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 CF_911_A {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        int min = scanner.nextInt();
        int minPos = 0;
        int minDist = n;
        for (int i = 1; i < n; i++) {
            int a = scanner.nextInt();
            if (a < min) {
                min = a;
                minPos = i;
                minDist = n;
            } else if (a == min) {
                minDist = Math.min(i - minPos, minDist);
                minPos = i;
            }
        }
        System.out.println(minDist);
    }
}
