#include <iostream>
#include <algorithm>
#define N 5010
using namespace std;
int a[N][N];
char s[N];
int main()
{
	int n,ans = 0;
	scanf("%d",&n);
	scanf("%s",s + 1);
	for(int i = 1;i <= n;i ++)
		for(int j = 1;j <= n;j ++)
		{
			if(s[i] == s[j])
				a[i][j] = 1 + a[i - 1][j - 1];
			ans = max(ans,min(a[i][j],abs(j - i)));
		}
	cout << ans << endl;
	return 0;
}
### Prompt

In cpp, your task is to solve the following problem:

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 <iostream>
#include <algorithm>
#define N 5010
using namespace std;
int a[N][N];
char s[N];
int main()
{
	int n,ans = 0;
	scanf("%d",&n);
	scanf("%s",s + 1);
	for(int i = 1;i <= n;i ++)
		for(int j = 1;j <= n;j ++)
		{
			if(s[i] == s[j])
				a[i][j] = 1 + a[i - 1][j - 1];
			ans = max(ans,min(a[i][j],abs(j - i)));
		}
	cout << ans << endl;
	return 0;
}
```