100881: [AtCoder]ABC088 B - Card Game for Two

Memory Limit:256 MB Time Limit:2 S
Judge Style:Text Compare Creator:
Submit:0 Solved:0

Description

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.


Sample Input 1

2
3 1

Sample Output 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 $3$ - $1$ = $2$.


Sample Input 2

3
2 7 4

Sample Output 2

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 $3$ - $1$ = $2$.


Sample Input 3

4
20 18 2 18

Sample Output 3

18

Input

题意翻译

两人轮流取牌,双方都会选择当前最优策略。问所有牌被取完后先取的人比后取的分数高多少 感谢@长河落日 提供的翻译

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