The Ladder Paradox

A truck carrying a long ladder drives towards the open front door of a barn which is exactly as long as the ladder. As soon as the back of the ladder enters the barn, the front door is closed and since the ladder is length-contracted it is entirely inside the barn with room to spare before the front of the ladder hits the back wall. But from the point of view of the truck driver, the barn is length-contracted and so not long enough to ever contain the ladder. What’s up? Does the ladder ever fit entirely inside the barn or not?