3. Möbius Houses

In the the third seminar, we showed that connecting three houses to three utilities is not possible in the plane without crossings. However, we also showed that it is possible on the torus. Your task is to solve this problem on the Möbius band.

Formally, produce a non-crossing drawing of the graph $K_{3,3}$ on the Möbius band. Recall that we can represent Möbius using the following diagram where left and right sides are glued together in opposite orientation.