Three numbers, , , , are drawn randomly and without replacement from the set . Three other numbers, , , , are then drawn randomly and without replacement from the remaining set of 997 numbers. Let be the probability that, after a suitable rotation, a brick of dimensions can be enclosed in a box of dimensions , with the sides of the brick parallel to the sides of the box. If is written as a fraction in lowest terms, what is the sum of the numerator and denominator?
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