Fibonacci Sequence:
Fibonacci representation _%7B%7D)
: Any natural number

can be expressed as the sum of a set of different Fibonacci numbers.
In particular:

and

are two different Fibonacci numbers.
For example:

indicates that

corresponds to at least two Fibonacci representations.
The value of the Fibonacci representation )_%7B%7D)
: defined as the product of the Fibonacci numbers in the representation .
For example:

. In this representation, the value
)_%7B%7D)
is:

.
With the above definitions, now, find the sum of all Fibonacci representations’ value of a given number

.
To simplify the question, please output the answer modulo lovely

.