An algebra problem by mridul jain

Algebra Level 4

Let $$f(x)$$ be a third-degree polynomial with real coefficients satisfying $$|f(1)|=|f(2)|=|f(3)|=|f(5)|=|f(6)|=|f(7)|=12$$. Find $$|f(0)|$$. '

This problem is from 2015 AIME.

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