Pacman And Numbers

Pacman and his girlfriend Pacwoman love to eat numbers. They were out walking when they found a square park with numbers laying around in the form of a square matrix of size $n$ x $n$. Pacman and pacwoman mutually decide to eat all the numbers at the perimeter of the square alternatively. So first, pacman eats all the numbers at the perimeter, then pacwoman eats all the numbers in the perimeter of