Repovive

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Rayan and Sarah each have $n$ magical stones. Rayan's stones have values $a_1, a_2, \ldots, a_n$ , and Sarah's stones have values $b_1, b_2, \ldots, b_n$ .

They want to pair their stones: each of Rayan's stones must be paired with exactly one of Sarah's stones, and vice versa. The dissonance of a pairing is the sum of absolute differences between paired stones. Formally, if after reordering Sarah's stones become $b'_1, b'_2, \ldots, b'_n$ , the dissonance is $\sum_{i=1}^{n} |a_i - b'_i|$ .

Sarah can reorder her stones in any way before the pairing. Find the minimum possible dissonance.

Constraints

$1 \le t \le 1000$
$1 \le n \le 1000$
$1 \le a_i \le 1000$
$1 \le b_i \le 1000$
The sum of $n$ over all test cases does not exceed $10^4$ .

Rayan and Sarah each have $n$ magical stones. Rayan's stones have values $a_1, a_2, \ldots, a_n$ , and Sarah's stones have values $b_1, b_2, \ldots, b_n$ .

Sarah can reorder her stones in any way before the pairing. Find the minimum possible dissonance.

Constraints

$1 \le t \le 1000$
$1 \le n \le 1000$
$1 \le a_i \le 1000$
$1 \le b_i \le 1000$
The sum of $n$ over all test cases does not exceed $10^4$ .

1A. Magical Stones

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