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 P911A
{
    public static void main(String[] args)
    {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        Integer minimum = null;
        Integer ans = null;
        Integer previous = null;
        for(int i = 1; i <= n; ++i)
        {
            int x = in.nextInt();
            if(minimum != null)
            {
                if(x == minimum)
                {
                    int t = i - previous;
                    if(ans == null || ans > t)
                    {
                        ans = t;
                    }
                    previous = i;
                }
                else if(x < minimum)
                {
                    minimum = x;
                    ans = null;
                    previous = i;
                }
            }
            else
            {
                minimum = x;
                previous = 1;
            }
        }

        System.out.println(ans);
    }
}
