Max it out

Algebra Level 4

Let \(x_1, x_2, ... , x_n\) be a sequence of integers such that

(i) \(-1 \leq x_i \leq 2\), for \(i = 1, 2, ... , n\);

(ii) \(x_1 + x_2 + ... + x_n = 19\);

(iii) \(x_1^2 + x_2^2 + ... + x_n^2 = 99\).

Determine the maximum possible value of

\(x_1^3 + x_2^3 + ... + x_n^3\)?

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