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def solve123(al,sh):
al=list(al)
sh=list(sh)
s=[]
if sh[0]==al[3] and sh[2]==al[1]: s.append(0)
elif sh[0]==al[3] and sh[2]==al[2]: s.append(1)
elif sh[0]==al[4] and sh[2]==al[1]: s.append(4)
elif sh[0]==al[4] and sh[2]==al[2]: s.append(5)
if sh[1]==al[3] and sh[5]==al[1]: s.append(0)
elif sh[1]==al[3] and sh[5]==al[2]: s.append(1)
elif sh[1]==al[4] and sh[5]==al[1]: s.append(4)
elif sh[1]==al[4] and sh[5]==al[2]: s.append(5)
if sh[6]==al[1]:
s.append(2)
if sh[7]==al[0]: lt=True
elif sh[7]==al[-1]: lt=False
else:
s.append(3)
if sh[7]==al[0]: lt=False
elif sh[7]==al[-1]: lt=True
if sh[9]==al[2]:
s.append(3)
if sh[8]==al[0]: rt=True
elif sh[8]==al[-1]: rt=False
else:
s.append(2)
if sh[8]==al[0]: rt=False
elif sh[8]==al[-1]: rt=True
if sh[-2]==al[3] and sh[10]==al[1]: s.append(0)
elif sh[-2]==al[3] and sh[10]==al[2]: s.append(1)
elif sh[-2]==al[4] and sh[10]==al[1]: s.append(4)
elif sh[-2]==al[4] and sh[10]==al[2]: s.append(5)
if sh[-1]==al[3] and sh[13]==al[1]: s.append(0)
elif sh[-1]==al[3] and sh[13]==al[2]: s.append(1)
elif sh[-1]==al[4] and sh[13]==al[1]: s.append(4)
elif sh[-1]==al[4] and sh[13]==al[2]: s.append(5)
sh=s
ans=[]
if lt:
if sh[2]==2: pass
else:
i0=sh.index(0)
i1=sh.index(1)
i2=sh.index(2)
i3=sh.index(3)
i4=sh.index(4)
i5=sh.index(5)
sh[i0],sh[i1],sh[i2],sh[i3],sh[i4],sh[i5]=sh[i1],sh[i0],sh[i3],sh[i2],sh[i5],sh[i4]
elif rt:
ans.append('M')
sh[2],sh[3]=sh[3],sh[2]
lt,rt=rt,lt
if sh[2]==2: pass
else:
i0=sh.index(0)
i1=sh.index(1)
i2=sh.index(2)
i3=sh.index(3)
i4=sh.index(4)
i5=sh.index(5)
sh[i0],sh[i1],sh[i2],sh[i3],sh[i4],sh[i5]=sh[i1],sh[i0],sh[i3],sh[i2],sh[i5],sh[i4]
else:
ans.append('L')
sh[4],sh[0]=sh[0],sh[4]
lt=not(lt)
if sh[2]==2: pass
else:
i0=sh.index(0)
i1=sh.index(1)
i2=sh.index(2)
i3=sh.index(3)
i4=sh.index(4)
i5=sh.index(5)
sh[i0],sh[i1],sh[i2],sh[i3],sh[i4],sh[i5]=sh[i1],sh[i0],sh[i3],sh[i2],sh[i5],sh[i4]
if sh[0]==0 and sh[1]==1:
if sh[4]==4 and sh[5]==5: pass
else:
ans.append('D')
sh[4],sh[5]=sh[5],sh[4]
elif sh[0]==1 and sh[1]==0:
if sh[4]==4 and sh[5]==5:
ans.append('U')
sh[1],sh[0]=sh[0],sh[1]
else:
ans.append('U')
sh[1],sh[0]=sh[0],sh[1]
ans.append('D')
sh[4],sh[5]=sh[5],sh[4]
elif sh[0]==0:
if sh[4]==4 or sh[4]==5:
ans.append('R')
sh[1],sh[5]=sh[5],sh[1]
rt=not(rt)
else:
