{"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 will pour $x~\\mathrm{cm}^3$ of water into the bottle, and gradually tilt the bottle around one of the sides of the base.\nWhen will the water be spilled? More formally, find the maximum angle in which we can tilt the bottle without spilling any water.\n\n## Constraints\n\n*   All values in input are integers.\n*   $1 \\leq a \\leq 100$\n*   $1 \\leq b \\leq 100$\n*   $1 \\leq x \\leq a^2b$\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$a$ $b$ $x$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc144_d","tags":[],"sample_group":[["2 2 4","45.0000000000\n\nThis bottle has a cubic shape, and it is half-full. The water gets spilled when we tilt the bottle more than $45$ degrees."],["12 21 10","89.7834636934\n\nThis bottle is almost empty. When the water gets spilled, the bottle is nearly horizontal."],["3 1 8","4.2363947991\n\nThis bottle is almost full. When the water gets spilled, the bottle is still nearly vertical."]],"created_at":"2026-03-03 11:01:14"}}