Let \(A_1, A_2, A_3, \ldots , A_n \) denote vertices of a regular \(n\) sided polygon inscribed in a circle of radius \(R\).

If \( (A_1 A_2)^2 + (A_1 A_3)^2 + \cdots + (A_1 A_n)^2 = 14R^2 \), find the number of sides of the polygon.

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