12157 4227
4226 12160
4224 12162 12163 4221 4220 12166 12167 4217 4216 12170 12171 4213 4212 12174
12175 4209 4208 12178 12179 4205 4204 12182 12183 4201 4200 12186 12187 4197
4196 12190 12191 4193 4192 12194 12195 4189 4188 12198 12199 4185 4184 12202
12203 4181 4180 12206 12207 4177 4176 12210 12211 4173 4172 12214 12215 4169
4168 12218 12219 4165 4164 12222 12223 4161 4160 12226 12227 4157 4156 12230
12231 4153 4152 12234 12235 4149 4148 12238 12239 4145 4144 12242 12243 4141
4140 12246 12247 4137 4136 12250 12251 4133 4132 12254 12255 4129 4128 12258
12259 4125 4124 12262 12263 4121 4120 12266 12267 4117 4116 12270 12271 4113
4112 12274 12275 4109 4108 12278 12279 4105 4104 12282 12283 4101 4100 12286
12287 4097
4096 12290 12291 4093 4092 12294 12295 4089 4088 12298 12299 4085 4084 12302
12303 4081 4080 12306 12307 4077 4076 12310 12311 4073 4072 12314 12315 4069
4068 12318 12319 4065 4064 12322 12323 4061 4060 12326 12327 4057 4056 12330
12331 4053 4052 12334 12335 4049 4048 12338 12339 4045 4044 12342 12343 4041
4040 12346 12347 4037 4036 12350 12351 4033 4032 12354 12355 4029 4028 12358
12359 4025 4024 12362 12363 4021 4020 12366 12367 4017 4016 12370 12371 4013
4012 12374 12375 4009 4008 12378 12379 4005 4004 12382 12383 4001 4000 12386
12387 3997 3996 12390 12391 3993 3992 12394 12395 3989 3988 12398 12399 3985
3984 12402 12403 3981 3980 12406 12407 3977 3976 12410 12411 3973 3972 12414
12415 3969
12417 3967 3966 12420 12421 3963 3962 12424 12425 3959 3958 12428 12429 3955
3954 12432 12433 3951 3950 12436 12437 3947 3946 12440 12441 3943 3942 12444
12445 3939 3938 12448 12449 3935 3934 12452 12453 3931 3930 12456 12457 3927
3926 12460 12461 3923 3922 12464 12465 3919 3918 12468 12469 3915 3914 12472
12473 3911 3910 12476 12477 3907 3906 12480 12481 3903 3902 12484 12485 3899
3898 12488 12489 3895 3894 12492 12493 3891 3890 12496 12497 3887 3886 12500
12501 3883 3882 12504 12505 3879 3878 12508 12509 3875 3874 12512 12513 3871
3870 12516 12517 3867 3866 12520 12521 3863 3862 12524 12525 3859 3858 12528
12529 3855 3854 12532 12533 3851 3850 12536 12537 3847 3846 12540 12541 3843
3842 12544
12545 3839 3838 12548 12549 3835 3834 12552 12553 3831 3830 12556 12557 3827
3826 12560 12561 3823 3822 12564 12565 3819 3818 12568 12569 3815 3814 12572
12573 3811 3810 12576 12577 3807 3806 12580 12581 3803 3802 12584 12585 3799
3798 12588 12589 3795 3794 12592 12593 3791 3790 12596 12597 3787 3786 12600
12601 3783 3782 12604 12605 3779 3778 12608 12609 3775 3774 12612 12613 3771
3770 12616 12617 3767 3766 12620 12621 3763 3762 12624 12625 3759 3758 12628
12629 3755 3754 12632 12633 3751 3750 12636 12637 3747 3746 12640 12641 3743
3742 12644 12645 3739 3738 12648 12649 3735 3734 12652 12653 3731 3730 12656
12657 3727 3726 12660 12661 3723 3722 12664 12665 3719 3718 12668 12669 3715
3714 12672
3712 12674 12675 3709 3708 12678 12679 3705 3704 12682 12683 3701 3700 12686
12687 3697 3696 12690 12691 3693 3692 12694 12695 3689 3688 12698 12699 3685
3684 12702 12703 3681 3680 12706 12707 3677 3676 12710 12711 3673 3672 12714
12715 3669 3668 12718 12719 3665 3664 12722 12723 3661 3660 12726 12727 3657
3656 12730 12731 3653 3652 12734 12735 3649 3648 12738 12739 3645 3644 12742
12743 3641 3640 12746 12747 3637 3636 12750 12751 3633 3632 12754 12755 3629
3628 12758 12759 3625 3624 12762 12763 3621 3620 12766 12767 3617 3616 12770
12771 3613 3612 12774 12775 3609 3608 12778 12779 3605 3604 12782 12783 3601
3600 12786 12787 3597 3596 12790 12791 3593 3592 12794 12795 3589 3588 12798
12799 3585
3584 12802 12803 3581 3580 12806 12807 3577 3576 12810 12811 3573 3572 12814
12815 3569 3568 12818 12819 3565 3564 12822 12823 3561 3560 12826 12827 3557
3556 12830 12831 3553 3552 12834 12835 3549 3548 12838 12839 3545 3544 12842
12843 3541 3540 12846 12847 3537 3536 12850 12851 3533 3532 12854 12855 3529
3528 12858 12859 3525 3524 12862 12863 3521 3520 12866 12867 3517 3516 12870
12871 3513 3512 12874 12875 3509 3508 12878 12879 3505 3504 12882 12883 3501
3500 12886 12887 3497 3496 12890 12891 3493 3492 12894 12895 3489 3488 12898
12899 3485 3484 12902 12903 3481 3480 12906 12907 3477 3476 12910 12911 3473
3472 12914 12915 3469 3468 12918 12919 3465 3464 12922 12923 3461 3460 12926
12927 3457
12929 3455 3454 12932 12933 3451 3450 12936 12937 3447 3446 12940 12941 3443
3442 12944 12945 3439 3438 12948 12949 3435 3434 12952 12953 3431 3430 12956
12957 3427 3426 12960 12961 3423 3422 12964 12965 3419 3418 12968 12969 3415
3414 12972 12973 3411 3410 12976 12977 3407 3406 12980 12981 3403 3402 12984
12985 3399 3398 12988 12989 3395 3394 12992 12993 3391 3390 12996 12997 3387
3386 13000 13001 3383 3382 13004 13005 3379 3378 13008 13009 3375 3374 13012
13013 3371 3370 13016 13017 3367 3366 13020 13021 3363 3362 13024 13025 3359
3358 13028 13029 3355 3354 13032 13033 3351 3350 13036 13037 3347 3346 13040
13041 3343 3342 13044 13045 3339 3338 13048 13049 3335 3334 13052 13053 3331
3330 13056
13057 3327 3326 13060 13061 3323 3322 13064 13065 3319 3318 13068 13069 3315
3314 13072 13073 3311 3310 13076 13077 3307 3306 13080 13081 3303 3302 13084
13085 3299 3298 13088 13089 3295 3294 13092 13093 3291 3290 13096 13097 3287
3286 13100 13101 3283 3282 13104 13105 3279 3278 13108 13109 3275 3274 13112
13113 3271 3270 13116 13117 3267 3266 13120 13121 3263 3262 13124 13125 3259
3258 13128 13129 3255 3254 13132 13133 3251 3250 13136 13137 3247 3246 13140
13141 3243 3242 13144 13145 3239 3238 13148 13149 3235 3234 13152 13153 3231
3230 13156 13157 3227 3226 13160 13161 3223 3222 13164 13165 3219 3218 13168
13169 3215 3214 13172 13173 3211 3210 13176 13177 3207 3206 13180 13181 3203
3202 13184
3200 13186 13187 3197 3196 13190 13191 3193 3192 13194 13195 3189 3188 13198
13199 3185 3184 13202 13203 3181 3180 13206 13207 3177 3176 13210 13211 3173
3172 13214 13215 3169 3168 13218 13219 3165 3164 13222 13223 3161 3160 13226
