{"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$$\u0027]]\n }\n });\n\u003c/script\u003e\n\u003cscript type\u003d\"text/javascript\" async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS_HTML-full\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003eYou are given a rooted undirected tree consisting of $$$n$$$ vertices. Vertex $$$1$$$ is the root.\u003c/p\u003e\u003cp\u003eLet\u0027s denote a \u003cspan class\u003d\"tex-font-style-it\"\u003edepth array\u003c/span\u003e of vertex $$$x$$$ as an infinite sequence $$$[d_{x, 0}, d_{x, 1}, d_{x, 2}, \\dots]$$$, where $$$d_{x, i}$$$ is the number of vertices $$$y$$$ such that both conditions hold:\u003c/p\u003e\u003cul\u003e \u003cli\u003e $$$x$$$ is an ancestor of $$$y$$$; \u003c/li\u003e\u003cli\u003e the simple path from $$$x$$$ to $$$y$$$ traverses exactly $$$i$$$ edges. \u003c/li\u003e\u003c/ul\u003e\u003cp\u003eThe \u003cspan class\u003d\"tex-font-style-it\"\u003edominant index\u003c/span\u003e of a \u003cspan class\u003d\"tex-font-style-it\"\u003edepth array\u003c/span\u003e of vertex $$$x$$$ (or, shortly, the \u003cspan class\u003d\"tex-font-style-it\"\u003edominant index\u003c/span\u003e of vertex $$$x$$$) is an index $$$j$$$ such that:\u003c/p\u003e\u003cul\u003e \u003cli\u003e for every $$$k \u0026lt; j$$$, $$$d_{x, k} \u0026lt; d_{x, j}$$$; \u003c/li\u003e\u003cli\u003e for every $$$k \u0026gt; j$$$, $$$d_{x, k} \\le d_{x, j}$$$. \u003c/li\u003e\u003c/ul\u003e\u003cp\u003eFor every vertex in the tree calculate its \u003cspan class\u003d\"tex-font-style-it\"\u003edominant index\u003c/span\u003e.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe first line contains one integer $$$n$$$ ($$$1 \\le n \\le 10^6$$$) — the number of vertices in a tree.\u003c/p\u003e\u003cp\u003eThen $$$n - 1$$$ lines follow, each containing two integers $$$x$$$ and $$$y$$$ ($$$1 \\le x, y \\le n$$$, $$$x \\ne y$$$). This line denotes an edge of the tree.\u003c/p\u003e\u003cp\u003eIt is guaranteed that these edges form a tree.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003eOutput $$$n$$$ numbers. $$$i$$$-th number should be equal to the \u003cspan class\u003d\"tex-font-style-it\"\u003edominant index\u003c/span\u003e of vertex $$$i$$$.\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\n1 2\n2 3\n3 4\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e0\n0\n0\n0\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\n1 2\n1 3\n1 4\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e1\n0\n0\n0\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\n1 2\n2 3\n2 4\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e2\n1\n0\n0\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}