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 a[100005];
bool f[100005];
int n;
vector<int> t;
bool ok() {
  int i, m;
  t.clear();
  for (i = 0; i < (n); i++)
    if (!f[i]) t.push_back(a[i]);
  m = t.size();
  for (i = 1; i < m - 1; i++) {
    if (t[i] * t[i] == t[i - 1] * t[i + 1]) {
      if (t[i] == 0) {
        if (t[i + 1] != 0) return false;
      }
    } else
      return false;
  }
  return true;
}
int main() {
  int i, flag;
  while (scanf(" %d", &n) == 1) {
    for (i = 0; i < (n); i++) scanf(" %d", &a[i]);
    if (n == 1) {
      printf("0\n");
      continue;
    }
    if (n == 2) {
      if (a[0] == 0 && a[1] != 0)
        printf("1\n");
      else
        printf("0\n");
      continue;
    }
    memset(f, 0, sizeof(f));
    flag = 0;
    for (i = 1; i < n - 1; i++) {
      if (a[i] * a[i] == a[i - 1] * a[i + 1]) {
        if (a[i] == 0) {
          if (a[i + 1] != 0) {
            flag = 1;
            break;
          }
        }
      } else {
        flag = 1;
        break;
      }
    }
    if (flag == 0) {
      printf("0\n");
      continue;
    }
    flag = 2;
    if (n == 3) {
      if (a[1] == 0 && a[2] != 0)
        ;
      else
        flag = 1;
    } else {
      for (i = 2; i < n - 1; i++) {
        if (a[i] * a[i] == a[i - 1] * a[i + 1]) {
          if (a[i] == 0) {
            if (a[i + 1] != 0) {
              flag = 0;
              break;
            }
          }
        } else {
          flag = 0;
          break;
        }
      }
      if (flag == 0)
        flag = 2;
      else
        flag = 1;
    }
    if (flag == 1) {
      printf("1\n");
      continue;
    }
    if (n == 3) {
      if (a[0] == 0 && a[1] != 0)
        ;
      else
        flag = 1;
    } else {
      for (i = 1; i < n - 2; i++) {
        if (a[i] * a[i] == a[i - 1] * a[i + 1]) {
          if (a[i] == 0) {
            if (a[i + 1] != 0) {
              flag = 0;
              break;
            }
          }
        } else {
          flag = 0;
          break;
        }
      }
      if (flag == 0)
        flag = 2;
      else
        flag = 1;
    }
    if (flag == 1) {
      printf("1\n");
      continue;
    }
    vector<int> v;
    if (n == 3) {
      if (a[0] == 0 && a[2] != 0)
        ;
      else
        flag = 1;
    } else {
      for (i = 1; i < n - 1; i++) {
        if (a[i] * a[i] == a[i - 1] * a[i + 1]) {
          if (a[i] == 0) {
            if (a[i + 1] != 0) {
              v.push_back(i);
              v.push_back(i - 1);
              v.push_back(i + 1);
              break;
            }
          }
        } else {
          v.push_back(i);
          v.push_back(i - 1);
          v.push_back(i + 1);
          break;
        }
      }
    }
    if (flag == 1) {
      printf("1\n");
      continue;
    }
    for (i = 0; i < (v.size()); i++) {
      f[v[i]] = 1;
      if (ok()) {
        flag = 1;
        break;
      }
      f[v[i]] = 0;
    }
    printf("%d\n", flag);
  }
  return 0;
}
