JEE Advanced 2024 Mathematics question on Permutations and Combinations

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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 $Y = \{R \in X : \text{The range of R has exactly one element}\}$ and

$Z = \{R \in X : R \text{ is a function from S to S}\}$.

Let $n(A)$ denote the number of elements in a set $A$.

If $n(X) = {}^{m}C_{6}$, then the value of $m$ is __________.