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 cond = 1;
int t[100005];
const int BAD = 1000000;
int e = -1;
int n;
bool allZeroes() {
  for (int i = 1; i < n; ++i)
    if (i != e && t[i] != 0) return false;
  return true;
}
bool gotZero() {
  for (int i = 0; i < n; ++i)
    if (i != e && t[i] == 0) return true;
  return false;
}
bool isZero(double x) { return x > -1e-9 && x < 1e-9; }
bool geometric() {
  if (allZeroes()) return true;
  if (gotZero()) return false;
  int prev = BAD;
  double dd = 0;
  for (int i = 0; i < n; ++i) {
    if (i == e) continue;
    if (prev != BAD) {
      double cd = t[i] / double(prev);
      if (!isZero(dd) && !isZero(dd - cd)) return false;
      dd = cd;
    }
    prev = t[i];
  }
  return true;
}
int main() {
  scanf("%d", &n);
  for (int i = 0; i < (n); i++) scanf("%d", &t[i]);
  if (geometric()) {
    printf("0\n");
    return 0;
  }
  if (gotZero()) {
    bool triedZero = false, triedNonzero = false;
    for (int i = 0; i < n; ++i)
      if (t[i] == 0 && !triedZero) {
        e = i;
        if (geometric()) {
          printf("1\n");
          return 0;
        }
        triedZero = true;
      } else if (i != 0 && t[i] != 0 && !triedNonzero) {
        e = i;
        if (geometric()) {
          printf("1\n");
          return 0;
        }
        triedNonzero = true;
      }
    printf("2\n");
  } else {
    int prev = BAD;
    double dd = 0;
    for (int i = 0; i < n; ++i) {
      if (prev != BAD) {
        double cd = t[i] / double(prev);
        if (!isZero(dd) && !isZero(dd - cd)) {
          e = i - 2;
          if (geometric()) {
            printf("1\n");
            return 0;
          }
          e = i - 1;
          if (geometric()) {
            printf("1\n");
            return 0;
          }
          e = i;
          if (geometric()) {
            printf("1\n");
            return 0;
          }
          printf("2\n");
          return 0;
        }
        dd = cd;
      }
      prev = t[i];
    }
  }
  return 0;
}
