Multiple layer intersection

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I am trying to find a way with qgis/python to get the intersection area of more than 2 layers.All the tools in Qgis take just the 2 input layers. ='(
For example in the image below, I have 4 layers and I want to retrieve just the black area.
Further more, I need to retrieve the count attribute and add it to the intersected area attribute table (in this case 4)




I know there is a tool that does the trick in ArcGis, but if anyone has an openSource solution, that would be great !
Cheers



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