Monster Hunter

Little Q is fighting against scary monsters in the game "Monster Hunter". The battlefield consists of n intersections, labeled by 1, 2, ..., n, connected by n - 1 bidirectional roads like a tree. Little Q is now at intersection 1 and has X health points (HP).

There is a monster at each intersection except intersection 1. When Little Q moves to the k-th intersection for the first time, he must fight the monster at that intersection. During the fight, he will lose a_i HP. And when he finally beats the monster, he will be awarded b_i HP. Note that when HP becomes negative (< 0), the game will end, so never let this happen. If Little Q visits the same intersection more than once, the fight happens only on the first visit, as monsters do not have an extra life.

When 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.

The first line of the input contains an integer T (1 ≤ T ≤ 2000), denoting the number of test cases.

In each test case, there is one integer n (2 ≤ n ≤ 100 000) on the first line, denoting the number of intersections.

Each of the next n - 1 lines contains two integers a_i and b_i (0 ≤ a_i, b_i ≤ 10^9) describing monsters at intersections 2, 3, ..., n.

Each of the next n - 1 lines contains two integers u and v (1 ≤ u, v ≤ n, u ≠ v) denoting a bidirectional road between intersection u and intersection v. It is guaranteed that the roads form a tree.

It is guaranteed that the sum of all n is at most 10^6.

For each test case, print a single line containing an integer, denoting the minimum initial HP required to win the game.