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<cstdio>
#include<iostream>
#include<algorithm>
#include<string.h>
#include<queue>
#define lowbit(x) (x)&(-x)
using namespace std;
int n,ans,tou,wei,a[5010],c[5010],dp[5010][5010];
char ch;
int main()
{
	cin>>n;
	for(int i=1;i<=n;i++)
		cin>>ch,a[i]=ch-'a';
	for(int i=n;i>=1;i--)
		for(int j=i-1;j>=1;j--)
			if(a[i]==a[j]&&j+dp[j+1][i+1]<i)
				dp[j][i]=1+dp[j+1][i+1],ans=max(ans,dp[j][i]);
	printf("%lld",ans);
	return 0;
}