[This image](https://i.imgur.com/1j8pqtc.jpg) shows a made-up trail with a restroom (cyan point). I would like to add 2 more restrooms where the maximum distance along trail from anywhere on the trail to the closest of the 3 restrooms is minimized.

```
# Data

# trail is a list of segments between the magenta and/or cyan points (in the image).
# Each of the segments in turn is a list of endpoints.
trail = [[[0, 0], [1, 0]], [[2, 0], [3, 0]], [[3, 0], [4, 0]], [[4, 0], [5, 0]], [[6, 0], [7, 0]], [[5, 1], [6, 1]], [[1, 2], [2, 2]], [[4, 2], [5, 2]], [[1, -1], [2, -1]], [[3, -1], [4, -1]], [[5, -1], [6, -1]], [[4, -2], [5, -2]], [[1, 2], [1, 0]], [[1, 0], [1, -1]], [[2, 2], [2, 0]], [[2, 0], [2, -1]], [[3, 2], [3, 0]], [[4, 2], [4, 0]], [[4, 0], [4, -1]], [[4, -1], [4, -2]], [[5, 2], [5, 1]], [[5, 1], [5, 0]], [[5, 0], [5, -1]], [[5, -1], [5, -2]], [[6, 1], [6, 0]], [[6, 0], [6, -1]], [[3, -1], [4, 0]]]

restroom = [0, 0]

```

This is a simplified version of [this question](https://gis.stackexchange.com/questions/78714/minimax-the-locations-of-restrooms-on-a-trail-arcgis-10-2).

Hints will be appreciated as well.
Thanks.