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;
long long n, m, k, p;
int main() {
  cin >> n;
  long long a[n], b[n];
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    b[i] = a[i];
  }
  m = n + 1;
  sort(b, b + n);
  for (int i = 0; i < n; i++) {
    if (a[i] == b[0]) {
      if (p == 1) {
        m = min(m, k);
        k = 0;
      }
      p = 1;
      k++;
      continue;
    } else if (p == 1)
      k++;
  }
  cout << m;
  return 0;
}
