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>
const int MAXN = 100000 + 100;
int arr[MAXN];
int n;
bool isok(int *arr, int n) {
  for (int i = 1; i < n - 1; ++i) {
    if (arr[i] * arr[i] != arr[i - 1] * arr[i + 1]) return false;
  }
  if (n == 2) {
    if (arr[0] == 0)
      return arr[1] == 0;
    else
      return true;
  }
  int zc = 0;
  for (int i = 1; i < n; ++i) zc += arr[i] == 0;
  if (zc != 0 && zc != n - 1) return false;
  return true;
}
bool checkit(int *arr, int n, int xxx) {
  bool deled = false;
  int delind = 0;
  for (int i = 1; i < n; ++i) {
    if (deled && delind == i - 1) {
      if (arr[i] != arr[i - 2] * xxx) {
        return false;
      }
    } else {
      if (arr[i] != arr[i - 1] * xxx) {
        if (deled)
          return false;
        else {
          deled = true;
          delind = i;
        }
      }
    }
  }
  return true;
}
int main() {
  scanf("%d", &n);
  for (int i = 0; i < n; ++i) {
    scanf("%d", arr + i);
  }
  if (isok(arr, n)) {
    puts("0");
  } else {
    if (n < 100) {
      bool succ = false;
      for (int i = 0; i < n; ++i) {
        int arr2[100];
        for (int j = 0, k = 0; j < n; ++j) {
          if (j != i) arr2[k++] = arr[j];
        }
        if (isok(arr2, n - 1)) {
          succ = true;
          break;
        }
      }
      puts(succ ? "1" : "2");
    } else {
      if (checkit(arr, n, 1) || checkit(arr, n, -1) || checkit(arr, n, 0)) {
        puts("1");
      } else if (isok(arr + 1, n - 1)) {
        puts("1");
      } else {
        puts("2");
      }
    }
  }
  return 0;
}
