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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