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() {
  int n, mi = (int)1e9;
  cin >> n;
  vector<int> v(n), pos;
  for (int i = 0; i < n; i++) cin >> v[i];
  for (int i = 0; i < n; i++) {
    if (v[i] < mi) {
      mi = v[i];
      pos.clear();
      pos.push_back(i);
    } else if (v[i] == mi) {
      pos.push_back(i);
    }
  }
  int mindis = (int)1e9;
  for (int i = 0; i < pos.size() - 1; i++)
    mindis = min(mindis, pos[i + 1] - pos[i]);
  cout << mindis << endl;
}
