KöMaL 2010 A510

There is given a positive integer $n$ and some straight lines in the plane such that none of the lines passes through (0,0), and every lattice point ($a$,$b$), where 0$\le a$,$b \le n$ are integers and $a$+$b$>0, is contained by at least $a$+$b$+1 of the lines. Prove that the number of the lines is at least $n$($n$+3).