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() {
  int n;
  cin >> n;
  vector<int> v(n);
  for (int i = 0; i < n; i++) cin >> v[i];
  vector<int> vv = v;
  sort(vv.begin(), vv.end());
  int mn = vv[0];
  vector<int> c;
  for (int i = 0; i < n; i++)
    if (v[i] == mn) c.push_back(i);
  int res = 1 << 30;
  for (int i = 1; i < c.size(); i++) res = min(res, c[i] - c[i - 1]);
  cout << res;
  return 0;
}
