{"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\u003eVasya has recently started to learn English. Now he needs to remember how to write English letters. He isn\u0027t sure about some of them, so he decided to train a little.\u003c/p\u003e\u003cp\u003eHe found a sheet of squared paper and began writing arbitrary English letters there. In the end Vasya wrote \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e lines containing \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/span\u003e characters each. Thus, he got a rectangular \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e × \u003ci\u003em\u003c/i\u003e\u003c/span\u003e table, each cell of the table contained some English letter. Let\u0027s number the table rows from top to bottom with integers from 1 to \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e, and columns — from left to right with integers from 1 to \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eAfter that Vasya looked at the resulting rectangular table and wondered, how many subtables are there, that matches both following conditions:\u003c/p\u003e\u003cul\u003e \u003cli\u003e the subtable contains at most \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e cells with \"\u003cspan class\u003d\"tex-font-style-tt\"\u003ea\u003c/span\u003e\" letter; \u003c/li\u003e\u003cli\u003e all letters, located in all four corner cells of the subtable, are equal. \u003c/li\u003e\u003c/ul\u003e \u003cp\u003eFormally, a subtable\u0027s definition is as follows. It is defined by four integers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ex\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e1\u003c/sub\u003e, \u003ci\u003ey\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e1\u003c/sub\u003e, \u003ci\u003ex\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e2\u003c/sub\u003e, \u003ci\u003ey\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e2\u003c/sub\u003e\u003c/span\u003e such that \u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003ex\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e1\u003c/sub\u003e \u0026lt; \u003ci\u003ex\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e2\u003c/sub\u003e ≤ \u003ci\u003en\u003c/i\u003e\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003ey\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e1\u003c/sub\u003e \u0026lt; \u003ci\u003ey\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e2\u003c/sub\u003e ≤ \u003ci\u003em\u003c/i\u003e\u003c/span\u003e. Then the subtable contains all such cells \u003cspan class\u003d\"tex-span\"\u003e(\u003ci\u003ex\u003c/i\u003e, \u003ci\u003ey\u003c/i\u003e)\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ex\u003c/i\u003e\u003c/span\u003e is the row number, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ey\u003c/i\u003e\u003c/span\u003e is the column number), for which the following inequality holds \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ex\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e1\u003c/sub\u003e ≤ \u003ci\u003ex\u003c/i\u003e ≤ \u003ci\u003ex\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e2\u003c/sub\u003e, \u003ci\u003ey\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e1\u003c/sub\u003e ≤ \u003ci\u003ey\u003c/i\u003e ≤ \u003ci\u003ey\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e2\u003c/sub\u003e\u003c/span\u003e. The corner cells of the table are cells \u003cspan class\u003d\"tex-span\"\u003e(\u003ci\u003ex\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e1\u003c/sub\u003e, \u003ci\u003ey\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e1\u003c/sub\u003e)\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e(\u003ci\u003ex\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e1\u003c/sub\u003e, \u003ci\u003ey\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e2\u003c/sub\u003e)\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e(\u003ci\u003ex\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e2\u003c/sub\u003e, \u003ci\u003ey\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e1\u003c/sub\u003e)\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e(\u003ci\u003ex\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e2\u003c/sub\u003e, \u003ci\u003ey\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e2\u003c/sub\u003e)\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eVasya is already too tired after he\u0027s been writing letters to a piece of paper. That\u0027s why he asks you to count the value he is interested in.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe first line contains three integers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e, \u003ci\u003em\u003c/i\u003e, \u003ci\u003ek\u003c/i\u003e\u003c/span\u003e \u003cspan class\u003d\"tex-span\"\u003e(2 ≤ \u003ci\u003en\u003c/i\u003e, \u003ci\u003em\u003c/i\u003e ≤ 400;\u0026nbsp;0 ≤ \u003ci\u003ek\u003c/i\u003e ≤ \u003ci\u003en\u003c/i\u003e·\u003ci\u003em\u003c/i\u003e)\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eNext \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e lines contain \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/span\u003e characters each — the given table. Each character of the table is a lowercase English letter.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003ePrint a single integer — the number of required subtables.\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\u003e3 4 4\naabb\nbaab\nbaab\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e2\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\u003e4 5 1\nababa\nccaca\nccacb\ncbabc\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e1\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\u003eThere are two suitable subtables in the first sample: the first one\u0027s upper left corner is cell \u003cspan class\u003d\"tex-span\"\u003e(2, 2)\u003c/span\u003e and lower right corner is cell \u003cspan class\u003d\"tex-span\"\u003e(3, 3)\u003c/span\u003e, the second one\u0027s upper left corner is cell \u003cspan class\u003d\"tex-span\"\u003e(2, 1)\u003c/span\u003e and lower right corner is cell \u003cspan class\u003d\"tex-span\"\u003e(3, 4)\u003c/span\u003e.\u003c/p\u003e"}}]}