# Counting Triples

Let $$N$$ be the number of ordered triples $$(a,b,c)$$ of positive integers such that $$a,b,c\in\{1,2,3,\cdots,2014\}$$ and $$a+b+c$$ is divisible by $$3$$. Determine the remainder when $$N$$ is divided by $$1000$$.

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