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;
unordered_map<long long, long long> m;
int main() {
  ios_base::sync_with_stdio(false);
  long long n, x, i, a[100005], mini = 10000000000001, mi = 1000000000010101;
  cin >> n;
  for (i = 1; i <= n; i++) {
    cin >> a[i];
    mi = min(mi, a[i]);
  }
  for (i = 1; i <= n; i++) {
    if (!m[a[i]])
      m[a[i]] = i;
    else if (a[i] == mi) {
      mini = min(i - m[a[i]], mini);
      m[a[i]] = i;
    }
  }
  cout << mini;
}
