Front or Back

There were $N$ people lined up in a queue. The people are numbered $1$, $2$, $\ldots$, $N$ but not necessarily in the order they are lined up. Unfortunately, some of them can't even understand where the front of the queue is. So, some people are looking towards the front of the queue and some people are looking towards the back of the queue. The $i$-th person reports $A_i$ as the number of peop