In an octagon ABCDEFGH of equal side, what is the sum of $\overrightarrow{AB} + \overrightarrow{AC} + \overrightarrow{AD} + \overrightarrow{AE} + \overrightarrow{AF} + \overrightarrow{AG} + \overrightarrow{AH}$, if $\overrightarrow{AO} = 2\hat{i} + 3\hat{j} - 4\hat{k}$ [add image]