Let \(F(x) \) denote a monic \(7^\text{th} \) degree polynomial with satisfying the following

\( F(2) = 2, F(3) = 3, F(4) =4, F(5) = 5, F(6) = 6, F(7) =7, F(8) = 8 \)

What is the value of \( F(9) \bmod 7 \)?

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