Card Game for Two

AtCoder

IDabc088_b

Time2000ms

Memory256MB

Difficulty—

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: $N$ $a_1$ $a_2$ $a_3$ $...$ $a_N$ [samples]

Samples

Input #1

2
3 1

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

Input #2

3
2 7 4

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

Input #3

4
20 18 2 18

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Card Game for Two",
    "description": {
      "content": "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 gam",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc088_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have $N$ cards. A number $a_i$ is written on the $i$\\-th card.  \nAlice and Bob will play a game using these cards. In this game, Alice and Bob alternately take one card. Alice goes first.  \nThe gam...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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