Let F₀ = 1, F₁ = 1, and F_k = F_k-2 + F_k-1 for k > 2. Suppose we have a sequence of n operations, each increment the counter by 1. The cost of such an operation depends on the current value of counter, which is equal to:

counter, if counter is equal to F_i for some i 1.

1, otherwise. Initially, counter is 1. Show that each increment takes O(1) amortized cost.