Display records between two search strings using sed

I have input file like

AAA
AAA
CCC
CCC
CCC
EEE
EEE
EEE
EEE
FFF
FFF
GGG
GGG

i was trying to retrieve data between two strings using sed.

sed -n /CCC/,/FFF/p input_file

Am getting output like

CCC
CCC
CCC
EEE
EEE
EEE
EEE
FFF

The above command retrieves the data till to the first occurence of the destination string (i.e., till 1st occurence off FFF record)
I need to search the records till last occurence.
Expected output is

CCC
CCC
CCC
EEE
EEE
EEE
EEE
FFF
FFF

Plz help on this query.

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I could see the same HERE...