# Almost Primes Square

Algebra Level 5

You're given a $$4\times 4$$ magic square, where the sum of every row, column, or diagonal equals to 180, and all the letters $$A$$ to $$O$$ represent distinct 2-digit prime numbers apart from 49 as shown.

The unit numbers never repeat in any sum, and the corner numbers are arranged such that the product $$AOLC$$ is maximum.

If $$A$$ > $$O$$ > $$L$$ > $$C$$, what is the value of $$A$$ + $$B$$ - $$C$$ + $$D$$ - $$E$$ + $$F$$ - $$G$$ + $$H$$ - $$I$$ + $$J$$ - $$K$$ + $$L$$ - $$M$$ + $$N$$ - $$O$$?

×