Given is a string S of length N.

Find the maximum length of a non-empty string that occurs twice or more in S as contiguous substrings without overlapping.

More formally, find the maximum positive integer len such that there exist integers l_1 and l_2 ( 1 \leq l_1, l_2 \leq N - len + 1 ) that satisfy the following:

* l_1 + len \leq l_2

* S[l_1+i] = S[l_2+i] (i = 0, 1, ..., len - 1)




If there is no such integer len, print 0.

Constraints

* 2 \leq N \leq 5 \times 10^3
* |S| = N
* S consists of lowercase English letters.

Input

Input is given from Standard Input in the following format:


N
S


Output

Print the maximum length of a non-empty string that occurs twice or more in S as contiguous substrings without overlapping. If there is no such non-empty string, print 0 instead.

Examples

Input

5
ababa


Output

2


Input

2
xy


Output

0


Input

13
strangeorange


Output

5
#include <bits/stdc++.h>
using namespace std;

int main()
{
  int n;
  string s;
  cin >> n >> s;

  vector<vector<int>> t(n + 1, vector<int>(n + 1));

  for (int i = n - 1; i >= 0; i--) {
    for (int j = n - 1; j >= i; j--) {
      if (s[i] == s[j]) {
        t[i][j] = t[i + 1][j + 1] + 1;
      }
    }
  }

  int ans = 0;

  for (int i = 0; i < n; i++) {
    for (int j = i + 1; j < n; j++) {
      if (t[i][j] <= j - i) {
        ans = max(ans, t[i][j]);
      }
    }
  }

  cout << ans << endl;
}
