Polynomials and mod?

Algebra Level 4

Let \(f(x)\) be a third-degree polynomial with real coefficients satisfying

\(\left| f(1) \right| = \left| f(2) \right| = \left| f(3) \right| = \left| f(5) \right| = \left| f(6) \right| = \left| f(7) \right| = 12.\)

Find \(\left| f(0) \right|\)

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