{"trustable":true,"prependHtml":"\u003cscript\u003e\n window.katexOptions \u003d {\n delimiters: [\n {left: \u0027\\\\(\u0027, right: \u0027\\\\)\u0027, display: false},\n ]\n };\n\u003c/script\u003e\n","sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003e\nThe wheel of the history rolling forward, our king conquered a new region in a distant continent.\n\u003c/p\u003e\n\u003cp\u003e\nThere are N towns (numbered from 1 to N) in this region connected by several roads. It\u0027s confirmed that there is exact one route between any two towns. Traffic is important while controlled colonies are far away from the local country. We define the capacity C(i, j) of a road indicating it is allowed to transport at most C(i, j) goods between town i and town j if there is a road between them. And for a route between i and j, we define a value S(i, j) indicating the maximum traffic capacity between i and j which is equal to the minimum capacity of the roads on the route.\n\u003c/p\u003e\n\u003cp\u003e\nOur king wants to select a center town to restore his war-resources in which the total traffic capacities from the center to the other N - 1 towns is maximized. Now, you, the best programmer in the kingdom, should help our king to select this center.\n\u003c/p\u003e\n\u003ch4\u003eInput\u003c/h4\u003e\n\u003cp\u003e\nThere are multiple test cases.\n\u003c/p\u003e\n\u003cp\u003e\nThe first line of each case contains an integer N. (1 ≤ N ≤ 200,000)\n\u003c/p\u003e\n\u003cp\u003e\nThe next N - 1 lines each contains three integers a, b, c indicating there is a road between town a and town b whose capacity is c. (1 ≤ a, b ≤ N, 1 ≤ c ≤ 100,000)\n\u003c/p\u003e\n\u003ch4\u003eOutput\u003c/h4\u003e\n\u003cp\u003e\nFor each test case, output an integer indicating the total traffic capacity of the chosen center town.\n\u003c/p\u003e\n\u003ch4\u003eSample\u003c/h4\u003e\n\u003ctable class\u003d\"vjudge_sample\"\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 2\n2 4 1\n2 3 1\n4\n1 2 1\n2 4 1\n2 3 1\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e4\n3\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\n"}}]}