Complexity of the realization of a linear function in the class of $\Pi$-circuits

It is proved that the linear function $g_n(x_1,\dots,x_n)=x_1+\dots+x_n\mod2$ is realized in the class of $\Pi$-circuits with complexity $L_\pi(g_n)\geqslant n^2$. Combination of this result with S. V. Yablonskii's upper bound yields $L_\pi(g_n)\genfrac{}{}{0pt}{}{\smile}{\frown} n^2$.