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;
const int size = 1e5 + 9;
int n;
int tab[size];
int main(int argc, const char* argv[]) {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  int m = 1e9 + 7;
  cin >> n;
  for (int i = 0; i < n; i++) {
    int first;
    cin >> first;
    tab[i] = first;
    m = min(m, first);
  }
  int l = -1e9;
  int d = 1e9;
  for (int i = 0; i < n; i++) {
    if (tab[i] == m) {
      d = min(d, i - l);
      l = i;
    }
  }
  cout << d << "\n";
  return 0;
}
