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 small 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, 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
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.
Output
For each case of input, print the case number and the result.
Sample
| Sample Input | Sample Output |
|---|---|
2 4 2 3 4 5 4 6 7 8 9 3 100 200 300 1 150 | Case 1: 3 Case 2: 0 |