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.HashSet;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		String s = in.next();
		// char[] s = in.next().toCharArray();

		HashSet<String> set = new HashSet<>();

		int len = 1;
		int lenMax = 0;
		for ( int st = 0; st + len - 1 < n; st++ ) {
			String temp = s.substring(st, st + len);

			while ( s.indexOf(temp, st + len) > st ) {
				len++;
				temp = s.substring(st, st + len);
			}
			lenMax = Math.max(lenMax, len - 1);
		}

		System.out.println(lenMax);
		in.close();
	}
}