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 N, a[100010], b[100010];
bool generate(int M) {
  int i;
  if (b[0] == 0 || b[1] == 0) return false;
  for (i = 2; i < M; i++) {
    if (b[i - 1] * b[i - 1] % b[i - 2] != 0) return false;
    b[i] = b[i - 1] * b[i - 1] / b[i - 2];
    if (((b[i]) > 0 ? (b[i]) : -(b[i])) > 10000) return false;
  }
  return true;
}
int func(void) {
  int ans = 2, i, j, k;
  if (N == 1) return 0;
  if (N == 2) {
    if (a[0] == 0 && a[1] == 0) return 0;
    if (a[0] != 0 && a[1] != 0) return 0;
    if (a[0] != 0 && a[1] == 0) return 0;
    return 1;
  }
  int nonzero = 0;
  for ((i) = 0; (i) < (int)(N); (i)++)
    if (a[i] != 0) nonzero++;
  ans = min(ans, nonzero);
  if (nonzero == 1 && a[0] != 0) return 0;
  if (nonzero == 2 && a[0] != 0) ans = min(ans, 1);
  b[0] = a[0];
  b[1] = a[1];
  if (generate(N)) {
    for ((i) = 0; (i) < (int)(N); (i)++)
      if (a[i] != b[i]) break;
    if (i == N) return 0;
  }
  for ((i) = 0; (i) < (int)(3); (i)++) {
    if (i == 0) {
      b[0] = a[0];
      b[1] = a[1];
    }
    if (i == 1) {
      b[0] = a[0];
      b[1] = a[2];
    }
    if (i == 2) {
      b[0] = a[1];
      b[1] = a[2];
    }
    if (!generate(N - 1)) continue;
    k = 0;
    for ((j) = 0; (j) < (int)(N - 1); (j)++) {
      while (k < N && a[k] != b[j]) k++;
      if (k == N) break;
      if (j == N - 2) ans = min(ans, 1);
      k++;
    }
  }
  return ans;
}
int main(void) {
  int i;
  scanf("%d", &N);
  for ((i) = 0; (i) < (int)(N); (i)++) scanf("%d", &a[i]);
  int ans = func();
  cout << ans << endl;
  return 0;
}
