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 maxn = 4e5 + 1;
const int INF = 1e9 + 7;
int a[maxn];
vector<int> val;
int main() {
  int n;
  cin >> n;
  for (int i = 1; i <= n; ++i) {
    cin >> a[i];
  }
  int mn = INF;
  for (int i = 1; i <= n; ++i) {
    if (mn > a[i]) {
      val.clear();
      mn = a[i];
      val.push_back(i);
    } else if (mn == a[i]) {
      val.push_back(i);
    }
  }
  int mn_dist = INF;
  for (int i = 0; i + 1 < val.size(); ++i) {
    mn_dist = min(mn_dist, val[i + 1] - val[i]);
  }
  cout << mn_dist;
}
