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: AAoBoooooBooooooooooooooCCooooooDDoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: ooAAoBCDoEEBCDFFooGHoooIGHJJJIGKKKoI
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: oAAooBoooCCBoooDoBEEEDFoooooFoooooFo
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: oooAABooooCBoDDoCBoEEoCooooFoooGGFHH
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: ooooooooooooooooooBAAoCoBoooCoDDooCo
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: BBBoooCooDDDCooooooooEoooooEoFoooAAF
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: ooooooooooooooAAoBCoDDoBCooooBCooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


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


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

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


Board size: 6x6
Board: AABoooooBooooooCCCDDEFFoooEoooooEooo
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: ooBCCCooBDooEoBDooEoooFoAAooFoGGoooo
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: oooBBBoAAooCoDEEoCoDoooCoDFFFooooooo
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: oBBBoCAAoooCoooDooooEDooooEDooooEFFF
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: oooooBoAAooBoooCoooooCoooooCDDoooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


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


Board size: 6x6
Board: oooBBBoCDooooCDoEooCDoEoooAAEoFFoooo
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: ooBCCCooBooooooAADoooooDoooooooEEEoo
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: ooooooooBoooooBoooAABoooCCCooDoooEED
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: oAAooBoooooBCoooooCoDoooooDoooooDooo
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: ooAAoBoooooBooCCoBDEEEooDoooooDoooFF
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: oooooooooooBoooAABCoDDEBCoooEoooooEo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


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

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

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

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


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

<think>
Shortest path found.
</think>
<answer>
Ev2,A>1
</answer>


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

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


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


Board size: 6x6
Board: oBBBoooooCoooooCoooDoCoEoDoooEoDAAoE
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: AAoBooCCoBDEFooBDEFGGoHoFoooHIooooHI
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: BoAACoBDooCoBDoECooooEoooooFGGHHoFoo
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: oooooooooooooAAoBoCoooBoCoooooCooooo
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: ooBBBoooAAoCoooooCoDEFFoGDEHHHGDoooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


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


Board size: 6x6
Board: ooooooooBAACooBDoCEooDooEooFFoEooooo
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: oBBBooooooCoooAACoooDDDEoooooEoFFooE
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: ooAABoooooBoooooooooooCCoDDDEFooooEF
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: BoooooBoooooBooooCoooooCAAoooCooDDDo
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: oBoAACoBDDoCoBEEFoGGoHFIJJoHoIooKKKo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


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

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


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

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

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


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

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


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


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


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


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


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

<think>
Shortest path found.
</think>
<answer>
D^3,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: ooooooooooBoooooBoAAooBooooooooCCCoo
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: ooooBoooooBoooooooooooooCCCoDooAAoDo
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: oooooooooooooooBBBoooAACoooooCDDDooo
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: ooBCCCAABooooooDDoEFooGoEFHHGoEFIIIo
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: oAABoooooBooooooooCCCoDoooEEDoooooDo
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: oooAABoooCCBoDDDoBEoooooEooFFoEGGHHH
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: ooooBoCoAABoCoooBoooooooDoooooDEEooo
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: oooooooooooooooBBBooAACoDDDoCooooooo
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: oooooooBCDDDEBCoooEFoooGEFAAoGoFoHHH
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


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


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


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


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


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

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


Board size: 6x6
Board: oooBoooAABooooooCCoooooooooooooDDooo
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: ooooBoooooBoCCCooooooDoooooDoooAADoo
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: ooooooBoooooBooAACBooooCooooooooDDDo
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: BBBoooooooooooooooAAoooCooooDCEEooDC
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: oooooooooooooAABooCDDBEECoooFoCoooFo
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: ooooooooBBBooCDooEFCDoGEFoooGEFoAAGo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: AAoooBoooooBooooooCoooooCoooDDCooooo
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: oooooooooooBCooooBCAADooCooDoooooEEo
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: oooooBooCAABooCooBooCoooooooDoooooDo
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: BBBoooooooooAAoooCooDooCooDooEooDooE
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: oooooooBBBCoooAACooDDoCoEoFFooEooooo
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: oooooooooooooBBBCoooAACooDDoCooooooo
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: BBBoooooooooooooooCooDooCooDooCAADoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


