On a $2\times10$ horizontal grid, there are $10$ ants on the top row, one on each square. The bottom row is initially empty. When a bell sounds, each ant moves to a vertically or horizontally adjacent square, with the following restrictions:
- No ant can move outside the 2x10 grid
- Ants cannot collide, i.e. if an ant is going right, the ant to his right cannot go left. If an ant is going left, the ant to his left cannot go right.
- After the moves are complete, there can be no more than one ant on any square
- The bell only rings once, and all ants move simultaneously.
In how many ways can this be done?