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 scan = new Scanner(System.in);
   int N = scan.nextInt();
   String S = scan.next();
   
   int max = 0;
   int tmp = 0;
   String target = "";
   for(int i=0; i<N; i++) {
     for(int j=max; i+j<N; j++) {
       target = S.substring(i, i+j+1);       
       tmp = S.lastIndexOf(target);
       if(tmp != i && tmp > i+j) {
         max = j+1;
       } else {
         break;
       }
     }
   }
   System.out.println(max);
 }
}