13227 3157 3156 13230 13231 3153 3152 13234 13235 3149 3148 13238 13239 3145
3144 13242 13243 3141 3140 13246 13247 3137 3136 13250 13251 3133 3132 13254
13255 3129 3128 13258 13259 3125 3124 13262 13263 3121 3120 13266 13267 3117
3116 13270 13271 3113 3112 13274 13275 3109 3108 13278 13279 3105 3104 13282
13283 3101 3100 13286 13287 3097 3096 13290 13291 3093 3092 13294 13295 3089
3088 13298 13299 3085 3084 13302 13303 3081 3080 13306 13307 3077 3076 13310
13311 3073
3072 13314 13315 3069 3068 13318 13319 3065 3064 13322 13323 3061 3060 13326
13327 3057 3056 13330 13331 3053 3052 13334 13335 3049 3048 13338 13339 3045
3044 13342 13343 3041 3040 13346 13347 3037 3036 13350 13351 3033 3032 13354
13355 3029 3028 13358 13359 3025 3024 13362 13363 3021 3020 13366 13367 3017
3016 13370 13371 3013 3012 13374 13375 3009 3008 13378 13379 3005 3004 13382
13383 3001 3000 13386 13387 2997 2996 13390 13391 2993 2992 13394 13395 2989
2988 13398 13399 2985 2984 13402 13403 2981 2980 13406 13407 2977 2976 13410
13411 2973 2972 13414 13415 2969 2968 13418 13419 2965 2964 13422 13423 2961
2960 13426 13427 2957 2956 13430 13431 2953 2952 13434 13435 2949 2948 13438
13439 2945
13441 2943 2942 13444 13445 2939 2938 13448 13449 2935 2934 13452 13453 2931
2930 13456 13457 2927 2926 13460 13461 2923 2922 13464 13465 2919 2918 13468
13469 2915 2914 13472 13473 2911 2910 13476 13477 2907 2906 13480 13481 2903
2902 13484 13485 2899 2898 13488 13489 2895 2894 13492 13493 2891 2890 13496
13497 2887 2886 13500 13501 2883 2882 13504 13505 2879 2878 13508 13509 2875
2874 13512 13513 2871 2870 13516 13517 2867 2866 13520 13521 2863 2862 13524
13525 2859 2858 13528 13529 2855 2854 13532 13533 2851 2850 13536 13537 2847
2846 13540 13541 2843 2842 13544 13545 2839 2838 13548 13549 2835 2834 13552
13553 2831 2830 13556 13557 2827 2826 13560 13561 2823 2822 13564 13565 2819
2818 13568
13569 2815 2814 13572 13573 2811 2810 13576 13577 2807 2806 13580 13581 2803
2802 13584 13585 2799 2798 13588 13589 2795 2794 13592 13593 2791 2790 13596
13597 2787 2786 13600 13601 2783 2782 13604 13605 2779 2778 13608 13609 2775
2774 13612 13613 2771 2770 13616 13617 2767 2766 13620 13621 2763 2762 13624
13625 2759 2758 13628 13629 2755 2754 13632 13633 2751 2750 13636 13637 2747
2746 13640 13641 2743 2742 13644 13645 2739 2738 13648 13649 2735 2734 13652
13653 2731 2730 13656 13657 2727 2726 13660 13661 2723 2722 13664 13665 2719
2718 13668 13669 2715 2714 13672 13673 2711 2710 13676 13677 2707 2706 13680
13681 2703 2702 13684 13685 2699 2698 13688 13689 2695 2694 13692 13693 2691
2690 13696
2688 13698 13699 2685 2684 13702 13703 2681 2680 13706 13707 2677 2676 13710
13711 2673 2672 13714 13715 2669 2668 13718 13719 2665 2664 13722 13723 2661
2660 13726 13727 2657 2656 13730 13731 2653 2652 13734 13735 2649 2648 13738
13739 2645 2644 13742 13743 2641 2640 13746 13747 2637 2636 13750 13751 2633
2632 13754 13755 2629 2628 13758 13759 2625 2624 13762 13763 2621 2620 13766
13767 2617 2616 13770 13771 2613 2612 13774 13775 2609 2608 13778 13779 2605
2604 13782 13783 2601 2600 13786 13787 2597 2596 13790 13791 2593 2592 13794
13795 2589 2588 13798 13799 2585 2584 13802 13803 2581 2580 13806 13807 2577
2576 13810 13811 2573 2572 13814 13815 2569 2568 13818 13819 2565 2564 13822
13823 2561
2560 13826 13827 2557 2556 13830 13831 2553 2552 13834 13835 2549 2548 13838
13839 2545 2544 13842 13843 2541 2540 13846 13847 2537 2536 13850 13851 2533
2532 13854 13855 2529 2528 13858 13859 2525 2524 13862 13863 2521 2520 13866
13867 2517 2516 13870 13871 2513 2512 13874 13875 2509 2508 13878 13879 2505
2504 13882 13883 2501 2500 13886 13887 2497 2496 13890 13891 2493 2492 13894
13895 2489 2488 13898 13899 2485 2484 13902 13903 2481 2480 13906 13907 2477
2476 13910 13911 2473 2472 13914 13915 2469 2468 13918 13919 2465 2464 13922
13923 2461 2460 13926 13927 2457 2456 13930 13931 2453 2452 13934 13935 2449
2448 13938 13939 2445 2444 13942 13943 2441 2440 13946 13947 2437 2436 13950
13951 2433
13953 2431 2430 13956 13957 2427 2426 13960 13961 2423 2422 13964 13965 2419
2418 13968 13969 2415 2414 13972 13973 2411 2410 13976 13977 2407 2406 13980
13981 2403 2402 13984 13985 2399 2398 13988 13989 2395 2394 13992 13993 2391
2390 13996 13997 2387 2386 14000 14001 2383 2382 14004 14005 2379 2378 14008
14009 2375 2374 14012 14013 2371 2370 14016 14017 2367 2366 14020 14021 2363
2362 14024 14025 2359 2358 14028 14029 2355 2354 14032 14033 2351 2350 14036
14037 2347 2346 14040 14041 2343 2342 14044 14045 2339 2338 14048 14049 2335
2334 14052 14053 2331 2330 14056 14057 2327 2326 14060 14061 2323 2322 14064
14065 2319 2318 14068 14069 2315 2314 14072 14073 2311 2310 14076 14077 2307
2306 14080
14081 2303 2302 14084 14085 2299 2298 14088 14089 2295 2294 14092 14093 2291
2290 14096 14097 2287 2286 14100 14101 2283 2282 14104 14105 2279 2278 14108
14109 2275 2274 14112 14113 2271 2270 14116 14117 2267 2266 14120 14121 2263
2262 14124 14125 2259 2258 14128 14129 2255 2254 14132 14133 2251 2250 14136
14137 2247 2246 14140 14141 2243 2242 14144 14145 2239 2238 14148 14149 2235
2234 14152 14153 2231 2230 14156 14157 2227 2226 14160 14161 2223 2222 14164
14165 2219 2218 14168 14169 2215 2214 14172 14173 2211 2210 14176 14177 2207
2206 14180 14181 2203 2202 14184 14185 2199 2198 14188 14189 2195 2194 14192
14193 2191 2190 14196 14197 2187 2186 14200 14201 2183 2182 14204 14205 2179
2178 14208
2176 14210 14211 2173 2172 14214 14215 2169 2168 14218 14219 2165 2164 14222
14223 2161 2160 14226 14227 2157 2156 14230 14231 2153 2152 14234 14235 2149
2148 14238 14239 2145 2144 14242 14243 2141 2140 14246 14247 2137 2136 14250
14251 2133 2132 14254 14255 2129 2128 14258 14259 2125 2124 14262 14263 2121
2120 14266 14267 2117 2116 14270 14271 2113 2112 14274 14275 2109 2108 14278
14279 2105 2104 14282 14283 2101 2100 14286 14287 2097 2096 14290 14291 2093
2092 14294 14295 2089 2088 14298 14299 2085 2084 14302 14303 2081 2080 14306
