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 Test{
    
    public static void main(String[] args) {
        Scanner sc=new Scanner(System.in);
        // int t=sc.nextInt();
        // while(t-->0)
        // {
        // }
        int n=sc.nextInt();
        int a[]=new int[n];
        int m=Integer.MAX_VALUE;
        for(int i=0;i<n;i++)
        {
            a[i]=sc.nextInt();
            if(a[i]<m)
                m=a[i];
        }
        int c=0,ans=Integer.MAX_VALUE,f1=-1,f2=-1,cou=0;
        for(int i=0;i<n;i++)
        {
            if(a[i]==m&&cou==1)
            {
                c=Math.abs(i-f1);
                if(ans>c)
                    ans=c;
                f1=i;
            }
            else if(a[i]==m&&cou==0)
            {
                f1=i;
                cou=1;
            }
            
        }
        System.out.println(ans);
    }
}    
                        
