You are an expert Rush Hour (4×4) solver.

Input: 16-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: 4x4
Board: BBBoAAooooCoDDCo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 4x4
Board: AAoooBBoCCDDEEFF
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 4x4
Board: BAAoBooCBooCDDDo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 4x4
Board: BAAoBCDDECooEFFF
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 4x4
Board: oAAoBoCCBDDoEEFF
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 4x4
Board: oAAoBoCCBoooDDEE
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 4x4
Board: oAABCCCBDDDoEEoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 4x4
Board: AAooBCCDBEEDFFoo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 4x4
Board: AAoBooCBooCooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 4x4
Board: BCDEBCDEAAooFFGG
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 4x4
Board: BoooBCooBCooAAoo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 4x4
Board: AAooBBCCDDooooEE
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


You are an expert Rush Hour (4×4) solver.

Input: 16-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: 4x4
Board: BAACBooCDDECooEo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 4x4
Board: BAAoBCDDBCEEFFoo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 4x4
Board: BoooBCooBCoDAAoD
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 4x4
Board: oAABCDDBCEEBooFF
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


Board size: 4x4
Board: AABCDoBCDoooEEEo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


Board size: 4x4
Board: oAABCCCBoDDDEEEo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


Board size: 4x4
Board: oooooAABCCoBooDD
Optimal length (moves): 3
Return only the <think> and <answer> blocks.


Board size: 4x4
Board: oBBBooCDooCDoAAD
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


Board size: 4x4
Board: AAoBCooBCoDDEEFF
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D<1,Bv1,A>2
</answer>


You are an expert Rush Hour (4×4) solver.

Input: 16-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: 4x4
Board: oBBBoooCDDDCoAAC
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


Board size: 4x4
Board: AAoBCCCBoDDDooEE
Optimal length (moves): 3
Return only the <think> and <answer> blocks.


Board size: 4x4
Board: oAABoCCBoDDDEEEo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.


Board size: 4x4
Board: oBBBAAoCoooCoDDD
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D<1,Cv1,A>2
</answer>


Board size: 4x4
Board: oBBBAAoCDDoCooEE
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E<1,Cv1,A>2
</answer>


Board size: 4x4
Board: BCooBCoDoCEDAAED
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


Board size: 4x4
Board: oAABoCCBDDoBooEE
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


Board size: 4x4
Board: oooBCAABCoDDCooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


Board size: 4x4
Board: oBBBCoooCAADoEED
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (4×4) solver.

Input: 16-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: 4x4
Board: AAoBoCCBDEEEDoFF
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A>1,D^2,E<1,Cv1,A>1
</answer>


Board size: 4x4
Board: AABCooBCoDoCoDEE
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 4x4
Board: BCCCBooDAAoDoEEo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 4x4
Board: BBBCDAACDoooDEEE
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,B>1,C^1,E<1,Dv1,A>1
</answer>


Board size: 4x4
Board: BBBoCDDDCooEAAoE
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 4x4
Board: oooBAAoBCDDDCEEE
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A>1,C^2,D<1,E<1,Cv2,A>1
</answer>


Board size: 4x4
Board: AABCDEBCDEoCDFFF
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>1,C^1,F<1,Cv1,A>1
</answer>


Board size: 4x4
Board: ooBoAABCoDDCooEE
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D<1,E<2,Bv2,Bv1,A>2
</answer>


You are an expert Rush Hour (4×4) solver.

Input: 16-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: 4x4
Board: BCCCBDDDoAAEoooE
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,B<1,C<1,E^2,A>1
</answer>


Board size: 4x4
Board: BCCCBooDBAADEEoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E>1,Bv1,B<1,D^1,A>1
</answer>


Board size: 4x4
Board: oBBBCDDDCAAEoooE
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<1,Cv1,C<1,E^2,A>1
</answer>


Board size: 4x4
Board: AABCooBCDoBCDoEE
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 4x4
Board: BCCCBDoEoDFEAAFE
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 4x4
Board: BBBoAAoCDEECDFFF
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 4x4
Board: AAoBCCoBDEEEDooo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A>1,C>1,D^2,E<1,Cv1,A>1
</answer>


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: oBAACoBDDCoEEEoooooFGGooF
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BBBoooAAoCDDoECoFFECoGGoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAooooooBoCCoBoDDEoFooEoF
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oooBCDooBCDoAAoEEFFGooHHG
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BoCCCBDooEoDAAEoDFFoooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BAAoCBoooCDDooooEEEFGGooF
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oBoCDoBoCDEBFCoEoFoGEAAoG
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BCAAoBCDDDEEFFFGHHooGIIJJ
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oBAAoCBDDDCEEFoooGFoHHGFo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oAAooBBoCCDDDEoFGGEoFHHoo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: BoAAoBoooCDoooCDEEoCFFGGG
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooAAoBBBooooooCoDDDCooEEE
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oBAAooBoCoDooCoDEoFFDEGGG
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BoAAoBCCCoDEooFDEoGFoEoGF
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooAABoCDDBoCEEoFoGHIFoGHI
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oBoooCBAAoCBDDDoEEFFGGooo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oooBooooBooooCDoooCDAAooD
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAoooBBoCCoooDooEEDooooDo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAAooooBBCDoEECDFFGoHHoGo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: AAooooooBBCCoooDoEEFDGGoF
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BoAACBooDCBEoDooEooooEFFo
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 (5×5) solver.

Input: 25-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: 5x5
Board: oAAooBCDDoBCEEoFGHoIFGHoI
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: ooBCDEoBCDEFBGooFoGoooAAo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooAAoBooCCBDEEooDFFFoGGoo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BBBoooCCCDooAADooEEooFFoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAAooBBCDDooCEoFFFEoooGGG
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BoCCCBDAAooDEEoFoGGGFooHH
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BCDDDBCAAEBCFoEGGFoEooHHo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BAAooBooCCoooDDEEFFFGGHHH
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BoAAoBCCDEFooDEFGGHEIIoHo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooAAoooooBCCCDBEFFDGEHHHG
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooooooAAooBBCDEFFCDEGGCoo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BooooBAAooBCCCDEFooDEFoGG
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: BCoooBCooooAADoEEoDFooGGF
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAAoBoCCoBDDDooEooFFEooGG
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAAooBCoDDBCEFFGGEHoIIEHo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BoCDEBoCDEFoGGGFoAAooHHHo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: AABoooCBooDCoEoDCoEoooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BCoDEBCoDEFCAAGFHIIGFHooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAAoBoCooBoCoDoEEEDoooFFF
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oBAAoCBDDDCEoFFCEGHoIIGHo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAoooBCoDEBCoDEBCFoEooFGG
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: oBAAoCBDDECFFFEoGGHIoooHI
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BooooBCDDDBCAAooEEEooooFF
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BoAACBoDoCBEDFoGEoFHGEIIH
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oBAACoBDDCEoFFoEGHHoEGIIo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BCAAoBCDDEFCooEFoGGoooHHo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oAAooBCoDDBCEFGBoEFGHHooo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: ooBCDEFBCDEFBoDEAAooooooo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oAAooBCCCoBDoEEFDoGGFDooo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooAABoCDoBECDooEFGGGEFoHH
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: ooBCDooBCDoEAAooEoFFGGHHH
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oooBCDEoBCDEoBooAAooFFFoo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: AAooBCDDEBCooEBCooEooFFFo
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 (5×5) solver.

Input: 25-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: 5x5
Board: oBBBooCoDEFCoDEFoAAoFGGHH
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooAABCoDoBCoDooEFFGHEooGH
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: AAooooBCDEoBCDEFoGGEFooHH
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BAAoCBDooCoDEEoFoGoHFoGoH
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BCDDDBCEEEoAAoooFFoGooooG
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oBAAooBoCDoooCDoEECDooooo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BCAADBCooDoEEEoFFGGGHHHII
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BoCCCBDDDEFGHoEFGHooFAAoo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BAACoBoDCEFGDCEFGDoHooIIH
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: AAooooBBoCDDEECFFFoooooGG
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oAAoooBBBooooooooCCCoDDDo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooooooBAAoCBooDCoEEDoFFFD
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: AAooBCCDDBEEEFoGGGFooHHoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAAooBCDoEBCDFEBCoFoooooo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BCDDDBCAAooooooEFGGHEFooH
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BoAAoBoCDEooCDEFGHHHFGIII
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BAACoBoDCEoFDoEoFooooFGGG
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: ooBBBoCCCoDEFoGDEFoGAAooG
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: ooAABCCCDBEFGDoEFGDoEFoHH
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAooBoCCDBEEEDoFFoGGHHoII
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BBBooCDEFoCDEFGCDAAGHHHoG
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oBoCoDBoCoDBECoooEooAAooo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: oooooBoAAoBCCooDDDEooFFEo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAoooBooCDBEECDFFGHHIIGJJ
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BCDDDBCAAoEEFGGHHFoIooooI
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: AABooCCBDooEoDoFEGGoFoHHo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAooBCCDEBFoDEBFoDEooGGGo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooAAoBBCDDoECoFoEGGFoEHHo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooAAoBCCCoBooDEFFFDEoGGDo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BBBoCDEFGCDEFGCDAAGooooHH
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BoAACBDDoCEFFooEoooGHHooG
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: ooAAooBBooCCCooDEFGoDEFGo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BoAAoBCCDEFGoDEFGoHHIIIoo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooBBBoCCCoDAAEoDoFEoDoFoo
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 (5×5) solver.

Input: 25-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: 5x5
Board: ooooooAAoBCCDDBEEEFBoooFo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BCoooBCoooDCAAEDFFFEGGooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAAoooBBBoooCCCDDDEEFFGGo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAooooBBBooCDEEoCDFFooooo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oBAAooBCoDooCEDoooEDFFGGG
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAAooBBooCDDooCEEFFCGGGHH
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BCAAoBCoDEBCFDEoGFDooGoHH
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oooooBCDooBCDEooCoEoAAooo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BAAooBCCooDDoooEEEFoGGoFo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BBBoooCooooCAAoDCEEEDFFGG
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BooooBAAoooCCooDDDoEFFGGE
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: ooAAoBBoCCoooDDooEEFoGGGF
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BooooBCCCDAAooDooEEooFFoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: ooAAooBBoooCDDooCoEoFFFEo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BBBooCDAAoCDoEECDFFoGGGoo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BCAAoBCDDDBEooooEoFFoGGGo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BCCCoBDAAoEDFGHEDFGHEIIGH
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: AAooBCCDDBoEEoBFGGGoFoHHo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAoooBBCCDooEoDFFEooGGooo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BoCooBoCooooCDEoooDEooAAE
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BAAooBCCDDBEFFoGEHHoGIIoo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAooooBBBCDDooCEEooooooFF
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: BAAooBCCCooDoEoFDoEoFoGGG
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BBBoCDEEECDoFoGDHFoGoHAAo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BCoDoBCoDoEFFFGEHAAGEHooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BAAooBCCDoEEEDoFFoDoooooo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oBCCCDBAAoDoEFoooEFoGGGoo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooAABCDEoBCDEoooDEFFoGGHH
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAoooooooBCDDDBCEEoBCoFFF
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAooooBoCDEBFCDEoFoDooFGG
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: AAooBooCCBDDDoBooEFoGGEFo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: ooAAooBBCCDDoEFGHoEFGHoII
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BCCCoBAAoDBoEoDFGEHoFGoHo
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 (5×5) solver.

Input: 25-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: 5x5
Board: BAAooBooCCDoEFGDoEFGDoHHH
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oBoCooBoCoDAAooDooEEFFFoo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BCoooBCAAoBoDoEFoDGEFooGo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAAoooBBoCooooCDDoEEoFFoo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BoCoDBECoDFEAAoFEGGoFoooo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BoCooBDCooBDCooooAAEooFFE
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BAAooBoCCDBEooDFEGGDFooHH
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: AAoooooooBCoDoBCoDEBoooEo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAooooBooCDBEoCDoEoFGGGoF
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oBAAooBCDDEoCFGEHoFGoHIII
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooAAoooBCDEEBCDFFFoooGGGo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BAAooBooCCDDEooooEooooooo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: BooooBCAAoDCEFFDGEoooGooo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooBoooCBooDCooEDoAAEDFFFo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oooooAAooBooCCBDDEEoooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oBAAooBCCDEoooDEooFDGGoFo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAoooBBCDooECDooEFFoGGHHH
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooAAooBBCDEFFCDEooooooooo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BCDDDBCoEFGCoEFGAAooGHHII
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: ooAAooBoooCBDDECoFFECGGGo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oooBCoooBCoAAooDEEEoDooFF
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BoAAoBCoooDCoEFDooEFooGGF
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BoAACBoooCoDEoCoDEoooFFGG
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 (5×5) solver.

