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;
  std::cin >> n;
  std::vector<int> a(n);
  std::copy_n(std::istream_iterator<int>{std::cin}, n, a.begin());
  auto it1 = std::min_element(a.cbegin(), a.cend());
  auto it_to_end = std::find(it1 + 1, a.cend(), *it1);
  int ans = it_to_end - it1;
  do {
    if (it_to_end - it1 < ans) ans = it_to_end - it1;
    it1 = it_to_end;
    it_to_end = std::find(it1 + 1, a.cend(), *it1);
  } while (it_to_end != a.cend());
  std::cout << ans << '\n';
}
