Parallelogram on the Coordinate Plane

Geometry Level 4

A parallelogram on the coordinate plane is defined by the following lines: {y=4x+5y=4x+3y=nx+5y=nx+3\left\{\begin{array}{l}y=4x+5 \\ y=4x+3 \\ y=nx+5\\ y=nx+3\end{array}\right.

If the area of the parallelogram is 1616, then nn can be expressed as pq\dfrac{p}{q}, where p,qp,q are coprime positive integers. Find the smallest possible value of p+qp+q.

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