Gram Schmidt process

Question

We have previously calculated the basis to be: $\left( \begin{pmatrix} -1 \\ 0 \\ 1 \end{pmatrix}, \begin{pmatrix} 2 \\ 1 \\ 0 \end{pmatrix}, \begin{pmatrix} 1 \\ -2 \\ 1 \end{pmatrix}\right)$. We would like to determine the orthonormal basis for $\mathbb{R}^3$. To do this we use the Gram-Schmidt process getting the answer to be: $$ \left( \begin{pmatrix} -\frac{\sqrt{2}}{2} \\ 0 \\ \frac{\sqrt{2}}{2} \end{pmatrix}, \begin{pmatrix} \frac{\sqrt{3}}{3} \\ \frac{\sqrt{3}}{3} \\ \frac{\sqrt{3}}{3}\end{pmatrix}, \begin{pmatrix}\frac{\sqrt{6}}{6} \\ -\frac{\sqrt{6}}{3} \\ \frac{\sqrt{6}}{6}\end{pmatrix}\right)$$ On our answer sheet it states that the last basis should be: $$ \begin{pmatrix} \frac{\sqrt{5}}{5} \\ -\frac{2\sqrt{5}}{5} \\ \frac{\sqrt{5}}{5}\end{pmatrix}$$ Are we wrong? Or is there a type mistake on our answer sheet?