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 NearestMinimum {
	public static void main(String args[])
	{
		Scanner sc=new Scanner(System.in);
		int t=sc.nextInt();
		long min=1999999991;
		long a[]=new long[t];
		for(int i=0;i<t;i++)
		{
			a[i]=sc.nextInt();
			
			if(min>a[i])
				min=a[i];
		}
		
		ArrayList<Integer> array=new ArrayList<Integer>();
		for(int i=0;i<t;i++)
		{
			if(a[i]==min)
				array.add(i);
		}
		
		int m=1999999991;
		for(int i=1;i<array.size();i++)
		{
			if(m>array.get(i)-array.get(i-1))
				m=array.get(i)-array.get(i-1);
		}
		System.out.println(m);
		sc.close();
	}
}
