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[100005];
int cal(int i, int j, int k) {
  while (j--) {
    --i;
    if (i == k) --i;
  }
  return i;
}
int check(int l, int r) {
  int tot = -1;
  if (a[l] == 0) {
    for (int i = l + 1; i <= r; ++i)
      if (a[i] != 0) {
        if (tot == -1)
          tot = i;
        else
          return -2;
      }
    return tot;
  }
  if (l + 1 <= r && a[l + 1] == 0) {
    for (int i = l + 2; i <= r; ++i)
      if (a[i] != 0) {
        if (tot == -1)
          tot = i;
        else
          return -2;
      }
    return tot;
  }
  for (int i = l + 2; i <= r; ++i)
    if (a[cal(i, 2, tot)] * a[i] != a[cal(i, 1, tot)] * a[cal(i, 1, tot)]) {
      if (tot == -1)
        tot = i;
      else
        return -2;
    }
  return tot;
}
int main() {
  scanf("%d", &n);
  for (int i = 0; i < n; ++i) scanf("%d", &a[i]);
  if (check(0, n - 1) == -1) {
    cout << 0 << endl;
    return 0;
  }
  bool flag = false;
  if (check(0, n - 1) != -2) flag = true;
  if (check(1, n - 1) == -1) flag = true;
  a[1] = a[0];
  if (check(1, n - 1) == -1) flag = true;
  if (flag) {
    cout << 1 << endl;
    return 0;
  }
  cout << 2 << endl;
  return 0;
}
