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() {
  cin.tie(0);
  cout.tie(0);
  ios_base::sync_with_stdio(0);
  int n;
  cin >> n;
  map<int, vector<int>> idx;
  for (int i = 0; i < n; i++) {
    int a;
    cin >> a;
    idx[a].push_back(i);
  }
  auto it = idx.begin();
  vector<int> v = (*it).second;
  int ret = 1e9, sz = v.size();
  for (int i = 0; i < sz - 1; i++) ret = min(ret, v[i + 1] - v[i]);
  cout << ret << endl;
  return 0;
}
