A8037 | Geometrical problem

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 $a_{1},a_{2},...,a_{k}$ , where $a_{i}=c·b^{i-1}$ 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.

The first line contains an integer $n$ ( $1<=n<=10^{5}$ ) — 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 $10^{4}$ .

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.