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.BufferedReader;
import java.io.InputStreamReader;
import java.util.Scanner;

public class NearestMinimums {

    public static void main(String[] args){
        Scanner in = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        int n = in.nextInt();
        int[] arr = new int[n];
        int min = Integer.MAX_VALUE;
        for (int i = 0; i < n; i++){
            arr[i] = in.nextInt();
            if (arr[i] < min) min = arr[i];
        }
        int last = -1, dis = n;
        for (int i = 0; i < n; i++){
            if (arr[i] == min){
                if (i - last < dis && last != -1){
                    dis = i-last;
                }
                last = i;
            }
        }
        System.out.println(dis);
    }

}
