BxMO 2009 Problem 1

Find all functions $f:\mathbb{Z}_{>0}\rightarrow\mathbb{Z}_{>0}$ that satisfy the following two conditions: [list] $\bullet\ f(n)$ is a perfect square for all $n\in\mathbb{Z}_{>0}$ $\bullet\ f(m+n)=f(m)+f(n)+2mn$ for all $m,n\in\mathbb{Z}_{>0}$ .[/list]