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.Map;
import java.util.Scanner;
import java.util.TreeMap;

public class Main {
    public static void main(String[] args) {
        // write your code here
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int min = Integer.MAX_VALUE;
        int minrast = Integer.MAX_VALUE;
        TreeMap<Integer, Integer> treeMap = new TreeMap<>();
        for (int i = 0; i < n; i++) {
            int a = sc.nextInt();
            if (a < min) {
                min = a;
                if (treeMap.containsKey(a)) {
                    minrast = i - treeMap.get(a);
                }
                else {
                    minrast=Integer.MAX_VALUE;
                }
            } else if (a == min && i - treeMap.get(a) < minrast) {
                minrast = i - treeMap.get(a);
            }
            treeMap.put(a, i);
        }
        System.out.println(minrast);
    }
}