{"trustable":true,"prependHtml":"\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 async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS-MML_HTMLorMML\" type\u003d\"text/javascript\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cdiv class\u003d\"panel_content\"\u003eLittle Q is fighting against scary monsters in the game ``Monster Hunter\u0027\u0027. The battlefield consists of $n$ intersections, labeled by $1,2,...,n$, connected by $n-1$ bidirectional roads. Little Q is now at the $1$-th intersection, with $X$ units of health point(HP).\u003cbr\u003eThere is a monster at each intersection except $1$. When Little Q moves to the $k$-th intersection, he must battle with the monster at the $k$-th intersection. During the battle, he will lose $a_i$ units of HP. And when he finally beats the monster, he will be awarded $b_i$ units of HP. Note that when HP becomes negative($\u0026lt;0$), the game will over, so never let this happen. There is no need to have a battle at the same intersection twice because monsters do not have extra life.\u003cbr\u003eWhen all monsters are cleared, Little Q will win the game. Please write a program to compute the minimum initial HP that can lead to victory.\u003cbr\u003e\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"The first line of the input contains an integer $T(1\\leq T\\leq2000)$, denoting the number of test cases.\u003cbr\u003eIn each test case, there is one integer $n(2\\leq n\\leq 100000)$ in the first line, denoting the number of intersections.\u003cbr\u003eFor the next $n-1$ lines, each line contains two integers $a_i,b_i(0\\leq a_i,b_i\\leq 10^9)$, describing monsters at the $2,3,...,n$-th intersection.\u003cbr\u003eFor the next $n-1$ lines, each line contains two integers $u$ and $v$, denoting a bidirectional road between the $u$-th intersection and the $v$-th intersection.\u003cbr\u003eIt is guaranteed that $\\sum n\\leq 10^6$.\u003cbr\u003e"}},{"title":"Output","value":{"format":"HTML","content":"For each test case, print a single line containing an integer, denoting the minimum initial HP.\u003cbr\u003e"}},{"title":"Sample","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\u003e1\t\r\n4\t\r\n2 6\r\n5 4\r\n6 2\r\n1 2\r\n2 3\r\n3 4\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e3\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}