#include <bits/stdc++.h>
using namespace std;
const long long M = 1e9 + 7;
vector<vector<int> > g;
int deg[300005];
vector<int> toposort;
int dp[300005];
void solve() {
  int n, m;
  cin >> n >> m;
  string s;
  cin >> s;
  g.resize(n + 1);
  for (int i = 0; i < m; i++) {
    int u, v;
    cin >> u >> v;
    g[u].push_back(v);
    deg[v]++;
  }
  queue<int> q;
  for (int i = 1; i <= n; i++)
    if (!deg[i]) q.push(i);
  int cnt = 0;
  while (!q.empty()) {
    cnt++;
    int x = q.front();
    toposort.push_back(x);
    q.pop();
    for (int y : g[x]) {
      deg[y]--;
      if (!deg[y]) q.push(y);
    }
  }
  if (cnt < n) {
    cout << -1;
    return;
  }
  int ans = 0;
  for (char ch = 'a'; ch <= 'z'; ch++) {
    memset(dp, 0, sizeof(dp));
    for (int x : toposort) {
      if (s[x - 1] == ch) dp[x]++;
      for (int y : g[x]) {
        dp[y] = max(dp[y], dp[x]);
      }
      ans = max(ans, dp[x]);
    }
  }
  cout << ans << "\n";
}
int main() {
  int t = 1;
  while (t--) solve();
  return 0;
}

### Prompt

Create a solution in CPP for 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 long long M = 1e9 + 7;
vector<vector<int> > g;
int deg[300005];
vector<int> toposort;
int dp[300005];
void solve() {
  int n, m;
  cin >> n >> m;
  string s;
  cin >> s;
  g.resize(n + 1);
  for (int i = 0; i < m; i++) {
    int u, v;
    cin >> u >> v;
    g[u].push_back(v);
    deg[v]++;
  }
  queue<int> q;
  for (int i = 1; i <= n; i++)
    if (!deg[i]) q.push(i);
  int cnt = 0;
  while (!q.empty()) {
    cnt++;
    int x = q.front();
    toposort.push_back(x);
    q.pop();
    for (int y : g[x]) {
      deg[y]--;
      if (!deg[y]) q.push(y);
    }
  }
  if (cnt < n) {
    cout << -1;
    return;
  }
  int ans = 0;
  for (char ch = 'a'; ch <= 'z'; ch++) {
    memset(dp, 0, sizeof(dp));
    for (int x : toposort) {
      if (s[x - 1] == ch) dp[x]++;
      for (int y : g[x]) {
        dp[y] = max(dp[y], dp[x]);
      }
      ans = max(ans, dp[x]);
    }
  }
  cout << ans << "\n";
}
int main() {
  int t = 1;
  while (t--) solve();
  return 0;
}

```