MathNet 2012 Question 99

Find the number of ordered $2012$-tuples of integers $(x_{1}, x_{2}, \ldots, x_{2012})$, with each integer between $0$ and $2011$ inclusive, such that the sum $x_{1} + 2x_{2} + 3x_{3} + \cdots + 2012x_{2012}$ is divisible by $2012$.