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

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

Board size: 6x6
Board: ooBBBCoAAooCoDDEooFooEGGFoooHHFIIIJJ
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^1,G<3,Cv2,Cv1,A>3
</answer>


Board size: 6x6
Board: oooBoCoAABoCooDDDCoooEEEFFooGoooHHGo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D<2,E<3,Bv2,Bv2,A>3
</answer>


Board size: 6x6
Board: BCoooDBCoAADoEFGGGHEFooIHJoooIHJKKKo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F^2,G<1,Iv1,Ev2,A>1
</answer>


Board size: 6x6
Board: ooBooCAABoDCoEEEDCoooFDooooFGGHHHFoo
Optimal length (moves): 9
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E<1,F^2,G<3,Cv3,Cv2,Cv2,C>3,Bv2,A>4
</answer>


Board size: 6x6
Board: oBAACooBooCooBoDDDooEEFoGGooFoooHHFo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
G>2,Bv3,C<2,Bv1,A>2
</answer>


Board size: 6x6
Board: oAAoBooCCCBoDEoFFFDEoGGHDEIIIHoJJJoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
J>1,Ev1,E<2,Bv1,A>3
</answer>


Board size: 6x6
Board: BAAoCDBoEECDoFFGGDHIIIooHoJKKKHoJooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv1,F<1,G<1,Cv1,A>3
</answer>


Board size: 6x6
Board: oooooooooBoooooBCoDDDoCoAAEoCFooEooF
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


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

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

Board size: 6x6
Board: ooBoooooBCCCoooooooAAoDooEooDooEooDo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A<1,Bv4,B<2,C^3,A>4
</answer>


Board size: 6x6
Board: AABooCooBooCDDDooCooooooooEEooooooFF
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F<1,Cv3,C>3,Bv1,A>4
</answer>


Board size: 6x6
Board: oooooooooooooBBBoCoooDoCoAADoEoooDoE
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<1,C^2,D^2,E^2,A>3
</answer>


Board size: 6x6
Board: ooAAoBooooCBooooCBooDEEEooDooFooDooF
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: ooBBBCoooDoCAAoDoCEEooooooFGGGooFooo
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<2,D^1,A>3,F^2,G<1,Dv3,A>1
</answer>


Board size: 6x6
Board: ooAABCDoEoBCDoEooFoooooFoooooFoooGGG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,G<1,Fv1,Bv1,A>2
</answer>


Board size: 6x6
Board: oooooooooBBBoAAooCoooDoCEFFDoCEooDGG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,G<3,Cv1,Cv1,A>3
</answer>


Board size: 6x6
Board: ooBBBoooooooAAoCooDooCEoDooCEoDFFFEo
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>3
</answer>


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

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

Board size: 6x6
Board: ooBCoDoEBCoDoEAAoDFEGoooFoGoooooGHHH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: ooooBoAACoBoooCoDDoooEEooFoGHIoFoGHI
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv3,C<2,D<1,Bv2,A>4
</answer>


Board size: 6x6
Board: oooooBooAAoBCoooooCoDEEEoFDooooFDooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A>1,D^3,E<1,Cv2,A>1
</answer>


Board size: 6x6
Board: ooooooooooooooAAoBoooCoBoDoCoBoDoCEE
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: oAABooCCoBoooDEFFFoDEoooooooooGGGHHH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv1,Dv1,D<3,Bv1,A>3
</answer>


Board size: 6x6
Board: AAoooBoooooBCCoooBDoEFFFDoEoooDoEooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: ooBBBoooCoDoAACoDoooooDoooooEEoooFFF
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E<4,Cv2,F<2,Cv2,A>4
</answer>


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

<think>
Shortest path found.
</think>
<answer>
C^1,I^1,L<3,Iv1,Cv1,A>3
</answer>


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

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

Board size: 6x6
Board: oBCCCDoBAAoDoBEFFoGoEHHHGoEoIIGJJoKK
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv1,C>1,A>1,E^2,H<1,Ev1,A>1
</answer>


Board size: 6x6
Board: ooBCCCooBDooooBDoEFAAooEFooooEFooooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: AABooCDDBooCoEFFFoGEHIIIGEHJJJGoHKKo
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F>1,Bv1,A>3,D^1,F<1,Cv1,A>1
</answer>


Board size: 6x6
Board: ooooBooAAoBoooCCDDooooEoFGooEoFGoooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<2,D<2,Ev1,Bv2,A>3
</answer>


Board size: 6x6
Board: BoooCDBAAoCDBoooCDoEoooooEoFGGoooFoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F^2,G<2,Cv2,Cv2,A>3
</answer>


Board size: 6x6
Board: ooooooAAoBoooooBooCooBooCDDDEoCoooEo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A>1,C^2,D<1,Cv1,A>3
</answer>


Board size: 6x6
Board: oAABCooooBCooDDDCoooEEEooooFFooooGGG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


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

<think>
Shortest path found.
</think>
<answer>
D<3,E<2,Cv3,C>3,Bv1,A>4
</answer>


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

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

Board size: 6x6
Board: ooBBBoCDEEEoCDoFFFoDAAGHIoJoGHIoJoGH
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<1,Dv2,D<1,E<2,G^3,H^3,A>2
</answer>


Board size: 6x6
Board: ooooooAAooBooCooBooCDoEEoCDoooooFFFo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F>1,Dv1,D<2,Bv1,A>4
</answer>


Board size: 6x6
Board: ooooBoooooBCooAABCooDDEEoooFFFoooGGG
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,D<2,E<2,F<2,G<2,Bv3,A>2
</answer>


Board size: 6x6
Board: oooBCDoAABCDooEoCDoFEoooGFoHHoGFoooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,Cv2,H<1,Bv2,A>3
</answer>


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

<think>
Shortest path found.
</think>
<answer>
Cv2,C<1,Dv1,D<2,Bv1,A>3
</answer>


Board size: 6x6
Board: ooAABCDoEEBCDFoooCDFGHHHoFGoIIJJGKKK
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>1,Cv1,C<2,G^3,H<1,Cv1,A>1
</answer>


Board size: 6x6
Board: ooBCoDEoBCoDEoBCoDFoGHHHFoGooIFAAooI
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A>2,Gv1,G<1,I^1,A>1
</answer>


Board size: 6x6
Board: ooooBCoooDBCAAoDBCoooDooooooooooooEE
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E<3,Bv3,Bv3,Bv2,A>4
</answer>


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

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

Board size: 6x6
Board: ooBoCoAABoCoooooCDEFFooDEooGoDEooGHH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F>2,Bv4,E<1,Bv2,A>4
</answer>


Board size: 6x6
Board: oooBooooCBooAACBoooooDDDEoooFoEGGGFo
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,A>1,E^3,E<3,G<1,Cv3,A>3
</answer>


Board size: 6x6
Board: oooBBBoCCCoDAAoEoDoFoEoooFGGGooFooHH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<3,C<1,D^1,E^2,A>4
</answer>


Board size: 6x6
Board: ooBBBoCCCoDEFAAoDEFoGoDEHHGoooooGoII
Optimal length (moves): 9
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C>1,F^2,A<1,G^1,I<4,Ev2,Ev2,Ev1,A>4
</answer>


Board size: 6x6
Board: oAAooBoooooBCCoDDBEFGHHHEFGoooEFGooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A>2,G^3,H<1,Cv1,A>1
</answer>


