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 ProblemA{
	public static void main(String [] args){
		Scanner input = new Scanner(System.in);
		int n = input.nextInt();
		int [] array = new int[n];
		int min = Integer.MAX_VALUE;
		for(int i=0;i<n;i++){
			array[i]= input.nextInt();
			if(array[i]<min){
				min = array[i];
			}
		}

		int mindist = n;
		int minIndex = -1;
		for(int i=0;i<n;i++){
			if(array[i]==min && minIndex==-1){
				minIndex = i;
				continue;
			}
			if(array[i]==min){
				int dist = i-minIndex;
				minIndex = i;
				if(dist<mindist){
					mindist = dist;
				}
			}
		}
		System.out.println(mindist);
	}
}