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B - Card Game for Two

Score: $200$ points

Problem Statement

We have $N$ cards. A number $a_i$ is written on the $i$-th card.
Alice and Bob will play a game using these cards. In this game, Alice and Bob alternately take one card. Alice goes first.
The game ends when all the cards are taken by the two players, and the score of each player is the sum of the numbers written on the cards he/she has taken. When both players take the optimal strategy to maximize their scores, find Alice's score minus Bob's score.

Constraints

• $N$ is an integer between $1$ and $100$ (inclusive).
• $a_i \ (1 \leq i \leq N)$ is an integer between $1$ and $100$ (inclusive).

Input

Input is given from Standard Input in the following format:

$N$

$a_1$ $a_2$ $a_3$ $...$ $a_N$

Output

Print Alice's score minus Bob's score when both players take the optimal strategy to maximize their scores.

2
3 1

2

First, Alice will take the card with $3$. Then, Bob will take the card with $1$. The difference of their scores will be $3$ - $1$ = $2$.

3
2 7 4

5

First, Alice will take the card with $7$. Then, Bob will take the card with $4$. Lastly, Alice will take the card with $2$. The difference of their scores will be $7$ - $4$ + $2$ = $5$. The difference of their scores will be $3$ - $1$ = $2$.

4
20 18 2 18

18