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[100010], b[100010];
int n;
int gcd(int a, int b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
pair<int, int> norm(pair<int, int> c) {
  int a = c.first;
  int b = c.second;
  if (b < 0) return make_pair(-a, -b);
  return make_pair(a, b);
}
bool isprog() {
  if (n == 1) return true;
  bool f = false;
  for (int i = (0); i < (n); ++i) {
    if (a[i] == 0) f = true;
  }
  if (f) {
    for (int i = (1); i < (n); ++i) {
      if (a[i] != 0) return false;
    }
    return true;
  }
  int g = gcd(((a[0] > 0) ? a[0] : -(a[0])), ((a[1] > 0) ? a[1] : -(a[1])));
  pair<int, int> d;
  d.first = a[0] / g;
  d.second = a[1] / g;
  d = norm(d);
  for (int i = (1); i < (n - 1); ++i) {
    pair<int, int> dd;
    int g = gcd(((a[i] > 0) ? a[i] : -(a[i])),
                ((a[i + 1] > 0) ? a[i + 1] : -(a[i + 1])));
    dd.first = a[i] / g;
    dd.second = a[i + 1] / g;
    dd = norm(dd);
    if (dd != d) return false;
  }
  return true;
}
int main() {
  scanf("%d", &n);
  for (int i = (0); i < (n); ++i) scanf("%d", &a[i]);
  if (isprog()) {
    printf("0\n");
    return 0;
  }
  int cnt = 0;
  for (int i = (0); i < (n); ++i)
    if (a[i] == 0) cnt++;
  if (cnt >= 2) {
    for (int i = (0); i < (n); ++i) b[i] = a[i];
    for (int i = n - 1; i >= 0; --i)
      if (a[i] != 0) {
        for (int j = (i + 1); j < (n); ++j) a[j - 1] = a[j];
        break;
      }
    n--;
    if (isprog()) {
      printf("1\n");
      return 0;
    }
    n++;
    for (int i = (0); i < (n); ++i) a[i] = b[i];
    bool f = false;
    for (int i = (0); i < (n); ++i) b[i] = a[i];
    for (int i = (0); i < (n); ++i) {
      if ((!f) && (a[i] != 0))
        f = true;
      else if (f)
        a[i - 1] = a[i];
    }
    n--;
    if (isprog()) {
      printf("1\n");
      return 0;
    }
    n++;
    for (int i = (0); i < (n); ++i) a[i] = b[i];
    for (int i = (1); i < (n); ++i) a[i - 1] = a[i];
    n--;
    if (isprog())
      printf("1\n");
    else
      printf("2\n");
    return 0;
  }
  if (cnt == 1) {
    int k = -1;
    for (int i = (0); i < (n); ++i) b[i] = a[i];
    for (int i = (1); i < (n); ++i) a[i - 1] = a[i];
    n--;
    if (isprog()) {
      printf("1\n");
      return 0;
    }
    n++;
    for (int i = (0); i < (n); ++i) a[i] = b[i];
    bool f = false;
    for (int i = (0); i < (n); ++i) {
      if ((!f) && (a[i] == 0))
        f = true;
      else if (f)
        a[i - 1] = a[i];
    }
    n--;
    if (isprog())
      printf("1\n");
    else
      printf("2\n");
    return 0;
  }
  int g = gcd(((a[0] > 0) ? a[0] : -(a[0])), ((a[1] > 0) ? a[1] : -(a[1])));
  pair<int, int> d;
  d.first = a[0] / g;
  d.second = a[1] / g;
  d = norm(d);
  for (int i = (1); i < (n - 1); ++i) {
    pair<int, int> dd;
    int g = gcd(((a[i] > 0) ? a[i] : -(a[i])),
                ((a[i + 1] > 0) ? a[i + 1] : -(a[i + 1])));
    dd.first = a[i] / g;
    dd.second = a[i + 1] / g;
    dd = norm(dd);
    if (dd != d) {
      for (int j = (i - 2); j < (i + 3); ++j) {
        if (j < 0) continue;
        if (j >= n) break;
        for (int k = (0); k < (n); ++k) b[k] = a[k];
        for (int k = (0); k < (n); ++k) {
          if (k > j) a[k - 1] = a[k];
        }
        n--;
        if (isprog()) {
          printf("1\n");
          return 0;
        }
        n++;
        for (int k = (0); k < (n); ++k) a[k] = b[k];
      }
      printf("2\n");
      return 0;
    }
  }
  return 0;
}
