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;
  cin >> n;
  int lo = (long long)10000000000;
  vector<int> loc;
  for (int i = 0; i < n; i++) {
    int temp;
    cin >> temp;
    if (temp < lo) {
      lo = temp;
      loc.clear();
      loc.push_back(i);
    } else if (temp == lo) {
      loc.push_back(i);
    }
  }
  int lodist = (long long)10000000000;
  for (int i = 1; i < loc.size(); i++) {
    lodist = min(lodist, loc[i] - loc[i - 1]);
  }
  cout << lodist << endl;
}
