Trapezoid \(ABCD\) has \(\angle C=\angle D=90^\circ\) and \(AB=170\) with \(AD || BC,\) as shown above. Point \(E\) is picked on \(DC\) such that \(AE = 100\) and \(BE = 90.\) All of the segments \(AD, DE, EC,\) and \(CB\) have integer lengths.

What is the perimeter of trapezoid \(ABCD?\)

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