14307 2077 2076 14310 14311 2073 2072 14314 14315 2069 2068 14318 14319 2065
2064 14322 14323 2061 2060 14326 14327 2057 2056 14330 14331 2053 2052 14334
14335 2049
2048 14338 14339 2045 2044 14342 14343 2041 2040 14346 14347 2037 2036 14350
14351 2033 2032 14354 14355 2029 2028 14358 14359 2025 2024 14362 14363 2021
2020 14366 14367 2017 2016 14370 14371 2013 2012 14374 14375 2009 2008 14378
14379 2005 2004 14382 14383 2001 2000 14386 14387 1997 1996 14390 14391 1993
1992 14394 14395 1989 1988 14398 14399 1985 1984 14402 14403 1981 1980 14406
14407 1977 1976 14410 14411 1973 1972 14414 14415 1969 1968 14418 14419 1965
1964 14422 14423 1961 1960 14426 14427 1957 1956 14430 14431 1953 1952 14434
14435 1949 1948 14438 14439 1945 1944 14442 14443 1941 1940 14446 14447 1937
1936 14450 14451 1933 1932 14454 14455 1929 1928 14458 14459 1925 1924 14462
14463 1921
14465 1919 1918 14468 14469 1915 1914 14472 14473 1911 1910 14476 14477 1907
1906 14480 14481 1903 1902 14484 14485 1899 1898 14488 14489 1895 1894 14492
14493 1891 1890 14496 14497 1887 1886 14500 14501 1883 1882 14504 14505 1879
1878 14508 14509 1875 1874 14512 14513 1871 1870 14516 14517 1867 1866 14520
14521 1863 1862 14524 14525 1859 1858 14528 14529 1855 1854 14532 14533 1851
1850 14536 14537 1847 1846 14540 14541 1843 1842 14544 14545 1839 1838 14548
14549 1835 1834 14552 14553 1831 1830 14556 14557 1827 1826 14560 14561 1823
1822 14564 14565 1819 1818 14568 14569 1815 1814 14572 14573 1811 1810 14576
14577 1807 1806 14580 14581 1803 1802 14584 14585 1799 1798 14588 14589 1795
1794 14592
14593 1791 1790 14596 14597 1787 1786 14600 14601 1783 1782 14604 14605 1779
1778 14608 14609 1775 1774 14612 14613 1771 1770 14616 14617 1767 1766 14620
14621 1763 1762 14624 14625 1759 1758 14628 14629 1755 1754 14632 14633 1751
1750 14636 14637 1747 1746 14640 14641 1743 1742 14644 14645 1739 1738 14648
14649 1735 1734 14652 14653 1731 1730 14656 14657 1727 1726 14660 14661 1723
1722 14664 14665 1719 1718 14668 14669 1715 1714 14672 14673 1711 1710 14676
14677 1707 1706 14680 14681 1703 1702 14684 14685 1699 1698 14688 14689 1695
1694 14692 14693 1691 1690 14696 14697 1687 1686 14700 14701 1683 1682 14704
14705 1679 1678 14708 14709 1675 1674 14712 14713 1671 1670 14716 14717 1667
1666 14720
1664 14722 14723 1661 1660 14726 14727 1657 1656 14730 14731 1653 1652 14734
14735 1649 1648 14738 14739 1645 1644 14742 14743 1641 1640 14746 14747 1637
1636 14750 14751 1633 1632 14754 14755 1629 1628 14758 14759 1625 1624 14762
14763 1621 1620 14766 14767 1617 1616 14770 14771 1613 1612 14774 14775 1609
1608 14778 14779 1605 1604 14782 14783 1601 1600 14786 14787 1597 1596 14790
14791 1593 1592 14794 14795 1589 1588 14798 14799 1585 1584 14802 14803 1581
1580 14806 14807 1577 1576 14810 14811 1573 1572 14814 14815 1569 1568 14818
14819 1565 1564 14822 14823 1561 1560 14826 14827 1557 1556 14830 14831 1553
1552 14834 14835 1549 1548 14838 14839 1545 1544 14842 14843 1541 1540 14846
14847 1537
1536 14850 14851 1533 1532 14854 14855 1529 1528 14858 14859 1525 1524 14862
14863 1521 1520 14866 14867 1517 1516 14870 14871 1513 1512 14874 14875 1509
1508 14878 14879 1505 1504 14882 14883 1501 1500 14886 14887 1497 1496 14890
14891 1493 1492 14894 14895 1489 1488 14898 14899 1485 1484 14902 14903 1481
1480 14906 14907 1477 1476 14910 14911 1473 1472 14914 14915 1469 1468 14918
14919 1465 1464 14922 14923 1461 1460 14926 14927 1457 1456 14930 14931 1453
1452 14934 14935 1449 1448 14938 14939 1445 1444 14942 14943 1441 1440 14946
14947 1437 1436 14950 14951 1433 1432 14954 14955 1429 1428 14958 14959 1425
1424 14962 14963 1421 1420 14966 14967 1417 1416 14970 14971 1413 1412 14974
14975 1409
14977 1407 1406 14980 14981 1403 1402 14984 14985 1399 1398 14988 14989 1395
1394 14992 14993 1391 1390 14996 14997 1387 1386 15000 15001 1383 1382 15004
15005 1379 1378 15008 15009 1375 1374 15012 15013 1371 1370 15016 15017 1367
1366 15020 15021 1363 1362 15024 15025 1359 1358 15028 15029 1355 1354 15032
15033 1351 1350 15036 15037 1347 1346 15040 15041 1343 1342 15044 15045 1339
1338 15048 15049 1335 1334 15052 15053 1331 1330 15056 15057 1327 1326 15060
15061 1323 1322 15064 15065 1319 1318 15068 15069 1315 1314 15072 15073 1311
1310 15076 15077 1307 1306 15080 15081 1303 1302 15084 15085 1299 1298 15088
15089 1295 1294 15092 15093 1291 1290 15096 15097 1287 1286 15100 15101 1283
1282 15104
15105 1279 1278 15108 15109 1275 1274 15112 15113 1271 1270 15116 15117 1267
1266 15120 15121 1263 1262 15124 15125 1259 1258 15128 15129 1255 1254 15132
15133 1251 1250 15136 15137 1247 1246 15140 15141 1243 1242 15144 15145 1239
1238 15148 15149 1235 1234 15152 15153 1231 1230 15156 15157 1227 1226 15160
15161 1223 1222 15164 15165 1219 1218 15168 15169 1215 1214 15172 15173 1211
1210 15176 15177 1207 1206 15180 15181 1203 1202 15184 15185 1199 1198 15188
15189 1195 1194 15192 15193 1191 1190 15196 15197 1187 1186 15200 15201 1183
1182 15204 15205 1179 1178 15208 15209 1175 1174 15212 15213 1171 1170 15216
15217 1167 1166 15220 15221 1163 1162 15224 15225 1159 1158 15228 15229 1155
1154 15232
1152 15234 15235 1149 1148 15238 15239 1145 1144 15242 15243 1141 1140 15246
15247 1137 1136 15250 15251 1133 1132 15254 15255 1129 1128 15258 15259 1125
1124 15262 15263 1121 1120 15266 15267 1117 1116 15270 15271 1113 1112 15274
15275 1109 1108 15278 15279 1105 1104 15282 15283 1101 1100 15286 15287 1097
1096 15290 15291 1093 1092 15294 15295 1089 1088 15298 15299 1085 1084 15302
15303 1081 1080 15306 15307 1077 1076 15310 15311 1073 1072 15314 15315 1069
1068 15318 15319 1065 1064 15322 15323 1061 1060 15326 15327 1057 1056 15330
15331 1053 1052 15334 15335 1049 1048 15338 15339 1045 1044 15342 15343 1041
1040 15346 15347 1037 1036 15350 15351 1033 1032 15354 15355 1029 1028 15358
15359 1025
1024 15362 15363 1021 1020 15366 15367 1017 1016 15370 15371 1013 1012 15374
