<image>As shown in the figure, in the square $$ABCD$$ with a side length of $$2$$, $$E$$ is a moving point on the edge of the square. The plane of $$\triangle ADE$$ is folded along $$AE$$ so that the projection $$H$$ of point $$D$$ on plane $$ABC$$ lies on line $$AE$$. When $$E$$ moves from point $$D$$ to $$C$$, and then from $$C$$ to $$B$$, the length of the trajectory formed by point $$H$$ is ______ .