Grand son of Bonacci (TIEBREAKER)

The famous Fibonacci sequence as you all know A1 = 1, A2 = 2, Ai = Ai-1 + Ai-2 (i > 2). Now we represent a natural number N by the maximum numbers that are less than or equal to N in Fibonacci sequence: N = b1*A1 + b2*A2 + … Hence N can be represented as: bnbn-1…b1. For eg, 1 = 1f, 2 = 10f, etc. On writing all N successively in Fibonacci system, we will obtain a sequence like this: 110… We call