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 a[100000];
  long long n, min, ans = -1;
  long long idx = 0;
  cin >> n;
  for (int i = 0; i < n; ++i) cin >> a[i];
  for (int i = 1; i < n; ++i)
    if (a[i] < a[idx]) idx = i;
  min = a[idx];
  for (int i = idx + 1; i < n; ++i)
    if (a[i] == min) {
      if (i - idx < ans || ans == -1) ans = i - idx;
      idx = i;
    }
  cout << ans;
}
