Let the volume of the tetrahedron with vertices $\hat{i}-\hat{j}-2 \hat{k},-2 \hat{i}+\hat{j}-2 \hat{k},-\hat{i}-2 \hat{j}+\hat{k}, 2 \hat{i}+2 \hat{j}+a \hat{k}$ be $\frac{20}{3}$. Then the integral value of $a$ is