Gentle Pairs

AtCoder

IDabc187_b

Time2000ms

Memory256MB

Difficulty—

On the $xy$\-plane, We have $N$ points numbered $1$ to $N$. Point $i$ is at $(x_i, y_i)$, and the $x$\-coordinates of the $N$ points are pairwise different. Find the number of pairs of integers $(i, j)\ (i < j)$ that satisfy the following condition: * The line passing through Point $i$ and Point $j$ has a slope between $-1$ and $1$ (inclusive). ## Constraints * All values in input are integers. * $1 \le N \le 10^3$ * $|x_i|, |y_i| \le 10^3$ * $x_i \neq x_j$ for $i \neq j$. ## 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

2

The slopes of the lines passing through $(0, 0)$ and $(1, 2)$, passing through $(0, 0)$ and $(2, 1)$, and passing through $(1, 2)$ and $(2, 1)$ are $2$, $\frac{1}{2}$, and $-1$, respectively.

Input #2

1
-691 273

Output #2

Input #3

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Gentle Pairs",
    "description": {
      "content": "On the $xy$\\-plane, We have $N$ points numbered $1$ to $N$. Point $i$ is at $(x_i, y_i)$, and the $x$\\-coordinates of the $N$ points are pairwise different. Find the number of pairs of integers $(i, j",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc187_b"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "On the $xy$\\-plane, We have $N$ points numbered $1$ to $N$. Point $i$ is at $(x_i, y_i)$, and the $x$\\-coordinates of the $N$ points are pairwise different.\nFind the number of pairs of integers $(i, j...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments