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() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  const int INF = 0x3f3f3f3f;
  int n;
  cin >> n;
  unsigned int low = INF, a[n];
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    low = min(a[i], low);
  }
  int pre = -INF, lst = 0, dis = INF;
  for (int i = 0; i < n; i++) {
    if (low == a[i]) {
      lst = i;
      dis = min(lst - pre, dis);
      pre = lst;
    }
  }
  cout << dis << endl;
  return 0;
}
