Misha has a tree with characters written on the vertices. He can choose two vertices s and t of this tree and write down characters of vertices lying on a path from s to t. We'll say that such string corresponds to pair (s,t).
Misha has m queries of type: you are given 4 vertices a, b, c, d; you need to find the largest common prefix of the strings that correspond to pairs (a,b) and (c,d). Your task is to help him.
The first line contains integer n (1≤n≤300000) − the number of vertices in the tree.
Next follows a line consisting of n small English letters. The i-th character of the string corresponds to the character written on the i-th vertex.
Next n-1 lines contain information about edges. An edge is defined by a pair of integers u, v (1≤u,v≤n, u≠v), separated by spaces.
The next line contains integer m (1≤m≤1000000) − the number of queries.
Next m lines contain information about queries. A query is defined by four integers a, b, c, d (1≤a,b,c,d≤n), separated by spaces.
For each query print the length of the largest common prefix on a separate line.
6
bbbabb
2 1
3 2
4 3
5 2
6 5
6
2 5 3 1
1 5 2 3
5 6 5 6
6 3 4 1
6 2 3 4
2 2 4 5
2
2
2
0
1
0