{"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\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 type\u003d\"text/javascript\" async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS_HTML-full\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003eYou have a rectangular chocolate bar consisting of \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e × \u003ci\u003em\u003c/i\u003e\u003c/span\u003e single squares. You want to eat \u003cspan class\u003d\"tex-font-style-bf\"\u003eexactly\u003c/span\u003e \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e squares, so you may need to break the chocolate bar. \u003c/p\u003e\u003cp\u003eIn one move you can break any single rectangular piece of chocolate in two rectangular pieces. You can break only by lines between squares: horizontally or vertically. The cost of breaking is equal to square of the break length.\u003c/p\u003e\u003cp\u003eFor example, if you have a chocolate bar consisting of \u003cspan class\u003d\"tex-span\"\u003e2 × 3\u003c/span\u003e unit squares then you can break it horizontally and get two \u003cspan class\u003d\"tex-span\"\u003e1 × 3\u003c/span\u003e pieces (the cost of such breaking is \u003cspan class\u003d\"tex-span\"\u003e3\u003csup class\u003d\"upper-index\"\u003e2\u003c/sup\u003e \u003d 9\u003c/span\u003e), or you can break it vertically in two ways and get two pieces: \u003cspan class\u003d\"tex-span\"\u003e2 × 1\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e2 × 2\u003c/span\u003e (the cost of such breaking is \u003cspan class\u003d\"tex-span\"\u003e2\u003csup class\u003d\"upper-index\"\u003e2\u003c/sup\u003e \u003d 4\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eFor several given values \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e find the minimum total cost of breaking. You can eat exactly \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e squares of chocolate if after all operations of breaking there is a set of rectangular pieces of chocolate with the total size equal to \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e squares. The remaining \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e·\u003ci\u003em\u003c/i\u003e - \u003ci\u003ek\u003c/i\u003e\u003c/span\u003e squares are not necessarily form a single rectangular piece.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe first line of the input contains a single integer \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003et\u003c/i\u003e\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003et\u003c/i\u003e ≤ 40910\u003c/span\u003e)\u0026nbsp;— the number of values \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e to process.\u003c/p\u003e\u003cp\u003eEach of the next \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003et\u003c/i\u003e\u003c/span\u003e lines contains three integers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003en\u003c/i\u003e, \u003ci\u003em\u003c/i\u003e ≤ 30, 1 ≤ \u003ci\u003ek\u003c/i\u003e ≤ \u003ci\u003emin\u003c/i\u003e(\u003ci\u003en\u003c/i\u003e·\u003ci\u003em\u003c/i\u003e, 50)\u003c/span\u003e)\u0026nbsp;— the dimensions of the chocolate bar and the number of squares you want to eat respectively.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003eFor each \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e print the minimum total cost needed to break the chocolate bar, in order to make it possible to eat exactly \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e squares.\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\u003e4\n2 2 1\n2 2 3\n2 2 2\n2 2 4\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e5\n5\n4\n0\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\u003eIn the first query of the sample one needs to perform two breaks:\u003c/p\u003e\u003cul\u003e \u003cli\u003e to split \u003cspan class\u003d\"tex-span\"\u003e2 × 2\u003c/span\u003e bar into two pieces of \u003cspan class\u003d\"tex-span\"\u003e2 × 1\u003c/span\u003e (cost is \u003cspan class\u003d\"tex-span\"\u003e2\u003csup class\u003d\"upper-index\"\u003e2\u003c/sup\u003e \u003d 4\u003c/span\u003e), \u003c/li\u003e\u003cli\u003e to split the resulting \u003cspan class\u003d\"tex-span\"\u003e2 × 1\u003c/span\u003e into two \u003cspan class\u003d\"tex-span\"\u003e1 × 1\u003c/span\u003e pieces (cost is \u003cspan class\u003d\"tex-span\"\u003e1\u003csup class\u003d\"upper-index\"\u003e2\u003c/sup\u003e \u003d 1\u003c/span\u003e). \u003c/li\u003e\u003c/ul\u003e\u003cp\u003eIn the second query of the sample one wants to eat \u003cspan class\u003d\"tex-span\"\u003e3\u003c/span\u003e unit squares. One can use exactly the same strategy as in the first query of the sample.\u003c/p\u003e"}}]}