6,6,6,6,6 = T5   = all possible ways to fill first 5 locations
6,1,1,6,6 = B1,5 = ways to violate C1
6,5,1,1,6 = B2,5 = ways to violate C2 (but not C1)
            B3,5 = ways to violate C3 (not C1 nor C2)
6,5,5,1,1 + A,B,C,C,C (maybe C = A)
6,1,5,1,1 + A,A,B,B,B
            B4,5 = ways to maybe violate only C4
6,1,5,5,1 + A,A,B,C,C (maybe A=C)
6,5,1,5,1 + A,B,B,C,C (maybe A=C)
6,5,5,5,1 + A,B,C,D,D (maybe A=C, A=D, or B=D)
            B0,5 = T5 - B(1..4),5
6,5,5,1,5 + A,B,C,C,D (A!=B && B!=C && C!=D)
6,1,5,1,5 + A,A,B,B,C
6,1,5,5,5 + A,A,B,C,D
6,5,1,5,5 + A,B,B,C,D
6,5,5,5,5 + A,B,C,D,E