P4515 [COCI 2009/2010 #6] XOR

坐标系下有若干个等腰直角三角形，且每个等腰直角三角形的直角顶点都在左下方，两腰与坐标轴平行。被奇数个三角形覆盖的面积部分为灰色，被偶数个三角形覆盖的面积部分为白色，如下图所示。  已知 $N$个等腰直角三角形的顶点坐标及腰长，求灰色部分面积。 Mirko and Slavko have built their own LED display. The display is initially white. During each of the $N$ parts of the testing phase, Mirko attached three electrodes to the display in such way that they formed a right isosceles triangle. He noticed that, after attaching the electrodes, all pixels in the enclosing triangle are inverted (white pixels become black, and black pixels become white). Watching Mirko play with the electrodes, Slavko observed interesting shapes emerging on the screen. Mathematically inclined as he is, first thing that crossed his mind was how to calculate total area covered by black pixels. Help him by writing a program to do just that!

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$1 \leq N \leq 10, 1 \leq X, Y, R \leq 10^6$