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;
bool geometrica(vector<int> &v) {
  if (int(v.size()) <= 1) return true;
  if (v[0] == 0) {
    for (int i = 1; i < int(v.size()); i++)
      if (v[i] != 0) return false;
    return true;
  }
  for (int i = 2; i < int(v.size()); i++)
    if (v[i] * v[0] != v[i - 1] * v[1]) return false;
  return true;
}
vector<int> borra(vector<int> &v, int index) {
  vector<int> w;
  for (int i = 0; i < int(v.size()); i++)
    if (i != index) w.push_back(v[i]);
  return w;
}
int main() {
  int n;
  cin >> n;
  vector<int> v(n);
  for (int i = 0; i < n; i++) cin >> v[i];
  if (geometrica(v)) {
    cout << 0 << endl;
    exit(0);
  }
  if (n <= 2) {
    cout << 1 << endl;
    exit(0);
  }
  vector<int> w;
  w = borra(v, 0);
  if (geometrica(w)) {
    cout << 1 << endl;
    exit(0);
  }
  w = borra(v, 1);
  if (geometrica(w)) {
    cout << 1 << endl;
    exit(0);
  }
  if (v[0] == 0) {
    int numno0 = 0;
    for (int i = 1; i < n; i++)
      if (v[i] != 0) numno0++;
    if (numno0 >= 2)
      cout << 2 << endl;
    else
      cout << 1 << endl;
    exit(0);
  }
  int numfallos = 0;
  int fallo = -1;
  for (int i = 2; i < int(v.size()); i++) {
    if ((fallo != i - 1 and v[i] * v[0] != v[i - 1] * v[1]) or
        (fallo == i - 1 and v[i] * v[0] != v[i - 2] * v[1])) {
      fallo = i;
      numfallos++;
      if (numfallos >= 2) {
        cout << 2 << endl;
        exit(0);
      }
    }
  }
  cout << 1 << endl;
}
