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 EPS = 0.0000001;
double ABS(double a) {
  if (a > 0)
    return a;
  else
    return -a;
}
int main() {
  int n, err1 = 0, nullerr = 0, err2 = 1;
  cin >> n;
  vector<int> a(n);
  for (int i = 0; i < n; ++i) cin >> a[i];
  int kol = 0;
  for (int i = 0; i < n; ++i)
    if (a[i] == 0) {
      kol++;
    }
  if (kol == n) {
    cout << 0 << endl;
    return 0;
  } else if (kol == n - 1 && a[0] != 0) {
    cout << 0 << endl;
    return 0;
  } else if (kol == n - 1) {
    cout << 1 << endl;
    return 0;
  } else if (kol == n - 2 && kol != 0 && a[0] != 0) {
    cout << 1 << endl;
    return 0;
  } else if (kol > 1) {
    cout << 2 << endl;
    return 0;
  } else if (kol == 1) {
    nullerr++;
    n--;
    for (int i = 0; i < n; ++i)
      if (a[i] == 0) {
        for (int j = i; j < n; ++j) a[j] = a[j + 1];
        break;
      }
  }
  double q = (double)a[1] / a[0];
  for (int i = 1; i < n - 1; ++i) {
    if (ABS((double)a[i + 1] / a[i] - q) > EPS) {
      err1++;
      if (i + 2 < n && ABS((double)a[i + 2] / a[i] - q) > EPS) err1++;
      i++;
    }
  }
  q = (double)a[2] / a[1];
  for (int i = 2; i < n - 1; ++i) {
    if (ABS((double)a[i + 1] / a[i] - q) > EPS) {
      err2++;
      if (i + 2 < n && ABS((double)a[i + 2] / a[i] - q) > EPS) err2++;
      i++;
    }
  }
  int err = min(err1, err2);
  if (err + nullerr == 0) {
    cout << 0 << endl;
    return 0;
  } else if (err + nullerr == 1) {
    cout << 1 << endl;
    return 0;
  } else {
    cout << 2 << endl;
  }
  return 0;
}
