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 mi = 2e9;
int main() {
  int n, j, i, ans = 2000000, a;
  cin >> n;
  for (i = 1; i <= n; i++) {
    cin >> a;
    if (a < mi)
      mi = a, j = i, ans = 200000;
    else if (a == mi)
      ans = min(ans, i - j), j = i;
  }
  cout << ans << endl;
  return 0;
}