Input: 25-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: 5x5
Board: BoooCBoAACDoEEoDFooooFGGG
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BoAAoBCooDBCEEDooFFoGGHHo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: AAooBCCDEBooDEBFFoooooGGo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BBBooooooCDDDoCoEEEoooAAo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BoAAoBoCDDBoCooEEEFooooFo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oBBBoAAoCoDDDCEFGGoEFHHoE
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BCoDoBCoDEBAAoEooFGoHHFGo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BCCCoBoAAooDDoooEooooEooo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BCAAoBCDEEFCDoGFoHHGooooG
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooAAoBCCDEBFFDEBoGHHooGII
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BCooDBCooDBEEEoFoooGFoAAG
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: AAoooBBBCCDEEFFDGGGooHHHo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BoAAoBCooDECFFDECGGGooHHo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oBBBoAAooCooooCDDoEoFFFEo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: AAoooBoCoDBoCoDEECooooFFF
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooAAoBBCCoDDoEEFFGGoHHIIo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BCooDBCooDooEFoooEFoooAAo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oAAooooBCoDEBCFDEBoFDoooF
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: ooAAoBCoDEBCFDEBCFGGoooHH
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oBCoooBCooDoAAoDoEEEDoFFo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: AAoooBBCDoEFCDoEFCDoGGHHH
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BooCoBDECFoDECFAAoooGGooo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: AAooooBBCCoDDEFGGHEFooHII
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BoAAoBCDDDECFoGEoFHGEooHo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: oBBBoCoooDCooEDFooEDFAAEo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: ooBBBoCDDDoCAAoEEFFFGGHHH
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: AAoooooBBBCCDDooEFFGoEHHG
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAAooBBBoCoDoECoDoEFooGGF
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BBBooAAoooooooooCDEEoCDFF
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BCAAoBCooDoCoEDFooEDFGGEo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oBooCoBoDCAAoDoEEFooooFGG
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oBAAoCBoDoCEFDooEFGHIIFGH
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oAAooBBooooCCDDEoFooEoFGG
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BoAAoBooCDoEFCDoEFCoGGooo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BAAooBooCCDoEEoDFFGGooooo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: oBCDoEBCDoEAAooEFFGGHHoII
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooAABoCCoBoDEooFDEoGFDEoG
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oBoCooBDCooEDFGoEDFGooAAo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooooooAAooooooBCCooBDDEEB
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BoCoDBoCoDAAoEoFFFEoGGHHo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAAooBBBooCoDDDCEEoFoGGGF
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BoCCCBDEEEoDAAooDFFoGGGHH
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oBAAoCBDDoCooEEFGGGoFHHoo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oooooooooBAAooBCDEEoCDFFo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oooBoCoDBoCoDBEooAAEFFGGo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oBoooCBAADCoEFDGGEFoooEFo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: BBBooCDAAoCDoooEoFGGEoFoo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BBBCoAAoCooDDCEoFFoEoGGoE
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BAAooBCDooBCDEEooFGGHHFII
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAAoBCCooBooDooEEDFFGGHHH
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BooCoBAACoDDoCoooEoFooEoF
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oBCDEoBCDEoAAoFGoooFGHHHo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BoAACBDEFCGDEFoGDoHIoooHI
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BoCCCBoAADooEoDooEoooFFoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooAAoBBBCCDEEooDooFGHHoFG
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: oooooooBBBCoDooCoDoECAAoE
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: ooAAoooBBooCCDDoEEoFoGGGF
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooAAoBBooCDDDECFGHEoFGHEo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oBoooCBDooCBDooCAAooEEEoo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAAooBBoCCDEoooDEFGGDEFHH
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooAAooBCCCDBoEFDooEFDoGGG
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooAAoBCCDDBEEoFBGGoFoHHoF
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooAAoBBCCCooDDDEEFFFGGoHH
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oAAooBoCCCBDEEooDFFoGGHHo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oooooAABooooBCDEEoCDFFFoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAoooBBCCDEEFoDooFooGGGoo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BCoooBCDDDoEAAooEoFFGGHHo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: ooAAoBBoooCCoooooDooEEDFF
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BAACoBoDCoooDoEoFFFEGGHHo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oBooooBCooAACooDDoooooEEE
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: ooAABooooBCooooCooDDEEEFF
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAoBoCDDBoCoooooEEFFGGooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooAAoBCoDDBCoooBooooEEEFF
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BCAAoBCDDDoEFFoGEHHoGIIJJ
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: AAooBoooCBoDDCooooEFGGoEF
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAooooooBBooooooCDDEoCooE
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BBBCoDooCEDAAoEDFoGHoFoGH
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: ooAAooBCoooBCDDEECFFooGGo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: ooAABoooCBoDDCoEEEFFGGGoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooBCDooBCDEoBoDEFFFoooAAo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oAAoBooooBCoDDoCoEEFooGGF
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BAAoCBDEFCoDEFoGGGFoooHHo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: ooAAoBBoooCCDDEFGGGEFHHHE
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oBooooBoooCCCoDoEooDoEAAD
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAooooBBCoDooCEDFFoEoGGGo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BoAAoBCoDDECFFoEGGGHIIJJH
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oBAAooBoCDoEECDoFFFooGGHH
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oBoooCBAAoCDEEoCDoFFoGGHH
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BCAAoBCoooDDoooooEFGHHEFG
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: oAAoooBCCDoBEFDGoEFoGHHFo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BoAAoBCCDDEEEoFGGGoFHHooF
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oooooBoCooBoCooooAAooooDD
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooAAoooBCoDDBCEFoBoEFooGG
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooooooooooBBBooCAAooCoDDo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BCAADBCEoDoFEoooFoGGoHHII
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BoCDoBECDFGEAAFGHHHoGIIIo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: ooAAoBoCCCBDooEFDGGEFoooo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: AAooooBBBCoDEECFDGGoFoooo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAAoooBBooCooDDCEEoooFFoo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oAAoBCCCDBEEFDoGHFIIGHFJJ
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 (5×5) solver.

Input: 25-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: 5x5
Board: oooooooAAoBCCoDBoooDEEooD
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooooBooCoBAACooDEEEoDFFGG
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAoBoCooBoCDooEoDooEoFFGG
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAoooBBBCCDEooFDEoGFDEoGo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oAAooBBBoooCCoDEEFFDGGHHH
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAooBoCDDBoCEEooCFFoooGGG
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oBAAoCBDDoCBEEFGGGoFoHHoF
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAAooBCCCoBoDEFGGDEFooHHo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooAAooBoCooBoCoDBoCoDEEEo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooAAoBoooCBoDDCBooECFFoEo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BoAAoBoCooooCooDDooEFFGGE
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BBBooCCCDoEEEDooAADoooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: BoAAoBoCCoDDDEEFGGHHFIIIo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooAAoBBBCCDDDEEoFFFooGGoo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oAAooooBooooBCCDEFGGDEFHH
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: AAoooBBCCCoDEEEoDFFooDoGG
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oBAACoBDECFGDECFGDEoooHHo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BoCooBoCoDEoAADEFFGGEooHH
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAoooBBCCooooDEoooDEooFFo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BCCCoBoDDDBoAAooEEFFooGGo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BBBoooooooCoDDDCAAooCEEoo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: ooAAoBBBCooDDCoooEEoFFGGG
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BBBCoDEFCGDEFCGHoAAGHIIoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: oAAoBCCDDBEoooBEoFFoGGGoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BCDDDBCEFGBoEFGHooFGHAAoo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oAAoBCooDBCEEDBCFFFoGGHHo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooAAooBBBooCCCDoEEFDoooFo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oBAAoCBDoECoDoEFGGoHFoIIH
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oBoooCBoooCAAoDEFFFDEoGGo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BoCCCBoooooDEEEFDAAoFDooo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oBooCDBooCDBAAoEEEFFoooGG
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BCAADBCEEDFooGDFHoGoFHIIo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BoCCCBAAooDDEFFGHEooGHooo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAoooBBoCDEEoCDFGooDFGooo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: oooBCDDDBCoAAoooEEFFGGGHH
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oAAooBBBCCDooEFDooEFDGGEo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oBooCDBAACDEEooFFooooGGGo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAoooBCDDDBCEFoBCEFoooooo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooooBoCoDBECoDoEoAAooooFF
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BCoooBCoDoEoFDGEoFDGEAAoG
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BAAoCBDDECBoFECooFGoHHFGo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BCAAoBCDDEBFFoEoGHHooGIII
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BCDoEBCDFEGooFoGHHHoAAooo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooAAoBCCDDBooooooEEEooFFo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oBAACDBoECDBoECDooEooFFGG
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 (5×5) solver.

