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() {
  ios_base::sync_with_stdio(false);
  int n;
  cin >> n;
  int min;
  int *a = new int[n];
  for (int i = 0; i < n; i++) cin >> a[i];
  min = a[0];
  for (int i = 0; i < n; i++)
    if (a[i] < min) min = a[i];
  int k = 0, t, x = 0;
  int temp = 1;
  for (int i = 0; i < n; ++i) {
    if (min == a[i]) {
      ++x;
      if (x > 1) {
        k = i - t;
      }
      t = i;
      if (x == 2 || (x > 2 && temp >= k)) temp = k;
    }
  }
  cout << temp;
  cout << endl;
  return 0;
}
