A door of width $$w$$ has three identical hinges positioned at distances $$w/4$$, $$w/2$$, and $$3w/4$$ from the left edge. If a force $$F$$ is applied perpendicular to the door at its right edge, what fraction of the total torque is supported by the middle hinge (the one at $$w/2$$)? Assume the hinges only provide vertical reaction forces, and the sum of upward forces from the three hinges balances the downward force $$F$$ applied at the edge.