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;
bool check(long long a, long long b, long long c) {
  if (a == 0 && b != 0) {
    return false;
  }
  if (b == 0 && c != 0) {
    return false;
  }
  if (a * c != b * b) {
    return false;
  }
  return true;
}
bool ok(const vector<long long>& a, int bad) {
  for (int i = 1; i < (int)a.size() - 1; ++i) {
    if (i != bad && i - 1 != bad && i + 1 != bad) {
      if (!check(a[i - 1], a[i], a[i + 1])) {
        return false;
      }
    }
  }
  if (bad >= 2 && bad < (int)a.size() - 1) {
    if (!check(a[bad - 2], a[bad - 1], a[bad + 1])) {
      return false;
    }
  }
  if (bad >= 1 && bad < (int)a.size() - 2) {
    if (!check(a[bad - 1], a[bad + 1], a[bad + 2])) {
      return false;
    }
  }
  return true;
}
int main() {
  cout << fixed;
  cout.precision(16);
  int n;
  scanf("%i", &n);
  vector<long long> a(n);
  for (int i = 0; i < n; ++i) {
    int x;
    scanf("%i", &x);
    a[i] = x;
  }
  if (n == 1) {
    cout << 0;
    return 0;
  }
  if (n == 2) {
    if (a[0] == 0 && a[1] != 0) {
      cout << 1;
    } else {
      cout << 0;
    }
    return 0;
  }
  int bad = -1;
  for (int i = 1; i < n - 1; ++i) {
    if (!check(a[i - 1], a[i], a[i + 1])) {
      bad = i;
      break;
    }
  }
  if (bad == -1) {
    cout << "0";
    return 0;
  }
  for (int i = bad - 1; i <= bad + 1; ++i) {
    if (ok(a, i)) {
      cout << "1";
      return 0;
    }
  }
  cout << "2";
  return 0;
}
