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 a[100000];
bool Go(int b[], int n) {
  int i;
  if (b[0] == 0) {
    for (i = 1; i < n; i++)
      if (b[i]) break;
    return i >= n;
  }
  for (i = 2; i < n; i++)
    if (b[i - 1] * b[1] != b[0] * b[i]) break;
  return i >= n;
}
void One(int n) {
  int m, b[24], i, j;
  for (i = 0; i < n; i++) {
    m = 0;
    for (j = 0; j < n; j++) {
      if (i == j) continue;
      b[m++] = a[j];
    }
    if (Go(b, m)) {
      puts("1");
      break;
    }
  }
  if (i == n) puts("2");
}
int main() {
  int n, i, j;
  scanf("%d", &n);
  for (i = 0; i < n; i++) scanf("%d", &a[i]);
  if (n < 20) {
    if (a[0] == 0) {
      for (i = 1; i < n; i++)
        if (a[i]) break;
      if (i >= n)
        puts("0");
      else
        One(n);
    } else {
      for (i = 2; i < n; i++)
        if (a[i - 1] * a[1] != a[0] * a[i]) break;
      if (i >= n)
        puts("0");
      else
        One(n);
    }
  } else {
    if (a[0] == 0) {
      j = 0;
      for (i = 1; i < n; i++)
        if (a[i]) j++;
      if (j == 0)
        puts("0");
      else if (j == 1)
        puts("1");
      else if (Go(a + 1, n - 1))
        puts("1");
      else
        puts("2");
    } else {
      int zero = 0, k = 0;
      j = 0;
      for (i = 1; i < n; i++) {
        if (a[i] != a[0]) j++;
        if (a[i]) zero++;
        if ((i + k) & 1) {
          if (a[i] != -a[0]) k++;
        } else {
          if (a[i] != a[0]) k++;
        }
      }
      if (j == 0 || zero == 0 || k == 0)
        puts("0");
      else if (j == 1 || zero == 1 || k == 1)
        puts("1");
      else if (Go(a + 1, n - 1))
        puts("1");
      else
        puts("2");
    }
  }
}
