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來稿時間：2016年1月24日。
貼博客時間：2016年2月3日。
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◆重要訊息◆(2016年1月24日中午12:13分)
送上一款24阶类自然数2次幻方。K*(2^N)阶N-1次类自然数幻方存在。
四川：钟明
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欣賞導航：第一次突破2^n階的局面，而且是2次方的，……是四川達州的鐘明先生。
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24阶类自然数幻方(K=1，2) |
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9 | 73 | 137 | 31 | 95 | 159 | -11 | -75 | -139 | -29 | -93 | -157 | -42 | -106 | -170 | -64 | -128 | -192 | 44 | 108 | 172 | 62 | 126 | 190 |
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201 | 265 | 329 | 223 | 287 | 351 | -203 | -267 | -331 | -221 | -285 | -349 | -234 | -298 | -362 | -256 | -320 | -384 | 236 | 300 | 364 | 254 | 318 | 382 |
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393 | 457 | 521 | 415 | 479 | 543 | -395 | -459 | -523 | -413 | -477 | -541 | -426 | -490 | -554 | -448 | -512 | -576 | 428 | 492 | 556 | 446 | 510 | 574 |
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18 | 82 | 146 | 8 | 72 | 136 | -20 | -84 | -148 | -6 | -70 | -134 | -49 | -113 | -177 | -39 | -103 | -167 | 51 | 115 | 179 | 37 | 101 | 165 |
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0 |
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210 | 274 | 338 | 200 | 264 | 328 | -212 | -276 | -340 | -198 | -262 | -326 | -241 | -305 | -369 | -231 | -295 | -359 | 243 | 307 | 371 | 229 | 293 | 357 |
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402 | 466 | 530 | 392 | 456 | 520 | -404 | -468 | -532 | -390 | -454 | -518 | -433 | -497 | -561 | -423 | -487 | -551 | 435 | 499 | 563 | 421 | 485 | 549 |
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16 | 80 | 144 | 26 | 90 | 154 | -14 | -78 | -142 | -28 | -92 | -156 | -47 | -111 | -175 | -57 | -121 | -185 | 45 | 109 | 173 | 59 | 123 | 187 |
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208 | 272 | 336 | 218 | 282 | 346 | -206 | -270 | -334 | -220 | -284 | -348 | -239 | -303 | -367 | -249 | -313 | -377 | 237 | 301 | 365 | 251 | 315 | 379 |
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400 | 464 | 528 | 410 | 474 | 538 | -398 | -462 | -526 | -412 | -476 | -540 | -431 | -495 | -559 | -441 | -505 | -569 | 429 | 493 | 557 | 443 | 507 | 571 |
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23 | 87 | 151 | 1 | 65 | 129 | -21 | -85 | -149 | -3 | -67 | -131 | -56 | -120 | -184 | -34 | -98 | -162 | 54 | 118 | 182 | 36 | 100 | 164 |
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0 |
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215 | 279 | 343 | 193 | 257 | 321 | -213 | -277 | -341 | -195 | -259 | -323 | -248 | -312 | -376 | -226 | -290 | -354 | 246 | 310 | 374 | 228 | 292 | 356 |
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0 |
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407 | 471 | 535 | 385 | 449 | 513 | -405 | -469 | -533 | -387 | -451 | -515 | -440 | -504 | -568 | -418 | -482 | -546 | 438 | 502 | 566 | 420 | 484 | 548 |
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-17 | -81 | -145 | -7 | -71 | -135 | 19 | 83 | 147 | 5 | 69 | 133 | 50 | 114 | 178 | 40 | 104 | 168 | -52 | -116 | -180 | -38 | -102 | -166 |
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-209 | -273 | -337 | -199 | -263 | -327 | 211 | 275 | 339 | 197 | 261 | 325 | 242 | 306 | 370 | 232 | 296 | 360 | -244 | -308 | -372 | -230 | -294 | -358 |
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0 |
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-401 | -465 | -529 | -391 | -455 | -519 | 403 | 467 | 531 | 389 | 453 | 517 | 434 | 498 | 562 | 424 | 488 | 552 | -436 | -500 | -564 | -422 | -486 | -550 |