Board size: 6x6
Board: ooooBCoAAoBCooooBooDooEEoDoFFooDoGGG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E<2,Cv2,F<1,Bv2,A>3
</answer>


Board size: 6x6
Board: oooBoooooBoooAABoCDEEEoCDooooooooooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^2,D^2,E<1,Bv3,A>3
</answer>


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

<think>
Shortest path found.
</think>
<answer>
H>1,I>1,Dv2,D<1,Bv1,A>3
</answer>


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

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

Board size: 6x6
Board: oBoAACoBoDDCoBEFFFoGEHHHoGEoIIoGJJJo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


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

<think>
Shortest path found.
</think>
<answer>
Hv1,Cv1,C<1,F^2,I^2,A>1
</answer>


Board size: 6x6
Board: oooBooCCCBoooooDoooAADoEFGGGoEFooooE
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^3,F^2,G<1,Fv2,A>3
</answer>


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

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


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

<think>
Shortest path found.
</think>
<answer>
L>1,Ev1,E<2,Cv1,Cv1,A>2
</answer>


Board size: 6x6
Board: BCCCooBDDDooEEEoFoGoHIFJGoHIKJAAHoKJ
Optimal length (moves): 9
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F^2,F>3,H^1,K^1,A>3,Fv1,F<1,K^1,A>1
</answer>


Board size: 6x6
Board: oooooooBoCCCoBooDoooooDEAAooDEoooooE
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,B<2,D^1,E^2,A>4
</answer>


Board size: 6x6
Board: oAABCoDDDBCooooBEEoFooooGFooooGFHHoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
H>2,Bv3,D<2,Bv1,A>3
</answer>


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

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

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

<think>
Shortest path found.
</think>
<answer>
H^1,A>2,Dv2,E<2,H^1,A>2
</answer>


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

<think>
Shortest path found.
</think>
<answer>
B^1,A>3,Bv3,B<1,D^3,A>1
</answer>


Board size: 6x6
Board: ooooooBoCDDDBECooFBEAAoFoGHHIIoGoooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


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

<think>
Shortest path found.
</think>
<answer>
Gv1,A>1,Dv1,D<1,G^3,A>1
</answer>


Board size: 6x6
Board: ooooooooBCCCooBooooAAoDoooooDoEEEoDo
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A<1,Bv1,B<2,D^3,E>3,Dv2,A>4
</answer>


Board size: 6x6
Board: AAooBooCooBoDCooBoDCoEEEDooooooFFoGG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


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

<think>
Shortest path found.
</think>
<answer>
D^4,E<3,F<3,Cv3,Cv2,A>4
</answer>


Board size: 6x6
Board: oAAooBooCDDBooCooBoEFFGGoEoHHHoooIII
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^2,F<1,G<1,Bv1,A>3
</answer>


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

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

Board size: 6x6
Board: BCooooBCDDDEBooFoEoooFoEoAAFoooooooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,Bv2,B<2,F^1,A>3
</answer>


Board size: 6x6
Board: oooooBAAoooBooCooBoDCEEooDCFFFoDoGGG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


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

<think>
Shortest path found.
</think>
<answer>
G<2,J^1,K<2,Ev1,Bv1,A>4
</answer>


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

<think>
Shortest path found.
</think>
<answer>
A>1,E^2,F<3,Cv1,Cv1,A>3
</answer>


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

<think>
Shortest path found.
</think>
<answer>
C<1,E^3,F<3,Bv1,Bv1,A>4
</answer>


Board size: 6x6
Board: ooBBBooooCCCoooDooAAoDEoooooEoooooEo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<1,C<2,Dv2,D^3,A>4
</answer>


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

<think>
Shortest path found.
</think>
<answer>
D^1,I^1,J<2,Ev1,Ev1,A>3
</answer>


Board size: 6x6
Board: ooBCooAABCoDoEEEFDooGGFDHHooFooIIIoo
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv2,D<1,Ev1,E<2,Cv3,C>3,Bv2,A>4
</answer>


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

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

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

<think>
Shortest path found.
</think>
<answer>
F>2,H>1,Bv3,C<3,Bv2,A>4
</answer>


Board size: 6x6
Board: oooooooBCDDDoBCoooooCooEooAAoEooFFoE
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: ooooBoCCCoBoDoEFFFDoEooGAAoooGooHHoG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: ooooBCAAooBCoDEoBCoDEoFFoooooooooGGG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Ev2,E<2,Bv2,Bv2,A>4
</answer>


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

<think>
Shortest path found.
</think>
<answer>
Cv1,B>2,D^3,E<1,F^1,A>4
</answer>


Board size: 6x6
Board: oooooooAAooBCCoooBDEFFGGDEoHHoDEoIII
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A>1,C>2,E^3,F<1,G<1,Cv1,A>2
</answer>


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

<think>
Shortest path found.
</think>
<answer>
A>1,E^3,E<1,F<1,Dv2,A>2
</answer>


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

<think>
Shortest path found.
</think>
<answer>
B<1,C<1,E^4,D>2,E^2,A>4
</answer>


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

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

Board size: 6x6
Board: oooooooBooooCBooDoCEEEDooAAFDooooFoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,D^1,E<1,F^2,A>3
</answer>


Board size: 6x6
Board: oAAoBoCDDDBoCEEoFFGHHIoJGKKILJooooLo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,E<1,F<2,Cv1,A>3
</answer>


Board size: 6x6
Board: oooBBBCDDDoECFFFGEHoooGoHAAIGoHooIJJ
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,F<1,G^1,I^2,A>3
</answer>


Board size: 6x6
Board: oBBBoooooooCoDAAoCoDoooCoDEFGGHHEFII
Optimal length (moves): 14
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<1,E^1,F^1,H>2,Dv1,A<1,F^3,A>1,E^1,G<1,H<1,I<1,Dv2,A>2
</answer>


Board size: 6x6
Board: oBoooooBCCCooooooooooDooAAEDooooEDoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,B<2,D^2,E^2,A>4
</answer>


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

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


Board size: 6x6
Board: oooBBBoCCCoDooAAoDEFGHHDEFGIJJEFGIoo
Optimal length (moves): 10
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<3,C<1,D^1,A<1,H>1,I^4,I<1,J<1,Dv3,A>3
</answer>


Board size: 6x6
Board: oooooBoooooBoAAooBooCDEEFoCDooFoCDoo
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A<1,C^3,D^3,E<4,Bv3,Bv3,Bv3,A>4
</answer>


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

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

Board size: 6x6
Board: AABooCooBooCooBoDDEoFFooEGGGooEoHHHo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D<1,Cv1,F>1,Bv1,A>4
</answer>


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

<think>
Shortest path found.
</think>
<answer>
A<1,E^4,F<3,Cv2,Cv2,A>4
</answer>


Board size: 6x6
Board: BoCCCoBooDDDBoEFFFGoEooHGoEooHoAAooH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: BoAACoBDEECooDFGGGHIFJJJHIooKLHIooKL
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,Fv1,F<2,Dv1,A>2
</answer>


Board size: 6x6
Board: oAABooooCBooooCDDDEFGGHHEFoIIoooJJKK
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^3,Fv1,F<2,Dv2,D<3,Cv1,A>3
</answer>


Board size: 6x6
Board: oooBBBAACDooooCDoooEEFooGooFoHGooooH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E<1,Cv1,Fv1,Cv1,A>4
</answer>


