Water Bottle

AtCoder

IDabc144_d

Time2000ms

Memory256MB

Difficulty—

Takahashi has a water bottle with the shape of a rectangular prism whose base is a square of side $a~\mathrm{cm}$ and whose height is $b~\mathrm{cm}$. (The thickness of the bottle can be ignored.) We will pour $x~\mathrm{cm}^3$ of water into the bottle, and gradually tilt the bottle around one of the sides of the base. When will the water be spilled? More formally, find the maximum angle in which we can tilt the bottle without spilling any water. ## Constraints * All values in input are integers. * $1 \leq a \leq 100$ * $1 \leq b \leq 100$ * $1 \leq x \leq a^2b$ ## Input Input is given from Standard Input in the following format: $a$ $b$ $x$ [samples]

Samples

Input #1

2 2 4

Output #1

45.0000000000

This bottle has a cubic shape, and it is half-full. The water gets spilled when we tilt the bottle more than $45$ degrees.

Input #2

12 21 10

Output #2

89.7834636934

This bottle is almost empty. When the water gets spilled, the bottle is nearly horizontal.

Input #3

3 1 8

Output #3

4.2363947991

This bottle is almost full. When the water gets spilled, the bottle is still nearly vertical.

API Response (JSON)

{
  "problem": {
    "name": "Water Bottle",
    "description": {
      "content": "Takahashi has a water bottle with the shape of a rectangular prism whose base is a square of side $a~\\mathrm{cm}$ and whose height is $b~\\mathrm{cm}$. (The thickness of the bottle can be ignored.) We ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc144_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Takahashi has a water bottle with the shape of a rectangular prism whose base is a square of side $a~\\mathrm{cm}$ and whose height is $b~\\mathrm{cm}$. (The thickness of the bottle can be ignored.)\nWe ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments