Prime Independence(质因子分解+二分图最大独立集)

 Prime Independence

Time Limit:3000MS     Memory Limit:32768KB     64bit IO Format:%lld & %llu

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Description

A set of integers is called prime independent if none of its member is a prime multiple of another member. An integer a is said to be a prime multipleof b if,

a = b x k (where k is a prime [1])

So, 6 is a prime multiple of 2, but 8 is not. And for example, {2, 8, 17} is prime independent but {2, 8, 16} or {3, 6} are not.

Now, given a set of distinct positive integers, calculate the largest prime independent subset.

Input

Input starts with an integer T (≤ 20), denoting the number of test cases.

Each case starts with an integer N (1 ≤ N ≤ 40000) denoting the size of the set. Next line contains N integers separated by a single space. Each of these N integers are distinct and between 1 and 500000 inclusive.

Output

For each case, print the case number and the size of the largest prime independent subset.

Sample Input

3

5

2 4 8 16 32

5

2 3 4 6 9

3

1 2 3

Sample Output

Case 1: 3

Case 2: 3

Case 3: 2

感觉超棒的一道题，值得一做。。。挺巧妙的。。。

找出一个集合中的最大独立集，任意两数字之间不能是素数倍数的关系。

思路：

最大独立集，必然是二分图。

最大数字50w，考虑对每个数质因子分解，然后枚举所有除去一个质因子后的数是否存在，存在则建边，考虑到能这样建边的数一定是质因子个数奇偶不同，所以相当于按奇偶区分建立了二分图，然后求二分图最大匹配，得到最大独立集就行了。

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Hopcroft-Karp，数组有点乱。。。

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