# Electric Christmas Tree

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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