Swamp

The swamp has the form of a rectangle with sides parallel to the coordinate axes. Two opposite corners of the swamp have coordinates $(0,0)$ and (W, H), where $W$ and $H$ are positive integers. Inside the swamp, there are $N$ points (tussocks) with integer coordinates.

You are standing at the left edge of the swamp. You can cross the swamp by first jumping from the left bank to a point, then repeatedly jumping from point to point, and finally jumping from a point to the right bank.

However, for each jump, you require that the distance between each pair of consecutive points in your path is the same fixed value $L$, and the distances from the left bank to the first point and from the last point to the right bank must not exceed $L$.

Determine the minimal jump length $L$ that allows you to cross the swamp.