Functions can call other functions. For example, consider the following code:

define function a$($x$)=$ x $-1$

define function b$($y$)=$ a$($x $*3)$

z :$=$ b$(2)$

The b$(2)$ call is equivalent to writing out a$(2*3),$ from the definition of program function b$.$ Simplifying the parameter to program function a$,$ this is equivalent to a$(6).$ From the definition of program function a$,$ a$(6)$ is equivalent to $6-1.$ Simplifying this code down yields $5,$ ultimately resulting in program variable z holding the value $5.$

With all this in mind, consider the following code:

define function f$($x$)=$ x $+2$

define function g$($y$)=$ f$($y$)+$ f$($y $+1)$

z :$=$ g$(1)$

What value will program variable z hold when the above code completes?