A fence has been designed to surround three circular gardens of equal radii. The fence consists of three line segments and three portions of the circles as shown in the figure. Each circle has a radius of 9 units and the length of the fence can be written as \(x + \pi y\), where \(x\) and \(y\) are integers.

Find the value of \(\large\frac{y}{3}+x \).

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