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A question about masking input then share

cn flag

I am confused about a simple input-sharing schema.
The schema: a party that holds an input x, and generates a random variable r.
That party secret share r as [r], then distribute it to other parties.
Then broadcast x-r to other parties, then each other parties compute x-r+[r] as the share of [x].
What I am confused here is that if adding up [x], won't it become n-1(x-r)+r?
Thanks in advance

mangohost

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