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.Scanner;



public class Main{
    private static final int MAX_N = 303;
    public static void main(String[] args){
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int result= Integer.MAX_VALUE;
        int curMin = in.nextInt();
        int lastIndex = 0;

        for(int i =1;i<n;i++){
            int t = in.nextInt();
            if(t<curMin){
                curMin = t;
                lastIndex = i;
                result = Integer.MAX_VALUE;
            }else if(t==curMin){
                result = Math.min(result,i-lastIndex);
                lastIndex = i;
            }
        }
        System.out.println(result);
    }
}