a b a
a a
a A a : A xH -G,E2,B2
b a a
a a
a A b : B1 xB1 -A
b a a
a b
a A a : C1 xE1 -B1,C1,D
b a b
a a
a A a : D xG -E1,F,C2
a a a
b a
a A b : E1 xC1 -A
a a a
b b
a A a : F xF -B1,C1,D
a a b
b a
a A a : C2 xE2 -E1,F,C2
a a a
a a
b A b : G xD -A
a a a
a b
b A a : E2 xC2 -B1,C1,D
a a b
a a
b A a : B2 xB2 -E1,F,C2
a a a
a a
a B a : H xA -H
+---+===+---+---+
|C1 |AE2|C2 |AE2|
| |DE1| |DE1|
+---+---+---+===+
|AE2║AG ║AE2|AG |
|DE1║ ║DE1| |
+---+---+---+===+
|C2 |AE2|C1 |AE2|
| |DE1| |DE1|
+---+===+---+---+
║AE2|AG |AE2║AG ║
║DE1| |DE1║ ║
+---+===+---+---+
+---+---+---+---+
║AB2|DF |AB2║AG ║
║FB1| |FB1║ ║
+---+---+---+---+
|AB2║AG ║AB2|DF |
|FB1║ ║FB1| |
+---+---+---+---+
║AB2|DF |AB2║AG ║
║FB1| |FB1║ ║
+---+---+---+---+
|AB2║AG ║AB2|DF |
|FB1║ ║FB1| |
+---+---+---+---+
+---+---+---+---+
|DF |DF |DF |DF |
| | | | |
+---+---+---+---+
║AG ║AG ║AG ║AG ║
║ ║ ║ ║ ║
+---+---+---+---+
|DF |DF |DF |DF |
| | | | |
+---+---+---+---+
║AG ║AG ║AG ║AG ║
║ ║ ║ ║ ║
+---+---+---+---+
+---+===+---+---+
|R |R |L ║L |
| | | ║ |
+===+---+---+---+
|R |L ║L |R |
| | ║ | |
+---+---+---+===+
|L ║L |R |R |
| ║ | | |
+---+---+===+---+
║L |R |R |L ║
║ | | | ║
+---+===+---+---+
+---+---+---+---+
| ║ | ║ |
| ║ | ║ |
+---+---+---+---+
║ | ║ | ║
║ | ║ | ║
+---+---+---+---+
| ║ | ║ |
| ║ | ║ |
+---+---+---+---+
║ | ║ | ║
║ | ║ | ║
+---+---+---+---+
b b b
a a
a A a : A xF -D,B2
b a a
b b
a A b : B1 xB1 -A
b a b
b b
a A a : C xD -B1,C
a a a
b b
b A b : D xC -A
a a b
b b
b A a : B2 xB2 -B1,C
a b a
a a
a B a : E xE -F
a a a
a a
b B b : F xA -E
a b a
b a
a A b : A1 xE1 -C,A2
a b a
b b
a A a : B xG -D
a b a
a a
b A b : C xF -C,A2
a b a
a b
b A a : A2 xE2 -D
b a b
a a
b A b : D xD -A1,B
b a a
a b
a B a : E1 xA1 -E1,F
b a b
a a
a B a : F xC -G,E2
a a a
b b
a B a : G XB -E1,F
a a b
b a
a B a : E2 xA2 -G,E2
b c b
a a
a A a : A xP -L,J2,G2,C2
c b c
a a
a A a : B xN -J1,K,H2,D2
c a a
b b
a A c : C1 xC1 -A
c a a
b c
a A b : D1 xG1 -B
c a b
b c
a A a : E1 xJ1 -C1,D1,E1,F
c a c
b b
a A a : F xL -G1,H1,I,E2
b a a
c b
a A c : G1 xD1 -A
b a a
c c
a A b : H1 xH1 -B
b a b
c c
a A a : I xK -C1,D1,E1,F
b a c
c b
a A a : E2 xJ2 -G1,H1,I,E2
a a a
c b
b A c : J1 xE1 -A
a a a
c c
b A b : K xI -B
a a b
c c
b A a : H2 xH2 -C1,D1,E1,F
a a c
