How to visualize the intersection of 2 rectangles or more in a different color with Matplotlib-CodePudding

I have this demo code which generates colored rectangles with Matlplotlib. After several hours searching everywhere, I still do not understand how to visualize the intersection between 2 rectangles or more in a different color. Thank you very much.

import matplotlib
import matplotlib.pyplot as plt

fig = plt.figure()
ax = fig.add_subplot(111)

rect1 = matplotlib.patches.Rectangle((-675, -374),
                                    744, 412,
                                    color ='green')

rect2 = matplotlib.patches.Rectangle((-48, -454),
                                    116, 491,
                                    color ='blue')

rect3 = matplotlib.patches.Rectangle((-1009, -189),
                                    1074, 225,
                                    color ='yellow')

ax.add_patch(rect1)
ax.add_patch(rect2)
ax.add_patch(rect3)

plt.xlim([-1100, 1100])
plt.ylim([-1100, 1100])

plt.show()