Given the following 4 by 4 square grid of points, determine the number of ways we can label ten different points A, B, C, D, E, F, G, H, I, J such that the lengths of the nine segments
A B, B C, C D, D E, E F, F G, G H, H I, I J
are in strictly increasing order.
\begin{array}{cccc}
\cdot & \cdot & \cdot & \cdot \\
\cdot & \cdot & \cdot & \cdot \\
\cdot & \cdot & \cdot & \cdot \\
\cdot & \cdot & \cdot & \cdot
\end{array}