The sum of all values of α, for which the shortest distance between the lines (x+1)/(α)=(y-2)/-1=(z-4)/(-α) and x/(α)=(y-1)/2=(z-1)/(2 α) is √ 2, is

The sum of all values of $\displaystyle \alpha$, for which the shortest distance between the lines $\displaystyle \frac{x+1}{\alpha}=\frac{y-2}{-1}=\frac{z-4}{-\alpha}$ and $\displaystyle \frac{x}{\alpha}=\frac{y-1}{2}=\frac{z-1}{2 \alpha}$ is $\displaystyle \sqrt{2}$, is