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The numbers 1, 2, . . . , 2012 are written on a blackboard. Each minute, a student goes up to the board,
chooses two numbers x and y, erases them, and writes the number 2x + 2y on the board. This
continues until only one number N remains. Find the remainder when the maximum possible value of
N is divided by 1000.
The answer is 538.
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