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 N = 100005;
int n, a[N], b[N];
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cin >> n;
  for (int i = 1; i <= n; i++) cin >> a[i];
  if (n == 1) {
    cout << 0;
    return 0;
  }
  if (n == 2) {
    if (a[1] == 0 && a[2] != 0) {
      cout << 1;
      return 0;
    } else {
      cout << 0;
      return 0;
    }
  }
  int wrong = 0;
  for (int i = 3; i <= n; i++) {
    if (a[1] * a[i] != a[2] * a[i - 1]) {
      wrong++;
      if (i < n) {
        if (a[i + 1] * a[1] != a[i - 1] * a[2])
          wrong++;
        else
          i++;
      }
    }
    if (a[1] == 0 && a[i] != 0) wrong++;
  }
  if (wrong < 2) {
    cout << wrong;
    return 0;
  } else {
    wrong = 0;
    for (int i = 4; i <= n; i++) {
      if (a[2] * a[i] != a[3] * a[i - 1]) {
        wrong++;
        if (i < n) {
          if (a[i + 1] * a[2] != a[i - 1] * a[3])
            wrong++;
          else
            i++;
        }
      }
      if (a[2] == 0 && a[i] != 0) wrong++;
    }
    if (wrong == 0) {
      cout << 1;
      return 0;
    } else {
      wrong = 0;
      a[2] = a[1];
      for (int i = 4; i <= n; i++) {
        if (a[2] * a[i] != a[3] * a[i - 1]) {
          wrong++;
          if (i < n) {
            if (a[i + 1] * a[2] != a[i - 1] * a[3])
              wrong++;
            else
              i++;
          }
        }
        if (a[2] == 0 && a[i] != 0) wrong++;
      }
      if (wrong == 0) {
        cout << 1;
        return 0;
      } else {
        cout << 2;
        return 0;
      }
    }
  }
}
