B. Fake Plastic Treestime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputWe are given a rooted tree consisting of n vertices numbered from 1 to n. The root of the tree is the vertex 1 and the parent of the vertex v is p_v.There is a number written on each vertex, initially all numbers are equal to 0. Let's denote the number written on the vertex v as a_v.For each v, we want a_v to be between l_v and r_v (l_v \leq a_v \leq r_v).In a single operation we do the following:   Choose some vertex v. Let b_1, b_2, \ldots, b_k be vertices on the path from the vertex 1 to vertex v (meaning b_1 = 1, b_k = v and b_i = p_{b_{i + 1}}). Choose a non-decreasing array c of length k of nonnegative integers: 0 \leq c_1 \leq c_2 \leq \ldots \leq c_k. For each i (1 \leq i \leq k), increase a_{b_i} by c_i. What's the minimum number of operations needed to achieve our goal?InputThe first line contains an integer t (1\le t\le 1000)  — 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 2 \cdot 10^5)  — the number of the vertices in the tree.The second line of each test case contains n - 1 integers, p_2, p_3, \ldots, p_n (1 \leq p_i < i), where p_i denotes the parent of the vertex i.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).It is guaranteed that the sum of n over all test cases doesn't exceed 2 \cdot 10^5.OutputFor each test case output the minimum number of operations needed.ExampleInput
4
2
1
1 5
2 9
3
1 1
4 5
2 4
6 10
4
1 2 1
6 9
5 6
4 5
2 4
5
1 2 3 4
5 5
4 4
3 3
2 2
1 1
Output
1
2
2
5
NoteIn the first test case, we can achieve the goal with a single operation: choose v = 2 and c = [1, 2], resulting in a_1 = 1, a_2 = 2.In the second test case, we can achieve the goal with two operations: first, choose v = 2 and c = [3, 3], resulting in a_1 = 3, a_2 = 3, a_3 = 0. Then, choose v = 3, c = [2, 7], resulting in a_1 = 5, a_2 = 3, a_3 = 7.
4
2
1
1 5
2 9
3
1 1
4 5
2 4
6 10
4
1 2 1
6 9
5 6
4 5
2 4
5
1 2 3 4
5 5
4 4
3 3
2 2
1 1

1 2 2 5 
['dfs and similar', 'dp', 'greedy', 'trees', '*1700']