# Weird sum

Algebra Level 4

Let $f (a, b, c)=\frac {1}{1+a+ab+abc}$ If $$w, x, y, z$$ are real numbers such that $$wxyz=1$$, let $$M$$ and $$m$$ be the maximum and minimum values of $f (w, x, y)+f (x, y, z)+f (y, z, w)+f (z, w, x)$ respectively. Find $$M-m$$.

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