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 arr[100005];
int tar[100005];
int n;
bool check(int *arr, bool fix, int left) {
  bool bad = false;
  for (int i = 1; i < left - 1; i++) {
    if (arr[i - 1] * arr[i + 1] != arr[i] * arr[i] ||
        (arr[i - 1] * arr[i + 1] == arr[i] * arr[i] && arr[i - 1] == 0 &&
         arr[i + 1] != 0)) {
      if (bad) {
        return false;
      } else {
        arr[i + 1] = arr[i];
        arr[i] = arr[i - 1];
        bad = true;
      }
    }
  }
  if (fix) {
    return true;
  } else {
    return !bad;
  }
}
int main() {
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> arr[i];
  }
  if (n == 2 && arr[1] != 0 && arr[0] == 0) {
    printf("1\n");
    return 0;
  }
  memcpy(tar, arr, sizeof arr);
  if (check(tar, false, n)) {
    cout << 0 << endl;
    return 0;
  }
  memcpy(tar, arr, sizeof arr);
  if (check(tar + 1, false, n - 1)) {
    cout << 1 << endl;
    return 0;
  }
  memcpy(tar, arr, sizeof arr);
  tar[1] = tar[0];
  if (check(tar + 1, false, n - 1)) {
    cout << 1 << endl;
    return 0;
  }
  memcpy(tar, arr, sizeof arr);
  if (check(tar, true, n)) {
    cout << 1 << endl;
    return 0;
  } else {
    cout << 2 << endl;
    return 0;
  }
  return 0;
}
