Nikoli the snake wants to slither along a loop through a four-by-four grid of points. To form a loop, Nikoli can connect any horizontally or vertically adjacent points with a line segment. However, Nikoli has certain standards when it comes to loop construction. In particular:
- The loop can never cross over itself.
- No two corners of the loop can meet at the same point.
- Once Nikoli has crossed the connection between two points, Nikoli can’t cross it again (in either direction).
For example, the following are two constructions of valid loops.
Meanwhile, the following three constructions are not valid. The one on the left crosses over itself, the one in the middle has two corners that meet at a single point, and the one on the right requires Nikoli to pass over the same line segment twice.
How many unique loops can Nikoli make on the four-by-four grid? (For any given loop, Nikoli can travel in two directions around it. However, these should still be counted as a single loop.)