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: ooooAAooBCCoBDDD
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


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

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


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


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

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


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


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


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


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


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


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


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


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

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
B<1,F^1,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: AAoBCCoBooDDoEEE
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


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


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


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

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


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

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


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

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


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

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


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

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


Board size: 4x4
Board: oBBBCDDDCooEAAoE
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>


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: BBBCAAoCDoEEDFFF
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


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

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


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

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


Board size: 4x4
Board: BCCCBooDAAoDoooo
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: AAoBCCoBDEEEDFFo
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>


Board size: 4x4
Board: oBBBAAoCDEECDFFF
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: oooBAAoBCDDDCoEE
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: AABCooBCoDBCoDEE
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>


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: BoooBCCCoooDAAoD
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


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

<think>
Shortest path found.
</think>
<answer>
Cv1,D^1,E<2,Bv1,A>2
</answer>


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

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


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

<think>
Shortest path found.
</think>
<answer>
C^1,D<1,E<1,Cv2,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: oBAACDBooCDEoooDEFFFoGGGo
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: AAoooBoCCCBDDEFoGGEFoHHHo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


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

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


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


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


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


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


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


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

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


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


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

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


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


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


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

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


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


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


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


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


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


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

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


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


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

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


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


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


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


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


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

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


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


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


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


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

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


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


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


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


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


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


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

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


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

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


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


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

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


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


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


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


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


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


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

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


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


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


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


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


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

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


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

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


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

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


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


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

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


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


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

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


You are an expert Rush Hour (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: oBAACoBoDCEFFDoEooDooooGG
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: BCAAoBCoDDECFooEoFGGEHHHo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


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


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


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

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


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


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


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


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

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


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


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


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


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


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


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

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


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


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


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


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


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


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

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


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

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


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

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


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

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


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


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


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


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


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


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


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


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


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

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


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

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


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


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


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


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


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


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


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


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

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


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

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


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

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


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


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

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


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

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


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


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


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


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

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


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


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

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


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

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


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


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

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


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


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


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


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


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

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


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


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

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


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

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


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


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


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


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

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


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


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

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


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


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


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


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

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


You are an expert Rush Hour (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: oBBBooCooooCoDooooDoAAoDo
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: oooBCDEoBCDEFooAAFooGGGoo
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: BAAooBCCDDooEEEFFGGGooHHH
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


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

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


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

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


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


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


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


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

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


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


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


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


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

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


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


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

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


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

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


You are an expert Rush Hour (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: ooAAoooBBCDEEoCDoFoCGGFoo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


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


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


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

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


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

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


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


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


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


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

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


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

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


You are an expert Rush Hour (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: AAooBooCDBEoCDoEoCFFGGoHH
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: AAoooBoCooBoCooooooDooooD
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


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


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


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


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


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

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


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

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


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


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

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


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


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


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


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

<think>
Shortest path found.
</think>
<answer>
F^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: ooAAooBBBooCoDDECFGoECFGo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


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


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


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


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


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

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


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


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

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


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


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


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


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


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


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


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

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


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

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


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


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


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

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


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


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


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


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

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


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


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

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


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


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


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


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


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

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


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


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


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


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


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


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

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


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

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


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


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


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


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


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


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


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

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


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

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


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


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


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


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


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


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

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


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


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

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


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


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

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


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


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


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


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


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

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


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

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


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


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


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


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


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


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


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

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


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

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


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


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


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


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


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


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


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

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


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

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


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


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


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


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

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


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


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


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


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

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


You are an expert Rush Hour (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: AAooooBCDEoBCDEoBCooFFGGG
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


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

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


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

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


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


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


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


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


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

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


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

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


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


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


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

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


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


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


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


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

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


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

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


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


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


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


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

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


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


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

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


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


Board size: 5x5
Board: BAAooBooCCBoDDDooEEooFFFo
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: BAAoCBDDoCBoEEooFGGooFoHH
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: oBCDoEBCDoEoCoFoooGFAAoGo
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: AAooBCCCDBEEoDooFFFoooGGo
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: BoooCBAAoCBDEFooDEFooGGHH
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: AAoooBCCDEBFFDEBGoHHoGoII
Optimal length (moves): 1
Return only the <think> and <answer> blocks.

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


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


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


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

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


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

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


You are an expert Rush Hour (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: ooBBBooAAooCCCoDooooDEEoo
Optimal length (moves): 1
Return only the <think> and <answer> blocks.


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

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


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


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


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


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


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


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


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


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

<think>
Shortest path found.
</think>
<answer>
Ev1,E<2,Cv1,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: BoAACBDDDCEEoFFoooooGGGHH
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


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

<think>
Shortest path found.
</think>
<answer>
Ev2,E<1,Cv2,A>1
</answer>


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

<think>
Shortest path found.
</think>
<answer>
Dv2,Dv1,A>2
</answer>


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

<think>
Shortest path found.
</think>
<answer>
Dv1,E<1,Cv1,A>2
</answer>


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

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


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

<think>
Shortest path found.
</think>
<answer>
Gv1,Bv1,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: BBBoCoAADCEEoDooooooFFFGG
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv2,Cv1,A>2
</answer>


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

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
E<2,Cv2,Cv1,A>3
</answer>


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

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


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

<think>
Shortest path found.
</think>
<answer>
E<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: oAABCoDDBCooooCEFoooEFGGG
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: ooBooCDBoECDBFEoDoFGAAoFG
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Dv1,G>2,Cv1,A>3
</answer>


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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Gv1,Cv1,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: BBBoooCCCDEooFDEAAFoGGGHH
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


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

<think>
Shortest path found.
</think>
<answer>
Hv1,Dv1,A>1
</answer>


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

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


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

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


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


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

<think>
Shortest path found.
</think>
<answer>
E<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: BCAADBCooDBCooEFFFoEGGGoo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Ev1,Dv1,A>1
</answer>


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

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


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


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

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


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

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


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

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


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

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


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

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