Prime Independence

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 multiple of b if, a=b×k (wherekisaprime[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 (≤ 25), 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. Notes:

1. An integer is said to be a prime if it’s divisible by exactly two distinct integers. First few prime numbers are 2, 3, 5, 7, 11, 13, ... Sample Input 3 5 2 4 8 16 32 5 23469 3 123 Sample Output Case 1: 3 Case 2: 3 Case 3: 2