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;
void solve() {
  int n;
  cin >> n;
  vector<pair<int, int>> vp;
  for (int i = 0; i < n; i++) {
    int val;
    cin >> val;
    vp.push_back({val, i});
  }
  sort(vp.begin(), vp.end());
  int ans = INT_MAX;
  for (int i = 0; i < n - 1; i++) {
    if (vp[i].first == vp[i + 1].first) {
      ans = min(ans, abs(vp[i].second - vp[i + 1].second));
    } else
      break;
  }
  if (vp[0].first != vp[1].first) ans = abs(vp[0].second - vp[1].second);
  cout << ans << endl;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  ;
  for (int i = 1, t = 1; i <= t; i++) {
    solve();
  }
  return 0;
}
