A variation of divisibility rule of 3?

Four true facts:

123456789123456789 is divisible by 3.
12345+678912345+6789 is divisible by 3.
123+456+789123+456+789 is divisible by 3.
12+3456+78+912+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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