Geometric Sequence

A sequence of integers is called a geometric sequence if the ratio of consecutive numbers is constant.
For example, (3,6,12,24) is a geometric sequence (each term is equal to twice the previous number)

Now, with such a sequence, we will shuffle it around and remove some of the elements.
Given the result of such a transformation, try to recover the "geometric ratio" of the original sequence.

If there are multiple values, output the one with the greatest absolute value (if there's still a tie, output the positive one)
If there is no such sequence, output 0.

Input

The number of integers, 2 ≤ N ≤ 100,000
N lines, each with one non-zero integer x ( |x| ≤ 10^18 )

Output

The ratio of the original sequence (if one exists).
The relative error of the answer must be within 10^-9. ( |answer - expected| / |expected| < 10^-9 )

Sample Input

3
1 3 27


Sample Output

3

The original sequence could have been 1,3,9,27 or 27,9,3,1; the former has the greater ratio.

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Point Value: 10
Time Limit: 1.00s
Memory Limit: 64M
Added: Sep 26, 2008
Author: hansonw1

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• Math

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