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;
int nums[100000];
int isGeometric(int s, int n) {
  if (s == n - 1) return 0;
  int c = nums[s];
  if (c == 0) {
    int ch = 0;
    for (int i = s; i < n; i++)
      if (nums[i] != 0) ch++;
    return ch;
  }
  double b = nums[s + 1] / (1.0 * c);
  int ch = 0;
  c *= b;
  for (int i = s + 2; i < n; i++) {
    if (nums[i] != c * b) {
      ch++;
    } else {
      c *= b;
    }
  }
  return ch;
}
int main() {
  int n;
  cin >> n;
  for (int i = 0; i < n; i++) cin >> nums[i];
  if (isGeometric(0, n) == 0)
    cout << "0" << endl;
  else if (isGeometric(0, n) == 1)
    cout << "1" << endl;
  else if (isGeometric(1, n) == 0) {
    cout << "1" << endl;
  } else {
    swap(nums[0], nums[1]);
    if (isGeometric(1, n) == 0)
      cout << "1" << endl;
    else
      cout << "2" << endl;
  }
  return 0;
}
