Let $\overrightarrow{\mathrm{a}}=-\hat{i}+2 \hat{j}+2 \hat{k}, \overrightarrow{\mathrm{~b}}=8 \hat{i}+7 \hat{j}-3 \hat{k}$ and $\overrightarrow{\mathrm{c}}$ be a vector such that $\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{c}}=\overrightarrow{\mathrm{b}}$. If $\overrightarrow{\mathrm{c}} \cdot(\hat{i}+\hat{j}+\hat{k})=4$, then $|\overrightarrow{\mathrm{a}}+\overrightarrow{\mathrm{c}}|^2$ is equal to: