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() {
  long long n;
  cin >> n;
  long long a[n], i, mi = INT_MAX, ma = INT_MAX, diff;
  vector<long long> v;
  for (i = 0; i < n; i++) {
    cin >> a[i];
    if (a[i] < mi) {
      mi = a[i];
      v.clear();
      v.push_back(i);
    } else if (a[i] == mi) {
      v.push_back(i);
    }
  }
  for (auto it = v.begin(); it != v.end() - 1; it++) {
    diff = (*(it + 1)) - *it;
    ma = min(ma, diff);
  }
  cout << endl;
  cout << ma;
  return 0;
}
