Cinema Ticketing Queue

There are $N$ people, numbered from $1$ to $N$. They go to a cinema hall. Each of them buys a ticket, which has a number written on it. The number on the ticket of the $i^{th}$ person is $A_i$. There are infinite seats in the cinema hall. The seats are numbered sequentially starting from $1$. All the $N$ people stand in a queue to get their respective seats. Person $1$ stands at the front of the