Chords

AtCoder

IDabc338_e

Time2000ms

Memory256MB

Difficulty—

There are $2N$ points placed at equal intervals on a circle, numbered $1$ to $2N$ in a clockwise direction starting from a certain point. There are also $N$ chords on the circle, with the $i$\-th chord connecting points $A_i$ and $B_i$. It is guaranteed that all the values $A_1,\dots,A_N,B_1,\dots,B_N$ are distinct. Determine whether there is an intersection between the chords. ## Constraints * $2\leq N \leq 2\times 10^5$ * $1\leq A_i,B_i \leq 2N$ * $A_1,\dots,A_N,B_1,\dots,B_N$ are all distinct * All input values are integers ## Input The input is given from Standard Input in the following format: $N$ $A_1$ $B_1$ $A_2$ $B_2$ $\vdots$ $A_N$ $B_N$ [samples]

Samples

Input #1

Output #1

Yes

![image](https://img.atcoder.jp/abc338/de1d9dd6cf38caec1c69fe035bdba545.png)
As shown in the figure, chord $1$ (the line segment connecting points $1$ and $3$) and chord $2$ (the line segment connecting points $4$ and $2$) intersect, so print `Yes`.

Input #2

Output #2

No

![image](https://img.atcoder.jp/abc338/1b3b982c8d6ca59f00ca0edd218fb9c4.png)
As shown in the figure, there is no intersection between the chords, so print `No`.

Input #3

Output #3

Yes

API Response (JSON)

{
  "problem": {
    "name": "Chords",
    "description": {
      "content": "There are $2N$ points placed at equal intervals on a circle, numbered $1$ to $2N$ in a clockwise direction starting from a certain point. There are also $N$ chords on the circle, with the $i$\\-th chor",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc338_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $2N$ points placed at equal intervals on a circle, numbered $1$ to $2N$ in a clockwise direction starting from a certain point.\nThere are also $N$ chords on the circle, with the $i$\\-th chor...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments