The fast breeder reactor uses the following moderator

In the given Venn diagram $n\left(A\right)$ is

Let $A$ be the set of vectors $a=\left(a_1,a_2,a_3\right)$ satisfying ${\left(\sum _{i=1}^3\frac{a_i}{2^i}\right)}^2=\sum _{i=1}^3\frac{a_i^2}{2^i}$. Then,