Lottery Tickets

There were $N$ lottery tickets with numbers $A_i$. Each number was distinct. Chef bought the first ticket, i.e. $A_1$. He is now wondering whether he won the lottery. Here is how the winner is decided: - A number $X$ is decided in the range $[1, 10^{6}]$, and then whoever has the closest ticket to $X$ wins the lottery. If there is a tie, all of them are winners. How many numbers $X$ exist such