$S_{10}$
$${\rm LOG}\left(S_{10}\right)=\frac{2}{5}\pi
\left[\begin{array}{rrrrrrrrrr}
\bullet & \bullet & \bullet & \bullet & \bullet & \bullet & \bullet & \bullet & \bullet & \bullet\\
\bullet & 1 & 2 & 3 & 4 & 4 & \bullet & 1 & 2 & 3\\
\bullet & 2 & 4 & 1 & 3 & 1 & 3 & \bullet & 2 & 4\\
\bullet & 3 & 1 & 4 & 2 & 1 & 4 & 2 & \bullet & 3\\
\bullet & 4 & 3 & 2 & 1 & 4 & 3 & 2 & 1 & \bullet\\
\bullet & 3 & 2 & 2 & 3 & \bullet & 1 & 4 & 4 & 1\\
\bullet & 2 & \bullet & 4 & 4 & 3 & 2 & 3 & 1 & 1\\
\bullet & 1 & 3 & 1 & \bullet & 2 & 4 & 3 & 4 & 2\\
\bullet & \bullet & 1 & 3 & 1 & 2 & 2 & 4 & 3 & 4\\
\bullet & 4 & 4 & \bullet & 2 & 3 & 1 & 1 & 3 & 2
\end{array}\right]$$