# Cute numbers!

Define a cute number as a 16 digit number whose difference in pair of each consecutive digits is $$1$$ and each digit belongs to the set $$\{ 1,2,3 \}$$.

If the the sum of all cute numbers can be expressed as $$2^{a} \times b$$ where $$b$$ is not divisible by $$2$$, and both $$a$$ and $$b$$ are positive integers.Evaluate $$a+b$$.

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