The math team at Jupiter Falls Middle School meets twice a month during the summer, and the math team coach, Mr. Fischer, prepares some Olympics-themed problems for his students. One of the problems Joshua and Alexis work on boils down to a system of equations:

\[\begin{align*}
2x+3y+3z &= 8,\\
3x+2y+3z &= 808,\\
3x+3y+2z &= 80808.
\end{align*}\]

Their goal is not to find a solution \((x,y,z)\) to the system, but instead to compute the sum of the variables. Find the value of \(x+y+z\).

Let's think step by step and output the final answer within \boxed{}.
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