CN-TST 2019 Problem 23

Find all integer $n$ such that the following property holds: for any positive real numbers $a,b,c,x,y,z$ , with $max(a,b,c,x,y,z)=a$ , $a+b+c=x+y+z$ and $abc=xyz$ , the inequality $$a^n+b^n+c^n \ge x^n+y^n+z^n$$ holds.