loopmates

You get a fixed number of ticks per loop. Arrow keys or WASD move you one tile per tick, space waits. When a loop ends (time runs out, or you press enter) it replays as a ghost from the start, at the same time as your next loop.

A lowercase tile is a button. The matching capital tile is a door. A door is open on a tick when a ghost is standing on its button on that tick. You cannot hold a door for yourself, you need a past loop to do it.

Reach E before time runs out. Fewer loops is better. Par is the true minimum, found by an exhaustive solver.