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D. Substring

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 $$$n, m$$$ ($$$1 \leq n, m \leq 300\,000$$$), 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 $$$x, y$$$ ($$$1 \leq x, y \leq n$$$), 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 $$$1 \to 3 \to 4 \to 5$$$. The value is $$$3$$$ because the letter 'a' appears $$$3$$$ times.

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