If $$\(i\)$$ is the imaginary unit, there are two ordered pairs of integers ( $$\(a, b\)$$ ) for which $$\(a+b i\)$$ is a solution of $$\(x^{2}+3 x+3=i\)$$. The two ordered pairs of integers can be written in the form ( $$\(a 1, b 1\)$$ ) and ( $$\(a 2, b 2\)$$ ). Please enter the value of $$\(a 1+b 1+a 2+b 2\)$$.

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