AMO 2027 Grades 10-12 SET 2 - Self-study Question 14

If $a,b,c\in\mathbb R$, $a+b+c=36$ and $\frac1a+\frac1b+\frac1c=39$, find $$\frac ab+\frac bc+\frac ca+\frac ac+\frac cb+\frac ba.$$

Enter one whole number, without units.