c b
b A a : D2 xG2 -G1,H1,I,E2
a a a
b b
c A c : L xF -A
a a a
b c
c A b : J2 xE2 -B
a a b
b c
c A a : G2 xD2 -C1,D1,E1,F
a a c
b b
c A a : C2 xC2 -G1,H1,I,E2
a c a
a a
a B a : M xO -N
a a a
a a
c B c : N xB -M
a b a
a a
a C a : O xM -P
a a a
a a
b C b : P xA -O
a c a
b a
a A b : A1 xM1 -H,C2
a c a
b b
a A a : B xO -I,F2
a b a
c a
a A c : C1 xJ1 -E,A2
a b a
c c
a A a : D xL -F1,G
a c a
a a
b A b : E xN -H,C2
a c a
a b
b A a : A2 xM2 -I,F2
c a b
a a
b A c : F1 xF1 -A1,B
c a c
a a
b A b : G xI -C1,D
a b a
a a
c A c : H xK -E,A2
a b a
a c
c A a : C2 xJ2 -F1,G
b a b
a a
c A c : I xG -A1,B
b a c
a a
c A b : F2 xF2 -C1,D
c a a
a c
a B a : J1 xC1 -J1,K
c a c
a a
a B a : K xH -L,J2
a a a
c c
a B a : L xD -J1,K
a a c
c a
a B a : J2 xC2 -L,J2
b a a
a b
a C a : M1 xA1 -M1,N
b a b
a a
a C a : N xE -O,M2
a a a
b b
a C a : O xB -M1,N
a a b
b a
a C a : M2 xA2 -O,M2
b c b
b b
a A a : A xL -E,C2
b b b
c c
a A a : B xI -C1,D
c a b
b b
b A c : C1 xC1 -A
c a c
b b
b A b : D xE -B
b a b
b b
c A c : E xD -A
b a c
b b
c A b : C2 xC2 -B
c b a
a a
a B c : F1 xF1 -H
c b c
a a
a B a : G xJ -I
a c a
a a
b B b : H xK -J,F2
a a a
c c
b B b : I xB -F1,G
a b a
a a
c B c : J xG -H
a b c
a a
c B a : F2 xF2 -I
b b b
a a
a C a : K xH -L
a a a
b b
b C b : L xA -K
b c b
a a
b A b : A xP -G,E2,B2
c b a
a b
b A c : B1 xI1 -A
c b a
a c
b A b : C1 xL1 -B1,C1,D
c b c
a a
b A b : D xN -E1,F,C2
a b a
c b
b A c : E1 xJ1 -A
a b a
c c
b A b : F xM -B1,C1,D
a b c
c a
b A b : C2 xL2 -E1,F,C2
a b a
b b
c A c : G xK -A
a b a
b c
c A b : E2 xJ2 -B1,C1,D
a b c
b a
c A b : B2 xI2 -E1,F,C2
a c a
b b
a B a : H xO -N,L2,I2
c a b
b a
a B c : I1 xB1 -H
c a b
b c
a B a : J1 xE1 -I1,J1,K
c a c
b b
a B a : K xG -L1,M,J2
b a b
c a
a B c : L1 xC1 -H
b a b
c c
a B a : M xF -I1,J1,K
b a c
c b
a B a : J2 xE2 -L1,M,J2
b a b
a a
c B c : N xD -H
b a b
a c
c B a : L2 xC2 -I1,J1,K
b a c
a b
c B a : I2 xB2 -L1,M,J2
a b a
b b
a C a : O xH -P
b a b
a a
b C b : P xA -O
c d c
b b
a A a : A xK -E,C2
c b c
d d
a A a : B xG -C1,D
d a b
c c
b A d : C1 xC1 -A
d a d
c c
b A b : D xE -B
b a b
c c
d A d : E xD -A
b a d
c c
d A b : C2 xC2 -B
d c d
a a
a B a : F xI -G
a a a
d d
c B c : G xB -F
a d a
a a
b C b : H xJ -I
a b a
a a
d C d : I xF -H
b c b
a a
a D a : J xH -K
a a a
b b
c D c : K xA -J
c d c
a a
b A b : A xL -E,C2
d c d
a a
b A b : B xJ -C1,D
a b a
d c
c A d : C1 xF1 -A
a b a
d d
c A c : D xH -B
a b a
c c
d A d : E xG -A
a b a
c d
d A c : C2 xF2 -B
d a c
c d
a B a : F1 xC1 -F1,G
d a d
c c
a B a : G xE -H,F2
c a c
d d
a B a : H xD -F1,G
c a d
d c
a B a : F2 xC2 -H,F2
a d a
b b
a C a : I xK -J
b a b
a a
d C d : J xB -I
a c a
b b
a D a : K xI -L
b a b
a a
c D c : L xA -K
a a b a a
a a A a a : A xL -K,I2,F2,B2
a b a a a
a a A b a : B1 xB1
a b a a a
a a A a b : C1 xF1 -B1,C1,D1,E
a b a a b
a a A a a : D1 xI1 -F1,G1,H,D2
a b a b a
a a A a a : E xK -I1,J,G2,C2
b a a a a
a a A b a : F1 xC1
b a a a a
a a A a b : G1 xG1 -B1,C1,D1,E
b a a a b
a a A a a : H xJ -F1,G1,H,D2
b a a b a
a a A a a : D2 xI2 -I1,J,G2,C2
a a a a a
b a A b a : I1 xD1
a a a a a
b a A a b : J xH -B1,C1,D1,E
a a a a b
b a A a a : G2 xG2 -F1,G1,H,D2
a a a b a
b a A a a : C2 xF2 -I1,J,G2,C2
a a a a a
a b A b a : K xE
a a a a a
a b A a b : I2 xD2 -B1,C1,D1,E
a a a a b
a b A a a : F2 xC2 -F1,G1,H,D2
a a a b a
a b A a a : B2 xB2 -I1,J,G2,C2
a a a a a
a a B a a : L xA -L
So there are theoretically 27 distinct configurations, although only some of them are possible; for example if you choose E2/C2 in second row, then you must have either E1/C1 or C2/E2 in third row.
wendy wrote:I'm still trying to figure out how Marek14's code work. At the moment, I am relying on Klitzing's piccies to get info.
a | a
--+--
a | b
a a b
b A a
a | a | b
--+---+--
b | A | a
a | a
--+--
a | B | A | b
--+---+---+--
a | A | A | a
--+--
a | b
Klitzing wrote:But again, as already stated above, there are some gaps to be filled in within some details - already in his outline of [a,a,a,a,b].
--- rk
Marek14 wrote:Klitzing wrote:But again, as already stated above, there are some gaps to be filled in within some details - already in his outline of [a,a,a,a,b].
--- rk
[...]
As for the disallowance you asked about (i.e. how to infer valid vertex sequences from the set of all possible sequences):
[...]
Now, let's select an invalid sequence:
[...]
We'll join it with the mirror image:
[...]
And now you can see the problem: You can't write the proper polygons.
If you start with AE2... then you can't continue.
[...]
a b b b a
a a A a a : A xI -G,E2,B2
b b a a a
a a A b b : B1 xB1 -A
b b a a b
a a A a b : C1 xE1 -B1,C1,D
b b a b b
a a A a a : D xG -E1,F,C2
b a a a a
b a A b b : E1 xC1 -A
b a a a b
b a A a b : F xF -B1,C1,D
b a a b b
b a A a a : C2 xE2 -E1,F,C2
a a a a a
b b A b b : G xD -A
a a a a b
b b A a b : E2 xC2 -B1,C1,D
a a a b b
b b A a a : B2 xB2 -E1,F,C2
a a b a a
a a B a a : H xH -I
a a a a a
a b B b a : I xA -H
b a b a a
a a A b a : A1 xG1 -E,A2
b a b a b
a a A a a : B xI -F,C2
a b a a b
b a A b a : C1 xC1 -A1,B
a b a b a
b a A a b : D xF -C1,D
a a b a a
a b A b a : E xH -E,A2
a a b a b
a b A a a : A2 xG2 -F,C2
b a a a b
a b A b a : F xD -A1,B
b a a b a
a b A a b : C2 xC2 -C1,D
a b a a a
a a B a b : G1 xA1 -G1,H
a b a b a
a a B a a : H xE -I,G2
a a a a a
b a B a b : I xB -G1,H
a a a b a
b a B a a : G2 xA2 -I,G2
+===+---+===+---+===+---+
| 1 ║ 2 ║ 1 | 3 | 1 ║ 2 ║
| ║ ║ | | ║ ║
+===+---+===+---+===+---+
║ 1 | 3 | 1 ║ 2 ║ 1 | 3 |
║ | | ║ ║ | |
+===+---+===+---+===+---+
| 1 ║ 2 ║ 1 | 3 | 1 ║ 2 ║
| ║ ║ | | ║ ║
+===+---+===+---+===+---+
║ 1 | 3 | 1 ║ 2 ║ 1 | 3 |
║ | | ║ ║ | |
+===+---+===+---+===+---+
| 1 ║ 2 ║ 1 | 3 | 1 ║ 2 ║
| ║ ║ | | ║ ║
+===+---+===+---+===+---+
║ 1 | 3 | 1 ║ 2 ║ 1 | 3 |
║ | | ║ ║ | |
+===+---+===+---+===+---+
+===+---+===+---+===+---+
║ 1 | 2 ║ 1 | 2 ║ 1 | 2 ║
║ | ║ | ║ | ║
+===+---+===+---+===+---+
| 1 ║ 2 | 1 ║ 2 | 1 ║ 2 |
| ║ | ║ | ║ |
+===+---+===+---+===+---+
║ 1 | 2 ║ 1 | 2 ║ 1 | 2 ║
║ | ║ | ║ | ║
+===+---+===+---+===+---+
| 1 ║ 2 | 1 ║ 2 | 1 ║ 2 |
| ║ | ║ | ║ |
+===+---+===+---+===+---+
║ 1 | 2 ║ 1 | 2 ║ 1 | 2 ║
║ | ║ | ║ | ║
+===+---+===+---+===+---+
| 1 ║ 2 | 1 ║ 2 | 1 ║ 2 |
| ║ | ║ | ║ |
+===+---+===+---+===+---+
+---+===+---+===+---+===+
║ | ║ | ║ | ║
║ | ║ | ║ | ║
+===+---+===+---+===+---+
| ║ | ║ | ║ |
| ║ | ║ | ║ |
+---+===+---+===+---+===+
║ | ║ | ║ | |
║ | ║ | ║ | |
+===+---+===+---+===+---+
| ║ | ║ | ║ |
| ║ | ║ | ║ |
+---+===+---+===+---+===+
║ | ║ | ║ | |
║ | ║ | ║ | |
+===+---+===+---+===+---+
| ║ | ║ | ║ |
| ║ | ║ | ║ |
+---+===+---+===+---+===+
+===+---+===+---+===+---+
| 1 | 2 ║ 3 ║ 2 | 1 | 2 ║
| | ║ ║ | | ║
+===+---+===+---+===+---+
║ 3 ║ 2 | 1 | 2 ║ 3 ║ 2 |
║ ║ | | ║ ║ |
+===+---+===+---+===+---+
| 1 | 2 ║ 3 ║ 2 | 1 | 2 ║
| | ║ ║ | | ║
+===+---+===+---+===+---+
║ 3 ║ 2 | 1 | 2 ║ 3 ║ 2 |
║ ║ | | ║ ║ |
+===+---+===+---+===+---+
| 1 | 2 ║ 3 ║ 2 | 1 | 2 ║
| | ║ ║ | | ║
+===+---+===+---+===+---+
║ 3 ║ 2 | 1 | 2 ║ 3 ║ 2 |
║ ║ | | ║ ║ |
+===+---+===+---+===+---+
+===+---+===+---+===+---+
║ 3 ║ 1 ║ 3 ║ 1 ║ 3 ║ 1 ║
║ ║ ║ ║ ║ ║ ║
+===+---+===+---+===+---+
| 1 | 2 | 1 | 2 | 1 | 2 |
| | | | | | |
+===+---+===+---+===+---+
║ 3 ║ 1 ║ 3 ║ 1 ║ 3 ║ 1 ║
║ ║ ║ ║ ║ ║ ║
+===+---+===+---+===+---+
| 1 | 2 | 1 | 2 | 1 | 2 |
| | | | | | |
+===+---+===+---+===+---+
║ 3 ║ 1 ║ 3 ║ 1 ║ 3 ║ 1 ║
║ ║ ║ ║ ║ ║ ║
+===+---+===+---+===+---+
| 1 | 2 | 1 | 2 | 1 | 2 |
| | | | | | |
+===+---+===+---+===+---+
b b b b b
a a A a a : A xH -D,B2
b b a a b
b a A b b : B1 xB1 -A
b b a b b
b a A a b : C xD -B1,C
b a a a b
b b A b b : D xC -A
b a a b b
b b A a b : B2 xB2 -B1,C
a b b a a
a a B b a : E1 xE1 -G,E2
a b b b a
a a B a a : F xG -H
a a b a a
a b B b a : G xF -G,E2
a a b b a
a b B a a : E2 xE2 -H
a a a a a
b b B b b : H xA -E1,F
a b b a a
b a A b b : A1 xP1 -H1,G2,I,C2
a b b a b
b a A a b : B1 xU1 -J1,K
a b b b a
b a A b a : C1 xX1 -L,E2,H2,A2
a b b b a
b a A a b : D x Z -M,J2
b a b a a
b a A b b : E1 xQ1 -H1,G2,I,C2
b a b a b
b a A a b : F xV -J1,K
b a b b a
b a A b a : G1 xW2 -L,E2,H2,A2
b a b b a
b a A a b : B2 xU2 -M,J2
a b b a a
a b A b b : H1 xR1 -H1,G2,I,C2
a b b a b
a b A a b : G2 xW1 -J1,K
a b b b a
a b A b a : I xY -L,E2,H2,A2
a b b b a
a b A a b : C2 xX2 -M,J2
b b a b a
a b A b b : J1 xJ1 -A1,B1,C1,D
b b a b b
a b A b a : K xM -E1,F,G1,B2
a a b a a
b b A b b : L xS -H1,G2,I,C2
a a b a b
b b A a b : E2 xQ2 -J1,K
a a b b a
b b A b a : H2 xR2 -L,E2,H2,A2
a a b b a
b b A a b : A2 xP2 -M,J2
a b a b a
b b A b b : M xK -A1,B1,C1,D
a b a b b
b b A b a : J2 xJ2 -E1,F,G1,B2
b a b a a
a a B a b : N1 xN1 -X1,W2,Y,R2
b a b a b
a a B a a : O xT -Z,U2,X2,P2
b b a a b
a a B b a : P1 xA1 -N1,O
b b a a b
a a B a b : Q1 xE1 -P1,Q1,R1,S
b b a b a
a a B b a : R1 xH1 -T,N2
b b a b b
a a B a a : S xL -U1/V/W1/Q2
a a b a a
b a B a b : T xO -X1,W2,Y,R2
a a b a b
b a B a a : N2 xN2 -Z,U2,X2,P2
b a a a b
b a B b a : U1 xB1 -N1,O
b a a a b
b a B a b : V xF -P1,Q1,R1,S
b a a b a
b a B b a : W1 xG2 -T,N2
b a a b b
b a B a a : Q2 xE2 -U1/V/W1/Q2
a b a a b
a b B b a : X1 xC1 -N1,O
a b a a b
a b B a b : W2 xG1 -P1,Q1,R1,S
a b a b a
a b B b a : Y xI -T,N2
a b a b b
a b B a a : R2 xH2 -U1/V/W1/Q2
b a a a b
a b B b a : Z xD -N1,O
b a a a b
a b B a b : U2 xB2 -P1,Q1,R1,S
b a a b a
a b B b a : X2 xC2 -T,N2
b a a b b
a b B a a : P2 xA2 -U1/V/W1/Q2
a b c b a
a a A a a : A xAa -W,U2,R2,N2,I2,C2
a c b c a
a a A a a : B xY -U1,V,S2,O2,J2,D2
b c a a a
a a A c b : C1 xC1 -A
b c a a a
a a A b c : D1 xI1 -B
b c a a b
a a A a c : E1 xN1 -C1,D1,E1,F1,G1,H
b c a a c
a a A a b : F1 xR1 -I1,J1,K1,L1,M,G2
b c a b c
a a A a a : G1 xU1 -N1,O1,P1,Q,L2,F2
b c a c b
a a A a a : H xW -R1,S1,T,P2,K2,E2
c b a a a
a a A c b : I1 xD1 -A
c b a a a
a a A b c : J1/J1 -B
c b a a b
a a A a c : K1 xO1 -C1,D1,E1,F1,G1,H
c b a a c
a a A a b : L1 xS1 -I1,J1,K1,L1,M,G2
c b a b c
a a A a a : M xV -N1,O1,P1,Q,L2,F2
c b a c b
a a A a a : G2 xU2 -R1,S1,T,P2,K2,E2
c a a a a
b a A c b : N1 xE1 -A
c a a a a
b a A b c : O1 xK1 -B
c a a a b
b a A a c : P1 xP1 -C1,D1,E1,F1,G1,H
c a a a c
b a A a b : Q xT -I1,J1,K1,L1,M,G2
c a a b c
b a A a a : L2 xS2 -N1,O1,P1,Q,L2,F2
c a a c b
b a A a a : F2 xR2 -R1,S1,T,P2,K2,E2
b a a a a
c a A c b : R1 xF1 -A
b a a a a
c a A b c : S1 xL1 -B
b a a a b
c a A a c : T xQ -C1,D1,E1,F1,G1,H
b a a a c
c a A a b : P2 xP2 -I1,J1,K1,L1,M,G2
b a a b c
c a A a a : K2 xO2 -N1,O1,P1,Q,L2,F2
b a a c b
c a A a a : E2 xN2 -R1,S1,T,P2,K2,E2
a a a a a
c b A c b : U1 xG1 -A
a a a a a
c b A b c : V xM -B
a a a a b
c b A a c : S2 xL2 -C1,D1,E1,F1,G1,H
a a a a c
c b A a b : O2 xK2 -I1,J1,K1,L1,M,G2
a a a b c
c b A a a : J2 xJ2 -N1,O1,P1,Q,L2,F2
a a a c b
c b A a a : D2 xI2 -R1,S1,T,P2,K2,E2
a a a a a
b c A c b : W xH -A
a a a a a
b c A b c : U2 xG2 -B
a a a a b
b c A a c : R2 xF2 -C1,D1,E1,F1,G1,H
a a a a c
b c A a b : N2 xE2 -I1,J1,K1,L1,M,G2
a a a b c
b c A a a : I2 xD2 -N1,O1,P1,Q,L2,F2
a a a c b
b c A a a : C2 xC2 -R1,S1,T,P2,K2,E2
a a c a a
a a B a a : X xZ -Y
a a a a a
a c B c a : Y xB -X
a a b a a
a a C a a : Z xX -Aa
a a a a a
a b C b a : Aa xA -Z
b a c a a
a a A b a : A1 xT1 -O,C2
b a c a b
a a A a a : B xV -P,M2,I2,E2
c a b a a
a a A c a : C1 xQ1 -L,A2
c a b a c
a a A a a : D xS -M1,N,J2,F2
a c a a b
b a A c a : E1 xE1 -A1,B
a c a a c
b a A b a : F1 xI1 -C1,D
a c a b a
b a A a c : G1 xM1 -E1,F1,G1,H
a c a c a
b a A a b : H xP -I1,J1,K,G2
a b a a b
c a A c a : I1 xF1 -A1,B
a b a a c
c a A b a : J1 xJ1 -C1,D
a b a b a
c a A a c : K xN -E1,F1,G1,H
a b a c a
c a A a b : G2 xM2 -I1,J1,K,G2
a a c a a
a b A b a : L xU -O,C2
a a c a b
a b A a a : A2 xT2 -P,M2,I2,E2
c a a a b
a b A c a : M1 xG1 -A1,B
c a a a c
a b A b a : N xK -C1,D
c a a b a
a b A a c : J2 xJ2 -E1,F1,G1,H
c a a c a
a b A a b : F2 xI2 -I1,J1,K,G2
a a b a a
a c A c a : O xR -L,A2
a a b a c
a c A a a : C2 xQ2 -M1,N,J2,F2
b a a a b
a c A c a : P xH -A1,B
b a a a c
a c A b a : M2 xG2 -C1,D
b a a b a
a c A a c : I2 xF2 -E1,F1,G1,H
b a a c a
a c A a b : E2 xE2 -I1,J1,K,G2
a c a a a
a a B a c : Q1 xC1 -Q1,R
a c a c a
a a B a a : R xO -S,Q2
a a a a a
c a B a c : S xD -Q1,R
a a a c a
c a B a a : Q2 xC2 -S,Q2
a b a a a
a a C a b : T1 xA1 -T1,U
a b a b a
a a C a a : U xL -V,T2
a a a a a
b a C a b : V xB -T1,U
a a a b a
b a C a a : T2 xA2 -V,T2
a a c a a
b a A a b : A xG -E,C2
a a b a a
c a A a c : B xF -C1,D
a c a b a
a b A c a : C1 xC1 -A
a c a c a
a b A b a : D xE -B
a b a b a
a c A c a : E xD -A
a b a c a
a c A b a : C2 xC2 -B
c a a a c
a a B a a : F xB -F
b a a a b
a a C a a : G xA -G
b b c b b
a a A a a : A xS -L,J2,G2,C2
c b b b c
a a A a a : B xP -J1,K,H2,D2
b c a a b
b a A c b : C1 xC1 -A
b c a a c
b a A b b : D1 xG1 -B
b c a b b
b a A a c : E1 xJ1 -C1,D1,E1,F
b c a c b
b a A a b : F xL -G1,H1,I,E2
b b a a b
c a A c b : G1 xD1 -A
b b a a c
c a A b b : H1 xH1 -B
b b a b b
c a A a c : I xK -C1,D1,E1,F
b b a c b
c a A a b : E2 xJ2 -G1,H1,I,E2
c a a a b
b b A c b : J1 xE1 -A
c a a a c
b b A b b : K xI -B
c a a b b
b b A a c : H2 xH2 -C1,D1,E1,F
c a a c b
b b A a b : D2 xG2 -G1,H1,I,E2
b a a a b
b c A c b : L xF -A
b a a a c
b c A b b : J2 xE2 -B
b a a b b
b c A a c : G2 xD2 -C1,D1,E1,F
b a a c b
b c A a b : C2 xC2 -G1,H1,I,E2
a c b a a
a a B c a : M1 xM1 -O
a c b c a
a a B a a : N xQ -P
a a c a a
a b B b a : O xR -Q,M2
a a a a a
c b B b c : P xB -M1,N
a a b a a
a c B c a : Q xN -O
a a b c a
a c B a a : M2 xM2 -P
a b b b a
a a C a a : R xO -S
a a a a a
b b C b b : S xA -R
b c b c b
a a A a a : A xF -D,B2
c b a a b
b a A b c : B1 xB1 -A
c b a b c
b a A a b : C xD -B1,C
b a a a b
c b A b c : D xC -A
b a a b c
c b A a b : B2 xB2 -B1,C
a b c b a
a a B a a : E xG -F
a a a a a
b c B c b : F xA -E
a a b a a
a b C b a : G xE -G
b a c a a
b a A b b : A1 xP1 -H,C2
b a c a b
b a A a b : B xR -I,F2
a b b b a
c a A c a : C1 xM1 -E,A2
a b b b a
c a A a c : D xO -F1,G
a a c a a
b b A b b : E xQ -H,C2
a a c a b
b b A a b : A2 xP2 -I,F2
a c a b b
b b A c a : F1 xF1 -A1,B
a c a c a
b b A b b : G xI -C1,D
a b b b a
a c A c a : H xN -E,A2
a b b b a
a c A a c : C2 xM2 -F1,G
b b a b b
a c A c a : I xG -A1,B
b b a c a
a c A b b : F2 xF2 -C1,D
c a b a a
a a B a c : J1 xJ1 -M1,N
c a b a c
a a B a a : K xL -O,M2
a a b a a
c a B a c : L xK -M1,N
a a b a c
c a B a a : J2 xJ2 -O,M2
a c a a c
a b B b a : M1 xC1 -J1,K
a c a c a
a b B b a : N xH -L,J2
c a a a c
a b B b a : O xD -J1,K
c a a c a
a b B b a : M2 xC2 -L,J2
b b a a b
a a C a b : P1 xA1 -P1,Q
b b a b b
a a C a a : Q xE -R,P2
b a a a b
b a C a b : R xB -P1,Q
b a a b b
b a C a a : P2 xA2 -R,P2
a c b a a
b a A c b : A1 xL1 -F
a c b a c
b a A a b : B1 xO1 -G1,H
a c b c a
b a A a b : C xQ -I,G2
c a b a a
b a A c b : D1 xM1 -F
c a b a c
b a A a b : E xP -G1,H
c a b c a
b a A a b : B2 xO2 -I,G2
a b c b a
a b A b a : F xS -J,D2,A2
c b a b a
a b A b c : G1 xG1 -A1,B1,C
c b a b c
a b A b a : H xI -D1,E,B2
a b a b a
c b A b c : I xH -A1,B1,C
a b a b c
c b A b a : G2 xG2 -D1,E,B2
a a b a a
b c A c b : J xN -F
a a b a c
b c A a b : D2 xM2 -G1,H
a a b c a
b c A a b : A2 xL2 -I,G2
b a c a b
a a B a a : K xR -Q,O2,L2
b c a a b
a a B c a : L1 xA1 -K
b c a a b
a a B a c : M1 xD1 -L1,M1,N
b c a c b
a a B a a : N xJ -O1,P,M2
b a a a b
c a B c a : O1 xB1 -K
b a a a b
c a B a c : P xE -L1,M1,N
b a a c b
c a B a a : M2 xD2 -O1,P,M2
b a a a b
a c B c a : Q xC -K
b a a a b
a c B a c : O2 xB2 -L1,M1,N
b a a c b
a c B a a : L2 xA2 -O1,P,M2
a a b a a
b a C a b : R xK -S
a b a b a
a b C b a : S xF -R
a b c b a
b a A a b : A xS -J,G2
b a b a a
c a A b c : B1 xK1 -E1,D2,F
b a b a b
c a A a c : C xO -G1,H
b a b c a
c a A b a : D1 xP2 -I,B2,E2
a c b a a
a b A b c : E1 xL1 -E1,D2,F
a c b a b
a b A a c : D2 xP1 -G1,H
a c b c a
a b A b a : F xQ -I,B2,E2
b c a b a
a b A c b : G1 xG1 -A
b c a c b
a b A b a : H xJ -B1,C,D1
a a b a a
c b A b c : I xM -E1,D2,F
a a b a b
c b A a c : B2 xK2 -G1,H
a a b c a
c b A b a : E2 xL2 -I,B2,E2
a b a b a
b c A c b : J xH -A
a b a c b
b c A b a : G2 xG2 -B1,C,D1
c b a a c
a a B a b : K1 xB1 -K1,L1,M
c b a b a
a a B c a : L1 xE1 -N
c b a b c
a a B a a : M xI -O,P1,K2
a a c a a
b a B a b : N xR -P2,Q,L2
c a a a c
b a B a b : O xC -K1,L1,M
c a a b a
b a B c a : P1 xD2 -N
c a a b c
b a B a a : K2 xB2 -O,P1,K2
a b a a c
a c B a b : P2 xD1 -K1,L1,M
a b a b a
a c B c a : Q xF -N
a b a b c
a c B a a : L2 xE2 -O,P1,K2
b a b a b
a a C a a : R xN -S
b a a a b
a b C b a : S xA -R
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