scalars

Problem Description

You are given two vectors v1=(x₁,x₂,...,x_n) and v2=(y₁,y₂,...,y_n). The scalar product of these vectors is a single number, calculated as x₁y₁+x₂y₂+...+x_ny_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

For each test case, the first line contains integer number n. The next two lines contain n integers each, giving the coordinates of v1 and v2 respectively.

Output

For each test case, output a single number Y, which is the minimum scalar product of all permutations of the two given vectors.

Limits

Subtask 1 (50%): 1 <= n <= 8 and -1000 <= x_i, y_i <= 1000

Subtask 2 (50%): 1 <= n <= 800 and -100000 <= x_i, y_i <= 100000

Subtask 3 (0%): Sample Testcases

Acknowledgements

This question is not original, it is from Raffles Algo Express Day 6 (Class A) - Contest 1

Sample Input

3
1 3 -5
-2 4 1

Sample Output

-25

Explanation of Sample Output

 (-5 * 4) + (-2 * 3) + (1 * 1) = (-20) + (-6) + 1 = -25