Let \(F_1 = \left( -3, 1 - \frac{\sqrt{5}}{4} \right)\) and \(F_ 2= \left( -3, 1 + \frac{\sqrt{5}}{4} \right)\) (foci). Then the set of points \(P\) such that
\(|PF_1 - PF_2| = 1\)
form a hyperbola. The equation of this hyperbola can be written as
\(\frac{(y - k)^2}{a^2} - \frac{(x - h)^2}{b^2} = 1\)
where \(a, b > 0.\) Find \(h + k + a + b.\)
