Quelle class3mflds.gi Sprache: unbekannt

################################################################################
##<#GAPDoc Label="SCNrCyclic3Mflds">
## <ManSection>
## <Func Name="SCNrCyclic3Mflds" Arg="i"/>
## <Returns> integer upon success, <K>fail</K> otherwise.</Returns>
## <Description>
## Returns the number of combinatorial 3-manifolds with transitive cyclic
## symmetry with <Arg>i</Arg> vertices.
##
## See <Cite Key="Spreer11CyclicCombMflds"/> for more about the classification
## of combinatorial 3-manifolds with transitive cyclic symmetry up to
## <M>22</M> vertices.
## <Example><![CDATA[
## gap> SCNrCyclic3Mflds(22);
## ]]></Example>
## </Description>
## </ManSection>
##<#/GAPDoc>
################################################################################
InstallGlobalFunction(SCNrCyclic3Mflds,
function(i)
local allowedInts;

allowedInts:=[0, 0, 0, 0, 1, 1, 1, 2, 2, 8, 6, 20, 15, 50, 34, 107, 89, 319,
    279, 1008, 1038, 3090];
if i < 5 or i > 22 then
  Info(InfoSimpcomp,1,"SCSeriesCyclic3Mflds: argument must be a positive ",
      "integer 5 <= i <= 22.");
  return fail;
fi;

return allowedInts[i];

end);

################################################################################
##<#GAPDoc Label="SCCyclic3MfldTopTypes">
## <ManSection>
## <Func Name="SCCyclic3MfldTopTypes" Arg="i"/>
## <Returns> a list of strings upon success, <K>fail</K> otherwise.</Returns>
## <Description>
## Returns a list of all topological types that occur in the classification
## combinatorial 3-manifolds with transitive cyclic symmetry with <Arg>i</Arg>
## vertices.
##
## See <Cite Key="Spreer11CyclicCombMflds"/> for more about the classification
## of combinatorial 3-manifolds with transitive cyclic symmetry up to
## <M>22</M> vertices.
## <Example><![CDATA[
## gap> SCCyclic3MfldTopTypes(19);
## ]]></Example>
## </Description>
## </ManSection>
##<#/GAPDoc>
################################################################################
InstallGlobalFunction(SCCyclic3MfldTopTypes,
function(i)
local tt;

tt:=[
[],
[],
[],
[],
["S^3"],
["S^3"],
["S^3"],
["S^3"],
["S^2~S^1","S^3"],
["S^2xS^1","S^2~S^1","S^3"],
["S^2~S^1","S^3"],
["(S^2xS^1)#2","S^2xS^1","S^2~S^1","S^3"],
["S^2~S^1","S^3"],
["L(3,1)","S^2xS^1","S^2~S^1","S^3"],
["RP^3","S^2~S^1","S^3","S^3/Q8","T^3"],
["(S^2xS^1)#5","B2","L(3,1)","S^2xS^1","S^2~S^1","S^3","S^3/P24","T^3"],
["B2","RP^2xS^1","RP^3","S^2~S^1","S^3","Sigma^3","T^3"],
["(S^2xS^1)#7","(S^2~S^1)#7","B2","B4","K^2xS^1","L(5,1)","L(8,3)","RP^3",
    "SFS[RP^2:(2,1)(2,1)(2,1)]","SFS[T^2:(1,1)]",
"S^2xS^1","S^2~S^1","S^3","S^3/Q8","T^3"],
["B2","RP^2xS^1","SFS[RP^2:(2,1)(3,1)]","S^2~S^1","S^3","Sigma(2,3,7)","T^3"],
["(S^2xS^1)#4","(S^2xS^1)#6","(S^2~S^1)#6","(S^2~S^1)#9","B2","B4","G2",
    "K^2xS^1","L(3,1)","L(8,3)","RP^2xS^1",
    "SFS[D:(3,1)(3,1)]U/mSFS[D:(3,1)(3,1)],m=[-4,5|-3,4]","SFS[K^2/n2:(1,5)]",
    "SFS[RP^2:(2,1)(3,1)]","SFS[RP^2:(3,1)(3,2)]","SFS[S^2:(3,1)(3,1)(4,-3)]",
    "S^2xS^1","S^2~S^1","S^3","S^3/Q28","T^3"],
["(RP^2)#3xS^1","(S^2xS^1)#12","B2","G3","K^2xS^1","L(3,1)","RP^2xS^1",
    "RP^3","SFS[K^2:(2,1)(2,1)(2,1)]","SFS[K^2:(2,1)]",
    "SFS[RP^2:(2,1)(2,1)(2,1)]","SFS[RP^2:(3,1)(3,1)(3,1)]",
    "SFS[RP^2:(3,1)(3,1)(3,2)]","SFS[S^2:(2,1)(2,1)(2,1)(3,-5)]",
    "SFS[S^2:(3,2)(3,2)(3,-1)]","SFS[S^2:(4,1)(4,1)(4,-3)]",
    "SFS[S^2:(5,1)(5,1)(5,-4)]","SFS[T^2:(1,7)]","S^2~S^1","S^3","S^3/Q8",
    "T^3"],
["(S^2xS^1)#12","(S^2~S^1)#12","B2","B4","HS","K^2xS^1","L(15,4)",
    "L(3,1)","L(5,1)","L(7,1)","L(8,3)","RP^2xS^1","RP^3",
    "SFS[(RP^2)#3:(1,1)]","SFS[A:(2,1)(2,1)]/[1,-11|1,-10]",
    "SFS[D:(2,1)(2,1)]U/mSFS[D:(2,1)(3,1)],m=[-5,11|-4,9]",
    "SFS[D:(2,1)(3,1)]U/mSFS[D:(3,1)(3,1)],m=[-8,11|-5,7]",
    "SFS[D_:(3,1)(3,1)]","SFS[K^2:(2,1)(2,1)]","SFS[K^2:(2,1)]",
    "SFS[K^2:(3,1)]","SFS[RP^2:(2,1)(3,1)]","SFS[RP^2:(2,1)(5,1)]",
    "SFS[RP^2:(3,1)(3,2)]","SFS[RP^2:(3,1)(4,3)]","SFS[RP^2:(5,2)(5,3)]",
    "SFS[S^2:(2,1)(2,1)(3,1)(3,-2)]","SFS[S^2:(2,1)(2,1)(3,1)(3,-4)]",
    "SFS[S^2:(3,1)(3,1)(5,-3)]","SFS[S^2:(3,1)(3,1)(9,-7)]",
    "SFS[S^2:(3,2)(4,1)(4,-3)]","SFS[S^2:(4,1)(5,2)(5,-3)]","S^2xS^1",
    "S^2~S^1","S^3","S^3/P24","S^3/Q16","S^3/Q32","Sigma^3","T^3"]
];

if i > 22 then
  Info(InfoSimpcomp,1,"SCCyclic3MfldsTopTypes: argument must be a positive ",
      "integer < 23.");
  return fail;
else
  return tt[i];
fi;
end);

SCIntFunc.SCCyclic3MfldEx:=function(i,j,type)
local all,dc,list,c,k,l,allowedInts,topTypes;

# type = 0: normal
# type = 1: first of given type
# type = 2: list of indices of all of given type
if type = 0 then
  if not IsPosInt(j) or not IsPosInt(i) then
   Info(InfoSimpcomp,1,"SCCyclic3MfldsEx: arguments must be positive ",
        "integers.");
   return fail;
  fi;

  if i < 5 or i > 22 then
   Info(InfoSimpcomp,1,"SCCyclic3MfldsEx: first argument must be a ",
        "positive integer 5 <= i <= 22.");
   return fail;
  fi;

  allowedInts:=[0, 0, 0, 0, 1, 1, 1, 2, 2, 8, 6, 20, 15, 50, 34, 107, 89,
      319, 279, 1008, 1038, 3090];
  if j > allowedInts[i] then
   Info(InfoSimpcomp,1,"SCCyclic3MfldsEx: if first argument i = ",i,
        ", then second argument must be a positive integer j <= ",
        allowedInts[i],".");
   return fail;
  fi;
fi;