Board size: 6x6
Board: oooBoCDAABoCDEEEoooFoGGooFHooooFHoII
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,E<1,G>1,Cv4,F<1,Cv2,A>3
</answer>


Board size: 6x6
Board: oooooBoCAAoBoCoooBDCoEEEDFFGHHDooGoo
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,D^3,E<3,G^2,H<1,Dv2,A>2
</answer>


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

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

Board size: 6x6
Board: ooAAoBoooCCBoDDDoBEFFFGGEHHIIIJJJKKK
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: BooCCCBoAADoEFFoDoEGoHHHEGIJJJoGIooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: oAABooCCoBooDooBoEDoFFFEDooGGGHHIIIo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C>1,D^2,F<2,Cv1,A>3
</answer>


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

<think>
Shortest path found.
</think>
<answer>
Bv1,A>3,C^1,F<1,Cv1,A>1
</answer>


Board size: 6x6
Board: ooooooAAoooBooCooBDECFFFDECooooEoooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A>3,C^2,F<1,Cv1,A>1
</answer>


Board size: 6x6
Board: oooooooooooBoAAooBoooCoBoDoCEEoDoCoo
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A>1,D^4,A<1,D^2,E<3,Cv2,Cv2,A>3
</answer>


Board size: 6x6
Board: oooBoooAABoooooBooCooDDoCooEEECoFFoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^2,D<2,E<3,Bv2,A>3
</answer>


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

<think>
Shortest path found.
</think>
<answer>
D^2,E<2,F^1,G<2,Cv3,A>4
</answer>


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

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

Board size: 6x6
Board: oBoCoooBoCooAAoCooooooooDooEEEDFFooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A>1,D^2,E<3,Cv3,A>3
</answer>


Board size: 6x6
Board: oBCooooBCDDDAACoEFooooEFooooEFoGGooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Ev1,Ev1,G<1,Cv3,A>4
</answer>


Board size: 6x6
Board: ooooooooBoooooBCCCAABooDoooooDoEEooD
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^1,A>3,E<1,Bv3,B<1,D^3,A>1
</answer>


Board size: 6x6
Board: ooooooooBoooooBoooooBCCCDDDoEFAAooEF
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^1,C<2,E^1,F^1,A>4
</answer>


Board size: 6x6
Board: ooooooooooBCoAAoBCoDoEoCoDoEFFoooooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^1,E^3,F<1,Dv2,A>3
</answer>


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

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


Board size: 6x6
Board: ooAABCDDDoBCEEEoBCFoGGHHFIIJJJFoKKKo
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D>1,E>1,F^3,G<2,H<2,Cv1,Cv1,A>2
</answer>


Board size: 6x6
Board: BooCoDBooCoDoAACEDFoGGEoFoooEoFHHHoo
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv3,Dv1,D^1,E<1,H<1,Cv3,A>3
</answer>


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

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

Board size: 6x6
Board: ooooBCooooBCAAoDBCoooDoooEooFFoEoooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^2,F<2,Cv3,Cv3,A>4
</answer>


Board size: 6x6
Board: oooBoooooBoooAABoooCCooooDoooooDoEEE
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C>3,D^1,E<3,Bv3,A>3
</answer>


Board size: 6x6
Board: BoooCDBAAoCDEEFoooooFGGGHHoIIIJJoKKK
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Fv2,F<2,Cv2,Cv2,A>3
</answer>


Board size: 6x6
Board: BooooCBDoAACoDoEECoFGoHHIFGJJJIFoKKK
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
G^1,H<1,J<1,Cv2,A>1
</answer>


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

<think>
Shortest path found.
</think>
<answer>
Cv1,A>3,D^1,E<1,Dv1,A>1
</answer>


Board size: 6x6
Board: oooAABoCCCoBDoEEoBDFFFGGHooIIIHoJJoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: AABCoDooBCoDoEoooDFEooGGFHHHIIoJJKKK
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,Bv1,G<1,Bv1,A>4
</answer>


Board size: 6x6
Board: oooBBBoooCDooAACDoEooCDoEoFFFoEooooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^2,F<2,Dv2,Dv2,A>3
</answer>


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

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

Board size: 6x6
Board: ooooooBCoAADBCoooDBCEEFFooGHHoooGIII
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: oooooooBBBoooooooooAACDEFooCDEFooCDE
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: ooooBoAAoCBDoEECBDFFooGGooHHHIoJJJoI
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
H<2,J<1,Cv3,F<2,Bv2,Bv1,A>4
</answer>


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

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


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

<think>
Shortest path found.
</think>
<answer>
A<1,D^2,E<3,Bv2,Bv2,A>3
</answer>


Board size: 6x6
Board: AAooBooCCCBoooooBoooDEEEFFDoooooGGGo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
G>1,Dv1,D<2,Bv1,A>4
</answer>


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

<think>
Shortest path found.
</think>
<answer>
D>1,E^3,F<1,G<1,Cv1,A>3
</answer>


Board size: 6x6
Board: oooBCooooBCooAAoCDoEoFFDoEGooDoEGHHH
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A>1,E^3,F<3,G^1,H<2,Dv3,Dv1,A>2
</answer>


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

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

Board size: 6x6
Board: oBoooCDBEEECDAAooCFGooHHFGoIIooGJJKK
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A>1,G^1,H<1,J<1,K<1,Cv3,A>2
</answer>


Board size: 6x6
Board: ooBBBooooCCCDoEEEoDooFoGAAoFoGoooFoG
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: BBBoCDEoAACDEFFoCDEGGooooHoIIIoHoJJJ
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: oAAoBCDDDoBCooEEECFoGoHHFoGIIoFoGoJJ
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: oooBBBoooooooooCCCoAADEoooFDEoooFDEo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: ooooBoAAoCBoDooCEEDFoooGDFHHoGoFoooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,E<3,Bv2,Bv2,A>4
</answer>


Board size: 6x6
Board: oBBBooooooooCCCoooDoEFFFDoEGHoAAEGHo
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B>2,C>3,D^2,E^3,F<3,G^1,H^1,A>4
</answer>


Board size: 6x6
Board: ooBBBCoDoAACEDFFGCEDHoGoEoHIIIooHJJJ
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv2,Dv1,D<2,H^2,I<1,Cv2,A>1
</answer>


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

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

Board size: 6x6
Board: ooooBoAAooBooCCoDDoooEFooooEFGHHHEoG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<1,D<2,Fv1,Bv2,A>4
</answer>


Board size: 6x6
Board: oAAoBoCoDoBoCEDFFFGEDoHHGEoIIIGooJJJ
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv2,Dv1,D<2,Bv1,A>3
</answer>


Board size: 6x6
Board: ooooBoAAooBoooooBooCoDDooCEFFFoCEooo
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A>2,C^3,D<3,E^2,F<2,Cv2,A>2
</answer>


Board size: 6x6
Board: ooooBoAAoCBooooCoooDoEEooDFooooDFooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E<1,Bv4,D>2,Bv1,A>4
</answer>


Board size: 6x6
Board: BCCCoDBoAAoDBooooDEFGoooEFGHHHEoGIIo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: ooBoooooBCCCoooDooAAoDoEooFFFEoGGGoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Ev1,E<2,G<1,Dv2,A>4
</answer>


Board size: 6x6
Board: AABoooooBCoooDECFoGDEoFoGHHHoIoooooI
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
I^2,I>2,Ev1,Bv1,A>4
</answer>


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

<think>
Shortest path found.
</think>
<answer>
G<1,K^1,L<1,Iv1,Dv2,A>1
</answer>


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

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

Board size: 6x6
Board: BCCCoDBEoAADBEoFFDoEoGGGooHIIIooHJJJ
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
H^3,H<1,I<1,Dv2,A>1
</answer>


Board size: 6x6
Board: oBBBoCoooooCooAAoCooDEEoooDFFFGGoooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A>1,D^1,F<1,Cv3,A>1
</answer>


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

<think>
Shortest path found.
</think>
<answer>
D<1,F<1,Bv2,G<1,Bv2,A>4
</answer>


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

<think>
Shortest path found.
</think>
<answer>
B^1,A>3,Bv2,B<1,D^1,A>1
</answer>


Board size: 6x6
Board: oBAAoCoBooDCoBooDEooooDEooFFoEooGGHH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
G<1,H<1,Ev1,Cv1,A>2
</answer>


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

<think>
Shortest path found.
</think>
<answer>
A<2,D^1,G<3,Bv1,Bv1,A>3
</answer>


Board size: 6x6
Board: ooBBBoAAooCDEoooCDEFGGGHoFIIIHoFoJJJ
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A>2,F^3,G<1,Dv1,J<1,Hv1,Dv1,A>2
</answer>


Board size: 6x6
Board: BBBoooooCoDoAACEDoooCEDooooEooooFFoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv2,F<2,Cv2,Cv1,A>4
</answer>


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

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

Board size: 6x6
Board: ooBCCCooBoooAABoDEooooDEFGoHHHFGoooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv3,B<2,C^2,D^2,A>4
</answer>


Board size: 6x6
Board: BCDEEEBCDFoGBCoFoGHoAAIGHJJJIooooKKK
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv1,D<1,G^1,I^2,A>2
</answer>


Board size: 6x6
Board: oAABoooCoBoooCDDDooEEoooFooGGGFooooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E>1,Cv2,C<2,Bv1,A>3
</answer>


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

<think>
Shortest path found.
</think>
<answer>
I<3,Dv1,K<2,Fv2,Cv2,A>3
</answer>


Board size: 6x6
Board: ooooBooAAoBoCoooBoCDEEFFCDoooooDoooo
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A>1,C^2,D^3,E<2,F<2,Dv2,A>2
</answer>


Board size: 6x6
Board: oooooBooCooBAACooBooCDDDoEEooooooooo
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E<1,Cv2,A>3,C^3,D<1,Cv3,A>1
</answer>


Board size: 6x6
Board: oBBBooCoDAAECoDooEooDFFFoGGHHHIIoJJJ
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B>2,D^1,F<1,Ev1,A>1
</answer>


Board size: 6x6
Board: oAAooBCooooBCDDDEECFFFGGoHHIIIoooJJJ
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv2,C<1,D<1,Bv1,A>3
</answer>


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

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

Board size: 6x6
Board: oAAoBoooooBoCoooBoCoDEEFooDooFooDGGF
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A<1,C^1,D^3,E<3,Bv1,Bv1,A>4
</answer>


Board size: 6x6
Board: ooooooooBBBCoAADECooFDEGooFHHGIIFooG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<2,C^1,D^2,E^2,A>3
</answer>


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

<think>
Shortest path found.
</think>
<answer>
D^1,E<4,Bv1,Bv1,Bv1,A>4
</answer>


Board size: 6x6
Board: ooBoooooBCooooBCoDooooEDAAoFEDGGoFEo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,D^1,E^2,F^2,A>4
</answer>


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

<think>
Shortest path found.
</think>
<answer>
Ev2,F<1,Dv1,H<1,Cv2,A>4
</answer>


Board size: 6x6
Board: oooBBBooCCCoooooooDAAoEFDGGoEFDHHoEo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<2,C<1,E^3,F^2,A>3
</answer>


Board size: 6x6
Board: BooCCCBooDDDoooEooAAoEFGHoIIFGHJJoFG
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<2,D<2,F^3,G^3,I<1,Gv2,A>4
</answer>


Board size: 6x6
Board: oooBooCCCBoooooDDDooEEEFoGGGHFoAAoHF
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


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

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

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

<think>
Shortest path found.
</think>
<answer>
F<2,Bv1,J<1,Gv1,Bv1,A>4
</answer>


Board size: 6x6
Board: ooBBBooCoDDDoCAAEoooooEFGGGHIFoooHIF
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: ooooooooooBCAAooBCooDDBEooFFFEooGGGE
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,F<1,G<1,Cv2,A>4
</answer>


Board size: 6x6
Board: oooBBBAAooCoDDEoCooFEGGGoFooHooFooHo
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A>2,Ev2,D>2,E^3,F<2,Dv1,A>2
</answer>


Board size: 6x6
Board: ooooBooAACBoDooCooDoEEEoDFFGHHoIIGoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: oooooBooAAoBoooooBoCCDooEoFDGGEoFDoo
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A<1,C<1,D^2,F^2,G<3,Bv2,Bv1,A>3
</answer>


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

<think>
Shortest path found.
</think>
<answer>
C^2,D^2,E<3,Cv2,Cv2,A>4
</answer>


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

<think>
Shortest path found.
</think>
<answer>
F<1,G<1,I<1,K<1,Dv3,A>1
</answer>


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

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

Board size: 6x6
Board: BBBoCooAAoCoDDDoCoooEEoooFoGHHoFoGoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E<1,G^2,H<2,Cv2,A>3
</answer>


Board size: 6x6
Board: BBBCDooAACDoooEEooooFFFooGGHHHIIIJJJ
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E<1,F<2,Cv2,Cv2,A>3
</answer>


Board size: 6x6
Board: oooAABoooooBoooCCBDEFFGGDEHHHoIIIoJJ
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: ooooooooBoooooBCCCooBDoEoooDoEooAAoE
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: oooBBBCDEFFFCDEGooAAEGoHoIIooHJJJKKH
Optimal length (moves): 11
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^1,H^1,I<1,K>1,Gv2,A>3,Bv2,B<1,E<1,G^2,A>1
</answer>


Board size: 6x6
Board: oAAoBoCoDDBoCoEoFooGEoFooGEoHHoGoIII
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,C<2,E^1,H<2,Fv1,Bv1,A>3
</answer>


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

<think>
Shortest path found.
</think>
<answer>
Bv1,G^1,K<1,Iv1,Bv1,A>4
</answer>


Board size: 6x6
Board: oooBoooooBooAAoBooCoDDDoCoooEECooooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A>1,C^3,D<2,Cv3,A>3
</answer>


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

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

Board size: 6x6
Board: AAooBoooCCBDEEFoBDGGFHHIoJJJoIooKKKI
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<2,F^1,H<1,Bv1,A>4
</answer>


Board size: 6x6
Board: ooooBoooooBoooAABCoooooCoDoEECoDoFFo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,E<1,F<1,Bv3,A>2
</answer>


Board size: 6x6
Board: oAABCoDooBCoDooEEEDoFGGGoHFIJooHFIJo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv2,D<3,Bv1,Bv1,A>3
</answer>


