ILL 1990 Problem 71

Given a point $P = (p_1, p_2, \ldots, p_n)$ in $n$ -dimensional space . Find point $X = (x_1, x_2, \ldots, x_n)$ , such that $x_1 \leq x_2 \leq\cdots \leq x_n$ and $\sqrt{(x_1-p_1)^2 + (x_2-p_2)^2+\cdots+(x_n-p_n)^2}$ is minimal.