all:=[];
all[1]:=[];
all[2]:=[];
all[3]:=[];
all[4]:=[];
all[5]:=[[1,1,1,2]];
all[6]:=[[1,1,1,3],[1,2,1,2]];
all[7]:=[[1,1,1,4],[1,1,2,3],[1,1,3,2],[1,2,1,3],
[1,2,2,2]];
all[8]:=[[1,1,1,5],[1,1,2,4],[1,1,3,3],[1,1,4,2],
[1,2,1,4],[1,2,2,3],[1,2,3,2],[1,3,1,3],
[1,3,2,2],[2,2,2,2]];
all[9]:=[[1,1,1,6],[1,1,2,5],[1,1,3,4],[1,1,4,3],
[1,1,5,2],[1,2,1,5],[1,2,2,4],[1,2,4,2],
[1,3,1,4],[1,3,2,3],[1,4,2,2],[2,2,2,3]];
all[10]:=[[1,1,1,7],[1,1,2,6],[1,1,3,5],[1,1,4,4],
[1,1,5,3],[1,1,6,2],[1,2,1,6],[1,2,2,5],
[1,2,3,4],[1,2,4,3],[1,2,5,2],[1,3,1,5],
[1,3,2,4],[1,3,3,3],[1,3,4,2],[1,4,1,4],
[1,4,2,3],[1,4,3,2],[1,5,2,2],[2,2,2,4],
[2,2,3,3],[2,3,2,3]];
all[11]:=[[1,1,1,8],[1,1,2,7],[1,1,3,6],[1,1,4,5],
[1,1,5,4],[1,1,6,3],[1,1,7,2],[1,2,1,7],
[1,2,2,6],[1,2,3,5],[1,2,4,4],[1,2,5,3],
[1,2,6,2],[1,3,1,6],[1,3,2,5],[1,3,3,4],
[1,3,4,3],[1,3,5,2],[1,4,1,5],[1,4,2,4],
[1,4,3,3],[1,4,4,2],[1,5,2,3],[1,5,3,2],
[1,6,2,2],[2,2,2,5],[2,2,3,4],[2,2,4,3],
[2,3,2,4],[2,3,3,3]];
all[12]:=[[1,1,1,9],[1,1,2,8],[1,1,3,7],[1,1,4,6],
[1,1,5,5],[1,1,6,4],[1,1,7,3],[1,1,8,2],
[1,2,1,8],[1,2,2,7],[1,2,3,6],[1,2,4,5],
[1,2,5,4],[1,2,6,3],[1,2,7,2],[1,3,1,7],
[1,3,2,6],[1,3,3,5],[1,3,5,3],[1,3,6,2],
[1,4,1,6],[1,4,2,5],[1,4,3,4],[1,4,5,2],
[1,5,1,5],[1,5,2,4],[1,5,3,3],[1,5,4,2],
[1,6,2,3],[1,6,3,2],[1,7,2,2],[2,2,2,6],
[2,2,3,5],[2,2,5,3],[2,3,2,5],[2,3,3,4],
[2,3,4,3],[2,4,2,4],[2,4,3,3],[3,3,3,3]];
all[13]:=[[1,1,1,10],[1,1,2,9],[1,1,3,8],[1,1,4,7],
[1,1,5,6],[1,1,6,5],[1,1,7,4],[1,1,8,3],
[1,1,9,2],[1,2,1,9],[1,2,2,8],[1,2,3,7],
[1,2,4,6],[1,2,5,5],[1,2,6,4],[1,2,7,3],
[1,2,8,2],[1,3,1,8],[1,3,2,7],[1,3,3,6],
[1,3,4,5],[1,3,5,4],[1,3,6,3],[1,3,7,2],
[1,4,1,7],[1,4,2,6],[1,4,3,5],[1,4,4,4],
[1,4,5,3],[1,4,6,2],[1,5,1,6],[1,5,2,5],
[1,5,3,4],[1,5,4,3],[1,5,5,2],[1,6,2,4],
[1,6,3,3],[1,6,4,2],[1,7,2,3],[1,7,3,2],
[1,8,2,2],[2,2,2,7],[2,2,3,6],[2,2,4,5],
[2,2,5,4],[2,2,6,3],[2,3,2,6],[2,3,3,5],
[2,3,4,4],[2,3,5,3],[2,4,2,5],[2,4,3,4],
[2,4,4,3],[2,5,3,3],[3,3,3,4]];
all[14]:=[[1,1,1,11],[1,1,2,10],[1,1,3,9],[1,1,4,8],
[1,1,5,7],[1,1,6,6],[1,1,7,5],[1,1,8,4],
[1,1,9,3],[1,1,10,2],[1,2,1,10],[1,2,2,9],
[1,2,3,8],[1,2,4,7],[1,2,5,6],[1,2,6,5],
[1,2,7,4],[1,2,8,3],[1,2,9,2],[1,3,1,9],
[1,3,2,8],[1,3,3,7],[1,3,4,6],[1,3,5,5],
[1,3,6,4],[1,3,7,3],[1,3,8,2],[1,4,1,8],
[1,4,2,7],[1,4,3,6],[1,4,4,5],[1,4,5,4],
[1,4,6,3],[1,4,7,2],[1,5,1,7],[1,5,2,6],
[1,5,3,5],[1,5,4,4],[1,5,5,3],[1,5,6,2],
[1,6,1,6],[1,6,2,5],[1,6,3,4],[1,6,4,3],
[1,6,5,2],[1,7,2,4],[1,7,3,3],[1,7,4,2],
[1,8,2,3],[1,8,3,2],[1,9,2,2],[2,2,2,8],
[2,2,3,7],[2,2,4,6],[2,2,5,5],[2,2,6,4],
[2,2,7,3],[2,3,2,7],[2,3,3,6],[2,3,4,5],
[2,3,5,4],[2,3,6,3],[2,4,2,6],[2,4,3,5],
[2,4,4,4],[2,4,5,3],[2,5,2,5],[2,5,3,4],
[2,5,4,3],[2,6,3,3],[3,3,3,5],[3,3,4,4],
[3,4,3,4]];
all[15]:=[[1,1,1,12],[1,1,2,11],[1,1,3,10],[1,1,4,9],
[1,1,5,8],[1,1,6,7],[1,1,7,6],[1,1,8,5],
[1,1,9,4],[1,1,10,3],[1,1,11,2],[1,2,1,11],
[1,2,2,10],[1,2,3,9],[1,2,4,8],[1,2,5,7],
[1,2,6,6],[1,2,7,5],[1,2,8,4],[1,2,9,3],
[1,2,10,2],[1,3,1,10],[1,3,2,9],[1,3,3,8],
[1,3,4,7],[1,3,5,6],[1,3,6,5],[1,3,7,4],
[1,3,8,3],[1,3,9,2],[1,4,1,9],[1,4,2,8],
[1,4,3,7],[1,4,4,6],[1,4,6,4],[1,4,7,3],
[1,4,8,2],[1,5,1,8],[1,5,2,7],[1,5,3,6],
[1,5,4,5],[1,5,6,3],[1,5,7,2],[1,6,1,7],
[1,6,2,6],[1,6,3,5],[1,6,4,4],[1,6,5,3],
[1,6,6,2],[1,7,2,5],[1,7,3,4],[1,7,4,3],
[1,7,5,2],[1,8,2,4],[1,8,3,3],[1,8,4,2],
[1,9,2,3],[1,9,3,2],[1,10,2,2],[2,2,2,9],
[2,2,3,8],[2,2,4,7],[2,2,5,6],[2,2,6,5],
[2,2,7,4],[2,2,8,3],[2,3,2,8],[2,3,3,7],
[2,3,4,6],[2,3,6,4],[2,3,7,3],[2,4,2,7],
[2,4,3,6],[2,4,4,5],[2,4,5,4],[2,4,6,3],
[2,5,2,6],[2,5,3,5],[2,5,4,4],[2,6,3,4],
[2,6,4,3],[2,7,3,3],[3,3,3,6],[3,3,4,5],
[3,3,5,4],[3,4,3,5],[3,4,4,4]];
all[16]:=[[1,1,1,13],[1,1,2,12],[1,1,3,11],[1,1,4,10],
[1,1,5,9],[1,1,6,8],[1,1,7,7],[1,1,8,6],
[1,1,9,5],[1,1,10,4],[1,1,11,3],[1,1,12,2],
[1,2,1,12],[1,2,2,11],[1,2,3,10],[1,2,4,9],
[1,2,5,8],[1,2,6,7],[1,2,7,6],[1,2,8,5],
[1,2,9,4],[1,2,10,3],[1,2,11,2],[1,3,1,11],
[1,3,2,10],[1,3,3,9],[1,3,4,8],[1,3,5,7],
[1,3,6,6],[1,3,7,5],[1,3,8,4],[1,3,9,3],
[1,3,10,2],[1,4,1,10],[1,4,2,9],[1,4,3,8],
[1,4,4,7],[1,4,5,6],[1,4,6,5],[1,4,7,4],
[1,4,8,3],[1,4,9,2],[1,5,1,9],[1,5,2,8],
[1,5,3,7],[1,5,4,6],[1,5,5,5],[1,5,6,4],
[1,5,7,3],[1,5,8,2],[1,6,1,8],[1,6,2,7],
[1,6,3,6],[1,6,4,5],[1,6,5,4],[1,6,6,3],
[1,6,7,2],[1,7,1,7],[1,7,2,6],[1,7,3,5],
[1,7,4,4],[1,7,5,3],[1,7,6,2],[1,8,2,5],
[1,8,3,4],[1,8,4,3],[1,8,5,2],[1,9,2,4],
[1,9,3,3],[1,9,4,2],[1,10,2,3],[1,10,3,2],
[1,11,2,2],[2,2,2,10],[2,2,3,9],[2,2,4,8],
[2,2,5,7],[2,2,6,6],[2,2,7,5],[2,2,8,4],
[2,2,9,3],[2,3,2,9],[2,3,3,8],[2,3,4,7],
[2,3,5,6],[2,3,6,5],[2,3,7,4],[2,3,8,3],
[2,4,2,8],[2,4,3,7],[2,4,4,6],[2,4,5,5],
[2,4,6,4],[2,4,7,3],[2,5,2,7],[2,5,3,6],
[2,5,4,5],[2,5,5,4],[2,5,6,3],[2,6,2,6],
[2,6,3,5],[2,6,4,4],[2,6,5,3],[2,7,3,4],
[2,7,4,3],[2,8,3,3],[3,3,3,7],[3,3,4,6],
[3,3,5,5],[3,3,6,4],[3,4,3,6],[3,4,4,5],
[3,4,5,4],[3,5,3,5],[3,5,4,4],[4,4,4,4]];
all[17]:=[[1,1,1,14],[1,1,2,13],[1,1,3,12],[1,1,4,11],
[1,1,5,10],[1,1,6,9],[1,1,7,8],[1,1,8,7],
[1,1,9,6],[1,1,10,5],[1,1,11,4],[1,1,12,3],
[1,1,13,2],[1,2,1,13],[1,2,2,12],[1,2,3,11],
[1,2,4,10],[1,2,5,9],[1,2,6,8],[1,2,7,7],
[1,2,8,6],[1,2,9,5],[1,2,10,4],[1,2,11,3],
[1,2,12,2],[1,3,1,12],[1,3,2,11],[1,3,3,10],
[1,3,4,9],[1,3,5,8],[1,3,6,7],[1,3,7,6],
[1,3,8,5],[1,3,9,4],[1,3,10,3],[1,3,11,2],
[1,4,1,11],[1,4,2,10],[1,4,3,9],[1,4,4,8],
[1,4,5,7],[1,4,6,6],[1,4,7,5],[1,4,8,4],
[1,4,9,3],[1,4,10,2],[1,5,1,10],[1,5,2,9],
[1,5,3,8],[1,5,4,7],[1,5,5,6],[1,5,6,5],
[1,5,7,4],[1,5,8,3],[1,5,9,2],[1,6,1,9],
[1,6,2,8],[1,6,3,7],[1,6,4,6],[1,6,5,5],
[1,6,6,4],[1,6,7,3],[1,6,8,2],[1,7,1,8],
[1,7,2,7],[1,7,3,6],[1,7,4,5],[1,7,5,4],
[1,7,6,3],[1,7,7,2],[1,8,2,6],[1,8,3,5],
[1,8,4,4],[1,8,5,3],[1,8,6,2],[1,9,2,5],
[1,9,3,4],[1,9,4,3],[1,9,5,2],[1,10,2,4],
[1,10,3,3],[1,10,4,2],[1,11,2,3],[1,11,3,2],
[1,12,2,2],[2,2,2,11],[2,2,3,10],[2,2,4,9],
[2,2,5,8],[2,2,6,7],[2,2,7,6],[2,2,8,5],
[2,2,9,4],[2,2,10,3],[2,3,2,10],[2,3,3,9],
[2,3,4,8],[2,3,5,7],[2,3,6,6],[2,3,7,5],
[2,3,8,4],[2,3,9,3],[2,4,2,9],[2,4,3,8],
[2,4,4,7],[2,4,5,6],[2,4,6,5],[2,4,7,4],
[2,4,8,3],[2,5,2,8],[2,5,3,7],[2,5,4,6],
[2,5,5,5],[2,5,6,4],[2,5,7,3],[2,6,2,7],
[2,6,3,6],[2,6,4,5],[2,6,5,4],[2,6,6,3],
[2,7,3,5],[2,7,4,4],[2,7,5,3],[2,8,3,4],
[2,8,4,3],[2,9,3,3],[3,3,3,8],[3,3,4,7],
[3,3,5,6],[3,3,6,5],[3,3,7,4],[3,4,3,7],
[3,4,4,6],[3,4,5,5],[3,4,6,4],[3,5,3,6],
[3,5,4,5],[3,5,5,4],[3,6,4,4],[4,4,4,5]];
all[18]:=[[1,1,1,15],[1,1,2,14],[1,1,3,13],[1,1,4,12],
[1,1,5,11],[1,1,6,10],[1,1,7,9],[1,1,8,8],
[1,1,9,7],[1,1,10,6],[1,1,11,5],[1,1,12,4],
[1,1,13,3],[1,1,14,2],[1,2,1,14],[1,2,2,13],
[1,2,3,12],[1,2,4,11],[1,2,5,10],[1,2,6,9],
[1,2,7,8],[1,2,8,7],[1,2,9,6],[1,2,10,5],
[1,2,11,4],[1,2,12,3],[1,2,13,2],[1,3,1,13],
[1,3,2,12],[1,3,3,11],[1,3,4,10],[1,3,5,9],
[1,3,6,8],[1,3,7,7],[1,3,8,6],[1,3,9,5],
[1,3,10,4],[1,3,11,3],[1,3,12,2],[1,4,1,12],
[1,4,2,11],[1,4,3,10],[1,4,4,9],[1,4,5,8],
[1,4,6,7],[1,4,7,6],[1,4,8,5],[1,4,9,4],
[1,4,10,3],[1,4,11,2],[1,5,1,11],[1,5,2,10],
[1,5,3,9],[1,5,4,8],[1,5,5,7],[1,5,7,5],
[1,5,8,4],[1,5,9,3],[1,5,10,2],[1,6,1,10],
[1,6,2,9],[1,6,3,8],[1,6,4,7],[1,6,5,6],
[1,6,7,4],[1,6,8,3],[1,6,9,2],[1,7,1,9],
[1,7,2,8],[1,7,3,7],[1,7,4,6],[1,7,5,5],
[1,7,6,4],[1,7,7,3],[1,7,8,2],[1,8,1,8],
[1,8,2,7],[1,8,3,6],[1,8,4,5],[1,8,5,4],
[1,8,6,3],[1,8,7,2],[1,9,2,6],[1,9,3,5],
[1,9,4,4],[1,9,5,3],[1,9,6,2],[1,10,2,5],
[1,10,3,4],[1,10,4,3],[1,10,5,2],[1,11,2,4],
[1,11,3,3],[1,11,4,2],[1,12,2,3],[1,12,3,2],
[1,13,2,2],[2,2,2,12],[2,2,3,11],[2,2,4,10],
[2,2,5,9],[2,2,6,8],[2,2,7,7],[2,2,8,6],
[2,2,9,5],[2,2,10,4],[2,2,11,3],[2,3,2,11],
[2,3,3,10],[2,3,4,9],[2,3,5,8],[2,3,6,7],
[2,3,7,6],[2,3,8,5],[2,3,9,4],[2,3,10,3],
[2,4,2,10],[2,4,3,9],[2,4,4,8],[2,4,5,7],
[2,4,7,5],[2,4,8,4],[2,4,9,3],[2,5,2,9],
[2,5,3,8],[2,5,4,7],[2,5,5,6],[2,5,6,5],
[2,5,7,4],[2,5,8,3],[2,6,2,8],[2,6,3,7],
[2,6,4,6],[2,6,5,5],[2,6,7,3],[2,7,2,7],
[2,7,3,6],[2,7,4,5],[2,7,5,4],[2,7,6,3],
[2,8,3,5],[2,8,4,4],[2,8,5,3],[2,9,3,4],
[2,9,4,3],[2,10,3,3],[3,3,3,9],[3,3,4,8],
[3,3,5,7],[3,3,7,5],[3,3,8,4],[3,4,3,8],
[3,4,4,7],[3,4,5,6],[3,4,6,5],[3,4,7,4],
[3,5,3,7],[3,5,4,6],[3,5,5,5],[3,5,6,4],
[3,6,3,6],[3,6,4,5],[3,6,5,4],[3,7,4,4],
[4,4,4,6],[4,4,5,5],[4,5,4,5]];
all[19]:=[[1,1,1,16],[1,1,2,15],[1,1,3,14],[1,1,4,13],
[1,1,5,12],[1,1,6,11],[1,1,7,10],[1,1,8,9],
[1,1,9,8],[1,1,10,7],[1,1,11,6],[1,1,12,5],
[1,1,13,4],[1,1,14,3],[1,1,15,2],[1,2,1,15],
[1,2,2,14],[1,2,3,13],[1,2,4,12],[1,2,5,11],
[1,2,6,10],[1,2,7,9],[1,2,8,8],[1,2,9,7],
[1,2,10,6],[1,2,11,5],[1,2,12,4],[1,2,13,3],
[1,2,14,2],[1,3,1,14],[1,3,2,13],[1,3,3,12],
[1,3,4,11],[1,3,5,10],[1,3,6,9],[1,3,7,8],
[1,3,8,7],[1,3,9,6],[1,3,10,5],[1,3,11,4],
[1,3,12,3],[1,3,13,2],[1,4,1,13],[1,4,2,12],
[1,4,3,11],[1,4,4,10],[1,4,5,9],[1,4,6,8],
[1,4,7,7],[1,4,8,6],[1,4,9,5],[1,4,10,4],
[1,4,11,3],[1,4,12,2],[1,5,1,12],[1,5,2,11],
[1,5,3,10],[1,5,4,9],[1,5,5,8],[1,5,6,7],
[1,5,7,6],[1,5,8,5],[1,5,9,4],[1,5,10,3],
[1,5,11,2],[1,6,1,11],[1,6,2,10],[1,6,3,9],
[1,6,4,8],[1,6,5,7],[1,6,6,6],[1,6,7,5],
[1,6,8,4],[1,6,9,3],[1,6,10,2],[1,7,1,10],
[1,7,2,9],[1,7,3,8],[1,7,4,7],[1,7,5,6],
[1,7,6,5],[1,7,7,4],[1,7,8,3],[1,7,9,2],
[1,8,1,9],[1,8,2,8],[1,8,3,7],[1,8,4,6],
[1,8,5,5],[1,8,6,4],[1,8,7,3],[1,8,8,2],
[1,9,2,7],[1,9,3,6],[1,9,4,5],[1,9,5,4],
[1,9,6,3],[1,9,7,2],[1,10,2,6],[1,10,3,5],
[1,10,4,4],[1,10,5,3],[1,10,6,2],[1,11,2,5],
[1,11,3,4],[1,11,4,3],[1,11,5,2],[1,12,2,4],
[1,12,3,3],[1,12,4,2],[1,13,2,3],[1,13,3,2],
[1,14,2,2],[2,2,2,13],[2,2,3,12],[2,2,4,11],
[2,2,5,10],[2,2,6,9],[2,2,7,8],[2,2,8,7],
[2,2,9,6],[2,2,10,5],[2,2,11,4],[2,2,12,3],
[2,3,2,12],[2,3,3,11],[2,3,4,10],[2,3,5,9],
[2,3,6,8],[2,3,7,7],[2,3,8,6],[2,3,9,5],
[2,3,10,4],[2,3,11,3],[2,4,2,11],[2,4,3,10],
[2,4,4,9],[2,4,5,8],[2,4,6,7],[2,4,7,6],
[2,4,8,5],[2,4,9,4],[2,4,10,3],[2,5,2,10],
[2,5,3,9],[2,5,4,8],[2,5,5,7],[2,5,6,6],
[2,5,7,5],[2,5,8,4],[2,5,9,3],[2,6,2,9],
[2,6,3,8],[2,6,4,7],[2,6,5,6],[2,6,6,5],
