Special Order I

Consider the sequence of characters A B C D, each character being taken twice.

It is possible to order this sequence in such a way that:
- There is 1 character between 2 As
- There are 2 characters between 2 Bs
- There are 3 characters between 2 Cs
- There are 4 characters between 2 Ds

$B\underset{2}{\underbrace{CD}}BA\underset{1}{\underbrace{C}}AD$
$BC\stackrel{3}{\overbrace{DBA}}CAD$
$BCD\stackrel{4}{\overbrace{BACA}}D$

Find the last such order in lexicographic order for the sequence ABCDEFGHIJKLMNOPQRSTUVWXYZ_ (each character is taken twice)


[My timing: < 1 sec]