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-10 | -74 | -138 | -32 | -96 | -160 | 12 | 76 | 140 | 30 | 94 | 158 | 41 | 105 | 169 | 63 | 127 | 191 | -43 | -107 | -171 | -61 | -125 | -189 |
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-202 | -266 | -330 | -224 | -288 | -352 | 204 | 268 | 332 | 222 | 286 | 350 | 233 | 297 | 361 | 255 | 319 | 383 | -235 | -299 | -363 | -253 | -317 | -381 |
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-394 | -458 | -522 | -416 | -480 | -544 | 396 | 460 | 524 | 414 | 478 | 542 | 425 | 489 | 553 | 447 | 511 | 575 | -427 | -491 | -555 | -445 | -509 | -573 |
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-24 | -88 | -152 | -2 | -66 | -130 | 22 | 86 | 150 | 4 | 68 | 132 | 55 | 119 | 183 | 33 | 97 | 161 | -53 | -117 | -181 | -35 | -99 | -163 |
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0 |
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-216 | -280 | -344 | -194 | -258 | -322 | 214 | 278 | 342 | 196 | 260 | 324 | 247 | 311 | 375 | 225 | 289 | 353 | -245 | -309 | -373 | -227 | -291 | -355 |
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0 |
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-408 | -472 | -536 | -386 | -450 | -514 | 406 | 470 | 534 | 388 | 452 | 516 | 439 | 503 | 567 | 417 | 481 | 545 | -437 | -501 | -565 | -419 | -483 | -547 |
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0 |
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-15 | -79 | -143 | -25 | -89 | -153 | 13 | 77 | 141 | 27 | 91 | 155 | 48 | 112 | 176 | 58 | 122 | 186 | -46 | -110 | -174 | -60 | -124 | -188 |
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0 |
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-207 | -271 | -335 | -217 | -281 | -345 | 205 | 269 | 333 | 219 | 283 | 347 | 240 | 304 | 368 | 250 | 314 | 378 | -238 | -302 | -366 | -252 | -316 | -380 |
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0 |
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-399 | -463 | -527 | -409 | -473 | -537 | 397 | 461 | 525 | 411 | 475 | 539 | 432 | 496 | 560 | 442 | 506 | 570 | -430 | -494 | -558 | -444 | -508 | -572 |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
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2次检验 |
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81 | 5329 | 18769 | 961 | 9025 | 25281 | -121 | -5625 | -19321 | -841 | -8649 | -24649 | -1764 | -11236 | -28900 | -4096 | -16384 | -36864 | 1936 | 11664 | 29584 | 3844 | 15876 | 36100 |
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0 |
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40401 | 70225 | 108241 | 49729 | 82369 | 123201 | -41209 | -71289 | -109561 | -48841 | -81225 | -121801 | -54756 | -88804 | -131044 | -65536 | -102400 | -147456 | 55696 | 90000 | 132496 | 64516 | 101124 | 145924 |
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0 |
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154449 | 208849 | 271441 | 172225 | 229441 | 294849 | -156025 | -210681 | -273529 | -170569 | -227529 | -292681 | -181476 | -240100 | -306916 | -200704 | -262144 | -331776 | 183184 | 242064 | 309136 | 198916 | 260100 | 329476 |
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0 |
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324 | 6724 | 21316 | 64 | 5184 | 18496 | -400 | -7056 | -21904 | -36 | -4900 | -17956 | -2401 | -12769 | -31329 | -1521 | -10609 | -27889 | 2601 | 13225 | 32041 | 1369 | 10201 | 27225 |
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44100 | 75076 | 114244 | 40000 | 69696 | 107584 | -44944 | -76176 | -115600 | -39204 | -68644 | -106276 | -58081 | -93025 | -136161 | -53361 | -87025 | -128881 | 59049 | 94249 | 137641 | 52441 | 85849 | 127449 |
