Special sequence

Algebra Level 4

A function \(J(x)\) follows the following conditions:

\[\begin{cases} J(0) = J(1) = 2 \\ J(2) = J(1) + J(0) + 2 = 6 \\ J(3) = J(1) + 1 = 3 \\ J(x) = J(|x-1|) + J(|x-2|) + J(|x-3|) - J(|x-4|); \quad x > 3 \end{cases} \]

Then, find the value of \(J(9)\).

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