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>
int main() {
  int32_t num_elements;
  std::cin >> num_elements;
  int32_t* elements = new int32_t[num_elements];
  for (int32_t i = 0; i < num_elements; i++) std::cin >> elements[i];
  bool has_zero = false;
  int32_t num_zeroes = 0;
  for (int32_t i = 0; i < num_elements; i++)
    if (elements[i] == 0) {
      has_zero = true;
      num_zeroes++;
    }
  if (has_zero) {
    if (num_zeroes == num_elements ||
        (num_zeroes == num_elements - 1 && elements[0] != 0))
      std::cout << 0;
    else {
      if (num_zeroes == num_elements - 1 ||
          (num_zeroes == num_elements - 2 && elements[0] != 0))
        std::cout << 1;
      else if (num_zeroes == 1) {
        int32_t index_of_zero;
        for (int32_t i = 0; i < num_elements; i++)
          if (elements[i] == 0) {
            index_of_zero = i;
            break;
          }
        std::vector<double> deltas;
        for (int32_t i = 1; i < num_elements; i++) {
          if (i == index_of_zero) continue;
          if (i == index_of_zero + 1) {
            if (i > 1)
              deltas.push_back((double)elements[i] / (double)elements[i - 2]);
          } else
            deltas.push_back((double)elements[i] / (double)elements[i - 1]);
        }
        bool equal = true;
        for (int32_t i = 1; i < deltas.size(); i++)
          if (fabs(deltas[i] - deltas[0]) > 0.000001) {
            equal = false;
            break;
          }
        if (equal) {
          std::cout << 1;
        } else {
          std::cout << 2;
        }
      } else
        std::cout << 2;
    }
    return 0;
  }
  std::vector<double> deltas;
  for (int32_t i = 1; i < num_elements; i++)
    deltas.push_back((double)elements[i] / (double)elements[i - 1]);
  bool equal = true;
  for (int32_t i = 1; i < deltas.size(); i++)
    if (fabs(deltas[i] - deltas[0]) > 0.000001) {
      equal = false;
      break;
    }
  if (equal) {
    std::cout << 0;
    return 0;
  }
  bool equal_without_1 = true;
  for (int32_t i = 2; i < deltas.size(); i++)
    if (fabs(deltas[i] - deltas[1]) > 0.000001) {
      equal_without_1 = false;
      break;
    }
  bool equal_without_last = true;
  for (int32_t i = 1; i < deltas.size() - 1; i++)
    if (fabs(deltas[i] - deltas[0]) > 0.000001) {
      equal_without_last = false;
      break;
    }
  if (equal_without_1 || equal_without_last) {
    std::cout << 1;
    return 0;
  }
  int32_t first_weird;
  for (int32_t i = 1; i < deltas.size(); i++)
    if (fabs(deltas[i] - deltas[0]) > 0.000001) {
      first_weird = i;
      break;
    }
  bool can_delete = true;
  for (int32_t i = first_weird + 2; i < deltas.size(); i++) {
    if (fabs(deltas[i] - deltas[0]) > 0.000001) {
      can_delete = false;
      break;
    }
  }
  can_delete = can_delete && fabs((double)elements[first_weird + 2] /
                                      (double)elements[first_weird] -
                                  deltas[0]) <= 0.000001;
  std::cout << (can_delete ? 1 : 2);
  return 0;
}
