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 NearestMinimum {

	public static void main(String[] args) {
		// TODO Auto-generated method stub

		Scanner input = new Scanner(System.in);		
		int n = input.nextInt();
		long[] arr = new long[n];
		for(int i=0; i<n;i++)arr[i] = input.nextLong();
		long min = Long.MAX_VALUE;
		int prev = -1;
		int dist = n;
		for(int i=0; i<n;i++){
			if(arr[i]<min){
				prev = i;
			   min = arr[i];
			   dist = n;
			}
			else if(arr[i]==min){
				dist = Math.min(dist,i-prev);
				prev = i;
			}
			
		}
		System.out.println(dist);
	}

}
