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 int oo = 0x3f3f3f3f;
const double eps = 1e-9;
int N, sequ[110000];
map<pair<int, int>, int> M;
int gcd(int a, int b) { return (b == 0) ? a : gcd(b, a % b); }
pair<int, int> getfrac(int a, int b) {
  if (a == 0 || b == 0) return pair<int, int>(0, 0);
  if (b < 0) {
    a = -a;
    b = -b;
  }
  int g = gcd(abs(a), abs(b));
  return pair<int, int>(a / g, b / g);
}
void insert(pair<int, int> p) { M[p]++; }
void remove(pair<int, int> p) {
  M[p]--;
  if (M[p] == 0) M.erase(p);
}
int main() {
  scanf("%d", &N);
  for (int i = (0); i < (N); i++) scanf("%d", &sequ[i]);
  for (int i = (1); i < (N); i++) M[getfrac(sequ[i], sequ[i - 1])]++;
  int res = 2;
  if (int((M).size()) <= 1 && M.find(pair<int, int>(0, 0)) == M.end()) {
    res = 0;
  } else {
    for (int i = (0); i < (N); i++) {
      if (i < N - 1) remove(getfrac(sequ[i + 1], sequ[i]));
      if (i > 0) remove(getfrac(sequ[i], sequ[i - 1]));
      if (i > 0 && i < N - 1) insert(getfrac(sequ[i + 1], sequ[i - 1]));
      if (int((M).size()) <= 1 && M.find(pair<int, int>(0, 0)) == M.end()) {
        res = 1;
        break;
      }
      if (i < N - 1) insert(getfrac(sequ[i + 1], sequ[i]));
      if (i > 0) insert(getfrac(sequ[i], sequ[i - 1]));
      if (i > 0 && i < N - 1) remove(getfrac(sequ[i + 1], sequ[i - 1]));
    }
  }
  int nzero = 0;
  for (int i = (1); i < (N); i++)
    if (sequ[i] == 0) nzero++;
  if (nzero == N - 1) res = 0;
  if (nzero == N - 2) res = min(res, 1);
  cout << res << endl;
  return 0;
}
