{"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$$\u0027]]\n }\n });\n\u003c/script\u003e\n\u003cscript type\u003d\"text/javascript\" async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS_HTML-full\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003eYou are given an undirected unrooted tree, i.e. a connected undirected graph without cycles.\u003c/p\u003e\u003cp\u003eYou must assign a \u003cspan class\u003d\"tex-font-style-bf\"\u003enonzero\u003c/span\u003e integer weight to each vertex so that the following is satisfied: if any vertex of the tree is removed, then each of the remaining connected components has the same sum of weights in its vertices.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe input consists of multiple test cases. The first line contains a single integer $$$t$$$ ($$$1 \\leq t \\leq 10^4$$$) — the number of test cases. Description of the test cases follows.\u003c/p\u003e\u003cp\u003eThe first line of each test case contains an integer $$$n$$$ ($$$3 \\leq n \\leq 10^5$$$) — the number of vertices of the tree.\u003c/p\u003e\u003cp\u003eThe next $$$n-1$$$ lines of each case contain each two integers $$$u, v$$$ ($$$1 \\leq u,v \\leq n$$$) denoting that there is an edge between vertices $$$u$$$ and $$$v$$$. It is guaranteed that the given edges form a tree.\u003c/p\u003e\u003cp\u003eThe sum of $$$n$$$ for all test cases is at most $$$10^5$$$.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003eFor each test case, you must output one line with $$$n$$$ space separated integers $$$a_1, a_2, \\ldots, a_n$$$, where $$$a_i$$$ is the weight assigned to vertex $$$i$$$. \u003cspan class\u003d\"tex-font-style-bf\"\u003eThe weights must satisfy $$$-10^5 \\leq a_i \\leq 10^5$$$ and $$$a_i \\neq 0$$$.\u003c/span\u003e\u003c/p\u003e\u003cp\u003eIt can be shown that there always exists a solution satisfying these constraints. If there are multiple possible solutions, output any of them.\u003c/p\u003e"}},{"title":"Examples","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e2\n5\n1 2\n1 3\n3 4\n3 5\n3\n1 2\n1 3\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e-3 5 1 2 2\n1 1 1\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"Note","value":{"format":"HTML","content":"\u003cp\u003eIn the first case, when removing vertex $$$1$$$ all remaining connected components have sum $$$5$$$ and when removing vertex $$$3$$$ all remaining connected components have sum $$$2$$$. When removing other vertices, there is only one remaining connected component so all remaining connected components have the same sum.\u003c/p\u003e"}}]}