[2,6,7,4],[2,6,8,3],[2,7,2,8],[2,7,3,7],
[2,7,4,6],[2,7,5,5],[2,7,6,4],[2,7,7,3],
[2,8,3,6],[2,8,4,5],[2,8,5,4],[2,8,6,3],
[2,9,3,5],[2,9,4,4],[2,9,5,3],[2,10,3,4],
[2,10,4,3],[2,11,3,3],[3,3,3,10],[3,3,4,9],
[3,3,5,8],[3,3,6,7],[3,3,7,6],[3,3,8,5],
[3,3,9,4],[3,4,3,9],[3,4,4,8],[3,4,5,7],
[3,4,6,6],[3,4,7,5],[3,4,8,4],[3,5,3,8],
[3,5,4,7],[3,5,5,6],[3,5,6,5],[3,5,7,4],
[3,6,3,7],[3,6,4,6],[3,6,5,5],[3,6,6,4],
[3,7,4,5],[3,7,5,4],[3,8,4,4],[4,4,4,7],
[4,4,5,6],[4,4,6,5],[4,5,4,6],[4,5,5,5]];
all[20]:=[[1,1,1,17],[1,1,2,16],[1,1,3,15],[1,1,4,14],
[1,1,5,13],[1,1,6,12],[1,1,7,11],[1,1,8,10],
[1,1,9,9],[1,1,10,8],[1,1,11,7],[1,1,12,6],
[1,1,13,5],[1,1,14,4],[1,1,15,3],[1,1,16,2],
[1,2,1,16],[1,2,2,15],[1,2,3,14],[1,2,4,13],
[1,2,5,12],[1,2,6,11],[1,2,7,10],[1,2,8,9],
[1,2,9,8],[1,2,10,7],[1,2,11,6],[1,2,12,5],
[1,2,13,4],[1,2,14,3],[1,2,15,2],[1,3,1,15],
[1,3,2,14],[1,3,3,13],[1,3,4,12],[1,3,5,11],
[1,3,6,10],[1,3,7,9],[1,3,8,8],[1,3,9,7],
[1,3,10,6],[1,3,11,5],[1,3,12,4],[1,3,13,3],
[1,3,14,2],[1,4,1,14],[1,4,2,13],[1,4,3,12],
[1,4,4,11],[1,4,5,10],[1,4,6,9],[1,4,7,8],
[1,4,8,7],[1,4,9,6],[1,4,10,5],[1,4,11,4],
[1,4,12,3],[1,4,13,2],[1,5,1,13],[1,5,2,12],
[1,5,3,11],[1,5,4,10],[1,5,5,9],[1,5,6,8],
[1,5,7,7],[1,5,8,6],[1,5,9,5],[1,5,10,4],
[1,5,11,3],[1,5,12,2],[1,6,1,12],[1,6,2,11],
[1,6,3,10],[1,6,4,9],[1,6,5,8],[1,6,6,7],
[1,6,7,6],[1,6,8,5],[1,6,9,4],[1,6,10,3],
[1,6,11,2],[1,7,1,11],[1,7,2,10],[1,7,3,9],
[1,7,4,8],[1,7,5,7],[1,7,6,6],[1,7,7,5],
[1,7,8,4],[1,7,9,3],[1,7,10,2],[1,8,1,10],
[1,8,2,9],[1,8,3,8],[1,8,4,7],[1,8,5,6],
[1,8,6,5],[1,8,7,4],[1,8,8,3],[1,8,9,2],
[1,9,1,9],[1,9,2,8],[1,9,3,7],[1,9,4,6],
[1,9,5,5],[1,9,6,4],[1,9,7,3],[1,9,8,2],
[1,10,2,7],[1,10,3,6],[1,10,4,5],[1,10,5,4],
[1,10,6,3],[1,10,7,2],[1,11,2,6],[1,11,3,5],
[1,11,4,4],[1,11,5,3],[1,11,6,2],[1,12,2,5],
[1,12,3,4],[1,12,4,3],[1,12,5,2],[1,13,2,4],
[1,13,3,3],[1,13,4,2],[1,14,2,3],[1,14,3,2],
[1,15,2,2],[2,2,2,14],[2,2,3,13],[2,2,4,12],
[2,2,5,11],[2,2,6,10],[2,2,7,9],[2,2,8,8],
[2,2,9,7],[2,2,10,6],[2,2,11,5],[2,2,12,4],
[2,2,13,3],[2,3,2,13],[2,3,3,12],[2,3,4,11],
[2,3,5,10],[2,3,6,9],[2,3,7,8],[2,3,8,7],
[2,3,9,6],[2,3,10,5],[2,3,11,4],[2,3,12,3],
[2,4,2,12],[2,4,3,11],[2,4,4,10],[2,4,5,9],
[2,4,6,8],[2,4,7,7],[2,4,8,6],[2,4,9,5],
[2,4,10,4],[2,4,11,3],[2,5,2,11],[2,5,3,10],
[2,5,4,9],[2,5,5,8],[2,5,6,7],[2,5,7,6],
[2,5,8,5],[2,5,9,4],[2,5,10,3],[2,6,2,10],
[2,6,3,9],[2,6,4,8],[2,6,5,7],[2,6,6,6],
[2,6,7,5],[2,6,8,4],[2,6,9,3],[2,7,2,9],
[2,7,3,8],[2,7,4,7],[2,7,5,6],[2,7,6,5],
[2,7,7,4],[2,7,8,3],[2,8,2,8],[2,8,3,7],
[2,8,4,6],[2,8,5,5],[2,8,6,4],[2,8,7,3],
[2,9,3,6],[2,9,4,5],[2,9,5,4],[2,9,6,3],
[2,10,3,5],[2,10,4,4],[2,10,5,3],[2,11,3,4],
[2,11,4,3],[2,12,3,3],[3,3,3,11],[3,3,4,10],
[3,3,5,9],[3,3,6,8],[3,3,7,7],[3,3,8,6],
[3,3,9,5],[3,3,10,4],[3,4,3,10],[3,4,4,9],
[3,4,5,8],[3,4,6,7],[3,4,7,6],[3,4,8,5],
[3,4,9,4],[3,5,3,9],[3,5,4,8],[3,5,5,7],
[3,5,6,6],[3,5,7,5],[3,5,8,4],[3,6,3,8],
[3,6,4,7],[3,6,5,6],[3,6,6,5],[3,6,7,4],
[3,7,3,7],[3,7,4,6],[3,7,5,5],[3,7,6,4],
[3,8,4,5],[3,8,5,4],[3,9,4,4],[4,4,4,8],
[4,4,5,7],[4,4,6,6],[4,4,7,5],[4,5,4,7],
[4,5,5,6],[4,5,6,5],[4,6,4,6],[4,6,5,5],
[5,5,5,5]];
all[21]:=[[1,1,1,18],[1,1,2,17],[1,1,3,16],[1,1,4,15],
[1,1,5,14],[1,1,6,13],[1,1,7,12],[1,1,8,11],
[1,1,9,10],[1,1,10,9],[1,1,11,8],[1,1,12,7],
[1,1,13,6],[1,1,14,5],[1,1,15,4],[1,1,16,3],
[1,1,17,2],[1,2,1,17],[1,2,2,16],[1,2,3,15],
[1,2,4,14],[1,2,5,13],[1,2,6,12],[1,2,7,11],
[1,2,8,10],[1,2,9,9],[1,2,10,8],[1,2,11,7],
[1,2,12,6],[1,2,13,5],[1,2,14,4],[1,2,15,3],
[1,2,16,2],[1,3,1,16],[1,3,2,15],[1,3,3,14],
[1,3,4,13],[1,3,5,12],[1,3,6,11],[1,3,7,10],
[1,3,8,9],[1,3,9,8],[1,3,10,7],[1,3,11,6],
[1,3,12,5],[1,3,13,4],[1,3,14,3],[1,3,15,2],
[1,4,1,15],[1,4,2,14],[1,4,3,13],[1,4,4,12],
[1,4,5,11],[1,4,6,10],[1,4,7,9],[1,4,8,8],
[1,4,9,7],[1,4,10,6],[1,4,11,5],[1,4,12,4],
[1,4,13,3],[1,4,14,2],[1,5,1,14],[1,5,2,13],
[1,5,3,12],[1,5,4,11],[1,5,5,10],[1,5,6,9],
[1,5,7,8],[1,5,8,7],[1,5,9,6],[1,5,10,5],
[1,5,11,4],[1,5,12,3],[1,5,13,2],[1,6,1,13],
[1,6,2,12],[1,6,3,11],[1,6,4,10],[1,6,5,9],
[1,6,6,8],[1,6,8,6],[1,6,9,5],[1,6,10,4],
[1,6,11,3],[1,6,12,2],[1,7,1,12],[1,7,2,11],
[1,7,3,10],[1,7,4,9],[1,7,5,8],[1,7,6,7],
[1,7,8,5],[1,7,9,4],[1,7,10,3],[1,7,11,2],
[1,8,1,11],[1,8,2,10],[1,8,3,9],[1,8,4,8],
[1,8,5,7],[1,8,6,6],[1,8,7,5],[1,8,8,4],
[1,8,9,3],[1,8,10,2],[1,9,1,10],[1,9,2,9],
[1,9,3,8],[1,9,4,7],[1,9,5,6],[1,9,6,5],
[1,9,7,4],[1,9,8,3],[1,9,9,2],[1,10,2,8],
[1,10,3,7],[1,10,4,6],[1,10,5,5],[1,10,6,4],
[1,10,7,3],[1,10,8,2],[1,11,2,7],[1,11,3,6],
[1,11,4,5],[1,11,5,4],[1,11,6,3],[1,11,7,2],
[1,12,2,6],[1,12,3,5],[1,12,4,4],[1,12,5,3],
[1,12,6,2],[1,13,2,5],[1,13,3,4],[1,13,4,3],
[1,13,5,2],[1,14,2,4],[1,14,3,3],[1,14,4,2],
[1,15,2,3],[1,15,3,2],[1,16,2,2],[2,2,2,15],
[2,2,3,14],[2,2,4,13],[2,2,5,12],[2,2,6,11],
[2,2,7,10],[2,2,8,9],[2,2,9,8],[2,2,10,7],
[2,2,11,6],[2,2,12,5],[2,2,13,4],[2,2,14,3],
[2,3,2,14],[2,3,3,13],[2,3,4,12],[2,3,5,11],
[2,3,6,10],[2,3,7,9],[2,3,8,8],[2,3,9,7],
[2,3,10,6],[2,3,11,5],[2,3,12,4],[2,3,13,3],
[2,4,2,13],[2,4,3,12],[2,4,4,11],[2,4,5,10],
[2,4,6,9],[2,4,7,8],[2,4,8,7],[2,4,9,6],
[2,4,10,5],[2,4,11,4],[2,4,12,3],[2,5,2,12],
[2,5,3,11],[2,5,4,10],[2,5,5,9],[2,5,6,8],
[2,5,8,6],[2,5,9,5],[2,5,10,4],[2,5,11,3],
[2,6,2,11],[2,6,3,10],[2,6,4,9],[2,6,5,8],
[2,6,6,7],[2,6,7,6],[2,6,8,5],[2,6,9,4],
[2,6,10,3],[2,7,2,10],[2,7,3,9],[2,7,4,8],
[2,7,5,7],[2,7,6,6],[2,7,8,4],[2,7,9,3],
[2,8,2,9],[2,8,3,8],[2,8,4,7],[2,8,5,6],
[2,8,6,5],[2,8,7,4],[2,8,8,3],[2,9,3,7],
[2,9,4,6],[2,9,5,5],[2,9,6,4],[2,9,7,3],
[2,10,3,6],[2,10,4,5],[2,10,5,4],[2,10,6,3],
[2,11,3,5],[2,11,4,4],[2,11,5,3],[2,12,3,4],
[2,12,4,3],[2,13,3,3],[3,3,3,12],[3,3,4,11],
[3,3,5,10],[3,3,6,9],[3,3,7,8],[3,3,8,7],
[3,3,9,6],[3,3,10,5],[3,3,11,4],[3,4,3,11],
[3,4,4,10],[3,4,5,9],[3,4,6,8],[3,4,8,6],
[3,4,9,5],[3,4,10,4],[3,5,3,10],[3,5,4,9],
[3,5,5,8],[3,5,6,7],[3,5,7,6],[3,5,8,5],
[3,5,9,4],[3,6,3,9],[3,6,4,8],[3,6,5,7],
[3,6,6,6],[3,6,7,5],[3,6,8,4],[3,7,3,8],
[3,7,4,7],[3,7,5,6],[3,7,6,5],[3,8,4,6],
[3,8,5,5],[3,8,6,4],[3,9,4,5],[3,9,5,4],
[3,10,4,4],[4,4,4,9],[4,4,5,8],[4,4,6,7],
[4,4,7,6],[4,4,8,5],[4,5,4,8],[4,5,5,7],
[4,5,6,6],[4,5,7,5],[4,6,4,7],[4,6,5,6],
[4,6,6,5],[4,7,5,5],[5,5,5,6]];
all[22]:=[[1,1,1,19],[1,1,2,18],[1,1,3,17],[1,1,4,16],
[1,1,5,15],[1,1,6,14],[1,1,7,13],[1,1,8,12],
[1,1,9,11],[1,1,10,10],[1,1,11,9],[1,1,12,8],
[1,1,13,7],[1,1,14,6],[1,1,15,5],[1,1,16,4],
[1,1,17,3],[1,1,18,2],[1,2,1,18],[1,2,2,17],
[1,2,3,16],[1,2,4,15],[1,2,5,14],[1,2,6,13],
[1,2,7,12],[1,2,8,11],[1,2,9,10],[1,2,10,9],
[1,2,11,8],[1,2,12,7],[1,2,13,6],[1,2,14,5],
[1,2,15,4],[1,2,16,3],[1,2,17,2],[1,3,1,17],
[1,3,2,16],[1,3,3,15],[1,3,4,14],[1,3,5,13],
[1,3,6,12],[1,3,7,11],[1,3,8,10],[1,3,9,9],
[1,3,10,8],[1,3,11,7],[1,3,12,6],[1,3,13,5],
[1,3,14,4],[1,3,15,3],[1,3,16,2],[1,4,1,16],
[1,4,2,15],[1,4,3,14],[1,4,4,13],[1,4,5,12],
[1,4,6,11],[1,4,7,10],[1,4,8,9],[1,4,9,8],
[1,4,10,7],[1,4,11,6],[1,4,12,5],[1,4,13,4],
[1,4,14,3],[1,4,15,2],[1,5,1,15],[1,5,2,14],
[1,5,3,13],[1,5,4,12],[1,5,5,11],[1,5,6,10],
[1,5,7,9],[1,5,8,8],[1,5,9,7],[1,5,10,6],
[1,5,11,5],[1,5,12,4],[1,5,13,3],[1,5,14,2],
[1,6,1,14],[1,6,2,13],[1,6,3,12],[1,6,4,11],
[1,6,5,10],[1,6,6,9],[1,6,7,8],[1,6,8,7],
[1,6,9,6],[1,6,10,5],[1,6,11,4],[1,6,12,3],
[1,6,13,2],[1,7,1,13],[1,7,2,12],[1,7,3,11],
[1,7,4,10],[1,7,5,9],[1,7,6,8],[1,7,7,7],
[1,7,8,6],[1,7,9,5],[1,7,10,4],[1,7,11,3],
[1,7,12,2],[1,8,1,12],[1,8,2,11],[1,8,3,10],
[1,8,4,9],[1,8,5,8],[1,8,6,7],[1,8,7,6],
[1,8,8,5],[1,8,9,4],[1,8,10,3],[1,8,11,2],
[1,9,1,11],[1,9,2,10],[1,9,3,9],[1,9,4,8],
[1,9,5,7],[1,9,6,6],[1,9,7,5],[1,9,8,4],
[1,9,9,3],[1,9,10,2],[1,10,1,10],[1,10,2,9],
[1,10,3,8],[1,10,4,7],[1,10,5,6],[1,10,6,5],
[1,10,7,4],[1,10,8,3],[1,10,9,2],[1,11,2,8],
[1,11,3,7],[1,11,4,6],[1,11,5,5],[1,11,6,4],
[1,11,7,3],[1,11,8,2],[1,12,2,7],[1,12,3,6],
[1,12,4,5],[1,12,5,4],[1,12,6,3],[1,12,7,2],
[1,13,2,6],[1,13,3,5],[1,13,4,4],[1,13,5,3],
[1,13,6,2],[1,14,2,5],[1,14,3,4],[1,14,4,3],
[1,14,5,2],[1,15,2,4],[1,15,3,3],[1,15,4,2],
[1,16,2,3],[1,16,3,2],[1,17,2,2],[2,2,2,16],
[2,2,3,15],[2,2,4,14],[2,2,5,13],[2,2,6,12],
[2,2,7,11],[2,2,8,10],[2,2,9,9],[2,2,10,8],
[2,2,11,7],[2,2,12,6],[2,2,13,5],[2,2,14,4],
[2,2,15,3],[2,3,2,15],[2,3,3,14],[2,3,4,13],
[2,3,5,12],[2,3,6,11],[2,3,7,10],[2,3,8,9],
[2,3,9,8],[2,3,10,7],[2,3,11,6],[2,3,12,5],
[2,3,13,4],[2,3,14,3],[2,4,2,14],[2,4,3,13],
[2,4,4,12],[2,4,5,11],[2,4,6,10],[2,4,7,9],
[2,4,8,8],[2,4,9,7],[2,4,10,6],[2,4,11,5],
[2,4,12,4],[2,4,13,3],[2,5,2,13],[2,5,3,12],
[2,5,4,11],[2,5,5,10],[2,5,6,9],[2,5,7,8],
[2,5,8,7],[2,5,9,6],[2,5,10,5],[2,5,11,4],
[2,5,12,3],[2,6,2,12],[2,6,3,11],[2,6,4,10],
[2,6,5,9],[2,6,6,8],[2,6,7,7],[2,6,8,6],
[2,6,9,5],[2,6,10,4],[2,6,11,3],[2,7,2,11],
[2,7,3,10],[2,7,4,9],[2,7,5,8],[2,7,6,7],
[2,7,7,6],[2,7,8,5],[2,7,9,4],[2,7,10,3],
[2,8,2,10],[2,8,3,9],[2,8,4,8],[2,8,5,7],
[2,8,6,6],[2,8,7,5],[2,8,8,4],[2,8,9,3],
[2,9,2,9],[2,9,3,8],[2,9,4,7],[2,9,5,6],
[2,9,6,5],[2,9,7,4],[2,9,8,3],[2,10,3,7],
[2,10,4,6],[2,10,5,5],[2,10,6,4],[2,10,7,3],
[2,11,3,6],[2,11,4,5],[2,11,5,4],[2,11,6,3],
[2,12,3,5],[2,12,4,4],[2,12,5,3],[2,13,3,4],
[2,13,4,3],[2,14,3,3],[3,3,3,13],[3,3,4,12],
[3,3,5,11],[3,3,6,10],[3,3,7,9],[3,3,8,8],
[3,3,9,7],[3,3,10,6],[3,3,11,5],[3,3,12,4],
[3,4,3,12],[3,4,4,11],[3,4,5,10],[3,4,6,9],
[3,4,7,8],[3,4,8,7],[3,4,9,6],[3,4,10,5],
[3,4,11,4],[3,5,3,11],[3,5,4,10],[3,5,5,9],
[3,5,6,8],[3,5,7,7],[3,5,8,6],[3,5,9,5],
[3,5,10,4],[3,6,3,10],[3,6,4,9],[3,6,5,8],
[3,6,6,7],[3,6,7,6],[3,6,8,5],[3,6,9,4],
[3,7,3,9],[3,7,4,8],[3,7,5,7],[3,7,6,6],
[3,7,7,5],[3,7,8,4],[3,8,3,8],[3,8,4,7],
[3,8,5,6],[3,8,6,5],[3,8,7,4],[3,9,4,6],
[3,9,5,5],[3,9,6,4],[3,10,4,5],[3,10,5,4],
[3,11,4,4],[4,4,4,10],[4,4,5,9],[4,4,6,8],
[4,4,7,7],[4,4,8,6],[4,4,9,5],[4,5,4,9],
[4,5,5,8],[4,5,6,7],[4,5,7,6],[4,5,8,5],
[4,6,4,8],[4,6,5,7],[4,6,6,6],[4,6,7,5],
[4,7,4,7],[4,7,5,6],[4,7,6,5],[4,8,5,5],
[5,5,5,7],[5,5,6,6],[5,6,5,6]];

