\qquad
\left\{
\begin{array}{lcl}
-d_{\mathsf{N}} & = & \dfrac{2^{\mathsf{N} -n.a_{\mathsf{N}}}{2} \\
-c_{\mathsf{N}} = \mathsf{N} - d_{\mathsf{N}}
+d_{\mathsf{N}} & = & \dfrac{2^{\mathsf{N}} -n.a_{\mathsf{N}}}{2} \\
+c_{\mathsf{N}} &= &\mathsf{N} - d_{\mathsf{N}}
\end{array}
\right.
$$
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}