Codeforces Round 722 (Div. 1) |
---|

Finished |

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

dfs and similar

divide and conquer

dp

greedy

trees

*1600

No tag edit access

The problem statement has recently been changed. View the changes.

×
A. Parsa's Humongous Tree

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputParsa 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.

Input

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 $$$2 \cdot 10^5$$$.

Output

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

Example

Input

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

Output

7 8 62

Note

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 $$$|1 - 5| + |5 - 9| = 8$$$

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Apr/21/2024 03:13:22 (h1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|