You are given an array of n integer numbers a0, a1, ..., an - 1. Find the distance between two closest (nearest) minimums in it. It is guaranteed that in the array a minimum occurs at least two times.

Input

The first line contains positive integer n (2 ≤ n ≤ 105) — size of the given array. The second line contains n integers a0, a1, ..., an - 1 (1 ≤ ai ≤ 109) — elements of the array. It is guaranteed that in the array a minimum occurs at least two times.

Output

Print the only number — distance between two nearest minimums in the array.

Examples

Input

2
3 3


Output

1


Input

3
5 6 5


Output

2


Input

9
2 1 3 5 4 1 2 3 1


Output

3
import java.util.*;

public class Main {
  public static void main(String[] args) {
    Scanner scan = new Scanner(System.in);
    int n = scan.nextInt();
    scan.nextLine();
    int min = Integer.MAX_VALUE;
    int index = -1;
    int minDist = Integer.MAX_VALUE;
    for (int i = 0; i < n; i++) {
      
      int next = scan.nextInt();
      
      // Same as min.
      if (next == min) {
        int dist = i - index;
        if (minDist > dist) {
          minDist = dist;
        }
        index = i;
      }
      
      // Smaller than min (update to new min)
      if (next < min) {
        min = next;
        index = i;
        minDist = Integer.MAX_VALUE;
        continue;
      }
      
      // Not min.
      if (next > min) {
        continue;
      }
      
    }
    System.out.println(minDist);
  }
}
 		 	 		 			  		 		  	 				 			