# 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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