Interval Game

AtCoder

IDagc025_c

Time2000ms

Memory256MB

Difficulty—

Takahashi and Aoki will play a game with a number line and some segments. Takahashi is standing on the number line and he is initially at coordinate $0$. Aoki has $N$ segments. The $i$\-th segment is $[L_i,R_i]$, that is, a segment consisting of points with coordinates between $L_i$ and $R_i$ (inclusive). The game has $N$ steps. The $i$\-th step proceeds as follows: * First, Aoki chooses a segment that is still not chosen yet from the $N$ segments and tells it to Takahashi. * Then, Takahashi walks along the number line to some point within the segment chosen by Aoki this time. After $N$ steps are performed, Takahashi will return to coordinate $0$ and the game ends. Let $K$ be the total distance traveled by Takahashi throughout the game. Aoki will choose segments so that $K$ will be as large as possible, and Takahashi walks along the line so that $K$ will be as small as possible. What will be the value of $K$ in the end? ## Constraints * $1 ≤ N ≤ 10^5$ * $-10^5 ≤ L_i < R_i ≤ 10^5$ * $L_i$ and $R_i$ are integers. ## Input Input is given from Standard Input in the following format: $N$ $L_1$ $R_1$ : $L_N$ $R_N$ [samples]

Samples

Input #1

Output #1

10

One possible sequence of actions of Takahashi and Aoki is as follows:

*   Aoki chooses the first segment. Takahashi moves from coordinate $0$ to $-4$, covering a distance of $4$.
*   Aoki chooses the third segment. Takahashi stays at coordinate $-4$.
*   Aoki chooses the second segment. Takahashi moves from coordinate $-4$ to $3$, covering a distance of $7$.
*   Takahashi moves from coordinate $3$ to $0$, covering a distance of $3$.

The distance covered by Takahashi here is $14$ (because Takahashi didn't move optimally). It turns out that if both players move optimally, the distance covered by Takahashi will be $10$.

Input #2

Output #2

Input #3

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Interval Game",
    "description": {
      "content": "Takahashi and Aoki will play a game with a number line and some segments. Takahashi is standing on the number line and he is initially at coordinate $0$. Aoki has $N$ segments. The $i$\\-th segment is ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc025_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Takahashi and Aoki will play a game with a number line and some segments. Takahashi is standing on the number line and he is initially at coordinate $0$. Aoki has $N$ segments. The $i$\\-th segment is ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments