{"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\u0027re given a tree with \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e vertices rooted at \u003cspan class\u003d\"tex-span\"\u003e1\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eWe say that there\u0027s a \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e-ary heap of depth \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/span\u003e located at \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eu\u003c/i\u003e\u003c/span\u003e if the following holds:\u003c/p\u003e\u003cul\u003e \u003cli\u003e For \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003em\u003c/i\u003e \u003d 1\u003c/span\u003e \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eu\u003c/i\u003e\u003c/span\u003e itself is a \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e-ary heap of depth \u003cspan class\u003d\"tex-span\"\u003e1\u003c/span\u003e. \u003c/li\u003e\u003cli\u003e For \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003em\u003c/i\u003e \u0026gt; 1\u003c/span\u003e vertex \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eu\u003c/i\u003e\u003c/span\u003e is a \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e-ary heap of depth \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/span\u003e if \u003cspan class\u003d\"tex-font-style-bf\"\u003eat least\u003c/span\u003e \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e of its children are \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e-ary heaps of depth \u003cspan class\u003d\"tex-font-style-bf\"\u003eat least\u003c/span\u003e \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003em\u003c/i\u003e - 1\u003c/span\u003e. \u003c/li\u003e\u003c/ul\u003e\u003cp\u003eDenote \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003edp\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/sub\u003e(\u003ci\u003eu\u003c/i\u003e)\u003c/span\u003e as maximum depth of \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e-ary heap in the subtree of \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eu\u003c/i\u003e\u003c/span\u003e (including \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eu\u003c/i\u003e\u003c/span\u003e). Your goal is to compute \u003cimg align\u003d\"middle\" class\u003d\"tex-formula\" src\u003d\"CDN_BASE_URL/72bb344d5f3b04e27fa0de7b670a3dec?v\u003d1714167367\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe first line contains an integer \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e denoting the size of the tree \u003cspan class\u003d\"tex-span\"\u003e(2 ≤ \u003ci\u003en\u003c/i\u003e ≤ 3·10\u003csup class\u003d\"upper-index\"\u003e5\u003c/sup\u003e)\u003c/span\u003e. \u003c/p\u003e\u003cp\u003eThe next \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e - 1\u003c/span\u003e lines contain two integers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eu\u003c/i\u003e\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ev\u003c/i\u003e\u003c/span\u003e each, describing vertices connected by \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e-th edge.\u003c/p\u003e\u003cp\u003eIt\u0027s guaranteed that the given configuration forms a tree.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003eOutput the answer to the task.\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 3\n2 3\n4 3\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e21\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\n3 4\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e22\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\u003eConsider sample case one.\u003c/p\u003e\u003cp\u003eFor \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e ≥ 3\u003c/span\u003e all \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003edp\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e will be equal to \u003cspan class\u003d\"tex-span\"\u003e1\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eFor \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e \u003d 2\u003c/span\u003e \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003edp\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e is \u003cspan class\u003d\"tex-span\"\u003e2\u003c/span\u003e if \u003cimg align\u003d\"middle\" class\u003d\"tex-formula\" src\u003d\"CDN_BASE_URL/8dcb0f5d5b69a1257bf46d6652932371?v\u003d1714167367\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e and \u003cspan class\u003d\"tex-span\"\u003e1\u003c/span\u003e otherwise.\u003c/p\u003e\u003cp\u003eFor \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e \u003d 1\u003c/span\u003e \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003edp\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e values are \u003cspan class\u003d\"tex-span\"\u003e(3, 1, 2, 1)\u003c/span\u003e respectively.\u003c/p\u003e\u003cp\u003eTo sum up, \u003cspan class\u003d\"tex-span\"\u003e4·1 + 4·1 + 2·2 + 2·1 + 3 + 1 + 2 + 1 \u003d 21\u003c/span\u003e.\u003c/p\u003e"}}]}