Movie Hype

Chef decided to watch a movie, and has just entered the theater. The theater has $2N+1$ seats arranged in a row. The seats are numbered $1$ to $2N+1$ from left to right. Currently, the seats numbered $1, 3, 5, 7, \ldots, 2N+1$ are occupied, and the seats numbered $2, 4, 6, \ldots, 2N$ are empty. Chef must decide which empty seat to sit in. For each $i = 1, 2, 3, \ldots, N+1$, The person sit