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

<think>
Shortest path found.
</think>
<answer>
C^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: oooBoooAABooCooBooCoooDDCooooooooooo
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: oooooooBCooDoBCooDoooAADooooooEEEFFF
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: oooBoooooBooooooCoooAACoooDDoooooooo
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: ooooooooooooooBBBCoooAACoooooCoooooo
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: ooAABooCCoBoooooooooooooooooDDoEEEoo
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: oBoCDooBoCDEoFFFDEooGAAEHHGoooooGIII
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: oooooooooBBBoooooCoooAACDDDooooEEEoo
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: oooooooBoooooBooCoAAooCooooooooooooo
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: oooooBoooooBAAoooBCCCooooooooooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: AAoooBoCoooBoCoooooCDDEoooooEoooooEo
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: ooooooooooooAAooBoCDooBoCDoEEEoDoooo
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: oooooBAAoooBoCCoooDoEoooDoEooFDooooF
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: oooooooooBBBoooooCoAAooCoDDDoooooooo
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: oAAoBoCoooBDCEEoBDooFooDGGFooooooooo
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: oooooooooooooAAooBoCoooBoCoooooCoooo
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: oooooooBBBoCAAoooCooDDDCEoooooEooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv2,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: oooooooooBooAAoBoooCCCDDEFoGGGEFoooo
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: oooooooooooooAAoBoCCCoBDoooooDoEEooD
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: oBBBCoooooCDEFooCDEFAAoDooGoHHIIGooo
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: oooooooooBoooooBCoooooCoAAooCooooDDD
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: oBCooooBCoooDBoooEDooooEFooAAEFooooo
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: ooooooooBoooAABoooooBoooCCoooooooDDo
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: ooooooAAooBoooCoBoooCoBooooooooooooo
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: ooAAoBoooooBoCoooooCoooooooooooooooo
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: BCCCooBoDDDEBFAAoEoFGGHIJJooHIooKKKI
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^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: oBBBoooAACooDDoCoooooCEoFFFoEooGGoEo
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: oBAACooBooCoooooCoooDEooooDEFFooDEoo
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: oooooooooBBBAAoooCoDoooCoDoooooooooo
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: ooooooAAoBoooCoBDDoCoBEEoCoooooooFFo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: BoCCCoBooooooAADoooooDoooooooooooooo
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: oBooCooBooCooBooooooooooAADoooooDooo
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: ooBBBoooooooooooooooooooooAAoCoDDooC
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: ooooooooAABooooCBooooCooDDDCoooooooo
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: AAooBoooooBoooCoooooCDDDoooooooooEEo
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: BBBoooooAACoooooCoDDoooooooooooEEooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


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


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


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


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

<think>
Shortest path found.
</think>
<answer>
Cv1,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: ooooooooooooooooooooBBBCoooooCooAAoC
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: oooooooooooBoooAABoooooooCoooDoCoooD
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: oooooooBoooooBoAACoooDoCoEoDoooEoDoo
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: oooooooooooBAAoooBooCCCooooooooooooo
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: ooBCooooBCoDoEBAADoEooFoGGHHFoooIIFo
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: oAAooBCCoDoBoEFDGooEFDGooEoHHHIIoooo
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: ooBBBooooooCooDAACooDooCooDEoooooEoo
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: oooooooooooooooooBoAAooBCCDDoooooooo
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: BAAoCoBooDCoEFoDCoEFooooEGGGHHooIIoo
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: oBoCoooBoCoooBoAADooooEDFFFoEoooGGoo
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: oooBBBCCCoooDDDoooooAAoEoooooEoooooo
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: BBBooooooCoooDoCoooDEEEFGGGooFAAoooF
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: oooBooAAoBoooooooCoooooCooooooDDoooo
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: ooBAACooBooCooDDoCoooooooEoFFFoEooGG
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: oBBBoooooooCooooDCooooDoooAADooooooo
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: oAABoooCoBDDoCoBooEFFooGEHHHoGoIIIoG
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: oooooooooBBBCoAADoCooEDoCooEDFoooEoF
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: oooooooooBBBooooooooooooooooCoooAACo
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: oooooooooBoooAABooCooooDCoEEEDCoFFoD
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: ooAABoooooBoCDDDBoCoEFooooEFGGHHEFoo
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: oooooBoAAooBoooooooooooooooooooooCCC
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: oooAABoCoDDBoCoooBoCooEoFFFoEooooooo
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: oooooooooAABoooooBCDoEEBCDooooCooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


