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 A911 {

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int N = in.nextInt();
        int[] A = new int[N];
        int min = Integer.MAX_VALUE;
        for (int n=0; n<N; n++) {
            A[n] = in.nextInt();
            min = Math.min(min, A[n]);
        }
        int answer = Integer.MAX_VALUE;
        int previous = -1;
        for (int n=0; n<N; n++) {
            if (A[n] == min) {
                if (previous != -1) {
                    answer = Math.min(answer, n-previous);
                }
                previous = n;
            }
        }
        System.out.println(answer);
    }

}
