Crossword Genius

Food, right on the seaside (4)

Ross

I believe the answer is:

pier

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'the seaside' is the definition.
Although both the answer and definition are singular nouns, I cannot understand how they can define each other.

'food right on' is the wordplay.
'food' becomes 'pie' (pie is a kind of food).
'right' becomes 'R' (common abbreviation).
'on' says to put letters next to each other.
'pie'+'r'='PIER'

Can you help me to learn more?

(Other definitions for pier that I've seen before include "Seaside resort feature" , "Buttress; landing place" , "Quay" , "One jutting into sea" , "Seaside attraction" .)

I've seen this clue in The Hindu.
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