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

<think>
Shortest path found.
</think>
<answer>
D^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: oBBBooCooooDCooooDCoAAoDoooEEEFFoooo
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: BoooooBAAooCBooooCooDDooooooooEEEooo
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: oooooBCAAooBCoDoooCoDoooooEEFGooooFG
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: AAooBooCCoBoDDDEoFGHoEoFGHoEoFGoIIoo
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: oBoooooBoooooBAAoCoooooCooooooDDoooo
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: ooBoooooBooooooooooooooooooCoooAACoo
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: ooBoooooBoCoAAooCooooooooooooooooooo
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: oooooooBoooCoBoooCoooAACDoooooDooooo
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: BoooooBoooooooooooAAooCooDEECooDoooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^2,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: ooAAoBooCCoBooooDoEoooDoEooFDoEooFoo
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: oooBBBooooooooCAADoECooDoEoooooEoFFF
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: oAABoooooBCoDoooCoDEEECoDooFFFooGGGo
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: ooooooooooooooBoooooBoooooAACoDDooCo
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: ooooooooooooooooooBoAAoCBooDDCBooooC
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: BCooooBCoDDDBCooooAAEoooooEFFFooEooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: BoooooBooooCoAAooCDDDoooEoooooEooFFo
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: oooooooooAABCooooBCooooBCooooooooDDo
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: ooooooBoCCCoBooDooBoEDoFooEDoFoAAooF
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: BoooooBoooooBooAACoooooCDDoEEEFFoooo
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: oooooooooAABoooCoBDooCooDooooooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


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


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


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


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


Board size: 6x6
Board: oooBoooooBooooooooCooAADCooooDCooooD
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: BoCCCoBooAADEoFFoDEGGGoDoHHHoooooIII
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: oooooooBoooooBooCoooooCooAAoCooDDooo
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: oooooooooooBoooooBooooooAACoooooCDDD
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: BCooooBCDooooCDooooAAooEoFFFoEoooooE
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: oooAABCCoooBoooooBoooDDoooooooEEoooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


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


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

<think>
Shortest path found.
</think>
<answer>
G^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: oBooCooBooCoooooCDooAAoDooEEooFFoooo
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: oooooooooooooBBBooooCoDoooCoDoAAooDo
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: oooooooooooBoooooBoCDAAEoCDFoEoCoFoo
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: oAAooBoooooBooCCCooooooooooooooDDDoo
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: AAooBooCCoBDEFFFoDEoGGGDHHHIoJKKoIoJ
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: ooBBBooooooooooooooooooCoAAooCoDDooC
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: oooBCoDooBCEDooBCEDoAAoEFoooooFoGGGo
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: oooBBBCoooooCDoooooDoooEoDoooEooAAoE
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


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


Board size: 6x6
Board: oooooooooAABooCCoBDDDEoooFoEoooFoEGG
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: ooBoooooBoooooBooooAAoCoooooCDooooCD
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: ooooooooooooooooBoCoAABoCoooBoCooooo
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: BooAACBooooCBoDooooEDooooEoFFFooGGoo
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: oooooooooooooooooooBooCDoBooCDoBAAoD
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: oooBBBoooooooooCoooooCoooAAoDoooooDo
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: ooooooooooBoCAAoBoCoDoooooDoEEooDFFo
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: oooooooooAABCooooBCoooooCDDooooooooo
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: oooooBoooooBoooooCoooAACoDDooooooooo
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: ooooooooooooooooooBAAooCBoDDoCBoEEEo
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: AAoooBoooooBoooooooCCooooooDoooooDoo
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: ooBBBCDooAACDEEooCFFFGoooHoGoooHoGII
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


