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E. Misha and LCP on Tree

time limit per test

8 secondsmemory limit per test

512 megabytesinput

standard inputoutput

standard outputMisha 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.

Input

The first line contains integer *n* (1 ≤ *n* ≤ 300 000) — 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* ≤ 1 000 000) — 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.

Output

For each query print the length of the largest common prefix on a separate line.

Examples

Input

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

Output

2

2

2

0

1

0

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

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