Weird condition for a maxima

Maximise $\displaystyle a^{12}+b^{12}+c^{12}$ if $\displaystyle -1\le a,b,c\le1$ and $\displaystyle a+b+c=-\frac{1}{2}$ .

If the maximum value is $\displaystyle\alpha$ , find the integer closest to $\displaystyle 10^{7}\alpha$