Unit eigenvector of symmetric matrix

Let $A=\begin{pmatrix} 1 & -1 & 2 \ -1 & 0 & 1 \ 2 & 1 & 1 \end{pmatrix}$ and let $\begin{pmatrix} x_1 \ x_2 \ x_3 \end{pmatrix}$ be an eigenvector corresponding to the smallest eigenvalue of $A$, satisfying $x_1^2+x_2^2+x_3^2=1$. Then the value of $|x_1|+|x_2|+|x_3|$ equals __________ (round off to $2$ decimal places)