{"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 \u003cspan class\u003d\"tex-font-style-bf\"\u003edirected\u003c/span\u003e graph \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eG\u003c/i\u003e\u003c/span\u003e with \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e vertices and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/span\u003e arcs (\u003cspan class\u003d\"tex-font-style-bf\"\u003emultiple arcs and self-loops\u003c/span\u003e are allowed). You have to paint each vertex of the graph into one of the \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e \u003cspan class\u003d\"tex-span\"\u003e(\u003ci\u003ek\u003c/i\u003e ≤ \u003ci\u003en\u003c/i\u003e)\u003c/span\u003e colors in such way that for all arcs of the graph leading from a 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, vertex \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ev\u003c/i\u003e\u003c/span\u003e is painted with the \u003cspan class\u003d\"tex-font-style-it\"\u003enext color\u003c/span\u003e of the color used to paint vertex \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eu\u003c/i\u003e\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eThe colors are numbered cyclically \u003cspan class\u003d\"tex-span\"\u003e1\u003c/span\u003e through \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e. This means that for each color \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e \u003cspan class\u003d\"tex-span\"\u003e(\u003ci\u003ei\u003c/i\u003e \u0026lt; \u003ci\u003ek\u003c/i\u003e)\u003c/span\u003e its next color is color \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e + 1\u003c/span\u003e. In addition, the next color of color \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e is color \u003cspan class\u003d\"tex-span\"\u003e1\u003c/span\u003e. Note, that if \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e \u003d 1\u003c/span\u003e, then the next color for color \u003cspan class\u003d\"tex-span\"\u003e1\u003c/span\u003e is again color \u003cspan class\u003d\"tex-span\"\u003e1\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eYour task is to find and print the largest possible value of \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e \u003cspan class\u003d\"tex-span\"\u003e(\u003ci\u003ek\u003c/i\u003e ≤ \u003ci\u003en\u003c/i\u003e)\u003c/span\u003e such that it\u0027s possible to color \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eG\u003c/i\u003e\u003c/span\u003e as described above with \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e colors. Note that you don\u0027t necessarily use all the \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e colors (that is, for each color \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e there does not necessarily exist a vertex that is colored with color \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e).\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe first line contains two space-separated integers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003en\u003c/i\u003e, \u003ci\u003em\u003c/i\u003e ≤ 10\u003csup class\u003d\"upper-index\"\u003e5\u003c/sup\u003e\u003c/span\u003e), denoting the number of vertices and the number of arcs of the given digraph, respectively.\u003c/p\u003e\u003cp\u003eThen \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/span\u003e lines follow, each line will contain two space-separated integers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eb\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e, \u003ci\u003eb\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e ≤ \u003ci\u003en\u003c/i\u003e\u003c/span\u003e), which means that the \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e-th arc goes from vertex \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e to vertex \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eb\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eMultiple arcs and self-loops are allowed.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003ePrint a single integer — the maximum possible number of the colors that can be used to paint the digraph (i.e. \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e, as described in the problem statement). Note that the desired value of \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e must satisfy the inequality \u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003ek\u003c/i\u003e ≤ \u003ci\u003en\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\u003e4 4\n1 2\n2 1\n3 4\n4 3\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":"","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 2\n1 4\n2 5\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e5\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\u003e4 5\n1 2\n2 3\n3 1\n2 4\n4 1\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e3\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\u003e4 4\n1 1\n1 2\n2 1\n1 2\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":"Note","value":{"format":"HTML","content":"\u003cp\u003eFor the first example, with \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e \u003d 2\u003c/span\u003e, this picture depicts the two colors (arrows denote the next color of that color).\u003c/p\u003e\u003ccenter\u003e \u003cimg class\u003d\"tex-graphics\" src\u003d\"CDN_BASE_URL/10c814b215b2fea3b8572a55b23ddab8?v\u003d1715691856\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e \u003c/center\u003e\u003cp\u003eWith \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e \u003d 2\u003c/span\u003e a possible way to paint the graph is as follows.\u003c/p\u003e\u003ccenter\u003e \u003cimg class\u003d\"tex-graphics\" src\u003d\"CDN_BASE_URL/62143d222eb5ec18cf9a7b15cea7a3eb?v\u003d1715691856\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e \u003c/center\u003e\u003cp\u003eIt can be proven that no larger value for \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e exists for this test case.\u003c/p\u003e\u003cp\u003eFor the second example, here\u0027s the picture of the \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e \u003d 5\u003c/span\u003e colors.\u003c/p\u003e\u003ccenter\u003e \u003cimg class\u003d\"tex-graphics\" src\u003d\"CDN_BASE_URL/13096bf3e5be2cd0f23c244e5840c1a9?v\u003d1715691856\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e \u003c/center\u003e\u003cp\u003eA possible coloring of the graph is:\u003c/p\u003e\u003ccenter\u003e \u003cimg class\u003d\"tex-graphics\" src\u003d\"CDN_BASE_URL/f2aefbe3e02d7aaa23cb1fc77e949801?v\u003d1715691856\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e \u003c/center\u003e\u003cp\u003eFor the third example, here\u0027s the picture of the \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e \u003d 3\u003c/span\u003e colors.\u003c/p\u003e\u003ccenter\u003e \u003cimg class\u003d\"tex-graphics\" src\u003d\"CDN_BASE_URL/2cbbb52ecfc2bad89561807efb2c88c9?v\u003d1715691856\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e \u003c/center\u003e\u003cp\u003eA possible coloring of the graph is:\u003c/p\u003e\u003ccenter\u003e \u003cimg class\u003d\"tex-graphics\" src\u003d\"CDN_BASE_URL/459b96c8d60d922d8cf938a3e03f5d12?v\u003d1715691856\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e \u003c/center\u003e"}}]}