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 H[100100];
int n;
bool geo(int f, int s) {
  double c = H[f];
  if (c == 0) {
    bool valid = H[s] == 0;
    for (int i = s + 1; i < n && valid; i++) valid = valid && H[i] == 0;
    return valid;
  }
  bool valid = true;
  double b = H[s] / c;
  double p = b * b;
  for (int i = s + 1; i < n && valid; i++) {
    valid = valid && fabs(H[i] - (c * p)) < 1E-9;
    p *= b;
  }
  return valid;
}
int main() {
  scanf("%d", &n);
  for (int i = 0; i < n; i++) {
    scanf("%d", H + i);
  }
  if (n == 1) {
    cout << 0 << endl;
    return 0;
  }
  if (n == 2) {
    if (H[0] == 0) {
      cout << (H[1] == 0 ? 0 : 1) << endl;
      return 0;
    }
    cout << 0 << endl;
    return 0;
  }
  if (geo(0, 1)) {
    cout << 0 << endl;
    return 0;
  }
  if (n == 3) {
    cout << 1 << endl;
    return 0;
  }
  if (geo(1, 2) || geo(0, 2)) {
    cout << 1 << endl;
    return 0;
  }
  double c = H[0];
  if (c == 0) {
    int cnt = 0;
    for (int i = 1; i < n; i++) cnt += H[i] != 0;
    if (cnt == 1)
      cout << 1 << endl;
    else
      cout << 2 << endl;
    return 0;
  }
  int cnt = 0;
  double b = H[1] / c;
  double p = b * b;
  for (int i = 2; i < n; i++) {
    if (!(fabs(H[i] - (c * p)) < 1E-9))
      cnt++;
    else
      p *= b;
  }
  if (cnt <= 1)
    cout << 1 << endl;
  else
    cout << 2 << endl;
  return 0;
}
