Dad and mum are out of the country (6)

I believe the answer is:
panama
'country' is the definition.
(Panama is an example)
'dad and mum are out' is the wordplay.
I cannot really understand how this works, but
'dad' could be 'pa' (both can mean one's father) and 'pa' is present in the answer.
'and' could be 'n' (common abbreviation for 'and') and 'n' is present in the answer.
'mum' could be 'ma' (both can mean mother) and 'ma' is located in the answer.
'are' could be 'a' (short for 'are', historical unit of measurement) and 'a' is present in the answer.
This accounts for all the letters.
This explanation may well be incorrect...
'of the' is the link.
Can you help me to learn more?
(Other definitions for panama that I've seen before include "Great canal connecting Atlantic and Pacific" , "Land - hat - cigar" , "Canal state; hat" , "Wide-brimmed hat" , "Man's hat" .)
