Sorting by Full directory path

I have a text file with full list of files with their full path. I wanted to sort it by directory then files then subdirectory by alphabetically. When I used the sort command it doesn't give like what I want. Could somebody help me on this.
Here is the ex:
This is what I'm getting

parent/childDir
parent/childDir/A_subdir
parent/childDir/A_subdir/A_File.txt
parent/childDir/A_subdir/AF_File.txt
parent/childDir/A_subdir/AF2_File.txt
parent/childDir/A_subdir/B_File.txt
parent/childDir/A_subdir/E_File.txt
parent/childDir/A_subdir/L_File.txt
parent/childDir/A_subdir/P_File.txt
parent/childDir/A_subdir/T_File.txt
parent/childDir/A_subdir/a_File.txt
parent/childDir/A_subdir/a_v_File.txt
parent/childDir/A_subdir/al_File.txt
parent/childDir/A_subdir/au_File.txt
parent/childDir/A_subdir/B_subdir
parent/childDir/A_subdir/B_subdir/M_File
parent/childDir/A_subdir/B_subdir/a_File.txt
parent/childDir/A_subdir/B_subdir/c_File.txt
parent/childDir/A_subdir/B_subdir/v_File.txt
parent/childDir/A_subdir/c_File.txt
parent/childDir/A_subdir/d_File.txt
parent/childDir/A_subdir/f_File.txt
 

but I wanted like this

parent/childDir
parent/childDir/A_subdir
parent/childDir/A_subdir/A_File.txt
parent/childDir/A_subdir/ab_File.txt
parent/childDir/A_subdir/AF_File.txt
parent/childDir/A_subdir/AF2_File.txt
parent/childDir/A_subdir/al_File.txt
parent/childDir/A_subdir/au_File.txt
parent/childDir/A_subdir/a_v_File.txt
parent/childDir/A_subdir/B_File.txt
parent/childDir/A_subdir/c_File.txt
parent/childDir/A_subdir/d_File.txt
parent/childDir/A_subdir/E_File.txt
parent/childDir/A_subdir/f_File.txt
parent/childDir/A_subdir/L_File.txt
parent/childDir/A_subdir/P_File.txt
parent/childDir/A_subdir/T_File.txt
parent/childDir/A_subdir/B_subdir
parent/childDir/A_subdir/B_subdir/a_File.txt
parent/childDir/A_subdir/B_subdir/c_File.txt
parent/childDir/A_subdir/B_subdir/M_File
parent/childDir/A_subdir/B_subdir/v_File.txt

Thanks

please ignore.

Assuming your desired output is a bit different:

LC_COLLATE=en_US sort infile