On the coordinate plane, $\Gamma$ is a square with side length 4, centered at the point $(1,1)$, with sides parallel to the coordinate axes. The graph of the function $y = a \times 2 ^ { x }$ intersects $\Gamma$, where $a$ is a real number. The maximum possible range of $a$ is (22)(23) $\leq a \leq$ (24).