You are given a tree (a connected acyclic undirected graph) of n vertices. Vertices are numbered from 1 to n and each vertex is assigned a character from a to t.

A path in the tree is said to be palindromic if at least one permutation of the labels in the path is a palindrome.

For each vertex, output the number of palindromic paths passing through it.

Note: The path from vertex u to vertex v is considered to be the same as the path from vertex v to vertex u, and this path will be counted only once for each of the vertices it passes through.

The first line contains an integer n (2 ≤ n ≤ 2·10⁵)  — the number of vertices in the tree.

The next n - 1 lines each contain two integers u and v (1  ≤  u, v  ≤  n, u ≠ v) denoting an edge connecting vertex u and vertex v. It is guaranteed that the given graph is a tree.

The next line contains a string consisting of n lowercase characters from a to t where the i-th (1 ≤ i ≤ n) character is the label of vertex i in the tree.

Print n integers in a single line, the i-th of which is the number of palindromic paths passing through vertex i in the tree.