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1149 - Factors and Multiples
  PDF (English) Statistics Forum
Time Limit: 2 second(s) Memory Limit: 32 MB

You will be given two sets of integers. Let's call them set A and set B. Set A contains n elements and set B contains m elements. You have to remove k1 elements from set A and k2 elements from set B so that of the remaining values no integer in set B is a multiple of any integer in set A. k1 should be in the range [0, n] and k2 in the range [0, m].

You have to find the value of (k1 + k2) such that (k1 + k2) is as low as possible. P is a multiple of Q if there is some integer K such that P = K * Q.

Suppose set A is {2, 3, 4, 5} and set B is {6, 7, 8, 9}. By removing 2 and 3 from A and 8 from B, we get the sets {4, 5} and {6, 7, 9}. Here none of the integers 6, 7 or 9 is a multiple of 4 or 5.

So for this case the answer is 3 (two from set A and one from set B).


Input starts with an integer T (≤ 50), denoting the number of test cases.

The first line of each case starts with an integer n followed by n positive integers. The second line starts with m followed by m positive integers. Both n and m will be in the range [1, 100]. Each element of the two sets will fit in a 32 bit signed integer.


For each case of input, print the case number and the result.

Sample Input

Output for Sample Input


4 2 3 4 5

4 6 7 8 9

3 100 200 300

1 150

Case 1: 3

Case 2: 0


Problem Setter: Sohel Hafiz
Special Thanks: Jane Alam Jan
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