# Fibonacci Sum

Zeckendorf's Theorem states that every positive integer can be written uniquely as a sum of distinct non-neighboring Fibonacci number.

Find the sum of indices (0-indexing) such that their responding Fibonacci terms sums up to 99887766554433221100.

Clarification:

• $$F_0 = 1, F_1 = 1$$ and so on.
• For 10, the answer is $$F_5 + F_2 = 8 + 2 = 10$$. Sum of indices is $$5+2=7$$.
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