Find the sum of the squares of the distances from the vertices of a regular $n$-gon inscribed in a circle of radius $R$ to an arbitrary line passing through the center of the polygon.

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Let $\boldsymbol{e}_{1}, \ldots, \boldsymbol{e}_{n}$ be vectors from the center of a given $n$-gon to its vertices; $\boldsymbol{x}$ be a unit vector perpendicular to the line $l$. The desired sum is $\sum\left(\boldsymbol{e}_{i}, \boldsymbol{x}\right)^{2}=1 / 2 n R^{2}$ (see problem $\underline{57083}$ ).