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


Board size: 6x6
Board: oooBBBoCoooooCoooooCoooDoEoooDoEoAAD
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: oooooooooAABCDDooBCooooooEooFooEooFo
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: ooooooAAoBoooooBCCoooBoooooooooDDooo
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: oooooooooooBoCoooBDCoAABDooEEoDFFooo
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: oAAoBooooCBDoEECoDFGGCHHFIIJJJFooKKo
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: oooBBBoooCCCoooooDoooooDooooEooAAoEo
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: ooAABoCCCoBoooooooDDDEFFoooEoooooEoo
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: oAAooBooCCCBoDDoEoFFFoEoGGHHIIJJJooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


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

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


Board size: 6x6
Board: oooBBBoAAooCDooEECDooooCoooFoooooFoo
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: oBBBooooooooooooCooDAACooDooCooDoEEE
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: BooCCCBoooooBooooooooooDooAAoDoooEED
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: ooooBoAAooBoooooBoooooooCCooooDDoooo
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: oAAooBCCDDDBoooooBEooFooEooFooEooFoo
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: AAoooBoooooBoooCCBooooooDDDooooooooo
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: ooooooooooBoooAABooCooDEoCooDEoCoFFE
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: BooCCCBoooDoooAADoooooDooooooooooooo
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: oooooooooooooooBoooooBoCoooAACoooDDC
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: ooooooooAAoBoCCooBDoEFooDGEFHHDGEFoo
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: AAoBoooCoBoooCoBDDoEEooooFFFoooooGGo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


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


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

<think>
Shortest path found.
</think>
<answer>
Gv2,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: oooBBBooCoooAACoooooooooDDDoEEFFFooo
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: oooBoooooBooooooooCoooooCooooDooAAoD
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: oooooBoooooBCCCooBoooooooooDooAAoDoo
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: oBBBoooAAooCoDDEFCGGGEFCHHooFooooIII
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: ooooooooBBBooooAACoooooCDDoooooooooo
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: oooooooAAoBooCCoBooooooooooooooooDDD
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: oBBBoooCDDDooCoooEoCoAAEoooooEoooooo
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: ooooooBoooooBooCooAAoCoooooCoooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


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

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

Board size: 6x6
Board: ooooooBoooooBooAACoDoooCoDoooCoDoooo
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: oooooooBoooooBooooCBooDoCoooDooAAoDo
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: BoooCoBDooCEBDoAAEFoooooFGoHHHFGoooo
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: oBCooooBCAADoECooDFEGGGoFoHHooFIIIJJ
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: BBBCCCoDoEEEoDAAoFGooooFGooHHFGoIIIo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


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


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


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


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


Board size: 6x6
Board: BBBoooooooooooCCCoooDDDEoAAooEFFoooE
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: AAoBooCooBooCooBooDDDoooooooEEoooooo
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: oooBooAAoBooooooooooooooooCCoDoooooD
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: ooooooooooBoooooBoCCCDBooooDooAAoDoo
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: oBBBooooooooooooooooooCoAAooCooooDDo
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: oBCooooBCooooBDDDEFFFooEGoAAoEGHHooo
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: ooooooBoooooBoooooCoooooCoAAoDCooooD
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: ooooooooooBoooAABooCCCoooooooooooooo
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: oooooooooooooooooBAAoooBCCoooooooooo
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: oooooBooAAoBCoooooCoooooooooooooDDoo
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: oAAooBooCooBoDCEEooDCFFFGGoHHHoIIooo
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: oBooCooBAACoooooCooooooooooooooooooo
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: BBBooCoDAAoCoDoooCoDoEoooooEooFFoooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


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


Board size: 6x6
Board: oooBooAAoBooCoooooCooooooooDooEEoDoo
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: oBAAoCDBEEoCDBooooDFFGGGHooIIIHooooo
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: oooooooBoCoooBoCooDDDCEooAAoEooooooo
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: AAoBoooooBoooooBooooCoooooCoooooCooo
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: ooooooooooooooooBoAAooBooooCBooooCoo
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: BBBooooAACooDDDCooEoFCooEGFooooGFHHH
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: BBBCCCDEAAoFDEGGHFDoIIHoJoKKKoJooLLo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


