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 int n;
  cin >> n;
  long long int arr[n];
  long long int ans = INT_MAX;
  for (int i = 1; i <= n; i++) {
    cin >> arr[i];
    ans = min(ans, arr[i]);
  }
  vector<long long int> v, v2;
  for (int i = 1; i <= n; i++) {
    if (arr[i] == ans) {
      v.push_back(i);
    }
  }
  long long int tmp = INT_MAX;
  for (int i = 1; i < v.size(); i++) tmp = min(tmp, v[i] - v[i - 1]);
  cout << tmp << endl;
  return 0;
}