ans.append('D')
sh[4],sh[5]=sh[5],sh[4]
ans.append('R')
sh[1],sh[5]=sh[5],sh[1]
rt=not(rt)
elif sh[0]==1:
if sh[4]==4 or sh[4]==5:
ans.append('R')
sh[1],sh[5]=sh[5],sh[1]
rt=not(rt)
else:
ans.append('D')
sh[4],sh[5]=sh[5],sh[4]
ans.append('R')
sh[1],sh[5]=sh[5],sh[1]
rt=not(rt)
elif sh[1]==0:
ans.append('U')
sh[1],sh[0]=sh[0],sh[1]
if sh[4]==4 or sh[4]==5:
ans.append('R')
sh[1],sh[5]=sh[5],sh[1]
rt=not(rt)
else:
ans.append('D')
sh[4],sh[5]=sh[5],sh[4]
ans.append('R')
sh[1],sh[5]=sh[5],sh[1]
rt=not(rt)
elif sh[1]==1:
ans.append('U')
sh[1],sh[0]=sh[0],sh[1]
if sh[4]==4 or sh[4]==5:
ans.append('R')
sh[1],sh[5]=sh[5],sh[1]
rt=not(rt)
else:
ans.append('D')
sh[4],sh[5]=sh[5],sh[4]
ans.append('R')
sh[1],sh[5]=sh[5],sh[1]
rt=not(rt)
else:
ans.append('R')
sh[1],sh[5]=sh[5],sh[1]
ans.append('U')
sh[1],sh[0]=sh[0],sh[1]
ans.append('R')
sh[1],sh[5]=sh[5],sh[1]
ans.append('D')
sh[4],sh[5]=sh[5],sh[4]
ans.append('R')
sh[1],sh[5]=sh[5],sh[1]
rt=not(rt)
if sh[0]!=0:
ans.append('U')
sh[1],sh[0]=sh[0],sh[1]
if sh[4]!=4:
ans.append('D')
sh[4],sh[5]=sh[5],sh[4]
if rt==False: ans+=['R','U','R','U','R','U']
results=[]
for item in ans:
if results and item==results[-1]: results.pop()
else: results.append(item)
ans=results
if len(ans)>1:
if (ans[-1]=='U' and ans[-2]=='D') or (ans[-1]=='D' and ans[-2]=='U'):
del ans[-1]
ans[-1]='M'
return ans
def solve122(al,sh):
al=list(al)
sh=list(sh)
s=[]
if sh[-2]==al[3] and sh[4]==al[-1]: s.append(1)
elif sh[-2]==al[3] and sh[4]==al[0]: s.append(2)
elif sh[-2]==al[4] and sh[4]==al[0]: s.append(0)
elif sh[-2]==al[4] and sh[4]==al[-1]: s.append(3)
if sh[0]==al[3] and sh[2]==al[0]: s.append(1)
elif sh[0]==al[3] and sh[2]==al[-1]: s.append(2)
elif sh[0]==al[4] and sh[2]==al[-1]: s.append(0)
elif sh[0]==al[4] and sh[2]==al[0]: s.append(3)
if sh[1]==al[3] and sh[3]==al[-1]: s.append(1)
elif sh[1]==al[3] and sh[3]==al[0]: s.append(2)
elif sh[1]==al[4] and sh[3]==al[0]: s.append(0)
elif sh[1]==al[4] and sh[3]==al[-1]: s.append(3)
if sh[-1]==al[3] and sh[-3]==al[0]: s.append(1)
elif sh[-1]==al[3] and sh[-3]==al[-1]: s.append(2)
elif sh[-1]==al[4] and sh[-3]==al[-1]: s.append(0)
elif sh[-1]==al[4] and sh[-3]==al[0]: s.append(3)
sh=s
if sh[0]==0: fans=[0,1,2,3]
elif sh[0]==1: fans=[1,0,3,2]
elif sh[0]==2: fans=[2,3,0,1]
else: fans=[3,2,1,0]
ans=[]
if sh!=fans:
ans.append('R')
