Sum of Prefix Sums

We define the sum of prefix sums of an array [s_1, s_2, ..., s_k] as s_1 + (s_1 + s_2) + (s_1 + s_2 + s_3) + ... + (s_1 + s_2 + ... + s_k).

You are given a tree consisting of n vertices. Each vertex i has an integer a_i written on it. We define the value of the simple path from vertex u to vertex v as follows: consider all vertices appearing on the path from u to v, write down all the numbers written on these vertices in the order they appear on the path, and compute the sum of prefix sums of the resulting sequence.

Your task is to calculate the maximum value over all paths in the tree.

Input

The first line contains one integer n (2 ≤ n ≤ 150000) — the number of vertices in the tree.

Then n - 1 lines follow, representing the edges of the tree. Each line contains two integers u_i and v_i (1 ≤ u_i, v_i ≤ n, u_i ≠ v_i), denoting an edge between vertices u_i and v_i. It is guaranteed that these edges form a tree.

The last line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^6).

Output

Print one integer — the maximum value over all paths in the tree.

Example

Input

4 4 2 3 2 4 1 1 3 3 7

Output

36

Note

The best path in the first example is from vertex 3 to vertex 1. It gives the sequence [3, 3, 7, 1], and the sum of prefix sums is 36.

inputFormat

Input

The first line contains one integer n (2 ≤ n ≤ 150000) — the number of vertices in the tree.

Then n - 1 lines follow, representing the edges of the tree. Each line contains two integers u_i and v_i (1 ≤ u_i, v_i ≤ n, u_i ≠ v_i), denoting an edge between vertices u_i and v_i. It is guaranteed that these edges form a tree.

The last line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^6).

outputFormat

Output

Print one integer — the maximum value over all paths in the tree.

Example

Input

4 4 2 3 2 4 1 1 3 3 7

Output

36

Note

The best path in the first example is from vertex 3 to vertex 1. It gives the sequence [3, 3, 7, 1], and the sum of prefix sums is 36.

样例

4
4 2
3 2
4 1
1 3 3 7

36

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