Board size: 6x6
Board: oooooooooBBBoCCCooDDDoEoooFoEoAAFoEo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<2,E^3,E>3,F^1,A>4
</answer>


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

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


Board size: 6x6
Board: oBBBCDooooCDAAoooDoEEEFFGooHHHGooIIo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E<1,F<1,H<1,Dv3,A>4
</answer>


Board size: 6x6
Board: ooooBoooooBCoAAoBCoooDDDooEFFFooEooo
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,A<1,E^4,E<2,F<2,Cv3,A>4
</answer>


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

<think>
Shortest path found.
</think>
<answer>
H>1,Ev2,E<3,Cv2,Cv1,A>3
</answer>


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

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

Board size: 6x6
Board: oAABoCDDEBoCFoEGGoFHHHoIFJoKKIoJLLLI
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A<1,Cv1,D^1,Fv1,F<3,Bv1,Bv1,A>4
</answer>


Board size: 6x6
Board: oooooBoAAooBoCoooBoCDDEEFGGHHHFoooII
Optimal length (moves): 9
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A>1,C^1,D<1,E<1,F^2,G<1,H<1,Bv2,A>2
</answer>


Board size: 6x6
Board: BooCCCBoooooBoDEEEFGDooHFGooIHoAAoIH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^2,E<1,H^1,I^1,A>3
</answer>


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

<think>
Shortest path found.
</think>
<answer>
D<1,F^3,G<3,Cv2,Cv1,A>4
</answer>


Board size: 6x6
Board: ooooBoAAooBoooCDDDEoCoFFEGoHHHEGoIII
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv2,C<2,E<2,Bv2,A>4
</answer>


Board size: 6x6
Board: AAoBCoDooBCoDooBEEDoFoooGHFIIoGHoooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
I>1,Bv3,D<2,Bv1,A>4
</answer>


Board size: 6x6
Board: BooooCBoDooCBoDAACooDEEEoFoooooFooGG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,E<1,G<1,Dv3,A>1
</answer>


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

<think>
Shortest path found.
</think>
<answer>
C>1,F^2,H^2,I<1,Fv1,A>1
</answer>


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

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

Board size: 6x6
Board: BCCCooBooDDDooEEEFoGGGHFoAAIHoJJoIKK
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: BAAoCoBoDoCoBoDEEEooDFFFGGooHooIIoHo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
I<1,Dv2,D<2,Cv1,A>3
</answer>


Board size: 6x6
Board: ooBBBooCoooooCoDDDooooEFGoAAEFGoooEo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: ooooooooooBCoDDDBCoAAEBCoooEooFFFEoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: oooooBoCAAoBoCoooBDoEFFFDoEoooooEooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: oBAACooBoDCooBEDFFGHEoooGHooIoJJJoIo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv2,Dv1,D<2,Cv1,A>2
</answer>


Board size: 6x6
Board: BCAAoDBCEooDoCEFFFGGHHIoJoKKIoJLLoIo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: BoooooBoooooBooCCCooooooAAoDoooooDoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A>1,Bv3,B<3,D^2,A>3
</answer>


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

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

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

<think>
Shortest path found.
</think>
<answer>
C>1,E^3,E<2,F<1,Bv2,A>3
</answer>


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

<think>
Shortest path found.
</think>
<answer>
A>1,C^1,D<2,E<2,Bv3,A>2
</answer>


Board size: 6x6
Board: oBoooooBCDDDEoCFooEAAFoGooHHHGoIIJJG
Optimal length (moves): 9
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
G^1,H<2,J>1,Fv2,A>2,Cv1,C<1,F^2,A>1
</answer>


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

<think>
Shortest path found.
</think>
<answer>
D<1,Bv1,H<1,Ev1,Bv1,A>4
</answer>


Board size: 6x6
Board: oooBBBCDooooCDoEEEAAooFGHHooFGooIIFG
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<2,A>2,H>2,Dv2,D<2,F^3,G^3,A>2
</answer>


Board size: 6x6
Board: ooBCCCDoBoEFDAAoEFDGHHEoIGoJJJIGKKKo
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A>1,G^2,J<2,Gv2,K<1,Fv2,A>2
</answer>


Board size: 6x6
Board: ooBoooooBoooooBCCCoooooDAAoEoDoooEoD
Optimal length (moves): 10
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv3,B<3,E^4,C>3,D^2,A>3,Cv2,C<1,E^2,A>1
</answer>


Board size: 6x6
Board: oooooBooooCBooAACBooooCoDDoEEooooFFF
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E<1,F<2,Bv3,Bv2,A>2
</answer>


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

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

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

<think>
Shortest path found.
</think>
<answer>
K>2,Fv2,F<1,H<1,Dv2,A>1
</answer>


Board size: 6x6
Board: BBBCooAAoCooDoEEEoDooFFFoGooHooGIIHo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv2,D<2,E<3,Cv2,A>4
</answer>


Board size: 6x6
Board: oooAABCDEEEBCDoFFBCoGooHIIGooHooGJJJ
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
G^1,J<1,Hv1,Bv1,A>1
</answer>


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

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


Board size: 6x6
Board: oBoCCCDBoEEEDBoFFFDoGAAHooGIJHKKKIJH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: oooBBBAAoooCooDooCooDooCooDEEEoooFFo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A>3,D^1,E<1,Dv1,A>1
</answer>


Board size: 6x6
Board: BBBoCooAAoCooooDDDooEEFFooGoHHIIGJJJ
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: BooCCCBoAAoDoEoooDoEFGGGooFHHHooFooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


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

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

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

<think>
Shortest path found.
</think>
<answer>
C^1,F<3,G<3,Bv3,Cv2,A>3
</answer>


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

<think>
Shortest path found.
</think>
<answer>
J>2,Ev2,F<2,Cv1,Cv1,A>2
</answer>


Board size: 6x6
Board: oooBBBooCDDDooCEoFooCEoFooAAoFoGGGoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: BooCCCBoDDDoBEEEFGoHHHFGAAIoooooIoJJ
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<2,D<1,F^2,G^2,G>2,H>2,I^2,A>4
</answer>


Board size: 6x6
Board: oooooooAAoBoooooBoCDDEFFCooEooCooEoo
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^3,D<1,E^3,F<2,Dv3,E>2,Cv2,A>3
</answer>


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

<think>
Shortest path found.
</think>
<answer>
A<2,C^2,D<4,Bv2,Bv2,A>4
</answer>


Board size: 6x6
Board: oooBBBAACoooooCoDoEoFFDoEooGDoEooGoo
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<2,D^2,F>1,Dv3,E<1,Cv2,A>4
</answer>


Board size: 6x6
Board: oooooBoooooBooCCCBoAADEFGooDEFGooDEo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<2,D^3,E^3,Fv1,A>3
</answer>


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

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

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

<think>
Shortest path found.
</think>
<answer>
A>2,Bv1,B<2,D^1,E^3,A>2
</answer>


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

<think>
Shortest path found.
</think>
<answer>
A>1,E^3,F<1,G<1,Cv2,A>1
</answer>


Board size: 6x6
Board: oBBBCDEoAACDEFoooooFoGGGHHHoIIooJJoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: ooooBoooooBoAAoCBoDDDCoooEFFFooEoGGo
Optimal length (moves): 9
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^2,A>2,D>2,E^3,E<1,F<1,G<1,Cv3,A>2
</answer>


