Finding list of all shapefiles that overlap with single shapefile using QGIS?

Question

I have a list of 34 shapefiles. These shapefiles are range maps for different species. I would like to take 4 of these shapefiles and document a list of those shapefiles (within the 30 shapefiles), whose ranges overlap with these 4 shapefiles. I wouldn't mind comparing them one at a time ie. Shapefile 1 with the other 30 shapefiles; Shapefile2 with the other 30 shapefile..

Is there a way to do this in QGIS/PyQGIS?

I tried using the Intersect tool, but that would only give me the features that are common to both the files chosen.

I basically need a table that gives me : shapefile1 and all the names of the shapefiles that overlap with shapefile1

EDIT: Following @xunik's suggestion:

ISSUE I am having right now is that the script is not picking up every possible combination(even if they are slightly touching each other). Attached is an image that shows the script being written to a csv file.

EDIT 2

The script suggested by @xunilk below is not working and is actually showing incorrect information. Any suggestions?

See Image below. The output is showing that these two features intersect, when in reality, they dont. Please Help!

Answer 1

In this case, it is preferable to use itertools module to avoid repeated indexes. I assumed one feature for each shapefile in next situation:

Next code prints all the names of the shapefiles that overlap with each other.

import itertools

mapcanvas = iface.mapCanvas()

layers = mapcanvas.layers()

feats = []

for layer in layers:
    for feat in layer.getFeatures():
        feats.append(feat)

n = len(layers)

comb = range(n)

for i, j in itertools.combinations(comb, 2):
    if feats[i].geometry().intersects(feats[j].geometry()):
        print layers[i].name() + " intersects with " + layers[j].name()

After running the code at the Python Console of QGIS I got:

It works as expected.

Editing Note:

When each layer can have more than one feature, next version of former script works:

import itertools

mapcanvas = iface.mapCanvas()

layers = mapcanvas.layers()

n = len(layers)

feats = [ [] for i in range(n) ]

idx_layers = []

for i, layer in enumerate(layers):
    for feat in layer.getFeatures():
        feats[i].append( feat )
        idx_layers.append(i)

len_feats = [ len(item) for item in feats ]

idx_feats = []

for item in len_feats:
    idx_feats.append(range(item))

#flattened list
idx_feats = [ item for element in idx_feats for item in element ]

n = sum(len_feats)

comb = range(n)

#flattened list
feats = [ item for element in feats for item in element ]

for i, j in itertools.combinations(comb, 2):
    if feats[i].geometry().intersects(feats[j].geometry()):
        print "feature:", idx_feats[i] , "from layer:", idx_layers[i], " intersects feature:", idx_feats[j], "from layer:", idx_layers[j]

I tried out with these new shapefiles:

and results at Python Console of QGIS were as expected.