Arya and the Grid of Stars

Arya is planning to go back to Winterfell. In order to reach there and survive, she must collect maximum stars from a maze. The maze is in the form of a grid of size $m \times n$. Each cell is either blank, has a star or has a stone. She starts from $(1,1)$ to reach $(m, n)$ using right and bottom moves and then she returns to $(1, 1)$ using top and left moves. The only constraint is that i