# Fibonacci Sum

**Computer Science**Level 5

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 \(5+2=7\).