Taking the middle

AtCoder

IDagc053_b

Time2000ms

Memory256MB

Difficulty—

We have $2N$ cards, with ID numbers from $1$ through $2N$. Card $i$ has a value of $V_i$. Takahashi and Aoki will do the following procedure $N$ times so that each of them gets $N$ cards. * First, Takahashi chooses one card that is not yet chosen and gets it. Then, Aoki chooses the card whose **ID number** is the median of those of the cards not yet chosen and gets it. Find the maximum possible sum of the values of cards Takahashi has in the end. ## Constraints * $1\leq N\leq 2\times 10^5$ * $0\leq V_i\leq 10^9$ * $V_i$ is an integer. ## Input Input is given from Standard Input in the following format: $N$ $V_1$ $V_2$ $\cdots$ $V_{2N}$ [samples]

Samples

Input #1

3
1 2 3 4 5 6

Output #1

15

Takahashi can get Cards $4$, $5$, and $6$ as follows:

*   First, Takahashi chooses Card $6$, which makes Aoki choose Card $3$.
*   Next, Takahashi chooses Card $5$, which makes Aoki choose Card $2$.
*   Lastly, Takahashi chooses Card $4$, which makes Aoki choose Card $1$.

Input #2

4
1 4 5 8 7 6 3 2

Output #2

API Response (JSON)

{
  "problem": {
    "name": "Taking the middle",
    "description": {
      "content": "We have $2N$ cards, with ID numbers from $1$ through $2N$. Card $i$ has a value of $V_i$. Takahashi and Aoki will do the following procedure $N$ times so that each of them gets $N$ cards. *   First, ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc053_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have $2N$ cards, with ID numbers from $1$ through $2N$. Card $i$ has a value of $V_i$. Takahashi and Aoki will do the following procedure $N$ times so that each of them gets $N$ cards.\n\n*   First, ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments