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 cnt[100100 + 1];
const int mod = 998244353;
bool prime[100100];
vector<int> v;
void solve() {
  int n;
  cin >> n;
  int a[n];
  map<int, vector<int>> m;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    m[a[i]].push_back(i + 1);
  }
  int mn = INT_MAX;
  for (auto i : m) {
    vector<int> v;
    v = i.second;
    for (int i = 1; i < v.size(); i++) {
      int tmp = v[i] - v[i - 1];
      mn = min(mn, tmp);
    }
    break;
  }
  cout << mn << endl;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  ;
  int t;
  t = 1;
  while (t--) solve();
  return 0;
}
