Given number of regions, find maximum number of boundaries

Question

Problem: Supoose we want to divide $\mathbb{R^2}$ into $N$ regions separated by straight lines. What is the maximum number of boundary lines we could have? I also pose the restriction that between any two regions, there can be only one boundary line (so zigzagging a boundary does not increase the count). For example, here I attempt to find the maximum number of boundaries for $N = 4$ regions in $\mathbb{R}^2$, and I count 6 boundary lines. But is there a general formula for general integer $N$? Can someone point me to a reference on this problem?