Problem 2

Let $A=\{1,2,\ldots,n\}$ and $C$ is the set of all bijective function from $A$ to itself. Define the function $T:C\rightarrow \mathbb{R}$ as follow: for all $f\in C$, $T(f)$ be the number of pair $(x,y)\in A\times A$ such that $f(x)>f(y)$ whenever $x<y$. Evaluate the following summation!
$$\sum\limits_{f\in C}\prod\limits_{x=1}^n (-1)^{T(f)}x^{f(x)}$$