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0 |
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161604 | 217156 | 280900 | 153664 | 207936 | 270400 | -163216 | -219024 | -283024 | -152100 | -206116 | -268324 | -187489 | -247009 | -314721 | -178929 | -237169 | -303601 | 189225 | 249001 | 316969 | 177241 | 235225 | 301401 |
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256 | 6400 | 20736 | 676 | 8100 | 23716 | -196 | -6084 | -20164 | -784 | -8464 | -24336 | -2209 | -12321 | -30625 | -3249 | -14641 | -34225 | 2025 | 11881 | 29929 | 3481 | 15129 | 34969 |
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0 |
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43264 | 73984 | 112896 | 47524 | 79524 | 119716 | -42436 | -72900 | -111556 | -48400 | -80656 | -121104 | -57121 | -91809 | -134689 | -62001 | -97969 | -142129 | 56169 | 90601 | 133225 | 63001 | 99225 | 143641 |
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160000 | 215296 | 278784 | 168100 | 224676 | 289444 | -158404 | -213444 | -276676 | -169744 | -226576 | -291600 | -185761 | -245025 | -312481 | -194481 | -255025 | -323761 | 184041 | 243049 | 310249 | 196249 | 257049 | 326041 |
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0 |
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529 | 7569 | 22801 | 1 | 4225 | 16641 | -441 | -7225 | -22201 | -9 | -4489 | -17161 | -3136 | -14400 | -33856 | -1156 | -9604 | -26244 | 2916 | 13924 | 33124 | 1296 | 10000 | 26896 |
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0 |
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46225 | 77841 | 117649 | 37249 | 66049 | 103041 | -45369 | -76729 | -116281 | -38025 | -67081 | -104329 | -61504 | -97344 | -141376 | -51076 | -84100 | -125316 | 60516 | 96100 | 139876 | 51984 | 85264 | 126736 |
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0 |
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165649 | 221841 | 286225 | 148225 | 201601 | 263169 | -164025 | -219961 | -284089 | -149769 | -203401 | -265225 | -193600 | -254016 | -322624 | -174724 | -232324 | -298116 | 191844 | 252004 | 320356 | 176400 | 234256 | 300304 |
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0 |
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-289 | -6561 | -21025 | -49 | -5041 | -18225 | 361 | 6889 | 21609 | 25 | 4761 | 17689 | 2500 | 12996 | 31684 | 1600 | 10816 | 28224 | -2704 | -13456 | -32400 | -1444 | -10404 | -27556 |
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0 |
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-43681 | -74529 | -113569 | -39601 | -69169 | -106929 | 44521 | 75625 | 114921 | 38809 | 68121 | 105625 | 58564 | 93636 | 136900 | 53824 | 87616 | 129600 | -59536 | -94864 | -138384 | -52900 | -86436 | -128164 |
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0 |
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-160801 | -216225 | -279841 | -152881 | -207025 | -269361 | 162409 | 218089 | 281961 | 151321 | 205209 | 267289 | 188356 | 248004 | 315844 | 179776 | 238144 | 304704 | -190096 | -250000 | -318096 | -178084 | -236196 | -302500 |
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0 |
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-100 | -5476 | -19044 | -1024 | -9216 | -25600 | 144 | 5776 | 19600 | 900 | 8836 | 24964 | 1681 | 11025 | 28561 | 3969 | 16129 | 36481 | -1849 | -11449 | -29241 | -3721 | -15625 | -35721 |
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0 |
