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)  {
        // write your code here
        Scanner sc= new Scanner(System.in);
        int n= sc.nextInt();
        boolean app=false;
        int [] good=new  int[n];
        int mmin= Integer.MAX_VALUE;
        int idx1=-1;
        int idx2=-1;
        int mmm=mmin;

        for (int i = 0; i <n ; i++) {good[i]=sc.nextInt(); mmin= good[i]<mmin?good[i]:mmin;}
        for (int i = 0; i <n; i++) {
            if(!app&&good[i]==mmin){app=true;idx1=i;}
            if(app&&i!=idx1&&good[i]==mmin){idx2=i;
            mmm=(idx2-idx1)<mmm?(idx2-idx1):mmm;
            idx1=idx2;
            }
        }
        System.out.println(mmm);

    }
}