Michelle is at the bottom-left corner of a 6 \times 6 lattice grid, at (0,0). The grid also contains a pair of onetime-use teleportation devices located at (2,2) and (3,3); the first time Michelle moves to one of these points she is instantly teleported to the other point, and the devices disappear. If she can only move up or to the right in unit increments, find the number of ways in which can she reach the point (5,5).