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
import java.util.Scanner;

class Solver {
    void solve(Scanner sc) {
        int N = sc.nextInt();
        String S = sc.next();

        int[] len = new int[(N - 1) * N];
        int max = 0;
        char[] chars = S.toCharArray();
        for (int i = 0; i < N - 1; i++) {
            char c = chars[i];
            for (int offset = N - i - 1; offset > max; offset--) {
                if (c != chars[i + offset]) continue;
                int combo = i > 0 ? len[(offset - 1) * N + i - 1] + 1 : 1;
                if (combo >= offset){
                    max = offset;
                    break;
                }
                max = Math.max(max, len[(offset - 1) * N + i] = combo);
            }
        }
        System.out.println(max);
    }
}

class Main {
    public static void main(String... args) {
        Scanner in = new Scanner(System.in);

        new Solver().solve(in);

        in.close();
    }
}