Sum Minus Product

Algebra Level 4

How many ordered tuples of 7 integers $$\{ x_i \} _{i=1}^7$$ are there, such that

$x_1 + x_2 + x_3 + x_4 + x_ 5 + x_6 + x_7 - x_1 x_2 x_3 x_4 x_5x_6x_7= 6,$

and $$1 \leq x_i \leq 8$$.

This problem is proposed by Wei Liang G.

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