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

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


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

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


Board size: 6x6
Board: BoCoooBoCoooooCooooooDooAAoDoooooDoo
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: oooBoooooBooAACooooDCooooDCooooDoEEE
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: ooooooBBBooooooCCCoooAADEFFooDEoGGoo
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: ooAABoooooBoooooBoooooooooooCCooDDoo
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: oooooooooooooooBoooCoBDooCAADoooooDo
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: oooooooooBBBCCCooooDoooooDoooEoooAAE
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: BoAACoBoDDCooEooCooEoFoGHHHFoGoooFoo
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: ooooooBooooCBoAAoCoooooCDDoooooEEEoo
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: ooooBoooooBoAAooBoCDoooECDFFoECDoooo
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: ooBoooooBAACooBooCDDoooooooooooooooo
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: ooooBooCooBooCDoBoooDAAEFFFooEooGGoE
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


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


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

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


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


Board size: 6x6
Board: oAAoBoooooBCoooooCoooooCoooooooooooo
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: oooooooooooooBBBoooAAoCoooooCooooooo
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: oBoAACoBoooCoooooooooooooooDDooooooo
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: BAAoCoBoDDCEBooooEFGHoooFGHIIIFGHJJJ
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: BBBoooCDEoFGCDEoFGoAAoFooooHHHoooooo
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: AAoooBoCCCoBDDEFFoGoEHIoGoEHIoGJJHIo
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: BooCooBooCooDooAAEDFooGEDFooGooFooGo
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: ooBBBoooooCoAAooCoooDoooooDoooooDooo
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: ooooBoAAooBoooooBooCCCoooooooooooooo
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: BBBooooooooooooooooCCCDooEooDooEAADo
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: ooooBooAAoBooCCCBoDDDooooooooooooooo
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: oooBooooCBooooCBDoooAADoEEoooooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


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


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


Board size: 6x6
Board: ooooooBBBooCoooooCoDEAACoDEooFoDEooF
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: oBoooooBooooooCoooooCooDooCAADoooooD
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: oooooooAAoBoooooBoooooooooooCoooooCo
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: oBoooCoBoAACDBooooDoooooDooooooooooo
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: BoooooBoooooBooooCoooAACDDoooCoooooo
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: oooBBBCCCoooooooooooooooooooDooAAoDo
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: ooAAoBoooooBooooooCoDDDoCoooooooEEoo
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: ooooooBooCooBooCoooooAADoooooDoEEEoD
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: ooBoooooBooCooDDDCoAAooCEEEoooooFFoo
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: oooBBBoCoooooCAADoECFGDoEHFGooEHoIII
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: BBBooooooAACoooooCoDDoEooFFGEooooGEo
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: oooBBBooCoooDoCoooDoCEooAAoEooooooFF
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: ooooooAABoooCoBoDDCEooFooEooFooEoooo
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: oooBBBAAoooCoooooCDoooooDoooooDooooo
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: ooooooooooooooooooBoooooBoCooDooCAAD
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


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

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

Board size: 6x6
Board: oooooBoooooBoooooBooAACooDDoCoEEEooo
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: BBBoooooooCoooAACoooDDDoooooooooEEoo
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: ooBCCCooBooooDooooEDoooFEDoooFEAAooF
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: oooooBoooooBooCDooooCDoEFGoAAEFGHHII
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: BoooooBooCCCBoAAoDEEFFGDoooHGDIIIHGo
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: oAAoBooooCBoDDoCooEFFCooEooGGGEHHooo
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: oAAooBCCoooBoDDDooEEooFoooooFooGGoFo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


