CN-TST 2022 Problem 10

Given a positive integer $n$ , find all $n$ -tuples of real number $(x_1,x_2,\ldots,x_n)$ such that $$f(x_1,x_2,\cdots,x_n)=\sum_{k_1=0}^{2} \sum_{k_2=0}^{2} \cdots \sum_{k_n=0}^{2} \big| k_1x_1+k_2x_2+\cdots+k_nx_n-1 \big|$$ attains its minimum.