Sets $A = \{ 1,2,3 \}$ and $B = \{ 2,3,4,5 \}$ are given.
Given this, how many functions $\mathbf { f } : \mathbf { A } \rightarrow \mathbf { B }$ can be defined such that for every $a \in A$
$$a + f ( a ) \leq 6$$
A) 12\\
B) 18\\
C) 20\\
D) 24\\
E) 27