Problem Description

Still remember those games we played in our childhood? Folding and cutting paper must be among the most popular ones. Clever children will always search for something new, even when they play games like cutting paper. Now, Carol, a smart girl, asks her brother Mike to solve a puzzle. However, as always, Mike cannot find the solution, therefore he turns to you for help.

Carol's puzzle is simple to state. She folds the paper in a certain manner and then uses a knife to cut through the folded paper. What Mike needs to do is to tell how many pieces the folded paper will turn into after it is cut. To eliminate the ambiguity, we can coordinate the paper as [0, 1] * [0, 1], with the coordinates of lower left corner (0, 0). A fold is denoted by two points (x1, y1) and (x2, y2) on the folding line, with which, the direction of the line is determined by from (x1, y1) to (x2, y2). Carol will always fold