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, a[100000], i, min = 0, s, b[100000], k;
  scanf("%d", &n);
  if (n == 0) {
    printf("0");
    return 0;
  }
  scanf("%d", &a[0]);
  min = a[0];
  for (i = 1; i < n; i++) {
    scanf("%d", &a[i]);
    if (a[i] < min) min = a[i];
  }
  k = 0;
  for (i = 0; i < n; i++)
    if (a[i] == min) {
      b[k] = i;
      ++k;
    }
  min = 100000000;
  for (i = 0; i < k - 1; i++)
    if (b[i + 1] - b[i] < min) min = b[i + 1] - b[i];
  printf("%d", min);
  return 0;
}
