Two-row table

You are given a positive integer $N$. The integers $1, 2, 3, \dots, 2N$ are split into three sets $A$, $B$ and $C$. Count the number of ways to fill a table with two rows and $N$ columns so that all of the following hold.

• Each cell of the table holds a single integer.
• The integers of set $A$ go in the first row.
• The integers of set $B$ go in the second row.
• The integers of set $C$ can go in either row.
• The numbers in each row increase from left to right.
• The numbers in each column increase from top to bottom.

Every integer from $1$ to $2N$ appears in the table exactly once.

For $N = 4$, $A = \{2, 3\}$, $B = \{4, 7, 8\}$ and $C = \{1, 5, 6\}$, exactly two tables satisfy the conditions.

1 2 3 5
4 6 7 8

1 2 3 6
4 5 7 8

The first line holds the integer $N$. ($1 < N \le 35$)

The second line holds $M$, the number of elements of set $A$, followed by the elements of $A$. ($0 \le M \le N$)

The third line holds $K$, the number of elements of set $B$, followed by the elements of $B$. ($0 \le K \le N$)

$A$ and $B$ are disjoint, and every element of both sets is an integer between $1$ and $2N$. The elements on a line are not necessarily sorted. The integers that belong to neither $A$ nor $B$ form set $C$.

Print the number of tables that satisfy the conditions on a single line. Print $0$ if no such table exists.