Move and Swap

You are given n - 1 integers a_2, ..., a_n and a tree with n vertices rooted at vertex 1. The leaves are all at the same distance d from the root.

Recall that a tree is a connected undirected graph without cycles. The distance between two vertices is the number of edges on the simple path between them. All non-root vertices with degree 1 are leaves. If vertices s and f are connected by an edge and the distance of f from the root is greater than the distance of s from the root, then f is called a child of s.

Initially, there are a red coin and a blue coin on the vertex 1. Let r be the vertex where the red coin is and let b be the vertex where the blue coin is. You should make d moves. A move consists of three steps:

• Move the red coin to any child of r.
• Move the blue coin to any vertex b' such that dist(1, b') = dist(1, b) + 1. Here dist(x, y) indicates the length of the simple path between x and y. Note that b and b' are not necessarily connected by an edge.
• You can optionally swap the two coins (or skip this step).

Note that r and b can be equal at any time, and there is no number written on the root.

After each move, you gain |a_r - a_b| points. What's the maximum number of points you can gain after d moves?

Input

The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of test cases.

The first line of each test case contains a single integer n (2 ≤ n ≤ 2 ⋅ 10^5) — the number of vertices in the tree.

The second line of each test case contains n-1 integers v_2, v_3, ..., v_n (1 ≤ v_i ≤ n, v_i ≠ i) — the i-th of them indicates that there is an edge between vertices i and v_i. It is guaranteed, that these edges form a tree.

The third line of each test case contains n-1 integers a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the numbers written on the vertices.

It is guaranteed that the sum of n for all test cases does not exceed 2 ⋅ 10^5.

Output

For each test case, print a single integer: the maximum number of points you can gain after d moves.

Example

Input

4 14 1 1 1 2 3 4 4 5 5 6 7 8 8 2 3 7 7 6 9 5 9 7 3 6 6 5 6 1 2 2 3 4 32 78 69 5 41 15 1 15 1 10 4 9 11 2 4 1 8 6 10 11 62 13 12 43 39 65 42 86 25 38 19 19 43 62 15 11 2 7 6 9 8 10 1 1 1 5 3 15 2 50 19 30 35 9 45 13 24 8 44 16 26 10 40

Output

14 45 163 123

Note

In the first test case, an optimal solution is to:

• move 1: r = 4, b = 2; no swap;
• move 2: r = 7, b = 6; swap (after it r = 6, b = 7);
• move 3: r = 11, b = 9; no swap.

The total number of points is |7 - 2| + |6 - 9| + |3 - 9| = 14.

In the second test case, an optimal solution is to:

• move 1: r = 2, b = 2; no swap;
• move 2: r = 3, b = 4; no swap;
• move 3: r = 5, b = 6; no swap.

The total number of points is |32 - 32| + |78 - 69| + |5 - 41| = 45.

inputFormat

Input

The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of test cases.

The first line of each test case contains a single integer n (2 ≤ n ≤ 2 ⋅ 10^5) — the number of vertices in the tree.

The second line of each test case contains n-1 integers v_2, v_3, ..., v_n (1 ≤ v_i ≤ n, v_i ≠ i) — the i-th of them indicates that there is an edge between vertices i and v_i. It is guaranteed, that these edges form a tree.

The third line of each test case contains n-1 integers a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the numbers written on the vertices.

It is guaranteed that the sum of n for all test cases does not exceed 2 ⋅ 10^5.

outputFormat

Output

For each test case, print a single integer: the maximum number of points you can gain after d moves.

Example

Input

4 14 1 1 1 2 3 4 4 5 5 6 7 8 8 2 3 7 7 6 9 5 9 7 3 6 6 5 6 1 2 2 3 4 32 78 69 5 41 15 1 15 1 10 4 9 11 2 4 1 8 6 10 11 62 13 12 43 39 65 42 86 25 38 19 19 43 62 15 11 2 7 6 9 8 10 1 1 1 5 3 15 2 50 19 30 35 9 45 13 24 8 44 16 26 10 40

Output

14 45 163 123

Note

In the first test case, an optimal solution is to:

• move 1: r = 4, b = 2; no swap;
• move 2: r = 7, b = 6; swap (after it r = 6, b = 7);
• move 3: r = 11, b = 9; no swap.

The total number of points is |7 - 2| + |6 - 9| + |3 - 9| = 14.

In the second test case, an optimal solution is to:

• move 1: r = 2, b = 2; no swap;
• move 2: r = 3, b = 4; no swap;
• move 3: r = 5, b = 6; no swap.

The total number of points is |32 - 32| + |78 - 69| + |5 - 41| = 45.

样例

4
14
1 1 1 2 3 4 4 5 5 6 7 8 8
2 3 7 7 6 9 5 9 7 3 6 6 5
6
1 2 2 3 4
32 78 69 5 41
15
1 15 1 10 4 9 11 2 4 1 8 6 10 11
62 13 12 43 39 65 42 86 25 38 19 19 43 62
15
11 2 7 6 9 8 10 1 1 1 5 3 15 2
50 19 30 35 9 45 13 24 8 44 16 26 10 40

14
45
163
123

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