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;

public class Main{
  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);
    int N = sc.nextInt();
    String S = sc.next();
    int[][] dp = new int[N+1][N+1];
    for(int i = N-1; i >= 0; i--){
      for(int j = N-1; j >= 0; j--){
        if(S.charAt(i)==S.charAt(j)){
          dp[i][j]=dp[i+1][j+1]+1;
        }
      }
    }
    int ans = 0;
    for(int i = 0; i < N; i++){
      for(int j = 0; j < N; j++){
        if(i > j){
          continue;
        }
        ans = Math.max(ans, Math.min(dp[i][j], j-i));
      }
    }
    System.out.println(ans);
  }
}