Rectangles

AtCoder

IDabc218_d

Time4000ms

Memory256MB

Difficulty—

We have $N$ distinct points on a two-dimensional plane, numbered $1,2,\ldots,N$. Point $i$ $(1 \leq i \leq N)$ has the coordinates $(x_i,y_i)$. How many rectangles are there whose vertices are among the given points and whose edges are parallel to the $x$\- or $y$\-axis? ## Constraints * $4 \leq N \leq 2000$ * $0 \leq x_i, y_i \leq 10^9$ * $(x_i,y_i) \neq (x_j,y_j)$ $(i \neq j)$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $x_1$ $y_1$ $x_2$ $y_2$ $ \vdots $ $x_N$ $y_N$ [samples]

Samples

Input #1

Output #1

3

There are three such rectangles:
the rectangle whose vertices are Points $1$, $2$, $3$, $4$,
the rectangle whose vertices are Points $1$, $2$, $5$, $6$,
and the rectangle whose vertices are Points $3$, $4$, $5$, $6$.

Input #2

Output #2

Input #3

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Rectangles",
    "description": {
      "content": "We have $N$ distinct points on a two-dimensional plane, numbered $1,2,\\ldots,N$. Point $i$ $(1 \\leq i \\leq N)$ has the coordinates $(x_i,y_i)$. How many rectangles are there whose vertices are among t",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 4000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc218_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have $N$ distinct points on a two-dimensional plane, numbered $1,2,\\ldots,N$. Point $i$ $(1 \\leq i \\leq N)$ has the coordinates $(x_i,y_i)$.\nHow many rectangles are there whose vertices are among t...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments