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 YearCounter{


    public static void main(String[] args)
    {
       Scanner scanner = new Scanner(System.in);
       int n = scanner.nextInt();
       int k = 1;
       ArrayList<Integer> list = new ArrayList<>();
       long min = Long.MAX_VALUE;
       for (int i = 0; i < n; i++){
           long j = scanner.nextLong();
           if (j == min){
               list.add(k);
               k = 1;
           }
           else if (j < min){
               list.clear();
               min = j;
               k = 1;
           }
           else k++;
       }
        System.out.println(Collections.min(list));
    }
}