Clean Sequence (Easy)

A clean sequence is a sequence of length $2N$ in which each integer from $1$ to $N$ appears exactly twice.

The score of a clean sequence is the sum, over every integer $i$ from $1$ to $N$, of the following value.

• (sum of the numbers between the two $i$s) × $i$

Here, "between" includes the two endpoint $i$s.

Count the clean sequences of length $2N$ whose score is minimal.

The first line contains an integer $N$ ($1 \le N \le 10$).

On the first line, print the number of clean sequences of length $2N$ whose score is minimal.

For example, $[3, 1, 2, 1, 3, 2]$ is a clean sequence with $N = 3$. Its score is calculated as follows, giving 50 points.

The numbers between the two $1$s are $[1, 2, 1]$, so $(1 + 2 + 1) \times 1$ is added to the score.

The numbers between the two $2$s are $[2, 1, 3, 2]$, so $(2 + 1 + 3 + 2) \times 2$ is added.

The numbers between the two $3$s are $[3, 1, 2, 1, 3]$, so $(3 + 1 + 2 + 1 + 3) \times 3$ is added.

The score of this sequence is $4 + 16 + 30$, which is 50. This sequence does not have the minimum score among clean sequences with $N = 3$.