dc:=[];
dc[5]:=[[[1],"S^3"]];

dc[6]:=[[[1,2],"S^3"]];

dc[7]:=[[[1,4],"S^3"]];

dc[8]:=[[[1,5,8],"S^3"],[[1,7],"S^3"]];

dc[9]:=[[[1,6,9],"S^3"],[[2,5,6],"S^2~S^1"]];

dc[10]:=[[[1,7,12,16],"S^3"],[[1,7,14],"S^3"],
[[1,11,22],"S^3"],[[2,3,8,22],"S^3"],
[[2,6,7],"S^2xS^1"],[[3,4,13,22],"S^2xS^1"],
[[3,5,12,22],"S^2~S^1"],[[8,11,16,19],"S^2~S^1"]];

dc[11]:=[[[1,8,14,19],"S^3"],[[1,8,17],"S^3"],
[[1,11,16,18],"S^3"],[[1,11,20,22],"S^2~S^1"],
[[2,6,9,14],"S^2~S^1"],[[2,7,8],"S^2~S^1"]];

dc[12]:=[[[1,9,16,21,25],"S^3"],[[1,10,24,34],"S^3"],
[[1,12,22,24,38],"S^2xS^1"],[[1,13,23,24],"S^2~S^1"],
[[1,15,35],"S^3"],[[2,7,10,16],"S^2xS^1"],
[[2,8,9],"S^2xS^1"],[[3,6,16,29,38],"S^2xS^1"],
[[4,5,22,38],"S^2xS^1"],[[4,6,21,38],"S^2xS^1"],
[[9,11,20,25,29],"S^2~S^1"],
[[9,12,20,25,27],"S^2~S^1"],[[9,14,20,38],"S^2xS^1"],
[[10,15,21,25,31],"S^2~S^1"],
[[11,12,25,32,36],"(S^2xS^1)#2"],
[[11,15,17,20,38],"S^2xS^1"],[[11,15,25,30],"S^2~S^1"],
[[12,14,18,19,38],"S^2xS^1"],
[[12,14,25,27,32],"(S^2xS^1)#2"],
[[18,19,25,27],"S^2~S^1"]];

dc[13]:=[[[1,10,18,25,31],"S^3"],[[1,10,18,28],"S^3"],
[[1,12,35,48],"S^3"],[[1,13,26,30,51],"S^2~S^1"],
[[1,13,28,30,36],"S^3"],[[1,13,38,52],"S^2~S^1"],
[[1,14,25,30,33],"S^2~S^1"],[[1,14,32,35],"S^2~S^1"],
[[1,17,49,52,53],"S^2~S^1"],[[1,17,50],"S^3"],
[[2,3,14,27,43],"S^3"],[[2,7,11,19,25],"S^2~S^1"],
[[2,8,11,18],"S^2~S^1"],[[2,9,10],"S^2~S^1"],
[[3,4,19,47,51],"S^2~S^1"]];

dc[14]:=[[[1,11,20,28,35,41],"S^3"],[[1,11,20,32],"S^3"],
[[1,11,24,31,33],"S^3"],[[1,11,24,37,39],"S^2~S^1"],
[[1,11,26,73],"S^3"],[[1,12,34,57,67],"S^3"],
[[1,14,22,27,73],"S^3"],[[1,14,29,34,52,67],"S^3"],
[[1,14,29,34,63,67],"S^2xS^1"],
[[1,14,29,34,65,67],"L(3,1)"],
[[1,14,32,34,41,46],"S^3"],[[1,14,45,52,67,68],"S^3"],
[[1,14,45,63,67,68],"S^2xS^1"],
[[1,14,45,65,67,68],"L(3,1)"],
[[1,15,30,34,71,73],"S^3"],[[1,15,36,40,67],"S^2xS^1"],
[[1,16,37,40],"S^2~S^1"],[[1,19,58,67],"S^3"],
[[2,3,12,58,67],"S^3"],[[2,5,12,21,29,67],"S^3"],
[[2,8,12,21,28],"S^2xS^1"],[[2,9,12,20],"S^2xS^1"],
[[2,10,11],"S^2xS^1"],[[3,4,13,14,22,73],"S^3"],
[[3,4,21,52,58,67],"S^3"],
[[3,4,21,58,63,67],"S^2xS^1"],
[[3,4,21,58,65,67],"L(3,1)"],
[[3,7,20,46,49,67],"S^2~S^1"],
[[3,8,20,49,52],"S^2xS^1"],[[3,8,20,49,63],"S^2xS^1"],
[[3,8,20,49,65],"S^2xS^1"],
[[3,8,21,28,58,67],"S^2~S^1"],
[[3,9,20,58,67],"S^2~S^1"],[[4,5,12,14,57,67],"S^3"],
[[4,5,22,27,34,73],"S^3"],[[4,5,29,52,67],"S^3"],
[[4,5,29,63,67],"S^2xS^1"],[[4,5,29,65,67],"L(3,1)"],
[[4,5,33,44,64,67],"L(3,1)"],
[[4,7,28,46,67],"S^2~S^1"],[[4,8,28,52],"S^2xS^1"],
[[4,8,28,63],"S^2xS^1"],[[4,8,28,65],"S^2xS^1"],
[[5,6,36,67],"S^2xS^1"],[[5,7,35,67],"S^2~S^1"],
[[11,14,20,34,41,46],"S^2~S^1"],
[[11,15,20,34,41,43],"S^2~S^1"],
[[11,16,26,37,40,73],"S^2~S^1"],
[[12,19,34,53,73],"S^2~S^1"],
[[23,26,41,44],"S^2~S^1"]];

dc[15]:=[[[1,12,22,31,38,44],"S^3"],
[[1,12,26,38,42,46],"S^2~S^1"],
[[1,12,27,41,42],"S^2~S^1"],[[1,12,29,87],"S^3"],
[[1,14,43,68,86,87],"RP^3"],[[1,15,24,30,87],"S^3"],
[[1,15,28,30,47,84],"S^3"],
[[1,15,32,37,72,77],"S^2~S^1"],
[[1,15,49,69,70,75],"S^2~S^1"],
[[1,15,49,72,80],"S^2~S^1"],[[1,15,49,73,87],"S^3/Q8"],
[[1,16,33,37,86],"S^2~S^1"],
[[1,16,39,43,77],"S^2~S^1"],[[1,16,53,78],"S^2~S^1"],
[[1,17,26,27,41,43],"S^2~S^1"],
[[1,17,34,37,79,80],"S^3/Q8"],
[[1,17,38,43,46],"S^2~S^1"],
[[1,17,40,43,86,87],"S^3/Q8"],[[1,17,45,49],"S^2~S^1"],
[[1,19,24,30,47,74],"S^3"],
[[1,21,67,74,75,79],"S^2~S^1"],
[[1,21,69,72,76,80],"S^2~S^1"],
[[1,21,70,75,76],"S^2~S^1"],[[1,21,71,86,87],"RP^3"],
[[2,8,13,23,32,38],"S^2~S^1"],
[[2,8,18,26,63,78],"S^2~S^1"],
[[2,9,13,23,31],"S^2~S^1"],[[2,10,13,22],"S^2~S^1"],
[[2,11,12],"S^2~S^1"],[[3,4,23,67,72,77],"S^2~S^1"],
[[4,5,15,16,33,86],"S^2~S^1"],
[[4,5,32,72,77],"S^2~S^1"],
[[4,5,37,49,72,80],"S^2~S^1"],
[[15,19,32,37,54,56],"T^3"]];

