Let the vectors $\overrightarrow{\mathrm{a}}=-\hat{i}+\hat{j}+3 \hat{k}$ and $\overrightarrow{\mathrm{b}}=\hat{i}+3 \hat{j}+\hat{k}$. For some $\lambda, \mu \in \mathbf{R}$, let $\overrightarrow{\mathrm{c}}=\lambda \overrightarrow{\mathrm{a}}+\mu \overrightarrow{\mathrm{b}}$. If $\overrightarrow{\mathrm{c}} \cdot(3 \hat{i}-6 \hat{j}+2 \hat{k})=10$ and $\overrightarrow{\mathrm{c}} \cdot(\hat{i}+\hat{j}+\hat{k})=-2$, then $|\overrightarrow{\mathrm{c}}|^2$ is equal to: