{"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\u003eNow Fox Ciel becomes a commander of Tree Land. Tree Land, like its name said, has \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e cities connected by \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e - 1\u003c/span\u003e undirected roads, and for any two cities there always exists a path between them.\u003c/p\u003e\u003cp\u003eFox Ciel needs to assign an officer to each city. Each officer has a rank — a letter from \u0027\u003cspan class\u003d\"tex-font-style-tt\"\u003eA\u003c/span\u003e\u0027 to \u0027\u003cspan class\u003d\"tex-font-style-tt\"\u003eZ\u003c/span\u003e\u0027. So there will be 26 different ranks, and \u0027\u003cspan class\u003d\"tex-font-style-tt\"\u003eA\u003c/span\u003e\u0027 is the topmost, so \u0027\u003cspan class\u003d\"tex-font-style-tt\"\u003eZ\u003c/span\u003e\u0027 is the bottommost.\u003c/p\u003e\u003cp\u003eThere are enough officers of each rank. But there is a special rule must obey: if \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ex\u003c/i\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ey\u003c/i\u003e\u003c/span\u003e are two distinct cities and their officers have the same rank, then on the simple path between \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ex\u003c/i\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ey\u003c/i\u003e\u003c/span\u003e there must be a city \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ez\u003c/i\u003e\u003c/span\u003e that has an officer with higher rank. The rule guarantee that a communications between same rank officers will be monitored by higher rank officer.\u003c/p\u003e\u003cp\u003eHelp Ciel to make a valid plan, and if it\u0027s impossible, output \"\u003cspan class\u003d\"tex-font-style-tt\"\u003eImpossible!\u003c/span\u003e\".\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 ≤ 10\u003csup class\u003d\"upper-index\"\u003e5\u003c/sup\u003e\u003c/span\u003e) — the number of cities in Tree Land.\u003c/p\u003e\u003cp\u003eEach of the following \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e - 1\u003c/span\u003e lines contains two integers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ea\u003c/i\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eb\u003c/i\u003e\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003ea\u003c/i\u003e, \u003ci\u003eb\u003c/i\u003e ≤ \u003ci\u003en\u003c/i\u003e, \u003ci\u003ea\u003c/i\u003e ≠ \u003ci\u003eb\u003c/i\u003e\u003c/span\u003e) — they mean that there will be an undirected road between \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ea\u003c/i\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eb\u003c/i\u003e\u003c/span\u003e. Consider all the cities are numbered from 1 to \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eIt guaranteed that the given graph will be a tree.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003eIf there is a valid plane, output \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e space-separated characters in a line — \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e-th character is the rank of officer in the city with number \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e. \u003c/p\u003e\u003cp\u003eOtherwise output \"\u003cspan class\u003d\"tex-font-style-tt\"\u003eImpossible!\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\u003e4\n1 2\n1 3\n1 4\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eA B B B\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\u003e10\n1 2\n2 3\n3 4\n4 5\n5 6\n6 7\n7 8\n8 9\n9 10\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eD C B A D C B D C D\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 example, for any two officers of rank \u0027\u003cspan class\u003d\"tex-font-style-tt\"\u003eB\u003c/span\u003e\u0027, an officer with rank \u0027\u003cspan class\u003d\"tex-font-style-tt\"\u003eA\u003c/span\u003e\u0027 will be on the path between them. So it is a valid solution.\u003c/p\u003e"}}]}