{"problem":{"name":"Alchemist","description":{"content":"You have a pot and $N$ ingredients. Each ingredient has a real number parameter called _value_, and the value of the $i$\\-th ingredient $(1 \\leq i \\leq N)$ is $v_i$. When you put two ingredients in th","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc138_c"},"statements":[{"statement_type":"Markdown","content":"You have a pot and $N$ ingredients. Each ingredient has a real number parameter called _value_, and the value of the $i$\\-th ingredient $(1 \\leq i \\leq N)$ is $v_i$.\nWhen you put two ingredients in the pot, they will vanish and result in the formation of a new ingredient. The value of the new ingredient will be $(x + y) / 2$ where $x$ and $y$ are the values of the ingredients consumed, and you can put this ingredient again in the pot.\nAfter you compose ingredients in this way $N-1$ times, you will end up with one ingredient. Find the maximum possible value of this ingredient.\n\n## Constraints\n\n*   $2 \\leq N \\leq 50$\n*   $1 \\leq v_i \\leq 1000$\n*   All values in input are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$\n$v_1$ $v_2$ $\\ldots$ $v_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc138_c","tags":[],"sample_group":[["2\n3 4","3.5\n\nIf you start with two ingredients, the only choice is to put both of them in the pot. The value of the ingredient resulting from the ingredients of values $3$ and $4$ is $(3 + 4) / 2 = 3.5$.\nPrinting `3.50001`, `3.49999`, and so on will also be accepted."],["3\n500 300 200","375\n\nYou start with three ingredients this time, and you can choose what to use in the first composition. There are three possible choices:\n\n*   Use the ingredients of values $500$ and $300$ to produce an ingredient of value $(500 + 300) / 2 = 400$. The next composition will use this ingredient and the ingredient of value $200$, resulting in an ingredient of value $(400 + 200) / 2 = 300$.\n*   Use the ingredients of values $500$ and $200$ to produce an ingredient of value $(500 + 200) / 2 = 350$. The next composition will use this ingredient and the ingredient of value $300$, resulting in an ingredient of value $(350 + 300) / 2 = 325$.\n*   Use the ingredients of values $300$ and $200$ to produce an ingredient of value $(300 + 200) / 2 = 250$. The next composition will use this ingredient and the ingredient of value $500$, resulting in an ingredient of value $(250 + 500) / 2 = 375$.\n\nThus, the maximum possible value of the last ingredient remaining is $375$.\nPrinting `375.0` and so on will also be accepted."],["5\n138 138 138 138 138","138"]],"created_at":"2026-03-03 11:01:13"}}