Assume that Algorithm $6\mathrm{.}3$ returns a set of n$!$ distinct n$-$tuples.

Compute $($in terms of n $>1)$ the number of union $(\backslash$cup $)$ operations that Algorithm $6\mathrm{.}3$ performs. $($Note that Algorithm $6\mathrm{.}3$ uses Algorithm $6\mathrm{.}4)$