$i$ ${\omega }_{{i}^{\prime }}^{\left(2\right)}$ ${\omega }_{\left(i-{i}^{\prime }\right)}^{\left(1\right)}$ ${i}^{\prime }$ ${C}_{8}^{{i}^{\prime }}$ ${\left({P}_{A}^{\left(2\right)}\right)}^{\left(8-{i}^{\prime }\right)}{\left({P}_{B}^{\left(2\right)}\right)}^{\left({i}^{\prime }\right)}$ $\left(i-{i}^{\prime }\right)$ ${C}_{4}^{\left(i-{i}^{\prime }\right)}$ ${\left({P}_{A}^{\left(1\right)}\right)}^{\left[4-\left(i-{i}^{\prime }\right)\right]}{\left({P}_{B}^{\left(1\right)}\right)}^{\left(i-{i}^{\prime }\right)}$ $0\le i\le 4$ 0 0 1 ${\left({P}_{A}^{\left(2\right)}\right)}^{8}{\left({P}_{B}^{\left(2\right)}\right)}^{0}$ 0 1 ${\left({P}_{A}^{\left(1\right)}\right)}^{4}{\left({P}_{B}^{\left(1\right)}\right)}^{0}$ 1 0 1 ${\left({P}_{A}^{\left(2\right)}\right)}^{8}{\left({P}_{B}^{\left(2\right)}\right)}^{0}$ 1 4 ${\left({P}_{A}^{\left(1\right)}\right)}^{3}{\left({P}_{B}^{\left(1\right)}\right)}^{1}$ 1 1 8 ${\left({P}_{A}^{\left(2\right)}\right)}^{7}{\left({P}_{B}^{\left(2\right)}\right)}^{1}$ 0 1 ${\left({P}_{A}^{\left(1\right)}\right)}^{4}{\left({P}_{B}^{\left(1\right)}\right)}^{0}$ 2 0 1 ${\left({P}_{A}^{\left(2\right)}\right)}^{8}{\left({P}_{B}^{\left(2\right)}\right)}^{0}$ 2 6 ${\left({P}_{A}^{\left(1\right)}\right)}^{2}{\left({P}_{B}^{\left(1\right)}\right)}^{2}$ 2 1 8 ${\left({P}_{A}^{\left(2\right)}\right)}^{7}{\left({P}_{B}^{\left(2\right)}\right)}^{1}$ 1 4 ${\left({P}_{A}^{\left(1\right)}\right)}^{3}{\left({P}_{B}^{\left(1\right)}\right)}^{1}$ 2 2 28 ${\left({P}_{A}^{\left(2\right)}\right)}^{6}{\left({P}_{B}^{\left(2\right)}\right)}^{2}$ 0 1 ${\left({P}_{A}^{\left(1\right)}\right)}^{4}{\left({P}_{B}^{\left(1\right)}\right)}^{0}$ 3 0 1 ${\left({P}_{A}^{\left(2\right)}\right)}^{8}{\left({P}_{B}^{\left(2\right)}\right)}^{0}$ 3 4 ${\left({P}_{A}^{\left(1\right)}\right)}^{1}{\left({P}_{B}^{\left(1\right)}\right)}^{3}$ 3 1 8 ${\left({P}_{A}^{\left(2\right)}\right)}^{7}{\left({P}_{B}^{\left(2\right)}\right)}^{1}$ 2 6 ${\left({P}_{A}^{\left(1\right)}\right)}^{2}{\left({P}_{B}^{\left(1\right)}\right)}^{2}$ 3 2 28 ${\left({P}_{A}^{\left(2\right)}\right)}^{6}{\left({P}_{B}^{\left(2\right)}\right)}^{2}$ 1 4 ${\left({P}_{A}^{\left(1\right)}\right)}^{3}{\left({P}_{B}^{\left(1\right)}\right)}^{1}$ 3 3 56 ${\left({P}_{A}^{\left(2\right)}\right)}^{5}{\left({P}_{B}^{\left(2\right)}\right)}^{3}$ 0 1 ${\left({P}_{A}^{\left(1\right)}\right)}^{4}{\left({P}_{B}^{\left(1\right)}\right)}^{0}$ 4 0 1 ${\left({P}_{A}^{\left(2\right)}\right)}^{8}{\left({P}_{B}^{\left(2\right)}\right)}^{0}$ 4 1 ${\left({P}_{A}^{\left(1\right)}\right)}^{0}{\left({P}_{B}^{\left(1\right)}\right)}^{4}$ 4 1 8 ${\left({P}_{A}^{\left(2\right)}\right)}^{7}{\left({P}_{B}^{\left(2\right)}\right)}^{1}$ 3 4 ${\left({P}_{A}^{\left(1\right)}\right)}^{1}{\left({P}_{B}^{\left(1\right)}\right)}^{3}$ 4 2 28 ${\left({P}_{A}^{\left(2\right)}\right)}^{6}{\left({P}_{B}^{\left(2\right)}\right)}^{2}$ 2 6 ${\left({P}_{A}^{\left(1\right)}\right)}^{2}{\left({P}_{B}^{\left(1\right)}\right)}^{2}$ 4 3 56 ${\left({P}_{A}^{\left(2\right)}\right)}^{5}{\left({P}_{B}^{\left(2\right)}\right)}^{3}$ 1 4 ${\left({P}_{A}^{\left(1\right)}\right)}^{3}{\left({P}_{B}^{\left(1\right)}\right)}^{1}$ 4 4 70 ${\left({P}_{A}^{\left(2\right)}\right)}^{4}{\left({P}_{B}^{\left(2\right)}\right)}^{4}$ 0 1 ${\left({P}_{A}^{\left(1\right)}\right)}^{4}{\left({P}_{B}^{\left(1\right)}\right)}^{0}$ $4 5 1 8 ${\left({P}_{A}^{\left(2\right)}\right)}^{7}{\left({P}_{B}^{\left(2\right)}\right)}^{1}$ 4 1 ${\left({P}_{A}^{\left(1\right)}\right)}^{0}{\left({P}_{B}^{\left(1\right)}\right)}^{4}$ 5 2 28 ${\left({P}_{A}^{\left(2\right)}\right)}^{6}{\left({P}_{B}^{\left(2\right)}\right)}^{2}$ 3 4 ${\left({P}_{A}^{\left(1\right)}\right)}^{1}{\left({P}_{B}^{\left(1\right)}\right)}^{3}$ 5 3 56 ${\left({P}_{A}^{\left(2\right)}\right)}^{5}{\left({P}_{B}^{\left(2\right)}\right)}^{3}$ 2 6 ${\left({P}_{A}^{\left(1\right)}\right)}^{2}{\left({P}_{B}^{\left(1\right)}\right)}^{2}$ 5 4 70 ${\left({P}_{A}^{\left(2\right)}\right)}^{4}{\left({P}_{B}^{\left(2\right)}\right)}^{4}$ 1 4 ${\left({P}_{A}^{\left(1\right)}\right)}^{3}{\left({P}_{B}^{\left(1\right)}\right)}^{1}$ 5 5 56 ${\left({P}_{A}^{\left(2\right)}\right)}^{3}{\left({P}_{B}^{\left(2\right)}\right)}^{5}$ 0 1 ${\left({P}_{A}^{\left(1\right)}\right)}^{4}{\left({P}_{B}^{\left(1\right)}\right)}^{0}$ 6 2 28 ${\left({P}_{A}^{\left(2\right)}\right)}^{6}{\left({P}_{B}^{\left(2\right)}\right)}^{2}$ 4 1 ${\left({P}_{A}^{\left(1\right)}\right)}^{0}{\left({P}_{B}^{\left(1\right)}\right)}^{4}$ 6 3 56 ${\left({P}_{A}^{\left(2\right)}\right)}^{5}{\left({P}_{B}^{\left(2\right)}\right)}^{3}$ 3 4 ${\left({P}_{A}^{\left(1\right)}\right)}^{1}{\left({P}_{B}^{\left(1\right)}\right)}^{3}$ 6 4 70 ${\left({P}_{A}^{\left(2\right)}\right)}^{4}{\left({P}_{B}^{\left(2\right)}\right)}^{4}$ 2 6 ${\left({P}_{A}^{\left(1\right)}\right)}^{2}{\left({P}_{B}^{\left(1\right)}\right)}^{2}$ 6 5 56 ${\left({P}_{A}^{\left(2\right)}\right)}^{3}{\left({P}_{B}^{\left(2\right)}\right)}^{5}$ 1 4 ${\left({P}_{A}^{\left(1\right)}\right)}^{3}{\left({P}_{B}^{\left(1\right)}\right)}^{1}$ 6 6 28 ${\left({P}_{A}^{\left(2\right)}\right)}^{2}{\left({P}_{B}^{\left(2\right)}\right)}^{6}$ 0 1 ${\left({P}_{A}^{\left(1\right)}\right)}^{4}{\left({P}_{B}^{\left(1\right)}\right)}^{0}$ 7 3 56 ${\left({P}_{A}^{\left(2\right)}\right)}^{5}{\left({P}_{B}^{\left(2\right)}\right)}^{3}$ 4 1 ${\left({P}_{A}^{\left(1\right)}\right)}^{0}{\left({P}_{B}^{\left(1\right)}\right)}^{4}$ 7 4 70 ${\left({P}_{A}^{\left(2\right)}\right)}^{4}{\left({P}_{B}^{\left(2\right)}\right)}^{4}$ 3 4 ${\left({P}_{A}^{\left(1\right)}\right)}^{1}{\left({P}_{B}^{\left(1\right)}\right)}^{3}$ 7 5 56 ${\left({P}_{A}^{\left(2\right)}\right)}^{3}{\left({P}_{B}^{\left(2\right)}\right)}^{5}$ 2 6 ${\left({P}_{A}^{\left(1\right)}\right)}^{2}{\left({P}_{B}^{\left(1\right)}\right)}^{2}$ 7 6 28 ${\left({P}_{A}^{\left(2\right)}\right)}^{2}{\left({P}_{B}^{\left(2\right)}\right)}^{6}$ 1 4 ${\left({P}_{A}^{\left(1\right)}\right)}^{3}{\left({P}_{B}^{\left(1\right)}\right)}^{1}$ 7 7 8 ${\left({P}_{A}^{\left(2\right)}\right)}^{1}{\left({P}_{B}^{\left(2\right)}\right)}^{7}$ 0 1 ${\left({P}_{A}^{\left(1\right)}\right)}^{4}{\left({P}_{B}^{\left(1\right)}\right)}^{0}$ 8 4 70 ${\left({P}_{A}^{\left(2\right)}\right)}^{4}{\left({P}_{B}^{\left(2\right)}\right)}^{4}$ 4 1 ${\left({P}_{A}^{\left(1\right)}\right)}^{0}{\left({P}_{B}^{\left(1\right)}\right)}^{4}$