note that $2023$ would be the theoretical max. however, it is impossible to split the numbers $1,2,3,\cdots,2022$ into two equal groups, as this sum is $1011\cdot2023.$ however, it is possible to split the numbers $2,3,4,\cdots,2022$ into two equal groups. Thus, the minimum of $||\cdots||x_1-x_2|-x_3|-\cdots|-x_2022|$ is $1,$ and our answer is $\boxed{2022}.$