The shortest distance between the line passing through the point $\overline{\mathrm{i}}+2\overline{\mathrm{j}}+3\overline{\mathrm{k}}$ and parallel to the vector $2\overline{\mathrm{i}}+3\overline{\mathrm{j}}+4\overline{\mathrm{k}}$ and the line passing through the point $2\overline{\mathrm{i}}+4\overline{\mathrm{j}}+5\overline{\mathrm{k}}$ and parallel to the vector $3\overline{\mathrm{i}}+4\overline{\mathrm{j}}+5\overline{\mathrm{k}},$ is