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 Nearest {
public static void main(String[] args) {
    Scanner sc=new Scanner(System.in);
    int n=sc.nextInt();
    int minv=Integer.MAX_VALUE;
    List<Integer> temp=new ArrayList<Integer>();
    for(int i=0;i<n;i++){
        int a=sc.nextInt();
        if(minv>a ){
            temp=new ArrayList<Integer>();
            minv=a;
            temp.add(i);
        }
        else if(minv==a)
        temp.add(i);

    }
    
    int minx=Integer.MAX_VALUE;
    for(int j=0;j<temp.size()-1;j++){
        int a=temp.get(j);
        int b=temp.get(j+1);
        if(minx>(b-a)){
            minx=b-a;
        }

    }
    System.out.println(minx);

}
    
}