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;
vector<int> seq;
bool geom(vector<int> v) {
  int n = v.size();
  for (int i = 0; i + 1 < n; i++)
    if (v[i] == 0 && v[i + 1] != 0) return false;
  for (int i = 1; i + 1 < n; i++)
    if (v[i] * v[i] != v[i - 1] * v[i + 1]) return false;
  return true;
}
bool test(vector<int> v, int val, int mult) {
  int n = v.size(), skip = 0;
  for (int i = 0; i < n; i++)
    if (v[i] == val)
      val = mult * val;
    else
      skip++;
  return skip <= 1;
}
int main() {
  cin >> N;
  seq.resize(N);
  for (int i = 0; i < N; i++) cin >> seq[i];
  if (geom(seq)) {
    cout << "0\n";
    return 0;
  }
  if (N <= 100) {
    for (int i = 0; i < N; i++) {
      vector<int> v;
      for (int j = 0; j < N; j++)
        if (i != j) v.push_back(seq[j]);
      if (geom(v)) {
        cout << "1\n";
        return 0;
      }
    }
  } else {
    int num;
    if (abs(seq[0]) == abs(seq[1]))
      num = abs(seq[0]);
    else if (abs(seq[1]) == abs(seq[2]))
      num = abs(seq[1]);
    else if (abs(seq[2]) == abs(seq[0]))
      num = abs(seq[2]);
    else {
      cout << "2\n";
      return 0;
    }
    if (test(seq, num, 1) || test(seq, -num, 1) || test(seq, num, -1) ||
        test(seq, -num, -1)) {
      cout << "1\n";
      return 0;
    }
  }
  cout << "2\n";
  return 0;
}
