(Monotonicity) Clockwise along $\partial\Sigma$, the function $\text{Re }F$ is increasing on the $L$ boundary portion, but decreasing on the $L^{\prime}=L_{1}\cup L_{2}$ boundary portion. In particular,

$$0=\text{Re }F(q)\leq\text{Re }F\leq\text{Re }F(p).$$

More intrinsically, the real part of the complex volume forms on the moduli spaces are nonnegative.