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-40804 | -70756 | -108900 | -50176 | -82944 | -123904 | 41616 | 71824 | 110224 | 49284 | 81796 | 122500 | 54289 | 88209 | 130321 | 65025 | 101761 | 146689 | -55225 | -89401 | -131769 | -64009 | -100489 | -145161 |
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0 |
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-155236 | -209764 | -272484 | -173056 | -230400 | -295936 | 156816 | 211600 | 274576 | 171396 | 228484 | 293764 | 180625 | 239121 | 305809 | 199809 | 261121 | 330625 | -182329 | -241081 | -308025 | -198025 | -259081 | -328329 |
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0 |
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-576 | -7744 | -23104 | -4 | -4356 | -16900 | 484 | 7396 | 22500 | 16 | 4624 | 17424 | 3025 | 14161 | 33489 | 1089 | 9409 | 25921 | -2809 | -13689 | -32761 | -1225 | -9801 | -26569 |
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0 |
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-46656 | -78400 | -118336 | -37636 | -66564 | -103684 | 45796 | 77284 | 116964 | 38416 | 67600 | 104976 | 61009 | 96721 | 140625 | 50625 | 83521 | 124609 | -60025 | -95481 | -139129 | -51529 | -84681 | -126025 |
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0 |
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-166464 | -222784 | -287296 | -148996 | -202500 | -264196 | 164836 | 220900 | 285156 | 150544 | 204304 | 266256 | 192721 | 253009 | 321489 | 173889 | 231361 | 297025 | -190969 | -251001 | -319225 | -175561 | -233289 | -299209 |
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0 |
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-225 | -6241 | -20449 | -625 | -7921 | -23409 | 169 | 5929 | 19881 | 729 | 8281 | 24025 | 2304 | 12544 | 30976 | 3364 | 14884 | 34596 | -2116 | -12100 | -30276 | -3600 | -15376 | -35344 |
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0 |
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-42849 | -73441 | -112225 | -47089 | -78961 | -119025 | 42025 | 72361 | 110889 | 47961 | 80089 | 120409 | 57600 | 92416 | 135424 | 62500 | 98596 | 142884 | -56644 | -91204 | -133956 | -63504 | -99856 | -144400 |
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0 |
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-159201 | -214369 | -277729 | -167281 | -223729 | -288369 | 157609 | 212521 | 275625 | 168921 | 225625 | 290521 | 186624 | 246016 | 313600 | 195364 | 256036 | 324900 | -184900 | -244036 | -311364 | -197136 | -258064 | -327184 |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
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抹去负号 |
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9 | 73 | 137 | 31 | 95 | 159 | 11 | 75 | 139 | 29 | 93 | 157 | 42 | 106 | 170 | 64 | 128 | 192 | 44 | 108 | 172 | 62 | 126 | 190 |
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201 | 265 | 329 | 223 | 287 | 351 | 203 | 267 | 331 | 221 | 285 | 349 | 234 | 298 | 362 | 256 | 320 | 384 | 236 | 300 | 364 | 254 | 318 | 382 |
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393 | 457 | 521 | 415 | 479 | 543 | 395 | 459 | 523 | 413 | 477 | 541 | 426 | 490 | 554 | 448 | 512 | 576 | 428 | 492 | 556 | 446 | 510 | 574 |
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18 | 82 | 146 | 8 | 72 | 136 | 20 | 84 | 148 | 6 | 70 | 134 | 49 | 113 | 177 | 39 | 103 | 167 | 51 | 115 | 179 | 37 | 101 | 165 |
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210 | 274 | 338 | 200 | 264 | 328 | 212 | 276 | 340 | 198 | 262 | 326 | 241 | 305 | 369 | 231 | 295 | 359 | 243 | 307 | 371 | 229 | 293 | 357 |
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402 | 466 | 530 | 392 | 456 | 520 | 404 | 468 | 532 | 390 | 454 | 518 | 433 | 497 | 561 | 423 | 487 | 551 | 435 | 499 | 563 | 421 | 485 | 549 |