Input: 25-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: 5x5
Board: BoooCBoDoCooDoCAAoooooEEE
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BoAACBDDECBFFECoGGEooHHII
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BCCCoBAAooooDDEFFGGEooooo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: ooAAoooBCoDoBCEDFFFEDGGoE
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooAAoooBCooDBCooDBEooooEo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BAAooBoCCDEEFoDooFooGGFHH
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oBBBCDoooCDAAooooEoFooEoF
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oAAooBoCCoBoooDEoFFDEGGGo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: AAoooooooooBBBooooooooCCo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oBAAooBoooCBoooCDDDEooFFE
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oBAACDBooCDBooooEEFGoooFG
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooBBBoooCDooECDoFEoDoFAAo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oAAooBBCDDooCEFGGGEFHHHoF
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: oAABoCCoBoDDDooEEoooFFoGG
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: ooAAooBCoDEBCoDEFFFooGGGo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BBBoCDDDECFAAEoFoGGHFoooH
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BBBooAAooCDDEECooFFCGGHHo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BCCCoBoAAoDEFFFDEoooGGGHH
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BCDDDBCoooEoFGoEHFGIoHAAI
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oBBBoooAAooooooooCoDooCoD
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooAAoBooCCBoDDoBooooEEoFF
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oBBBCooooCDEEEoDFAAooFooo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oAAooBooCDBooCDBEooooEoFF
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: oBBBoCoAAoCooooDDEEFGGHHF
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooAAoBCCCoBDDDoBEooooEoFF
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooAAoooBBCDEEoCDooFFDGGGo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oAAooBBoCCDEFoGDEFoGDEFoG
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooBooooBCoDoBCoDAAooDoooo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BoAAoBCDEooCDEFGGGoFHHooo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BAAooBoCDDooCoEFGooEFGooE
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: AAoooBCCooBDEEEoDoFooooFo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAoooBoooCBoDDCBoEEoFFoGG
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BCCCDBoEFDBoEFoooEooooAAo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oBBBCooooCAAooooDEFFoDEGG
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BCDDDBCAAEBoooEFGGoEFoooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oBAAoCBoDoCBEDooFEGHoFoGH
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: oBAAooBoCoDEFCGDEFHGoEFHo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oBCCCoBAAoDoooEDooFEGGGFo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oAAooBCCDoBEEDoBooFooooFo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAoooBBooooCCooDEFFoDEGGG
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooAAoBBCooooCooDEFFGDEHHG
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BAAooBCCooDDEoFooEoFGGEHH
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BoAAoBCCDDooEFGooEFGHHIII
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BCDDDBCoooBAAooooEEEoFFoo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooooBooAABoCCCBDEEooDoooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BoooCBoooCBDAAoEDoFFEDooo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: AAoBoCCoBDooooDooEFFGGEoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BAAooBoCooBoCDEFFoDEoooDE
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oAAooBBCDooECDooEoDFGGHHF
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: oAAooBooooBoCCCDEFFoDEooo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oBBBoCDEEECDAAoFFFGHIIIGH
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: ooBBBCDoooCDEFGCoEFGAAoFo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BBBCoDEFCGDEFoGoAAooHHooo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: ooAAooBCCCoBoDooooDoooEEE
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooBBBCoDDDCEAAooEFFFoEoGG
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: AAooBooooBCCoDoEoFDGEoFDG
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: AAoooBooooBCCCoDDoEEFFFGG
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BoCDEBFCDEoFooooFAAooGGoo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oAAoooBBooCCCooooDDDEEooo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooAAoBCoDDBCoooBEEoFGGooF
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oAABoCCoBDEFGoDEFGHIoooHI
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 (5×5) solver.

