Let the minimum value of $\sqrt { 2{ x }^{ 2 }+2{ y }^{ 2 } } +\sqrt { { y }^{ 2 }+{ x }^{ 2 }-4y+4 } +\sqrt { { x }^{ 2 }+{ y }^{ 2 }-4y-4x+8 }$ be $a\sqrt { b }$ such that $b$ is square free.
Find $a+b$.

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