{"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\"\u003eTonyfang is a clever student. The teacher is teaching he and other students \"bao\u0027sou\".\u003cbr\u003eThe teacher drew an n*n matrix with zero or one filled in every grid, he wanted to judge if there is a rectangle with 1 filled in each of 4 corners.\u003cbr\u003eHe wrote the following pseudocode and claim it runs in $O(n^2)$:\u003cbr\u003e\u003cbr\u003e\u003cpre\u003elet count be a 2d array filled with 0s\u003cbr\u003eiterate through all 1s in the matrix:\u003cbr\u003e suppose this 1 lies in grid(x,y)\u003cbr\u003e iterate every row r:\u003cbr\u003e if grid(r,y)\u003d1:\u003cbr\u003e ++count[min(r,x)][max(r,x)]\u003cbr\u003e if count[min(r,x)][max(r,x)]\u0026gt;1:\u003cbr\u003e claim there is a rectangle satisfying the condition\u003cbr\u003eclaim there isn\u0027t any rectangle satisfying the condition\u003c/pre\u003e\u003cbr\u003e\u003cbr\u003eAs a clever student, Tonyfang found the complexity is obviously wrong. But he is too lazy to generate datas, so now it\u0027s your turn.\u003cbr\u003ePlease hack the above code with an n*n matrix filled with zero or one without any rectangle with 1 filled in all 4 corners.\u003cbr\u003eYour constructed matrix should satisfy $1 \\leq n \\leq 2000$ and number of 1s not less than 85000.\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"Nothing.\u003cbr\u003e"}},{"title":"Output","value":{"format":"HTML","content":"The first line should be one positive integer n where $1 \\leq n \\leq 2000$.\u003cbr\u003e\u003cbr\u003en lines following, each line contains only a string of length n consisted of zero and one.\u003cbr\u003e"}},{"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\u003e(nothing here)\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e3\r\n010\r\n000\r\n000\r\n(obviously it\u0027s not a correct output, it\u0027s just used for showing output format)\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}