Before Lunar New Year 2016 ends...

One common example of Chinese New Year symbolism is the red diamond-shaped 福 characters ("fortune"), which are displayed on the entrances of Chinese homes. This sign is usually seen hanging upside down, since the Chinese word 倒 ("upside down"), sounds like the Chinese word 到 ("arrive"). Therefore, it symbolizes the arrival of luck, happiness, and prosperity.

In the above circuit shaped in the Chinese character 福, the 14 tiny grey rectangles are all resistors with identical resistance 1 ohm. The effective resistance across \(AB\) can be expressed in simplest form as \(\frac{x}{y}\) where \(x\) and \(y\) are coprime. Find \(x+y\).

Note: The isolated red smaller rectangle in the diagram is not part of the circuit. Additionally, as you may have noticed, the break in the circuit is intended. There is no difference between the red and grey wires of the circuit.

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