Define a finite sequence $\left( s_i \right)_{1\le i\le 2004}$ with initial conditions $s_0 + 2 = s_1 + 1 = s_2 = 2$ and the recurrence relation:
$$ s_n = 1 + s_{n-1} + s_{n-2} - s_{n-3}. $$
Calculate its last element.

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