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;
int n, i;
pair<int, int> A[100001];
int first(int x, int y) {
  int num, den, i, second = 2, j, s1 = 0, s2 = 0, mx;
  num = A[y].second;
  den = A[x].second;
  if (!den) {
    second = 1;
    for (i = y, j = y; i < n; i++)
      if (!A[i].second) second++;
  } else
    for (i = y + 1, j = y; i < n; i++)
      if (A[i].second * den == num * A[j].second) {
        second++;
        j = i;
      }
  return second;
}
int main() {
  scanf("%d", &n);
  for (i = 0; i < n; i++) {
    scanf("%d", &A[i].second);
    A[i].first = abs(A[i].second);
  }
  if (n <= 2) {
    if (n == 2 && A[0].second == 0 && A[1].second != 0)
      printf("1");
    else
      printf("0");
    return 0;
  }
  if (first(0, 1) == n)
    printf("0");
  else if (first(0, 2) == n - 1 || first(1, 2) == n - 1 || first(0, 1) == n - 1)
    printf("1");
  else
    printf("2");
  return 0;
}
