In the above circuit shaped like a Christmas tree, the 17 tiny grey rectangles are all resistors with identical resistance 1 ohm. (Light grey line segments are not part of the circuit.)

The effective resistance across A and B can be expressed as \(\dfrac{x}{y}\) ohms, where \(x\) and \(y\) are coprime positive integers. Find \(x+y\). (Your answer should be three digits long)

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