{"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$$\u0027]]\n }\n });\n\u003c/script\u003e\n\u003cscript type\u003d\"text/javascript\" async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS_HTML-full\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003eYou are given a connected undirected graph consisting of $$$n$$$ vertices and $$$m$$$ edges. There are no self-loops or multiple edges in the given graph.\u003c/p\u003e\u003cp\u003eYou have to direct its edges in such a way that the obtained directed graph does not contain any paths of length two or greater (where the length of path is denoted as the number of traversed edges).\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe first line contains two integer numbers $$$n$$$ and $$$m$$$ ($$$2 \\le n \\le 2 \\cdot 10^5$$$, $$$n - 1 \\le m \\le 2 \\cdot 10^5$$$) — the number of vertices and edges, respectively.\u003c/p\u003e\u003cp\u003eThe following $$$m$$$ lines contain edges: edge $$$i$$$ is given as a pair of vertices $$$u_i$$$, $$$v_i$$$ ($$$1 \\le u_i, v_i \\le n$$$, $$$u_i \\ne v_i$$$). There are no multiple edges in the given graph, i. e. for each pair ($$$u_i, v_i$$$) there are no other pairs ($$$u_i, v_i$$$) and ($$$v_i, u_i$$$) in the list of edges. It is also guaranteed that the given graph is connected (there is a path between any pair of vertex in the given graph).\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003eIf it is impossible to direct edges of the given graph in such a way that the obtained directed graph does not contain paths of length at least two, print \"\u003cspan class\u003d\"tex-font-style-tt\"\u003eNO\u003c/span\u003e\" in the first line.\u003c/p\u003e\u003cp\u003eOtherwise print \"\u003cspan class\u003d\"tex-font-style-tt\"\u003eYES\u003c/span\u003e\" in the first line, and then print \u003cspan class\u003d\"tex-font-style-bf\"\u003eany\u003c/span\u003e suitable orientation of edges: a binary string (the string consisting only of \u0027\u003cspan class\u003d\"tex-font-style-tt\"\u003e0\u003c/span\u003e\u0027 and \u0027\u003cspan class\u003d\"tex-font-style-tt\"\u003e1\u003c/span\u003e\u0027) of length $$$m$$$. The $$$i$$$-th element of this string should be \u0027\u003cspan class\u003d\"tex-font-style-tt\"\u003e0\u003c/span\u003e\u0027 if the $$$i$$$-th edge of the graph should be directed from $$$u_i$$$ to $$$v_i$$$, and \u0027\u003cspan class\u003d\"tex-font-style-tt\"\u003e1\u003c/span\u003e\u0027 otherwise. Edges are numbered in the order they are given in the input.\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\u003e6 5\n1 5\n2 1\n1 4\n3 1\n6 1\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eYES\n10100\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\u003eThe picture corresponding to the first example: \u003cimg class\u003d\"tex-graphics\" src\u003d\"CDN_BASE_URL/b00bc3f1bce931f46bb3ce76e05266ea?v\u003d1715377236\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e\u003c/p\u003e\u003cp\u003eAnd one of possible answers: \u003cimg class\u003d\"tex-graphics\" src\u003d\"CDN_BASE_URL/e1c2d13d51cb68c6fe1d30c86c0c3d89?v\u003d1715377236\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e\u003c/p\u003e"}}]}