## Sunday, October 07, 2018

### Latin Squares for Constructing "Williams Designs" - Balanced for First-order Carry-over (Residual) Effects

Courtesy from the website http://statpages.info/latinsq.html, the list below contains the Williams design with 2 to 26 treatment groups. It is unlikely to have a clinical trial with 26 treatment groups. The most number of treatment groups I see is a study with 6 treatment groups.

In one of my previous posts, I described the Williams design and its usefulness in phase I or clinical pharmacology studies. In a SAS SUGI paper "Generating Randomization Schedules Using SAS Programming", I described how to use SAS program to construct the randomization schedule for a study with Williams design.

With the limited sample size, the Williams design is the most efficient design and minimizes the potential impact of the carryover effect. In Williams design with an even number of n treatment groups, there will be n number of sequences or an "n by n" square. Each treatment only occurs one time in one sequence, in one period. Furthermore, each treatment only follows another treatment one time.

If the number of treatments (n) is an odd number, there will be 2 x n number of sequences or two n by n squares. Each treatment only occurs once in one sequence and in two periods. Each treatment only follows another treatment twice.

With the Latin Square listed below, we can easily construct the crossover design with treatments, periods, and sequences. For example, a study design with 3 treatment groups will have the following assignments: three treatment groups (A, B, C), three periods (period 1, period 2, and period 3), and six sequences (ABC, BCA, CAB, CBA, ACB, and BAC).

 Treatment Sequence Period 1 Period 2 Period 3 1 A B C 2 B C A 3 C A B 4 C B A 5 A C B 6 B A C

• Since it is the crossover design, there should be a washout period between each period. It is very common that the washout period is 5 times the half-life.
• Randomization is for the sequence, not the treatment group.
• Once we know the number of subjects is needed for each sequence, we will know the total number of subjects for the entire study.
• Usually, the mixed model is needed for statistical analysis. The statistical model will need to consider the treatment, period, and sequence. An example of the SAS codes for analysis was provided in one of the previous posts "Cookbook SAS Codes for Bioequivalence Test in 2x2x2 Crossover Design"

### Williams Design by the Number of Treatment Groups:

```Size = 2

A B
B A

```
```Size = 3

A B C
B C A
C A B
C B A
A C B
B A C

Size = 4

A B D C
B C A D
C D B A
D A C B

Size = 5

A B E C D
B C A D E
C D B E A
D E C A B
E A D B C
D C E B A
E D A C B
A E B D C
B A C E D
C B D A E

Size = 6

A B F C E D
B C A D F E
C D B E A F
D E C F B A
E F D A C B
F A E B D C

Size = 7

A B G C F D E
B C A D G E F
C D B E A F G
D E C F B G A
E F D G C A B
F G E A D B C
G A F B E C D
E D F C G B A
F E G D A C B
G F A E B D C
A G B F C E D
B A C G D F E
