It’s universally acknowledged that there’re innumerable trees in the campus of HUST.
Given a sequence of numbers a₁,a₂,…,a_n, please find the maximum average sequence of a subsequence of those numbers. The definition of average sequence is that the number of pairs that satisfy u divides v or v divides u, divides by the length of the sequence.
For example, in the sequence {1,2,3,4}, the maximum average sequence is {1,2,4}. There are three pairs (<1,2>,<1,4>,<2,4>) that satisfy u divides v or v divides u, and the length of the sequence is 3, so the answer is 3÷3=1.

There is an integer N(1≤N≤100) in the first line, indicating the length of the sequence.
Then there are N integers xi (1≤xi≤109) in the next line, the elements of the sequence.

Output the answer of the problem, Let the standard answer be a, and your answer is b, your answer will be considered as correct if and only if 

4
1 2 3 4

1.0000000000

2
3 5

0.0000000000