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.ArrayList;
import java.util.Scanner;

public class Main{

  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    int n = sc.nextInt();
    int min = sc. nextInt();
    ArrayList<Integer> list = new ArrayList<>();
    list.add(0);
    for(int i=1;i<n;i++){
      int a = sc.nextInt();
      if(a==min){
        list.add(i);
      }else if(a<min){
        list = new ArrayList<>();
        min = Math.min(a,min);
        list.add(i);
      }
    }
    int ans = Integer.MAX_VALUE;
    for(int i=0;i<list.size()-1;i++){
      ans = Math.min(ans,list.get(i+1)-list.get(i));
    }
    System.out.println(ans);
  }
}