C B D A E G F
D C E B F A G

Size = 8

A B H C G D F E
B C A D H E G F
C D B E A F H G
D E C F B G A H
E F D G C H B A
F G E H D A C B
G H F A E B D C
H A G B F C E D

Size = 9

A B I C H D G E F
B C A D I E H F G
C D B E A F I G H
D E C F B G A H I
E F D G C H B I A
F G E H D I C A B
G H F I E A D B C
H I G A F B E C D
I A H B G C F D E
F E G D H C I B A
G F H E I D A C B
H G I F A E B D C
I H A G B F C E D
A I B H C G D F E
B A C I D H E G F
C B D A E I F H G
D C E B F A G I H
E D F C G B H A I

Size = 10

A B J C I D H E G F
B C A D J E I F H G
C D B E A F J G I H
D E C F B G A H J I
E F D G C H B I A J
F G E H D I C J B A
G H F I E J D A C B
H I G J F A E B D C
I J H A G B F C E D
J A I B H C G D F E

Size = 11

A B K C J D I E H F G
B C A D K E J F I G H
C D B E A F K G J H I
D E C F B G A H K I J
E F D G C H B I A J K
F G E H D I C J B K A
G H F I E J D K C A B
H I G J F K E A D B C
I J H K G A F B E C D
J K I A H B G C F D E
K A J B I C H D G E F
G F H E I D J C K B A
H G I F J E K D A C B
I H J G K F A E B D C
J I K H A G B F C E D
K J A I B H C G D F E
A K B J C I D H E G F
B A C K D J E I F H G
C B D A E K F J G I H
D C E B F A G K H J I
E D F C G B H A I K J
F E G D H C I B J A K

```
```Size = 12

A B L C K D J E I F H G
B C A D L E K F J G I H
C D B E A F L G K H J I
D E C F B G A H L I K J
E F D G C H B I A J L K
F G E H D I C J B K A L
G H F I E J D K C L B A
H I G J F K E L D A C B
I J H K G L F A E B D C
J K I L H A G B F C E D
K L J A I B H C G D F E
L A K B J C I D H E G F

Size = 13

A B M C L D K E J F I G H
B C A D M E L F K G J H I
C D B E A F M G L H K I J
D E C F B G A H M I L J K
E F D G C H B I A J M K L
F G E H D I C J B K A L M
G H F I E J D K C L B M A
H I G J F K E L D M C A B
I J H K G L F M E A D B C
J K I L H M G A F B E C D
K L J M I A H B G C F D E
L M K A J B I C H D G E F
M A L B K C J D I E H F G
H G I F J E K D L C M B A
I H J G K F L E M D A C B
J I K H L G M F A E B D C
K J L I M H A G B F C E D
L K M J A I B H C G D F E
M L A K B J C I D H E G F
A M B L C K D J E I F H G
B A C M D L E K F J G I H
C B D A E M F L G K H J I
D C E B F A G M H L I K J
E D F C G B H A I M J L K
F E G D H C I B J A K M L
G F H E I D J C K B L A M

Size = 14

A B N C M D L E K F J G I H
B C A D N E M F L G K H J I
C D B E A F N G M H L I K J
D E C F B G A H N I M J L K
E F D G C H B I A J N K M L
F G E H D I C J B K A L N M
G H F I E J D K C L B M A N
H I G J F K E L D M C N B A
I J H K G L F M E N D A C B
J K I L H M G N F A E B D C
K L J M I N H A G B F C E D
L M K N J A I B H C G D F E
M N L A K B J C I D H E G F
N A M B L C K D J E I F H G

Size = 15

A B O C N D M E L F K G J H I
B C A D O E N F M G L H K I J
C D B E A F O G N H M I L J K
D E C F B G A H O I N J M K L
E F D G C H B I A J O K N L M
F G E H D I C J B K A L O M N
G H F I E J D K C L B M A N O
H I G J F K E L D M C N B O A
I J H K G L F M E N D O C A B
J K I L H M G N F O E A D B C
K L J M I N H O G A F B E C D
L M K N J O I A H B G C F D E
M N L O K A J B I C H D G E F
