# Fibonacci + Factorials = Fibatorials!

We define:

• $$F(n)$$ denote the $$n$$-th Fibonacci Number.
• $$\Psi (n)$$ denote the sum of digits of $$n$$.
• $$\phi (n)$$ denote the sum of digits of $$n!$$.

Find the sum of all integers between 1 and 1000 inclusive such that $$\phi (n) = \phi (\Psi (F(n)))$$.

Note: $$F_0 = 0, F_1=1$$.

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