Opposite

AtCoder

IDabc197_d

Time2000ms

Memory256MB

Difficulty—

On a two-dimensional coordinate plane where the $\mathrm{x}$ axis points to the right and the $\mathrm{y}$ axis points up, we have a regular $N$\-gon with $N$ vertices $p_0, p_1, p_2, \dots, p_{N - 1}$. Here, $N$ is guaranteed to be even, and the vertices $p_0, p_1, p_2, \dots, p_{N - 1}$ are in counter-clockwise order. Let $(x_i, y_i)$ denotes the coordinates of $p_i$. Given $x_0$, $y_0$, $x_{\frac{N}{2}}$, and $y_{\frac{N}{2}}$, find $x_1$ and $y_1$. ## Constraints * $4 \le N \le 100$ * $N$ is even. * $0 \le x_0, y_0 \le 100$ * $0 \le x_{\frac{N}{2}}, y_{\frac{N}{2}} \le 100$ * $(x_0, y_0) \neq (x_{\frac{N}{2}}, y_{\frac{N}{2}})$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $x_0$ $y_0$ $x_{\frac{N}{2}}$ $y_{\frac{N}{2}}$ [samples]

Samples

Input #1

4
1 1
2 2

Output #1

2.00000000000 1.00000000000

We are given $p_0 = (1, 1)$ and $p_2 = (2, 2)$.  
The fact that $p_0$, $p_1$, $p_2$, and $p_3$ form a square and they are in counter-clockwise order uniquely determines the coordinates of the other vertices, as follows:

*   $p_1 = (2, 1)$
*   $p_3 = (1, 2)$

Input #2

6
5 3
7 4

Output #2

5.93301270189 2.38397459622

API Response (JSON)

{
  "problem": {
    "name": "Opposite",
    "description": {
      "content": "On a two-dimensional coordinate plane where the $\\mathrm{x}$ axis points to the right and the $\\mathrm{y}$ axis points up, we have a regular $N$\\-gon with $N$ vertices $p_0, p_1, p_2, \\dots, p_{N - 1}",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc197_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "On a two-dimensional coordinate plane where the $\\mathrm{x}$ axis points to the right and the $\\mathrm{y}$ axis points up, we have a regular $N$\\-gon with $N$ vertices $p_0, p_1, p_2, \\dots, p_{N - 1}...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments