I'm trying to find $c,d \in \mathbb R$ s.t. the function below is continuous at $x_0=2n, n \in \mathbb N$.$$f(x)= \begin{cases} x+c & \text{if $x=2m, m \in \mathbb Z$} \\ \lceil x \rceil & \text{if $2m<x \leq 2m+1, m \in \mathbb Z$} \\ \lfloor x \rfloor + d & \text{if $2m-1<x<2m, m \in \mathbb Z$} \end{cases}$$
By equating left and right limit I found $c=1, d=2$. However I'm wondering if there exists other values for $c$ and $d$ s.t. the function is continuous at $x_0$. My guess is no since because it seems like for whatever value of $n$ $x+c$ and $\lfloor x \rfloor + d$ are dependent on $\lceil x \rceil$ but I'm not sure if I'm correct.