LU Head node in the upper left corner $$\left (M_{r}^{\prime } = M_{r} + 1 \right) \& \left (M_{c}^{\prime } = M_{c} - 1 \right)$$
RU Head node in the upper right corner $$\left (M_{r}^{\prime } = M_{r} + 1 \right) \& \left (M_{c}^{\prime } = M_{c} + 1 \right)$$
LD Head node in the lower left corner $$\left (M_{r}^{\prime } = M_{r} - 1 \right) \& \left (M_{c}^{\prime } = M_{c} - 1 \right)$$
RD Head node in the lower right corner $$\left (M_{r}^{\prime } = M_{r} - 1 \right) \& \left (M_{c}^{\prime } = M_{c} + 1 \right)$$
UG Head node in the grid above $$\left (M_{r}^{\prime } = M_{r} + 1 \right) \& \left (M_{c}^{\prime } = M_{c}\right)$$
DG Head node in the grid below $$\left (M_{r}^{\prime } = M_{r} - 1 \right) \& \left (M_{c}^{\prime } = M_{c} \right)$$
LG Head node in the left grid $$\left (M_{r}^{\prime } = M_{r} \right) \& \left (M_{c}^{\prime } = M_{c} - 1 \right)$$
RG Head node in the right grid $$\left (M_{r}^{\prime } = M_{r} \right) \& \left (M_{c}^{\prime } = M_{c} + 1 \right)$$ 