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time limit per test

3 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou are given a graph with *n* nodes and *m* directed edges. One lowercase letter is assigned to each node. We define a path's value as the number of the most frequently occurring letter. For example, if letters on a path are "abaca", then the value of that path is 3. Your task is find a path whose value is the largest.

Input

The first line contains two positive integers *n*, *m* (1 ≤ *n*, *m* ≤ 300 000), denoting that the graph has *n* nodes and *m* directed edges.

The second line contains a string *s* with only lowercase English letters. The *i*-th character is the letter assigned to the *i*-th node.

Then *m* lines follow. Each line contains two integers *x*, *y* (1 ≤ *x*, *y* ≤ *n*), describing a directed edge from *x* to *y*. Note that *x* can be equal to *y* and there can be multiple edges between *x* and *y*. Also the graph can be not connected.

Output

Output a single line with a single integer denoting the largest value. If the value can be arbitrarily large, output -1 instead.

Examples

Input

5 4

abaca

1 2

1 3

3 4

4 5

Output

3

Input

6 6

xzyabc

1 2

3 1

2 3

5 4

4 3

6 4

Output

-1

Input

10 14

xzyzyzyzqx

1 2

2 4

3 5

4 5

2 6

6 8

6 5

2 10

3 9

10 9

4 6

1 10

2 8

3 7

Output

4

Note

In the first sample, the path with largest value is 1 → 3 → 4 → 5. The value is 3 because the letter 'a' appears 3 times.

Codeforces (c) Copyright 2010-2018 Mike Mirzayanov

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