{"trustable":true,"prependHtml":"\u003cstyle type\u003d\u0027text/css\u0027\u003e\n .input, .output {\n border: 1px solid #888888;\n }\n .output {\n margin-bottom: 1em;\n position: relative;\n top: -1px;\n }\n .output pre, .input pre {\n background-color: #EFEFEF;\n line-height: 1.25em;\n margin: 0;\n padding: 0.25em;\n }\n \u003c/style\u003e\n \u003clink rel\u003d\"stylesheet\" href\u003d\"//codeforces.org/s/96598/css/problem-statement.css\" type\u003d\"text/css\" /\u003e\n\u003cscript\u003e\n window.katexOptions \u003d {\n delimiters: [\n {left: \u0027$$$$$$\u0027, right: \u0027$$$$$$\u0027, display: true},\n {left: \u0027$$$\u0027, right: \u0027$$$\u0027, display: false},\n {left: \u0027$$\u0027, right: \u0027$$\u0027, display: true},\n {left: \u0027$\u0027, right: \u0027$\u0027, display: false}\n ]\n };\n\u003c/script\u003e\n","sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003eThere is a rectangular grid of \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e rows of \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/span\u003e initially-white cells each.\u003c/p\u003e\u003cp\u003eArkady performed a certain number (possibly zero) of operations on it. In the \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e-th operation, a non-empty subset of rows \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eR\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e and a non-empty subset of columns \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eC\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e are chosen. For each row \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003er\u003c/i\u003e\u003c/span\u003e in \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eR\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e and each column \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ec\u003c/i\u003e\u003c/span\u003e in \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eC\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e, the intersection of row \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003er\u003c/i\u003e\u003c/span\u003e and column \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ec\u003c/i\u003e\u003c/span\u003e is coloured black.\u003c/p\u003e\u003cp\u003eThere\u0027s another constraint: a row or a column can only be chosen at most once among all operations. In other words, it means that no pair of \u003cspan class\u003d\"tex-span\"\u003e(\u003ci\u003ei\u003c/i\u003e, \u003ci\u003ej\u003c/i\u003e)\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e \u0026lt; \u003ci\u003ej\u003c/i\u003e\u003c/span\u003e) exists such that \u003cimg align\u003d\"middle\" class\u003d\"tex-formula\" src\u003d\"CDN_BASE_URL/25c07d94ebe88f052433bf43b60ec92f?v\u003d1726407941\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e or \u003cimg align\u003d\"middle\" class\u003d\"tex-formula\" src\u003d\"CDN_BASE_URL/980e01e590ae5c05bcc41cadb75522a8?v\u003d1726407941\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e, where \u003cimg align\u003d\"middle\" class\u003d\"tex-formula\" src\u003d\"CDN_BASE_URL/d5c54b58b06881cf8bf5f714c981f106?v\u003d1726407941\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e denotes intersection of sets, and \u003cimg align\u003d\"middle\" class\u003d\"tex-formula\" src\u003d\"CDN_BASE_URL/699ff61b945398e5ff232a1b36732c11?v\u003d1726407941\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e denotes the empty set.\u003c/p\u003e\u003cp\u003eYou are to determine whether a valid sequence of operations exists that produces a given final grid.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe first line contains two space-separated integers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/span\u003e \u003cspan class\u003d\"tex-span\"\u003e(1 ≤ \u003ci\u003en\u003c/i\u003e, \u003ci\u003em\u003c/i\u003e ≤ 50\u003c/span\u003e)\u0026nbsp;— the number of rows and columns of the grid, respectively.\u003c/p\u003e\u003cp\u003eEach of the following \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e lines contains a string of \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/span\u003e characters, each being either \u0027\u003cspan class\u003d\"tex-font-style-tt\"\u003e.\u003c/span\u003e\u0027 (denoting a white cell) or \u0027\u003cspan class\u003d\"tex-font-style-tt\"\u003e#\u003c/span\u003e\u0027 (denoting a black cell), representing the desired setup.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003eIf the given grid can be achieved by any valid sequence of operations, output \"\u003cspan class\u003d\"tex-font-style-tt\"\u003eYes\u003c/span\u003e\"; otherwise output \"\u003cspan class\u003d\"tex-font-style-tt\"\u003eNo\u003c/span\u003e\" (both without quotes).\u003c/p\u003e\u003cp\u003eYou can print each character in any case (upper or lower).\u003c/p\u003e"}},{"title":"Examples","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\u003e5 8\n.#.#..#.\n.....#..\n.#.#..#.\n#.#....#\n.....#..\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eYes\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"","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\u003e5 5\n..#..\n..#..\n#####\n..#..\n..#..\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eNo\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"","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\u003e5 9\n........#\n#........\n..##.#...\n.......#.\n....#.#.#\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eNo\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"Note","value":{"format":"HTML","content":"\u003cp\u003eFor the first example, the desired setup can be produced by \u003cspan class\u003d\"tex-span\"\u003e3\u003c/span\u003e operations, as is shown below.\u003c/p\u003e\u003ccenter\u003e \u003cimg class\u003d\"tex-graphics\" src\u003d\"CDN_BASE_URL/a25a43020729ef18abb6d53586abc186?v\u003d1726407941\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e \u003c/center\u003e\u003cp\u003eFor the second example, the desired setup cannot be produced, since in order to colour the center row, the third row and all columns must be selected in one operation, but after that no column can be selected again, hence it won\u0027t be possible to colour the other cells in the center column.\u003c/p\u003e"}}]}