Let $\vec{a}=3 \hat{i}+\hat{j}-\hat{k}$ and $\vec{c}=2 \hat{i}-3 \hat{j}+3 \hat{k}$. If $\vec{b}$ is a vector such that $\vec{a}=\vec{b} \times \vec{c}$ and $|\vec{b}|^2=50$, then $\left|72-|\overrightarrow{\mathrm{b}}+\overrightarrow{\mathrm{c}}|^2\right|$ is equal to
