{"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\n\u003cscript\u003e\n window.katexOptions \u003d {\n delimiters: [\n {left: \u0027$$$$$$\u0027, right: \u0027$$$$$$\u0027, display: true},\n {left: \u0027$$$\u0027, right: \u0027$$$\u0027, display: false},\n {left: \u0027$$\u0027, right: \u0027$$\u0027, display: true},\n {left: \u0027$\u0027, right: \u0027$\u0027, display: false}\n ]\n };\n\u003c/script\u003e\n","sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003eBob\u0027s new favourite toy is a rooted tree that consists of \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e vertices numbered from 1 to \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e. The number of the root vertex is 1. The tree has \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003el\u003c/i\u003e\u003c/span\u003e leafs (the root is not considered to be a leaf). Each leaf of the tree has an integer written in it.\u003c/p\u003e\u003cp\u003eThis birthday Bob received \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e - \u003ci\u003el\u003c/i\u003e\u003c/span\u003e stickers as a gift: \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e of them are labelled \"\u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003emin\u003c/i\u003e\u003c/span\u003e\", and the other \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e - \u003ci\u003el\u003c/i\u003e - \u003ci\u003ek\u003c/i\u003e\u003c/span\u003e are labelled \"\u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003emax\u003c/i\u003e\u003c/span\u003e\". Bob has decided to place the stickers on the internal vertices of the tree, a single sticker on each internal vertex.\u003c/p\u003e\u003cp\u003eOnce he has placed all the stickers on the tree, Bob would like to calculate a function \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ef\u003c/i\u003e\u003c/span\u003e for each vertex \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ev\u003c/i\u003e\u003c/span\u003e of the tree in the following fashion: \u003c/p\u003e\u003cul\u003e \u003cli\u003e If \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ev\u003c/i\u003e\u003c/span\u003e is a leaf, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ef\u003c/i\u003e(\u003ci\u003ev\u003c/i\u003e)\u003c/span\u003e is equal to the integer that is written in \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ev\u003c/i\u003e\u003c/span\u003e. \u003c/li\u003e\u003cli\u003e If \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ev\u003c/i\u003e\u003c/span\u003e has a \"\u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003emin\u003c/i\u003e\u003c/span\u003e\" sticker, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ef\u003c/i\u003e(\u003ci\u003ev\u003c/i\u003e)\u003c/span\u003e is equal to the minimum value of \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ef\u003c/i\u003e(\u003ci\u003eu\u003c/i\u003e)\u003c/span\u003e, where \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eu\u003c/i\u003e\u003c/span\u003e is any child of \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ev\u003c/i\u003e\u003c/span\u003e. \u003c/li\u003e\u003cli\u003e If \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ev\u003c/i\u003e\u003c/span\u003e has a \"\u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003emax\u003c/i\u003e\u003c/span\u003e\" sticker, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ef\u003c/i\u003e(\u003ci\u003ev\u003c/i\u003e)\u003c/span\u003e is equal to the maximum value of \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ef\u003c/i\u003e(\u003ci\u003eu\u003c/i\u003e)\u003c/span\u003e, where \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eu\u003c/i\u003e\u003c/span\u003e is any child of \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ev\u003c/i\u003e\u003c/span\u003e. \u003c/li\u003e\u003c/ul\u003e\u003cp\u003eBob isn\u0027t yet sure how to place his stickers on the tree, but he is interested in the value of \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ef\u003c/i\u003e\u003c/span\u003e in the root vertex. Given the tree and the stickers, help Bob calculate the minimum and the maximum possible value of \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ef\u003c/i\u003e(1)\u003c/span\u003e!\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe first line contains two space-separated integers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e2 ≤ \u003ci\u003en\u003c/i\u003e ≤ 10\u003csup class\u003d\"upper-index\"\u003e5\u003c/sup\u003e\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e0 ≤ \u003ci\u003ek\u003c/i\u003e ≤ \u003ci\u003en\u003c/i\u003e\u003c/span\u003e). The second line contains \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e - 1\u003c/span\u003e space-separated integer numbers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ep\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e2\u003c/sub\u003e, \u003ci\u003ep\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e3\u003c/sub\u003e, ..., \u003ci\u003ep\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003ep\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e ≤ \u003ci\u003en\u003c/i\u003e\u003c/span\u003e). The number \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ep\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e denotes the parent of the vertex numbered \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e. The third line contains \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e space-separated integer numbers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e1\u003c/sub\u003e, \u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e2\u003c/sub\u003e, ..., \u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e0 ≤ \u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e ≤ 10\u003csup class\u003d\"upper-index\"\u003e9\u003c/sup\u003e\u003c/span\u003e). If the vertex \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e is a leaf, then \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e is the number written in that vertex. Otherwise \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e will be equal to 0.\u003c/p\u003e\u003cp\u003eIt is guaranteed that the given graph will be a tree. It is guaranteed that \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e + \u003ci\u003el\u003c/i\u003e ≤ \u003ci\u003en\u003c/i\u003e\u003c/span\u003e.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003eIn a single line output two integers separated by a space\u0026nbsp;— the minimum and the maximum possible value of \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ef\u003c/i\u003e(1)\u003c/span\u003e.\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\u003e6 1\n1 1 2 2 3\n0 0 0 1 3 2\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e2 3\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\u003eA \u003cspan class\u003d\"tex-font-style-underline\"\u003etree\u003c/span\u003e is a connected graph that has no cycles. A rooted tree is a tree with one vertex being the \u003cspan class\u003d\"tex-font-style-underline\"\u003eroot vertex\u003c/span\u003e. In a rooted tree, a vertex \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eu\u003c/i\u003e\u003c/span\u003e is a \u003cspan class\u003d\"tex-font-style-underline\"\u003echild\u003c/span\u003e of \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ev\u003c/i\u003e\u003c/span\u003e if and only if there is an edge between \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ev\u003c/i\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eu\u003c/i\u003e\u003c/span\u003e, and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eu\u003c/i\u003e\u003c/span\u003e does not belong to the path that connects the root vertex with \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ev\u003c/i\u003e\u003c/span\u003e. The vertex \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ev\u003c/i\u003e\u003c/span\u003e then is called the \u003cspan class\u003d\"tex-font-style-underline\"\u003eparent\u003c/span\u003e of \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eu\u003c/i\u003e\u003c/span\u003e. A vertex of a rooted tree is called a \u003cspan class\u003d\"tex-font-style-underline\"\u003eleaf\u003c/span\u003e if and only if it has no children. Otherwise the vertex is called an \u003cspan class\u003d\"tex-font-style-underline\"\u003einternal vertex\u003c/span\u003e.\u003c/p\u003e"}}]}