{"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 are given a tree (a connected acyclic undirected graph) of \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e vertices. Vertices are numbered from \u003cspan class\u003d\"tex-span\"\u003e1\u003c/span\u003e to \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e and each vertex is assigned a character from \u003cspan class\u003d\"tex-font-style-tt\"\u003ea\u003c/span\u003e to \u003cspan class\u003d\"tex-font-style-tt\"\u003et\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eA path in the tree is said to be palindromic if at least one permutation of the labels in the path is a palindrome.\u003c/p\u003e\u003cp\u003eFor each vertex, output the number of palindromic paths passing through it. \u003c/p\u003e\u003cp\u003e\u003cspan class\u003d\"tex-font-style-bf\"\u003eNote:\u003c/span\u003e The path from vertex \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eu\u003c/i\u003e\u003c/span\u003e to vertex \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ev\u003c/i\u003e\u003c/span\u003e is considered to be the same as the path from vertex \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ev\u003c/i\u003e\u003c/span\u003e to vertex \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eu\u003c/i\u003e\u003c/span\u003e, and this path will be counted only once for each of the vertices it passes through.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe first line contains an integer \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e2 ≤ \u003ci\u003en\u003c/i\u003e ≤ 2·10\u003csup class\u003d\"upper-index\"\u003e5\u003c/sup\u003e\u003c/span\u003e) \u0026nbsp;— the number of vertices in the tree.\u003c/p\u003e\u003cp\u003eThe next \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e - 1\u003c/span\u003e lines each contain two integers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eu\u003c/i\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ev\u003c/i\u003e\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003eu\u003c/i\u003e, \u003ci\u003ev\u003c/i\u003e ≤ \u003ci\u003en\u003c/i\u003e, \u003ci\u003eu\u003c/i\u003e ≠ \u003ci\u003ev\u003c/i\u003e\u003c/span\u003e) denoting an edge connecting vertex \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eu\u003c/i\u003e\u003c/span\u003e and vertex \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ev\u003c/i\u003e\u003c/span\u003e. It is guaranteed that the given graph is a tree.\u003c/p\u003e\u003cp\u003eThe next line contains a string consisting of \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e lowercase characters from \u003cspan class\u003d\"tex-font-style-tt\"\u003ea\u003c/span\u003e to \u003cspan class\u003d\"tex-font-style-tt\"\u003et\u003c/span\u003e where the \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e-th (\u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003ei\u003c/i\u003e ≤ \u003ci\u003en\u003c/i\u003e\u003c/span\u003e) character is the label of vertex \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e in the tree.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003ePrint \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e integers in a single line, the \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e-th of which is the number of palindromic paths passing through vertex \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e in the tree.\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\n1 2\n2 3\n3 4\n3 5\nabcbb\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e1 3 4 3 3 \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\u003e7\n6 2\n4 3\n3 7\n5 2\n7 2\n1 4\nafefdfs\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e1 4 1 1 2 4 2 \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 case, the following paths are palindromic:\u003c/p\u003e\u003cp\u003e\u003cspan class\u003d\"tex-span\"\u003e2 - 3 - 4\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class\u003d\"tex-span\"\u003e2 - 3 - 5\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class\u003d\"tex-span\"\u003e4 - 3 - 5\u003c/span\u003e\u003c/p\u003e\u003cp\u003eAdditionally, all paths containing only one vertex are palindromic. Listed below are a few paths in the first sample that are not palindromic:\u003c/p\u003e\u003cp\u003e\u003cspan class\u003d\"tex-span\"\u003e1 - 2 - 3\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class\u003d\"tex-span\"\u003e1 - 2 - 3 - 4\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class\u003d\"tex-span\"\u003e1 - 2 - 3 - 5\u003c/span\u003e\u003c/p\u003e"}}]}