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 <cmath>
#include <iostream>
#include <vector>
#include <tuple>
#include <string>

int main(){
  int N;
  std::cin >> N;

  std::string S;
  std::cin >> S;
  int ms = 0;
  for(int i = 1; i < N; i++){
    int ts = 0;
    for(int j = 0; j < N-i; j++){
      if(S[j] == S[j+i]){
        ts++;
        ms = std::max(ms, ts);
        if(ts == i) break;
      }else{
        ts = 0;
      }
    }
  }
  std::cout << ms << std::endl;

  return 0;
}

