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, q = 100000000, temp;
  cin >> n;
  pair<int, int> p[n];
  for (int i = 0; i < n; i++) {
    cin >> p[i].first;
    p[i].second = i;
  }
  sort(p, p + n);
  for (int i = 1; i < n; i++) {
    if (p[i].first == p[0].first) {
      temp = abs(p[i].second - p[i - 1].second);
      if (temp < q) {
        q = temp;
      }
    } else {
      break;
    }
  }
  cout << q;
}