dc[16]:=[[[1,13,24,34,43,51,58],"S^3"],
[[1,13,24,34,47],"S^3"],[[1,13,28,45,49,107,114],"S^3"],
[[1,13,28,47,49,58,60],"S^3"],
[[1,13,29,43,49,54],"S^2~S^1"],
[[1,13,29,53,56],"S^2~S^1"],
[[1,14,35,57,81,104],"S^3"],[[1,14,42,81,95],"S^3"],
[[1,15,50,83,114],"S^3"],[[1,16,35,42,74,95],"S^3"],
[[1,16,35,42,89,95,100],"S^2xS^1"],
[[1,16,35,42,93,95],"L(3,1)"],[[1,16,57,74,104],"S^3"],
[[1,16,57,79,81,94],"S^3"],
[[1,16,57,89,100,104],"S^2xS^1"],
[[1,16,57,90,111],"S^2~S^1"],
[[1,16,57,93,104],"L(3,1)"],
[[1,16,57,94,105,113],"S^2~S^1"],
[[1,17,44,50,95,100],"S^2xS^1"],
[[1,17,47,50,58,64],"S^3"],[[1,17,63,96,107,114],"S^3"],
[[1,18,52,57,100],"S^2xS^1"],
[[1,19,53,57],"S^2~S^1"],[[1,23,74,84,94,104],"S^3"],
[[1,23,75,77,105],"S^3"],[[1,23,82,95],"S^3"],
[[1,23,84,89,94,100,104],"S^2xS^1"],
[[1,23,84,90,94,111],"S^2~S^1"],
[[1,23,84,93,94,104],"L(3,1)"],
[[1,23,84,105,113],"S^2~S^1"],[[1,23,88,114],"S^3"],
[[2,3,14,88,114],"S^3"],[[2,3,17,36,75,114],"S^3"],
[[2,6,17,26,75,83,114],"S^3"],
[[2,9,14,25,35,43],"S^2xS^1"],
[[2,10,14,25,34],"S^2xS^1"],[[2,11,14,24],"S^2xS^1"],
[[2,12,13],"S^2xS^1"],[[3,4,25,74,88,114],"S^3"],
[[3,4,25,84,94,104],"B2"],[[3,4,25,87,90,105],"B2"],
[[3,4,25,88,93,114],"S^3/P24"],
[[3,4,28,44,58,85,92],"S^3"],
[[3,4,28,45,74,87,114],"S^3"],
[[3,4,28,45,87,93,114],"S^3/P24"],
[[3,4,28,49,58,60,71],"S^2~S^1"],
[[3,4,29,46,88,94,114],"S^3/P24"],
[[3,4,30,45,58,62,71],"S^2~S^1"],
[[3,4,33,50,83,114],"S^3"],
[[3,5,15,17,26,36,114],"S^3"],
[[3,6,28,35,58,87,101],"S^3"],
[[3,8,24,64,68,71,100],"S^2xS^1"],
[[3,9,25,35,43,88,114],"S^2~S^1"],
[[3,10,24,54,56,87],"S^2xS^1"],
[[3,10,24,71,74],"S^2xS^1"],
[[3,10,24,71,89,100],"S^2xS^1"],
[[3,10,24,71,93],"S^2xS^1"],
[[3,10,25,34,88,114],"S^2~S^1"],
[[3,10,28,34,45,87,114],"S^2~S^1"],
[[3,11,24,88,114],"S^2~S^1"],
[[4,5,35,74,82,88,114],"S^3"],
[[4,5,35,82,88,93,114],"S^3/P24"],
[[4,5,42,57,74,104],"S^3"],
[[4,5,42,57,89,100,104],"S^2xS^1"],
[[4,5,42,57,90,111],"S^2~S^1"],
[[4,5,42,57,93,104],"L(3,1)"],
[[4,8,34,64,68,100],"S^2xS^1"],
[[4,8,42,50,65,68,100],"S^2xS^1"],
[[4,9,14,16,43,81],"S^2xS^1"],
[[4,9,34,68,82,88,114],"S^2~S^1"],
[[4,9,35,43,74],"S^2xS^1"],
[[4,9,35,43,89,100],"S^2xS^1"],
[[4,9,35,43,93],"S^2xS^1"],[[4,10,34,74],"S^2xS^1"],
[[4,10,34,89,100],"S^2xS^1"],
[[4,10,34,90,104,111],"T^3"],[[4,10,34,93],"S^2xS^1"],
[[5,6,15,17,83,114],"S^3"],[[5,8,43,64,100],"S^2xS^1"],
[[5,9,43,82,88,114],"S^2~S^1"],
[[6,7,52,100],"S^2xS^1"],[[6,8,51,100],"S^2xS^1"],
[[13,16,24,42,51,58,68],"S^2~S^1"],
[[13,17,24,34,50,58,64],"S^2~S^1"],
[[13,17,24,42,58,65],"S^2~S^1"],
[[13,17,32,36,42,114],"S^2~S^1"],
[[13,17,32,63,96,111,114],"S^2~S^1"],
[[13,23,29,53,56,88,114],"S^2~S^1"],
[[14,17,42,44,50,81,100],"S^2xS^1"],
[[14,17,42,63,81,100,101],"S^2xS^1"],
[[14,21,24,32,81],"S^2xS^1"],
[[16,21,24,32,35,74],"S^2xS^1"],
[[16,21,24,32,35,89,100],"S^2xS^1"],
[[16,21,24,32,35,93],"S^2xS^1"],
[[17,18,27,28,96,100,112],"(S^2xS^1)#5"],
[[17,18,27,31,65,96,100],"(S^2xS^1)#5"],
[[17,18,28,31,61,96,100],"(S^2xS^1)#5"],
[[17,18,36,37,96,100,115],"(S^2xS^1)#5"],
[[17,18,36,41,66,96,100],"(S^2xS^1)#5"],
[[17,18,37,41,62,96,100],"(S^2xS^1)#5"],
[[17,18,61,65,96,100,112],"(S^2xS^1)#5"],
[[17,18,62,66,96,100,115],"(S^2xS^1)#5"],
[[17,23,44,50,82,100],"S^2xS^1"],
[[18,21,44,49,61,66,100],"(S^2xS^1)#5"],
[[24,27,41,58,65],"S^2~S^1"],
[[24,28,41,58,61],"S^2~S^1"],
[[24,31,41,114],"S^2~S^1"]];

dc[17]:=[[[1,14,26,37,47,56,64],"S^3"],
[[1,14,26,37,52],"S^3"],[[1,14,26,42,51,53],"S^3"],
[[1,14,26,42,59,61],"S^2~S^1"],
[[1,14,26,44,140],"S^3"],[[1,14,28,62,131],"S^3"],
[[1,14,30,49,54,136],"S^2~S^1"],
[[1,14,30,52,54,72],"S^3"],
[[1,14,30,74,137],"S^2~S^1"],
[[1,14,31,41,42,51,54],"S^3"],
[[1,14,31,47,54,56,67],"S^2~S^1"],
[[1,14,31,52,54,64,67],"S^3"],
[[1,14,31,56,62,66],"S^2~S^1"],
[[1,14,31,58,62,127],"S^3"],
[[1,14,32,59,62],"S^2~S^1"],[[1,14,35,132],"S^3"],
[[1,14,35,134,137,138],"S^2~S^1"],
[[1,15,41,79,94,134],"S^3"],
[[1,15,46,89,123,134],"S^3"],[[1,15,46,94,113],"S^3"],
[[1,16,50,79,96,118,140],"RP^3"],
[[1,16,55,96,137,140],"RP^3"],
[[1,17,28,36,134,137,138],"S^2~S^1"],
[[1,17,38,41,79,86,134],"S^3"],
[[1,17,38,46,86,113],"S^3"],
[[1,17,38,46,103,110,116],"S^2~S^1"],
[[1,17,63,86,110,113,124],"S^3"],
[[1,17,63,97,99,103,119],"S^2~S^1"],
[[1,17,63,97,99,106,140],"Sigma^3"],
[[1,17,63,103,116,124],"S^2~S^1"],
[[1,18,30,33,67,75,112],"S^2~S^1"],
[[1,18,48,55,89,91,118],"S^2~S^1"],
[[1,18,48,55,90,92,112],"S^2~S^1"],
[[1,18,48,55,110,116],"S^2~S^1"],
[[1,18,70,110,121],"S^2~S^1"],
[[1,18,70,111,137,140],"Sigma^3"],
[[1,19,49,55,136],"S^2~S^1"],[[1,19,52,55,72],"S^3"],
[[1,19,54,55,74,137],"S^2~S^1"],
[[1,19,57,63,116],"S^2~S^1"],[[1,19,75,117],"S^2~S^1"],
[[1,20,28,31,63,131],"S^3"],
[[1,20,28,36,58,104],"S^3"],
[[1,20,31,32,59,63],"S^2~S^1"],
[[1,20,56,63,66],"S^2~S^1"],
[[1,20,58,63,136,137,140],"Sigma^3"],
[[1,20,65,70],"S^2~S^1"],
[[1,22,43,46,89,91,134],"S^3"],
[[1,25,95,103,106,114,118],"S^2~S^1"],
[[1,25,95,105,108,110,122],"S^2~S^1"],
[[1,25,95,107,108,114],"S^2~S^1"],
[[1,25,97,103,109,116,124],"S^2~S^1"],
[[1,25,97,119,120,122,133],"Sigma^3"],
[[1,25,98,105,109,138,139],"RP^3"],
[[1,25,99,103,109,119],"S^2~S^1"],
[[1,25,99,108,109,112,114],"S^2~S^1"],
[[1,25,99,117,120],"S^2~S^1"],
[[1,25,102,133,135,136,139],"RP^2xS^1"],
[[1,25,102,137,140],"RP^3"],
[[2,3,15,99,117,120],"S^2~S^1"],
[[2,3,21,42,90,99,117],"S^2~S^1"],
[[2,9,15,27,38,48,56],"S^2~S^1"],
[[2,9,15,31,42,117,120],"S^2~S^1"],
[[2,9,21,31,90,117],"S^2~S^1"],
[[2,9,21,33,76,90,112],"S^2~S^1"],
[[2,10,15,27,38,47],"S^2~S^1"],
[[2,10,20,32,76,89,118],"S^2~S^1"],
[[2,10,22,32,91,110,111],"S^2~S^1"],
[[2,11,15,27,37],"S^2~S^1"],[[2,12,15,26],"S^2~S^1"],
[[2,13,14],"S^2~S^1"],[[3,4,16,20,28,58,104],"S^3"],
[[3,4,27,95,103,110,116],"S^2~S^1"],
[[3,4,30,54,72,83],"S^2~S^1"],
[[3,4,33,49,74,83],"S^2~S^1"],
[[3,4,35,49,74,97,104],"S^2~S^1"],
[[3,6,26,61,69,99,117],"B2"],
[[3,12,26,99,117,120],"B2"],
[[4,5,28,36,39,70,111],"S^3"],
[[4,5,38,103,110,116],"S^2~S^1"],
[[4,5,46,63,103,116,124],"S^2~S^1"],
[[4,6,39,55,63,104,136],"S^2~S^1"],
[[4,9,15,17,48,56,94],"S^2~S^1"],
[[4,10,15,17,47,94],"S^2~S^1"],
[[5,6,48,110,116],"S^2~S^1"],
[[5,6,55,70,110,121],"S^2~S^1"],
[[14,18,33,50,55,69,76],"B2"],
[[17,21,38,46,82,104,110],"T^3"],
[[17,21,63,82,104,124],"T^3"]];

