Catherine has a plate containing 300 circular crumbling mooncakes, arranged as follows:
(This continues for 100 total columns). She wants to pick some of the mooncakes to eat, however whenever she takes a mooncake all adjacent mooncakes will be destroyed and cannot be eaten. Let M be the maximal number of mooncakes she can eat, and let n be the number of ways she can pick M mooncakes to eat (Note: the order in which she picks mooncakes does not matter). Compute the ordered pair (M, n).