There are $100$ people in a queue waiting to enter a hall. The hall has exactly $100$ seats numbered from $1$ to $100$. The first person in the queue enters the hall, chooses any seat and sits there. The $n$-th person in the queue where $n$ can be $2,\ldots,100$, enters the hall after $(n-1)$-th person is seated. He sists in seat number $n$ if he finds it vacant; otherwise he takes any unoccupied seat. Find the total number of ways in which $100$ seats can be filled up, provided the $100$-th person occupies seat number $100$.
I could not realise how this chaotic behaviour will end. I think the solution lies in finding that. Please help.