[จูกัดเหลียง]

Find all function satisfy the following condition,
$f:\mathbf{R^+} \rightarrow \mathbf{R^+}$ $$f(x+y)=2f(x)-x+f(f(y))$$
$i)$ $f(cx)=cf(x),$ for any $c\in\mathbb{R^+}$
$ii)$ $f(1)=1$
for any $x,y\in\mathbb{R^+}$