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


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


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


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


Board size: 6x6
Board: ooBBBoooooooAAoooCoDDooCoooEEEoooooo
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: BCooDEBCFGDEBCFGoEAAFoooooHIIIooHoJJ
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: ooooooBBBCoooAACoooooCoooooooooooooo
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: oooooooooBoooooBoooAABoooCooDDoCoooo
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: oooooooooBoooAABooooooooCCoDEEoooDFF
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


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


Board size: 6x6
Board: oooBBBooCoooooCDoooEoDFooEoDFooEAAFo
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: oBBBoCoAAooCDDooECFFFoEoGGHHHoIIJJKK
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: BoooooBooooooooooooAAooCoooDoCoEEDoC
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: BBBCCCoAAooDEEFooDooFGHoIIIGHoJJJGHo
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: BCDEEEBCDFooBGDFoHIGAAoHIJKLLLIJKooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: BBBooooAACoooooCoooooCoooDoooooDoooo
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: oooooooAAooBoooooBCooooBCDooEoCDooEo
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: AAoBooCCoBoooooBoooooooooooooooooooo
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: ooBBBoAAoooCDooooCDEoFooDEoFoooEoFGG
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: oooooooooooooooBBBooAAoCDDoooCoooooo
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: oooooooooooBCDAAoBCDoooooooEEooooooo
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: oooBBBoooCCCoooAADooEFoDooEFooGGGFoo
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: oooooooooAABoooooBooooCoooDDCoooooCo
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: AABoooCCBoooooBooooooDDDEooooFEoGGoF
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


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

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


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

<think>
Shortest path found.
</think>
<answer>
Bv2,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: BBBoooooooCoAAooCoDoooCoDoooooDoEEoo
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: AAoooBCooooBCooDoooooDooEEEooooooooo
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: BoCooDBoCooDooCAADEEoooooooFFooooGGo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv3,A>1
</answer>


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


Board size: 6x6
Board: oBoCCCoBooooAAooDooEooDooEoooFoooooF
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: ooBBBoooooCooAAoCoooooCooooooooooooo
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: AABoooooBCoooDBCEEoDoFFFGDoHHoGooIII
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: ooooooooBCooooBCoooooCDoAAooDoooooDo
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: ooAAoBCCCoDBooEEDBooooDoFGHIIIFGHoJJ
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: oAABoooooBCoDEEoCoDoooFFDGGHHooooIII
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


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


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


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


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

<think>
Shortest path found.
</think>
<answer>
Gv2,A>1
</answer>


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


Board size: 6x6
Board: oooooooooooooAAooBooooCBooDDCBEEEoCo
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: ooooooooAABoooooBooCoDoooCoDoEoooDoE
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: oooooooooAABoooooBoCCCoBoooooooooDDD
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: oooBBBooCCCDoAAooDEoFFFDEooooooooGGo
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: oooooooooooooBooCooBAACooBoDCEoFFDoE
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^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: oBoooCoBAAoCoBoooooooooooooooooooooo
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: oBoooooBoooCAAoooCDooEooDooEooDoFFoo
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: ooBBBooooooooAAooCoooooCDoooEEDooooo
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: oooooooooooBooCooBooCDoBoooDoooAADoo
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: oooooooooooBoCCCoBoooAABooooooDDDooo
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: AAooBoooooBooooooCDEFGHCDEFGHoooooII
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: ooBoooooBCDoooBCDoAAoCooooooEooFFFEo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


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

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


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


Board size: 6x6
Board: oooooooBoooooBoooooooooooooCoooAACoo
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: oooBooAAoBoooooBooCCDoEEooDoooooDFFo
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: BoCoooBoCDDDBoCAAEFFFoGEHHooGEIIJJGo
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: oooooooooooooAAooBCCCooBoooDoooooDEE
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: oooAABoooooBoooooBooCCCoDEEFFFDGGoHH
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: ooooooooooooBBBooooooooooooooCAAoooC
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: oooBBBoooCCCDoooooDooEFoDGoEFooGAAFo
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: oooooooBBBooooooCoooooCDoooAADoooooD
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^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: oooooBooAAoBoooooBoCCCDoooEoDoooEoFF
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: oAAoBoCoooBoCoooBoCoooooDDooEoooFFEo
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: oAAoBoooooBooooooooCoooooCoooDoooooD
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


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

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


Board size: 6x6
Board: AAoBoooooBooooooooooCCCoooDDDooooEEE
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: ooBoooooBoooooBooCooDAACooDooCEEDFFF
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: BBBoCoooooCooAAoCoDDDEoFoooEoFoooooF
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: ooooBoooAABoCCCoBoDoooooDoEoooDoEooo
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: oooooooooBoooAABooooooCoDoooCoDoooCo
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: BAACooBooCoooDDoEoFoGGEHFoIJEHFoIJoH
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: oBoooooBoooooooooooCooDooCooDooCAADo
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: oooooooooBBBoooCCCAADoooooDoooooDooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: oooooooBoooooBoCoooooCDoooooDoAAooDo
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: oBoooooBoCoooAACoooooCooDoooooDooooo
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: ooBBBoAAooCoDDDoCooEoFCooEoFoooEoFoo
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: BBBooooooooCDAAooCDEoooFGEHooFGoHooo
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: ooAAoBoCCoDBEoFFDBEGGoDoHIJJooHIoKKK
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: ooAAoBoCCCoBoooooBoDEEooFDGGGHFooooH
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: ooooooooooooAAoBoooCoBoooCoBoooCoooo
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: oooooooooAABooCDoBooCDoBoooooooooooo
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: oooBBBoAAoCooDDoCoEEoFCoooGFooooGFoo
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: BoCoooBoCooDBoCooDoooAADoooooooooooo
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: oBoooCoBoooCoBAAoCoooooooooooooooooo
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: oooBoooAABoooooooooCoooooCoooooCoDDD
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: ooooooooooBooAAoBoCooDDDCEEoFoCGGGFo
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: oooBBBoooooooooooooAAooCDooooCDoooEE
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: oooooBoooAABooCCCooooooooooDDooooEEE
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: ooBoooooBooooooooooCAAoDoCoooDoCoEED
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: BoooooBoooooBooooCAAoooCoooooCoooooo
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: oooooBoooooBoooooooooCoooooCooAAoCoo
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: BCCCoDBEAAoDBEoooooEooooooFoooooFooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv2,A>2
</answer>


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

<think>
Shortest path found.
</think>
<answer>
Cv1,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: oooBBBoooooooAAooCDDDEoCoooEoCoooEoo
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: ooBooCooBoDCooBoDCoAAoDoEoooFoEoooFo
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: oAAoBoooooBoooooBoooooooCCCDDooEEEoo
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: oooooBooCCCBoooooDoooooDooooEoooAAEo
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: AAoBoooooBoooooBoooCoooDoCoooDoCEEoD
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: BCooooBCoDDDBAAooEooooFEooooFoGGooFo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Ev1,A>3
</answer>


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


Board size: 6x6
Board: ooooooBBBoooCCCooDoooooDAAoooDoooooo
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: ooooooooBBBCoAAooCDDoooCooEoooooEooo
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: oooooBoooAABCCoDoBoooDooEEEFFooooGGG
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: BoooooBoooooBoooCoAAooCooooooooooooo
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: ooBBBCoAAooCoooooooDoooooDoooooDEEEo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


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


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


Board size: 6x6
Board: AAooBoooCoBoooCooooDCoEFoDooEFoDooEo
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: ooooooooAAoBooCooBooCoDoooCoDoooooDo
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: oAAooBCooooBCooooBoooooooooooDoooooD
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: oooAABoCDoEBFCDoEoFCGGHoFIIoHJKKooHJ
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: BBBCCCAAoooDoooooDooooEooFFFEooGGGEo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv1,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: ooooBooooCBooAACoooooooooooooooooooo
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: oBCDDDEBCoooEoCoooEFGooHoFGAAHoFGooH
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: ooooooBoooooBAAooCBooooCoooooCDDoooo
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: oooooooooooBooAAoBooooooooooCCoooooo
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: ooBBBoCooooDCooooDCEAAoDoEoFFFoEoooo
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: oooooBooCAABooCooBoooooooDDDoooooooo
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: AAoBoooooBCCoooBoooDooEEoDoooooooooo
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: ooooooooooooooooBoAAooBooooooooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^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: BBBoooooooCoooooCoooooCDoEEEoDoooAAD
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: ooooooooBoooooBoooAAoCoooooCoooooCDD
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: ooAAoBoooooBooCCCooDEFFGoDEHHGooEIIG
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: oooooooooooBCCCooBoooooBooooDooAAoDo
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: oooBBBoCDEoooCDEoooooooFoooooFAAoooF
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: ooooBoCoooBoCoooDoCooEDooooEoooAAEoo
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: oooooBooooCBoAAoCooDEEFoGDHIFoGDHIoo
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: AABoooooBoooCoBDDoCoooEEoooooooFFFoo
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: oooBBBooooooAACoooooCooooooDDooooooo
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: oooBoooCoBoooCAAoDoooEoDoooEoDoooEoo
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: BoooooBCoooooCDoooooDooEFGDooEFGAAoE
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: ooooBoCoooBoCooooDCEAAoDoEoooDoEoFFF
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: oooBoooooBoCoooAACoooooCooDDoooooooo
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: AABoooooBCCoooooooooooDoEoooDoEooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


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


Board size: 6x6
Board: ooAAoBoooooBoooooBooCCCoDDoEoooooEoo
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: oooBooAAoBoooooooooCoooDECoooDECFFFo
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: oAABooCDEBFFCDEBooGGooHoooooHoIIooHo
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: oooBBBoooooooCCCoooooooDooAAoDoooooo
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: BoooooBooooCBoAAoCoooDDDoEoFFFoEoooo
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: oAAooBoooooBCoDEooCoDEFFCooEoooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


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


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

<think>
Shortest path found.
</think>
<answer>
Gv1,A>1
</answer>


Board size: 6x6
Board: oooBCooooBCooDDDCEooFAAEooFGGEoHHHoo
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: ooBoooooBoooAAooCoooooCDoEoooDoEoooD
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: ooooooBoooooBooooCoAAooCoooooooDDooo
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: ooooooooAABooCCoBooDoooooDEoFooDEoFo
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: oBBBooooAACooDooCooDoooooDooEoFFooEo
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: oAAooBoooooBooooooooooCoDoooCoDoooCo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: oAAooBoooooBoooooBooooooooooooCCoooo
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: BoooooBoooooBooCoDoooCoDooAAoDoEEooo
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: oooooooooBoooAABooooooCCDDoEoooooEoo
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: oooBBBoCCCooAAooDooEFGDHoEFGoHoEFGoH
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: AAoBoooooBoCDDoooCooooooooEEEooooooo
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: ooBoooAABoooooBoooooooooooooCCoooooo
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: AAooBooCCCBoDDooBoEFFooGEooHHGooIIoG
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


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

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


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


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


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


Board size: 6x6
Board: BCDDDoBCoEooBCoEoooooEoFoAAooFoGGGoF
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: ooBoooooBoooooBoCoooAACooooooooooooo
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: oooooBoCCCoBooooooDEooFoDEAAFoDEoooo
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: AAoooBCCoooBoooooBoooDoooEoDoFoEoooF
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: BAAoCoBoooCoBooooooDDoooEFFFGGEoHHHo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,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: ooooBoAAooBooCCooDoooooDoooooooooooo
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: BBBoooooooCooAAoCooDooCooDoooooEEooo
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: oAAoBoooooBCoDDooCEEEoooFFFGGGoooooo
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: AAoooBoooooBooCCCBooooooDDoooooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


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

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


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


Board size: 6x6
Board: ooooooAAoooBoCCCoBDoEEooDoooFFDooGGG
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: ooBoooCoBooDCoBooDCoEAADooEoooooFFFo
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: ooooooooooooooooBoooAABoCCoooooooooo
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: ooBAACDoBooCDoBooCDoEFFooGEooooGEooo
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: oBoCCCoBoDoooBoDooooooEoFGAAEoFGooEo
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: BoooooBoooooBooooooooAACoooooCoooooo
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: oooooooAAoBoooooBoCDDoBoCoooooCooooo
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: oooBCooDEBCFGDEBoFGDAAoHGoooIHoJJoIo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Hv1,A>2
</answer>


Board size: 6x6
Board: oBoCDooBECDFooECDFooEAAFooGHHoooGIII
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: ooAABoooooBooCCoooDDooEoooooEoooooEo
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: oooooBCDDDEBCAAoEoCooFFFGGooooHHIIJJ
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: oBCooDoBCoEDFoAAEoFoGGooooHIIJKKHooJ
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: oooBBBooCCCDoooAADooEFoDooEFooGGoFoo
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: oooBBBooooCooooDCoEAADooEoFoGGEoFHHo
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: oooooooBoCoooBoCoooAAoDoooooDoooooDo
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: oooooooAAooBoooooBooooooooCCoDoooooD
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: oooBooAAoBooooCBooDoCoooDoCoEEDooFFF
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: ooooBoooAABooCoDoooCEDoooCEoooooEooo
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: oooAABCCCooBooDDDoEFoGGGEFHIJJEFHIoo
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: BoooooBooooCBoAAoCoooooooooDDooooooo
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: ooooBoooooBooAAoCoooooCoooooCooooooo
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: ooBoooooBoooooooooooAAoCoooooCoooooC
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: ooBoooooBoooooBAACoooooCoDDooCoooEEo
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: oooBBBoAACoooooCoooDoCoooDoooEoDoooE
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


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

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


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


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


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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Bv2,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: ooooooBBBooooooooCDEoAACDEooFCDEooFo
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: AAoBoooooBCoDDEoCoooEFFoGGoHHHoooIII
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


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


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


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


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


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


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


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


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

<think>
Shortest path found.
</think>
<answer>
F^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: oBBBoooooooooooCoooooCoDoooooDoooAAD
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


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


Board size: 6x6
Board: oooooooBBBoCoDDDoCAAEooooFEooooFoGGG
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: AAoBoooooBooCoooooCDoEEECDFFoooDoooo
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: oooBBBoooCCCoAAoDooEEEDoooFoDoooFooo
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: ooooBoooooBoooCooDooCAADoECooooEoooo
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: ooBoooCoBoooCoBoooDDDoooooAAEoooooEo
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: oAAooBoCooDBoCooDooEoFDGHEoFoGHIIIoo
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: ooAAoBCCoDDBoEEoFBGooHFoGIIHFoGJJKKK
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: oAAooBCooooBCooooBooooooDEEoooDooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


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


Board size: 6x6
Board: oBBBoooAAoCDEoooCDEooooDEooFFFoooooo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,F<1,Cv1,A>3
</answer>


Board size: 6x6
Board: AAoBCooooBCoDDooCEFGHHoEFGoooEFooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: ooBBBCooooDCooooDCAAooDoooEEoFoooooF
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: ooAAoBoCCooBDDDEoBFFGEHHIIGJoKoooJoK
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^1,H<1,Bv1,A>2
</answer>


Board size: 6x6
Board: oooBoooAABooooCCDoooooDoooEEEooooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<1,Bv2,A>3
</answer>


Board size: 6x6
Board: AABoCoDoBoCoDoooooDoEoooooEFFFooEooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: BoooooBooooooooooooooCDEoAACDEoooCDE
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: oooooBAAoooBoooCCCDoooooDoooEoDoooEo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<1,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: ooBoooAABoCoDoBoCoDoooooDooooooooEEE
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,Bv1,A>4
</answer>


Board size: 6x6
Board: oBBBoCooAAoCoDDooCoooooooEoFFFoEGGGo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F<1,Cv2,A>2
</answer>


Board size: 6x6
Board: BooooCBooAACBDDDoCEEoFFFGoHIIoGoHooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: oAAooBCCoDDBEooFFFEoGGoooooHoIoooHoI
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F<1,Bv1,A>3
</answer>


Board size: 6x6
Board: ooBBBoooooCDooooCDooAACooooEEEooooFF
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: ooooooooBoCDooBoCDooAACDooooEEoooFFo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: ooooooooooooooooBooAACBDEEoCBDooFFFo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: oBBBoooooooooCCCoDAAooEDoFFoEDoGGoEo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^2,E^3,A>4
</answer>