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$\{x_i\}_{i = 1}^7$ is a set of 7 integers that satisfy $1≤ x_i ≤ 8$. How many such ordered sets of $7$ integers are there, such that $$x_1 + x_2 + x_3 + x_4 + x_5 + x_6 + x_7 - x_1x_2x_3x_4x_5x_6x_7 = 6?$$

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