Table

Let $n$ be a positive integer. Integers $1$, $2$, $3$, $\dots$, $2n$ are divided into three sets $A$, $B$ and $C$. Write a program, which calculates the number of ways to fill the table with two rows and $n$ columns so that:

• Each cell of the table contains a single integer;

• The integers of the set $A$ should be written on the first row of the table;

• The integers of the set $B$ should be written on the second row of the table;

• The integers of the set $C$ can be written on any table row;

• The numbers in each row of the table should form an increasing sequence;

• The numbers in each column of the table should form an increasing sequence.

For example, if n = 4, A = \{2, 3\}, B = \{4, 7, 8\} and C = \{1, 5, 6\}, then there are exactly two tables of required type.