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.Scanner;
public class nearesrtmin {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner sc1 = new Scanner(System.in);
		int n = sc1.nextInt();
		int a[] = new int[n];
		for(int i=0;i<n;i++){
			a[i] = sc1.nextInt();
		}
		int distance = 0, recent = 0;
		int min = a[0];
		for(int i=1;i<n;i++){
			if(a[i]<min){
				min = a[i];
				recent = i;
				//System.out.println(recent+"recent");
			}
		}
		distance = Integer.MAX_VALUE;
		for(int i=recent+1;i<n;i++){
			if(a[i]==min){
				if(distance>=(i-recent)){
					distance = i-recent;
					
				}
				recent = i;
			}
		}
		System.out.println(distance);
		
	}

}
