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 minDistance{
    public static void main(String[] args){
        Scanner scan = new Scanner(System.in);
        int t = scan.nextInt();
        long[] arr = new long[t];
       long  min=scan.nextLong();
       int index=0;
       int indexMin=t;
        for(int i=1; i<t; i++){
            long temp= scan.nextLong();
            if(temp<min) {min=temp; index=i; indexMin=t;}
            else if(temp==min){if(i-index<indexMin) indexMin=i-index;
                index=i;
            }
            
        }
      System.out.println(indexMin);
    }
}