Input: 25-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: 5x5
Board: oAAoBCDDEBCFGEBCFGooHHGoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooAAoooBBoCCDDDEFGGHEFIIH
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAoooBoCooBDCEEBDoFooooFo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BCAAoBCDDoBEFooGEFooGoFHH
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oBAAoCBDooCEDooFEGGoFEHHo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oBBBoAAoooCoDoECoDoECoDoE
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooAAoBCoDDBCooooCoEFoGGEF
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooBBBCAAooCDDDooEFFGoEHHG
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BAAooBCCCoBDDEFGHIEFGHIEF
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BCAAoBCoDDoCoEEFFGoHIIGoH
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BoAAoBoCCCBooDooEFDooEFoo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BAAooBCCDEoooDEFFoDEoGGHH
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oAAoBooCCBooDooEEDFFoGGoo
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 (5×5) solver.

Input: 25-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: 5x5
Board: BCDooBCDooBEDoooEAAFoGGGF
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BCDooBCDEoBFGEHIFGoHIFAAH
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oBCCCoBoooAAoooDDoEEooFFo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oBBBoCDAAoCDooooDooEooooE
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BoCCCBoAAoDEEFFDGHooDGHoo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooAAoBBCooDDCooEoCoFEoGGF
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BAAooBCDooBCDooECooFEGGGF
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAoooBooCDBooCDBEECFooooF
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: AAoBoooCBoDDCoEoFCoEoFooE
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAooBCooDBCooDoEEFFGoHHoG
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: AAoooBBooCDoEECDoFGGooFoo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: AAoooBooCDBEECDoFFFGHHIIG
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BAAoCBDEoCFDEGoFDEGHIIIoH
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oooooBCCCoBoAAoBDEEEoDFFF
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BCooDBCEFDoCEFGHIIIGHAAoo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oooBooooBoCAAooCoDDoEEoFF
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BAAooBCCDEBFFDEGGoHEIIIHo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: AAooooBBoCDDDoCEooooEFFFo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAAoBCCooBDoEEoDoFFGoHHHG
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BoAAoBCCCoDoEEoDFFFoDGGHH
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAABooooBCDDooCEooFFEoGGG
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: AAoBoooCBDooCoDEECooooFFo
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 (5×5) solver.

Input: 25-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: 5x5
Board: AAoooBBCCCDDooEFoooEFGGGo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oBBBoCoAAoCDDDoEFFGGEoooo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BAAooBoCCoDDDEEFFooGHHHoG
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BoAACBDDDCEFGGoEFHHHoIIJJ
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AABooooBoCooooCDooEoDFFEo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: AAooooBBBooCDEFoCDEFGGDEo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BBBoooCAADoCooDEEFFDGGGoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AABooooBCCoooDDooEFFooEGG
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooAABoooCBoooCoDEEEFDGGGF
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BoAAoBCDDDBCooEooooEoFFFo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: BoAAoBCCCoooDDEooFFEGGooo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooAABCCooBoDooooDEEFoGGoF
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BoAAoBCCoooooDEFGoDEFGHHE
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooBBBoAAooooCCoDoEEEDooFF
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BCCCoBAADoEFoDGEFHDGooHoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oooooAAoooBBCDDEECFFooooo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oBCCCDBoooDBEooDoEFoAAoFo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BCDDDBCoooBoAAooEEEFGGHHF
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooAABCoDEBCoDEooooooFFooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAoooBCCCDBoEEDFooooFoooo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: ooAAoBooCDBEoCDBEoCooooFF
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: BoCCCBoooooAAoDEEEFDGGGFo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: AAooBoCCCBDDDEBFGoEoFGoHH
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: ooooooBBBCDoAACDEEEooFFoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: ooAABCCCoBDoEEBDFGooDFGoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oBCoDoBCEDoooEooAAooFFoGG
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAAoooBoooCBoooCDDDoCoEEE
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oAAoooBCCCoBDEFooDEFGGDHH
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: BoAACBDEoCFDEGGFHoIIoHooo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Ev2,F<1,Cv1,A>1
</answer>


Board size: 5x5
Board: oBBBoooCCCoooooDoAAEDFFoE
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BCDDDBCEooFoEGHFAAGHIIIJJ
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: oAABCDDoBCoEoooFEGHHFoGoo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BBBoCoooDCAAEDoooEFFoGGHH
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,G<1,Ev1,A>3
</answer>


