{"raw_statement":[{"iden":"problem statement","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."},{"iden":"constraints","content":"*   All values in input are integers.\n*   $1 \\leq N \\leq 300$\n*   $1 \\leq a_i \\leq 3$"},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$\n$a_1$ $a_2$ $\\ldots$ $a_N$"},{"iden":"sample input 1","content":"3\n1 1 1"},{"iden":"sample output 1","content":"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 $1 + 1.5 + 3 = 5.5$."},{"iden":"sample input 2","content":"1\n3"},{"iden":"sample output 2","content":"3\n\nOutputs such as `3.00`, `3.000000003` and `2.999999997` will also be accepted."},{"iden":"sample input 3","content":"2\n1 2"},{"iden":"sample output 3","content":"4.5"},{"iden":"sample input 4","content":"10\n1 3 2 3 3 2 3 2 1 3"},{"iden":"sample output 4","content":"54.48064457488221"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}