{"problem":{"name":"Sushi","description":{"content":"There are $N$ dishes, numbered $1, 2, \\ldots, N$. Initially, for each $i$ ($1 \\leq i \\leq N$), Dish $i$ has $a_i$ ($1 \\leq a_i \\leq 3$) pieces of sushi on it. Taro will perform the following operation","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"dp_j"},"statements":[{"statement_type":"Markdown","content":"There are $N$ dishes, numbered $1, 2, \\ldots, N$. Initially, for each $i$ ($1 \\leq i \\leq N$), Dish $i$ has $a_i$ ($1 \\leq a_i \\leq 3$) pieces of sushi on it.\nTaro will perform the following operation repeatedly until all the pieces of sushi are eaten:\n\n*   Roll a die that shows the numbers $1, 2, \\ldots, N$ with equal probabilities, and let $i$ be the outcome. If there are some pieces of sushi on Dish $i$, eat one of them; if there is none, do nothing.\n\nFind the expected number of times the operation is performed before all the pieces of sushi are eaten.\n\n## Constraints\n\n*   All values in input are integers.\n*   $1 \\leq N \\leq 300$\n*   $1 \\leq a_i \\leq 3$\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$\n$a_1$ $a_2$ $\\ldots$ $a_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"dp_j","tags":[],"sample_group":[["3\n1 1 1","5.5\n\nThe expected number of operations before the first piece of sushi is eaten, is $1$. After that, the expected number of operations before the second sushi is eaten, is $1.5$. After that, the expected number of operations before the third sushi is eaten, is $3$. Thus, the expected total number of operations is $1 + 1.5 + 3 = 5.5$."],["1\n3","3\n\nOutputs such as `3.00`, `3.000000003` and `2.999999997` will also be accepted."],["2\n1 2","4.5"],["10\n1 3 2 3 3 2 3 2 1 3","54.48064457488221"]],"created_at":"2026-03-03 11:01:14"}}