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Find the number of permutations $$x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8$$ of the integers $$-3, -2, -1, 0, 1, 2, 3, 4$$ that satisfy the chain of inequalities $$x_1x_2 < x_2x_3 < x_3x_4 < x_4x_5 < x_5x_6 < x_6x_7 < x_7x_8$$.
Correct Answer: 1
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