Crossword Genius

A great big hug goes to men's heart (4)

Ross

I believe the answer is:

huge

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'a great' is the definition.
(I've seen this in another clue)

'hug goes to men's heart' is the wordplay.
'goes to' means one lot of letters go next to another.
'heart' indicates the central letters.
The centre of 'men' is 'e'.
'hug'+'e'='HUGE'

'big' is the link.
This may not be right. It may be part of another bit of the clue.

Can you help me to learn more?

(Other definitions for huge that I've seen before include "Vast; immense" , "Unusually large" , "Great in size or amount" , "Colossal" , "Massive" .)

I've seen this clue in the Evening Standard.
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