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Suppose $f\colon \mathbb R\to\mathbb R$ is a strictly decreasing function which satisfies the relation $$f(x+y) + f( f(x) + f(y) ) = f( f( x+f(y) ) + f( y+f(x) ) ) , \quad \forall x , y \in\mathbb R $$

Find a relation between $f( f(x))$ and $x$.

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