#include <bits/stdc++.h>
using namespace std;

int main() {
    long long N;
    string S;

    cin >> N;
    cin >> S;

    long long m = 0;
    for(int i=1; i<S.length(); ++i) {
	long long c = 0;

	for(int j=0; j<S.length()-i; ++j) {
	    if (S[j] == S[j+i]) {
		++c;
		if (c > m && c <= i) {
		    m = c;
		}
	    } else {
		c = 0;
	    }
	}
    }

    cout << m << endl;


    return 0;
}

### Prompt

Construct a CPP code solution to the problem outlined:

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() {
    long long N;
    string S;

    cin >> N;
    cin >> S;

    long long m = 0;
    for(int i=1; i<S.length(); ++i) {
	long long c = 0;

	for(int j=0; j<S.length()-i; ++j) {
	    if (S[j] == S[j+i]) {
		++c;
		if (c > m && c <= i) {
		    m = c;
		}
	    } else {
		c = 0;
	    }
	}
    }

    cout << m << endl;


    return 0;
}

```