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[110000];
bool ok(int a[], int n) {
  int c = a[0], b;
  if (a[0] == 0)
    b = 0;
  else
    b = a[1] / a[0];
  if (c == 0) {
    for (int i = 1; i < n; i++)
      if (a[i]) return false;
    return true;
  }
  for (int i = 1; i < n; i++) {
    if (a[i] * a[0] != a[i - 1] * a[1]) return false;
  }
  return true;
}
bool ok(int a[], int n, int c, int b) {
  if (c == 0) {
    int skip = 0;
    for (int i = 0; i < n; i++) {
      if (a[i]) skip++;
    }
    return skip <= 1;
  }
  int last = 0, skip = 0;
  for (int i = 1; i < n; i++) {
    if (a[i] * a[0] != a[last] * a[1]) {
      skip++;
      continue;
    }
    last = i;
  }
  return skip <= 1;
}
int main() {
  int n;
  scanf("%d", &n);
  for (int i = 0; i < n; i++) {
    scanf("%d", a + i);
  }
  if (ok(a, n)) {
    puts("0");
    return 0;
  }
  if (ok(a + 1, n - 1)) {
    puts("1");
    return 0;
  }
  swap(a[0], a[1]);
  if (ok(a + 1, n - 1)) {
    puts("1");
    return 0;
  }
  swap(a[0], a[1]);
  int c = a[0], b;
  if (a[0] == 0)
    b = 0;
  else
    b = a[1] / a[0];
  if (ok(a, n, c, b)) {
    puts("1");
  } else {
    puts("2");
  }
  return 0;
}
