One of the points of intersection of the curves $y = 1 + 3x - 2x^2$ and $y = \frac{1}{x}$ is $\left(\frac{1}{2}, 2\right)$. Let the area of the region enclosed by these curves be $\frac{1}{24}\left(l\sqrt{5} + m\right) - n \log_e(1 + \sqrt{5})$, where $l, m, n \in \mathbb{N}$. Then $l + m + n$ is equal to:
