Let $\left\lbrace \vec{e}_1, \ \vec{e}_2, \ \vec{e}_3, \ \vec{e}_4, \ \vec{e}_5, \ \vec{e}_6 \right\rbrace$ be the standard basis in ${\mathbb R}^6$. Find the length of the vector $\vec{x} = 2\vec{e}_1 + 2\vec{e}_2 + 5\vec{e}_3 + 2\vec{e}_4 + 3\vec{e}_5 + 3\vec{e}_6$.

$\| \vec{x} \| =$ .