15375 1009 1008 15378 15379 1005 1004 15382 15383 1001 1000 15386 15387 997
996 15390 15391 993 992 15394 15395 989 988 15398 15399 985 984 15402 15403
981 980 15406 15407 977 976 15410 15411 973 972 15414 15415 969 968 15418
15419 965 964 15422 15423 961 960 15426 15427 957 956 15430 15431 953 952
15434 15435 949 948 15438 15439 945 944 15442 15443 941 940 15446 15447 937
936 15450 15451 933 932 15454 15455 929 928 15458 15459 925 924 15462 15463
921 920 15466 15467 917 916 15470 15471 913 912 15474 15475 909 908 15478
15479 905 904 15482 15483 901 900 15486 15487 897
15489 895 894 15492 15493 891 890 15496 15497 887 886 15500 15501 883 882
15504 15505 879 878 15508 15509 875 874 15512 15513 871 870 15516 15517 867
866 15520 15521 863 862 15524 15525 859 858 15528 15529 855 854 15532 15533
851 850 15536 15537 847 846 15540 15541 843 842 15544 15545 839 838 15548
15549 835 834 15552 15553 831 830 15556 15557 827 826 15560 15561 823 822
15564 15565 819 818 15568 15569 815 814 15572 15573 811 810 15576 15577 807
806 15580 15581 803 802 15584 15585 799 798 15588 15589 795 794 15592 15593
791 790 15596 15597 787 786 15600 15601 783 782 15604 15605 779 778 15608
15609 775 774 15612 15613 771 770 15616
15617 767 766 15620 15621 763 762 15624 15625 759 758 15628 15629 755 754
15632 15633 751 750 15636 15637 747 746 15640 15641 743 742 15644 15645 739
738 15648 15649 735 734 15652 15653 731 730 15656 15657 727 726 15660 15661
723 722 15664 15665 719 718 15668 15669 715 714 15672 15673 711 710 15676
15677 707 706 15680 15681 703 702 15684 15685 699 698 15688 15689 695 694
15692 15693 691 690 15696 15697 687 686 15700 15701 683 682 15704 15705 679
678 15708 15709 675 674 15712 15713 671 670 15716 15717 667 666 15720 15721
663 662 15724 15725 659 658 15728 15729 655 654 15732 15733 651 650 15736
15737 647 646 15740 15741 643 642 15744
640 15746 15747 637 636 15750 15751 633 632 15754 15755 629 628 15758 15759
625 624 15762 15763 621 620 15766 15767 617 616 15770 15771 613 612 15774
15775 609 608 15778 15779 605 604 15782 15783 601 600 15786 15787 597 596
15790 15791 593 592 15794 15795 589 588 15798 15799 585 584 15802 15803 581
580 15806 15807 577 576 15810 15811 573 572 15814 15815 569 568 15818 15819
565 564 15822 15823 561 560 15826 15827 557 556 15830 15831 553 552 15834
15835 549 548 15838 15839 545 544 15842 15843 541 540 15846 15847 537 536
15850 15851 533 532 15854 15855 529 528 15858 15859 525 524 15862 15863 521
520 15866 15867 517 516 15870 15871 513
512 15874 15875 509 508 15878 15879 505 504 15882 15883 501 500 15886 15887
497 496 15890 15891 493 492 15894 15895 489 488 15898 15899 485 484 15902
15903 481 480 15906 15907 477 476 15910 15911 473 472 15914 15915 469 468
15918 15919 465 464 15922 15923 461 460 15926 15927 457 456 15930 15931 453
452 15934 15935 449 448 15938 15939 445 444 15942 15943 441 440 15946 15947
437 436 15950 15951 433 432 15954 15955 429 428 15958 15959 425 424 15962
15963 421 420 15966 15967 417 416 15970 15971 413 412 15974 15975 409 408
15978 15979 405 404 15982 15983 401 400 15986 15987 397 396 15990 15991 393
392 15994 15995 389 388 15998 15999 385
16001 383 382 16004 16005 379 378 16008 16009 375 374 16012 16013 371 370
16016 16017 367 366 16020 16021 363 362 16024 16025 359 358 16028 16029 355
354 16032 16033 351 350 16036 16037 347 346 16040 16041 343 342 16044 16045
339 338 16048 16049 335 334 16052 16053 331 330 16056 16057 327 326 16060
16061 323 322 16064 16065 319 318 16068 16069 315 314 16072 16073 311 310
16076 16077 307 306 16080 16081 303 302 16084 16085 299 298 16088 16089 295
294 16092 16093 291 290 16096 16097 287 286 16100 16101 283 282 16104 16105
279 278 16108 16109 275 274 16112 16113 271 270 16116 16117 267 266 16120
16121 263 262 16124 16125 259 258 16128
16129 255 254 16132 16133 251 250 16136 16137 247 246 16140 16141 243 242
16144 16145 239 238 16148 16149 235 234 16152 16153 231 230 16156 16157 227
226 16160 16161 223 222 16164 16165 219 218 16168 16169 215 214 16172 16173
211 210 16176 16177 207 206 16180 16181 203 202 16184 16185 199 198 16188
16189 195 194 16192 16193 191 190 16196 16197 187 186 16200 16201 183 182
16204 16205 179 178 16208 16209 175 174 16212 16213 171 170 16216 16217 167
166 16220 16221 163 162 16224 16225 159 158 16228 16229 155 154 16232 16233
151 150 16236 16237 147 146 16240 16241 143 142 16244 16245 139 138 16248
16249 135 134 16252 16253 131 130 16256
128 16258 16259 125 124 16262 16263 121 120 16266 16267 117 116 16270 16271
113 112 16274 16275 109 108 16278 16279 105 104 16282 16283 101 100 16286
16287 97 96 16290 16291 93 92 16294 16295 89 88 16298 16299 85 84 16302
16303 81 80 16306 16307 77 76 16310 16311 73 72 16314 16315 69 68 16318
16319 65 64 16322 16323 61 60 16326 16327 57 56 16330 16331 53 52 16334
16335 49 48 16338 16339 45 44 16342 16343 41 40 16346 16347 37 36 16350
16351 33 32 16354 16355 29 28 16358 16359 25 24 16362 16363 21 20 16366
16367 17 16 16370 16371 13 12 16374 16375 9 8 16378 16379 5 4 16382 16383 1
nigel
2008-10-02 11:15:40 UTC
Permalink
Post by Carl G.
An idea for a lottery system just struck me which is so barkingly mad that
it might be fun to try. The problem is that it needs a very large magic
square as a driver, at least 100x100 but the bigger the better up to
256x256 (the maximum number of columns per page in my spreadsheet
software).
Does anyone know where I could obtain such a magic square? I'd like to be
able to load it straight into the spreadsheet so comma delimited format
would be ideal.
Thanks for your help,
NigelH
If you know someone with the MatLab program, the magic() function creates
magic squares of a specified size. Below is the result from magic(128),
which creates a 128 by 128 magic square. You will have to undo the
reformatting created by the newsreader. I apologize for the size of this
response (at least it is in plain text format).
- Carl G.
Thanks Carl.

