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;
const double inf = 1e18;
const double eps = 1e-6;
const int maxn = 100010;
const int mod = 1000000007;
int a[maxn];
double b[maxn], c[maxn];
int main() {
  ios::sync_with_stdio(false);
  int n;
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
  }
  for (int i = 2; i <= n; i++) {
    if (a[i] == 0)
      b[i] = 0;
    else if (a[i - 1] == 0)
      b[i] = inf;
    else
      b[i] = a[i] * 1.0 / a[i - 1];
  }
  for (int i = 3; i <= n; i++) {
    if (a[i] == 0)
      c[i] = 0;
    else if (a[i - 2] == 0)
      c[i] = inf;
    else
      c[i] = a[i] * 1.0 / a[i - 2];
  }
  int flag = 1, ans = 2;
  for (int i = 2; i <= n; i++) {
    if (abs(b[i] - b[2]) > eps || abs(b[i] - inf) < eps) {
      flag = 0;
      break;
    }
  }
  if (flag) ans = 0;
  flag = 1;
  for (int i = 3; i <= n; i++) {
    if (abs(b[i] - b[3]) > eps) {
      flag = 0;
      break;
    }
  }
  if (flag) ans = min(ans, 1);
  flag = 1;
  for (int i = 4; i <= n; i++) {
    if (abs(b[i] - c[3]) > eps) {
      flag = 0;
      break;
    }
  }
  if (flag) ans = min(ans, 1);
  flag = 1;
  int temp = 0;
  if (abs(b[2] - inf) > eps) {
    for (int i = 3; i <= n; i++) {
      if (abs(b[i] - b[2]) > eps) {
        if (i < n && temp == 0 && abs(c[i + 1] - b[2]) < eps) {
          i++;
          temp = 1;
        } else if (i != n || temp != 0) {
          flag = 0;
          break;
        }
      }
    }
    if (flag) ans = min(ans, 1);
  }
  cout << ans << "\n";
  return 0;
}
