Two Contests

AtCoder

IDagc040_b

Time2000ms

Memory256MB

Difficulty—

$10^9$ contestants, numbered $1$ to $10^9$, will compete in a competition. There will be two contests in this competition. The organizer prepared $N$ problems, numbered $1$ to $N$, to use in these contests. When Problem $i$ is presented in a contest, it will be solved by all contestants from Contestant $L_i$ to Contestant $R_i$ (inclusive), and will not be solved by any other contestants. The organizer will use these $N$ problems in the two contests. Each problem must be used in exactly one of the contests, and each contest must have at least one problem. The _joyfulness_ of each contest is the number of contestants who will solve all the problems in the contest. Find the maximum possible total joyfulness of the two contests. ## Constraints * $2 \leq N \leq 10^5$ * $1 \leq L_i \leq R_i \leq 10^9$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $L_1$ $R_1$ $L_2$ $R_2$ $\vdots$ $L_N$ $R_N$ [samples]

Samples

Input #1

Output #1

6

The optimal choice is:

*   Use Problem $1$ and $3$ in the first contest. Contestant $5$, $6$, and $7$ will solve both of them, so the joyfulness of this contest is $3$.
*   Use Problem $2$ and $4$ in the second contest. Contestant $2$, $3$, and $4$ will solve both of them, so the joyfulness of this contest is $3$.
*   The total joyfulness of these two contests is $6$. We cannot make the total joyfulness greater than $6$.

Input #2

Output #2

Input #3

10
457835016 996058008
456475528 529149798
455108441 512701454
455817105 523506955
457368248 814532746
455073228 459494089
456651538 774276744
457667152 974637457
457293701 800549465
456580262 636471526

Output #3

540049931

API Response (JSON)

{
  "problem": {
    "name": "Two Contests",
    "description": {
      "content": "$10^9$ contestants, numbered $1$ to $10^9$, will compete in a competition. There will be two contests in this competition. The organizer prepared $N$ problems, numbered $1$ to $N$, to use in these con",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc040_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "$10^9$ contestants, numbered $1$ to $10^9$, will compete in a competition. There will be two contests in this competition.\nThe organizer prepared $N$ problems, numbered $1$ to $N$, to use in these con...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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