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.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        char[] arr = sc.next().toCharArray();
        int[][] lengths = new int[n * 2][n * 2];
        int max = 0;
        for (int i = 0; i < n - 1; i++) {
            for (int j = i + 1; j < n; j++) {
                if (arr[i] == arr[j]) {
                    lengths[i][j] = 1;
                    max = 1;
                }
            }
        }
        for (int i = 1; i < n / 2; i *= 2) {
            for (int j = 0; j < n - 1; j++) {
                for (int k = j + i + 1; k < n; k++) {
                    if (lengths[j][k] != i) {
                        continue;
                    }
                    lengths[j][k] = Math.min(lengths[j][k] + lengths[j + i][k + i], k - j);
                    max = Math.max(max, lengths[j][k]);
                }
            }
        }
        System.out.println(max);
    }
}