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;

public class Another {
    public static void main(String[] args) {
        Scanner input = new Scanner(System.in);
        int minDistance = 1000000;
        int currentDistance = 0;
        int n = input.nextInt();
        int min = input.nextInt();
        for (int i = 0; i < n - 1; i++) {
           int in = input.nextInt();
           currentDistance++;
           if (in < min){
               min = in;
               currentDistance = 0;
               minDistance = 1000000;
           } else if (in == min){
               if (currentDistance < minDistance){
                   minDistance = currentDistance;
               }
               currentDistance = 0;
           }
        }
        System.out.println(minDistance);
    }
}