I don't know of anyone with MatLab but I'll ask around.

I've been kicking some numbers around and I reckon that it will take a
very long time for me to generate a system based around 256 x 256 or
even 128 x 128 because of an exponential processing factor. Although the
bigger the magic square the better (if my barkingly mad idea has any
validity), perhaps I should start out with something a bit smaller as a
test of concept.

If you have a spare moment I wonder if I might prevail upon you to
generate 29 x 29 for me. From some crude calculations, each lottery ball
is likely to have a unique draw history by 29 draws and I reckon that is
pretty much the smallest number which might produce a useable system.

Many thanks for your help,

NigelH
Carl G.
2008-10-02 15:18:19 UTC
Permalink
Post by nigel
Post by Carl G.
Post by nigel
An idea for a lottery system just struck me which is so barkingly mad
that it might be fun to try. The problem is that it needs a very large
magic square as a driver, at least 100x100 but the bigger the better up
to 256x256 (the maximum number of columns per page in my spreadsheet
software).
Does anyone know where I could obtain such a magic square? I'd like to be
able to load it straight into the spreadsheet so comma delimited format
would be ideal.
Thanks for your help,
NigelH
If you know someone with the MatLab program, the magic() function creates
magic squares of a specified size. Below is the result from magic(128),
which creates a 128 by 128 magic square. You will have to undo the
reformatting created by the newsreader. I apologize for the size of this
response (at least it is in plain text format).
- Carl G.
Thanks Carl.
I don't know of anyone with MatLab but I'll ask around.
I've been kicking some numbers around and I reckon that it will take a
very long time for me to generate a system based around 256 x 256 or even
128 x 128 because of an exponential processing factor. Although the bigger
the magic square the better (if my barkingly mad idea has any validity),
perhaps I should start out with something a bit smaller as a test of
concept.
If you have a spare moment I wonder if I might prevail upon you to
generate 29 x 29 for me. From some crude calculations, each lottery ball
is likely to have a unique draw history by 29 draws and I reckon that is
pretty much the smallest number which might produce a useable system.
Many thanks for your help,
NigelH
There is a simple algorithm for generating magic squares with odd sides.
Assume the magic square wraps around (like a torus), so that the bottom is
just above the top row and the right column is just to the left of the left
column. Start with a "1" in the first row, center column. Place the next
number in the cell that is diagonally up and to the right of the previous
cell (this places the "2" in the bottom row, one column right of center).
If a cell already contains a number, drop down to the next row. MatLab's
magic(29) results in the square below. I believe that it uses the odd-side
magic square algorithm.

