Five rectangles, $A$, $B$, $C$, $D$, and $E$, are arranged in a square as shown below. These rectangles have dimensions $2\times 3$, $1\times 6$, $2\times 4$, $5\times 6$, and $2\times 7$ respectively. (The figure is not drawn to scale.) Which of the five rectangles is the shaded one in the middle?