{"trustable":false,"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\n\u003cscript\u003e\n window.katexOptions \u003d {\n delimiters: [\n {left: \u0027$$$$$$\u0027, right: \u0027$$$$$$\u0027, display: true},\n {left: \u0027$$$\u0027, right: \u0027$$$\u0027, display: false},\n {left: \u0027$$\u0027, right: \u0027$$\u0027, display: true},\n {left: \u0027$\u0027, right: \u0027$\u0027, display: false}\n ]\n };\n\u003c/script\u003e\n","sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003eThere is a graph consists of \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e nodes connected with \u003cspan class\u003d\"tex-span\"\u003e(\u003ci\u003en\u003c/i\u003e - 1)\u003c/span\u003e edges. Nasif decided to color each node. The colors are described by positive integers, starting from \u003cspan class\u003d\"tex-span\"\u003e1\u003c/span\u003e. Nasif wants to choose the colors in a special way. More precisely, he wants to use such colors that if \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ea\u003c/i\u003e\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eb\u003c/i\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ec\u003c/i\u003e\u003c/span\u003e are distinct nodes that \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 have a direct edge between them, and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eb\u003c/i\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ec\u003c/i\u003e\u003c/span\u003e have a direct edge between them, then colors on these three nodes are distinct.\u003c/p\u003e\n\u003cp\u003eNasif wants to use as little different colors as possible. Help him to choose the colors!\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe first line contains single integer \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e3 ≤ \u003ci\u003en\u003c/i\u003e ≤ 2·10\u003csup class\u003d\"upper-index\"\u003e5\u003c/sup\u003e\u003c/span\u003e)\u0026nbsp;— the number of nodes.\u003c/p\u003e\n\u003cp\u003eEach of the next \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\u003ex\u003c/i\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ey\u003c/i\u003e\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003ex\u003c/i\u003e, \u003ci\u003ey\u003c/i\u003e ≤ \u003ci\u003en\u003c/i\u003e\u003c/span\u003e)\u0026nbsp;— the indices of two nodes connected by a edges.\u003c/p\u003e\n\u003cp\u003eIt is guaranteed that any node is reachable from any other using the edges.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003eIn the first line print single integer \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e\u0026nbsp;— the minimum number of colors.\u003c/p\u003e\n\u003cp\u003eIn the second line print \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e integers, the \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e-th of them should be equal to the balloon color on the \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e-th node. Each of these numbers should be within range from \u003cspan class\u003d\"tex-span\"\u003e1\u003c/span\u003e to \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e.\u003c/p\u003e"}},{"title":"Examples","value":{"format":"HTML","content":"\u003cdiv class\u003d\"sample-test\"\u003e\n \u003cdiv class\u003d\"input\"\u003e\n \u003cdiv class\u003d\"title\"\u003e\n Input\n \u003c/div\u003e\n \u003cpre\u003e3\u003cbr\u003e2 3\u003cbr\u003e1 3\u003cbr\u003e\u003c/pre\u003e\n \u003c/div\u003e\n \u003cdiv class\u003d\"output\"\u003e\n \u003cdiv class\u003d\"title\"\u003e\n Output\n \u003c/div\u003e\n \u003cpre\u003e3\u003cbr\u003e1 3 2 \u003c/pre\u003e\n \u003c/div\u003e\n \u003cdiv class\u003d\"input\"\u003e\n \u003cdiv class\u003d\"title\"\u003e\n Input\n \u003c/div\u003e\n \u003cpre\u003e5\u003cbr\u003e2 3\u003cbr\u003e5 3\u003cbr\u003e4 3\u003cbr\u003e1 3\u003cbr\u003e\u003c/pre\u003e\n \u003c/div\u003e\n \u003cdiv class\u003d\"output\"\u003e\n \u003cdiv class\u003d\"title\"\u003e\n Output\n \u003c/div\u003e\n \u003cpre\u003e5\u003cbr\u003e1 3 2 5 4 \u003c/pre\u003e\n \u003c/div\u003e\n \u003cdiv class\u003d\"input\"\u003e\n \u003cdiv class\u003d\"title\"\u003e\n Input\n \u003c/div\u003e\n \u003cpre\u003e5\u003cbr\u003e2 1\u003cbr\u003e3 2\u003cbr\u003e4 3\u003cbr\u003e5 4\u003cbr\u003e\u003c/pre\u003e\n \u003c/div\u003e\n \u003cdiv class\u003d\"output\"\u003e\n \u003cdiv class\u003d\"title\"\u003e\n Output\n \u003c/div\u003e\n \u003cpre\u003e3\u003cbr\u003e1 2 3 1 2 \u003c/pre\u003e\n \u003c/div\u003e\n\u003c/div\u003e"}},{"title":"Note","value":{"format":"HTML","content":""}}]}