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

<think>
Shortest path found.
</think>
<answer>
F^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: oooooooBoooooBoooooooooCoAAooCoooooC
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: oooooooooooBCooAABCoooDoCoooDoooooDo
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: oooBooAAoBooCCooDDEEooooooFFFooGGGoo
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: oooBBBooooooooooooooCCCooAAooDooEEoD
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: ooooooAABoooooBoooCoBoooCooDEECooDoo
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: ooBBBoCDDDooCoooEoCAAoEooFFooooooooo
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: oBoCCCoBDooooBDoooooDEoooAAEoooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


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

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


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

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

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


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

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


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

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


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

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


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


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


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

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


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

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

<think>
Shortest path found.
</think>
<answer>
Gv2,A>2
</answer>


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

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


Board size: 6x6
Board: ooAABoCCooBoooooooDDoEoooooEoooooEoo
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: ooooooAAoooBCooDDBCoooooooEoooooEooo
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: BBBoCoooooCooDoooooDoooEooAAoEoFFFoE
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: ooooooooooBCoDDDBCoAAoBooooEoooooEoo
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: BBBooooooooooAAooCooooDCEEFFDooGGGoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


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

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

Board size: 6x6
Board: ooooBoAAooBooooCBooooCoooooCoooooDDD
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: BoooooBAACoooooCoooooCDEoFooDEoFooDE
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: oooAABoooooBCCCooooooDDDoooooooooEEE
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: ooAAoBooooCBooooCBooDoEoooDoEoooDooo
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: oBBBoCDDDEoCoFoEGCoFAAGoHFoIIIHJJJoo
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: ooooooBooooCBooooCBoDAACooDoooEEDFFF
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: oooooooooBBBoooCCCDoooooDEEEoFDoAAoF
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


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

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


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

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

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

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


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


Board size: 6x6
Board: ooooooBoooooBCooooBCoooDoCoooDoooAAD
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: oooooBoCAAoBoCooDooCooDooEEoDooooFFF
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: oAAoBoooooBooooooooCoooooCDDDooCoooo
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: ooooooBBBooooooooooooCooAAoCoooooCoo
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: BAAoCoBoooCoBoooCooooooooDoooooDoooo
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: ooooooooBBBCAAoooCDEEoFGDHHHFGDoooFG
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: ooooooAAoooBCCCooBDDoEEBFFGGoooooHHo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: oooooooooooBoAAooBCCoooBoooDoooooDoo
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: BoooooBooooooooooCDEoAACDEooooDEoooo
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: BoAAoCBoDDDCBoEEoCFFooooGGHHHIooJJoI
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: AAoBooCCCBDooooBDoooooDoooooEEoooFFF
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: AAoBoooooBoooooooooCDEoFoCDEoFoCoooF
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


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

<think>
Shortest path found.
</think>
<answer>
Cv2,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: ooAAoBooCCDBEoooDBEFGoDoEFGoHHoFoIII
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: ooBAACDoBooCDoBooCEFoGGoEFHHHoEIIJJJ
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: ooooooooBoooooBCCCAABooooDDoEEoooooo
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: oooBooCoDBoECoDooECoDAAEoFGGHHoFoooo
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: ooooooooBCoDooBCoDAAoCoooooooooooEEE
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: oooooooooooooooooooooAABooCCCBoooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: ooooBoooooBooCoooooCooDoAAooDooooooo
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: oBBBoooAAooCoooooCoooDEooooDEooooDoo
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: oooBoooooBooAAoBooooCooDooCooDooCooD
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: AAoBoooooBooooooooooCCCoDDDoEooFFFEo
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: ooooooooooBoooooBoooAABoCooDooCooDoo
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: oooAABCDEEoBCDooooCDFFGooHHHGooIIoGo
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: ooooooAAoBoooooBooooCoooooCDDoooCEEE
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


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

<think>
Shortest path found.
</think>
<answer>
Dv2,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: ooBBBooooCCCDDDEEEoooooooFFFoGooAAoG
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: oooooooBoCCCoBoAADoBoooDoooooDoooooo
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: BooAACBooooCooooooooooDEFFFoDEooooDE
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: oBCCCoDBEEEoDBAAoFDooooFoooooFoooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


