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;
using ll = int64_t;
const ll MOD = 1e9+7;
const ll inf = (LLONG_MAX>>2);
int main(){
  ios::sync_with_stdio(0);
  cin.tie(0);
  ll n;
  string s;
  cin >> n >> s;
  ll ans = 0;
  for(ll l = n-1; l > 0; --l){
    ll crt = 0;
    for(ll i = 0; i+l < n; ++i){
      if(s[i] == s[i+l]){
        ++crt;
        ans = max(ans,min(l,crt));
      }
      else crt = 0;
    }
  }
  cout << ans;
  return 0;
}