Cutting Lines

A rectangle has corners $(0,0)$, $(W,0)$, $(0,H)$, and $(W,H)$. There are $N$ cut segments, each parallel to a side. Segment $i$ runs from $(A_i,B_i)$ to $(C_i,D_i)$ with exactly one of $A_i=C_i$ or $B_i=D_i$. Parallel segments never share a point, and no parallel segment touches the paper border. After cutting along every segment, how many pieces remain?

The first line has $W$, $H$, and $N$. The next $N$ lines give each segment's endpoints.

Print the number of pieces on one line.

$1 \le W,H \le 10^9$, $1 \le N \le 10^5$.