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

public class Solution{ 

	
 public static void main(String[] args) {
     
     Scanner in = new Scanner(System.in);
     
     int n,i,min=1000000001,min_dist=100000,previous=-1;
     int[] a;
     
     n=in.nextInt();
     a=new int[n+1];
     
     for(i=0;i<n;i++)a[i]=in.nextInt();
     
     for(i=0;i<n;i++){
    	 if(a[i]<min)min=a[i];
     }
     
     for(i=0;i<n;i++){
    	 if(a[i]==min){
    		 if(previous==-1){
    			 previous=i;
    		 }
    		 else{
    			 if(i-previous<min_dist){
    				 min_dist=i-previous;
    			 }
    			 previous=i;
    		 }
    	 }
     }
     System.out.println(min_dist);
     
     
     
 }
}