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 1 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 _______.