sh[2],sh[3]=sh[3],sh[2]
if sh!=fans:
ans.append('U')
sh[2],sh[1]=sh[1],sh[2]
if sh!=fans:
ans.append('R')
sh[2],sh[3]=sh[3],sh[2]
if sh!=fans:
ans.append('U')
sh[2],sh[1]=sh[1],sh[2]
if sh!=fans:
ans.append('R')
sh[2],sh[3]=sh[3],sh[2]
if len(ans)==5: ans=['U']
if len(ans)==4: ans=['U','R']
return ans
def solve222(inp):
ts=[[inp[0],inp[5],inp[15]],[inp[1],inp[8],inp[14]],[inp[2],inp[11],inp[17]],[inp[3],inp[6],inp[16]]]
bs=[[inp[-3],inp[4],inp[12]],[inp[-4],inp[9],inp[13]],[inp[-1],inp[10],inp[18]],[inp[-2],inp[7],inp[19]]]
t=[{'W','R','G'},{'W','O','G'},{'W','O','B'},{'W','R','B'},{'Y','R','G'},{'Y','O','G'},{'Y','O','B'},{'Y','R','B'}]
for i in range(4):
ts[i]=[t.index(set(ts[i]))+1,ts[i]]
bs[i]=[t.index(set(bs[i]))+1,bs[i]]
turns=[]
for v in range(1,5):
if ts[3][0]==v:
turns.extend("D' B' D".split())
bs.insert(0,ts.pop())
ts.append(bs.pop())
bs[2],bs[3]=bs[3],bs[2]
ts[3][1].reverse()
bs[0][1].append(bs[0][1].pop(0))
bs[1][1].append(bs[1][1].pop(1))
bs[3][1].insert(0,bs[3][1].pop())
elif ts[1][0]==v:
turns.extend("R B R'".split())
store=ts[1]
ts[1]=bs.pop(1)
bs.append(store)
bs.reverse()
ts[1][1][0],ts[1][1][1]=ts[1][1][1],ts[1][1][0]
bs[0][1].insert(0,bs[0][1].pop())
bs[1][1].append(bs[1][1].pop(0))
bs[3][1][1],bs[3][1][2]=bs[3][1][2],bs[3][1][1]
elif ts[2][0]==v:
turns.extend("R' B2 R".split())
store=ts[2]
ts[2]=bs.pop(0)
bs.insert(0,store)
bs.append(bs.pop(2))
ts[2][1].reverse()
bs[0][1].reverse()
bs[2][1].reverse()
bs[3][1].reverse()
elif bs[3][0]==v:
turns.append("B'")
bs.insert(0,bs.pop())
for i in range(4):
bs[i][1][1],bs[i][1][2]=bs[i][1][2],bs[i][1][1]
elif bs[1][0]==v:
turns.append("B")
bs.append(bs.pop(0))
for i in range(4):
bs[i][1][1],bs[i][1][2]=bs[i][1][2],bs[i][1][1]
elif bs[2][0]==v:
turns.append("B2")
bs[0],bs[2]=bs[2],bs[0]
bs[1],bs[3]=bs[3],bs[1]
elif ts[0][0]==v and ts[0][1][0]!='W':
turns.extend("U B U' B'".split())
store=ts[0]
ts[0]=bs.pop(0)
ts[0][1].reverse()
bs.insert(0,store)
bs[1],bs[2]=bs[2],bs[1]
bs[0][1][0],bs[0][1][1]=bs[0][1][1],bs[0][1][0]
bs[1][1].reverse()
bs[2][1][1],bs[2][1][2]=bs[2][1][2],bs[2][1][1]
if bs[0][1][2]=='W' and bs[0][0]==v:
turns.extend("U B U'".split())
store=ts[0]
if v==1: ts[0]=[1,['W','R','G']]
elif v==2: ts[0]=[2,['W','G','O']]
elif v==3: ts[0]=[3,['W','O','B']]
else: ts[0]=[4,['W','B','R']]
