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<iostream>
#include<cstring>
using namespace std;
string a;
int ans=0;
int main()
{
	int n;	cin>>n;
	cin>>a;
	for(int i=1;i<n;i++)
	{
		int x=0;
		for(int j=0;j+i<n;j++)
			if(a[j]==a[i+j])
				ans=max(ans , min(++x , i));
			else
				x=0;
	}
	cout<<ans<<endl;
}