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 test{
	public static void main(String[] args){
		Scanner s=new Scanner(System.in);
		int min,temp;
		int dist=100000,i=0;
		int n=s.nextInt();
		int arr[]=new int[n];
		arr[0]=s.nextInt();
		min=arr[0];
		for(i=1;i<n;i++){
			arr[i]=s.nextInt();
			if(arr[i]<min)
				min=arr[i];
		}
		i=0;
		while(arr[i] != min){
			i=i+1;
		}
		temp=i;
		for(int j=i+1;j<n;j++){
			if(arr[j]==min){
				if((j-temp)<dist)
					dist=j-temp;
				temp=j;
			}
		}
		System.out.println(dist);	
	}
}