dc[18]:=[[[1,15,28,40,51,60,68,76],"S^3"],
[[1,15,28,45,60,65,71],"S^2~S^1"],
[[1,15,28,45,63,65,165],"S^3"],
[[1,15,28,46,64,65],"S^2~S^1"],
[[1,15,28,48,167],"S^3"],
[[1,15,30,66,151,157,159],"RP^3"],
[[1,15,31,74,153],"S^3"],[[1,15,32,43,49,167],"S^3"],
[[1,15,32,53,58,159,161],"S^3/Q8"],
[[1,15,32,81,158,165,167],"S^3"],
[[1,15,32,81,159,161,162],"S^3/Q8"],
[[1,15,33,54,58,165,167],"S^3"],
[[1,15,33,62,66,157,159,161],"S^3/Q8"],
[[1,15,34,45,46,64,66],"S^2~S^1"],
[[1,15,34,60,66,71],"S^2~S^1"],
[[1,15,34,63,66,165],"S^3"],
[[1,15,34,70,74],"S^2~S^1"],
[[1,15,38,148,150,159,160],"RP^3"],
[[1,15,38,152,157,159],"RP^3"],
[[1,15,38,154,158,160,165,167],"S^3"],
[[1,15,38,154,159,160,161,162],"S^3/Q8"],
[[1,15,38,156],"S^3"],[[1,16,41,67,107,136,144],"S^3"],
[[1,16,50,107,124,136],"S^3"],
[[1,17,55,91,109,134],"S^3"],[[1,17,59,109,159],"S^3"],
[[1,17,59,114,134,149],"S^3"],
[[1,18,30,39,152,157,159],"RP^3"],
[[1,18,34,39,63,148],"S^3"],
[[1,18,41,50,98,124,136],"S^3"],
[[1,18,41,50,117,124,131,136],"S^2xS^1"],
[[1,18,41,50,122,124,136,165],"L(8,3)"],
[[1,18,63,91,121,148,150],"S^3"],
[[1,18,63,91,121,154,161,162],"S^3/Q8"],
[[1,18,65,89,91,121,159],"T^3"],
[[1,18,67,98,136,144],"S^3"],
[[1,18,67,105,107,123,136],"S^3"],
[[1,18,67,117,131,136,144],"S^2xS^1"],
[[1,18,67,118,152,157,159,161],"S^3/Q8"],
[[1,18,67,118,156,161],"S^3/Q8"],
[[1,18,67,120,136,155,162,165],"L(8,3)"],
[[1,18,67,121,138,154,161],"S^3/Q8"],
[[1,18,67,122,136,144,165],"L(8,3)"],
[[1,19,31,32,43,50,167],"S^3"],
[[1,19,35,39,73,92,149],"S^3"],
[[1,19,42,50,148,150,160],"S^2~S^1"],
[[1,19,42,50,149,151,155],"S^2~S^1"],
[[1,19,42,50,152,157],"S^2~S^1"],
[[1,19,42,50,154,160,161,162],"SFS[RP^2:(2,1)(2,1)(2,1)]"],
[[1,19,42,50,155,158,161,163],"SFS[RP^2:(2,1)(2,1)(2,1)]"],
[[1,19,42,50,156,159],"T^3"],
[[1,19,44,50,72,84,154,161],"S^3/Q8"],
[[1,19,46,50,71,155,159],"T^3"],
[[1,19,46,50,74,93,149],"S^3"],
[[1,19,49,50,74,153],"S^3"],
[[1,19,52,59,98,117,124,136],"S^3"],
[[1,19,52,59,124,131,136],"S^2xS^1"],
[[1,19,52,59,124,133,136,165],"L(5,1)"],
[[1,19,72,84,87,127,161],"S^3/Q8"],
[[1,19,75,124,136,141],"S^2xS^1"],
[[1,19,75,125,157],"S^2~S^1"],
[[1,20,43,49,58,59,167],"S^3"],
[[1,20,45,50,79,88,154,161],"S^3/Q8"],
[[1,20,57,59,80,158,161],"S^3/Q8"],
[[1,20,61,67,98,117,136],"S^3"],
[[1,20,61,67,131,136],"S^2xS^1"],
[[1,20,61,67,133,136,165],"L(5,1)"],
[[1,20,82,98,117,136,137],"S^3"],
[[1,20,82,98,123,135,136,139],"S^3"],
[[1,20,82,131,136,137],"S^2xS^1"],
[[1,20,82,132,157,159,161],"S^3/Q8"],
[[1,20,82,133,136,137,165],"L(5,1)"],
[[1,20,82,135,145,154,156,161],"S^3/Q8"],
[[1,21,54,58,66,67,165,167],"S^3"],
[[1,21,54,59,132,136,158,165],"L(5,1)"],
[[1,21,62,67,157,159,161],"S^3/Q8"],
[[1,21,66,67,86,162,165,167],"S^3"],
[[1,21,69,75,136],"S^2xS^1"],[[1,22,70,75],"S^2~S^1"],
[[1,23,46,50,129,144,161],"S^3/Q8"],
[[1,23,54,59,83,136,158,165],"L(5,1)"],
[[1,24,47,50,127,148,150],"S^3"],
[[1,24,47,50,127,154,161,162],"S^3/Q8"],
[[1,25,30,39,65,121],"S^3"],
[[1,25,37,39,121,150,164],"S^3"],
[[1,27,98,110,123,136,144],"S^3"],
[[1,27,98,112,117,135,136,137],"S^3"],
[[1,27,98,112,123,136,139],"S^3"],
[[1,27,99,101,136,145],"S^3"],[[1,27,108,124,136],"S^3"],
[[1,27,110,117,123,131,136,144],"S^2xS^1"],
[[1,27,110,122,123,136,144,165],"L(8,3)"],
[[1,27,112,117,123,131,136,139],"S^2xS^1"],
[[1,27,112,122,123,136,139,165],"L(8,3)"],
[[1,27,112,131,135,136,137],"S^2xS^1"],
[[1,27,112,133,135,136,137,165],"L(5,1)"],
[[2,3,16,108,124,136],"S^3"],
[[2,3,16,112,131,135,136,137],"S^2xS^1"],
[[2,3,16,113,131,132,136,140],"S^2xS^1"],
[[2,3,19,47,72,99,160],"S^3"],
[[2,3,24,42,72,99,127],"S^3"],
[[2,5,16,29,41,124,136],"S^3"],
[[2,5,24,35,51,104,125],"S^2xS^1"],
[[2,7,16,29,41,52,61,136],"S^3"],
[[2,7,24,36,52,53,105,136],"S^2~S^1"],
[[2,10,16,29,41,52,60],"S^2xS^1"],
[[2,11,16,29,41,51],"S^2xS^1"],
[[2,11,24,35,104,124,125,136],"S^2xS^1"],
[[2,11,24,35,104,141,157],"S^2~S^1"],
[[2,12,16,29,40],"S^2xS^1"],[[2,13,16,28],"S^2xS^1"],
[[2,14,15],"S^2xS^1"],[[3,4,17,18,34,63,148],"S^3"],
[[3,4,29,98,108,124,136],"S^3"],
[[3,4,29,108,117,124,131,136],"S^2xS^1"],
[[3,4,29,108,122,124,136,165],"L(8,3)"],
[[3,4,29,110,123,136,144],"B2"],
[[3,4,29,112,117,135,136,137],"B2"],
[[3,4,29,112,123,136,139],"B2"],
[[3,4,29,113,117,132,136,140],"B2"],
[[3,4,29,115,118,136,145],"B2"],
[[3,4,29,115,120,136,140],"B2"],
[[3,4,32,53,116,118,136,145],"B2"],
[[3,4,32,53,116,120,136,140],"B2"],
[[3,4,32,56,76,84,112,120],"S^2~S^1"],
[[3,4,32,58,76,84,95],"S^2~S^1"],
[[3,4,33,51,66,76,78,95],"S^2~S^1"],
[[3,4,33,54,110,122,136,144],"B2"],
[[3,4,33,54,112,122,136,139],"B2"],
[[3,4,33,56,76,79,112,120],"S^2~S^1"],
[[3,4,33,58,76,79,95],"S^2~S^1"],
[[3,4,35,51,62,76,81,95],"S^2~S^1"],
[[3,4,36,53,76,86,95],"S^2~S^1"],
[[3,4,36,54,76,81,95],"S^2~S^1"],
[[3,4,38,53,76,86,110,118],"S^2~S^1"],
[[3,4,38,54,76,81,110,118],"S^2~S^1"],
[[3,4,39,55,91,109,134],"S^3"],
[[3,6,28,66,73,113,133],"K^2xS^1"],
[[3,7,29,42,53,115,136,145],"B2"],
[[3,7,30,42,61,116,136,146],"B2"],
[[3,7,32,42,112,136,160,162],"B2"],
[[3,7,32,42,116,136,145],"B2"],
[[3,7,33,42,76,110,155,163],"S^2~S^1"],
[[3,7,36,42,76,86,95,118],"S^2~S^1"],
[[3,7,38,42,76,83,93,109],"S^2~S^1"],
[[3,7,38,42,76,86,110],"S^2~S^1"],
[[3,9,28,83,88,92,95,136],"S^2~S^1"],
[[3,9,29,44,55,115,136,140],"B2"],
[[3,10,28,88,92,95,131],"S^2xS^1"],
[[3,10,30,42,60,116,146],"T^3"],
[[3,10,35,45,112,136,137,165],"L(5,1)"],
[[3,10,35,48,70,73,113,167],"S^2~S^1"],
[[3,11,28,92,95,124,136],"S^2~S^1"],
[[3,12,28,95,98],"S^2xS^1"],
[[3,12,28,95,117,131],"S^2xS^1"],
[[3,12,28,95,122,165],"S^2xS^1"],
[[3,12,29,40,108,124,136],"S^2~S^1"],
[[3,13,28,108,124,136],"S^2~S^1"],
[[3,13,28,112,131,135,136,137],"B4"],
[[4,5,16,18,107,124,136],"S^3"],
[[4,5,18,19,31,32,43,167],"S^3"],
[[4,5,18,19,42,152,157],"S^2~S^1"],
[[4,5,28,33,66,76,78,92],"S^2~S^1"],
[[4,5,28,35,62,76,81,92],"S^2~S^1"],
[[4,5,41,98,124,136],"S^3"],
[[4,5,41,98,125,141,157],"S^2~S^1"],
[[4,5,41,117,124,131,136],"S^2xS^1"],
[[4,5,41,122,124,136,165],"L(8,3)"],
[[4,5,50,67,98,136,144],"S^3"],
[[4,5,50,67,117,131,136,144],"S^2xS^1"],
[[4,5,50,67,122,136,144,165],"L(8,3)"],
[[4,7,16,18,52,61,107,136],"S^3"],
[[4,7,29,31,43,123,136,144],"B2"],
[[4,7,41,52,61,98,136],"S^3"],
[[4,9,29,33,45,123,136,139],"B2"],
[[4,9,40,83,88,92,136],"S^2~S^1"],
[[4,9,45,53,76,120,154,155],"S^2~S^1"],
[[4,9,45,54,118,136,158,160],"B2"],
[[4,9,45,54,122,136,139],"B2"],
[[4,9,45,56,76,79,120],"S^2~S^1"],
[[4,9,45,58,76,79,95,112],"S^2~S^1"],
[[4,9,50,59,83,89,92,136],"S^2~S^1"],
[[4,10,16,18,52,60,107],"S^2xS^1"],
[[4,10,22,24,40,92,125],"S^2xS^1"],
[[4,10,40,88,92,131],"S^2xS^1"],
[[4,10,41,52,60,98],"S^2xS^1"],
[[4,10,42,52,91,94,98],"S^2xS^1"],
[[4,10,50,59,89,92,131],"S^2xS^1"],
[[4,11,16,18,51,107],"S^2xS^1"],
[[4,11,23,24,42,52,118,136],"S^2~S^1"],
[[4,11,23,25,40,118,136],"S^2~S^1"],
[[4,11,40,92,124,136],"S^2~S^1"],
[[4,11,40,92,125,141,157],"B2"],
[[4,11,41,51,98],"S^2xS^1"],
[[4,11,41,51,117,131],"S^2xS^1"],
[[4,11,41,51,122,165],"S^2xS^1"],
[[4,12,40,98],"S^2xS^1"],[[4,12,40,117,131],"S^2xS^1"],
[[4,12,40,122,148,151,152],"T^3"],
[[4,12,40,122,165],"S^2xS^1"],
[[5,6,19,20,43,49,58,167],"S^3"],
[[5,6,19,20,57,80,158,161],"S^3/Q8"],
[[5,6,31,32,43,50,59,167],"S^3"],
[[5,6,42,50,59,152,157],"S^2~S^1"],
[[5,6,52,98,117,124,136],"S^3"],
[[5,6,52,124,131,136],"S^2xS^1"],
[[5,6,52,124,133,136,165],"L(5,1)"],
[[5,6,59,75,124,136,141],"S^2xS^1"],
[[5,6,59,75,125,157],"S^2~S^1"],
[[5,9,40,50,67,84,89,136],"S^2~S^1"],
[[5,9,51,83,88,136],"S^2~S^1"],
[[5,9,59,67,84,88,136],"S^2~S^1"],
[[5,10,22,24,51,125],"S^2xS^1"],
[[5,10,51,88,98,117],"S^2xS^1"],
[[5,10,51,88,131],"S^2xS^1"],
[[5,10,51,88,133,165],"S^2xS^1"],
[[5,10,52,60,124,136],"S^2~S^1"],
[[5,11,51,124,136],"S^2~S^1"],
[[5,11,51,125,141,157],"B2"],
[[6,7,16,20,41,107,136,144],"S^3"],
[[6,7,18,20,98,136,144],"S^3"],
[[6,7,18,20,105,107,123,136],"S^3"],
[[6,7,18,20,121,138,154,161],"S^3/Q8"],
[[6,7,30,32,109,116,136,145],"B2"],
[[6,7,30,38,76,83,93],"S^2~S^1"],
[[6,7,30,38,76,86,109,110],"S^2~S^1"],
[[6,7,43,49,58,59,67,167],"S^3"],
[[6,7,43,49,66,132,136,158],"L(5,1)"],
[[6,7,61,98,117,136],"S^3"],
[[6,7,61,109,116,136,146],"B2"],
[[6,7,61,131,136],"S^2xS^1"],
[[6,7,61,133,136,165],"L(5,1)"],
[[6,7,66,81,132,136,165],"L(5,1)"],
[[6,9,60,83,136],"S^2~S^1"],
[[6,10,60,98,117],"S^2xS^1"],
[[6,10,60,109,116,146],"T^3"],[[6,10,60,131],"S^2xS^1"],
[[6,10,60,133,165],"S^2xS^1"],
[[7,8,69,110,112,147,154,167],"(S^2xS^1)#7"],
[[7,8,69,110,115,144,147,167],"(S^2xS^1)#7"],
[[7,8,69,112,115,139,147,167],"(S^2xS^1)#7"],
[[7,8,69,118,120,147,163,167],"(S^2xS^1)#7"],
[[7,8,69,118,123,145,147,167],"(S^2xS^1)#7"],
[[7,8,69,120,123,140,147,167],"(S^2xS^1)#7"],
[[7,8,69,136],"S^2xS^1"],
[[7,8,69,139,144,147,154,167],"(S^2xS^1)#7"],
[[7,8,69,140,145,147,163,167],"(S^2xS^1)#7"],
[[7,9,68,110,112,147,154,167],"(S^2~S^1)#7"],
[[7,9,68,110,115,144,147,167],"(S^2~S^1)#7"],
[[7,9,68,112,115,139,147,167],"(S^2~S^1)#7"],
[[7,9,68,118,120,147,163,167],"(S^2~S^1)#7"],
[[7,9,68,136],"S^2~S^1"],
[[15,17,39,51,60,68,76,95],"S^2~S^1"],
[[15,18,28,50,60,68,76,92],"S^2~S^1"],
[[15,18,39,60,68,76,93],"S^2~S^1"],
[[15,18,39,66,148,165],"S^2xS^1"],
[[15,19,28,40,59,68,76,88],"S^2~S^1"],
[[15,19,28,50,68,76,89],"S^2~S^1"],
[[15,19,39,68,76,89,92,93],"S^2~S^1"],
[[15,20,28,40,51,67,76,83],"S^2~S^1"],
[[15,20,28,40,59,76,84],"S^2~S^1"],
[[15,20,28,50,76,84,88,89],"S^2~S^1"],
[[15,21,28,40,51,67,76,78],"S^2~S^1"],
[[15,22,28,48,70,75,167],"S^2~S^1"],
[[15,22,39,88,95,109,125],"S^2xS^1"],
[[15,24,39,95,109,131],"S^2xS^1"],
[[15,26,39,98],"S^2xS^1"],
[[15,26,39,117,131],"S^2xS^1"],
[[15,26,39,122,165],"S^2xS^1"],
[[16,18,50,67,101,123,167],"S^2~S^1"],
[[16,19,50,52,59,107,131],"S^2xS^1"],
[[16,19,50,75,104,146,148],"S^2xS^1"],
[[16,19,50,75,107,141],"S^2xS^1"],
[[16,22,45,107,125,128,155],"S^2xS^1"],
[[16,22,50,91,107,125],"S^2xS^1"],
[[16,24,29,37,40,106],"S^2xS^1"],
[[16,24,50,88,91,107,131],"S^2xS^1"],
[[16,25,28,38,107],"S^2xS^1"],
[[16,25,29,37,42,52,106],"S^2xS^1"],
[[16,25,42,73,107,155,165],"S^2xS^1"],
[[16,25,45,89,107,160,165],"S^2xS^1"],
[[16,25,48,99,108,167],"S^2~S^1"],
[[16,26,30,38,41,107],"S^2xS^1"],
[[16,26,41,60,68,76,93,107],"SFS[T^2:(1,1)]"],
[[16,27,40,51,60,68,76,97],"S^2~S^1"],
[[16,27,48,97,167],"S^2~S^1"],
[[16,27,50,101,110,167],"S^2~S^1"],
[[17,24,40,48,109,131,167],"SFS[T^2:(1,1)]"],
[[17,24,40,48,113,149,157,167],"S^2~S^1"],
[[17,25,42,48,52,109,131,167],"SFS[T^2:(1,1)]"],
[[17,26,51,60,68,76,95,98],"SFS[T^2:(1,1)]"],
[[17,27,29,35,94,151,165],"S^2xS^1"],
[[17,27,29,39,98],"S^2xS^1"],
[[17,27,29,39,117,131],"S^2xS^1"],
[[17,27,29,39,122,165],"S^2xS^1"],
[[17,27,40,48,96,167],"S^2~S^1"],
[[17,27,51,60,68,76,96],"S^2~S^1"],
[[17,27,52,75,104,107,148],"S^2xS^1"],
[[17,27,59,98,117,146],"S^2xS^1"],
[[17,27,59,131,146],"S^2xS^1"],
[[17,27,59,133,146,165],"S^2xS^1"],
[[17,27,59,135,151,160,165],"S^2xS^1"],
[[18,20,43,50,67,100,101,167],"S^2~S^1"],
[[18,24,41,50,88,91,117],"K^2xS^1"],
[[18,25,28,38,41,98],"S^2xS^1"],
[[18,25,28,38,41,117,131],"S^2xS^1"],
[[18,25,28,38,41,122,165],"S^2xS^1"],
[[18,25,41,50,92,94],"T^3"],
[[18,25,42,50,60,91,92],"T^3"],
[[19,23,73,92,120,158,165,167],"S^3"],
[[20,21,43,48,85,132,136,147],"(S^2~S^1)#7"],
[[20,23,43,48,83,85,136,147],"(S^2~S^1)#7"],
[[21,22,69,70,136],"S^2~S^1"],
[[21,23,43,48,78,85,136,147],"(S^2~S^1)#7"],
[[21,23,60,62,70,136],"S^2~S^1"],
[[28,33,40,51,66,76,78],"S^2~S^1"],
[[28,33,40,58,76,79],"S^2~S^1"],
[[33,36,76,79,101,105,124,147],"(S^2~S^1)#7"],
[[43,48,76,85],"S^2~S^1"]];