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

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

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


Board size: 6x6
Board: ooooooooooooAAooBoooCoBoooCoooooCooo
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: oooBBBCCCoooooDoooooDEooooDEoooAAEoo
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: oAABoooooBCCDoooooDooEEEDooooooFFFoo
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: BCoDDDBCAAoEBCoooEFoGGoEFHHHooFooooo
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: ooooooooooBooAAoBoCDooooCDooooCDoooo
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: ooooooooooooAABoooooBCCCDDDoEoooooEo
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: ooooooBCoDooBCoDooBooDEooAAoEooFFoEo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


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


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


Board size: 6x6
Board: ooooooooooooBCooooBCAADoBCooDoooooDo
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: oooooBoAAooBoCCooBoooDDooooooooooEEo
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: oooBBBoooCooAAoCooDDoooooooooooooooo
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: oooBooAAoBooCDDBEECFoooooFooGGoFHHII
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: AAoooBCoDDDBCoEEFBGGGoFoHHIIFJKKKooJ
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: oooooBCDoooBCDEoFBCDEGFHooEGoHAAoGoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: ooooooooooooAABoooooBCCDoooooDoooooD
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: oooooooBoooCoBAAoCoBooDDooooooEEoooo
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: oAABooCooBooCDooEEoDFoGGoDFHHHooFIII
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: oooooBoooAABoooooooooCCoDoooooDooooo
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: oAAoBoooooBooooooooooooCoooooCoooDDD
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: AAoBoooooBCDEFFoCDEGHHCDEGIJJJoGIKKK
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: BoooooBCCCDoAAooDoEEFFFoGGGooooooHHH
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: oBoooooBoooooBooooAAoCoooDoCoooDoCoo
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: oooooooooooooAAoBoooooBCoDDooCoooooo
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: oBoooooBoooooooCCCooDEooooDEooAADooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


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


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

<think>
Shortest path found.
</think>
<answer>
Dv1,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: ooAABoooooBoooooBooooooooooooooCCDDo
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: AAoooBoooCCBDEEFGBDooFGoHIIIJJHKKKoo
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: ooooooooooooooooooAAooBooCCCBoooDDoo
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: oooooBCooooBCDDDEBCAAoEoFFGHHHooGIII
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: oooooooooooooBoooCoBoAACoooooooooooo
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: oooooBoooooBCoooooCoAAoDCooEoDoooEoo
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: ooooooooooBoAAooBoCoDoEECoDoooooFFFo
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: ooooooAAoooBoooCCBoooooBooooooooDDoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: BBBooooooooCAAoooCoooooooooooDoooooD
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: ooooBooAAoBoCoooooCooDooCEEDoooooDoo
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: oooooooooBoooooBoooAAooCoooDoCoooDoC
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: ooBBBoooAACoDDDoCooEEFoGooHFIGJJHoIG
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: ooooooAAooBooCCCBoDooEBoDooEoooooEoo
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: oooBoooooBoooooooooAAoCoooooCooooDDo
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: oooooooBooooCBooooCBoAADCooooDoEEEoD
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: ooooooBooCooBAACooBooDDDoooEEEooFFoo
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: oooooooooBBBoooooooCDDDEFCAAoEFCoGGG
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: oooooBoCoooBoCooooooooooDoooEoDoAAEo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: BCCCooBoDDDoBoAAoEoFFFoEoGGooEoooHHo
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: oAABooCDDBoECooooEoooFFFoooGHHoooGoo
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: oBBBooCoooooCoDDDEoFGAAEHFGooEHFGoII
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: ooooooBoooooBAACooBooCoooooCooooooDD
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: BoooooBooooooCCCDoooooDoooAADooooooo
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: BBBoCoooooCoDDDoCoEAAooFEooooFEooooF
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


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


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

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


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


Board size: 6x6
Board: BBBooooooCooAAoCooDooCooDoooEEDooooo
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: oooooooooBoooAABoooooBCCooooooDDDooo
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: BBBoooooooCDooooCDAAooCooooEEEooFFoo
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: BBBooooCCCoooAAoDoEEFFDoooooooGGGHHH
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: ooAABoCCoDBooEFDoGoEFooGHEFooGHooIII
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: oBBBoooCAADoECooDFECGooFoHGIIooHGJJJ
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: oooooooooooooBCooooBCooDoBEEEDAAoooD
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: oooBBBoCCCoooAADoooooDEFGoooEFGoooEo
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: ooAABoooCoBoooCDBooEFDoooEFDGGooFooo
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: oooooooooBBBooAACoooDECoFGDECoFGoEoo
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: AAoBoooooBCoDDDBCoEoooFFEooGGGEoHHoo
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: oooooooBoAACoBDooCooDooCoEoFFooEooGG
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: ooooooAAoBooCCoBoooooBoDoooooDoooEEo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


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


Board size: 6x6
Board: oooooooooBoooooBooCooooDCooAADCooooD
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: BooooCBoAAoCDDDooCEoooooEoooooEFFFoo
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: ooooBooAAoBoooCoooDoCEooDoCEoFDooEoF
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: oooBBBoooooCAAoooCoooooCDoooooDooooo
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: BooCCCBAADooBooDoooooooooEEFFFoGGooo
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: oooBBBCooDooCooDooEooDoFEoAAoFoooooF
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: oBBBooooCCCoAAoooDEooooDEoooFFEoGGoo
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: oooooooBoooooBooooooooCoooooCoooAACo
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: BBBoooooooooooooCoAAooCoooDoooooDooo
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: oooAABoCCooBooooooooooDDoooooooooooo
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: ooooooooooooooBooCooBooCDoAAoCDooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


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


Board size: 6x6
Board: oBBBoooAAoCoooooCoooooooooooooooDDDo
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: ooooooooooBoooAABoooCDBEooCDoEooCooE
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: AAooBooCCCBoDDDoooEooooFEoGGGFEHHooF
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: ooooooooooooooAAoBoooooBooCoDDooCooo
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: ooooooBBBooooooooooooAACDEEooCDFFooo
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: ooooooooooooooBBBCooAAoCoooooCoooDDD
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: ooooooooBoooooBCCCooAADoooooDoooEEoo
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: oooooooAAoBoooooBoooooooooCooDooCooD
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: ooooooAAoooBCCDDoBEFGHHoEFGoooEFGooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: oBoooCoBoAACoBDDoCEEEooooFooGooFooGo
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: ooooooAABooooCBDDDoCoooooCEoooooEooo
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: BoAAoCBoDDECFFFoEooGGoEooHoIIIoHooJJ
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: ooooooooAAoBoCoooBoCDoEBooDFEoooDFEo
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: oooooBoooCoBoAACoooooCDDoooooooooooo
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: oooooooAAooBoooooBCDoEEBCDoFGoCDoFGo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


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

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


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

<think>
Shortest path found.
</think>
<answer>
Bv3,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: AABoooooBCCDoEBoFDoEooFooooooooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


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


Board size: 6x6
Board: oooooooooooooAAooBooCCoBoooDDDoooEEE
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: ooooooooooBooAAoBooCooBooCDooooCDooo
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: ooBBBooooooCoooooCDAAooCDooEEEDFFGGG
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: ooooooBoAACoBoooCooDDDCooooooooooEEo
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: ooooooBCoDooBCoDoooCEoooAAEoooooEooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^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: oBCooooBCDDDoBCooooAAoEooFFFEooooooo
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: oooooooBoooCoBoooCoBooooooDoooAADooo
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: oooooooooBoCoooBoCoooAACDoooooDooooo
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: ooooooBoooooBooooooooooooooAACoooDDC
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: BBBooooooooCooAAoCoooooDoooooDoooooD
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: BBBCoooooCoooAAooDoooooDEEEooooFFooo
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: ooooooooooooBooCooBooCooooDCooAADooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


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


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

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


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


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


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

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


Board size: 6x6
Board: oAAooBCCCooBoDoooBEDooFoEGGoFoEoHHFo
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: oBBBoooooCCCooooooooooDoAAooDooEEFFF
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: BBBooooCooDEoCooDEFCoAAEFooooGFooooG
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: oooooBoooAABooooooCCCooooDDEEEoooooo
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: oBBBooAAooCooDDDCooooECooFFEoooooEGG
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: oooooooooooBCAAooBCDDoEBoFFoEoooGGEo
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: oooooooooooooAAoBoCCooBDooEoBDooEooD
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


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

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


Board size: 6x6
Board: oAAooBooooCBoooDCoooEDFoooEoFoGGGooo
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: ooBoooooBCCCooBoooooooDEoFooDEoFAAoE
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: oooooooooooooooooBAAoooBooooCCDDoooo
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: oooooooooAABoCoooBoCooooooDDoooooooo
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: oooooooBoooCoBoAACoBoooooooooooooooo
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: ooAAoBoCCooBoDooooEDoooFEDGGGFEooooF
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: oBCCCooBoooooBoooDoEoAADoEFFoDoEooGG
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: ooooooooAABooCooBooCooBooDEooooDEooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: oooBoooAABooCCoBoooooooooDDooooEEEoo
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: ooooooooooooooBoooooBooCoAAooCDDDEEE
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: AAooBoooCCBoooooBooooooDoooooDoooooo
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: BoooooBoooooooooooCAAooDCooEoDCooEoD
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: oBoooCDBoEoCDBoEooooFFFooAAooGoooHHG
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


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


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

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


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

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

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


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


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


Board size: 6x6
Board: oooBBBoooCCCoooooooooooDEEEoFDAAooFo
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: oooooooooBoooCoBoooCoBoDAAoooDoooooD
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: oooooooBBBooCAAoDoCoooDEoooooEooFFFE
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: oooBooAAoBoooCCBDDoEoooooEoooooEoooo
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: AAoooBoooooBoooCoooooCDEFGGoDEFoooDE
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: AAoBoooooBCoDDDoCoooooEEooFFoooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


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

<think>
Shortest path found.
</think>
<answer>
Bv3,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: ooooBoooooBCDEooBCDEoFoCGEoFooGAAFoo
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: oBooooCBooooCoooooCooooDoooooDoAAooD
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: ooBoooAABooooooCCCDDooEEoooFFFoooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: oooBoooooBCDoooBCDAAooCoooooooooEEEo
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: ooooooooooooAAoBooCooBooCDooooCDoEEE
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: oooooBCooAABCoooooCooooooooDDDooooEE
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: oooAABoCCooBoDDooBoooooooEEFFooooooo
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: BCooooBCDooooCDoEooAAoEooooFFFoooooo
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: oBCDDDoBCoEFGoooEFGHHHEooIoooJoIoAAJ
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
J^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: AABooooCBoooDCoEEEDCooooFooGGoFoooHH
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: ooBoooCoBooDCoAAoDoooooDoooooooooooo
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: ooAABooCCoBDEEEoBDoooooDFFGGoooooHHH
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: oooooBooooCBooooCBoAAoCooooDDDoooooo
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: ooooooooBoooooBoooAABooooCCoooooooDD
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: oooooooooBoooAABooCDoEEoCDooooCooFFo
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: ooAABoCoooBoCoDDBECooFoEoGoFoEoGoFHH
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


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


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

<think>
Shortest path found.
</think>
<answer>
Bv3,A>1
</answer>


Board size: 6x6
Board: ooBoooooBooooAAoCooooDCooooDoooooDoo
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: AAoooBoooooBoooooBoCCDEooooDEooooDEo
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: oBBBoooooooooooooCoooooCAADoooooDooo
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: ooooooooBoooAABoooCoooooCoooDDEEEooo
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: ooooooooooooooooBoooAABoooooCCoooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^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: oooooooBBBooAAoooCDooooCDEooFoDEooFo
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: ooooBoAAooBoooooBoooooooooooooooCCDD
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: ooooooBoooooBoAAoCDoEEoCDFFFoCDGGGoo
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: oooooBoAAooBoooooBoCDDDooCoEoooCoEoo
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: ooooooooooooooooooBBBoCoooAACoooDDoo
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: ooooBoooooBooooCooDooCooDAACooDooooo
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: oBBBoCoooooCoooooCAAooDooEEoDoooooDo
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: ooooBooCCCBoDDDoBooooEooAAoEoooooFFF
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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

