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.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner s = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
		int  N, a, dist, i, minimus = Integer.MAX_VALUE, last = -1, minDist = Integer.MAX_VALUE;
		N =s.nextInt();
		for (i = 0; i < N; i++){
			a = s.nextInt();
			if (a == minimus){
				dist = i - last;
				if (dist < minDist)
					minDist = dist;
				last = i;
			}
			if (a < minimus){
				minimus = a;
				minDist = Integer.MAX_VALUE;
				last = i;
			}
		}
		System.out.println(minDist);
	}

}