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

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


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

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

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


Board size: 6x6
Board: oooooooooooooBBBoCoooAACoooDoCoooDoo
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: ooooooooooooAAooBoCoDoBoCoDEEooooooo
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: ooBBBoooooooAAoooCoooooCoooDDCoooooo
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: BBBooooooooCDoAAoCDEFFFGDEHooGoEHIIG
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: BBBooooooooCoAAooCooooDDooooEoooooEo
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: oBoAACDBoooCDBEFFCGHEIIoGHEJJJGHoKKo
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: ooooBoAAooBoCCooBoDoooooDooooooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: oooooooooAABooCCCBoDoooooDEoFFooEoGG
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: ooooBooAAoBoooooooooooooooCCoooooooo
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: oooBBBoAAoCoooooCoDEEFCoDooFooDooFoo
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: oooooooooBoCoooBoCoooBoCAADoooooDooo
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: oooAABoooooBoooCCooooDDDoooooooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: AAoBoooCCBooooooooooDoEoFGDoEoFGDoEo
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: oooooooooooooooooooBoooooBoCoooAACoo
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: oAAooBoCCCoBoooooBooDDoooooooooooooo
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: ooooooooooooAABoooooBoooCDDDEoCoooEo
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: AABoooCCBoooooBoooooooDoEoooDoEooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


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


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


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


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


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


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

<think>
Shortest path found.
</think>
<answer>
Hv1,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: oooAABoooCDBEEECDBFGGCDoFooHHHFIIIJJ
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: oBBBooAAoCooDDDCEEFFFCGGHHIoJKLLIoJK
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


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


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

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


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

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


Board size: 6x6
Board: oooooooooBoooooBooAAoBoooooCoooooCoo
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: AAooBooooCBooooCooDDooooooEoFoooEoFo
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: BoooooBooAACDDDEoCoFFEooGGoEoooooHHH
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: oooooooooooBoooooBCCCoDoooAADooEEEDo
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: ooooooBoooooBAAooCBoDooCEEDooCooDFFo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


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


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


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

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


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

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

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

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


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

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


Board size: 6x6
Board: oBoooooBoooCAAoooCDDDEEEFFFoGoooooGo
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: oooooooooBoooAABoooooBoooCCooooooooo
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: oBoAACoBooDCoBooDooooooooEEooFoGGooF
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: ooooooooooBoooAABoCDooooCDooooCDoooo
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: BBBooooooooCoAAooCDEoFFCDEooooDGGooo
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: oooooBAAoooBooooooooCoooooCoDDooCEEo
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: ooooBCooooBCoAADoooEFDoooEFDoooEFooo
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: BoCCCDBAAooDBoooooooEoFoooEoFoGGooFo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: BoooooBoooooBooCoooAACooDoooooDooooo
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: oAAoBooCooBooCooBooooooDoEoooDoEoFFD
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: ooAAoBooCCoBDDoooBooooooooooooEEoooo
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: oooBoooooBoooooBoooAAooCDooooCDooooC
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: BBBooooooooooooooooCAADooCooDooCoooo
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: BoooooBooCCCoooooDoAAooDoEEooooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


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


Board size: 6x6
Board: oBBBooAAooCoooDoCoooDoooooDooooooooo
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: AAooBoooCoBoooCDBEFFoDoEooGGoEoHHoII
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: ooooooooooooBooAACBDEooCoDEooCoDoooo
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: oooAABoCoooBoCoDooEFoDGGEFoDooEooooo
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: ooooooooooooAAoBoooooBoooooooooooCCo
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: ooooooooBBBoAAoCoooDDCoooooooooEEoFF
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


