Pandas - Compare two rows of a dataframe across specific columns and keep one based on certain conditions?

I have a pandas dataframe which looks like below (rows are always unique)

Start         End        Status       AB            DD         T_DOWN    TR            WE         T_UP       DD            RE         P_DOWN     TR            WE         R_WAITYT            GG         R_WAIT    GG            LO         P_DOWN  

What I want to do is to find out rows where Start value of one row equals End value of another row and Status value of such rows either contains the string T_DOWN or P_DOWN. So if such condition exists, then keep the row which contains Status value P_DOWN

So in the example above, the third row's Start value is DD which matches with first row's End value which is also DD and both the rows have presence of T_DOWN and P_DOWN. So I would keep the third row since it contains the Status value P_DOWN

As a counter example, notice the sixth row whose Start value is GG and the fifth row's End value is also GG. But the rows contain Status values have R_WAIT and P_DOWN. So these rows will not be considered.

So final result would look like

Start         End        Status       TR            WE         T_UP       DD            RE         P_DOWN     TR            WE         R_WAITYT            GG         R_WAIT    GG            LO         P_DOWN

But I just can't figure out how to do this comparison.I looked up some resources online where the comparison logic appears a little bit similar to what I am trying to do but yet not close enough to give me a head start.

Compare Multiple Columns to Get Rows that are Different in Two Pandas Dataframes

Pandas dataframe compare multiple rows with specific condition

Can anybody help me with this?