#include<bits/stdc++.h>
using namespace std;
int main(){
  int n,j,k;
  string s,t;
  cin>>n>>s;
  vector<int> dp(n);
  for(j=1;j<n;j++){
    t=s.substr(j-dp[j-1],dp[j-1]+1);
    for(k=0;k<j-2*dp[j-1];k++){
      if(s.substr(k,dp[j-1]+1)==t){
        dp[j]=dp[j-1]+1;
        break;
      }
    }
    if(k==j-2*dp[j-1]) dp[j]=dp[j-1];
  }
  cout<<dp[n-1]<<endl;
}
### Prompt

Please provide a cpp coded solution to the problem described below:

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

### Response

```cpp
#include<bits/stdc++.h>
using namespace std;
int main(){
  int n,j,k;
  string s,t;
  cin>>n>>s;
  vector<int> dp(n);
  for(j=1;j<n;j++){
    t=s.substr(j-dp[j-1],dp[j-1]+1);
    for(k=0;k<j-2*dp[j-1];k++){
      if(s.substr(k,dp[j-1]+1)==t){
        dp[j]=dp[j-1]+1;
        break;
      }
    }
    if(k==j-2*dp[j-1]) dp[j]=dp[j-1];
  }
  cout<<dp[n-1]<<endl;
}
```