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 Q1
{
	public static void main(String args[])
	{
		Scanner s=new Scanner(System.in);
		int n=s.nextInt();
        int arr[]=new int[n];
		int arr1[]=new int[n];
		
		for(int i=0;i<n;i++)
		{
			arr[i]=s.nextInt();
			arr1[i]=arr[i];
		}
		Arrays.sort(arr1);
		int i,min=arr1[0];
		int aa[]=new int[n];
        int f=0;		
		for(i=0;i<n;i++)
		{
			if(arr[i]==min)
				aa[f++]=i;
		}
		int a11[]=new int[n];
		int v=0;
        for(i=0;i<f-1;i++)
		{
			a11[v]=aa[i+1]-aa[i];
			v++;
		}
		Arrays.sort(a11,0,v);
		System.out.println(a11[0]);
	}
}