Board size: 6x6
Board: BCooooBCoooDoCoooDooAAoDoEEEoooooFFF
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: BooCCCBAADooEEEDFFGHHoIoGoJJIKGLLLIK
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv1,A>3
</answer>


Board size: 6x6
Board: oAABoooooBooCoooooCoDoooooDooooEEEoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>3
</answer>


Board size: 6x6
Board: BBBCCCAAooDoEEEoDoFFFGDHoooGoHoIIGoH
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv1,A>4
</answer>


Board size: 6x6
Board: oooAABCCoooBDooooBDEooooDEooFFoEoooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>1
</answer>


Board size: 6x6
Board: BoooCoBoooCooAAoCooooDoEoooDoEoooDoE
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv3,A>3
</answer>


Board size: 6x6
Board: BCooooBCooDoooooDooAAooEoooooEFFoooE
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^3,A>3
</answer>


Board size: 6x6
Board: oooooooBoooooBoooooBoooCDooooCDooAAC
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,A>1
</answer>


Board size: 6x6
Board: AABoooCoBDooCooDooooooooooEEEooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>4
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: BAAoCoBDDDCoooEoCoooEooooooFFFoooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,A>3
</answer>


Board size: 6x6
Board: ooBBBooooooooooooooAAoCoooooCoooDDDo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^2,A>3
</answer>


Board size: 6x6
Board: oooooooooooBooAAoBCCCDDoEEEooooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^1,A>2
</answer>


Board size: 6x6
Board: ooooooooBBBoooooooCoooDoCEooDFCEoAAF
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F^1,A>1
</answer>


Board size: 6x6
Board: AAoooBoooooBoooooBooooCoDDDoCoooooEE
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: ooBoooAABoooooBooooooooooooCCooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,A>4
</answer>


Board size: 6x6
Board: oooooooAAooBoCoooBoCDooBooDoooooEEoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>3
</answer>


Board size: 6x6
Board: AAooBoooooBoCCoooooDDDoooooooooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: oAAoBoCCDEBFGoDEoFGoDEHFoIIIHooJJoHo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: ooBBBooooooooooooooooAACooDDDCoEEEoC
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^3,A>1
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: ooooooooooBoooooBooAAoBoooooooCCCoDD
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^1,A>3
</answer>


Board size: 6x6
Board: oooooooBoooooBoAACooDDoCoooooCoooEEo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,A>1
</answer>


Board size: 6x6
Board: oooBBBoAAooCDDoooCoooooooooooooEEooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,A>3
</answer>


Board size: 6x6
Board: oooooooooooooooooooBooooCBooDoCBAADo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,A>2
</answer>


Board size: 6x6
Board: oBBBooooCoooAACooooooDEEoooDFoGGGDFo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv2,A>4
</answer>


Board size: 6x6
Board: oooBBBoooooCoooAACooooooooDoooooDooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv2,A>1
</answer>


Board size: 6x6
Board: BCCCDoBoooDoEEEoDoAAoFooGGGFHHoIIoJJ
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F^2,A>4
</answer>


Board size: 6x6
Board: oooAABoCCCoBoDDEEBoFFGooHoIGJJHoIKKK
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>1
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: oooooBooAAoBCoooooCooDDooooooEoooooE
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,A>2
</answer>


Board size: 6x6
Board: oooooooBBBooooooCoooooCoDooooEDAAooE
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^1,A>3
</answer>


Board size: 6x6
Board: ooAAoBoCCCoBooDDDoEoooFFEGGoHHEoIIIo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>2
</answer>


Board size: 6x6
Board: AAoBoooooBoCoooBoCoDDoECooooEoooooEo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>4
</answer>


Board size: 6x6
Board: oooooooooooBooAAoBooCDoEooCDFEooCoFE
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^1,A>2
</answer>


Board size: 6x6
Board: oBoooCoBDDDCoooAAEoooooEooooooFFFGGo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Ev1,A>1
</answer>


Board size: 6x6
Board: BoooooBoooooBoooCoooooCoAADoooooDEEE
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^2,A>4
</answer>


Board size: 6x6
Board: oBBBoooooooCoAAooCooDDDCoooooooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv2,A>3
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: BoooooBoooooBoooooooooCoDDDoCoooAACo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,A>2
</answer>


Board size: 6x6
Board: oooooBAAoooBooCCCooooooooDDooooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,A>4
</answer>


Board size: 6x6
Board: ooBBBooooooCAAoooCoooooCooooDoooooDo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv2,A>4
</answer>


Board size: 6x6
Board: oooooBoAAooBoooooBooCCCoooooooDDoooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,A>3
</answer>


Board size: 6x6
Board: oooooooooooBooCAABooCooBDoCoooDEEooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,A>1
</answer>


Board size: 6x6
Board: ooooooooooooooooooooBooCDoBooCDAAooC
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,A>3
</answer>


Board size: 6x6
Board: oBoooooBooooooooooCoAADoCoooDoEEEoDo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^3,A>2
</answer>


Board size: 6x6
Board: oooooooAAooBoooooBoooooooCoooooCDDoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>3
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: ooBBBooCoooooCoooDoCoooDAAoooDoooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,A>4
</answer>


Board size: 6x6
Board: oooooooooooooooAABoCCCoBoooooBoooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>1
</answer>


Board size: 6x6
Board: AABoooooBCCCooBDDDoEooFGHEooFGHEoooG
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>4
</answer>


Board size: 6x6
Board: oBBBoooooCooAAoCoooooCoooDDooooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv2,A>4
</answer>


Board size: 6x6
Board: oAAoBooCCCBooooooooDDoEEooooFFoooGGG
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: ooooBoooooBoAACoooooCoooooDDDooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^2,A>4
</answer>


Board size: 6x6
Board: ooooooBCooDoBCooDEoCoAAEooooooFFFooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^1,A>1
</answer>


Board size: 6x6
Board: ooooBoCDDDBECoAAoECooFGEoHHFGooIIFGo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Ev2,A>2
</answer>


Board size: 6x6
Board: oooBBBCoAAoDCooEEDCooFFDoGGGHoooooHo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv1,A>2
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: AAoooBoCCCDBEEFFDooGHoDooGHIJJoGHIoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: BBBooCoAAooCooDDDCooEoooFoEGooFoEGoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv2,A>3
</answer>


Board size: 6x6
Board: oooooBooCCCBooooooDoooooDooAAEDFFooE
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^2,A>1
</answer>


Board size: 6x6
Board: BoooooBooooCoooooCoAAooCooooDooEEoDo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,A>3
</answer>


Board size: 6x6
Board: oooooooooBooCooBooCooAADCooooDoEEooD
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^3,A>1
</answer>


Board size: 6x6
Board: BoooooBoCoooooCoooAACooooDDDoooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,A>4
</answer>


Board size: 6x6
Board: ooAABoooooBooooCBooDoCoooDoooooDoooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>2
</answer>


Board size: 6x6
Board: oooBoooooBooooAACoooooCoooooooDDoooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^2,A>2
</answer>


Board size: 6x6
Board: BoooooBoAACoooooCoDEooCFDEGooFDoGoHH
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,A>2
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: oAABoooooBooooooooooCCCoooooDoooEEDo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>3
</answer>


Board size: 6x6
Board: oBAACooBooCoooooooooooooDoooooDooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: BBBCCCAAooDoooooDoooooDoEEoooooFFFoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv1,A>4
</answer>


Board size: 6x6
Board: oBoooooBCCCDoBoooDoooAADoEooFFoEoGGo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,A>1
</answer>


Board size: 6x6
Board: oooAABCCCooBoooooooDDDooEoooooEooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>1
</answer>


Board size: 6x6
Board: oooBBBoCCCooDEooooDEooooDEAAFoooooFo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F^2,A>2
</answer>


Board size: 6x6
Board: oooooooooooooBoooooBAAoCoBoDoCoooDoC
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^3,A>2
</answer>


Board size: 6x6
Board: oAAoBoooooBoooooBoooooooCCoooooooDDo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: oooooooooooooooBBBAAoooCoooooCooDDoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,A>4
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: oBoCCCoBoooooBoooDooAAoDoooEEEoooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,A>2
</answer>


Board size: 6x6
Board: oBBBoCoDAAoCoDEEECoDoFFoGoHIIoGoHoJJ
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv2,A>2
</answer>


Board size: 6x6
Board: oooooooooAABCooDoBCoEDooooEDoooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: BBBooCAAoooCoDDDoCooooEooooFEooGGFEo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv2,A>4
</answer>


Board size: 6x6
Board: AAoooBoCCCoBooDDoBooEEFooGHoFooGHoFo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>4
</answer>


Board size: 6x6
Board: ooooooooooooooooooBoooooBooooCBoAAoC
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,A>2
</answer>


Board size: 6x6
Board: BoooCoBoDECoBoDEoFoGAAoFoGHHIoJJooIo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F^1,A>2
</answer>


Board size: 6x6
Board: oBBBooCCCoDooAAoDoooooDEoFoooEoFoooE
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv2,A>3
</answer>


Board size: 6x6
Board: oooBooAAoBoooooBooooooooCoooDoCoEEDo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,A>4
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: oBoooooBoCCCoBooooooooooDDDooEoooAAE
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^1,A>1
</answer>


Board size: 6x6
Board: oBoooooBoAACoBoooCoooooooooDoooooDoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,A>1
</answer>


Board size: 6x6
Board: BBBooooooooCAAoooCooDDDCoooooooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv2,A>4
</answer>


Board size: 6x6
Board: oBBBooCooooDCooAADCEEFFGoHoIJGoHoIJG
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,A>1
</answer>


Board size: 6x6
Board: oBoooooBooooooooooAAoooCDooooCDooooC
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^3,A>4
</answer>


Board size: 6x6
Board: ooAABoooooBoCooDooCooDooEEEooooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>2
</answer>


Board size: 6x6
Board: ooBBBooooCooAAoCoooooooooooooooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: ooooooBBBooCooAAoCDEEEoFDooooFDooooF
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,A>2
</answer>


Board size: 6x6
Board: ooooBoooooBooooooCoooAACoooooCoooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^2,A>1
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: BBBoooooooooCoooooCooooDCoEEEDoooAAD
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: oooooBoooooBoAAooBoCDEoooCDEoooCoEoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv3,A>3
</answer>


Board size: 6x6
Board: oooooBCoAAoBCooooBooooDoooooDooEEEoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,A>2
</answer>


Board size: 6x6
Board: BBBCCCAAooDooEEEDFooGHDFIJGHoFIJGoKK
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv1,A>4
</answer>


Board size: 6x6
Board: oooBoooooBoooAAoCoooooCooooDCoEEoDoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,A>3
</answer>


Board size: 6x6
Board: ooAABooCCoBDooEEoDFFFooGHHHooGooIIIG
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>2
</answer>


Board size: 6x6
Board: oooooBoooooBoAAooBCooDooCooDooCooDoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: BooCCCBoooooBoooooooooDooAAoDoEEoooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,A>3
</answer>


Board size: 6x6
Board: ooooooooooooooooBoooooBCoAAooCoooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,A>3
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: ooAAoBoooooBoooooooCoooooCoooooCooDD
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: oooBooAAoBooooooooooooooooCCDDoooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,A>4
</answer>


Board size: 6x6
Board: oBBBoooAACoooooCoDooEooDooEoFFGGEooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: oooAABCCCoDBooEEDBooooDoooFooGooFooG
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>1
</answer>


Board size: 6x6
Board: oooBoCoooBoCoAABoooooooDooooEDooooED
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv3,A>3
</answer>


Board size: 6x6
Board: ooAABoCoooBoCDDDooooooEEoooFFFGGoooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: oAAooBCooooBCooooBoooooooooooooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>3
</answer>


Board size: 6x6
Board: oooooooooooooAAooBoooooBoooooBooCCCo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: oAAooBooooCBooooCoooooooDDooooEEFFGG
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: oooooooBBBoooooooooooCoooAACoooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: ooooooBooooCBoDDDCoEoAACoEoooooEoFFF
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,A>1
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: ooooBoooooBoooAABoCCoooooooooooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv3,A>2
</answer>


Board size: 6x6
Board: oAAoBoCCooBDEooooDEFoGGDHFIoooHFIJJo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: oooooooooooooooooBoooooBooAACoooooCo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^2,A>2
</answer>


Board size: 6x6
Board: oooBBBoAAooCoooooCoooooCoooooooooDDo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,A>3
</answer>


Board size: 6x6
Board: oooooooooooooooBCoDooBCEDAAooEDooooE
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^2,A>3
</answer>


Board size: 6x6
Board: oBoooooBooCooAAoCooooooooooooooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,A>3
</answer>


Board size: 6x6
Board: ooBAACooBooCooooooDEooooDEFFoooEoooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,A>1
</answer>


Board size: 6x6
Board: ooooooBoooooBoooCooAAoCoDDDEEEooooFF
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: BAAoCoBoooCoDoEECoDFFFoGDooHHGooIIIG
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: oooooooooBoooAABooCoDoooCoDoEECoDFFo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^1,A>3
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: ooBoooooBooooAACoooDoCoEoDoooEoooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^2,A>3
</answer>


Board size: 6x6
Board: ooBooooCBDDDoCoooooCooooEoAAoFEooooF
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F^2,A>2
</answer>


Board size: 6x6
Board: ooooooAAooBoooooBoooooBoCCooooDDDooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>4
</answer>


Board size: 6x6
Board: oooooBoCoooBoCooDEoCooDEAAooDooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,A>4
</answer>


Board size: 6x6
Board: oBoCCCoBDDDooBooooooAAoEoooooEoooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^2,A>2
</answer>


Board size: 6x6
Board: BoAAoCBDDooCBooooCEEEFGoHHoFGooooFoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,A>2
</answer>


Board size: 6x6
Board: oooooooBoooooBooooooAACoooooCoDDooCo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^3,A>2
</answer>


Board size: 6x6
Board: ooooBoCCCDBoEAADooEoooFFGGGHHHoIIIJJ
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,A>3
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: BoooooBoCoooAACoooooCooooooooooooDDD
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv2,A>4
</answer>


Board size: 6x6
Board: ooooooooooooooooooBAAooCBooooCBoDDoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^2,A>3
</answer>


Board size: 6x6
Board: BoooooBooCCCBooooDoooooDoooEoDAAoEoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^1,A>4
</answer>


Board size: 6x6
Board: BAAoCoBDDoCEoooooEFGHHHoFGIIIJFGoooJ
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,A>3
</answer>


Board size: 6x6
Board: ooAAoBCDDoEBCFFoEBGoooooGooHHHooIIoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>2
</answer>


Board size: 6x6
Board: oooooBoooooBCAAooBCoooooCooooooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv3,A>3
</answer>


Board size: 6x6
Board: oBoooCoBAAoCoBooooooooooDDDEoFGGoEoF
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv2,A>2
</answer>


Board size: 6x6
Board: oooooooooooooAAoBoooCoBoooCDDDooCEEo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^2,A>3
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: oooBoooooBCoAAooCooooDCEFooDoEFooDoE
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv2,A>4
</answer>


Board size: 6x6
Board: oAAooBoooooBCCCoooooooDoEEooDooFFFDo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>3
</answer>


Board size: 6x6
Board: ooBBBooooooooCCCoDooAAoDooEEEDooooFF
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^2,A>2
</answer>


Board size: 6x6
Board: AAoooBoooooBoCooDooCoEDooCoEDoFFooGG
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>4
</answer>


Board size: 6x6
Board: oooBBBooCAADoECooDoECFoDoGoFoooGoFHH
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv1,A>1
</answer>


Board size: 6x6
Board: ooBooooCBDoooCBDooECAAFoEGGoFoEooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F^2,A>2
</answer>


Board size: 6x6
Board: ooooooooooooBooCCCBoAAoDooEEoDoooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv1,A>2
</answer>


Board size: 6x6
Board: ooAAoBoooooBCCoooBoooDEooooDEooooDEo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>2
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: oooBoooooBCoAAooCoDoooooDEEEooDooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,A>4
</answer>


Board size: 6x6
Board: BBBCCCAAoDoooEEDFFGHHDoIGoJooIGoJKKK
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv1,A>4
</answer>


Board size: 6x6
Board: BBBooooCCCDoooooDoooooDEAAoooEoooFFE
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^2,A>4
</answer>


Board size: 6x6
Board: oAAooBoooooBoCoooBoCoooooCoDoooooDoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>3
</answer>


Board size: 6x6
Board: oooooooBoooooBAAoCoBoooCooDDoooEEEoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^2,A>2
</answer>


Board size: 6x6
Board: oooooBooCCCBooAAoBoooooooDoooooDoooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv3,A>2
</answer>


Board size: 6x6
Board: oBoooooBoooCoAAooCooooooooooDEooooDE
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,A>3
</answer>


Board size: 6x6
Board: BBBooooooooCooAAoCooooDEooooDEooooDo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,A>2
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: ooAAoBoooooBoooooBoooCoooooCoooDDCoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>2
</answer>


Board size: 6x6
Board: oooooooooooooooooooAABoooooBoCoooBoC
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^3,A>3
</answer>


Board size: 6x6
Board: BAAooCBDoooCoDEEEooooooooFFoooGGooHH
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,A>3
</answer>


Board size: 6x6
Board: ooAABoooooBoooooBoCDEFooCDEFGGCoHHoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: AAoooBoooooBoCoooooCooDDoEEooooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>4
</answer>


Board size: 6x6
Board: AAoBoooCoBoooCoBoooDDoEEFoooooFooGGo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: BCooooBCooDoAAooDoooooDoEEEoooooFFoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv2,A>4
</answer>


Board size: 6x6
Board: ooAABoCCoDBooooDBoEooDooEoooFFoooGGG
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: oooooooBCDoooBCDoooAADooooooEoooooEo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,A>3
</answer>


Board size: 6x6
Board: ooBCCCAABoooooBooooooDEFoooDEFoooDEo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,A>4
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: oooooooooooooooooBAAoooBoCDooooCDooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^1,A>4
</answer>


Board size: 6x6
Board: BBBooooCooDooCooDooCAADooooEoooooEFF
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,A>2
</answer>


Board size: 6x6
Board: ooAABoooCCBooDDoBoEEooooooooFFoooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>2
</answer>


Board size: 6x6
Board: oooBoooooBooooooooAAooCooooDCooooDCo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^3,A>4
</answer>


Board size: 6x6
Board: ooooooooooBoCoooBoCooDBoAAoDoooooDoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^2,A>4
</answer>


Board size: 6x6
Board: oooBoooooBCoooAACoDoooCEDFFFoEDGGooE
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv2,A>2
</answer>


Board size: 6x6
Board: ooooooooooooooAABoooooBCooooBCoooooC
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: ooooooooooooooooooooooBoooAABoooooCC
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^1,A>2
</answer>


Board size: 6x6
Board: ooAABooCCCBoooooooooooooooooooooooDD
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: BoooooBoAAoCoooooCooooooDDoEEooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,A>2
</answer>


Board size: 6x6
Board: oBoooooBoooCoAAooCoDDDoooooEEoFFFGGG
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,A>3
</answer>


Board size: 6x6
Board: oooBooAAoBooCCoBoooDDooooooooooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,A>4
</answer>


Board size: 6x6
Board: AAooBoooooBooCCoBooDDDooEEoooooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>4
</answer>


Board size: 6x6
Board: ooooooooooooooAAoBoCoDEBoCFDEooCFDEo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^2,A>2
</answer>


Board size: 6x6
Board: AAoooBoooooBCCDDooooooooooooEEoFFoGG
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: oBBBooooCCCDooAAoDoEEoFGHHHIFGJJJIFo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,A>2
</answer>


Board size: 6x6
Board: ooBBBooooooCoDoooCoDAAoCoDEoooooEoFF
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,A>2
</answer>


Board size: 6x6
Board: oooBoooooBoooooooooooooCooAAoCDDDooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: AAoooBooCCCBoooDDBoEEoFooGGGFoooHHFo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: oBBBooooAAoCoooDDCoEEEoCooooFoooooFo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,A>2
</answer>


Board size: 6x6
Board: oooooBCoAAoBCoooooCoooooooooDDoooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,A>2
</answer>


Board size: 6x6
Board: oooooooBBBoooooooooooooCoooAACoDDooC
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^2,A>1
</answer>


Board size: 6x6
Board: BoCCCoBoooooBooooooAAoDooEooDooEoooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^2,A>3
</answer>


Board size: 6x6
Board: ooooBoooooBCooDooCooDoECooooEoAAooEo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^1,A>4
</answer>


Board size: 6x6
Board: oooAABoCCCoBDDEoooooEFFFoGGoHHIIoooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>1
</answer>


Board size: 6x6
Board: oBoAACoBoooCoBDDDooooooooEEFFooGGooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,A>1
</answer>


Board size: 6x6
Board: oooBooooCBooooCoDoooAADoooooDooooEEo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^2,A>2
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: ooooooooooooBBBoooCooAADCooooDCooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^2,A>1
</answer>


Board size: 6x6
Board: oooooooooooooooBBBoooooooooooCAAoooC
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,A>4
</answer>


Board size: 6x6
Board: ooooooooooBoooCoBoooCoBoAAoDoooooDoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^2,A>4
</answer>


Board size: 6x6
Board: AAoooBoooooBoooooBoCoooooCoooooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>4
</answer>


Board size: 6x6
Board: oooooBooAAoBoCoooooCooooooooDoooooDo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,A>2
</answer>


Board size: 6x6
Board: ooBoooooBoooooBooooooooooooAACDDDEEC
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^2,A>1
</answer>


Board size: 6x6
Board: oooooooooBBBCAAooDCEoooDCEooFDooGGFo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv1,A>3
</answer>


Board size: 6x6
Board: AABoooooBoooCoBoooCoooooCDDDoooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: BBBoooooooooooAACoooooCoDDooCooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,A>2
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: oooooooooBoooAABooCCDBooooDoooooDoEE
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,A>3
</answer>


Board size: 6x6
Board: ooooBoooooBoooooBoCAAooDCoEooDFFEooD
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^3,A>3
</answer>


Board size: 6x6
Board: oooBBBoAAoCoDDDoCoEFGoooEFGHHHoFGIIo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,A>3
</answer>


Board size: 6x6
Board: oAAoBoooCoBoooCoBDoECooDoEoooDoEoFFF
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>3
</answer>


Board size: 6x6
Board: ooAAoBCoDDoBCoooooCooooooEoooooEoooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>2
</answer>


Board size: 6x6
Board: BooooCBoAAoCDDooooooooooEoooooEooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv2,A>2
</answer>


Board size: 6x6
Board: oBBBooooooooooooooCoooooCDAAEooDooEo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^2,A>2
</answer>


Board size: 6x6
Board: BoooooBoooCoBooDCooAADoooooooooooEEo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,A>3
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: oBoooooBCoDooBCoDoooooDoooAAoEFFGGGE
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: oooooooAABoooooBoooCDooooCDooooCDoEE
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: ooooooBBBoCooAAoCoDDDoooooooEoooooEo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,A>3
</answer>


Board size: 6x6
Board: oooooooooooooooooBoAAooBooCooBDDCEEE
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^2,A>3
</answer>


Board size: 6x6
Board: ooBBBoCCCDooEEEDoFoGoDoFoGHAAFooHIIo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F^1,A>1
</answer>


Board size: 6x6
Board: oooBBBoooAACoooooCoooooCoooooooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,A>1
</answer>


Board size: 6x6
Board: oAAoBoCCooBoooooBoDDDoooooEoFFooEooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>3
</answer>


Board size: 6x6
Board: oAABooCCCBoooooBDDoooooooooEoooFFEGG
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: ooooooooooooooooooooBAACooBDoCooBDoC
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^3,A>1
</answer>


Board size: 6x6
Board: oooooooooooooooooBoooCoBoooCoBAAoCoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,A>4
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: oBCDDDoBCAAEoBFFoEGGooHooIIoHooJJJHo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Ev1,A>1
</answer>


Board size: 6x6
Board: oBoCoooBoCoooBooDooAAoDooooooooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,A>3
</answer>


Board size: 6x6
Board: oBBBooCCCDEooFoDEoGFAAoHGFooIHGoooIo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
H^2,A>2
</answer>


Board size: 6x6
Board: oooBoooCoBoooCoBDooCAADoooEFFFooEGGG
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,A>2
</answer>


Board size: 6x6
Board: ooAAoBoooooBoCoooooCDDooooEoFFooEooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>2
</answer>


Board size: 6x6
Board: oAAoBoCDEoBoCDEoBoCFFFooGHIIJJGHoKKK
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>3
</answer>


Board size: 6x6
Board: ooBoooAABoooooBooooCoooooCoooooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,A>4
</answer>


Board size: 6x6
Board: ooooBoooAABooooCooDEECooDFooooDFoooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,A>2
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: oooBooCCCBDooooBDEooooDEooFAAEooFooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^1,A>1
</answer>


Board size: 6x6
Board: ooBoooooBCooooBCoooDoCoooDooEoAAooEo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^1,A>4
</answer>


Board size: 6x6
Board: ooBBBoCooDooCooDooEoFFFGEooooGEoAAoG
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
G^1,A>2
</answer>


Board size: 6x6
Board: oooooooBBBooCCCooDoEooFDoEAAFooEGGFo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F^2,A>2
</answer>


Board size: 6x6
Board: oAAoBoooooBoCCCoBoDoEEooDooFFFGGGoHH
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: ooBBBCoAAooCoooooCoooDoooooDoooooDoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv2,A>3
</answer>


Board size: 6x6
Board: ooooooooooBoooAABoCoDDooCooEEECFFooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^1,A>2
</answer>


Board size: 6x6
Board: ooooooooBooCooBAACooooDCooooDoooooDo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv2,A>1
</answer>


Board size: 6x6
Board: oooBooCCCBooDoAAEoDooFEGoooFEGoHHFoG
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Ev1,A>2
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: oooBBBoAAooCooooDCooEEDoooooFFGGGoHH
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,A>3
</answer>


Board size: 6x6
Board: AAoooBoooooBoooooBCCooooDDoooooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>4
</answer>


Board size: 6x6
Board: BBBCCCoAAoDoEEEoDoFoGHDIFoGHoIJJGHoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv1,A>3
</answer>


Board size: 6x6
Board: BCCCooBooooooooooooooDoooAADoooEEDoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^2,A>3
</answer>


Board size: 6x6
Board: ooooBoooAABoCDDoBoCEEEooCooooooFFoGG
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,A>2
</answer>


Board size: 6x6
Board: oAAooBCDEooBCDEFoBCDEFooooooGGoHHHoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>3
</answer>


Board size: 6x6
Board: oBoooooBoAACoBoooCooooDCooEEDoooooDo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,A>1
</answer>


Board size: 6x6
Board: ooBBBooooCCCoooooooooooooooooDoAAooD
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,A>3
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: oooBBBAAoCooDooCooDooooooooEEoooFFoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,A>4
</answer>


Board size: 6x6
Board: BoooCoBoooCoBoAACooooooooooooooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv3,A>2
</answer>


Board size: 6x6
Board: BoAAoCBoDDDCoooooCooooEoooooEooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,A>2
</answer>


Board size: 6x6
Board: BooCDoBooCDoBooCoEFAAooEFGGHHHFIIooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^1,A>3
</answer>


Board size: 6x6
Board: ooooooBBBoooooooCoAAooCooDEEoooDoooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,A>4
</answer>


Board size: 6x6
Board: BBBooooAAoCoooooCoooooooooooooDDoooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,A>3
</answer>


Board size: 6x6
Board: AAoBoooooBoooooBCCDDDoEEoFoooooFoooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>4
</answer>


Board size: 6x6
Board: oBAACooBooCooBDDCEFGGooEFooooEHHHIII
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: oooooBooooCBoooDCooooDCoAAoDoooEEooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,A>4
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: oooBoooooBooCCCooDAAoooDEEFFFDoooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^2,A>4
</answer>


Board size: 6x6
Board: ooBBBoCCCooooDDDooAAoEoooooEoooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Ev1,A>4
</answer>


Board size: 6x6
Board: oAAoBoooooBooCCoBoDEooooDEoFooDEoFGG
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>3
</answer>


Board size: 6x6
Board: ooooooooBoooooBoooooBoooooAAoCoDDooC
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^2,A>2
</answer>


Board size: 6x6
Board: ooooooBoooooBooooooooooCooAAoCoDDooC
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: ooooooAAoBoooooBoooooBoCoooooCoooooC
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: AAoooBoCCCoBDoEFFoDoEoGHIIooGHoooJJJ
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: ooooooooooBoooooBoooooBoooCoooAACooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,A>4
</answer>


Board size: 6x6
Board: oBoCCCoBoooDEBoAADEoFFFDooooooGGHHoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv2,A>1
</answer>


Board size: 6x6
Board: BoooooBooooooooooooooCoooAACoooooCDD
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^2,A>3
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: ooooBooCooBooCoooooCAAoDEooooDEoFFoD
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^3,A>2
</answer>


Board size: 6x6
Board: ooooooooooooooooBoooCoBDooCooDAAoooD
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,A>4
</answer>


Board size: 6x6
Board: ooooooAABoooooBooCoooooCoooooooDDDoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>4
</answer>


Board size: 6x6
Board: ooAAoBoCCooBoooDDooooooooooooooooEEo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>2
</answer>


Board size: 6x6
Board: ooooooooooooooBooooCBAADoCoooDoCoooD
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^3,A>1
</answer>


Board size: 6x6
Board: oAAooBCCCooBooooooooDDDoooooooEEoFFo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>3
</answer>


Board size: 6x6
Board: ooAABoCCCoBoDDDoooEFGHHHEFGIIIoFoJJJ
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: oooooooBBBoooooooCAAoooCoooooCoooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^2,A>4
</answer>


Board size: 6x6
Board: oooooooooooooAAoBoooooBooooooCoooooC
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^2,A>3
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: ooooooAAooBoooooBoooooooooCCCoDDDooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: BBBoooooooooCoooooCooooDEEEooDooAAoD
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,A>2
</answer>


Board size: 6x6
Board: oooBooAAoBoooooBoCDDDooCooooEEFFFoGG
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,A>4
</answer>


Board size: 6x6
Board: oooooooooooBCoAAoBCooooBCoDDoooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,A>2
</answer>


Board size: 6x6
Board: oooooooooooooooooooBBBoCoooAACooDDoC
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^2,A>1
</answer>


Board size: 6x6
Board: ooBCCCDoBEEEDAAFooGHHFIJGKooIJGKooIo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Fv1,A>3
</answer>


Board size: 6x6
Board: oooooooooooooAABoooooBoooCCDDDoooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: oooBBBoCCCooooDDDoooEEEFoAAooFoooooF
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F^2,A>3
</answer>


Board size: 6x6
Board: ooooooooAAoBCCoooBoooDoBoooDooEEoDoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>2
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: ooooooooBoCDooBoCDEFAAoDEFooGGoFoooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: oBAAoCoBoDDCEEEoooFoGGHHFIIJJJooooKK
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,A>2
</answer>


Board size: 6x6
Board: oooBoooooBoooAAooCDooooCDooooCDoEEoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,A>3
</answer>


Board size: 6x6
Board: ooooBoooooBoooAABooooCoDoooCoDoEECoD
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv3,A>2
</answer>


Board size: 6x6
Board: ooAABoooooBooooooCoDDoECFGHHEoFGooEo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: oooooooooooooAABoooooBCCoDDEEEoFFooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^2,A>3
</answer>


Board size: 6x6
Board: ooooooBooooCBooooCBoAADoEEooDoooooDo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^3,A>2
</answer>


Board size: 6x6
Board: ooBoooooBoooooCCCoDEoooFDEAAoFDooooF
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F^2,A>2
</answer>


Board size: 6x6
Board: oooooooooooooooooooAABoooooBCCDDoBoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^3,A>3
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: oooooBoooAABoCCoooDoooEoDoooEoooooEo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,A>1
</answer>


Board size: 6x6
Board: ooBooCooBooCoooooooAADoooooDoooooDoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^3,A>3
</answer>


Board size: 6x6
Board: oAAooBCCCooBoooooBoooooooooooooooDDo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>3
</answer>


Board size: 6x6
Board: oooBBBCDooEoCDooEooooFEooAAFoooooFoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F^2,A>3
</answer>


Board size: 6x6
Board: oAAooBCCCoDBEEEoDBFFFGDoHIIGooHJJJKK
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: ooooooBCoooDBCoooDoCEooDooEFFFAAEooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^1,A>4
</answer>


Board size: 6x6
Board: oooBBBoCCCoooooooooDDDEoooooEoooAAEo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^1,A>2
</answer>


Board size: 6x6
Board: ooooooooooooooooooooAAoBoooooBooCCoB
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^3,A>2
</answer>


Board size: 6x6
Board: oooBoooooBooAAoBooCCooDDoooooooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv3,A>4
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: AAoBoooooBCCDDDBoooEEooFooGGGFHHIIIF
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>4
</answer>


Board size: 6x6
Board: BoooooBooooCBAAooCoDoooooDoooooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,A>3
</answer>


Board size: 6x6
Board: oBoooooBooCooBDoCEooDAAEFFoGGGHHHIII
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^1,A>1
</answer>


Board size: 6x6
Board: ooooBoooooBoooAABooooooooooooCoDDDoC
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv3,A>2
</answer>


Board size: 6x6
Board: BooCCCBooDDDoEEEooooooooooAAoFoooooF
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F^2,A>2
</answer>


Board size: 6x6
Board: oooooooooooooAABoooooBoCooDooCooDooC
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^2,A>3
</answer>


Board size: 6x6
Board: ooooBoooooBoCoAABoCoDDoooooooooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: oooooooooooBoAAooBCCDDooEEoooooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^1,A>3
</answer>


Board size: 6x6
Board: oooooBoooooBCCCooooooooDoooAADooEEEo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,A>1
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: oooooBoooooBoCAADooCEoDoooEoDoooEooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv1,A>2
</answer>


Board size: 6x6
Board: oBBBoooAAooCoooooCDoooECDoooEoooooEo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,A>3
</answer>


Board size: 6x6
Board: BoCDooBoCDEoBoooEooFGAAHoFGIIHoFGoJJ
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
H^2,A>1
</answer>


Board size: 6x6
Board: oooooooooooBoooAABoooooBooooooCCoooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,A>1
</answer>


Board size: 6x6
Board: ooooooooAAoBoooooBCCoDooooEDooooEDoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>2
</answer>


Board size: 6x6
Board: oAAooBCCoooBoooDooooEDooooEDoooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>3
</answer>


Board size: 6x6
Board: oooooBooAAoBooCCooooDDoooEEEoooooFFo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,A>2
</answer>


Board size: 6x6
Board: BCCCooBDoooEBDFFFEGAAooEGHHHIIGooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^1,A>3
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: oooAABooCCoBooDDoBoooooooEoFFFoEoooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>1
</answer>


Board size: 6x6
Board: oooBCoDDDBCoooooCoooAAoEFooGGEFHHHoE
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^3,A>2
</answer>


Board size: 6x6
Board: oooooooooooBCooooBCooAABoooDDooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^1,A>1
</answer>


Board size: 6x6
Board: oAAoBoCCooBooDooBooDEooooDEoFFooEooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: BBBCoooDoCEoFDGoEHFDGoEHIooAAHIJJJKK
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
H^1,A>1
</answer>


Board size: 6x6
Board: oooooooooooBoAAooBCCCoooooooDoooooDo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^1,A>3
</answer>


Board size: 6x6
Board: AAoBooooCBoDooCBEDooCoEoFFooEGoooooG
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>4
</answer>


Board size: 6x6
Board: oBoooooBAACooBooCDEFFooDEooGoDoooGHH
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,A>2
</answer>


Board size: 6x6
Board: oooooBooCAABooCooBoooooooooooooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,A>1
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: AABoooooBCCoooBDDDoooooooooooooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: oooooooooBoooAABooCoooooCoooooCooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: oooBBBooAACoDDDoCEFFFGCEoooGoEoooHHH
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: oooooooooAABoCoooBoCDDDBoooooooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>1
</answer>


Board size: 6x6
Board: BBBooCooDooCooDAACooDooooEEEoooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv3,A>1
</answer>


Board size: 6x6
Board: BBBoCoooAACoooDDooooooooooooEoooooEo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv2,A>2
</answer>


Board size: 6x6
Board: BBBoooooooooCCCoDoAAooDoooEEDoooooFF
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^2,A>4
</answer>


Board size: 6x6
Board: oooBBBoooooCAAoooCoDDooCoooooooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv2,A>4
</answer>


Board size: 6x6
Board: ooooooooooooooooooAAoooBooCooBooCooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^2,A>4
</answer>


Board size: 6x6
Board: BBBCooAAoCoooooCooDoooooDoooooDooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: oooooooooooooooBooAAoBoooooBooCCoooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: oooooBooCooBooCoooDooooEDooAAEDFFFoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^1,A>1
</answer>


Board size: 6x6
Board: oooBBBCoooooCoooooAAooDoooooDooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: BoCooDBoCoEDBooFEoGGGFEooAAFooooooHH
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F^1,A>3
</answer>


Board size: 6x6
Board: BoCCCoBoooooooooooAAoooDoooooDooEEoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: oooBBBoooooCoooAACoooooCoDoooooDEEEo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv2,A>1
</answer>


Board size: 6x6
Board: oooAABCCCDoBoooDoBEoFDooEoFGGoEoFHHH
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>1
</answer>


Board size: 6x6
Board: oooBoooooBoooCoooooCAAoDECoooDEooooD
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^3,A>2
</answer>


Board size: 6x6
Board: oooooooooooooooooBooAAoBoCCooBoooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^2,A>2
</answer>


Board size: 6x6
Board: BoooooBCCCDoEEEoDooooAAFGHHIIFGoJJoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F^2,A>1
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: oAABoooCoBDDoCEoooooEoooFoooGoFoooGo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>3
</answer>


Board size: 6x6
Board: oooooBooAAoBoCoooooCoooooooooooDDooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,A>2
</answer>


Board size: 6x6
Board: oAAooBoooCCBoDoooBoDEooooDEFFFGGEooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: oooooooooBBBooooCoooooCoooooCDoAAooD
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,A>3
</answer>


Board size: 6x6
Board: ooooooooooooooooBoCCCDBoAAoDoooooEEo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,A>4
</answer>


Board size: 6x6
Board: ooBooooCBooooCBoooDooEFoDooEFoAAooFo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F^1,A>4
</answer>


Board size: 6x6
Board: ooooBooAAoBooooooooooooooCCooooooDDD
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,A>3
</answer>


Board size: 6x6
Board: oooooooBCooDoBCAADoBCooDooooooEEoooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv2,A>1
</answer>


Board size: 6x6
Board: ooooBooAAoBooooCoooooCoDoooCoDoooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: oAAoBoCCCoBooooooooooDEEoFFDoooooDoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>3
</answer>


Board size: 6x6
Board: BoCoooBoCoooooCooDEoAAoDEooooDEoFFFo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^2,A>2
</answer>


Board size: 6x6
Board: ooBBBooAACoooooCooDDEoooooEoFGooooFG
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,A>3
</answer>


Board size: 6x6
Board: oooooooAAooBCooooBCoooooCooooooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: oooBoooooBCoDDDoCoEAAoCoEooFFoEGGHHH
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,A>3
</answer>


Board size: 6x6
Board: BCooooBCoooooCAAoDoEEEoDooFFoooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: oAAooBooCCCBDDooooooEoFoooEGFoooEGFo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: ooBBBoooCCCoDoooooDoAAoEDooFFEGGGooE
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^3,A>2
</answer>


Board size: 6x6
Board: oooBBBooooooooooooooAAoCoooDoCoooDoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^2,A>2
</answer>


Board size: 6x6
Board: ooBBBooooooooooAACDoEooCDoEoooDoEFFF
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^2,A>1
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: oooBBBAACoooDDCEEoFoCoGGFooHooFooHoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,A>4
</answer>


Board size: 6x6
Board: ooBoooooBoooooBooooooooCooAAoCDDDooC
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: oBoAACoBoooCoBoooooDDoEFoGoHEFoGoHEo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,A>1
</answer>


Board size: 6x6
Board: oooBoooCoBDooCAADooooEEoooFFFooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,A>2
</answer>


Board size: 6x6
Board: oBoAACoBoooCDBEEEoDoFGGGoHFIJooHFIJo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: BoooooBCooooBCoooooCAAoDoooooDoooooD
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^3,A>2
</answer>


Board size: 6x6
Board: ooooooooBoooooBoooooBCoooooCoooAACoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,A>3
</answer>


Board size: 6x6
Board: oooooBoooooBoooooBoAAoCoooooCoooDDCo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^3,A>3
</answer>


Board size: 6x6
Board: ooooooBBBCoooAACooDDoCoooooooooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv2,A>3
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: oooooooAAoBoooCCBoDoooBoDoooooDooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>3
</answer>


Board size: 6x6
Board: AABoooooBoooooooooooCCoooooooooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>4
</answer>


Board size: 6x6
Board: oooBBBoooooCAAoooCoDoooCoDoooooDoooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv2,A>4
</answer>


Board size: 6x6
Board: ooooooAABoooooBCCCoooooooooooooooDDD
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: oAAoBoooooBooCoooooCDDEEoCFGGGHHFIII
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: oooBoooooBoCoAAooCoDoooCoDoooooDEEEo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: oooooooooooooBBBoCooAAoCoDoooCoDoooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^2,A>2
</answer>


Board size: 6x6
Board: BCCCooBoDDDoooAAEoooFoEoooFoooGGFooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Ev1,A>2
</answer>


Board size: 6x6
Board: AAoooBoooooBCCCooBoooooooooooooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: oooBoooooBoooooBooooooCoAAooCooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,A>4
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: ooooBoooooBoAACoooooCoooooCooooooDDo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,A>4
</answer>


Board size: 6x6
Board: ooBCDEooBCDEoooCDEooAAFoooooFooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Fv1,A>2
</answer>


Board size: 6x6
Board: oooBBBCoooooCoAADoCoEoDoooEoooooEFFF
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv1,A>2
</answer>


Board size: 6x6
Board: oAAoBooooCBoDDoCooooooooooooEoooooEo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>3
</answer>


Board size: 6x6
Board: AAoBooCCDBoEooDooEooDoFFGGHHIIJJJoKK
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>4
</answer>


Board size: 6x6
Board: oooBoooAABoooooBCCDDoooEoooooEoooooE
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,A>3
</answer>


Board size: 6x6
Board: ooAABoooooBoooCCooooooooDDoooooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>2
</answer>


Board size: 6x6
Board: oooooBoAAooBoCCooooooooooooooooooDDD
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: oooooooBBBoooCCCoDAAoooDoooEEEFFFGGG
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,A>4
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: oooooooooBoooooBCooooBCoooAACooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,A>2
</answer>


Board size: 6x6
Board: oooBBBCCCoooDDDoEooAAoEoFFFGGGooHHoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^1,A>3
</answer>


Board size: 6x6
Board: oooBBBooooooooooooCoooDoCoAADoCoooDo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^2,A>2
</answer>


Board size: 6x6
Board: ooAABoooooBoooooBoooCoooooCooooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: ooooooooBoooooBooooooooCoooAACoooDDD
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,A>1
</answer>


Board size: 6x6
Board: oooAABoCCoDBEEEoDBooFoooGGFoooooFooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>1
</answer>


Board size: 6x6
Board: ooooooooBCCCooBoDooAAoDooooooooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv2,A>3
</answer>


Board size: 6x6
Board: oAAooBoooooBoooooBoooooooooCCoDDDEEo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>3
</answer>


Board size: 6x6
Board: ooAAoBoooooBooCoooooCoooooCooooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>2
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: oAAooBooCCoBoooooBoooDDooooEEEoooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: oooBoooAABooooooooooooCoooooCoooooCo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,A>3
</answer>


Board size: 6x6
Board: oooooBoooooBoAAooBCDooEoCDooEooDoooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv3,A>3
</answer>


Board size: 6x6
Board: oAAoBoCCooBoDDoooooooEoFoooEoFooGGGo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: oooBBBCDDDEoCoFoEoooFoEGooFAAGHHHIII
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
G^1,A>1
</answer>


Board size: 6x6
Board: oooooooooAABoooooBoooooBooCoooooCDDo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>1
</answer>


Board size: 6x6
Board: BoCoooBoCooDBoAAoDEEEooooooooooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,A>2
</answer>


Board size: 6x6
Board: AAoooBooCCCBoDDDEoFGoHEIFGoHEIFGoHoI
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>4
</answer>


Board size: 6x6
Board: oBAAoCoBoooCDBoEooDooEooDooFFFGGooHH
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,A>2
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: BBBooooCCCoDooAAoDoEoooFoEGGoFoEHHHF
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: oooBoooooBoooAABoooCoooDoCoooDoCoooD
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: oBCCCooBDDDoEBAAoFEGoHoFoGoHoIoGoHoI
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F^2,A>2
</answer>


Board size: 6x6
Board: oooBBBoooCCCAAoooDoEFooDoEFooDoEoooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv1,A>4
</answer>


Board size: 6x6
Board: oooooooBoooooBCooooBCooDooCAADEEEooD
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^2,A>1
</answer>


Board size: 6x6
Board: oooAABoooCCBDDDoooEFooooEFoGGoEFoHHH
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>1
</answer>


Board size: 6x6
Board: oooAABoooooBoooCoooooCoooooooooooDDo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: ooooooAAoooBoooCoBoooCoBoDDDoooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: ooooooooooooooooooBoooCDBoooCDBAAoCo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,A>3
</answer>


Board size: 6x6
Board: BoooooBoooooooooCoooAACooDEEoooDoooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,A>2
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: oooBBBooooooooCoooooCooDooCooDAAoooD
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,A>4
</answer>


Board size: 6x6
Board: ooAAoBCCCooBoooDDBEFFoooEooGGoEooHHH
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>2
</answer>


Board size: 6x6
Board: AABooooCBooooCooooooDDDooooEoooooEoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>4
</answer>


Board size: 6x6
Board: oooooooooooBooCooBoDCAABoDCooooooEEo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^1,A>1
</answer>


Board size: 6x6
Board: ooooBoooCoBDooCooDooCAADEEooFoooooFo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,A>1
</answer>


Board size: 6x6
Board: BooCCCBAAooDoooooDooooEDFFooEooGGGoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv1,A>3
</answer>


Board size: 6x6
Board: oooooBoooAABCCCooooooooooooooooDDooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,A>1
</answer>


Board size: 6x6
Board: oooBBBCoDDDECAAooEoFFooEGoooHoGoooHo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Ev2,A>3
</answer>