If $\bar{a}, \bar{b}, \bar{c}$ are three vectors which are perpendicular to $\overline{\mathrm{b}}+\overline{\mathrm{c}}, \overline{\mathrm{c}}+\overline{\mathrm{a}}$, and $\overline{\mathrm{a}}+\overline{\mathrm{b}}$ respectively, such that $|\overline{\mathrm{a}}|=2|\overline{\mathrm{b}}|=3,|\overline{\mathrm{c}}|=4$, then $|\overline{\mathrm{a}}+\overline{\mathrm{b}}+\overline{\mathrm{c}}|=$