Question 99
We denote $S = \{1, 2, \dots, 3000\}$. Find the maximum possible value of an integer $X$ that satisfies the following condition:
For any bijection $f: S \to S$, there exists a bijection $g: S \to S$ such that
$$
\sum_{k=1}^{3000} \left( \max\{f(f(k)), f(g(k)), g(f(k)), g(g(k))\} - \min\{f(f(k)), f(g(k)), g(f(k)), g(g(k))\} \right)
$$
is no less than $X$.
For any bijection $f: S \to S$, there exists a bijection $g: S \to S$ such that
$$
\sum_{k=1}^{3000} \left( \max\{f(f(k)), f(g(k)), g(f(k)), g(g(k))\} - \min\{f(f(k)), f(g(k)), g(f(k)), g(g(k))\} \right)
$$
is no less than $X$.