In Poker a straight is exactly five cards of sequential rank NOT all of the same suit. In this problem an ace can rank either high as in A-K-Q-J-10 or low as in 5-4-3-2-A, but cannot simultaneously rank both high and low, so Q-K-A-2-3 is not allowed.

There are $10200$ ways of choosing a straight from a normal $52$ card deck.
There are $31832952$ ways of choosing two disjoint straights from a single $52$ card deck.

Find the number of ways of choosing eight disjoint straights from a single $52$ card deck.
In this the order of choosing the straights does not matter.