N O M A L B K C J D I E H F G
O A N B M C L D K E J F I G H
I H J G K F L E M D N C O B A
J I K H L G M F N E O D A C B
K J L I M H N G O F A E B D C
L K M J N I O H A G B F C E D
M L N K O J A I B H C G D F E
N M O L A K B J C I D H E G F
O N A M B L C K D J E I F H G
A O B N C M D L E K F J G I H
B A C O D N E M F L G K H J I
C B D A E O F N G M H L I K J
D C E B F A G O H N I M J L K
E D F C G B H A I O J N K M L
F E G D H C I B J A K O L N M
G F H E I D J C K B L A M O N
H G I F J E K D L C M B N A O

Size = 16

A B P C O D N E M F L G K H J I
B C A D P E O F N G M H L I K J
C D B E A F P G O H N I M J L K
D E C F B G A H P I O J N K M L
E F D G C H B I A J P K O L N M
F G E H D I C J B K A L P M O N
G H F I E J D K C L B M A N P O
H I G J F K E L D M C N B O A P
I J H K G L F M E N D O C P B A
J K I L H M G N F O E P D A C B
K L J M I N H O G P F A E B D C
L M K N J O I P H A G B F C E D
M N L O K P J A I B H C G D F E
N O M P L A K B J C I D H E G F
O P N A M B L C K D J E I F H G
P A O B N C M D L E K F J G I H

```
```Size = 17

A B Q C P D O E N F M G L H K I J
B C A D Q E P F O G N H M I L J K
C D B E A F Q G P H O I N J M K L
D E C F B G A H Q I P J O K N L M
E F D G C H B I A J Q K P L O M N
F G E H D I C J B K A L Q M P N O
G H F I E J D K C L B M A N Q O P
H I G J F K E L D M C N B O A P Q
I J H K G L F M E N D O C P B Q A
J K I L H M G N F O E P D Q C A B
K L J M I N H O G P F Q E A D B C
L M K N J O I P H Q G A F B E C D
M N L O K P J Q I A H B G C F D E
N O M P L Q K A J B I C H D G E F
O P N Q M A L B K C J D I E H F G
P Q O A N B M C L D K E J F I G H
Q A P B O C N D M E L F K G J H I
J I K H L G M F N E O D P C Q B A
K J L I M H N G O F P E Q D A C B
L K M J N I O H P G Q F A E B D C
M L N K O J P I Q H A G B F C E D
N M O L P K Q J A I B H C G D F E
O N P M Q L A K B J C I D H E G F
P O Q N A M B L C K D J E I F H G
Q P A O B N C M D L E K F J G I H
A Q B P C O D N E M F L G K H J I
B A C Q D P E O F N G M H L I K J
C B D A E Q F P G O H N I M J L K
D C E B F A G Q H P I O J N K M L
E D F C G B H A I Q J P K O L N M
F E G D H C I B J A K Q L P M O N
G F H E I D J C K B L A M Q N P O
H G I F J E K D L C M B N A O Q P
I H J G K F L E M D N C O B P A Q

Size = 18

A B R C Q D P E O F N G M H L I K J
B C A D R E Q F P G O H N I M J L K
C D B E A F R G Q H P I O J N K M L
D E C F B G A H R I Q J P K O L N M
E F D G C H B I A J R K Q L P M O N
F G E H D I C J B K A L R M Q N P O
G H F I E J D K C L B M A N R O Q P
H I G J F K E L D M C N B O A P R Q
I J H K G L F M E N D O C P B Q A R
J K I L H M G N F O E P D Q C R B A
K L J M I N H O G P F Q E R D A C B
L M K N J O I P H Q G R F A E B D C
M N L O K P J Q I R H A G B F C E D
N O M P L Q K R J A I B H C G D F E
O P N Q M R L A K B J C I D H E G F
P Q O R N A M B L C K D J E I F H G
Q R P A O B N C M D L E K F J G I H
R A Q B P C O D N E M F L G K H J I

Size = 19

A B S C R D Q E P F O G N H M I L J K
B C A D S E R F Q G P H O I N J M K L
C D B E A F S G R H Q I P J O K N L M
D E C F B G A H S I R J Q K P L O M N
E F D G C H B I A J S K R L Q M P N O
F G E H D I C J B K A L S M R N Q O P
G H F I E J D K C L B M A N S O R P Q
H I G J F K E L D M C N B O A P S Q R
I J H K G L F M E N D O C P B Q A R S
J K I L H M G N F O E P D Q C R B S A
K L J M I N H O G P F Q E R D S C A B
L M K N J O I P H Q G R F S E A D B C
M N L O K P J Q I R H S G A F B E C D
N O M P L Q K R J S I A H B G C F D E
O P N Q M R L S K A J B I C H D G E F
P Q O R N S M A L B K C J D I E H F G
Q R P S O A N B M C L D K E J F I G H
R S Q A P B O C N D M E L F K G J H I
S A R B Q C P D O E N F M G L H K I J
K J L I M H N G O F P E Q D R C S B A
L K M J N I O H P G Q F R E S D A C B
M L N K O J P I Q H R G S F A E B D C
N M O L P K Q J R I S H A G B F C E D
O N P M Q L R K S J A I B H C G D F E
P O Q N R M S L A K B J C I D H E G F
Q P R O S N A M B L C K D J E I F H G
R Q S P A O B N C M D L E K F J G I H
S R A Q B P C O D N E M F L G K H J I
A S B R C Q D P E O F N G M H L I K J
B A C S D R E Q F P G O H N I M J L K
C B D A E S F R G Q H P I O J N K M L
D C E B F A G S H R I Q J P K O L N M
E D F C G B H A I S J R K Q L P M O N
F E G D H C I B J A K S L R M Q N P O
G F H E I D J C K B L A M S N R O Q P
H G I F J E K D L C M B N A O S P R Q
I H J G K F L E M D N C O B P A Q S R
J I K H L G M F N E O D P C Q B R A S

Size = 20

A B T C S D R E Q F P G O H N I M J L K
B C A D T E S F R G Q H P I O J N K M L
C D B E A F T G S H R I Q J P K O L N M
D E C F B G A H T I S J R K Q L P M O N
E F D G C H B I A J T K S L R M Q N P O
F G E H D I C J B K A L T M S N R O Q P
G H F I E J D K C L B M A N T O S P R Q
H I G J F K E L D M C N B O A P T Q S R
I J H K G L F M E N D O C P B Q A R T S
J K I L H M G N F O E P D Q C R B S A T
K L J M I N H O G P F Q E R D S C T B A
L M K N J O I P H Q G R F S E T D A C B
M N L O K P J Q I R H S G T F A E B D C
N O M P L Q K R J S I T H A G B F C E D
O P N Q M R L S K T J A I B H C G D F E
P Q O R N S M T L A K B J C I D H E G F
Q R P S O T N A M B L C K D J E I F H G
R S Q T P A O B N C M D L E K F J G I H
S T R A Q B P C O D N E M F L G K H J I
T A S B R C Q D P E O F N G M H L I K J

Size = 21

A B U C T D S E R F Q G P H O I N J M K L
B C A D U E T F S G R H Q I P J O K N L M
C D B E A F U G T H S I R J Q K P L O M N
D E C F B G A H U I T J S K R L Q M P N O
E F D G C H B I A J U K T L S M R N Q O P
F G E H D I C J B K A L U M T N S O R P Q
G H F I E J D K C L B M A N U O T P S Q R
H I G J F K E L D M C N B O A P U Q T R S
I J H K G L F M E N D O C P B Q A R U S T
J K I L H M G N F O E P D Q C R B S A T U
K L J M I N H O G P F Q E R D S C T B U A
L M K N J O I P H Q G R F S E T D U C A B
M N L O K P J Q I R H S G T F U E A D B C
N O M P L Q K R J S I T H U G A F B E C D
O P N Q M R L S K T J U I A H B G C F D E
P Q O R N S M T L U K A J B I C H D G E F
Q R P S O T N U M A L B K C J D I E H F G
R S Q T P U O A N B M C L D K E J F I G H
S T R U Q A P B O C N D M E L F K G J H I
T U S A R B Q C P D O E N F M G L H K I J
U A T B S C R D Q E P F O G N H M I L J K
L K M J N I O H P G Q F R E S D T C U B A
M L N K O J P I Q H R G S F T E U D A C B
N M O L P K Q J R I S H T G U F A E B D C
O N P M Q L R K S J T I U H A G B F C E D
P O Q N R M S L T K U J A I B H C G D F E
Q P R O S N T M U L A K B J C I D H E G F
R Q S P T O U N A M B L C K D J E I F H G
S R T Q U P A O B N C M D L E K F J G I H
T S U R A Q B P C O D N E M F L G K H J I
U T A S B R C Q D P E O F N G M H L I K J
A U B T C S D R E Q F P G O H N I M J L K
B A C U D T E S F R G Q H P I O J N K M L
C B D A E U F T G S H R I Q J P K O L N M
D C E B F A G U H T I S J R K Q L P M O N
E D F C G B H A I U J T K S L R M Q N P O
F E G D H C I B J A K U L T M S N R O Q P
G F H E I D J C K B L A M U N T O S P R Q
H G I F J E K D L C M B N A O U P T Q S R
I H J G K F L E M D N C O B P A Q U R T S
J I K H L G M F N E O D P C Q B R A S U T
K J L I M H N G O F P E Q D R C S B T A U

Size = 22

A B V C U D T E S F R G Q H P I O J N K M L
B C A D V E U F T G S H R I Q J P K O L N M
C D B E A F V G U H T I S J R K Q L P M O N
D E C F B G A H V I U J T K S L R M Q N P O
E F D G C H B I A J V K U L T M S N R O Q P
F G E H D I C J B K A L V M U N T O S P R Q
G H F I E J D K C L B M A N V O U P T Q S R
H I G J F K E L D M C N B O A P V Q U R T S
I J H K G L F M E N D O C P B Q A R V S U T
J K I L H M G N F O E P D Q C R B S A T V U
K L J M I N H O G P F Q E R D S C T B U A V
L M K N J O I P H Q G R F S E T D U C V B A
M N L O K P J Q I R H S G T F U E V D A C B
N O M P L Q K R J S I T H U G V F A E B D C
O P N Q M R L S K T J U I V H A G B F C E D
P Q O R N S M T L U K V J A I B H C G D F E
Q R P S O T N U M V L A K B J C I D H E G F
R S Q T P U O V N A M B L C K D J E I F H G
S T R U Q V P A O B N C M D L E K F J G I H
T U S V R A Q B P C O D N E M F L G K H J I
U V T A S B R C Q D P E O F N G M H L I K J
V A U B T C S D R E Q F P G O H N I M J L K

Size = 23

A B W C V D U E T F S G R H Q I P J O K N L M
B C A D W E V F U G T H S I R J Q K P L O M N
C D B E A F W G V H U I T J S K R L Q M P N O
D E C F B G A H W I V J U K T L S M R N Q O P
E F D G C H B I A J W K V L U M T N S O R P Q
F G E H D I C J B K A L W M V N U O T P S Q R
G H F I E J D K C L B M A N W O V P U Q T R S
H I G J F K E L D M C N B O A P W Q V R U S T
I J H K G L F M E N D O C P B Q A R W S V T U
J K I L H M G N F O E P D Q C R B S A T W U V
K L J M I N H O G P F Q E R D S C T B U A V W
L M K N J O I P H Q G R F S E T D U C V B W A
M N L O K P J Q I R H S G T F U E V D W C A B
N O M P L Q K R J S I T H U G V F W E A D B C
O P N Q M R L S K T J U I V H W G A F B E C D
P Q O R N S M T L U K V J W I A H B G C F D E
Q R P S O T N U M V L W K A J B I C H D G E F
R S Q T P U O V N W M A L B K C J D I E H F G
S T R U Q V P W O A N B M C L D K E J F I G H
T U S V R W Q A P B O C N D M E L F K G J H I
U V T W S A R B Q C P D O E N F M G L H K I J
V W U A T B S C R D Q E P F O G N H M I L J K
W A V B U C T D S E R F Q G P H O I N J M K L
M L N K O J P I Q H R G S F T E U D V C W B A
N M O L P K Q J R I S H T G U F V E W D A C B
O N P M Q L R K S J T I U H V G W F A E B D C
P O Q N R M S L T K U J V I W H A G B F C E D
Q P R O S N T M U L V K W J A I B H C G D F E
R Q S P T O U N V M W L A K B J C I D H E G F
S R T Q U P V O W N A M B L C K D J E I F H G
T S U R V Q W P A O B N C M D L E K F J G I H
U T V S W R A Q B P C O D N E M F L G K H J I
V U W T A S B R C Q D P E O F N G M H L I K J
W V A U B T C S D R E Q F P G O H N I M J L K
A W B V C U D T E S F R G Q H P I O J N K M L
B A C W D V E U F T G S H R I Q J P K O L N M
C B D A E W F V G U H T I S J R K Q L P M O N
D C E B F A G W H V I U J T K S L R M Q N P O
E D F C G B H A I W J V K U L T M S N R O Q P
F E G D H C I B J A K W L V M U N T O S P R Q
G F H E I D J C K B L A M W N V O U P T Q S R
H G I F J E K D L C M B N A O W P V Q U R T S
I H J G K F L E M D N C O B P A Q W R V S U T
J I K H L G M F N E O D P C Q B R A S W T V U
K J L I M H N G O F P E Q D R C S B T A U W V
L K M J N I O H P G Q F R E S D T C U B V A W

Size = 24

A B X C W D V E U F T G S H R I Q J P K O L N M
B C A D X E W F V G U H T I S J R K Q L P M O N
C D B E A F X G W H V I U J T K S L R M Q N P O
D E C F B G A H X I W J V K U L T M S N R O Q P
E F D G C H B I A J X K W L V M U N T O S P R Q
F G E H D I C J B K A L X M W N V O U P T Q S R
G H F I E J D K C L B M A N X O W P V Q U R T S
H I G J F K E L D M C N B O A P X Q W R V S U T
I J H K G L F M E N D O C P B Q A R X S W T V U
J K I L H M G N F O E P D Q C R B S A T X U W V
K L J M I N H O G P F Q E R D S C T B U A V X W
L M K N J O I P H Q G R F S E T D U C V B W A X
M N L O K P J Q I R H S G T F U E V D W C X B A
N O M P L Q K R J S I T H U G V F W E X D A C B
O P N Q M R L S K T J U I V H W G X F A E B D C
P Q O R N S M T L U K V J W I X H A G B F C E D
Q R P S O T N U M V L W K X J A I B H C G D F E
R S Q T P U O V N W M X L A K B J C I D H E G F
S T R U Q V P W O X N A M B L C K D J E I F H G
T U S V R W Q X P A O B N C M D L E K F J G I H
U V T W S X R A Q B P C O D N E M F L G K H J I
V W U X T A S B R C Q D P E O F N G M H L I K J
W X V A U B T C S D R E Q F P G O H N I M J L K
X A W B V C U D T E S F R G Q H P I O J N K M L

Size = 25

A B Y C X D W E V F U G T H S I R J Q K P L O M N
B C A D Y E X F W G V H U I T J S K R L Q M P N O
C D B E A F Y G X H W I V J U K T L S M R N Q O P
D E C F B G A H Y I X J W K V L U M T N S O R P Q
E F D G C H B I A J Y K X L W M V N U O T P S Q R
F G E H D I C J B K A L Y M X N W O V P U Q T R S
G H F I E J D K C L B M A N Y O X P W Q V R U S T
H I G J F K E L D M C N B O A P Y Q X R W S V T U
I J H K G L F M E N D O C P B Q A R Y S X T W U V
J K I L H M G N F O E P D Q C R B S A T Y U X V W
K L J M I N H O G P F Q E R D S C T B U A V Y W X
L M K N J O I P H Q G R F S E T D U C V B W A X Y
M N L O K P J Q I R H S G T F U E V D W C X B Y A
N O M P L Q K R J S I T H U G V F W E X D Y C A B
O P N Q M R L S K T J U I V H W G X F Y E A D B C
P Q O R N S M T L U K V J W I X H Y G A F B E C D
Q R P S O T N U M V L W K X J Y I A H B G C F D E
R S Q T P U O V N W M X L Y K A J B I C H D G E F
S T R U Q V P W O X N Y M A L B K C J D I E H F G
T U S V R W Q X P Y O A N B M C L D K E J F I G H
U V T W S X R Y Q A P B O C N D M E L F K G J H I
V W U X T Y S A R B Q C P D O E N F M G L H K I J
W X V Y U A T B S C R D Q E P F O G N H M I L J K
X Y W A V B U C T D S E R F Q G P H O I N J M K L
Y A X B W C V D U E T F S G R H Q I P J O K N L M
N M O L P K Q J R I S H T G U F V E W D X C Y B A
O N P M Q L R K S J T I U H V G W F X E Y D A C B
P O Q N R M S L T K U J V I W H X G Y F A E B D C
Q P R O S N T M U L V K W J X I Y H A G B F C E D
R Q S P T O U N V M W L X K Y J A I B H C G D F E
S R T Q U P V O W N X M Y L A K B J C I D H E G F
T S U R V Q W P X O Y N A M B L C K D J E I F H G
U T V S W R X Q Y P A O B N C M D L E K F J G I H
V U W T X S Y R A Q B P C O D N E M F L G K H J I
W V X U Y T A S B R C Q D P E O F N G M H L I K J
X W Y V A U B T C S D R E Q F P G O H N I M J L K
Y X A W B V C U D T E S F R G Q H P I O J N K M L
A Y B X C W D V E U F T G S H R I Q J P K O L N M
B A C Y D X E W F V G U H T I S J R K Q L P M O N
C B D A E Y F X G W H V I U J T K S L R M Q N P O
D C E B F A G Y H X I W J V K U L T M S N R O Q P
E D F C G B H A I Y J X K W L V M U N T O S P R Q
F E G D H C I B J A K Y L X M W N V O U P T Q S R
G F H E I D J C K B L A M Y N X O W P V Q U R T S
H G I F J E K D L C M B N A O Y P X Q W R V S U T
I H J G K F L E M D N C O B P A Q Y R X S W T V U
J I K H L G M F N E O D P C Q B R A S Y T X U W V
K J L I M H N G O F P E Q D R C S B T A U Y V X W
L K M J N I O H P G Q F R E S D T C U B V A W Y X
M L N K O J P I Q H R G S F T E U D V C W B X A Y

Size = 26

A B Z C Y D X E W F V G U H T I S J R K Q L P M O N
B C A D Z E Y F X G W H V I U J T K S L R M Q N P O
C D B E A F Z G Y H X I W J V K U L T M S N R O Q P
D E C F B G A H Z I Y J X K W L V M U N T O S P R Q
E F D G C H B I A J Z K Y L X M W N V O U P T Q S R
F G E H D I C J B K A L Z M Y N X O W P V Q U R T S
G H F I E J D K C L B M A N Z O Y P X Q W R V S U T
H I G J F K E L D M C N B O A P Z Q Y R X S W T V U
I J H K G L F M E N D O C P B Q A R Z S Y T X U W V
J K I L H M G N F O E P D Q C R B S A T Z U Y V X W
K L J M I N H O G P F Q E R D S C T B U A V Z W Y X
L M K N J O I P H Q G R F S E T D U C V B W A X Z Y
M N L O K P J Q I R H S G T F U E V D W C X B Y A Z
N O M P L Q K R J S I T H U G V F W E X D Y C Z B A
O P N Q M R L S K T J U I V H W G X F Y E Z D A C B
P Q O R N S M T L U K V J W I X H Y G Z F A E B D C
Q R P S O T N U M V L W K X J Y I Z H A G B F C E D
R S Q T P U O V N W M X L Y K Z J A I B H C G D F E
S T R U Q V P W O X N Y M Z L A K B J C I D H E G F
T U S V R W Q X P Y O Z N A M B L C K D J E I F H G
U V T W S X R Y Q Z P A O B N C M D L E K F J G I H
V W U X T Y S Z R A Q B P C O D N E M F L G K H J I
W X V Y U Z T A S B R C Q D P E O F N G M H L I K J
X Y W Z V A U B T C S D R E Q F P G O H N I M J L K
Y Z X A W B V C U D T E S F R G Q H P I O J N K M L
Z A Y B X C W D V E U F T G S H R I Q J P K O L N M
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