Given an directed acyclic graph (DAG). Each vertex is assigned a lowercase letter. A path's value is the number of most frequently occuring letter. For example, `marisa`, the value should be $2$ as letter `a` occurs $2$ times.
### Input
- The first line contains two integers $n,m$.
- The second line contains a string. The $i^{th}$ character is the letter assigned to vertex $i$.
- The next $m$ lines, each line contains two integers $u, v$ an edge directed from $u$ to $v$.
### Output
- Print the maximum value among all paths.
### Constraints
- $1 \le n,m \le 10^5$.
- $1 \le u,v\le n$.
### Example
Input:
```
5 4
abaca
1 2
1 3
3 4
4 5
```
Output:
```
3
```
