The "Brilliant" Set Part 2 Reposted

Given a Set $A=\{b,r,i,l,a,n,t\}$ . Then the number of ordered pairs $(P,Q,R,S)$ which can be formed such that $P \subseteq A$ , $Q \subseteq A$ , $R \subseteq A$ , $S \subseteq A$ And $(P\cup Q)\cap (R\cup S)=\emptyset$ .

• The answer is of the form $m^{n}$ where $m,n$ are primes. Find $m+n$

Also try The Brilliant Set