The permutation of the grid

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Permutation of the grids: If an Imaginary square shaped city has 9 horizontal streets and 16 vertical streets, A and B are the 2 diagonal points of the city, if I want to go from point A to point B, where all the streets which form this imaginary grid have distinct names, in how many ways can I walk from point A to B moving through different pathways? It is necessary to note that one has to choose the shortest paths, meaning that going opposite to the direction of destination is prohibited, However one is allowed all other freedoms like continuing on a horizontal or a vertical street till the edge of the grid city and so on and so forth.