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16 | 80 | 144 | 26 | 90 | 154 | 14 | 78 | 142 | 28 | 92 | 156 | 47 | 111 | 175 | 57 | 121 | 185 | 45 | 109 | 173 | 59 | 123 | 187 |
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208 | 272 | 336 | 218 | 282 | 346 | 206 | 270 | 334 | 220 | 284 | 348 | 239 | 303 | 367 | 249 | 313 | 377 | 237 | 301 | 365 | 251 | 315 | 379 |
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400 | 464 | 528 | 410 | 474 | 538 | 398 | 462 | 526 | 412 | 476 | 540 | 431 | 495 | 559 | 441 | 505 | 569 | 429 | 493 | 557 | 443 | 507 | 571 |
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23 | 87 | 151 | 1 | 65 | 129 | 21 | 85 | 149 | 3 | 67 | 131 | 56 | 120 | 184 | 34 | 98 | 162 | 54 | 118 | 182 | 36 | 100 | 164 |
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215 | 279 | 343 | 193 | 257 | 321 | 213 | 277 | 341 | 195 | 259 | 323 | 248 | 312 | 376 | 226 | 290 | 354 | 246 | 310 | 374 | 228 | 292 | 356 |
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407 | 471 | 535 | 385 | 449 | 513 | 405 | 469 | 533 | 387 | 451 | 515 | 440 | 504 | 568 | 418 | 482 | 546 | 438 | 502 | 566 | 420 | 484 | 548 |
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17 | 81 | 145 | 7 | 71 | 135 | 19 | 83 | 147 | 5 | 69 | 133 | 50 | 114 | 178 | 40 | 104 | 168 | 52 | 116 | 180 | 38 | 102 | 166 |
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209 | 273 | 337 | 199 | 263 | 327 | 211 | 275 | 339 | 197 | 261 | 325 | 242 | 306 | 370 | 232 | 296 | 360 | 244 | 308 | 372 | 230 | 294 | 358 |
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401 | 465 | 529 | 391 | 455 | 519 | 403 | 467 | 531 | 389 | 453 | 517 | 434 | 498 | 562 | 424 | 488 | 552 | 436 | 500 | 564 | 422 | 486 | 550 |
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10 | 74 | 138 | 32 | 96 | 160 | 12 | 76 | 140 | 30 | 94 | 158 | 41 | 105 | 169 | 63 | 127 | 191 | 43 | 107 | 171 | 61 | 125 | 189 |
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202 | 266 | 330 | 224 | 288 | 352 | 204 | 268 | 332 | 222 | 286 | 350 | 233 | 297 | 361 | 255 | 319 | 383 | 235 | 299 | 363 | 253 | 317 | 381 |
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394 | 458 | 522 | 416 | 480 | 544 | 396 | 460 | 524 | 414 | 478 | 542 | 425 | 489 | 553 | 447 | 511 | 575 | 427 | 491 | 555 | 445 | 509 | 573 |
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24 | 88 | 152 | 2 | 66 | 130 | 22 | 86 | 150 | 4 | 68 | 132 | 55 | 119 | 183 | 33 | 97 | 161 | 53 | 117 | 181 | 35 | 99 | 163 |
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216 | 280 | 344 | 194 | 258 | 322 | 214 | 278 | 342 | 196 | 260 | 324 | 247 | 311 | 375 | 225 | 289 | 353 | 245 | 309 | 373 | 227 | 291 | 355 |
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408 | 472 | 536 | 386 | 450 | 514 | 406 | 470 | 534 | 388 | 452 | 516 | 439 | 503 | 567 | 417 | 481 | 545 | 437 | 501 | 565 | 419 | 483 | 547 |
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15 | 79 | 143 | 25 | 89 | 153 | 13 | 77 | 141 | 27 | 91 | 155 | 48 | 112 | 176 | 58 | 122 | 186 | 46 | 110 | 174 | 60 | 124 | 188 |
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207 | 271 | 335 | 217 | 281 | 345 | 205 | 269 | 333 | 219 | 283 | 347 | 240 | 304 | 368 | 250 | 314 | 378 | 238 | 302 | 366 | 252 | 316 | 380 |
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399 | 463 | 527 | 409 | 473 | 537 | 397 | 461 | 525 | 411 | 475 | 539 | 432 | 496 | 560 | 442 | 506 | 570 | 430 | 494 | 558 | 444 | 508 | 572 |
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#VALUE! | 1 | 576 |
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