HMMT November 2009 F2

You start with a number. Every second, you can add or subtract any number of the form $n$ ! to your current number to get a new number. In how many ways can you get from 0 to 100 in 4 seconds? ( $n!$ is defined as $n \times(n-1) \times(n-2) \times \cdots \times 2 \times 1$, so $1!=1,2!=2,3!=6,4!=24$, etc.)