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Honor And Glory
Version where all letters are distinct and not interchangeable.
This solution optimized for rectilinear moves.

######################################################################
Rectilinear Solution
Rectilinear steps: 56
Straight-Line steps: 74
Unit steps: 100
######################################################################

#0:
H O N Q R
\$   \$   \$
g l o r y

#1. Move O south:
H   N Q R
\$ O \$   \$
g l o r y

#2. Move N west:
H N   Q R
\$ O \$   \$
g l o r y

#3. Move Q south:
H N     R
\$ O \$ Q \$
g l o r y

#4. Move R west 2 units:
H N R
\$ O \$ Q \$
g l o r y

#5. Move Q on a path of 2 segments ending east:
H N R   Q
\$ O \$   \$
g l o r y

#6. Move r north 2 units:
H N R r Q
\$ O \$   \$
g l o   y

#7. Move o on a path of 2 segments ending north:
H N R r Q
\$ O \$ o \$
g l     y

#8. Move l east 2 units:
H N R r Q
\$ O \$ o \$
g     l y

#9. Move g east 2 units:
H N R r Q
\$ O \$ o \$
g l y

#10. Move O on a path of 2 segments ending west:
H N R r Q
\$   \$ o \$
O   g l y

#11. Move N south 2 units:
H   R r Q
\$   \$ o \$
O N g l y

#12. Move H on a path of 2 segments ending south:
R r Q
\$ H \$ o \$
O N g l y

#13. Move R west 2 units:
R     r Q
\$ H \$ o \$
O N g l y

#14. Move r west 2 units:
R r     Q
\$ H \$ o \$
O N g l y

#15. Move o on a path of 2 segments ending west:
R r o   Q
\$ H \$   \$
O N g l y

#16. Move l north 2 units:
R r o l Q
\$ H \$   \$
O N g   y

#17. Move g on a path of 2 segments ending north:
R r o l Q
\$ H \$ g \$
O N     y

#18. Move N east 2 units:
R r o l Q
\$ H \$ g \$
O     N y

#19. Move O east 2 units:
R r o l Q
\$ H \$ g \$
O N y

#20. Move H on a path of 2 segments ending west:
R r o l Q
\$   \$ g \$
H   O N y

#21. Move r south 2 units:
R   o l Q
\$   \$ g \$
H r O N y

#22. Move o on a path of 2 segments ending south:
R     l Q
\$ o \$ g \$
H r O N y

#23. Move l west 2 units:
R l     Q
\$ o \$ g \$
H r O N y

#24. Move Q west 2 units:
R l Q
\$ o \$ g \$
H r O N y

#25. Move g on a path of 2 segments ending east:
R l Q   g
\$ o \$   \$
H r O N y

#26. Move N north:
R l Q   g
\$ o \$ N \$
H r O   y

#27. Move O east:
R l Q   g
\$ o \$ N \$
H r   O y

#28. Move Q east:
R l   Q g
\$ o \$ N \$
H r   O y

#29. Move l east:
R   l Q g
\$ o \$ N \$
H r   O y

#30. Move r east:
R   l Q g
\$ o \$ N \$
H   r O y

#31. Move o south:
R   l Q g
\$   \$ N \$
H o r O y

#32. Move R on a path of 2 segments ending south:
l Q g
\$ R \$ N \$
H o r O y

#33. Move l west 2 units:
l     Q g
\$ R \$ N \$
H o r O y

#34. Move Q west 2 units:
l Q     g
\$ R \$ N \$
H o r O y

#35. Move N on a path of 2 segments ending west:
l Q N   g
\$ R \$   \$
H o r O y

#36. Move O north 2 units:
l Q N O g
\$ R \$   \$
H o r   y

#37. Move y on a path of 2 segments ending north:
l Q N O g
\$ R \$ y \$
H o r

#38. Move r east 2 units:
l Q N O g
\$ R \$ y \$
H o     r

#39. Move o east 2 units:
l Q N O g
\$ R \$ y \$
H     o r

#40. Move R on a path of 2 segments ending east:
l Q N O g
\$   \$ y \$
H   R o r

#41. Move Q south 2 units:
l   N O g
\$   \$ y \$
H Q R o r

#42. Move N on a path of 2 segments ending south:
l     O g
\$ N \$ y \$
H Q R o r

#43. Move O west 2 units:
l O     g
\$ N \$ y \$
H Q R o r

#44. Move g west 2 units:
l O g
\$ N \$ y \$
H Q R o r

#45. Move y on a path of 2 segments ending east:
l O g   y
\$ N \$   \$
H Q R o r

#46. Move o north 2 units:
l O g o y
\$ N \$   \$
H Q R   r

#47. Move r on a path of 2 segments ending north:
l O g o y
\$ N \$ r \$
H Q R

#48. Move R east 2 units:
l O g o y
\$ N \$ r \$
H Q     R

#49. Move Q east 2 units:
l O g o y
\$ N \$ r \$
H     Q R

#50. Move N on a path of 2 segments ending east:
l O g o y
\$   \$ r \$
H   N Q R

#51. Move O south 2 units:
l   g o y
\$   \$ r \$
H O N Q R

#52. Move l on a path of 2 segments ending south:
g o y
\$ l \$ r \$
H O N Q R

#53. Move g west 2 units:
g     o y
\$ l \$ r \$
H O N Q R

#54. Move l north:
g l   o y
\$   \$ r \$
H O N Q R

#55. Move o west:
g l o   y
\$   \$ r \$
H O N Q R

#56. Move r north:
g l o r y
\$   \$   \$
H O N Q R

```