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;
bool isGeometrical(int *a, int n) {
  if (a[0] == 0) {
    for (int i = 0; i < n; i++)
      if (a[i] != 0) return false;
    return true;
  }
  for (int i = 0; i < n - 1; i++)
    if (a[i + 1] * a[0] != a[i] * a[1]) return false;
  return true;
}
int main() {
  int n;
  scanf("%d", &n);
  int a[100000], num0 = 0, pos0 = -1;
  for (int i = 0; i < n; i++) {
    scanf("%d", a + i);
    if (a[i] == 0) {
      num0++;
      if (pos0 == -1) pos0 = i;
    }
  }
  if (n <= 2) {
    printf("%d\n", isGeometrical(a, n) ? 0 : 1);
    return 0;
  }
  if (n == 3) {
    int ans = 2;
    if (isGeometrical(a, n))
      ans = 0;
    else {
      int b[2];
      b[0] = a[0], b[1] = a[1];
      if (isGeometrical(b, 2)) ans = 1;
      b[0] = a[0], b[1] = a[2];
      if (isGeometrical(b, 2)) ans = 1;
      b[0] = a[1], b[1] = a[2];
      if (isGeometrical(b, 2)) ans = 1;
    }
    printf("%d\n", ans);
    return 0;
  }
  if (num0 >= 2) {
    int cnt = 0;
    for (int i = 1; i < n; i++)
      if (a[i] != 0) cnt++;
    printf("%d\n", min(cnt, 2));
    return 0;
  }
  if (num0 == 1) {
    for (int i = pos0; i < n - 1; i++) a[i] = a[i + 1];
    printf("%d\n", isGeometrical(a, n - 1) ? 1 : 2);
    return 0;
  }
  if (isGeometrical(a, n)) {
    puts("0");
    return 0;
  }
  if (isGeometrical(a + 1, n - 1)) {
    puts("1");
    return 0;
  }
  swap(a[0], a[1]);
  if (isGeometrical(a + 1, n - 1)) {
    puts("1");
    return 0;
  }
  swap(a[0], a[1]);
  int cnt = 0;
  for (int i = 0; i < n - 1; i++) {
    if (a[i + 1] * a[0] != a[i] * a[1]) {
      cnt++;
      a[i + 1] = a[i];
    }
    if (cnt == 2) break;
  }
  printf("%d\n", cnt);
  return 0;
}
