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 seq[100010];
int main() {
  int i, n, f;
  double r;
  scanf("%d", &n);
  for (i = 0; i < n; i++) scanf("%d", &seq[i]);
  if (n == 1) {
    printf("0\n");
    return 0;
  }
  if (n == 2) {
    if (seq[0] == 0 && seq[1] != 0)
      printf("1\n");
    else
      printf("0\n");
    return 0;
  }
  if (n == 3) {
    if (seq[0] == 0) {
      if (seq[1] == 0 && seq[2] == 0) printf("0\n");
      if (seq[1] == 0 && seq[2] != 0) printf("1\n");
      if (seq[1] != 0 && seq[2] == 0) printf("1\n");
      if (seq[1] != 0 && seq[2] != 0) printf("1\n");
    } else {
      if (seq[1] * seq[1] == seq[0] * seq[2])
        printf("0\n");
      else
        printf("1\n");
    }
    return 0;
  }
  if (seq[0] == 0)
    r = 0;
  else
    r = (seq[1] * seq[1] * 1.0) / (seq[0] * seq[0]);
  if (seq[1] * seq[1] == seq[0] * seq[2] && seq[2] == seq[0] * r) {
    f = 0;
    for (i = 3; i < n; i++) {
      if (seq[i - 1] * seq[i - 1] != seq[i - 2] * seq[i] ||
          seq[i] != seq[i - 2] * r) {
        f++;
        if (f == 2 ||
            (i + f < n && (seq[i - 1] * seq[i - 1] != seq[i - 2] * seq[i + f] ||
                           seq[i + f] != seq[i - 2] * r))) {
          f = 2;
          break;
        }
        i += f;
        if (f == 2 || (i + f < n && (seq[i + f - 1] * seq[i + f - 1] !=
                                         seq[i - 2] * seq[i + f] ||
                                     seq[i + f] != seq[i - 2] * r))) {
          f = 2;
          break;
        }
        i += f;
      }
    }
  } else {
    if (seq[0] == 0)
      r = 0;
    else
      r = (seq[2] * seq[2] * 1.0) / (seq[0] * seq[0]);
    f = 1;
    if (seq[2] * seq[2] == seq[0] * seq[3] && seq[3] == seq[0] * r) {
      for (i = 4; i < n; i++) {
        if (seq[i - 1] * seq[i - 1] != seq[i - 2] * seq[i] ||
            seq[i] != seq[i - 2] * r) {
          f = 2;
          break;
        }
      }
    } else {
      if (seq[0] == 0)
        r = 0;
      else
        r = (seq[1] * seq[1] * 1.0) / (seq[0] * seq[0]);
      if (seq[1] * seq[1] == seq[0] * seq[3] && seq[3] == seq[0] * r) {
        if (n > 4 &&
            (seq[3] * seq[3] != seq[1] * seq[4] || seq[4] != seq[1] * r))
          f = 2;
        else {
          for (i = 5; i < n; i++) {
            if (seq[i - 1] * seq[i - 1] != seq[i - 2] * seq[i] ||
                seq[i] == seq[i - 2] * r) {
              f = 2;
              break;
            }
          }
        }
      } else {
        if (seq[1] == 0)
          r = 0;
        else
          r = (seq[2] * seq[2] * 1.0) / (seq[1] * seq[1]);
        if (seq[2] * seq[2] == seq[1] * seq[3] && seq[3] == seq[1] * r) {
          for (i = 4; i < n; i++) {
            if (seq[i - 1] * seq[i - 1] != seq[i - 2] * seq[i] ||
                seq[i] != seq[i - 2] * r) {
              f = 2;
              break;
            }
          }
        } else
          f = 2;
      }
    }
  }
  printf("%d\n", f);
  return 0;
}