437 468 499 530 561 592 623 654 685 716 747 778 809 840 1 32 63 94 125 156
187 218 249 280 311 342 373 404 435
467 498 529 560 591 622 653 684 715 746 777 808 839 29 31 62 93 124 155 186
217 248 279 310 341 372 403 434 436
497 528 559 590 621 652 683 714 745 776 807 838 28 30 61 92 123 154 185 216
247 278 309 340 371 402 433 464 466
527 558 589 620 651 682 713 744 775 806 837 27 58 60 91 122 153 184 215 246
277 308 339 370 401 432 463 465 496
557 588 619 650 681 712 743 774 805 836 26 57 59 90 121 152 183 214 245 276
307 338 369 400 431 462 493 495 526
587 618 649 680 711 742 773 804 835 25 56 87 89 120 151 182 213 244 275 306
337 368 399 430 461 492 494 525 556
617 648 679 710 741 772 803 834 24 55 86 88 119 150 181 212 243 274 305 336
367 398 429 460 491 522 524 555 586
647 678 709 740 771 802 833 23 54 85 116 118 149 180 211 242 273 304 335 366
397 428 459 490 521 523 554 585 616
677 708 739 770 801 832 22 53 84 115 117 148 179 210 241 272 303 334 365 396
427 458 489 520 551 553 584 615 646
707 738 769 800 831 21 52 83 114 145 147 178 209 240 271 302 333 364 395 426
457 488 519 550 552 583 614 645 676
737 768 799 830 20 51 82 113 144 146 177 208 239 270 301 332 363 394 425 456
487 518 549 580 582 613 644 675 706
767 798 829 19 50 81 112 143 174 176 207 238 269 300 331 362 393 424 455 486
517 548 579 581 612 643 674 705 736
797 828 18 49 80 111 142 173 175 206 237 268 299 330 361 392 423 454 485 516
547 578 609 611 642 673 704 735 766
827 17 48 79 110 141 172 203 205 236 267 298 329 360 391 422 453 484 515 546
577 608 610 641 672 703 734 765 796
16 47 78 109 140 171 202 204 235 266 297 328 359 390 421 452 483 514 545 576
607 638 640 671 702 733 764 795 826
46 77 108 139 170 201 232 234 265 296 327 358 389 420 451 482 513 544 575
606 637 639 670 701 732 763 794 825 15
76 107 138 169 200 231 233 264 295 326 357 388 419 450 481 512 543 574 605
636 667 669 700 731 762 793 824 14 45
106 137 168 199 230 261 263 294 325 356 387 418 449 480 511 542 573 604 635
666 668 699 730 761 792 823 13 44 75
136 167 198 229 260 262 293 324 355 386 417 448 479 510 541 572 603 634 665
696 698 729 760 791 822 12 43 74 105
166 197 228 259 290 292 323 354 385 416 447 478 509 540 571 602 633 664 695
697 728 759 790 821 11 42 73 104 135
196 227 258 289 291 322 353 384 415 446 477 508 539 570 601 632 663 694 725
727 758 789 820 10 41 72 103 134 165
226 257 288 319 321 352 383 414 445 476 507 538 569 600 631 662 693 724 726
757 788 819 9 40 71 102 133 164 195
256 287 318 320 351 382 413 444 475 506 537 568 599 630 661 692 723 754 756
787 818 8 39 70 101 132 163 194 225
286 317 348 350 381 412 443 474 505 536 567 598 629 660 691 722 753 755 786
817 7 38 69 100 131 162 193 224 255
316 347 349 380 411 442 473 504 535 566 597 628 659 690 721 752 783 785 816
6 37 68 99 130 161 192 223 254 285
346 377 379 410 441 472 503 534 565 596 627 658 689 720 751 782 784 815 5 36
67 98 129 160 191 222 253 284 315
376 378 409 440 471 502 533 564 595 626 657 688 719 750 781 812 814 4 35 66
97 128 159 190 221 252 283 314 345
406 408 439 470 501 532 563 594 625 656 687 718 749 780 811 813 3 34 65 96
127 158 189 220 251 282 313 344 375
407 438 469 500 531 562 593 624 655 686 717 748 779 810 841 2 33 64 95 126
157 188 219 250 281 312 343 374 405
nigel
2008-10-02 21:50:14 UTC
Permalink
Post by Carl G.
There is a simple algorithm for generating magic squares with odd sides.
Assume the magic square wraps around (like a torus), so that the bottom is
just above the top row and the right column is just to the left of the left
column. Start with a "1" in the first row, center column. Place the next
number in the cell that is diagonally up and to the right of the previous
cell (this places the "2" in the bottom row, one column right of center).
If a cell already contains a number, drop down to the next row. MatLab's
magic(29) results in the square below. I believe that it uses the odd-side
magic square algorithm.
<snip>

Many thanks. That was quite straightforward to incorporate into my
spreadsheet.

I'll post here how my barkingly mad idea works out, in case anyone's
interested.

NigelH
nigel
2008-10-06 18:14:32 UTC
Permalink
Post by nigel
I'll post here how my barkingly mad idea works out, in case anyone's
interested.
Not good, actually :(

It turns out that a magic square was unsuitable for my purpose. However
a square with each row, column and diagonal containing the numbers 1
thru 29 seemed more appropriate, and I was able to generate one from the
magic square by calculating mod(29) + 1 for every cell.

Aside 1: What is this sort of square called?

Aside 2: It would seem relatively easy to generate this sort of square.
Some web sites I visited in conjunction with magic squares suggested
that algorithmically generating squares with even numbered sides isn't
easy. I wonder if an algorithm could be produced using the 1-29 type
square then somehow reversing the mod(29) + 1.

It turned out that 29 draws is not sufficient history for each ball in a
6/49 lottery to have a unique history.

I was hoping to 'build' the system overnight on Thursday and Friday, but
in the end I was only able to 'build' on Friday night. The output is a
ranked list of the 49 numbers in order of 'likelihood' if the barkingly
mad idea works. I bought a ticket for the UK lottery and got one number
right.

I generated predictions for eight 6/49 lotteries around the world, using
both complete draw history and the draw history of the weekend draws
only. I noted the ranking positions of the actual drawn numbers. Twelve
performed worse than expectation (sum of rankings = 150), four did
better. Although not statistically significant, there seemed to be
enough bias towards the lower rankings to encourage further investigation.

Many thanks to everyone who helped, especially Carl for the 29 magic square.

NigelH
Jasen Betts
2008-10-07 09:20:04 UTC
Permalink
Post by nigel
It turns out that a magic square was unsuitable for my purpose. However
a square with each row, column and diagonal containing the numbers 1
thru 29 seemed more appropriate, and I was able to generate one from the
magic square by calculating mod(29) + 1 for every cell.
Aside 1: What is this sort of square called?
latin square.
Post by nigel
Aside 2: It would seem relatively easy to generate this sort of square.
Some web sites I visited in conjunction with magic squares suggested
that algorithmically generating squares with even numbered sides isn't
easy. I wonder if an algorithm could be produced using the 1-29 type
square then somehow reversing the mod(29) + 1.
no.
Post by nigel
I was hoping to 'build' the system overnight on Thursday and Friday, but
in the end I was only able to 'build' on Friday night. The output is a
ranked list of the 49 numbers in order of 'likelihood' if the barkingly
mad idea works. I bought a ticket for the UK lottery and got one number
right.
all balls are likely to be equally probable

the history of all draws is probably on the web somewhere,

You're probably better off looking for balls that are associated with
draws that pay a higher proportion of the prize pool on average. The
unpopular balls.

