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.*;

  public class A {

    public static void main(String args[]) {
      try (Scanner in = new Scanner(System.in)) {
        int n = in.nextInt();
        int[] arr = new int[n];
        for (int i = 0; i < n; i++) {
          arr[i] = in.nextInt();
        }
        System.out.println(f(n,arr));
      }



    }

    private static int f(int n, int[] arr){
      int min = Integer.MAX_VALUE;
      int count = 1;
      int res = Integer.MAX_VALUE;
      for (int i = 0; i < n; i++) {
        if (arr[i] < min){
          min = arr[i];
        }
      }
      for (int i = 0; i < n; i++) {
        if (arr[i] == min){
          while (i < n - 1 && arr[i + 1] != min ){
            count++;
            i++;
          }
          if (i < n - 1) {
            res = Math.min(res, count);
            count = 1;
          }
        }

      }
      return res;
    }
  }


