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 <bits/stdc++.h>
using namespace std;
using lint = long long int;

lint n;
string s;

bool check(lint len) {
    bool ok = false;
    for(lint i = 0; i + len < n; i++) {
        string sub = s.substr(i, len);
        if(s.substr(i+len).find(sub) != string::npos)  ok = true;
    }
    return ok;
}

int main() {
    cin >> n >> s;

    lint ok = 0;
    lint ng = n;
    while( abs(ok - ng) > 1 ) {
        lint m = (ok + ng) / 2;
        (check(m) ? ok : ng) = m;
    }

    cout << ok << endl;
}