 Solution

The root string through ${\alpha }_1$ in the ${\alpha }_2$ direction contains ${\alpha }_1$ and ${\alpha }_1+{\alpha }_2$, so ${\alpha }_1$ can be raised once by ${\alpha }_2$. The string through ${\alpha }_2$ in the ${\alpha }_1$ direction containsso ${\alpha }_2$ can be raised three times by ${\alpha }_1$.