Collinearity

AtCoder

IDabc181_c

Time2000ms

Memory256MB

Difficulty—

We have $N$ points on a two-dimensional infinite coordinate plane. The $i$\-th point is at $(x_i,y_i)$. Is there a triple of distinct points lying on the same line among the $N$ points? ## Constraints * All values in input are integers. * $3 \leq N \leq 10^2$ * $|x_i|, |y_i| \leq 10^3$ * If $i \neq j$, $(x_i, y_i) \neq (x_j, y_j)$. ## Input Input is given from Standard Input in the following format: $N$ $x_1$ $y_1$ $\vdots$ $x_N$ $y_N$ [samples]

Samples

Input #1

Output #1

Yes

The three points $(0, 1), (0, 2), (0, 3)$ lie on the line $x = 0$.

Input #2

Output #2

No

Input #3

Output #3

Yes

API Response (JSON)

{
  "problem": {
    "name": "Collinearity",
    "description": {
      "content": "We have $N$ points on a two-dimensional infinite coordinate plane. The $i$\\-th point is at $(x_i,y_i)$. Is there a triple of distinct points lying on the same line among the $N$ points?",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc181_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have $N$ points on a two-dimensional infinite coordinate plane.\nThe $i$\\-th point is at $(x_i,y_i)$.\nIs there a triple of distinct points lying on the same line among the $N$ points?\n\n## Constraint...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments