Putnam 2005 B4

For positive integers $m$ and $n$, let $f(m,n)$ denote the number of $n$-tuples $(x_1,x_2,\dots,x_n)$ of integers such that $|x_1| + |x_2| + \cdots + |x_n| \leq m$. Show that $f(m,n) = f(n,m)$.