{"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$$\u0027]]\n }\n });\n\u003c/script\u003e\n\u003cscript type\u003d\"text/javascript\" async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS_HTML-full\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003eA tree is an undirected graph with exactly one simple path between each pair of vertices. We call a set of simple paths $$$k$$$-valid if each vertex of the tree belongs to no more than one of these paths (including endpoints) and each path consists of exactly $$$k$$$ vertices.\u003c/p\u003e\u003cp\u003eYou are given a tree with $$$n$$$ vertices. For each $$$k$$$ from $$$1$$$ to $$$n$$$ inclusive find what is the maximum possible size of a $$$k$$$-valid set of simple paths.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe first line of the input contains a single integer $$$n$$$ ($$$2 \\le n \\le 100\\,000$$$)\u0026nbsp;— the number of vertices in the tree.\u003c/p\u003e\u003cp\u003eThen following $$$n - 1$$$ lines describe the tree, each of them contains two integers $$$v$$$, $$$u$$$ ($$$1 \\le v, u \\le n$$$)\u0026nbsp;— endpoints of the corresponding edge.\u003c/p\u003e\u003cp\u003eIt is guaranteed, that the given graph is a tree. \u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003eOutput $$$n$$$ numbers, the $$$i$$$-th of which is the maximum possible number of paths in an $$$i$$$-valid set of paths.\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\u003e7\n1 2\n2 3\n3 4\n4 5\n5 6\n6 7\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e7\n3\n2\n1\n1\n1\n1\n\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\u003e6\n1 2\n2 3\n2 4\n1 5\n5 6\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e6\n2\n2\n1\n1\n0\n\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\u003eOne way to achieve the optimal number of paths for the second sample is illustrated in the following picture:\u003c/p\u003e\u003cp\u003e\u003cimg class\u003d\"tex-graphics\" src\u003d\"CDN_BASE_URL/5a4b448359fd6aa9e455c0c9d9789f5d?v\u003d1714792737\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e\u003c/p\u003e"}}]}