Castles on campus symbolizes our founding principles academic prosperity. Statues of soldiers standing guard in each tower are representatives from the four schools that make up MaPP University and bear the symbol from each college on their shield. In a sign of unity guards are placed by specific University guidelines:

• Each castle cannot have a single guard from a school (but may have zero guards).

• All guards from the Dashing School of Science ($-$) insist on being exactly distance one apart (in adjacent towers), all guards from the Wedgington School of Technology ($wedge$) must be exactly distance two, all guards from the Nablanian School of Engineering ($nabla$) must be exactly distance three, and all guards from the Boxuto School of Mathematics ($square$) must be exactly distance four from each other.

You find three castles that have been partially guarded already; we cannot change those assignments. If we can assign as many guards as possible to each castle, following the above rules, then the unguarded towers should reveal the name of another secret word.