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 M = 100000 + 5;
int a[M];
int res[M];
int prefix[M];
int suffix[M];
int main() {
  int n;
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
  }
  if (n <= 2) {
    if (n == 1) cout << "0" << endl;
    if (n == 2) {
      if (a[0] == 0 && a[1] != 0) {
        cout << "1" << endl;
      } else {
        cout << "0" << endl;
      }
    }
  } else {
    for (int i = 1; i <= n - 2; i++) {
      res[i] = (a[i] * a[i] == a[i - 1] * a[i + 1] ? 0 : 1);
      if (a[i] == 0 && a[i - 1] == 0 && a[i + 1] != 0) {
        res[i] = 1;
      }
    }
    bool ok = true;
    for (int i = 1; i <= n - 2; i++) {
      if (res[i] == 1) {
        ok = false;
        break;
      }
    }
    if (ok == true) {
      cout << "0" << endl;
    } else {
      prefix[1] = res[1];
      for (int i = 2; i <= n - 2; i++)
        prefix[i] = (prefix[i - 1] + res[i] == 0 ? 0 : 1);
      suffix[n - 2] = res[n - 2];
      for (int i = n - 3; i >= 1; i--)
        suffix[i] = (suffix[i + 1] + res[i] == 0 ? 0 : 1);
      bool ok = false;
      for (int i = 0; i < n; i++) {
        int num = 0;
        if (i - 2 >= 1) num += prefix[i - 2];
        if (i + 2 <= n - 2) num += suffix[i + 2];
        if (i - 2 >= 0 && i + 1 < n) {
          num += (a[i - 1] * a[i - 1] == a[i - 2] * a[i + 1] ? 0 : 1);
          if (a[i - 2] == 0 && a[i - 1] == 0 && a[i + 1] != 0) {
            num = num + 1;
          }
        }
        if (i - 1 >= 0 && i + 2 < n) {
          num += (a[i + 1] * a[i + 1] == a[i - 1] * a[i + 2] ? 0 : 1);
          if (a[i - 1] == 0 && a[i + 1] == 0 && a[i + 2] != 0) {
            num = num + 1;
          }
        }
        if (num == 0) {
          ok = true;
          break;
        }
      }
      if (ok == true) {
        cout << "1" << endl;
      } else {
        cout << "2" << endl;
      }
    }
  }
  return 0;
}
