Fluffy the Fox and Speedy the Squirrel are going up a staircase with a certain number of steps. Fluffy goes three steps up with each jump (though if necessary, he will just jump the last step). Speedy goes seven steps up with each jump (though if necessary, he will just jump the last steps if there are fewer than 7 steps left). Suppose that Speedy takes 10 fewer jumps than Fluffy to reach the top of the staircase. Let $s$ denote the sum of all possible numbers of steps this staircase can have. What is the sum of the digits of $s$?