How prove this inequality: $\sum_{i,j=1}^{n}|x_{i}+x_{j}|\ge n\sum_{i=1}^{n}|x_{i}|$?

How prove this inequality: $\sum_{i,j=1}^{n}|x_{i}+x_{j}|\ge
n\sum_{i=1}^{n}|x_{i}|$?

Let $x_{1},x_{2},\cdots,x_{n}$ be real numbers. Show that
$$\sum_{i,j=1}^{n}|x_{i}+x_{j}|\ge n\sum_{i=1}^{n}|x_{i}|.$$
I think this problem may be solved using nice methods, but I can't find
them yet; I know this may be of use: $$|a|+|b|\ge |a+b|.$$ But I can't
make it work. Thank you everyone.