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 what is the value of the product ***yz*** ?