dc[19]:=[[[1,16,30,43,55,66,76,85],"S^3"],
[[1,16,30,43,55,71],"S^3"],
[[1,16,30,48,66,73,76,88],"S^2~S^1"],
[[1,16,30,48,71,73,85,88],"S^3"],
[[1,16,30,49,66,73,80],"S^2~S^1"],
[[1,16,30,49,79,82],"S^2~S^1"],
[[1,16,30,52,204],"S^3"],[[1,16,34,46,53,204],"S^3"],
[[1,16,34,51,53,89,201],"S^3"],
[[1,16,34,55,64,71,85,100],"S^3"],
[[1,16,34,57,64,175,188],"S^3"],
[[1,16,34,91,189,200,204],"S^3"],
[[1,16,35,55,64,71,95],"S^3"],
[[1,16,35,58,64,203],"S^2~S^1"],
[[1,16,35,68,74,193],"S^2~S^1"],
[[1,16,35,71,74,94],"S^3"],
[[1,16,35,97,194],"S^2~S^1"],
[[1,16,36,48,49,66,74,80],"S^2~S^1"],
[[1,16,36,59,64,195,197,200],"S^3"],
[[1,16,36,66,74,76,88],"S^2~S^1"],
[[1,16,36,69,74,200,203,204],"S^3"],
[[1,16,36,71,74,85,88],"S^3"],
[[1,16,36,76,83,87],"S^2~S^1"],
[[1,16,37,57,64,87,175,197],"S^3"],
[[1,16,37,79,83],"S^2~S^1"],
[[1,16,39,46,53,89,190],"S^3"],
[[1,16,41,182,190,191,193,195],"RP^2xS^1"],
[[1,16,41,185,194,196],"S^2~S^1"],
[[1,17,45,84,120,173,197],"S^3"],
[[1,17,48,103,118,155,168],"S^2~S^1"],
[[1,17,48,103,124,155,156,185],"S^2~S^1"],
[[1,17,49,70,75,119,171,195],"S^3"],
[[1,17,49,107,119,162,171],"S^3"],
[[1,17,49,107,124,186],"S^3"],
[[1,17,50,99,103,118,161,168],"S^2~S^1"],
[[1,17,54,117,164,184],"S^3"],
[[1,17,54,118,148,155,168,185],"S^2~S^1"],
[[1,17,54,124,148,155,156],"S^2~S^1"],
[[1,17,54,124,149],"S^3"],[[1,18,57,92,126,153],"S^3"],
[[1,18,65,126,182,184,192,197],"S^2~S^1"],
[[1,18,65,126,182,186,189,198],"S^2~S^1"],
[[1,18,65,126,184,186,189,204],"S^3"],
[[1,18,65,126,186,187,192],"S^2~S^1"],
[[1,18,65,126,192,197,198,204],"S^3"],
[[1,18,65,130,154,176,187,192],"S^2~S^1"],
[[1,19,36,42,69,176,200],"S^3"],
[[1,19,36,42,73,101,176,201],"S^3"],
[[1,19,40,42,69,101,176,197],"S^3"],
[[1,19,44,49,107,114,186],"S^3"],
[[1,19,44,54,114,149],"S^3"],
[[1,19,44,54,135,144,152,159],"S^2~S^1"],
[[1,19,48,54,67,85,139,148],"S^3"],
[[1,19,48,54,73,85,88,108],"S^2~S^1"],
[[1,19,49,54,70,114,150],"S^3"],
[[1,19,49,54,70,117,119,138],"S^3"],
[[1,19,50,54,69,85,90,108],"S^2~S^1"],
[[1,19,50,54,71,138,146,204],"S^3"],
[[1,19,68,98,139,185],"S^3"],
[[1,19,72,77,81,98,138,184],"S^3"],
[[1,19,72,95,98,139,184],"S^3"],
[[1,19,75,127,129,135,152,167],"S^2~S^1"],
[[1,19,75,135,152,159,172],"S^2~S^1"],
[[1,19,75,136,182,193],"S^2~S^1"],
[[1,19,75,138,164,171,184,195],"S^3"],
[[1,19,75,143,164,182,198],"S^2~S^1"],
[[1,19,75,143,164,184,204],"S^3"],
[[1,19,75,143,164,187,189,192],"S^2~S^1"],
[[1,20,33,34,51,54,89,201],"S^3"],
[[1,20,33,39,46,54,89,190],"S^3"],
[[1,20,45,54,185,188,194,196],"SFS[RP^2:(2,1)(3,1)]"],
[[1,20,56,65,117,119,152,166],"S^2~S^1"],
[[1,20,56,65,118,120,144,161],"S^2~S^1"],
[[1,20,56,65,119,121,144,154],"S^2~S^1"],
[[1,20,56,65,120,122,146,152],"S^2~S^1"],
[[1,20,56,65,144,152,159],"S^2~S^1"],
[[1,20,58,65,77,146,154,200],"S^3"],
[[1,20,63,65,82,118,120,147],"S^3"],
[[1,20,77,98,150,170,189,202],"S^3"],
[[1,20,83,91,92,146,189],"S^2~S^1"],
[[1,20,84,115,120,130,192],"S^3"],
[[1,20,84,117,119,166,169],"S^2~S^1"],
[[1,20,84,120,122,146,169],"S^2~S^1"],
[[1,20,84,128,130,147],"S^3"],
[[1,20,84,144,159,169],"S^2~S^1"],
[[1,21,34,35,58,65,203],"S^2~S^1"],
[[1,21,34,35,98,154,189,203],"S^2~S^1"],
[[1,21,35,38,58,65,88,189],"S^2~S^1"],
[[1,21,35,38,88,98,154],"S^2~S^1"],
[[1,21,46,52,71,75,99,101],"S^2~S^1"],
[[1,21,46,53,64,65,204],"S^3"],
[[1,21,67,75,118,120,161],"S^2~S^1"],
[[1,21,67,75,119,121,154],"S^2~S^1"],
[[1,21,67,75,152,159],"S^2~S^1"],
[[1,21,73,75,90,119,121,155],"S^2~S^1"],
[[1,21,92,126,129,180],"S^3"],
[[1,21,92,129,131,155],"S^2~S^1"],
[[1,21,92,152,165],"S^2~S^1"],[[1,21,92,153,175],"S^3"],
[[1,21,92,153,194,203,204],"Sigma(2,3,7)"],
[[1,22,58,61,80,84,163,167],"S^3"],
[[1,22,58,62,81,84,163,167],"S^2~S^1"],
[[1,22,58,64,69,75,102,197],"S^2~S^1"],
[[1,22,58,64,74,75,203],"S^2~S^1"],
[[1,22,58,65,157,163,192,198],"S^3"],
[[1,22,60,61,80,84,93],"S^3"],
[[1,22,60,62,81,84,93],"S^2~S^1"],
[[1,22,66,71,84,93],"S^3"],
[[1,22,66,75,79,94,200],"S^3"],
[[1,22,68,75,193],"S^2~S^1"],
[[1,22,70,72,81,84,93],"S^3"],
[[1,22,74,75,97,194],"S^2~S^1"],
[[1,22,77,84,159],"S^2~S^1"],
[[1,22,79,84,93,200],"S^3"],[[1,22,98,160],"S^2~S^1"],
[[1,23,36,37,79,84],"S^2~S^1"],
[[1,23,36,42,141,166,180,197],"S^2~S^1"],
[[1,23,69,75,161,165,203,204],"Sigma(2,3,7)"],
[[1,23,76,84,87],"S^2~S^1"],
[[1,23,78,84,193,194,203,204],"Sigma(2,3,7)"],
[[1,23,86,92],"S^2~S^1"],
[[1,24,49,54,117,119,184],"S^3"],
[[1,24,70,75,164,171,195],"S^3"],
[[1,24,73,75,105,127,129,189],"S^3"],
[[1,27,32,42,69,101,141,201],"S^3"],
[[1,27,32,42,73,137,166,201],"S^3"],
[[1,29,125,135,138,150,152,166],"S^2~S^1"],
[[1,29,125,135,139,144,157,161],"S^2~S^1"],
[[1,29,125,135,140,150,156],"S^2~S^1"],
[[1,29,125,137,140,148,166,201],"Sigma(2,3,7)"],
[[1,29,125,137,142,144,159,170],"S^2~S^1"],
[[1,29,125,139,142,144,163],"S^2~S^1"],
[[1,29,125,139,142,150,154,156],"S^2~S^1"],
[[1,29,125,148,155,156],"S^2~S^1"],
[[1,29,125,149],"S^3"],
[[1,29,126,154,173,176,187,197],"S^2~S^1"],
[[1,29,126,158,180],"S^3"],
[[1,29,127,135,143,152,159,172],"S^2~S^1"],
[[1,29,127,136,143,182,193],"S^2~S^1"],
[[1,29,127,164,182,198],"S^2~S^1"],
[[1,29,127,164,187,189,192],"S^2~S^1"],
[[1,29,129,135,143,146,148,157],"S^2~S^1"],
[[1,29,129,135,143,152,167],"S^2~S^1"],
[[1,29,129,152,158,165],"S^2~S^1"],
[[1,29,130,147,151],"S^3"],
[[1,29,130,160,164],"S^2~S^1"],
[[1,29,131,155,158],"S^2~S^1"],
[[1,29,134,182,184,192,197],"S^2~S^1"],
[[1,29,134,186,187,192],"S^2~S^1"],
[[1,29,134,191,201,202,203],"RP^2xS^1"],
[[2,3,17,125,148,155,156],"S^2~S^1"],
[[2,3,17,126,158,180],"S^3"],
[[2,3,17,129,152,158,165],"S^2~S^1"],
[[2,3,17,130,147,151],"S^3"],
[[2,3,17,130,160,164],"S^2~S^1"],
[[2,3,17,131,152,153,168],"S^2~S^1"],
[[2,3,17,131,155,158],"S^2~S^1"],
[[2,3,23,45,78,115,145],"S^3"],
[[2,3,23,45,78,118,126,181],"S^3"],
[[2,3,23,48,115,145,180,181],"S^3"],
[[2,3,23,48,118,126,180],"S^3"],
[[2,3,23,48,118,131,155],"S^2~S^1"],
[[2,3,23,50,99,118,131,161],"S^2~S^1"],
[[2,3,24,49,119,130,160],"S^2~S^1"],
[[2,3,24,49,119,132,162],"S^3"],
[[2,3,25,50,120,131,152,153],"S^2~S^1"],
[[2,5,17,31,49,70,150],"S^3"],
[[2,5,17,36,49,59,70,151],"S^3"],
[[2,5,24,31,70,119,150,164],"S^3"],
[[2,6,17,32,48,78,158,181],"S^3"],
[[2,6,23,32,45,48,118,180],"S^3"],
[[2,6,23,32,78,115,126,145],"S^3"],
[[2,6,23,32,78,118,181],"S^3"],
[[2,7,17,38,51,80,89,164],"S^3"],
[[2,10,17,31,44,56,67,76],"S^2~S^1"],
[[2,10,17,31,49,59,147,150],"S^3"],
[[2,10,17,36,49,147,151],"S^3"],
[[2,10,17,36,49,160,164],"S^2~S^1"],
[[2,10,17,36,51,104,151,154],"S^3"],
[[2,10,17,38,49,99,154,164],"S^2~S^1"],
[[2,10,24,36,119,160],"S^2~S^1"],
[[2,10,24,36,122,169,189],"S^2~S^1"],
[[2,10,24,38,99,119,154],"S^2~S^1"],
[[2,10,24,39,100,122,169,193],"S^2~S^1"],
[[2,11,17,31,44,56,66],"S^2~S^1"],
[[2,11,17,37,48,99,158,161],"S^2~S^1"],
[[2,11,17,37,50,152,153,168],"S^2~S^1"],
[[2,11,17,37,50,155,158],"S^2~S^1"],
[[2,11,23,37,48,50,118,155],"S^2~S^1"],
[[2,11,23,37,99,118,161],"S^2~S^1"],
[[2,11,25,37,120,152,153],"S^2~S^1"],
[[2,11,25,37,120,155,158,168],"S^2~S^1"],
[[2,11,25,39,104,120,146,152],"S^2~S^1"],
[[2,12,17,31,44,55],"S^2~S^1"],
[[2,12,24,38,104,119,144,154],"S^2~S^1"],
[[2,12,26,38,121,144,145,159],"S^2~S^1"],
[[2,13,17,31,43],"S^2~S^1"],
[[2,13,25,39,80,82,120,167],"S^3"],
[[2,14,17,30],"S^2~S^1"],[[2,15,16],"S^2~S^1"],
[[3,4,31,125,135,144,152,159],"S^2~S^1"],
[[3,4,35,55,74,94,111],"S^2~S^1"],
[[3,4,35,62,77,81,129,139],"S^2~S^1"],
[[3,4,35,62,95,129,138],"S^2~S^1"],
[[3,4,35,64,95,111],"S^2~S^1"],
[[3,4,38,55,68,97,111],"S^2~S^1"],
[[3,4,39,58,97,111],"S^2~S^1"],
[[3,4,41,58,93,106,127,137],"S^2~S^1"],
[[3,4,41,58,97,127,136],"S^2~S^1"],
[[3,4,42,57,92,126,153],"S^3"],
[[3,5,18,23,32,45,78,145],"S^3"],
[[3,6,30,67,83,90,131,154],"B2"],
[[3,6,30,73,83,129,152,165],"B2"],
[[3,6,30,73,83,131,155],"B2"],
[[3,6,36,48,74,83,131,155],"B2"],
[[3,7,30,56,63,91,132,161],"S^2~S^1"],
[[3,7,41,45,57,58,97,127],"S^2~S^1"],
[[3,7,42,45,92,126,136,153],"S^3"],
[[3,10,24,25,38,48,129,194],"S^2~S^1"],
[[3,10,31,45,57,76,133,173],"B2"],
[[3,10,32,45,67,76,134,174],"B2"],
[[3,10,34,45,76,134,173],"B2"],
[[3,11,32,45,66,134,174],"B2"],
[[3,11,34,45,66,67,134,173],"B2"],
[[3,11,35,46,87,94,131,202],"S^3"],
[[3,12,30,80,82,89,91,132],"S^2~S^1"],
[[3,12,30,80,82,111,141],"S^2~S^1"],
[[3,12,35,50,95,129,138,141],"S^2~S^1"],
[[3,12,36,48,88,89,125,151],"B2"],
[[3,13,31,43,130,160,164],"B2"],
[[3,13,37,43,57,87,133,197],"S^2~S^1"],
[[3,14,30,125,148,155,156],"B2"],
[[3,14,30,130,160,164],"B2"],
[[4,5,19,24,49,117,119,184],"S^3"],
[[4,5,30,35,74,94,108],"S^2~S^1"],
[[4,5,30,38,68,97,108],"S^2~S^1"],
[[4,5,30,40,68,97,137,145],"S^2~S^1"],
[[4,5,35,36,48,73,94,108],"S^2~S^1"],
[[4,5,44,135,144,152,159],"S^2~S^1"],
[[4,5,45,75,84,136,145,193],"S^2~S^1"],
[[4,5,49,70,117,119,138],"S^3"],
[[4,5,50,68,90,91,97,108],"S^2~S^1"],
[[4,5,54,75,135,152,159,172],"S^2~S^1"],
[[4,5,54,75,136,182,193],"S^2~S^1"],
[[4,6,19,21,45,57,182,193],"S^2~S^1"],
[[4,10,17,19,56,67,76,124],"S^2~S^1"],
[[4,10,45,57,76,139,194,196],"B2"],
[[4,11,17,19,56,66,124],"S^2~S^1"],
[[4,12,17,19,55,124],"S^2~S^1"],
[[4,12,43,80,82,141],"S^2~S^1"],
[[5,6,18,23,78,126,145],"S^3"],
[[5,6,20,21,34,35,58,203],"S^2~S^1"],
[[5,6,56,144,152,159],"S^2~S^1"],
[[5,6,65,83,91,92,146,189],"S^2~S^1"],
[[5,6,65,84,144,159,169],"S^2~S^1"],
[[5,7,45,54,57,75,182,193],"S^2~S^1"],
[[5,7,57,75,84,145,193],"S^2~S^1"],
[[5,7,64,75,84,91,145,197],"S^2~S^1"],
[[6,7,19,21,136,182,193],"S^2~S^1"],
[[6,7,34,35,58,65,75,203],"S^2~S^1"],
[[6,7,67,152,159],"S^2~S^1"],
[[6,10,67,76,126,134,174],"B2"],
[[6,11,66,126,134,174],"B2"],
[[6,11,66,128,134,152,171],"B2"],
[[7,10,76,127,133,172,194,203],"B2"],
[[16,20,34,57,64,84,145,193],"B2"],
[[16,20,34,84,91,145,197],"B2"],
[[16,20,39,57,65,76,102,104],"T^3"],
[[16,21,30,50,69,75,90,99],"B2"],
[[16,21,30,54,90,150,154,172],"S^2~S^1"],
[[16,21,36,57,65,102,189,193],"T^3"],
[[16,21,38,69,75,91,99],"B2"],
[[16,21,39,57,65,100,102],"T^3"],
[[19,25,75,110,136,172],"T^3"],
[[19,26,31,39,57,67,143,172],"B2"],
[[19,27,45,54,66,107,108],"T^3"],
[[19,27,66,84,107,108,145,182],"T^3"],
[[20,24,45,54,107,169,182],"T^3"],
[[20,24,84,107,145,169],"T^3"]];