Bye.
Jasen
nigel
2008-10-07 10:38:47 UTC
Permalink
Post by Jasen Betts
Post by nigel
It turns out that a magic square was unsuitable for my purpose. However
a square with each row, column and diagonal containing the numbers 1
thru 29 seemed more appropriate, and I was able to generate one from the
magic square by calculating mod(29) + 1 for every cell.
Aside 1: What is this sort of square called?
latin square.
Thanks.
Post by Jasen Betts
Post by nigel
Aside 2: It would seem relatively easy to generate this sort of square.
Some web sites I visited in conjunction with magic squares suggested
that algorithmically generating squares with even numbered sides isn't
easy. I wonder if an algorithm could be produced using the 1-29 type
square then somehow reversing the mod(29) + 1.
no.
Thanks again, you've discouraged me from wasting any time trying it!
Post by Jasen Betts
Post by nigel
I was hoping to 'build' the system overnight on Thursday and Friday, but
in the end I was only able to 'build' on Friday night. The output is a
ranked list of the 49 numbers in order of 'likelihood' if the barkingly
mad idea works. I bought a ticket for the UK lottery and got one number
right.
all balls are likely to be equally probable
the history of all draws is probably on the web somewhere,
Most/many lottery organisers only publish data going back a year, and
even then the data can be flawed. I only consider lotteries where I can
get the data from two different sources so I can cross-check.
Post by Jasen Betts
You're probably better off looking for balls that are associated with
draws that pay a higher proportion of the prize pool on average. The
unpopular balls.
It's not quite that simple because quite a lot of enthusiasts will adopt
exactly that approach. It's probably better to select a mixture of
popular and unpopular numbers.
Post by Jasen Betts
Bye.
Jasen
Thank you,

NigelH
nigel
2008-10-09 22:30:47 UTC
Permalink
Post by Jasen Betts
Post by nigel
It turns out that a magic square was unsuitable for my purpose. However
a square with each row, column and diagonal containing the numbers 1
thru 29 seemed more appropriate, and I was able to generate one from the
magic square by calculating mod(29) + 1 for every cell.
Aside 1: What is this sort of square called?
latin square.
I've just browsed the 'Latin Squares' entry on Wikipedia. As defined
there, they have is no requirement for a 29x29 Latin Square to have each
of the numbers 1-29 on each diagonal. The entry didn't seem to include a
name for such a special case.

NigelH
Chip Eastham
2008-10-11 16:00:02 UTC
Permalink
Post by nigel
Post by Jasen Betts
Post by nigel
It turns out that a magic square was unsuitable for my purpose. However
a square with each row, column and diagonal containing the numbers 1
thru 29 seemed more appropriate, and I was able to generate one from the
magic square by calculating mod(29) + 1 for every cell.
Aside 1: What is this sort of square called?
latin square.
I've just browsed the 'Latin Squares' entry on Wikipedia. As defined
there, they have is no requirement for a 29x29 Latin Square to have each
of the numbers 1-29 on each diagonal. The entry didn't seem to include a
name for such a special case.
NigelH
You are correct. I've never seen a special
name for this case either, although there
are problems like Sudoku that essentially
involve a Latin square with additional
constraints of the form putting each
symbol once into various suregions
(subsquares in the case of Sudoku,
but diagonals in your case).

It's not clear which "diagonals" you
want to constrain in this fashion,
perhaps just the main diagonal and
anti-diagonal, but possibly all the
wrap-around diagonals?

A related notion, which perhaps will
give examples of what you seek, is
an idempotent quasigroup. The
"multiplication table" for a quasigroup
is a Latin square, and the idempotent
property implies that each symbol
will appear exactly once on the main
diagonal.

There's a simple construction of a
symmetric idempotent quasigroup
for odd N, namely taking x,y to be
residues mod N and defining:

x * y = (x+y)/2 mod N

Note that division by 2 is well-defined
for odd N.

For N = 5 we get the following Latin
square:

0 3 1 4 2
3 1 4 2 0
1 4 2 0 3
4 2 0 3 1
2 0 3 1 4

As you can see, this construction gets
one of each symbol in the main diagonal
and in every wrap-around diagonal that
is parallel to it. However the main anti-
diagonal (and all the wrap-arounds
parallel to it) is constant, so fails to have
each symbol once entirely.

We can vary the formula (losing symmetry)
and get the anti-diagonals to have each
symbol once thusly:

x * y = (x/2) + y mod N

0 1 2 3 4
3 4 0 1 2
1 2 3 4 0
4 0 1 2 3
2 3 4 0 1


regards, chip
Peter Webb
2008-10-07 12:11:24 UTC
Permalink
Post by nigel
Post by Carl G.
There is a simple algorithm for generating magic squares with odd sides.
Assume the magic square wraps around (like a torus), so that the bottom
is just above the top row and the right column is just to the left of the
left column. Start with a "1" in the first row, center column. Place the
next number in the cell that is diagonally up and to the right of the
previous cell (this places the "2" in the bottom row, one column right of
center). If a cell already contains a number, drop down to the next row.
MatLab's magic(29) results in the square below. I believe that it uses
the odd-side magic square algorithm.
<snip>
Many thanks. That was quite straightforward to incorporate into my
spreadsheet.
I'll post here how my barkingly mad idea works out, in case anyone's
interested.
NigelH
This is an interesting algorithm, but it does place the numbers in a very
regular manner indeed, with 1 next to 2 next to 3 etc.

If your program requires any degree of randomness, you can randomise it
quite easily by using the fact that you can interchange any two rows or any
two columns in a magic square and its still magic. Just shuffle the 29 (or
whatever) rows and 29 columns separately and you will have a random magic
square.
nigel
2008-10-27 20:30:02 UTC
Permalink
Post by Peter Webb
Post by nigel
Post by Carl G.
There is a simple algorithm for generating magic squares with odd
sides. Assume the magic square wraps around (like a torus), so that
the bottom is just above the top row and the right column is just to
the left of the left column. Start with a "1" in the first row,
center column. Place the next number in the cell that is diagonally
up and to the right of the previous cell (this places the "2" in the
bottom row, one column right of center). If a cell already contains a
number, drop down to the next row. MatLab's magic(29) results in the
square below. I believe that it uses the odd-side magic square
algorithm.
<snip>
Many thanks. That was quite straightforward to incorporate into my
spreadsheet.
I'll post here how my barkingly mad idea works out, in case anyone's
interested.
NigelH
I'm continuing to monitor the original system, which overall is still
performing worse than expectation but seems to be regressing to the mean.
Post by Peter Webb
This is an interesting algorithm, but it does place the numbers in a
very regular manner indeed, with 1 next to 2 next to 3 etc.
If your program requires any degree of randomness, you can randomise it
quite easily by using the fact that you can interchange any two rows or
any two columns in a magic square and its still magic. Just shuffle the
29 (or whatever) rows and 29 columns separately and you will have a
random magic square.
Many thanks. I was very struck by your observation, so I produced a
second system by randomising the original 29x29 magic square as you
suggested.

