Problem
You are given two vectors v_{1}=(x_{1},x_{2},...,x_{n}) and v_{2}=(y_{1},y_{2},...,y_{n}). The scalar product of these vectors is a single number, calculated as x_{1}y_{1}+x_{2}y_{2}+...+x_{n}y_{n}.
Suppose you are allowed to permute the coordinates of each vector as you wish. Choose two permutations such that the scalar product of your two new vectors is the smallest possible, and output that minimum scalar product.
Input
The first line of the input file contains integer number T  the number of test cases. For each test case, the first line contains integer number n. The next two lines contain n integers each, giving the coordinates of v_{1} and v_{2} respectively.Output
For each test case, output a line
Case #X: Ywhere X is the test case number, starting from 1, and Y is the minimum scalar product of all permutations of the two given vectors.
Limits
Small dataset
T = 1000
1 ≤ n ≤ 8
1000 ≤ x_{i}, y_{i} ≤ 1000
Large dataset
T = 10
100 ≤ n ≤ 800
100000 ≤ x_{i}, y_{i} ≤ 100000
Sample
Input 
Output 
2

Case #1: 25

Points  Correct  Attempted 

5pt  2352  2567 
10pt  1048  2336 