#SWI-Prolog, 136 bytes
a:-(R=0;R=1),between(1,26,I),(I=1,R=0;I\=1,nl),between(1,26,J),(R=0,L=I;R=1,L is 27-I),(J=L,K is J+64,put(K);J\=L,K is J+96,put(K)),\+!.
Abusing backtracking to loop...
Fatalize
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