Let $$\overrightarrow{u},\overrightarrow{v}$$ and $$\overrightarrow{w}$$ be vectors in three-dimensional space, where $$\overrightarrow{u}$$ and $$\overrightarrow{v}$$ re unit vectors which are not perpendicular to each other and
$$\overrightarrow{u}.\overrightarrow{w} = 1, \overrightarrow{v}.\overrightarrow{w} = 1, \overrightarrow{w}\overrightarrow{w} = 4$$
If the volume of the parallelopiped, whose adjacent sides are represented by the vectors $$\overrightarrow{u},\overrightarrow{v}$$ and $$\overrightarrow{w}$$, is $$\sqrt{2}$$, then the value of $$\mid 3\overrightarrow{u} + 5 \overrightarrow{v} \mid$$ is ___ .