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.Scanner;

/**
 *
 * @author Ahmad
 */
public class JavaApplication1 {

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) {
        Scanner console = new Scanner (System.in) ;
        int n = console.nextInt() ; 
        int []x = new int [n] ;
        int count = 0 ; 
        int countt = 1000000000 ;
        int min = 1000000000 ;
        for (int i=0 ; i<x.length ; i++){
            x[i]=console.nextInt() ;
        }
        for (int i=0 ; i<x.length ; i++){
            if (x[i]<min){
                min=x[i] ;
                countt = 1000000000;
                count = 0 ;
            }
            else if (x[i]==min){
                countt=Math.min(countt, count) ;
                count = 0 ; 
            }
            else {
                count ++ ;
            }
        }
        System.out.println(countt+1);
   } 
}
