OMO 2012

The numbers $$1,2,3,4,\ldots,2012$$ are written on a blackboard. Each minute, a student goes to the blackboard,chooses two numbers $$x$$ and $$y$$, erases them and writes a new number $$2x+2y$$ on the blackboard. This process continues till only one number $$N$$ remains on the blackboard. Find the remainder when the maximum possible value of $$N$$ is divided by $$1000$$.

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