Delete the Array

You can perform the following operation on an array $A$: - Choose $1 \le i \lt |A|$ such that $A_i \ne A_{i + 1}$, and delete both $A_i$ and $A_{i + 1}$ from the array (renumbering the elements after $i + 1$). Define $f(A)$ as $f(A) = 1$ if the array $A$ can be changed into an empty array by deleting all elements using the above operation any number of times, otherwise $f(A) = 0$. Define $g(A)