Para cualquier permutación $ f : \{ 1, 2, \cdots , n \} \to \{1, 2, \cdots , n \} $ , define \[ A = \{ i | i > f(i) \} \] \[ B = \{ (i, j) | i<j \le f(j) < f(i) \ or \ f(j) < f(i) < i < j \} \] \[ C = \{ (i, j) | i<j \le f(i) < f(j) \ or \ f(i) < f(j) < i < j \} \] \[ D = \{ (i, j) | i< j \ and \ f(i) > f(j)\} \] Demuestra que $ |A| + 2|B| + |C| = |D| $ .