Board size: 6x6
Board: oooooBoAACoBDDoCoBoooCEEFFFoooGGGoHH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


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

<think>
Shortest path found.
</think>
<answer>
Fv1,Bv1,B<1,F^2,H^3,A>3
</answer>


Board size: 6x6
Board: oooBBBoooooCAADEoCFoDEooFoDoooooGGHH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv2,Dv1,G<2,Cv1,A>4
</answer>


Board size: 6x6
Board: AAoBoooCoBoooCoBooDoEEEoDooFFFDooooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A>1,D^3,E<2,Cv1,A>3
</answer>


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

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

Board size: 6x6
Board: oooBBBooCoDoAACoDoooooEEooFFFooooGGG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<2,D^1,F>1,Dv2,A>4
</answer>


Board size: 6x6
Board: AAoBooCCDBooEoDBFFEooGGGEHoIIIoHJJJo
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A>1,J>1,Dv3,C>1,D^2,F<3,Cv1,A>3
</answer>


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

<think>
Shortest path found.
</think>
<answer>
B<2,C^1,D^1,G^1,H^1,A>3
</answer>


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

<think>
Shortest path found.
</think>
<answer>
C<1,D<3,E^2,F<2,Bv2,A>4
</answer>


Board size: 6x6
Board: BBBooCoAAoDCoooEDoFGoEDHFGoooHFGIIJJ
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv1,G^1,I<1,J<1,Hv1,Cv2,A>3
</answer>


Board size: 6x6
Board: ooBoCDAABoCDooBooDEEEooooFFooooGGooo
Optimal length (moves): 9
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv4,D>3,E<1,Bv2,A>3,C^2,D<1,Cv2,A>1
</answer>


Board size: 6x6
Board: oooBoCoooBoCAADooCooDEEEoooFFFoooooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^2,E<1,F<1,Dv3,A>4
</answer>


Board size: 6x6
Board: ooBoooooBooooCCCoDooEooDooEFooAAEFoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^2,D>2,E^1,F^1,A>4
</answer>


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

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

Board size: 6x6
Board: oooBCooooBCoAADoCoooDEEoFoDooGFooooG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^2,E<3,Bv3,Cv3,A>4
</answer>


Board size: 6x6
Board: oooBoooAABCoooooCoooooCooDoEEEoDoFFF
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,D^2,E<2,Bv1,A>3
</answer>


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

<think>
Shortest path found.
</think>
<answer>
G<1,I<1,Bv3,B<2,C^1,A>4
</answer>


Board size: 6x6
Board: oooBoooAABCDoooECDoooEooFoooooFGGGoo
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,Cv1,F^1,G<1,Cv2,Bv2,A>3
</answer>


Board size: 6x6
Board: ooBBBoooAAoCoooDoCEFoDGGEFoDooEFHHHo
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<2,A<1,D^2,G<1,Dv3,F>1,Cv2,A>3
</answer>


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

<think>
Shortest path found.
</think>
<answer>
Fv1,F<1,Cv3,E>2,Bv1,A>4
</answer>


Board size: 6x6
Board: oBBBoCooDooCAADoECFGooEoFGHHEooGoIII
Optimal length (moves): 9
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,B>2,C^1,A>2,G^1,I<2,Dv2,Ev1,A>2
</answer>


Board size: 6x6
Board: oBCCCooBooDooBooDoEoAADFEooooFoooooF
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,B<1,D^1,F^3,A>2
</answer>


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

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

Board size: 6x6
Board: oAABCDoooBCDoEEooDoFoGGGoFoHoooFoHoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


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

<think>
Shortest path found.
</think>
<answer>
B<1,Cv1,C<1,G^2,Hv1,A>3
</answer>


Board size: 6x6
Board: ooBCCCooBoooooBoooAAoooDoooooDoooooD
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: oBCAADoBCEEDoBCFFFGHHHooGIoJJJGIooKK
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
H>2,Cv3,E<1,Cv1,A>1
</answer>


Board size: 6x6
Board: BBBCCCooDDDEoAAooEoFGHHHIFGoJJIooKKK
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Gv1,G<1,J<1,Ev2,A>3
</answer>


Board size: 6x6
Board: AAoBooCooBooCDDBEECooFFFoGHHHooGoIII
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: oAAooBoCCooBDEEFFFDGHIoooGHIJJoGHIKK
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^2,E<1,F<1,Cv1,A>3
</answer>


Board size: 6x6
Board: oooooBoooooBoAAooBCoDEEoCoDFFoCoDGGG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A>2,D^1,G<1,Bv3,A>1
</answer>


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

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

Board size: 6x6
Board: ooooooooBoooooBCCCoooDoEAAoDoEoooFFE
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^1,C<3,D^1,E^2,A>4
</answer>


Board size: 6x6
Board: oooooBoAAoCBooooCooDooCooDEFFooDEooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,E^2,F<1,Bv1,A>3
</answer>


Board size: 6x6
Board: AAooBCDoooBCDoEoBCoFEGGGoFoooooFoHHo
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A>2,E^1,F^3,G<2,Cv1,Cv1,A>2
</answer>


Board size: 6x6
Board: oooBBBoooCCCooDoEFooDGEFAAoGEFoooHHo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<2,E^1,F^1,G^1,A>4
</answer>


Board size: 6x6
Board: oooBBBCCCDDDEoFFFoEooooooAAGoHoooGoH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: ooooBoCCCoBDEAAoBDEoFFooooGGHHooIIoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,G<2,H<2,Bv3,A>3
</answer>


Board size: 6x6
Board: ooooooooBCCCDoBoEoDFAAEoDFooGoooooGo
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^2,Fv1,A<2,Cv3,C<2,D^1,A>4
</answer>


Board size: 6x6
Board: oooBBBooCCCoooooooDoEFFFDoEooGDoAAoG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


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

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

Board size: 6x6
Board: oooBBBCoDDDECAAFoECooFGGoooFoooooHHH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<1,E^1,H<3,Fv1,A>3
</answer>


Board size: 6x6
Board: ooBBBooooCoDoooCoDAAoCEFoooGEFoHHGoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<2,C^1,E^2,Fv1,A>4
</answer>


Board size: 6x6
Board: oBCooDoBCAADoEEoFGHoooFGHooIIIHJJoKK
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
I<1,K<1,Gv2,Dv2,A>1
</answer>


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

<think>
Shortest path found.
</think>
<answer>
C^1,A>2,F^2,G<1,Fv2,A>2
</answer>


Board size: 6x6
Board: AABCDoooBCDooooCDEFGGGoEFHIIIoFHoooo
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>1,Cv1,F^3,G<1,Cv1,A>3
</answer>


Board size: 6x6
Board: oooBoooooBCooAABCoDoooCoDooEEEoooooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,E<3,Bv3,Bv2,A>3
</answer>


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

<think>
Shortest path found.
</think>
<answer>
A<2,C^1,E<3,Bv1,Bv1,A>4
</answer>


Board size: 6x6
Board: AAooBooCooBooCDDDEoCFooEGGFoooooFooo
Optimal length (moves): 9
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Ev1,D>1,E^2,G>3,Cv2,Cv2,C<2,Bv1,A>4
</answer>


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

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

Board size: 6x6
Board: BoAACoBoooCooDDDEFoGooEFHGIoEFHGIJJo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
I^1,J<1,Ev1,Cv1,A>2
</answer>


