$$A3+2A2+A3+3A2+A+2+A+3$$
$2A+5A_{2}+2A_{3}+5$
$$2A_{3}+2A_{2}+3A_{2}+A+2+A+3$$
$$2A_{3}+5A_{2}+A+2+A+3$$
$$2A_{3}+5A_{2}+2A+2+3$$
$$2A_{3}+5A_{2}+2A+5$$
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$2$