If $\overline{\mathrm{AB}}=2\overline{\mathrm{a}}+\overline{\mathrm{b}}$ and $\overline{\mathrm{AD}}=\overline{\mathrm{a}}-2\overline{\mathrm{b}}$ where $\left|\overline{\mathrm{a}}\right| = 1, \left|\overline{\mathrm{b}}\right| = 1, (\overline{\mathrm{a}},\overline{\mathrm{b}}) = {60}^{\mathrm{o}}$ are the adjacent sides of a parallelogram, then the length of the diagonal $\overline{\mathrm{BD}}$ is