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.Arrays;
import java.util.Scanner;

public class pre87
{
    public static void main(String args[])
    {
        Scanner obj = new Scanner(System.in);
        int n = obj.nextInt(),min = Integer.MAX_VALUE;
        data[] arr = new data[n];
        for(int i=0;i<n;i++)
        {
            arr[i] = new data();
            arr[i].value = obj.nextInt();
            arr[i].index = i;
            min = (arr[i].value<min)?arr[i].value:min;
        }
        Arrays.sort(arr);
        int index = 1,dmin = Integer.MAX_VALUE;
        while( index<arr.length && arr[index].value==min)
        {
            if(Math.abs(arr[index-1].index-arr[index].index)<dmin)
                dmin = Math.abs(arr[index-1].index-arr[index].index);
            index++;
        }
        System.out.println(dmin);
    }
}
class data implements Comparable<data>
{
    int value,index;

    @Override
    public int compareTo(data o)
    {
        return this.value-o.value;
    }
}
