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 N = 1e5 + 100;
int sta[N], top;
int aa[N];
int n;
int f(int i, int j) {
  if (i <= 1 || i >= n) return 1;
  if (i == j) return 1;
  int a, b;
  if (i - 1 != j)
    a = aa[i - 1];
  else if (i - 2 >= 1)
    a = aa[i - 2];
  else
    return 1;
  if (i + 1 != j)
    b = aa[i + 1];
  else if (i + 2 <= n)
    b = aa[i + 2];
  else
    return 1;
  return a * b == aa[i] * aa[i];
}
int fun() {
  top = 0;
  for (int i = 2; i < n; i++) {
    if (aa[i] * aa[i] != aa[i - 1] * aa[i + 1]) {
      sta[top++] = i - 1;
      sta[top++] = i;
      sta[top++] = i + 1;
    }
  }
  sort(sta, sta + top);
  top = unique(sta, sta + top) - sta;
  if (top == 0) return 0;
  if (top > 20) return 2;
  for (int i = 0; i < top; i++) {
    int flag = 1;
    for (int j = 0; j < top; j++) {
      if (!f(sta[j] - 1, sta[i]) || !f(sta[j], sta[i]) ||
          !f(sta[j] + 1, sta[i])) {
        flag = 0;
        break;
      }
    }
    if (flag) return 1;
  }
  return 2;
}
int main() {
  while (scanf("%d", &n) != EOF) {
    int cnt = 0;
    for (int i = 1; i <= n; i++) scanf("%d", &aa[i]), cnt += aa[i] == 0;
    if (cnt == 0) {
      printf("%d\n", fun());
      continue;
    }
    if (aa[1] == 0) {
      if (cnt == n)
        printf("0\n");
      else if (cnt == n - 1)
        printf("1\n");
      else if (cnt == 1) {
        for (int i = 1; i <= n - 1; i++)
          if (aa[i] == 0) swap(aa[i], aa[i + 1]);
        n--;
        printf("%d\n", min(2, fun() + 1));
      } else
        printf("2\n");
      continue;
    }
    if (n <= 2)
      printf("0\n");
    else if (cnt == n - 1)
      printf("0\n");
    else if (cnt == n - 2)
      printf("1\n");
    else if (n == 3)
      printf("1\n");
    else if (cnt == 1) {
      for (int i = 1; i <= n - 1; i++)
        if (aa[i] == 0) swap(aa[i], aa[i + 1]);
      n--;
      printf("%d\n", min(2, fun() + 1));
    } else
      printf("2\n");
  }
  return 0;
}
