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 test(int x1, int x2, int x3) { return x2 * x2 == x1 * x3; }
int main() {
  int n;
  scanf("%d", &n);
  vector<int> a(n);
  int count0 = 0;
  int pos0;
  for (int i = 0; i < n; i++) {
    scanf("%d", &a[i]);
    if (a[i] == 0) {
      count0++;
      if (count0 == 1) pos0 = i;
    }
  }
  if (n == 1) {
    cout << "0" << endl;
    return 0;
  }
  if (n == 2) {
    if (a[0] != 0 || a[1] == 0)
      cout << "0" << endl;
    else
      cout << "1" << endl;
    return 0;
  }
  if (count0 > 1) {
    if (pos0 > 2) {
      cout << "2" << endl;
      return 0;
    }
    if (pos0 == 2) {
      if (count0 == n - 2)
        cout << "1" << endl;
      else
        cout << "2" << endl;
      return 0;
    }
    if (pos0 == 1) {
      if (count0 == n - 1)
        cout << "0" << endl;
      else if (count0 == n - 2)
        cout << "1" << endl;
      else
        cout << "2" << endl;
      return 0;
    }
    if (count0 == n) {
      cout << "0" << endl;
      return 0;
    }
    if (count0 == n - 1) {
      cout << "1" << endl;
      return 0;
    }
    cout << "2" << endl;
    return 0;
  }
  if (count0 > 0) {
    for (int i = pos0; i + 1 < n; i++) a[i] = a[i + 1];
    n--;
    for (int i = 1; i + 1 < n; i++)
      if (a[i] * a[i] != a[i - 1] * a[i + 1]) {
        cout << "2" << endl;
        return 0;
      }
    cout << "1" << endl;
    return 0;
  }
  int left = 1;
  for (left = 1; left + 1 < n; left++)
    if (a[left] * a[left] != a[left - 1] * a[left + 1]) break;
  if (left == n - 1) {
    cout << "0" << endl;
    return 0;
  }
  if (left == n - 2) {
    cout << "1" << endl;
    return 0;
  }
  int right;
  for (right = n - 2; right > 0; right--)
    if (a[right] * a[right] != a[right - 1] * a[right + 1]) break;
  if (right == 1) {
    cout << "1" << endl;
    return 0;
  }
  if (left + 2 < right) {
    cout << "2" << endl;
    return 0;
  }
  if (a[left] * a[left] == a[left - 1] * a[left + 2])
    if (left == n - 3 || (a[left + 2] * a[left + 2] == a[left] * a[left + 3] &&
                          right <= left + 2)) {
      cout << "1" << endl;
      return 0;
    }
  if (left == 1 || a[left - 1] * a[left - 1] == a[left - 2] * a[left + 1])
    if (a[left + 1] * a[left + 1] == a[left - 1] * a[left + 2] &&
        right <= left + 1) {
      cout << "1" << endl;
      return 0;
    }
  if (left == 2) {
    if (right <= 2 && (a[2] * a[2] == a[0] * a[3])) {
      cout << "1" << endl;
      return 0;
    }
  }
  cout << "2" << endl;
  return 0;
}
