Fibonacci sequence is defined as follow: $F_1 = 1$, $F_2 = 2$ , $F_i = F_{i-1} + F_{i-2} (i > 2)$ .

Every natural number $X$ can be represented in Fibonacci system such that $X$ is sum of one or more distinct Fibonacci numbers in such a way that the sum does not include any two consecutive Fibonacci numbers.

Let $X = A_1 * F_1 + A_2 * F_2 + A_3 * F_3 + …..…+ A_{k-1} * F_{k-1} + A_k * F_k$ where $0 <= A_p <= 1 \forall p < k$ and $A_k = 1$

We will represent $X$ in Fibonacci system as : $A_kA_{k-1}A_{k-2}………..A_1$ Example $1 = (1) _F , 2 = (10)_F , 3 = (100)_F , 4 = (101)_F$

If we write representation of all natural numbers in Fibonacci system consecutively we will obtain a new sequence ( say fragger sequence ) which will look like this : $1,1,0,1,0,0,1,0,1 …….$

You need to count the number of times $1$ appears in the first $10^{15}$ terms of fragger sequence.