Crossword Genius

Country song without ending is No.1 by midday (7)

Ross

I believe the answer is:

tunisia

I'm a little stuck... Click here to teach me more about this clue!

'country' is the definition.
(I know that Tunisia is African country)

'song without ending is no 1 by midday' is the wordplay.
I cannot quite see how this works, but
'is' is present in the answer.
'no' could be 'n' (common abbreviation) and 'n' is present in the answer.
'1' could be 'i' (Roman numeral) and 'i' is found within the answer.
The remaining letters 'tua' is a valid word which might be clued in a way I don't see.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for tunisia that I've seen before include "Country which contains the site of Carthage" , "Country where Carthage is found" , "Somewhere in North Africa" , "African republic on the Mediterranean coast" , "country-style" .)

I've seen this clue in the Sydney Morning Herald.
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