Eating Cakes

Problem Description

There are $n$ plates, numbered $1, 2, \dots, n$. The $i$-th plate holds $a_i$ ($1 \le a_i \le 3$) cakes. Little N will eat cakes according to the following rule, until all cakes are eaten:

Each time, he picks one of the $n$ plates uniformly at random. Suppose plate $i$ is chosen. If plate $i$ still has cakes, he eats one; if plate $i$ has no cakes, he does nothing.

Find the expected number of times he needs to eat all the cakes.

Input Format

The first line contains an integer $n$.

The next line contains $n$ integers $a_1, a_2, \dots, a_n$.

Output Format

Output the expected number of times needed to eat all the cakes. An absolute or relative error within $10^{-9}$ is considered correct.

Sample Input

2
1 2

Sample Output

4.5

Constraints

For all data, $1\le n\le 300, 1 \le a_i \le 3$.