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;
long double EPS(1.0e-10);
bool isValid(long double c, long double b, vector<int>& dat, int begin,
             bool ignore_once = false) {
  for (int i = (int)(begin); i < (int)(dat.size()); i++) {
    if (((dat[i] - dat[i - 1] * b) < 0 ? (-(dat[i] - dat[i - 1] * b))
                                       : (dat[i] - dat[i - 1] * b)) > EPS) {
      if (ignore_once) {
        ignore_once = false;
        if (i == (int)dat.size() - 1 ||
            ((dat[i + 1] - dat[i - 1] * b) < 0
                 ? (-(dat[i + 1] - dat[i - 1] * b))
                 : (dat[i + 1] - dat[i - 1] * b)) <= EPS)
          i++;
        else
          return false;
      } else
        return false;
    }
  }
  return true;
}
int main() {
  int n;
  scanf("%d", &n);
  vector<int> dat(n);
  for (int i = (int)(0); i < (int)(n); i++) scanf("%d", &dat[i]);
  long double c = dat[0];
  long double b = 0.0;
  int ans(2);
  if (dat.size() > 1) b = ((c) < 0 ? (-(c)) : (c)) > EPS ? dat[1] / c : 0.0;
  if (isValid(c, b, dat, 1))
    ans = 0;
  else {
    c = dat[1];
    if (dat.size() > 2) b = ((c) < 0 ? (-(c)) : (c)) > EPS ? dat[2] / c : 0.0;
    if (isValid(c, b, dat, 2))
      ans = 1;
    else {
      c = dat[0];
      if (dat.size() > 2) b = ((c) < 0 ? (-(c)) : (c)) > EPS ? dat[2] / c : 0.0;
      if (isValid(c, b, dat, 1, true))
        ans = 1;
      else {
        c = dat[0];
        if (dat.size() > 1)
          b = ((c) < 0 ? (-(c)) : (c)) > EPS ? dat[1] / c : 0.0;
        if (isValid(c, b, dat, 1, true)) ans = 1;
      }
    }
  }
  cout << ans << endl;
  return 0;
}