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


Board size: 6x6
Board: oooooBAAoooBoCCooooooooooDDooooooooo
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: oooooooBooooCBooDoCoAADoooooDooooooo
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: ooooooBBBoooooooooCooooDCoEAADCoEooD
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: ooBCCCooBoooooAAoDooooEDooooEDoFFFEo
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: BoAACoBoooCoooooCooooooooooooooDDooo
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: oooBCooooBCooooBCDoooooDooAAoDoooooo
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: ooooooBBBooooCoAADoCEooDooEFGGooEFoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: oAAooBoooooBooooooooCoooDoCEEEDoCooo
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: oooooooooooooooooBooAAoBooCCCooooooo
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: BAAoCoBDooCooDoooooDooooooooEEoooooo
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: oooooooooooooBBBooooAACoooooCoDDDooo
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: oooooBooooCBoDAACooDoooooEEoooooFFoo
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: AAoooBCCCooBooooooDEEFooDooFooDooFoo
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: oooooBoooooBCooDoBCooDooCEEEFooAAoFo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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

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


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


Board size: 6x6
Board: ooBBBooooCCCooAAoDoEoFoDoEoFoooEGGoo
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: ooooooooooBoCoAABoCoooooDDEEooooooFF
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: ooBBBooooooooCCCooooAAoDoooooDoooooD
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: oooooBoAAooBoCCoooDEFFGoDEooGoDEooGo
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: oBoooooBAAoCDDDooCoEFooooEFGGooEFooo
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: oooooooooooooooooBooCAABooCooBooCooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
F^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: oooooBooAAoBoooooBooooooCCCooooooDDo
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: oooBBBAACoooooCoooooCooooooooooooooo
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: oooooBoAAooBooooooooooooooCCDDoooooo
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: ooooooAAoooBooCDDBooCooBoEoooooEFFFo
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: BoooooBoooooBooAACDooooCDooooEoooooE
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: oooooooooooBAAoooBooCooBooCoooooCooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: ooooooooooooooBoooooBoooCoBoDoCAAoDo
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: ooooooBoCoooBoCooooooAADEooooDEFFooD
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: AAooBoooooBooCooBooCooooDEEEooDoooFF
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: ooBoooooBCooAAoCooooooooooDDoooEEEoo
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: oAAooBoooooBCoooooCoDoEEooDoooooDooo
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: BoooooBooooooooCoooooCoooooCoDAAoooD
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: ooBoooooBoooooAACoooDDCooooooooooooo
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: AAooBoooCCBooDDoBoooooooooooooEEEooo
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: oAAooBoooooBoooooooooCCCoDDDEEooFFFo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


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


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

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


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


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

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


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


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


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

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


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

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


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

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


Board size: 6x6
Board: oooBBBoCCCooDoAAoEDoFGHEooFGHooIIJJJ
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: ooAABoCCDoBoEFDoooEFDoooooGGooHHoIII
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: oooooBoooooBoooooBoooAACoooDoCEEoDoo
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: ooooooooooBoooooBoAAooBoooooooooooCC
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: oAABoooooBoooooooooooooooCCoDDoooooo
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: BoooooBooooooooooooCoooDoCoooDoCAAoD
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: oooooooAABoooooBoooCCBoooDoooooDoEEE
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


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

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


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

<think>
Shortest path found.
</think>
<answer>
Gv1,A>2
</answer>


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


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


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


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


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


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


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


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


Board size: 6x6
Board: oooBoooooBoooooBoCAAoooCoooooooooooo
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: oooooBoCAAoBoCooooDCoEooDooEooDoFFoo
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: oAAooBooCCCBoooDDoEFFGGGEooHHHEooooo
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: BoooooBCooooBCoDDDoAAoEoooooEooooooo
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: oooooooooooooooBoooooBoCAAoooCoooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: AABoooCCBoooDoBoooDooooEoooooEoFFFoE
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: oooBBBoAAoCoooooCoooooCooDDoooooEEEo
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: ooooooooooBoooooBoooAABoooCDDEooCooE
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: BoooooBoooooCCCooooooooDooEAADooEooD
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: oAAooBoooooBooCCCoDEoooFDEoooFDEoooF
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


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

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


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

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


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

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


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

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

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

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