Let $\mathrm{g}: \mathrm{N} \rightarrow \mathrm{N}$ be defined as
$$
\begin{aligned}
& g(3 n+1)=3 n+2 \\
& g(3 n+2)=3 n+3 \\
& g(3 n+3)=3 n+1, \text { for all } n \geq 0
\end{aligned}
$$
Then which of the following statements is true ?
Select the correct option:
A
There exists an onto function $f ; N \rightarrow N$ such that $f \circ g=f$
B
There exists a one-one function $f . \mathbf{N} \rightarrow \mathbf{N}$ such that $f \circ g=f$
C
gogog = g
D
There exists a function $f: N \rightarrow N$ such that $g$ of $=f$
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