Distribution of the length for the simple random walk on the infinite 2D grid if the U-turns are erased

Question

In connection with the flatland paradox, consider a 2D-random walk $(X_n)$ on $\mathbb{Z}^2$: the four moves of length one to W, E, N, and S are equally likely at each time. For a fixed number of moves $n>0$, what is the distribution of the length of $X_n$, considering that U-turns (e.g., $X_n=W$ and $X_{n+1}=E$) do not contribute to the length. Hence WENWNSNNEW is of length 4, like NWNN.