$$IABAYI$$
$BY\left(AI\right)^{2}$
$$B^{1}I^{1}A^{1}Y^{1}I^{1}A^{1}$$
$$B^{1}Y^{1}I^{1}I^{1}A^{1}A^{1}$$
$$B^{1}Y^{1}I^{1+1}A^{1+1}$$
$$B^{1}Y^{1}I^{2}A^{1+1}$$
$$B^{1}Y^{1}I^{2}A^{2}$$
$$BYI^{2}A^{2}$$
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$Y\left(AI\right)^{2}$