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
#include <bits/stdc++.h>
int main() {
  int n, i, a, k, min, c;
  scanf("%d", &n);
  scanf("%d", &a);
  min = a;
  k = 1;
  for (i = 2; i <= n; i++) {
    scanf("%d", &a);
    if (a < min) {
      min = a;
      k = i;
      c = 320000000;
    } else if (a == min) {
      if (i - k < c) c = i - k;
      k = i;
    }
  }
  printf("%d", c);
}
