{"problem":{"name":"Throwing the Die","description":{"content":"Let us play a game using a die. The game consists of at most $N$ turns, each of which goes as follows. *   Throw a $6$\\-sided die that shows $1,\\ldots,6$ with equal probability, and let $X$ be the nu","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc266_e"},"statements":[{"statement_type":"Markdown","content":"Let us play a game using a die. The game consists of at most $N$ turns, each of which goes as follows.\n\n*   Throw a $6$\\-sided die that shows $1,\\ldots,6$ with equal probability, and let $X$ be the number shown (each throw is independent of the others).\n*   If it is the $N$\\-th turn now, your **score** is $X$, and the game ends.\n*   Otherwise, choose whether to continue or end the game.\n    *   If you end the game, your score is $X$, and there is no more turn.\n\nFind the expected value of your score when you play the game to maximize this expected value.\n\n## Constraints\n\n*   $1 \\leq N \\leq 100$\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc266_e","tags":[],"sample_group":[["1","3.5000000000"],["2","4.2500000000"],["10","5.6502176688"]],"created_at":"2026-03-03 11:01:14"}}