{"raw_statement":[{"iden":"problem statement","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."},{"iden":"constraints","content":"*   $1 \\leq N \\leq 100$"},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$"},{"iden":"sample input 1","content":"1"},{"iden":"sample output 1","content":"3.5000000000"},{"iden":"sample input 2","content":"2"},{"iden":"sample output 2","content":"4.2500000000"},{"iden":"sample input 3","content":"10"},{"iden":"sample output 3","content":"5.6502176688"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}