## Inertia-a

Astrid the astronaut is floating in a grid. Each time she pushes off she keeps gliding until she collides with a solid wall, marked by a thicker line. From such a wall she can propel herself either parallel or perpendicular to the wall, but always travelling directly $$\leftarrow, \rightarrow, \uparrow, \downarrow$$. Floating out of the grid means death.

In this grid, Astrid can reach square Y from square . But if she starts from square there is no wall to stop her and she will float past Y and out of the grid.

In this grid, from square X Astrid can float to three different squares with one push (each is marked with an *). Push $$\leftarrow$$ is not possible from X due to the solid wall to the left. From X it takes three pushes to stop safely at square Y, namely $$\downarrow, \rightarrow, \uparrow$$. The sequence $$\uparrow, \rightarrow$$ would have Astrid float past Y and out of the grid.

Question:

In the following grid, what is the least number of pushes that Astrid can make to safely travel from X to Y?