GAIC Math 2024 Problem 138

let $a_{1}, a_{2}, \cdots, a_{9}$ be a permutation of $1,2, \cdots, 9$. If the permutation $C=\left(a_{1}, a_{2}, \cdots, a_{9}\right)$ can be obtained from $1,2, \cdots, 9$, by swapping two elements at most 4 times, the total number of permutations satisfying this condition is _____.