Performing multiple layer intersection in QGIS?

I am trying to find a way with QGIS 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.

Furthermore, 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 is there a QGIS solution?

Answer

Forgot to post my solution...
STEP 1 : Merge layers
In the end I changed my Qgis Version to 2.14.11, the algorithm takes a single input param (layers) separated by a semicolon :
processing.alghelp('qgis:mergevectorlayers')

ALGORITHM: Merge vector layers
    LAYERS 
    OUTPUT 

Prior it was :

processing.runalg('qgis:mergevectorlayers', layer1, layer2, output)

You can also do a loop to use this version of the algorithm

for i, layer in enumerate(layers):

            if i == 0:
                layer1 = layers[i]
                layer2 = slayers[i+1]
                processing.runalg('qgis:mergevectorlayers', layer1, layer2, savename)
            if i == leng-1:
                break

            else:
                layer1 = QgsVectorLayer(savename, 'temp', 'ogr')
                layer2 = sme_layers[i+1]
                savename = name          

                processing.runalg('qgis:mergevectorlayers', layer1, layer2,  savename)

STEP2 : overlay the layer with itself

processing.alghelp('grass:v.overlay')




ALGORITHM: v.overlay - Overlays two vector maps.
    ainput 
    atype 
    binput 
    operator 
    -t 
    GRASS_REGION_PARAMETER 
    GRASS_SNAP_TOLERANCE_PARAMETER 

    GRASS_MIN_AREA_PARAMETER 
    GRASS_OUTPUT_TYPE_PARAMETER 
    output 

STEP 3 Joseph answer seems decent