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 Equal(double a, double b) {
  if (abs(a - b) < 1e-9) return true;
  return false;
}
int n;
int a[100002];
bool Valid(int num, int den) {
  if (den != 0)
    return true;
  else if (num == 0)
    return true;
  return false;
}
double getFrac(double b, double num, double den) {
  if (den == 0)
    return 0;
  else
    return b * num / den;
}
int evalArr() {
  int num, den;
  int dels;
  den = a[0];
  num = a[1];
  if (Valid(num, den)) {
    dels = 0;
    for (int i = 1; i < n - 1; i++) {
      double next = getFrac(a[i], num, den);
      while (!Equal(next, a[i + 1])) {
        dels++;
        i++;
        if (dels > 1 || i >= n - 1) break;
      }
    }
    if (dels == 0) return 0;
    if (dels == 1) return 1;
  }
  num = a[2];
  if (Valid(num, den)) {
    dels = 0;
    for (int i = 2; i < n - 1; i++) {
      double next = getFrac(a[i], num, den);
      while (!Equal(next, a[i + 1])) {
        dels++;
        break;
      }
    }
    if (dels == 0) return 1;
  }
  den = a[1];
  num = a[2];
  if (Valid(num, den)) {
    dels = 0;
    for (int i = 2; i < n - 1; i++) {
      double next = getFrac(a[i], num, den);
      while (!Equal(next, a[i + 1])) {
        dels++;
        break;
      }
    }
    if (dels == 0) return 1;
  }
  return 2;
}
int main() {
  cin >> n;
  for (int i = 0; i < n; i++) cin >> a[i];
  int val = evalArr();
  cout << val << endl;
  return 0;
}