The revised system is currently performing better than expectation.
Something I noticed is that if the top six numbers had been played each
time, the result would have been 5 3-matches in 66 draws (against the
expected 1 in 57, although it should probably be compared with the 1 in
54 chance of winning any prize).

I've started work on a 59x59 magic square system, but there's an
exponential component in the development and it isn't finished yet.

NigelH

Jasen Betts
2008-10-02 11:42:11 UTC
Permalink
Post by nigel
An idea for a lottery system just struck me which is so barkingly mad
that it might be fun to try.
any attempt to game the lottery is by definition mad...
Post by nigel
The problem is that it needs a very large
magic square as a driver, at least 100x100 but the bigger the better up
to 256x256 (the maximum number of columns per page in my spreadsheet
software).
Does anyone know where I could obtain such a magic square?
it's easy to make a 9x9 square from a 3x3 (google for 9x9 magic square)

and a 16x16 from a 4x4

and a 256x256 from a 16x16

heres's a way to do 4x4 to 16 in a single step.

take a 4x4 square and raise it to the fourth power,

1 14 15 4
12 6 7 9
8 10 11 5
13 3 2 16

or zero-based

0 13 14 3
11 5 6 8
7 9 10 4
12 2 3 15

basically take the 0-based coorcinates of your cell eg (27,210)

and express them in base-4 ( 0123,3102 )

for each digit take a zero based value from the 4x4 square

the firsf pair is 0,3 which gives 3
the second is 1,1 which gives 5
the third is 2,0 which gives 7
the last is 3,2 which gives 2

so the number for 27,210 is (((3*16)+5*16)+7*16)+2 13682 (base 10)

add 1 if you want to get a 1 based magic square with (numbers 1 to 65536)

so in spot (27,210) put 13683
Post by nigel
I'd like to
be able to load it straight into the spreadsheet so comma delimited
format would be ideal.
your spreadsheet should be able to generate the square itself using
the above procedure (a bunch of lookups based on expressions involving row() and col() )



here's a program in yabasic that does the same thing.
http://www.yabasic.de/

rem 256x256 magic-square generator in yabasic.

data 1,15,14,4
data 12,6,7,9
data 8,10,11,5
data 13,3,2,16
print time$
rem load the generator square:
dim ms(4,4)
for y=1 to 4
for x=1 to 4
read ms(x,y)
next
next
rem print out the composite square
for r1=1 to 4
for r2=1 to 4
for r3=1 to 4
for r4=1 to 4
k=0
for c1=1 to 4
for c2=1 to 4
for c3=1 to 4
for c4=1 to 4
if k then
print ",";
end if
k=1
print (((ms(c1,r1)*16)+ms(c2,r2))*16+ms(c3,r3))*16+ms(c4,r4)-4368;
next:next:next:next
print
next:next:next:next

Bye.
Jasen
nigel
2008-10-02 22:02:03 UTC
Permalink
Post by Jasen Betts
Post by nigel
An idea for a lottery system just struck me which is so barkingly mad
that it might be fun to try.
any attempt to game the lottery is by definition mad...
I don't believe it's possible to prove that you can't predict a lottery
from its past history. In view of the number of people who have tried,
the circumstantial evidence against is pretty damning (I'd guess 99.999%
- possibly a few more 9s).

However most attempts will have followed similar patterns - hot/cold
numbers, hit and skip etc - most lottery software will have the usual
suspects. I think it's fun to try out barkingly mad ideas - how many
people will have tried predicting a lottery using a 256x256 magic
square? - so I may be trying something unique.

Thanks to the kind people who have responded, I am learning things I
didn't know about magic squares and I will be following that by honing
my spreadsheet skills. There's a UK lottery rollover on Saturday for
which I'd like to buy a ticket using this idea, so rounding up the usual
45% returns my expectation is probably to lose 50p.

In other words, yes, I'm mad. Woof woof!
Post by Jasen Betts
Post by nigel
The problem is that it needs a very large
magic square as a driver, at least 100x100 but the bigger the better up
to 256x256 (the maximum number of columns per page in my spreadsheet
software).
Does anyone know where I could obtain such a magic square?
it's easy to make a 9x9 square from a 3x3 (google for 9x9 magic square)
and a 16x16 from a 4x4
and a 256x256 from a 16x16
heres's a way to do 4x4 to 16 in a single step.
take a 4x4 square and raise it to the fourth power,
1 14 15 4
12 6 7 9
8 10 11 5
13 3 2 16
or zero-based
0 13 14 3
11 5 6 8
7 9 10 4
12 2 3 15
basically take the 0-based coorcinates of your cell eg (27,210)
and express them in base-4 ( 0123,3102 )
for each digit take a zero based value from the 4x4 square
the firsf pair is 0,3 which gives 3
the second is 1,1 which gives 5
the third is 2,0 which gives 7
the last is 3,2 which gives 2
so the number for 27,210 is (((3*16)+5*16)+7*16)+2 13682 (base 10)
add 1 if you want to get a 1 based magic square with (numbers 1 to 65536)
so in spot (27,210) put 13683
Post by nigel
I'd like to
be able to load it straight into the spreadsheet so comma delimited
format would be ideal.
your spreadsheet should be able to generate the square itself using
the above procedure (a bunch of lookups based on expressions involving row() and col() )
Many thanks for this. I have archived your post for later reference, but
I intend to try a proof-of-concept 29x29 magic square first.
Post by Jasen Betts
here's a program in yabasic that does the same thing.
http://www.yabasic.de/
rem 256x256 magic-square generator in yabasic.
data 1,15,14,4
data 12,6,7,9
data 8,10,11,5
data 13,3,2,16
print time$
dim ms(4,4)
for y=1 to 4
for x=1 to 4
read ms(x,y)
next
next
rem print out the composite square
for r1=1 to 4
for r2=1 to 4
for r3=1 to 4
for r4=1 to 4
k=0
for c1=1 to 4
for c2=1 to 4
for c3=1 to 4
for c4=1 to 4
if k then
print ",";
end if
k=1
print (((ms(c1,r1)*16)+ms(c2,r2))*16+ms(c3,r3))*16+ms(c4,r4)-4368;
next:next:next:next
print
next:next:next:next
Bye.
Jasen
Thanks Jasen,

NigelH
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