A change of basis

Consider two bases from a vector space $\mathbb{R}^3$: $e_1 = (1, 1, 1)$, $e_2 = (-1,1, 0)$, $e_3 =( 2, -2, -2)$ and $e'_1 = (3, -3, -2)$, $e'_2 = (3, 1, -2)$, $e'_3 =(1, 3, 0)$. Suppose we also know that the coordinates of a vector $v$ in basis $\mathbf{e'}$

are $\begin{pmatrix} -1\\ 1 \\ 1\end{pmatrix}$. What coordinates does the vector $v$ have in the basis $\mathbf{e}$?

In the answer, write the coordinates in the following form: if you have, for example, a vector $\begin{pmatrix} 1 \\ 2\ \\3 \end{pmatrix}$, then write $\begin{matrix} 1 \\ 2 \\ 3 \end{matrix}$.

Note: The transition matrix from $\mathbf{e}$ to $\mathbf{e'}$ is $C = \begin{pmatrix} 0 & 2 & 2 \\ -1 & 3 & 3 \\1 & 2 & 1 \end{pmatrix}.$