HMMT 2025 C7

Compute the number of ways to arrange 3 copies of each of the 26 lowercase letters of the English alphabet such that for any two distinct letters $x_{1}$ and $x_{2}$ , the number of $x_{2}$ 's between the first and second occurrences of $x_{1}$ equals the number of $x_{2}$ 's between the second and third occurrences of $x_{1}$ .