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;
  scanf("%d", &n);
  int a[100020];
  int i;
  for (i = 0; i < n; i++) scanf("%d", &a[i]);
  int min = 0;
  for (i = 1; i < n; i++)
    if (a[min] > a[i]) min = i;
  int k, t, d = 100010;
  i = min;
  k = min;
  while (k < n) {
    k++;
    if (a[k] == a[i]) {
      t = k - i;
      if (d > t) d = t;
      i = k;
    }
  }
  printf("%d\n", d);
  return 0;
}
