IMO 1959–1966 - Longlisted Problems (individual years unknown) Question 46

(YUG) Let
$$f(a,b,c)=\left|\frac{|b-a|}{|ab|}+\frac{b+a}{ab}-\frac2c\right|+\frac{|b-a|}{|ab|}+\frac{b+a}{ab}+\frac2c.$$
Prove that $f(a,b,c)=4\max\{1/a,1/b,1/c\}$.