{"trustable":true,"prependHtml":"\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 async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS-MML_HTMLorMML\" type\u003d\"text/javascript\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cdiv class\u003d\"panel_content\"\u003eGiven a simple unweighted graph $G$ (an undirected graph without self-loops or multiple edges) with $n$ nodes and $m$ edges. Let $T$ be a spanning tree of $G$. We say that a cut in G two-respects $T$ if and only if it \u003cb\u003ecuts just two edges of\u003c/b\u003e $T$.\u003cbr\u003e\u003cbr\u003eSince love needs good faith and hypocrisy return for only grief, you should find the minimum cut of graph $G$ two-respecting given spanning tree $T$. To simplify the problem, we guarantee that for each edge $(u,v)\\not\\in T$ in graph $G$, the unique path in $T$ between $u$ and $v$ must pass through the node $1$.\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"The input contains several test cases.\u003cbr\u003eThe first line of the input is a single integer $t~(1\\le t\\le 25)$ which is the number of test cases.\u003cbr\u003eThen $t$ test cases follow.\u003cbr\u003e\u003cbr\u003eEach test case contains several lines.\u003cbr\u003eThe first line contains the integer $n~(3\\le n\\le 20000)$ and the integer $m~(n-1\\le m\\le 100000)$.\u003cbr\u003eThe following $n-1$ lines describe the spanning tree $T$ and each of them contains two integers $u$ and $v$ corresponding to an edge.\u003cbr\u003eThe following $m-n+1$ lines describe the undirected graph $G$ and each of them contains two integers $u$ and $v$ corresponding to an edge which is no in the spanning tree.\u003cbr\u003e\u003cbr\u003eThe sum of $m$ for all test cases would not be larger than $500000$."}},{"title":"Output","value":{"format":"HTML","content":"For each test case, you should output the minimum cut of graph $G$ two-respecting given spanning tree $T$."}},{"title":"Sample","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\u003e2\r\n\r\n8 14\r\n1 2\r\n2 3\r\n1 4\r\n4 5\r\n1 6\r\n6 7\r\n6 8\r\n3 4\r\n2 5\r\n5 7\r\n1 7\r\n2 6\r\n2 8\r\n3 8\r\n\r\n4 6\r\n1 2\r\n1 3\r\n1 4\r\n2 3\r\n3 4\r\n4 2\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eCase #1: 3\r\nCase #2: 4\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}