Find the number of possible arrangements in Fisher Random Chess. The diagram below is one possible arrangement.

In a legal arrangement, the White's position must satisfy the following criteria:

• Eight pawns must be in the $2^{nd}$ row. (The same as regular chess)
• Two bishops must be in opposite colored squares (e.g. $b1$ and $e1$ in the above diagram)
•  King must locate between two rooks (e.g. in the diagram above, King is at $c1$ and two rooks are at $a1$ and $g1$)

The Black's position will be mirroring to the White's.