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() {
  ios_base::sync_with_stdio(0);
  cin.tie(0), cout.tie(0);
  int n, ar[100001];
  cin >> n;
  int mi = INT_MAX;
  for (int i = 0; i < n; i++) {
    cin >> ar[i];
    mi = min(mi, ar[i]);
  }
  long long int d = INT_MAX, prev = -INT_MAX;
  for (int i = 0; i < n; i++)
    if (ar[i] == mi) d = min(d, i - prev), prev = i;
  cout << d << endl;
  return 0;
}
