Consider the following turn models:

• West-first routing. Route a message first west, if necessary, and then adaptively south, east, and north.

• North-last routing. First adaptively route a message south, east, and west; route the message north last.

• Negative-first routing. First adaptively route a message along the negative X or Y axis;

that is, south or west, then adaptively route the message along the positive X or Y axis.

Show all the turns allowed in each of the above three routings.