{"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\u003eLittle Dima has two sequences of points with integer coordinates: sequence \u003cspan class\u003d\"tex-span\"\u003e(\u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e1\u003c/sub\u003e, 1), (\u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e2\u003c/sub\u003e, 2), ..., (\u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/sub\u003e, \u003ci\u003en\u003c/i\u003e)\u003c/span\u003e and sequence \u003cspan class\u003d\"tex-span\"\u003e(\u003ci\u003eb\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e1\u003c/sub\u003e, 1), (\u003ci\u003eb\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e2\u003c/sub\u003e, 2), ..., (\u003ci\u003eb\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/sub\u003e, \u003ci\u003en\u003c/i\u003e)\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eNow Dima wants to count the number of distinct sequences of points of length \u003cspan class\u003d\"tex-span\"\u003e2·\u003ci\u003en\u003c/i\u003e\u003c/span\u003e that can be assembled from these sequences, such that the \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ex\u003c/i\u003e\u003c/span\u003e-coordinates of points in the assembled sequence will \u003cspan class\u003d\"tex-font-style-bf\"\u003enot decrease\u003c/span\u003e. Help him with that. Note that each element of the initial sequences should be used exactly once in the assembled sequence.\u003c/p\u003e\u003cp\u003eDima considers two assembled sequences \u003cspan class\u003d\"tex-span\"\u003e(\u003ci\u003ep\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e1\u003c/sub\u003e, \u003ci\u003eq\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e1\u003c/sub\u003e), (\u003ci\u003ep\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e2\u003c/sub\u003e, \u003ci\u003eq\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e2\u003c/sub\u003e), ..., (\u003ci\u003ep\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e2·\u003ci\u003en\u003c/i\u003e\u003c/sub\u003e, \u003ci\u003eq\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e2·\u003ci\u003en\u003c/i\u003e\u003c/sub\u003e)\u003c/span\u003e and \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), ..., (\u003ci\u003ex\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e2·\u003ci\u003en\u003c/i\u003e\u003c/sub\u003e, \u003ci\u003ey\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e2·\u003ci\u003en\u003c/i\u003e\u003c/sub\u003e)\u003c/span\u003e distinct, if there is such \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e \u003cspan class\u003d\"tex-span\"\u003e(1 ≤ \u003ci\u003ei\u003c/i\u003e ≤ 2·\u003ci\u003en\u003c/i\u003e)\u003c/span\u003e, that \u003cspan class\u003d\"tex-span\"\u003e(\u003ci\u003ep\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e, \u003ci\u003eq\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e) ≠ (\u003ci\u003ex\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e, \u003ci\u003ey\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e)\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eAs the answer can be rather large, print the remainder from dividing the answer by number \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/span\u003e.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe first line contains integer \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e \u003cspan class\u003d\"tex-span\"\u003e(1 ≤ \u003ci\u003en\u003c/i\u003e ≤ 10\u003csup class\u003d\"upper-index\"\u003e5\u003c/sup\u003e)\u003c/span\u003e. The second line contains \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e integers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e1\u003c/sub\u003e, \u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e2\u003c/sub\u003e, ..., \u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e \u003cspan class\u003d\"tex-span\"\u003e(1 ≤ \u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e ≤ 10\u003csup class\u003d\"upper-index\"\u003e9\u003c/sup\u003e)\u003c/span\u003e. The third line contains \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e integers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eb\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e1\u003c/sub\u003e, \u003ci\u003eb\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e2\u003c/sub\u003e, ..., \u003ci\u003eb\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e \u003cspan class\u003d\"tex-span\"\u003e(1 ≤ \u003ci\u003eb\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e ≤ 10\u003csup class\u003d\"upper-index\"\u003e9\u003c/sup\u003e)\u003c/span\u003e. The numbers in the lines are separated by spaces.\u003c/p\u003e\u003cp\u003eThe last line contains integer \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/span\u003e \u003cspan class\u003d\"tex-span\"\u003e(2 ≤ \u003ci\u003em\u003c/i\u003e ≤ 10\u003csup class\u003d\"upper-index\"\u003e9\u003c/sup\u003e + 7)\u003c/span\u003e.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003eIn the single line print the remainder after dividing the answer to the problem by number \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/span\u003e. \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\u003e1\n1\n2\n7\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":"","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\u003e2\n1 2\n2 3\n11\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":"Note","value":{"format":"HTML","content":"\u003cp\u003eIn the first sample you can get only one sequence: \u003cspan class\u003d\"tex-span\"\u003e(1, 1), (2, 1)\u003c/span\u003e. \u003c/p\u003e\u003cp\u003eIn the second sample you can get such sequences : \u003cspan class\u003d\"tex-span\"\u003e(1, 1), (2, 2), (2, 1), (3, 2)\u003c/span\u003e; \u003cspan class\u003d\"tex-span\"\u003e(1, 1), (2, 1), (2, 2), (3, 2)\u003c/span\u003e. Thus, the answer is \u003cspan class\u003d\"tex-span\"\u003e2\u003c/span\u003e.\u003c/p\u003e"}}]}