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 ith 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≤n,m≤105.
- 1≤u,v≤n.
### Example
Input:
54abaca12133445
Output:
3