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;
const int Nmax = 5e4 + 2, mod = 1e9 + 7;
const unsigned long long inf = 2000000009;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int n, hV;
  int minimum, index = 0;
  int ans = mod;
  cin >> n;
  cin >> minimum;
  for (int i = 1; i < n; i++) {
    cin >> hV;
    if (hV == minimum) {
      ans = min(i - index, ans);
      index = i;
    }
    if (hV < minimum) {
      minimum = hV;
      index = i;
      ans = mod;
    }
  }
  cout << ans;
}