bs[0]=bs.pop(2)
bs.append(store)
bs[0][1].insert(0,bs[0][1].pop())
bs[2][1][1],bs[2][1][2]=bs[2][1][2],bs[2][1][1]
bs[3][1].append(bs[3][1].pop(0))
elif bs[0][1][1]=='W' and bs[0][0]==v:
turns.extend("L' B' L".split())
store=ts[0]
if v==1: ts[0]=[1,['W','R','G']]
elif v==2: ts[0]=[2,['W','G','O']]
elif v==3: ts[0]=[3,['W','O','B']]
else: ts[0]=[4,['W','B','R']]
bs[0]=store
bs.insert(0,bs.pop(2))
bs[0][1].append(bs[0][1].pop(0))
bs[1][1].insert(0,bs[1][1].pop())
bs[2][1][1],bs[2][1][2]=bs[2][1][2],bs[2][1][1]
elif bs[0][1][0]=='W' and bs[0][0]==v:
turns.extend("U B2 U' B' U B U'".split())
store=ts[0]
if v==1: ts[0]=[1,['W','R','G']]
elif v==2: ts[0]=[2,['W','G','O']]
elif v==3: ts[0]=[3,['W','O','B']]
else: ts[0]=[4,['W','B','R']]
bs.pop(0)
bs.append(store)
bs.append(bs.pop(1))
bs[0][1][0],bs[0][1][1]=bs[0][1][1],bs[0][1][0]
bs[1][1].append(bs[1][1].pop(0))
bs[2][1][0],bs[2][1][1]=bs[2][1][1],bs[2][1][0]
bs[3][1][1],bs[3][1][2]=bs[3][1][2],bs[3][1][1]
turns.append("F'")
ts.append(ts.pop(0))
for i in range(4):
ts[i][1][1],ts[i][1][2]=ts[i][1][2],ts[i][1][1]
turns.append("y2")
yel=0
for i in bs:
if i[1][0]=='Y': yel+=1
if yel==0:
if bs[0][1][2]==bs[1][1][2]==bs[2][1][2]==bs[3][1][2]=='Y':
turns.extend("R2 F2 R F2 R2".split())
bs.insert(0,bs.pop())
bs[0][1].reverse()
bs[1][1].reverse()
bs[2][1].reverse()
bs[3][1].reverse()
elif bs[0][1][1]==bs[1][1][1]==bs[2][1][1]==bs[3][1][1]=='Y':
turns.extend("F R2 F2 R F2 R2".split())
bs[0][1].append(bs[0][1].pop(0))
bs[1][1].append(bs[1][1].pop(0))
bs[2][1].append(bs[2][1].pop(0))
bs[3][1].append(bs[3][1].pop(0))
else:
while not(bs[1][1][1]==bs[2][1][1]=='Y'):
turns.append("F")
bs.append(bs.pop(0))
for i in range(4):
bs[i][1][1],bs[i][1][2]=bs[i][1][2],bs[i][1][1]
turns.extend("R F2 R2 F' R2 F' R2 F2 R".split())
bs=bs[2:]+bs[:2]
bs[0][1].append(bs[0][1].pop(0))
bs[1][1].insert(0,bs[1][1].pop())
bs[2][1].insert(0,bs[2][1].pop())
bs[3][1].append(bs[3][1].pop(0))
if yel==1:
while bs[3][1][0]!='Y':
turns.append("F")
bs.append(bs.pop(0))
for i in range(4):
bs[i][1][1],bs[i][1][2]=bs[i][1][2],bs[i][1][1]
if bs[2][1][2]=='Y':
turns.extend("L' F R F' L F R'".split())
bs.insert(0,bs.pop(2))
bs.append(bs.pop(2))
bs[0][1].insert(0,bs[0][1].pop())
bs[1][1].reverse()
bs[2][1].append(bs[2][1].pop(1))
bs[3][1].append(bs[3][1].pop(0))
else:
