The harmonic mean of a set of non-zero numbers is the reciprocal of the average of the reciprocals of the numbers. What is the harmonic mean of 1, 2, and 4?

A. $\frac{3}{7}$

B. $\frac{7}{12}$

C. $\frac{12}{7}$

D. $\frac{7}{4}$

E. $\frac{7}{3}$

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