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.*;
import java.io.*;
import java.math.*;

public class Main {

    static Scanner input = new Scanner(new BufferedReader(new InputStreamReader(System.in)));

    public static void main(String[] args) {
        int n = input.nextInt();
        int min = input.nextInt(), len = 1, minLen = n;
        for (int i = 1; i < n; i++, len++) {
            int in = input.nextInt();
            if (in < min) {
                min = in;
                len = 0;
                minLen = n;
            } else if (in == min) {
                if (len < minLen) {
                    minLen = len;
                }
                len = 0;
            }
        }
        System.out.println(minLen);
    }
}