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 A {
	public static void main(String args[]) {
		Scanner sc = new Scanner (System.in);
		int n = sc.nextInt();
		int a[] = new int[n];
		int b[] = new int[n];
		for(int i=0 ; i<n ; i++) {
			a[i] = sc.nextInt();
			b[i] = a[i];
		}
		Arrays.sort(b);
		int f = 0 , min = Integer.MAX_VALUE;
		int m = b[0] , prev = 0;
		for(int i=0 ; i<n ; i++) {
			if(a[i]==m && f==0) {
				prev = i;
				f=1;
			}
			else if(a[i] == m) {
				min = Math.min(i - prev, min);
				prev = i;
			}
		}
		System.out.println(min);
	}
}
