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;
const int INF = 2147483647;
const double PI = 3.141592653589793;
const int N = 100005;
int n, tab[N], l1, l2, i;
map<pair<int, int>, int> mapa;
map<pair<int, int>, int>::iterator it;
pair<int, int> res[N];
void wypisz() {
  for (it = mapa.begin(); it != mapa.end(); it++) {
    printf("%d %d %d  ", (*it).first.first, (*it).first.second, (*it).second);
  }
  printf("\n");
}
int nwd(int a, int b) {
  if (b == 0) return a;
  return nwd(b, a % b);
}
void daj(int a, int b, int &l1, int &l2) {
  if (tab[a] == 0) {
    l1 = 0;
    l2 = 1;
  } else {
    int k = nwd(abs(tab[a]), abs(tab[b]));
    l1 = tab[a] / k;
    l2 = tab[b] / k;
  }
}
bool usun(int a) {
  if (a == 0) {
    mapa[res[1]]--;
    if (mapa[res[1]] == 0) mapa.erase(res[1]);
    if (mapa.size() == 1) return true;
    mapa[res[1]]++;
    return false;
  }
  if (a == n - 1) {
    mapa[res[n - 1]]--;
    if (mapa[res[n - 1]] == 0) mapa.erase(res[n - 1]);
    if (mapa.size() == 1) return true;
    mapa[res[n - 1]]++;
    return false;
  }
  int l1, l2;
  mapa[res[a]]--;
  if (mapa[res[a]] == 0) mapa.erase(res[a]);
  mapa[res[a + 1]]--;
  if (mapa[res[a + 1]] == 0) mapa.erase(res[a + 1]);
  daj(a + 1, a - 1, l1, l2);
  if (l2 < 0) {
    l1 *= (-1);
    l2 *= (-1);
  }
  mapa[pair<int, int>(l1, l2)]++;
  if (mapa.size() == 1) return true;
  mapa[pair<int, int>(l1, l2)]--;
  if (mapa[pair<int, int>(l1, l2)] == 0) mapa.erase(pair<int, int>(l1, l2));
  mapa[res[a]]++;
  mapa[res[a + 1]]++;
  return false;
}
int main() {
  scanf("%d", &n);
  for (i = 0; i < n; i++) scanf("%d", &tab[i]);
  if (n == 2 && tab[0] == 0 && tab[1] != 0) {
    printf("1\n");
    return 0;
  }
  mapa.clear();
  for (i = 1; i < n; i++) {
    daj(i, i - 1, l1, l2);
    if (l2 < 0) {
      l1 *= (-1);
      l2 *= (-1);
    }
    mapa[pair<int, int>(l1, l2)]++;
    res[i] = pair<int, int>(l1, l2);
  }
  if (mapa.size() <= 1) {
    printf("0\n");
    return 0;
  }
  for (i = 0; i < n; i++)
    if (usun(i)) {
      printf("1\n");
      return 0;
    }
  printf("2\n");
  return 0;
}
