#include <bits/stdc++.h>
using namespace std;
const int MAXN = 300000 + 5;
int ch[MAXN];
vector<int> edge[MAXN];
bool vis[MAXN];
int dp[MAXN][26];
bool dfs(int u) {
  if (vis[u]) return 0;
  if (dp[u][ch[u]] > 0) return 1;
  vis[u] = 1;
  dp[u][ch[u]] = 1;
  for (int i = 0; i < edge[u].size(); i++) {
    int v = edge[u][i];
    if (!dfs(v)) return 0;
    for (int c = 0; c < 26; c++) {
      if (c == ch[u])
        dp[u][c] = max(dp[u][c], dp[v][c] + 1);
      else
        dp[u][c] = max(dp[u][c], dp[v][c]);
    }
  }
  vis[u] = 0;
  return 1;
}
int main() {
  int n, m;
  scanf("%d%d", &n, &m);
  getchar();
  for (int i = 1; i <= n; i++) {
    ch[i] = getchar() - 'a';
  }
  while (m--) {
    int u, v;
    scanf("%d%d", &u, &v);
    edge[u].push_back(v);
  }
  int ans = 0;
  for (int i = 1; i <= n; i++) {
    if (!dfs(i)) {
      printf("-1\n");
      return 0;
    }
    for (int j = 0; j < 26; j++) {
      ans = max(ans, dp[i][j]);
    }
  }
  printf("%d\n", ans);
  return 0;
}

### Prompt

Please formulate a CPP solution to the following problem:

You 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.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int MAXN = 300000 + 5;
int ch[MAXN];
vector<int> edge[MAXN];
bool vis[MAXN];
int dp[MAXN][26];
bool dfs(int u) {
  if (vis[u]) return 0;
  if (dp[u][ch[u]] > 0) return 1;
  vis[u] = 1;
  dp[u][ch[u]] = 1;
  for (int i = 0; i < edge[u].size(); i++) {
    int v = edge[u][i];
    if (!dfs(v)) return 0;
    for (int c = 0; c < 26; c++) {
      if (c == ch[u])
        dp[u][c] = max(dp[u][c], dp[v][c] + 1);
      else
        dp[u][c] = max(dp[u][c], dp[v][c]);
    }
  }
  vis[u] = 0;
  return 1;
}
int main() {
  int n, m;
  scanf("%d%d", &n, &m);
  getchar();
  for (int i = 1; i <= n; i++) {
    ch[i] = getchar() - 'a';
  }
  while (m--) {
    int u, v;
    scanf("%d%d", &u, &v);
    edge[u].push_back(v);
  }
  int ans = 0;
  for (int i = 1; i <= n; i++) {
    if (!dfs(i)) {
      printf("-1\n");
      return 0;
    }
    for (int j = 0; j < 26; j++) {
      ans = max(ans, dp[i][j]);
    }
  }
  printf("%d\n", ans);
  return 0;
}

```