<think>
Shortest path found.
</think>
<answer>
Cv3,A>4
</answer>


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

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


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

<think>
Shortest path found.
</think>
<answer>
Dv2,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: ooooooAAoBoooooBoooCCooooooooDoEEEoD
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: ooooooBBBooooooCooDEoCFoDEAAFooEooFo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: oooBBBoAAooCDDEooCFFEGHCoIoGHooIooHo
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: BBBooooooooooooooCooAAoCoooooCoDDooo
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: oBoooooBoAACoBoooCooDDoooooooooooEEE
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: ooooooooooooBoCoooBoCoooAACooooooooo
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: oooooBoAAooBooCooBDECoooDECoooDEoFFo
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: oooBBBCooDDDCoAAoECFGoHEIFGoHEIFJJHo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


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

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

Board size: 6x6
Board: oAAoBoooCCBoDDDEBFGHoEoFGHIIIJGHKKoJ
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: oooBoCoooBDCAAooDoooooooEEooooooFFoo
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: oBBBooooooCooAAoCooDDDoEoFFFoEGGGooE
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: ooAAoBoooooBoooooBoooooooooCCCoooDDD
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: oooBBBCooooDCooEoDooFEooooFEooAAFooo
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: oooBBBCCCoooDoAAEoDFFGEHoIIGEHoooGoH
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Cv3,A>4
</answer>


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


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


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


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


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

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


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


Board size: 6x6
Board: oBoooooBoCCCoooAADoEEEFDGHHHFDGoooFo
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: ooBAACDDBEoCFGGEoCFooEooHHHIIIJJKKKo
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: ooooBooAAoBoooooBoCoDDooCEooooCEoFFF
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: ooooooooooooooAAoBooCooBooCoooooooDD
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: oooooooooooBoAAooBooooCoDDEECFoooooF
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: BoooooBoooooBoooooooooCoooAACoooDDCo
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: oooooBooAAoBoCCDDooooooooooEEEoooFFF
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: ooooooooooooooAAoBCCCooBoooDoooEEDFF
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: oBoooooBoooooBoooCoooooCAAoooCDDooEE
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: oooooooooBoooAABoooooBCCDoooooDooooo
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: oBoooCoBAAoCoooooooooDDooooooooooooo
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: AAoBoooooBoooooBoooooooooooooooooCCC
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: ooAABoooooBoCCDoBooEDFoooEDFGGHHoFoo
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: AABoooooBoCCoDBooooDoooEoFGHoEoFGHoE
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


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


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


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

<think>
Shortest path found.
</think>
<answer>
C^3,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: BoCDooBoCDooBoCooooooooEAAoooEoooooE
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
B^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: ooooooooooBoooooBooAAooCoDDooCoooooo
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: oooooBAAoooBoCCoooooDoooooDEEEoooooo
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: oooooooBooooCBooooCBoooDoEEEoDAAoooD
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: BoooooBooAACoooDECFFoDECoooDEooooGGo
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: ooooooooooooooBoooAABooooooCoDoooCoD
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


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


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

<think>
Shortest path found.
</think>
<answer>
Cv3,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: oBAAoCoBoDoCoooDECooFDEoGHFIIIGHFJJJ
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: oooBoooCoBoooCoBooooAAoDEooooDEooooD
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: AAoBooCCoBDDoEEoFoGHIIFoGHJJFKoooooK
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: oooooBoCAAoBoCoDDoEEEooooFFFooGGGHHH
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: oooooooooooooBBBooCooAADCooooDCooooD
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: oooBBBoooooooCoooooCoooooCoooDoooAAD
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: oooooooooBoooAABoooooooCoDDooCoooooC
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: ooooooBCooooBCoooDBooooDoooAADoooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


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

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


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

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


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


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


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

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