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>
int p[100010];
int q[100010];
int n;
bool judge() {
  int i;
  for (i = 2; i <= n - 2; i++)
    if (q[i - 1] * q[i + 1] != q[i] * q[i]) return false;
  if (q[0] != 0 && q[1] == 0 && q[2] == 0) return false;
  if (q[n - 1] != 0 && q[n - 2] == 0 && q[n - 3] == 0) return false;
  return true;
}
int main() {
  int i, j;
  int num;
  scanf("%d", &n);
  for (i = 1; i <= n; i++) scanf("%d", &p[i]);
  for (i = 1; i <= n; i++)
    if (p[i] == 0) {
      if (i <= 3) {
        num = 0;
        for (j = 2; j <= n; j++)
          if (p[j] == 0) num++;
        if (num == n - 1) {
          printf("0\n");
          return 0;
        }
        if (num == n - 2) {
          printf("1\n");
          return 0;
        }
      }
      for (j = 1; j < i; j++) q[j] = p[j];
      for (j = i + 1; j <= n; j++) q[j - 1] = p[j];
      if (judge()) {
        printf("1\n");
        return 0;
      } else {
        printf("2\n");
        return 0;
      }
    }
  for (i = 2; i <= n - 1; i++)
    if (p[i - 1] * p[i + 1] != p[i] * p[i]) {
      for (j = 1; j < i; j++) q[j] = p[j];
      for (j = i + 1; j <= n; j++) q[j - 1] = p[j];
      if (judge()) {
        printf("1\n");
        return 0;
      }
      for (j = 1; j < i - 1; j++) q[j] = p[j];
      for (j = i; j <= n; j++) q[j - 1] = p[j];
      if (judge()) {
        printf("1\n");
        return 0;
      }
      for (j = 1; j <= i; j++) q[j] = p[j];
      for (j = i + 2; j <= n; j++) q[j - 1] = p[j];
      if (judge()) {
        printf("1\n");
        return 0;
      }
      printf("2\n");
      return 0;
    }
  printf("0\n");
  return 0;
}
