An $n $\backslash$times m$ board is filled with a collection of blocks. Some blocks are moveable and others are fixed. The player stands at one of the cells of the board. If a player is standing next to a moveable block, and the space opposite the player is empty, then the player can push the block onto that empty space.

In the example below, the player is the circle. Black cells are fixed blocks, and gray cells are moveable blocks. The player can push the block to her north, but not the blocks to her east or her south.

Show that the following problem is in PSPACE: given the description of a game board $($positions and type of blocks, and position of the player$),$ and the location of a target, decide whether the player can reach the target.