Answer the question based on the information given below: Let x and y be real numbers and let

$f(x, y) = |x+y|, F(f(x, y)) = -f(x,y) \text{ and } G(f(x, y)) = -F(f(x, y))$

What is the value of $f(G(f(1,0)), f(F(f(1,2)), G(f(1,2))))$?