Board size: 5x5
Board: oBCDooBCDEoFCoEoFoGHAAoGH
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAoBoCDDBoCEFFoGEHHHGoooo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Ev1,E<1,Bv1,A>3
</answer>


Board size: 5x5
Board: AAooBCDooBCDEEFooGGFoooHH
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
H<1,Fv1,Bv1,A>3
</answer>


Board size: 5x5
Board: ooBBBCCCDEoAADEoooFoGGoFo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AABCDoEBCDFEoooFGGoHFoIIH
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oBoooCBAADCEEEDFoGGGFoHHo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: ooBBBoooCDEooCDEoAADooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oBBBCAADoCooDEooFFEoGGGHH
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv2,F<1,Cv1,A>3
</answer>


Board size: 5x5
Board: AABoCoDBoCoDBoooEEooooooo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,E<1,Bv1,A>3
</answer>


Board size: 5x5
Board: ooooooAAoBCDEEBCDoFFooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F<1,Bv1,A>2
</answer>


Board size: 5x5
Board: BoAACBoooCBoDoEFoDGEFHHGo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Ev1,Cv1,A>1
</answer>


Board size: 5x5
Board: BAAoCBoDDCEFFFCEoGGGEoHHo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
G<1,Cv1,A>2
</answer>


Board size: 5x5
Board: ooBBBoCooooCooDoAAEDFFFEo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AABoCooBDCEEoDooFFDoGGoHH
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: BBBCDoAACDEEooooFFooGGooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BBBCDoAACDEFFooEoGGooooHH
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv2,G<1,Cv2,A>2
</answer>


Board size: 5x5
Board: ooBBBoCCCoDDDoEFGAAEFGooE
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BoCDoBoCDEFGoHEFGoHIFAAoI
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AABoCDDBoCEFBooEFoooGGGHH
Optimal length (moves): 3
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oAAoBCDooBCDoEFGooEFGHHEo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Fv1,Bv1,A>2
</answer>


Board size: 5x5
Board: AAoBoCDoBoCDEFGooEFGoHHHG
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
H<1,Fv1,Bv1,A>3
</answer>


Board size: 5x5
Board: oAABCoDDBCoEEFooGGFoooooo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,Fv1,Bv1,A>2
</answer>


Board size: 5x5
Board: BoCDoBoCDEFoCDEFoooGooAAG
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: AAoBCDDDBCEFoBoEFooGooHHG
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: ooBBBoCooooCDDDEEEFooAAFo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oBCoooBCoDEBCFDEAAFDGGoFo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AABooCDBEFCDGEFoDGHFoooHo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Gv1,Bv1,A>3
</answer>


Board size: 5x5
Board: ooAABoCCoBooDDDoEEoFooooF
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BAACDBEoCDBEooDFFoooGGGoo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oooBoCCCBoAAoDEoFFDEooGGo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^2,G<1,Ev1,A>3
</answer>


Board size: 5x5
Board: AABooCCBDoooBDEFoGGEFHHII
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^1,G>1,Bv1,A>3
</answer>


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: BBBoCoAAoCDDEEooooFFGGHHo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BooCoBAACoooDDDooEooFFEGG
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAoBooooBooooCCooDDooEEoo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<2,Bv1,A>3
</answer>


Board size: 5x5
Board: BAACDBEoCDFEoooFooooGGoHH
Optimal length (moves): 3
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: AAoBooooBooooCCooDooooDEE
Optimal length (moves): 3
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: AAooBCDEEBCDoFFCoGooooGHH
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAAoBCCCoBDEEFGDooFGooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Gv1,Bv1,A>2
</answer>


Board size: 5x5
Board: BCCCDBEEEDBoAAFGGGoFooHHH
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
H<1,Fv1,A>1
</answer>


Board size: 5x5
Board: oAABCDooBCDEoooFEGGHFIIoH
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: oBBBooooooAAoCDoEECDooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,C^2,A>3
</answer>


Board size: 5x5
Board: oAABooCCBoDDDBEoFFFEooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F<1,Bv1,A>2
</answer>


Board size: 5x5
Board: BoCooBoCDEBoFDEooFDGAAooG
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AABCDooBCDoEBoDoEoooFFGGo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

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