Square Fibonacci ? Sounds Crazy !

Fibonacci sequence is defined as \(F_0=0 , F_1=1\) and for \(n \geq 2\) \[F_n=F_{n-1}+F_{n-2}\]

So the Fibonacci sequence is \(0,1,1,2,3,5,8,13,...\)

Find the sum of all the terms in the Fibonacci sequence which are less than \(\textbf{1 billion}\) and are \(\textbf{perfect squares}\).


Details and assumptions:-

Perfect square means square of an integer.


This problem is a part of the set Crazy Fibonacci

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