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
/* package codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public final class Codechef
{
	public static void main (String[] args) throws java.lang.Exception
	{
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		long a[]=new long[n];
		int i,j,diff=n;
		for(i=0;i<n;i++)
		a[i]=sc.nextLong();
		long min=a[0];j=0;
		for(i=1;i<n;i++)
		if(a[i]<min){
		min=a[i];
		    j=i;
		}
		for(i=j+1;i<n;i++)
		if(a[i]==min){
		    if(i-j<diff)
		    diff=i-j;
		    j=i;
		}
		System.out.println(diff);
	}
}
