Let $S=\{1,2,3,4,5,6\}$ and $X$ be the set of all relations $R$ from $S$ to $S$ that satisfy both the following properties: i. $R$ has exactly 6 elements. ii. For each $(a, b) \in R$, we have $|a-b| \geq 2$. Let $Y=\{R \in X$ : The range of $R$ has exactly one element $\}$ and $Z=\{R \in X: R$ is a function from $S$ to $S\}$. Let $n(A)$ denote the number of elements in a set $A$. (There are two questions based on PARAGRAPH "I", the question given below is one of them) If the value of $n(Y)+n(Z)$ is $k^2$, then $|\mathrm{k}|$ is $\_\_\_\_$