Score: 200 points
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.
Input is given from Standard Input in the following format:
N a_1 a_2 a_3 ... a_N
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