Each new term in the Fibonacci sequence is generated by adding the previous two terms.
Starting with $1$ and $2$, the first $10$ terms will be: $1,2,3,5,8,13,21,34,55,89$.

Every positive integer can be uniquely written as a sum of nonconsecutive terms of the Fibonacci sequence. For example, $100=3+8+89$.
Such a sum is called the Zeckendorf representation of the number.

For any integer $n>0$, let $z(n)$ be the number of terms in the Zeckendorf representation of $n$.
Thus, $z(5)=1$, $z(14)=2$, $z(100)=3$ etc.
Also, for $0<n<{10}^6$, $\sum z(n)=7894453$.

Find $\sum z(n)$ for $0<n<{10}^{17}$.