turns.extend("U F U' F U F2 U'".split())
bs=bs[2:]+bs[:2]
bs[0][1].append(bs[0][1].pop(0))
bs[2][1].append(bs[2][1].pop(0))
bs[3][1].insert(0,bs[3][1].pop())
elif yel==2:
if bs[0][1][0]==bs[2][1][0]=='Y' or bs[1][1][0]==bs[3][1][0]=='Y':
while not(bs[0][1][1]=='Y'):
turns.append("F")
bs.append(bs.pop(0))
for i in range(4):
bs[i][1][1],bs[i][1][2]=bs[i][1][2],bs[i][1][1]
turns.extend("D R' D' R F R F' R'".split())
bs.insert(2,bs.pop(0))
bs[0][1][1],bs[0][1][2]=bs[0][1][2],bs[0][1][1]
bs[1][1].reverse()
bs[2][1].append(bs[2][1].pop(0))
else:
while not(bs[0][1][0]==bs[3][1][0]=='Y'):
turns.append("F")
bs.append(bs.pop(0))
for i in range(4):
bs[i][1][1],bs[i][1][2]=bs[i][1][2],bs[i][1][1]
if bs[1][1][1]=='Y':
turns.extend("D R F R' F' D'".split())
bs[0],bs[1]=bs[1],bs[0]
bs[2],bs[3]=bs[3],bs[2]
bs[0][1][0],bs[0][1][1]=bs[0][1][1],bs[0][1][0]
bs[1][1][1],bs[1][1][2]=bs[1][1][2],bs[1][1][1]
bs[2][1][1],bs[2][1][2]=bs[2][1][2],bs[2][1][1]
bs[3][1][0],bs[3][1][1]=bs[3][1][1],bs[3][1][0]
else:
turns.extend("R F R' F' R' D R D'".split())
bs.insert(0,bs.pop(2))
bs[0][1].insert(0,bs[0][1].pop())
bs[2][1].reverse()
bs[1][1][1],bs[1][1][2]=bs[1][1][2],bs[1][1][1]
same=0
if not(bs[0][1][2]==bs[1][1][2] and bs[2][1][2]==bs[3][1][2]):
for i in range(4):
if bs[0][1][2]==bs[1][1][2]:
same=1
break
turns.append("F")
bs.append(bs.pop(0))
for i in range(4):
bs[i][1][1],bs[i][1][2]=bs[i][1][2],bs[i][1][1]
if same==1:
turns.extend("R' D R' U2 R D' R' U2 R2".split())
bs.append(bs.pop(0))
bs[1],bs[2]=bs[2],bs[1]
bs[0][1][1],bs[0][1][2]=bs[0][1][2],bs[0][1][1]
bs[3][1][1],bs[3][1][2]=bs[3][1][2],bs[3][1][1]
else:
turns.extend("D R F' R' F' R F R' D' R F R' F' R' D R D'".split())
bs[1],bs[3]=bs[3],bs[1]
while bs!=sorted(bs):
turns.append("F")
bs.append(bs.pop(0))
for i in range(4):
bs[i][1][1],bs[i][1][2]=bs[i][1][2],bs[i][1][1]
ans=[]
for i in turns:
if ans and i[0]==ans[-1][0]:
if len(i)==1:
if len(ans[-1])==1: ans[-1]=i+'2'
elif ans[-1][1]=='2': ans[-1]=i+"'"
else: ans.pop()
elif i[1]=='2':
if len(ans[-1])==1: ans[-1]=ans[-1][0]+"'"
elif ans[-1][1]=='2': ans.pop()
else: ans[-1]=ans[-1][0]
else:
if len(ans[-1])==1: ans.pop()
elif ans[-1][1]=='2': ans[-1]=ans[-1][0]
else: ans[-1]=ans[-1][0]+'2'
else: ans.append(i)
if ans[-1]=='y2': ans.pop()
return ans
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