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;
signed main() {
  int n;
  cin >> n;
  vector<int> v(n);
  for (int& i : v) cin >> i;
  if (n == 1) {
    cout << 0;
    return 0;
  }
  if (n == 2) {
    if (v[0] == 0 && v[1] != 0)
      cout << 1;
    else
      cout << 0;
    return 0;
  }
  long long d1 = v[1], d2 = v[0], cur = v[0] * v[0];
  int minAns = 2, cntBad;
  if (d2 != 0) {
    cntBad = 0;
    for (int i = 0; i < n && cntBad <= 1; ++i) {
      if (cur % d2 == 0 && v[i] == cur / d2) {
        cur /= d2;
        cur *= d1;
      } else {
        cntBad++;
      }
    }
    if (cntBad == 0) {
      cout << 0;
      return 0;
    } else if (cntBad == 1)
      minAns = 1;
  }
  d1 = v[2], d2 = v[0], cur = v[0] * v[0];
  if (d2 != 0) {
    cntBad = 1;
    for (int i = 0; i < n && cntBad <= 1; ++i) {
      if (i == 1) continue;
      if (cur % d2 == 0 && v[i] == cur / d2) {
        cur /= d2;
        cur *= d1;
      } else {
        cntBad++;
      }
    }
    if (cntBad == 1) minAns = 1;
  }
  d1 = v[2], d2 = v[1], cur = v[1] * v[1];
  if (d2 != 0) {
    cntBad = 1;
    for (int i = 1; i < n && cntBad <= 1; ++i) {
      if (cur % d2 == 0 && v[i] == cur / d2) {
        cur /= d2;
        cur *= d1;
      } else {
        cntBad++;
      }
    }
    if (cntBad == 1) minAns = 1;
  }
  int cnt0 = 0;
  for (int i : v) cnt0 += (i == 0);
  if (cnt0 == n) {
    cout << 0;
    return 0;
  } else if (cnt0 == n - 1 && v[0] != 0) {
    cout << 0;
    return 0;
  } else if (cnt0 == n - 1)
    minAns = 1;
  else if (cnt0 == n - 2 && v[0] != 0)
    minAns = 1;
  cout << minAns;
}
