Proposed by Tho Nguyen Xuan, Hanoi University of Science and Technology,

Hanoi, Vietnam. What is the minimum value of

$|a+b+c|(\frac{1}{|a-b|}+\frac{1}{|b-c|}+\frac{1}{|c-a|})$

over all triples $a,b,c$ of distinct real numbers satisfying $a^2+b^2+c^2=2(ab+bc+ca)?$