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 arr[100000];
int main() {
  int n, i, mi = 1e9 + 1, ans, last;
  cin >> n, ans = n;
  for (i = 0; i < n; i++) cin >> arr[i], mi = min(mi, arr[i]);
  for (last = 0; arr[last] != mi; last++)
    ;
  for (i = last + 1; i < n; i++)
    if (arr[i] == mi) ans = min(i - last, ans), last = i;
  cout << ans << "\n";
}
