Let three vectors $$\vec{a}$$, $$\vec{b}$$ and $$\vec{c}$$ be such that $$\vec{c}$$ is coplanar with $$\vec{a}$$ and $$\vec{b}$$, $$\vec{a} \cdot \vec{c} = 7$$ and $$\vec{b}$$ is perpendicular to $$\vec{c}$$, where $$\vec{a} = -\hat{i} + \hat{j} + \hat{k}$$ and $$\vec{b} = 2\hat{i} + \hat{k}$$, then the value of $$|2\vec{a} + \vec{b} + \vec{c}|^2$$ is ______