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() {
  long long a, mini = 10000000001, x[100001], i;
  vector<int> vec;
  cin >> a;
  for (i = 1; i <= a; i++) {
    cin >> x[i];
    if (x[i] < mini) mini = x[i];
  }
  for (i = 1; i <= a; i++) {
    if (x[i] == mini) {
      vec.push_back(i);
    }
  }
  sort(vec.begin(), vec.end());
  int minii = 1000000, lll = vec.size();
  for (i = 0; i < lll - 1; i++) {
    if (abs(vec[i] - vec[i + 1]) < minii) minii = abs(vec[i] - vec[i + 1]);
  }
  cout << minii << endl;
  return 0;
}
