CF51D.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.

波利卡普热爱等比数列——他专门收集这类数列。然而，由于等比数列极为罕见，他也同样喜爱那些仅需删除一个元素即可变为等比数列的数字序列。

在本题中，我们将等比数列定义为有限的数字序列 $a_1,\,a_2,\,...,\,a_k$，其中对某个实数 $c$ 和 $b$，恒有 $a_i = c \cdot b^{i-1}$ 成立。例如，序列 $[2, -4, 8]$、$[0, 0, 0, 0]$、$[199]$ 均为等比数列，而 $[0, 1, 2, 3]$ 则不是。

最近，波利卡普发现了一个序列，却无法判定其类型。请帮助他完成分类：首先判断该序列本身是否为等比数列；若不是，则进一步检查：是否存在某个元素，使得删除它之后剩余序列构成等比数列。

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.

第一行包含一个整数 $n$（$1 \leq n \leq 10^5$）—— 给定序列中元素的个数。
第二行包含给定的序列，数字之间以空格分隔。
给定序列中的所有元素均为整数，且其绝对值不超过 $10^4$。

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.

如果给定序列是等比数列，则输出 0；否则，检查是否可以通过删除恰好一个元素使该序列变为等比数列：若可以，输出 1；若不可能，输出 2。