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## Problem Description

You are given two vectors v1=(x_{1},x_{2},...,x_{n}) and v2=(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

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

For the first 50% of the testcases, 1 <= *n* <= 8 and -1000 <= x_{i}, y_{i} <= 1000

For the other 50% of the testcases, 100 <= *n* <= 800 and -100000 <= x_{i}, y_{i} <= 100000

## Acknowledgements

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

It is not my fault that it had 510 testcases...

## 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

### Tags

### Subtasks and Limits

Subtask | Score | #TC | Time | Memory | Scoring |
---|---|---|---|---|---|

1 | 50 | 500 | 1s | 32MB | Average |

2 | 50 | 10 | 1s | 32MB | Average |

### Judge Compile Command

g++ ans.cpp -o scalars -Wall -static -O2 -lm -m64 -s -w -std=gnu++14 -fmax-errors=512