Counter Espionage Academy instructors have designed the following problem to see

how well trainees can detect SPY$$s in an nXn grid of letters S$,$ P$,$ and Y$.$ Trainees are

instructed to detect as many disjoint copies of the word SPY as possible in the given

grid. To form the word SPY in the grid they can start at any S$,$ move to a neighboring P$,$

then move to a neighboring Y$.($They can move north, east, south or west to get to a

neighbor.$)$ The following figure shows one such problem on the left, along with two

possible optimal solutions with three SPY$$s each on the right. Give an efficient network

flow$-$based algorithm to find the largest number of SPY$$s$.(20$ pts$)$

Note: We are only looking for the largest number of SPYs not the actual location of the

words. No proof is necessary