$ABC$ is a plane lamina of the shape of an equilateral triangle. $D , E$ are mid-points of $AB , AC$ and $G$ is the centroid of the lamina. Moment of inertia of the lamina about an axis passing through $G$ and perpendicular to the plane $ABC$ is $I _ { 0 }$. If part $ADE$ is removed, the moment of inertia of the remaining part about the same axis is $\frac { N I _ { 0 } } { 16 }$ where $N$ is an integer. Value of $N$ is: