A thin uniform square lamina of side $a$ is placed in the $x y$-plane with its sides parallel to $X$ and $Y$-axes and with its centre coinciding with origin. Its moment of inertia about an axis passing through a point on the $Y$-axis at a distance $Y=2 a$ and parallel to $X$-axis is equal to its moment of inertia about an axis passing through a point on the $X$-axis at a distance $x=d$ and perpendicular to $x y$-plane. Then value of $d$ is