Polycarp loves geometric progressions — he collects them. However, as such progressions occur very rarely, he also loves the sequences of numbers where it is enough to delete a single element to get a geometric progression.

In this task we shall define geometric progressions as finite sequences of numbers a1, a2, ..., ak, where ai = c·bi - 1 for some real numbers c and b. For example, the sequences [2, -4, 8], [0, 0, 0, 0], [199] are geometric progressions and [0, 1, 2, 3] is not.

Recently Polycarp has found a sequence and he can't classify it. Help him to do it. Determine whether it is a geometric progression. If it is not, check if it can become a geometric progression if an element is deleted from it.

Input

The first line contains an integer n (1 ≤ n ≤ 105) — the number of elements in the given sequence. The second line contains the given sequence. The numbers are space-separated. All the elements of the given sequence are integers and their absolute value does not exceed 104.

Output

Print 0, if the given sequence is a geometric progression. Otherwise, check if it is possible to make the sequence a geometric progression by deleting a single element. If it is possible, print 1. If it is impossible, print 2.

Examples

Input

4
3 6 12 24


Output

0


Input

4
-8 -16 24 -32


Output

1


Input

4
0 1 2 3


Output

2
#include <bits/stdc++.h>
using namespace std;
const int Maxn = 100000;
long double small = 0.00000001;
int n, a[Maxn];
int main() {
  int i, tmp1, tmp2;
  long double q;
  cin >> n;
  for (i = 0; i < n; i++) cin >> a[i];
  if (n == 1)
    cout << "0\n";
  else {
    if (a[0] == 0)
      q = 0;
    else
      q = (long double)a[1] / a[0];
    for (i = 1; i < n; i++)
      if (fabs(a[i] - a[i - 1] * q) > small) break;
    if (i == n)
      cout << "0\n";
    else {
      if (n == 2) {
        cout << "1\n";
        return 0;
      }
      bool mist = false;
      if (a[0] == 0)
        q = 0;
      else
        q = (long double)a[1] / a[0];
      for (i = 1; i < n; i++)
        if (fabs(a[i] - a[i - 1] * q) > small)
          if (mist)
            break;
          else {
            mist = true;
            tmp1 = i;
            tmp2 = a[i];
            a[i] = a[i - 1];
          }
      if (mist) a[tmp1] = tmp2;
      if (i == n)
        cout << "1\n";
      else {
        if (a[1] == 0)
          q = 0;
        else
          q = (long double)a[2] / a[1];
        for (i = 2; i < n; i++)
          if (fabs(a[i] - a[i - 1] * q) > small) break;
        if (i == n)
          cout << "1\n";
        else {
          a[1] = a[0];
          if (a[1] == 0)
            q = 0;
          else
            q = (long double)a[2] / a[1];
          for (i = 2; i < n; i++)
            if (fabs(a[i] - a[i - 1] * q) > small) break;
          if (i == n)
            cout << "1\n";
          else
            cout << "2\n";
        }
      }
    }
  }
  return 0;
}
