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Let $\color{#EC7300}{C}$ be the coefficient of $\color{#20A900}{x^2}$ in $\color{#69047E}{(1-x)(1+2x)(1-3x)(1+4x)\cdots (1+14x)(1-15x)}$. Find $\color{#EC7300}{|C|}$.

[2004 AIME 1 Problem 7]

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