For any set $X$ set $[X]^2 = \{\{x,y\}: x,y\in X, x\neq y\}$. If $n\geq 2$ is an integer, we endow $\mathbb{Z}$ with a graph structure in the following way. If $x,y\in \mathbb{Z}^n$ we say $x,y$ are *direct neighbors* if there is $k\in\{1,\ldots,n\}$ such that $|x_k-y_k|= 1$, and $x_i = y_i$ for all $i\in \{1,\ldots,n\}\setminus\{k\}$. Let $$E_n= \big\{\{x,y\}\in [\mathbb{Z}^n]^2: x,y \text{ are direct neighbors}\}.$$

For which $n\geq 2$ is there an orientation of $(\mathbb{Z}^n, E_n)$ such that for every two vertices $x,y\in \mathbb{Z}^n$ there is a directed path from $x$ to $y$?