Python Pandas - Get the rows of first and last day of particular months

My data set df looks as follows:

Date         Value
...
2012-07-31   61.9443
2012-07-30   62.1551
2012-07-27   62.3328
...          ... 
2011-10-04   48.3923
2011-10-03   48.5939
2011-09-30   50.0327
2011-09-29   51.8350
2011-09-28   50.5555
2011-09-27   51.8470
2011-09-26   49.6350
...          ...
2011-08-03   61.3948
2011-08-02   61.5476
2011-08-01   64.1407
2011-07-29   65.0364
2011-07-28   65.7065
2011-07-27   66.3463
2011-07-26   67.1508
2011-07-25   67.5577
...          ...
2010-10-05   57.3674
2010-10-04   56.3687
2010-10-01   57.6022
2010-09-30   58.0993
2010-09-29   57.9934

Below are the data type of the two columns:

Type                 Column Name              Example Value
-----------------------------------------------------------------
datetime64[ns]       Date                     2020-06-19 00:00:00
float64              Value                    108.82

I would like to have a subset of df that contains only the rows where the first entry in October and the last entry of July are selected:

Date         Value
...
2012-07-31   61.9443
2011-10-03   48.5939
2011-07-29   65.0364
2010-10-01   57.6022

Any idea how to do that?

from Python Pandas - Get the rows of first and last day of particular months