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;
bool Geo(vector<int>& a) {
  int n = a.size();
  if (n == 1) return true;
  if (n == 2) {
    if (a[0] == 0 && a[1] != 0) return false;
    return true;
  }
  if (a[1] == 0) {
    for (int i = 2; i < n; ++i)
      if (a[i] != 0) return false;
    return true;
  }
  if (a[0] == 0) return false;
  for (int i = 2; i < n; ++i)
    if (a[i] * a[0] != a[i - 1] * a[1]) return false;
  return true;
}
bool Spr(vector<int>& a, int nr) {
  vector<int> b;
  for (int i = 0; i < a.size(); ++i)
    if (i != nr) b.push_back(a[i]);
  return Geo(b);
}
int main() {
  ios_base::sync_with_stdio(0);
  int n;
  cin >> n;
  vector<int> a(n);
  for (int i = 0; i < n; ++i) cin >> a[i];
  if (Geo(a)) {
    cout << "0";
    return 0;
  }
  if (n == 2) {
    cout << "1";
    return 0;
  }
  int odp = 2;
  vector<bool> pref(n, false), suf(n, false);
  if (a[0] == 0 && a[1] == 0) {
    pref[0] = true;
    for (int i = 1; i < n; ++i)
      if (pref[i - 1] && a[i] == 0) pref[i] = true;
    if (a[n - 1] == 0) suf[n - 1] = true;
    for (int i = n - 2; i >= 0; --i)
      if (suf[i + 1] && a[i] == 0) suf[i] = true;
  }
  if (a[0] != 0 && a[1] == 0) {
    pref[0] = true;
    for (int i = 1; i < n; ++i)
      if (pref[i - 1] && a[i] == 0) pref[i] = true;
    if (a[n - 1] == 0) suf[n - 1] = true;
    for (int i = n - 2; i >= 0; --i)
      if (suf[i + 1] && a[i] == 0) suf[i] = true;
  }
  if (a[0] != 0 && a[1] != 0) {
    pref[0] = true;
    pref[1] = true;
    for (int i = 2; i < n; ++i)
      if (pref[i - 1] && a[i] * a[0] == a[i - 1] * a[1]) pref[i] = true;
    suf[n - 1] = true;
    for (int i = n - 2; i >= 0; --i)
      if (suf[i + 1] && a[i] * a[1] == a[i + 1] * a[0]) suf[i] = true;
  }
  for (int i = 2; i < n - 1; ++i)
    if (pref[i - 1] && suf[i + 1] && a[i + 1] * a[0] == a[i - 1] * a[1])
      odp = 1;
  if (Spr(a, 0) || Spr(a, 1) || Spr(a, n - 1)) odp = 1;
  cout << odp;
  return 0;
}
