A variation of divisibility rule of 3?

Four true facts:

\(123456789\) is divisible by 3.
\(12345+6789\) is divisible by 3.
\(123+456+789\) is divisible by 3.
\(12+3456+78+9\) is divisible by 3.

True or False?

No matter where and how many \(+\) signs you put in between the digits of the number 123456789, the resulting number is still divisible by 3.

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