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D. Geometrical problem

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputPolycarp 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.

Input

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}.

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

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