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 maxN = 100000 + 5;
int n;
int a[maxN];
inline bool isGeo(int *s, int *e) {
  int len = e - s;
  if (len == 1) return true;
  if (s[1] == 0) {
    for (int i = 1; i <= len; i++)
      if (s[i] != 0) return false;
    return true;
  }
  for (int i = 3; i <= len; i++)
    if (s[i] * s[1] != s[i - 1] * s[2]) {
      return false;
    }
  return true;
}
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) scanf("%d", &a[i]);
  if (isGeo(a, a + n)) {
    puts("0");
    return 0;
  }
  if (isGeo(a + 1, a + n)) {
    puts("1");
    return 0;
  }
  if (a[1] == 0) {
    int no0 = 0;
    for (int i = 2; i <= n; i++)
      if (a[i] != 0) no0++;
    if (no0 == 1)
      puts("1");
    else
      puts("2");
    return 0;
  }
  swap(a[1], a[2]);
  if (isGeo(a + 1, a + n)) {
    puts("1");
    return 0;
  }
  swap(a[1], a[2]);
  int cnt = 2, end = a[2];
  for (int i = 3; i <= n; i++)
    if (a[i] * a[1] == end * a[2]) {
      cnt++;
      end = a[i];
    }
  if (cnt == (n - 1))
    puts("1");
  else
    puts("2");
  return 0;
}
