Vector Algebra

$\overline{\mathrm{a}}, \overline{\mathrm{b}}, \overline{\mathrm{c}}$ are nonzero vectors such that $\overline{\mathrm{a}}$ is perpendicular to $\overline{\mathrm{b}}$ and $\overline{\mathrm{c}},|\overline{\mathrm{a}}|=1,|\overline{\mathrm{~b}}|=2,|\overline{\mathrm{c}}|=1$ and $\overline{\mathrm{b}} \cdot \overline{\mathrm{c}}=1$. There is nonzero vector $\overline{\mathrm{d}}$ coplanar with $\overline{\mathrm{a}}+\overline{\mathrm{b}}$ and $2 \overline{\mathrm{~b}}-\overline{\mathrm{c}}$. If $\overline{\mathrm{d}} \cdot \overline{\mathrm{a}}=1$, then $|\overline{\mathrm{d}}|^2=$