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 <vector>
#include <string>
using namespace std;
void chmax(int &a, int b) { if (a < b) a = b; }

int main() {
    int N; string S; cin >> N >> S;

    int res = 0;
    vector<vector<int> > dp(N+1, vector<int>(N+1, 0));
    for (int i = N-1; i >= 0; i--) {
        for (int j = N-1; j > i; j--) {
            if (S[i] == S[j]) chmax(dp[i][j], dp[i+1][j+1] + 1);
            chmax(res, min(dp[i][j], j-i));
        }
    }
    cout << res << endl;
}