{"trustable":true,"prependHtml":"\u003cscript\u003e window.katexOptions \u003d { disable: true }; \u003c/script\u003e\n\u003cscript type\u003d\"text/x-mathjax-config\"\u003e\n MathJax.Hub.Config({\n tex2jax: {\n inlineMath: [[\u0027$$$\u0027,\u0027$$$\u0027], [\u0027$\u0027,\u0027$\u0027]],\n displayMath: [[\u0027$$$$$$\u0027,\u0027$$$$$$\u0027], [\u0027$$\u0027,\u0027$$\u0027]]\n }\n });\n\u003c/script\u003e\n\u003cscript async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS-MML_HTMLorMML\" type\u003d\"text/javascript\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cdiv class\u003d\"panel_content\"\u003eToday we play a squiggly \u003ca href\u003d\"http://en.wikipedia.org/wiki/Sudoku\"\u003esudoku\u003c/a\u003e, The objective is to fill a 9*9 grid with digits so that each column, each row, and each of the nine Connecting-sub-grids that compose the grid contains all of the digits from 1 to 9.\u003cbr\u003eLeft figure is the puzzle and right figure is one solution.\u003cbr\u003e\u003ccenter\u003e\u003cimg style\u003d\"max-width:100%;\" src\u003d\"CDN_BASE_URL/81d0a321fa975770f72572233eaa0255?v\u003d1715677890\"\u003e\u003c/center\u003e \u003cbr\u003eNow, give you the information of the puzzle, please tell me is there no solution or multiple solution or one solution.\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"The first line is a number T(1\u0026lt;\u003dT\u0026lt;\u003d2500), represents the number of case. The next T blocks follow each indicates a case.\u003cbr\u003eEach case contains nine lines, Each line contains nine integers.\u003cbr\u003eEach module number tells the information of the gird and is the sum of up to five integers:\u003cbr\u003e0~9: \u00270\u0027 means this gird is empty, \u00271\u0027 - \u00279\u0027 means the gird is already filled in.\u003cbr\u003e16: wall to the up\u003cbr\u003e32: wall to the right\u003cbr\u003e64: wall to the down\u003cbr\u003e128: wall to the left\u003cbr\u003eI promise there must be nine Connecting-sub-grids, and each contains nine girds."}},{"title":"Output","value":{"format":"HTML","content":"For each case, if there are Multiple Solutions or no solution just output \"Multiple Solutions\" or \"No solution\". Else output the exclusive solution.(as shown in the sample output)"}},{"title":"Sample","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e3\r\n144 18 112 208 80 25 54 144 48\r\n135 38 147 80 121 128 97 130 32\r\n137 32 160 144 114 167 208 0 32\r\n192 100 160 160 208 96 183 192 101\r\n209 80 39 192 86 48 136 80 114\r\n152 48 226 144 112 160 160 149 48\r\n128 0 112 166 215 96 160 128 41\r\n128 39 153 32 209 80 101 136 35\r\n192 96 200 67 80 112 208 68 96 \r\n\r\n144 48 144 81 81 16 53 144 48\r\n128 96 224 144 48 128 103 128 38\r\n163 208 80 0 37 224 209 0 32\r\n135 48 176 192 64 112 176 192 104\r\n192 101 128 89 80 82 32 150 48\r\n149 48 224 208 16 48 224 192 33\r\n128 0 114 176 135 0 80 112 169\r\n137 32 148 32 192 96 176 144 32\r\n192 96 193 64 80 80 96 192 96\r\n\r\n144 88 48 217 16 16 80 112 176\r\n224 176 129 48 128 40 208 16 37\r\n145 32 128 96 196 96 176 136 32\r\n192 32 227 176 144 80 96 192 32\r\n176 192 80 98 160 145 80 48 224\r\n128 48 144 80 96 224 183 128 48\r\n128 36 224 144 51 144 32 128 105\r\n131 64 112 136 32 192 36 224 176\r\n224 208 80 64 64 116 192 83 96\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eCase 1:\r\n521439678\r\n763895124\r\n984527361\r\n346182795\r\n157964832\r\n812743956\r\n235678419\r\n479216583\r\n698351247\r\nCase 2:\r\nNo solution\r\nCase 3:\r\nMultiple Solutions\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}