Suppose you want to move from 0 to 100 on the number line. In each step, you either move right by a unit distance or you take a shortcut. A shortcut is simply a pre-specified pair of integers i,j with i<j. Given a shortcut i,j, if you are at position i on the number line, you may directly move to j.
Suppose T(k) denotes the smallest number of steps needed to move from k to 100. Suppose further that there is at most one shortcut involving any number, and in particular from 9 there is a shortcut to 15. Let y and z be such that
T(9)=1+min(T(y),T(z)).
Then the value of the product yz is __________.
(Answer in integer)