Parsa's Humongous Tree

题意翻译

多组数据 ($t$ 组) 给你大小为 $n$ 的一棵树，$i$ 号节点有权值范围 $[l_i,r_i]$，让你对每个节点赋予一个权值 $a_i$，使得每个节点权值都在规定的范围里并且对于每条边 $(u,v)$，$\sum{|a_u-a_v|}$ 最大，并求出这个最大值。 $2\le n\le 10^5,\sum n\le 2\times 10^5,1\le l_i\le r_i\le10^9$，时限 $1\text s$，空限 $256\text{MB}$ Translated by @[ZCPB](https://www.luogu.com.cn/user/80614)

题目描述

Parsa has a humongous tree on $ n $ vertices. On each vertex $ v $ he has written two integers $ l_v $ and $ r_v $ . To make Parsa's tree look even more majestic, Nima wants to assign a number $ a_v $ ( $ l_v \le a_v \le r_v $ ) to each vertex $ v $ such that the beauty of Parsa's tree is maximized. Nima's sense of the beauty is rather bizarre. He defines the beauty of the tree as the sum of $ |a_u - a_v| $ over all edges $ (u, v) $ of the tree. Since Parsa's tree is too large, Nima can't maximize its beauty on his own. Your task is to find the maximum possible beauty for Parsa's tree.

输入输出格式

输入格式

The first line contains an integer $ t $ $ (1\le t\le 250) $ — the number of test cases. The description of the test cases follows. The first line of each test case contains a single integer $ n $ $ (2\le n\le 10^5) $ — the number of vertices in Parsa's tree. The $ i $ -th of the following $ n $ lines contains two integers $ l_i $ and $ r_i $ $ (1 \le l_i \le r_i \le 10^9) $ . Each of the next $ n-1 $ lines contains two integers $ u $ and $ v $ $ (1 \le u , v \le n, u\neq v) $ meaning that there is an edge between the vertices $ u $ and $ v $ in Parsa's tree. It is guaranteed that the given graph is a tree. It is guaranteed that the sum of $ n $ over all test cases doesn't exceed $ 2 \cdot 10^5 $ .

输出格式

For each test case print the maximum possible beauty for Parsa's tree.

输入输出样例

输入样例 #1

3
2
1 6
3 8
1 2
3
1 3
4 6
7 9
1 2
2 3
6
3 14
12 20
12 19
2 12
10 17
3 17
3 2
6 5
1 5
2 6
4 6

输出样例 #1

7
8
62

说明

The trees in the example: In the first test case, one possible assignment is $ a = \{1, 8\} $ which results in $ |1 - 8| = 7 $ . In the second test case, one of the possible assignments is $ a = \{1, 5, 9\} $ which results in a beauty of $ |1 - 5| + |5 - 9| = 8 $