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;
vector<int> gener(vector<int> l, int a) {
  vector<int> l2;
  for (int i = 0; i < l.size(); i++)
    if (i != a) l2.push_back(l[i]);
  return l2;
}
bool isright(vector<int> list) {
  if (list.size() == 1) {
    return true;
  }
  vector<double> list1;
  for (int i = 1; i < list.size(); i++) {
    if (list[i - 1] == 0 && list[i] == 0) {
      list1.push_back(100000.0);
      continue;
    }
    if (list[i - 1] == 0) {
      list1.push_back(1000000.0);
      continue;
    }
    list1.push_back(list[i] * 1.0 / list[i - 1]);
  }
  double b = list1[0];
  bool s = true;
  for (int i = 1; i < list1.size(); i++) {
    if (b != list1[i] && list1[i] != 100000.0) s = false;
  }
  if (s && b <= 100000.0) {
    return true;
  }
  return false;
}
int main() {
  int n;
  cin >> n;
  vector<int> list;
  int a;
  for (int i = 0; i < n; i++) {
    cin >> a;
    list.push_back(a);
  }
  if (isright(list)) {
    cout << 0;
    return 0;
  }
  vector<double> list1;
  for (int i = 1; i < n; i++) {
    if (list[i - 1] == 0 && list[i] == 0) {
      list1.push_back(100000.0);
      continue;
    }
    if (list[i - 1] == 0) {
      list1.push_back(1000000.0);
      continue;
    }
    list1.push_back(list[i] * 1.0 / list[i - 1]);
  }
  vector<int> list2;
  list2.push_back(0);
  for (int i = 1; i < list1.size(); i++)
    if (list1[i] != list1[i - 1]) list2.push_back(i);
  if (list2.size() > 4) {
    cout << 2;
    return 0;
  }
  for (int i = 0; i < list2.size(); i++) {
    vector<int> list3 = gener(list, list2[i]);
    if (isright(list3)) {
      cout << 1;
      return 0;
    }
    list3 = gener(list, list2[i] + 1);
    if (isright(list3)) {
      cout << 1;
      return 0;
    }
  }
  cout << 2;
  return 0;
}
