{"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\u003eAlice got tired of playing the tag game by the usual rules so she offered Bob a little modification to it. Now the game should be played on an undirected rooted tree of \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e vertices. Vertex \u003cspan class\u003d\"tex-font-style-tt\"\u003e1\u003c/span\u003e is the root of the tree.\u003c/p\u003e\u003cp\u003eAlice starts at vertex \u003cspan class\u003d\"tex-font-style-tt\"\u003e1\u003c/span\u003e and Bob starts at vertex \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ex\u003c/i\u003e\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ex\u003c/i\u003e ≠ 1\u003c/span\u003e). The moves are made in turns, Bob goes first. In one move one can either stay at the current vertex or travel to the neighbouring one.\u003c/p\u003e\u003cp\u003eThe game ends when Alice goes to the same vertex where Bob is standing. Alice wants to minimize the total number of moves and Bob wants to maximize it.\u003c/p\u003e\u003cp\u003eYou should write a program which will determine how many moves will the game last.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe first line contains two integer numbers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ex\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, \u003cspan class\u003d\"tex-span\"\u003e2 ≤ \u003ci\u003ex\u003c/i\u003e ≤ \u003ci\u003en\u003c/i\u003e\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eEach of the next \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e - 1\u003c/span\u003e lines contains two integer numbers \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\u003c/span\u003e) — edges of the tree. It is guaranteed that the edges form a valid tree.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003ePrint the total number of moves Alice and Bob will make.\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 3\n1 2\n2 3\n2 4\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e4\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 2\n2 3\n3 4\n2 5\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e6\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 the tree looks like this:\u003c/p\u003e\u003ccenter\u003e \u003cimg class\u003d\"tex-graphics\" src\u003d\"CDN_BASE_URL/62ed8561a039ddede670ce86674e6c54?v\u003d1715642009\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e \u003c/center\u003e\u003cp\u003eThe red vertex is Alice\u0027s starting position, the blue one is Bob\u0027s. Bob will make the game run the longest by standing at the vertex \u003cspan class\u003d\"tex-font-style-tt\"\u003e3\u003c/span\u003e during all the game. So here are the moves:\u003c/p\u003e\u003cp\u003e\u003cspan class\u003d\"tex-font-style-bf\"\u003eB\u003c/span\u003e: stay at vertex \u003cspan class\u003d\"tex-font-style-tt\"\u003e3\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class\u003d\"tex-font-style-bf\"\u003eA\u003c/span\u003e: go to vertex \u003cspan class\u003d\"tex-font-style-tt\"\u003e2\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class\u003d\"tex-font-style-bf\"\u003eB\u003c/span\u003e: stay at vertex \u003cspan class\u003d\"tex-font-style-tt\"\u003e3\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class\u003d\"tex-font-style-bf\"\u003eA\u003c/span\u003e: go to vertex \u003cspan class\u003d\"tex-font-style-tt\"\u003e3\u003c/span\u003e\u003c/p\u003e\u003cp\u003eIn the second example the tree looks like this:\u003c/p\u003e\u003ccenter\u003e \u003cimg class\u003d\"tex-graphics\" src\u003d\"CDN_BASE_URL/6710684550e6a9867defe3ad61795a67?v\u003d1715642009\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e \u003c/center\u003e\u003cp\u003eThe moves in the optimal strategy are:\u003c/p\u003e\u003cp\u003e\u003cspan class\u003d\"tex-font-style-bf\"\u003eB\u003c/span\u003e: go to vertex \u003cspan class\u003d\"tex-font-style-tt\"\u003e3\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class\u003d\"tex-font-style-bf\"\u003eA\u003c/span\u003e: go to vertex \u003cspan class\u003d\"tex-font-style-tt\"\u003e2\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class\u003d\"tex-font-style-bf\"\u003eB\u003c/span\u003e: go to vertex \u003cspan class\u003d\"tex-font-style-tt\"\u003e4\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class\u003d\"tex-font-style-bf\"\u003eA\u003c/span\u003e: go to vertex \u003cspan class\u003d\"tex-font-style-tt\"\u003e3\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class\u003d\"tex-font-style-bf\"\u003eB\u003c/span\u003e: stay at vertex \u003cspan class\u003d\"tex-font-style-tt\"\u003e4\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class\u003d\"tex-font-style-bf\"\u003eA\u003c/span\u003e: go to vertex \u003cspan class\u003d\"tex-font-style-tt\"\u003e4\u003c/span\u003e\u003c/p\u003e"}}]}