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 INF = ~0U >> 3;
const int IMPOSSIBLE = INF + INF;
const int ANY = IMPOSSIBLE + 2;
vector<int> a;
int gcd(int a, int b) { return b ? gcd(b, a % b) : a; }
int get(int a, int b) {
  if (a == 0 && b == 0) return ANY;
  if (a == 0) return 0;
  if (b == 0) return IMPOSSIBLE;
  if (a < 0) a *= -1, b *= -1;
  int g = gcd(a, b);
  a /= g;
  b /= g;
  return a * 10000 + b;
}
int combine(int a, int b) {
  if (a == ANY) return b;
  if (b == ANY) return a;
  if (a == IMPOSSIBLE || b == IMPOSSIBLE) return IMPOSSIBLE;
  if (a != b) return IMPOSSIBLE;
  return a;
}
bool check(const vector<int>& a) {
  int now = get(a[1], a[0]);
  for (int i = 1; i < a.size(); i++) {
    now = combine(now, get(a[i], a[i - 1]));
    if (now == IMPOSSIBLE) return false;
  }
  return true;
}
bool tryDel(vector<int>& a, int it) {
  int tmp = a[it];
  a.erase(a.begin() + it);
  bool res = check(a);
  a.insert(a.begin() + it, tmp);
  return res;
}
int main() {
  int n, x;
  cin >> n;
  for (int i = 0; i < n; i++) scanf("%d", &x), a.push_back(x);
  if (check(a)) {
    cout << 0 << endl;
    return 0;
  }
  if (n < 4) {
    for (int i = 0; i < n; i++) {
      vector<int> next = a;
      next.erase(next.begin() + i);
      if (check(next)) {
        cout << 1 << endl;
        return 0;
      }
    }
    cout << 2 << endl;
    return 0;
  } else {
    for (int it = 0; it <= 3; it++) {
      if (it < 3) {
        if (tryDel(a, it)) {
          cout << 1 << endl;
          return 0;
        }
      } else {
        int x = a[0], y = a[1];
        if (x == 0 && y == 0) {
          int zeroCnt = count(a.begin(), a.end(), 0);
          if (zeroCnt >= n - 1) {
            cout << 1 << endl;
            return 0;
          } else {
            cout << 2 << endl;
            return 0;
          }
        }
        if (x == 0 && y != 0) {
          cout << 2 << endl;
          return 0;
        }
        if (true) {
          int it = get(y, x);
          vector<int> bad;
          for (int i = 1; i < n; i++)
            if (combine(it, get(a[i], a[i - 1])) == IMPOSSIBLE)
              bad.push_back(i);
          if (bad.size() > 2) {
            cout << 2 << endl;
            return 0;
          }
          for (typeof(bad.begin()) bIt = bad.begin(); bIt != bad.end(); bIt++) {
            int at = *bIt;
            if (tryDel(a, at) || tryDel(a, at - 1)) {
              cout << 1 << endl;
              return 0;
            }
          }
        }
      }
    }
  }
  cout << 2 << endl;
}
