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 nearest_minimums {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner in = new Scanner(System.in);
		int n=in.nextInt(),c=0,first=0;
		int arr[]=new int[n];
		ArrayList<Integer> list = new ArrayList<Integer>();
		for(int i=0;i<n;i++)
		{
			arr[i]=in.nextInt();
			list.add(arr[i]);
		}
		Arrays.sort(arr);
		boolean flag=false;
		int min=arr[0],size=0,max=100001;
		for(int i=0;i<list.size();i++)
		{
		    if(list.get(i)==min && flag==true)
		    {
		    	size=(i-first)-1;
		    	if(size==0)
		    	{
		    		System.out.println("1");
		    		System.exit(0);
		    	}
		    	flag=false;
		    	i--;
		    	if(max>size)
		    	{
					max=size;
				}
		    }
			if(list.get(i)==min)
			{
				first=i;
				flag=true;
			}
		}
		System.out.println(max+1);
	}
}