Board size: 6x6
Board: BBBoCoAAoDCooooDCoEEooFFooGGGooooooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
G<2,Dv3,E<2,Cv2,A>4
</answer>


Board size: 6x6
Board: oBoCCCoBAAoDEooooDEoFFoDGHIJJJGHIoKK
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F>1,I^2,J<1,Dv1,A>2
</answer>


Board size: 6x6
Board: BBBooCAADoECoFDGEHIFoGoHIoJJKKIooLLo
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv1,Dv1,J<1,K<1,Hv2,Cv2,A>4
</answer>


Board size: 6x6
Board: AABoooooBoCoooBoCDEEEFoDGGoFoDoooooo
Optimal length (moves): 9
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^2,F^2,F>3,Bv1,A>3,C^1,F<1,Cv1,A>1
</answer>


Board size: 6x6
Board: oAAoBoCCoDBoEFFDBoEooDGGoooooooooooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: ooBBBooooCoDoAACEDFoGoEDFoGoHHoIIIJJ
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<2,C^1,E^2,H<1,I<1,J<1,Ev2,A>3
</answer>


Board size: 6x6
Board: BAACDoBoECDoBoECDooFGGGooFooHHIIoJJo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


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

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

Board size: 6x6
Board: oooooBAACoDBEECoDBoFCGHoIFoGHoIFoGoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,Bv1,Hv1,Bv1,A>4
</answer>


Board size: 6x6
Board: BooooCBDDDoCBAAooCoooEEEFFGGoooHHIII
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E<1,H<1,I<1,Cv3,A>3
</answer>


Board size: 6x6
Board: oBBBoooooCoDAAECoDooEoFFooEGGooooooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<1,C^1,D^1,Ev1,A>4
</answer>


Board size: 6x6
Board: BBBooCoooAACoDDDEEFGHoIIFGHoJJFGKKLL
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: ooAABoCoDoBoCEDFGGHEDFIIHooJJoHKKoLL
Optimal length (moves): 9
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,H^1,J>1,Gv1,K<1,Dv2,F<2,Cv1,A>2
</answer>


Board size: 6x6
Board: ooooooBCDDDoBCoAAEBCFFFEGooHoEGIIHJJ
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^1,C^1,F<2,H^1,J<1,Ev1,A>1
</answer>


Board size: 6x6
Board: oBooCooBooCDoAAoCDooEFooooEFGGoHHFoo
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,A<1,E^3,F^2,G<3,Dv3,Ev2,A>4
</answer>


Board size: 6x6
Board: ooooBooAAoBooooooCDEFFFCDEGGHHoEoIIo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A>1,E^3,F<1,Cv2,A>2
</answer>


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

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

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

<think>
Shortest path found.
</think>
<answer>
I>1,Bv3,B<3,C<3,D^2,A>4
</answer>


Board size: 6x6
Board: oAAoBoCDDDBoCEEoBoCoFFGGHHoooooIIJJJ
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,F<2,G<2,Cv1,A>3
</answer>


Board size: 6x6
Board: ooBBBoooooCoooooCoDDDoEooFFFEGAAooEG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: oBCCCooBoDDDoooEoFoAAEGFooHHGFooooGo
Optimal length (moves): 9
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
H<1,Ev2,A>1,Bv2,B<1,C<2,E^2,F^3,A>2
</answer>


Board size: 6x6
Board: oooBBBooCoooooCDDDooCEooAAoEoooFFooo
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<3,F<1,Cv2,C<3,E^3,D>3,E^2,A>4
</answer>


Board size: 6x6
Board: ooBBBooooCooAADCEoFFDCEGHHHoEGIIIooG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B>1,Cv2,C^2,Dv1,A>4
</answer>


Board size: 6x6
Board: BBBCDoAAoCDoEEoCooooFFGoHoIoGoHoIJJo
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F<2,Cv2,I^1,J<1,Hv1,Cv2,A>4
</answer>


Board size: 6x6
Board: BBBoooCDAAoECDFooEoDFGGGHHHIoooooIJJ
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


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

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

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

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


Board size: 6x6
Board: ooBoooAABooCoooDoCoooDoCoEEFFFoooGGo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,E<1,F<1,Bv1,A>4
</answer>


Board size: 6x6
Board: ooBoooCoBoooCDDDEoAAoFEooooFoooooFoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,D<1,E^1,F^3,A>4
</answer>


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

<think>
Shortest path found.
</think>
<answer>
Cv2,F^3,G<1,H<1,Dv1,A>3
</answer>


Board size: 6x6
Board: ooooBCoAAoBCoDEEoCoDFFGGoDHHoooooIII
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: BoAACoBDDoCooEoFFFoEGHHHIIGJJJooGKKK
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D>1,E^2,F<2,Dv1,A>2
</answer>


Board size: 6x6
Board: ooooooBBBCDEFFFCDEGGGCHIoJooHIoJAAHI
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: ooBBBCoAAoDCEEEoDooFFoGGHoIooJHoIKKJ
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F<1,G<2,Cv2,Cv1,A>3
</answer>


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

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

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

<think>
Shortest path found.
</think>
<answer>
C^1,E^1,F<3,Bv2,Bv1,A>4
</answer>


Board size: 6x6
Board: oooBCDoooBCDooAACDEEooooFGHHHoFGoIII
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E>2,G^2,H<1,I<2,Cv3,Cv3,A>2
</answer>


Board size: 6x6
Board: ooooBCDAAoBCDooEBCDoFEoooGFoHHoGoooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F^1,H<2,Bv2,Bv2,A>3
</answer>


Board size: 6x6
Board: oooooBAAoCDBoooCDEFGGGoEFoHHooFIIIoo
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A>1,Dv1,Ev2,Bv2,E^3,F<1,Cv1,A>3
</answer>


Board size: 6x6
Board: oooBooCAABooCooBooCooDDDoooEEEoooooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,D<3,E<3,Cv2,A>3
</answer>


Board size: 6x6
Board: oAAoBoooCoBDEECoBDoFCGGHIFoooHIooJJo
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A<1,C^1,Fv1,F<3,Bv1,Bv1,A>4
</answer>


Board size: 6x6
Board: BBBoCooooDCEoAADFEGoooFoGHoIIIGHoJJJ
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,E^1,A>1,H^2,I<2,Gv1,A>2
</answer>


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

<think>
Shortest path found.
</think>
<answer>
C^1,D^2,E^3,F<2,Dv3,A>4
</answer>


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

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

Board size: 6x6
Board: ooooooooBCooAABCDoEoFCDGEoFoDGooFHHo
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^1,F^1,H<3,Cv2,Cv1,Cv1,A>4
</answer>


Board size: 6x6
Board: oBoCoooBoCoDAAECoDoFEGGooFEoHHIIoooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,Ev1,G>1,Cv3,A>4
</answer>


Board size: 6x6
Board: oAAoBoCooDBoCEEDBoCooDFFGoooooGoooHH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: BBBoooooCoooDECFFFDEoooGDAAHoGIIoHoG
Optimal length (moves): 9
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: ooooBCooAABCDDooBEooFGGEooFoooooFooo
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A<2,Ev2,Cv2,E^3,F<3,Bv2,Bv2,A>4
</answer>


Board size: 6x6
Board: oBBBCoooDoCoAADoCoEooFGGEooFHHEIIFoo
Optimal length (moves): 9
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<1,F^3,G<3,H<3,Cv3,Cv3,B>3,C^1,A>4
</answer>


