Evil Infection

$N$ people ordered $N$ takeouts at the same place. The arrival time of the $i^{th}$ takeout is $X_i$, and the arrival time of the $i^{th}$ person is $Y_i$ where $X_i < Y_i$. Also $X_1 < X_2 < \ldots < X_N$ and all $X_i, Y_i$ values are distinct (i.e. $X_i \ne X_j$ for all $i, j$; $Y_i \ne Y_j$ for all $i,j$; $X_i \ne Y_j$ for all $i,j$). Originally, everyone could happily get their own takeout,