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This is a Korean CSAT mathematics numerical-answer problem. Solve it and put only the final integer value inside \boxed{}.
Problem 29 Consider the parabola with focusF(p,0) (p >0) and directrixx=−p, as shown in the figure. Among the points on this parabola, letAbe a point in the first quadrant, and let Hbe the foot of the perpendicular fromAto the directrix. Consider the ellipse whose foci lie on thex-axis and which passes through the three pointsF,A, andH. LetBbe the focus of this ellipse with positivex-coordinate. Suppose that triangleAHBhas perimeter p+ 27 and area 2p+ 12. Let the length of segment HFbek. Computek 2. [4 points]
\boxed{360}
Comparative Analysis (P44) (Average across runs)
Averages use reported measurements only. Missing usage is not treated as zero.