$$
Since $a_{\mathsf{N}$ is even, $d_{\mathsf{N}}$ is defined.
-Both $c_{\mathsf{N}}$ and $d_{\mathsf{N}}$ are obviously positves.
+Moreover, both $c_{\mathsf{N}}$ and $d_{\mathsf{N}}$ are obviously positves.
+
+
+
+
\subsection{Toward a local uniform distribution of switches}