A positive integer $k \geqslant 3$ is called fibby if there exists a positive integer $n$ and positive integers $d_{1}<d_{2}<\ldots<d_{k}$ with the following properties:  - $d_{j+2}=d_{j+1}+d_{j}$ for every $j$ satisfying $1 \leqslant j \leqslant k-2$,  - $d_{1}, d_{2}, \ldots, d_{k}$ are divisors of $n$,  - any other divisor of $n$ is either less than $d_{1}$ or greater than $d_{k}$.  Find the largest fibby number.

Let's think step by step and output the final answer within \boxed{}.
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