If the circle $x^2 + y^2 + 2gx + 2fy + c = 0$ passes through the origin, has radius 3, and its center lies on the line $x + y = 4$, then $g + f =$
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Do not waste time using the radius or origin conditions! The question only requires matching the center $(-g, -f)$ on the line $x+y=4$, which directly yields $g+f = -4$ regardless of other parameters.