Inside triangle ABC there are three circles with radii \(r_1\), \(r_2\), and \(r_3\). Each is tangent to two sides of the triangle and to its incircle. The incircle has radius \(r\). All of \(r\), \(r_1\), \(r_2\), and \(r_3\) are distinct perfect square integers. Find the smallest possible value of inradius \(r\).
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