In an alternate reality, the $417$ staff are deciding where to travel to escape from their weekly duties. Robbie really

wants to go to Chicago but he$$s willing to change his mind, provided that more than $2/3$ of the TAs can agree on a

different place. Before starting the discussion, every TA writes up a Location Proposal detailing their ideal travel

spot.

$$ If more than $2/3$ of the TAs agree exactly on what place to visit, then Robbie is out of luck.

$$ Otherwise, the staff will travel to Chicago.

More formally, you have an array of n Locations $($called proposals$).$ You can call $.$equals$()$ on two Locations, but

it takes a long time. Even worse, there$$s no $.$compareTo$()$ implemented, nor a $.$hashcode$().$ So you can$$t sort these

Objects, nor put them in a hash table.