Let the line of the shortest distance between the lines $\mathrm{L}_1: \vec{r}=(\hat{\imath}+2 \hat{\jmath}+3 \hat{k})+\lambda(\hat{\imath}-\hat{\jmath}+\hat{k})$ and $\mathrm{L}_2: \overrightarrow{\mathrm{r}}= (4 \hat{\imath}+5 \hat{\jmath}+6 \hat{k})+\mu(\hat{\imath}+\hat{\jmath}-\hat{k})$ intersect $L_1$ and $L_2$ at $P$ and $Q$ respectively. If $(\alpha, \beta, \gamma)$ is the midpoint of the line segment PQ , then $2(\alpha+\beta+\gamma)$ is equal to