Board size: 6x6
Board: ooooBoooAABoCCoDBoEEoDFFoooGGGHHooII
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
G<3,Dv2,E<2,Bv2,A>2
</answer>


Board size: 6x6
Board: ooooooooBBBoooCDDDEoCooFEGGGoFEoAAoF
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


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

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

Board size: 6x6
Board: ooBoooooBoooAABoooCooooDCooooDCEEEoD
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,E>2,Bv3,A>3,D^1,E<1,Cv1,A>1
</answer>


Board size: 6x6
Board: ooooBoAAoCBooDDCBoooEoooooEoFFGGEHHo
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,C<1,E^2,F<4,Bv2,Bv1,A>4
</answer>


Board size: 6x6
Board: BBBooCDoAAoCDEEEFFGGHoIIooHJJJooHoKK
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B>1,D^1,E<1,F<1,I<1,Dv2,A>2
</answer>


Board size: 6x6
Board: AABooooCBDDooCEoFFGoEHIJGKKHIJGLLHIo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
G^2,K<1,Fv1,Bv1,A>4
</answer>


Board size: 6x6
Board: BCAADoBCoEDoFCGEHHFoGooooooIIIJJJoKK
Optimal length (moves): 13
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,Fv1,Bv1,A<2,E^1,F^2,G<2,I<2,Dv3,F>2,Bv1,Bv1,A>4
</answer>


Board size: 6x6
Board: oBoooCDBoooCDBAAoCDoEFFFooEooooGGHHH
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A>1,E^2,F<1,G<1,H<1,Cv3,A>1
</answer>


Board size: 6x6
Board: oBCCCoDBooEoDBooEoDAAoEooFoooooFoooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: oooBBBooCDDDooCooEAACooEooFFoEGGGHHH
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,A>3,F<2,Bv2,B<1,C<1,E^2,A>1
</answer>


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

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

Board size: 6x6
Board: ooAABCoooDBCoEoDFFGEHIooGEHIJJGoHIKK
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

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


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

<think>
Shortest path found.
</think>
<answer>
C>1,D^3,E<1,F<1,Cv1,A>2
</answer>


Board size: 6x6
Board: AAoBCoDooBCEDFFFoEoGGGHEooIoHJKKIoHJ
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,Cv2,E<1,Bv1,A>4
</answer>


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

<think>
Shortest path found.
</think>
<answer>
E<1,G>3,Cv2,C<2,Bv2,A>4
</answer>


Board size: 6x6
Board: oAABCoDooBCEDoFFCEooGGGEHHHIIIoooJJJ
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


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

<think>
Shortest path found.
</think>
<answer>
Cv1,Cv2,Ev1,E<2,Bv1,A>4
</answer>


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

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


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

<think>
Shortest path found.
</think>
<answer>
Cv2,F^1,I<2,Gv1,Bv2,A>3
</answer>


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

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

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

<think>
Shortest path found.
</think>
<answer>
B^1,Ev1,E<3,Bv2,Bv1,A>4
</answer>


Board size: 6x6
Board: oBBBCooAADCooooDoooEEDFFGoHIIJGoHooJ
Optimal length (moves): 12
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<1,A<1,D^1,E<1,H^3,G<2,I<2,Dv4,F>2,Cv2,Cv1,A>4
</answer>


Board size: 6x6
Board: oAABCooDDBCEoooBCEFFFGoHoIIGoHoJJJoH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,J<1,Gv1,Bv1,A>3
</answer>


Board size: 6x6
Board: oBBBooAACoooooCDooEEEDoooFFFoooGGooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F<1,Dv2,D>3,Cv1,A>4
</answer>


Board size: 6x6
Board: oBCDoooBCDEFGoAAEFGooooFGHHoIIoooJJJ
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^1,I<1,J<1,Fv2,A>2
</answer>


Board size: 6x6
Board: oAAooBoooCoBDDoCEEoooCFFGHHHoIGooooI
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D>1,G^2,H<1,Cv2,E<1,Bv1,A>3
</answer>


Board size: 6x6
Board: oBBBCooAADCooEEDCooFFFoooooGGGooHHHo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F<1,Dv1,G<2,Cv2,A>3
</answer>


Board size: 6x6
Board: ooooooooooBoooooBooCDoBooCDEFoAADEFo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


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

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

Board size: 6x6
Board: ooBCCCAABooDooEEoDooFFFoooooGGHHHoII
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E<2,G<1,I<1,Dv3,E>1,Bv2,A>4
</answer>


Board size: 6x6
Board: oBAAoCoBoDoCoBoDEEooFGGoHoFIIIHJJKKK
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F^1,G>1,H^2,I<3,Dv2,F<1,Cv1,A>2
</answer>


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

<think>
Shortest path found.
</think>
<answer>
C^2,D>3,Cv3,C<1,Bv2,A>4
</answer>


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

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


Board size: 6x6
Board: ooBAACooBDDCEoBooFEooGGFoHHHoFoIIJJJ
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
I<1,J<1,Fv1,Cv1,A>1
</answer>


Board size: 6x6
Board: AAoBCooDEBCFGDEBoFGoEHHFIJJKKKIooooo
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,D^1,G^1,H<3,Bv1,Bv1,A>4
</answer>


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

<think>
Shortest path found.
</think>
<answer>
E^2,A>3,Dv2,D<1,F^2,A>1
</answer>


Board size: 6x6
Board: oAAooBooCCDBooEFDGHHEFDGooIFoGJJIKKK
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<2,E^1,I^1,K<1,Gv1,Bv1,A>3
</answer>


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

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

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

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


Board size: 6x6
Board: oooBBBoAAoCooDEECooDoFGGHDIFooHoIJJJ
Optimal length (moves): 15
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A<1,Dv1,D<2,H^1,I^4,E>2,G^1,J<3,Hv1,H<2,Dv3,E>1,G>1,Bv2,A>4
</answer>


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

<think>
Shortest path found.
</think>
<answer>
I>1,Bv3,D<1,E<1,Bv1,A>2
</answer>


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

<think>
Shortest path found.
</think>
<answer>
Dv2,G<1,Dv1,I<1,Cv2,A>4
</answer>


Board size: 6x6
Board: ooooBoooAABoooooBoCoDDEECoooooCFFFGG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^3,D<2,E<2,Cv2,A>2
</answer>


Board size: 6x6
Board: ooooooooooBooCAABooCooBooCoDDDoooEEo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


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

<think>
Shortest path found.
</think>
<answer>
G^1,I<1,J<1,K<1,Ev3,A>2
</answer>


Board size: 6x6
Board: oooBBBoCCCoooooDooAAoDoEoFoDGEoFooGE
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<3,C<1,D^2,E^3,A>4
</answer>


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

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

Board size: 6x6
Board: AAooBoooCoBoDECFFFDEoGGoDEooHHooIIIo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv2,Dv1,D<2,Bv1,A>4
</answer>


Board size: 6x6
Board: ooBBBooAAoCooDDDCooooEFFoooEoooooEoo
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<2,D<1,E^3,F<3,Cv2,Cv1,A>3
</answer>


Board size: 6x6
Board: oBoCCCoBDEEEoBDooooFDAAGoFoHHGoFoooG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<1,Dv1,D<1,G^3,A>1
</answer>