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 isprog(vector<int> p) {
  if (p.size() == 1) return 1;
  if (p.size() == 2 && p[0] != 0) return 1;
  if (p.size() == 2 && p[0] == 0) return p[1] == 0;
  if (p[0] == 0 || p[1] == 0) {
    for (int i = 1; i < (int)p.size(); ++i)
      if (p[i] != 0) return 0;
    return 1;
  }
  for (int i = 1; i < (int)p.size() - 1; ++i)
    if (p[i - 1] * p[i + 1] != p[i] * p[i]) return 0;
  return 1;
}
vector<int> p, q;
int main() {
  int n;
  cin >> n;
  p.resize(n);
  for (int i = 0; i < n; ++i) cin >> p[i];
  if (isprog(p)) {
    cout << "0\n";
    return 0;
  }
  if (n > 1000) {
    int wr = 0;
    for (int i = 0; i < (int)p.size(); ++i)
      if (p[i] != p[0]) ++wr;
    if (wr <= 1) {
      cout << "1\n";
      return 0;
    }
    wr = 0;
    for (int i = 0; i < (int)p.size(); ++i)
      if (p[i] != p[1]) ++wr;
    if (wr <= 1) {
      cout << "1\n";
      return 0;
    }
    wr = 0;
    for (int i = 1; i < (int)p.size(); ++i)
      if (p[i] != 0) ++wr;
    if (wr <= 1) {
      cout << "1\n";
      return 0;
    }
    wr = 0;
    for (int i = 0; i < (int)p.size(); ++i)
      if (i != 1 && p[i] != 0) ++wr;
    if (wr <= 1) {
      cout << "1\n";
      return 0;
    }
    wr = 0;
    for (int i = 0, j = p[0]; i < (int)p.size(); ++i, j *= -1)
      if (p[i] != j) {
        ++wr;
        j *= -1;
      }
    if (wr <= 1) {
      cout << "1\n";
      return 0;
    }
    wr = 0;
    for (int i = 0, j = p[1]; i < (int)p.size(); ++i, j *= -1)
      if (p[i] != j) {
        ++wr;
        j *= -1;
      }
    if (wr <= 1) {
      cout << "1\n";
      return 0;
    }
    wr = 0;
    for (int i = 0, j = -p[0]; i < (int)p.size(); ++i, j *= -1)
      if (p[i] != j) {
        ++wr;
        j *= -1;
      }
    if (wr <= 1) {
      cout << "1\n";
      return 0;
    }
    wr = 0;
    for (int i = 0, j = -p[1]; i < (int)p.size(); ++i, j *= -1)
      if (p[i] != j) {
        ++wr;
        j *= -1;
      }
    if (wr <= 1) {
      cout << "1\n";
      return 0;
    }
    cout << "2\n";
    return 0;
  } else {
    for (int i = 0; i < (int)p.size(); ++i) {
      q = p;
      q.erase(q.begin() + i);
      if (isprog(q)) {
        cout << "1\n";
        return 0;
      }
    }
    cout << "2\n";
    return 0;
  }
  return 0;
}
