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>
using namespace std;
int main() {
  long n;
  cin >> n;
  int m[100002];
  long i;
  for (i = 0; i < n; i++) cin >> m[i];
  long x;
  x = m[0];
  for (i = 1; i < n; i++) {
    if (x > m[i]) x = m[i];
  }
  int j;
  int l = n;
  i = 0;
  while (m[i] != x) i++;
  for (j = i + 1; j < n; j++) {
    if (m[j] == x) {
      if (l > j - i) l = j - i;
      i = j;
    }
  }
  cout << l;
  return 0;
}