dc[20]:=[[[1,17,32,46,59,71,82,92,101],"S^3"],
[[1,17,32,46,59,77],"S^3"],
[[1,17,32,46,65,76,78],"S^3"],
[[1,17,32,46,65,86,88],"S^2~S^1"],
[[1,17,32,51,77,79,101,104],"S^3"],
[[1,17,32,52,64,65,76,79],"S^3"],
[[1,17,32,52,71,79,82,96],"S^2~S^1"],
[[1,17,32,52,77,79,92,96,101],"S^3"],
[[1,17,32,52,82,89,95],"S^2~S^1"],
[[1,17,32,53,86,89],"S^2~S^1"],
[[1,17,34,75,118,205,222,234],"S^2~S^1"],
[[1,17,34,80,210,229],"S^3"],
[[1,17,36,59,69,77,92,101,116],"S^3"],
[[1,17,36,61,69,218,224],"S^2~S^1"],
[[1,17,36,99,213,216,222],"S^2~S^1"],
[[1,17,36,99,218,233],"S^2~S^1"],
[[1,17,37,59,69,77,101,111],"S^3"],
[[1,17,37,65,69,76,78,101,111],"S^3"],
[[1,17,37,65,69,86,88,101,111],"S^2~S^1"],
[[1,17,37,66,69,87,88,101,111],"S^3"],
[[1,17,37,73,80,203,229],"S^3"],
[[1,17,37,77,80,101,110],"S^3"],
[[1,17,37,107,203,229,230],"S^3"],
[[1,17,38,71,77,90,101,103],"S^3"],
[[1,17,38,77,80,101,104],"S^3"],
[[1,17,39,52,53,86,90],"S^2~S^1"],
[[1,17,39,82,90,95],"S^2~S^1"],
[[1,17,39,94,99],"S^2~S^1"],[[1,17,44,211,229],"S^3"],
[[1,17,44,213,218,223,233],"S^2~S^1"],
[[1,17,44,216,222,223],"S^2~S^1"],
[[1,18,47,72,100,141,193,200],"S^3"],
[[1,18,47,81,141,180,200],"S^3"],
[[1,18,54,96,100,137,175,179],"S^2~S^1"],
[[1,18,58,141,163,180],"S^3"],
[[1,19,70,143,212,217,218,235],"RP^2xS^1"],
[[1,19,70,143,222,237,239,240],"RP^2xS^1"],
[[1,20,34,45,211,229],"S^3"],
[[1,20,34,45,213,218,223,233],"S^2~S^1"],
[[1,20,34,45,216,218,219,234],"S^2~S^1"],
[[1,20,34,45,216,222,223],"S^2~S^1"],
[[1,20,39,45,75,205,216,222],"S^2~S^1"],
[[1,20,47,49,100,160,195,212],"B2"],
[[1,20,47,58,130,163,180],"S^3"],
[[1,20,47,58,153,163,172,180,187],"S^2xS^1"],
[[1,20,47,58,153,163,176,180],"L(3,1)"],
[[1,20,47,58,156,170,194],"B2"],
[[1,20,47,58,160,165,195],"B2"],
[[1,20,47,58,161,163,180,243],"L(8,3)"],
[[1,20,51,58,79,101,104,124],"S^2~S^1"],
[[1,20,52,58,72,92,101,158,168],"S^3"],
[[1,20,52,58,75,156,169,194],"B2"],
[[1,20,52,58,79,92,96,101,124],"S^2~S^1"],
[[1,20,54,58,74,101,106,124],"S^2~S^1"],
[[1,20,54,58,75,92,98,101,124],"S^2~S^1"],
[[1,20,59,66,101,108,111,157,213],"S^2~S^1"],
[[1,20,72,92,101,119,158,215],"S^3"],
[[1,20,72,100,130,193,200],"S^3"],
[[1,20,72,100,139,141,162,193],"S^3"],
[[1,20,72,100,161,193,200,243],"L(8,3)"],
[[1,20,73,101,114,158,215],"S^3"],
[[1,20,75,119,130,149,151,213],"S^3"],
[[1,20,75,119,149,151,161,213,243],"L(8,3)"],
[[1,20,78,97,100,156,212,237],"SFS[K^2/n2:(1,5)]"],
[[1,20,78,97,100,156,216,233],"L(3,1)"],
[[1,20,81,130,144,146,195],"S^3"],
[[1,20,81,130,180,200],"S^3"],
[[1,20,81,144,146,153,172,187,195],"S^2xS^1"],
[[1,20,81,144,146,153,176,195],"L(3,1)"],
[[1,20,81,144,146,156,242],"S^2~S^1"],
[[1,20,81,144,146,161,195,243],"L(8,3)"],
[[1,20,81,146,149,156,183,213],"S^2~S^1"],
[[1,20,81,153,172,180,187,200],"S^2xS^1"],
[[1,20,81,153,176,180,200],"L(3,1)"],
[[1,20,81,154,203,211,229],"S^3"],
[[1,20,81,154,203,216,222,223],"S^2~S^1"],
[[1,20,81,161,180,200,243],"L(8,3)"],
[[1,21,48,58,211,221,226,227,229],"SFS[RP^2:(2,1)(3,1)]"],
[[1,21,51,58,71,79,101,104,121],"S^2~S^1"],
[[1,21,51,58,87,101,104,215,221],"S^3"],
[[1,21,54,58,71,74,101,106,121],"S^2~S^1"],
[[1,21,60,70,130,153,163,180],"S^3"],
[[1,21,60,70,133,135,172,187,194],"S^2xS^1"],
[[1,21,60,70,133,135,176,194],"L(3,1)"],
[[1,21,60,70,137,139,165,172,187],"S^2xS^1"],
[[1,21,60,70,137,139,165,176],"L(3,1)"],
[[1,21,60,70,153,156,170,194],"B2"],
[[1,21,60,70,153,160,165,195],"B2"],
[[1,21,60,70,153,161,163,180,243],"L(8,3)"],
[[1,21,60,70,163,172,180,187],"S^2xS^1"],
[[1,21,60,70,163,176,180],"L(3,1)"],
[[1,21,60,70,165,172,187,194,240],"B4"],
[[1,21,60,70,165,176,194,240],"SFS[RP^2:(3,1)(3,2)]"],
[[1,21,64,70,85,165,178,195],"L(3,1)"],
[[1,21,91,130,156,170,187,194,197],"S^2xS^1"],
[[1,21,91,130,160,165,187,195,197],"S^2xS^1"],
[[1,21,91,133,135,187,194,197],"S^2xS^1"],
[[1,21,91,137,139,165,187,197],"S^2xS^1"],
[[1,21,91,156,160,165,187,197,242],"B4"],
[[1,21,91,163,180,187,197],"S^2xS^1"],
[[1,21,91,164,221,226,227,229],"SFS[RP^2:(2,1)(3,1)]"],
[[1,21,91,165,187,194,197,240],"B4"],
[[1,21,91,165,191,195,221,230,243],"L(8,3)"],
[[1,21,91,170,187,194,195,197,242],"B4"],
[[1,21,91,170,191,221,225,226,229],"SFS[RP^2:(2,1)(3,1)]"],
[[1,22,36,37,59,70,77,101,111],"S^3"],
[[1,22,52,58,92,101,170,175,200],"S^3"],
[[1,22,59,70,77,92,101,116],"S^3"],
[[1,22,61,70,218,224],"S^2~S^1"],
[[1,22,69,70,99,213,216,222],"S^2~S^1"],
[[1,22,69,70,99,218,233],"S^2~S^1"],
[[1,22,72,81,130,153,180],"S^3"],
[[1,22,72,81,153,161,180,243],"L(8,3)"],
[[1,22,72,81,172,180,187],"S^2xS^1"],
[[1,22,72,81,176,180],"L(3,1)"],
[[1,22,74,81,98,101,106,177,184],"S^3"],
[[1,22,75,81,92,101,177,184],"S^3"],
[[1,22,78,81,97,175,180],"L(3,1)"],
[[1,22,100,130,153,193],"S^3"],
[[1,22,100,130,162,179,195],"S^3"],
[[1,22,100,137,139,160,162,179],"S^3"],
[[1,22,100,139,141,179,195,200],"S^3"],
[[1,22,100,153,161,193,243],"L(8,3)"],
[[1,22,100,156,162,175,201,234],"S^2~S^1"],
[[1,22,100,156,162,179,242],"S^2~S^1"],
[[1,22,100,160,162,179,194,240],"S^2~S^1"],
[[1,22,100,161,162,179,195,243],"L(8,3)"],
[[1,22,100,165,169,177,228,234],"B2"],
[[1,22,100,168,169,177,193],"B2"],
[[1,22,100,172,187,193],"S^2xS^1"],
[[1,22,100,173,224],"S^2~S^1"],
[[1,22,100,176,193],"L(3,1)"],
[[1,22,100,179,196,226],"S^2~S^1"],
[[1,23,34,37,81,210,229],"S^3"],
[[1,23,34,45,73,154,229],"S^3"],
[[1,23,73,81,203,229],"S^3"],
[[1,23,74,81,101,228,232],"S^3"],
[[1,23,83,91,180,187],"S^2xS^1"],
[[1,24,54,58,101,106,124,155,212],"S^2~S^1"],
[[1,24,77,80,90,91,101,104],"S^3"],
[[1,24,93,100,187],"S^2xS^1"],
[[1,25,47,58,75,170,194,213],"B2"],
[[1,25,52,58,169,173,177,215],"B2"],
[[1,25,52,58,169,194,213],"B2"],
[[1,25,64,70,173,221],"L(3,1)"],
[[1,25,64,70,178,195,219],"L(3,1)"],
[[1,25,75,81,144,146,213,242],"S^2~S^1"],
[[1,25,75,81,146,149,183],"S^2~S^1"],
[[1,25,94,100],"S^2~S^1"],
[[1,27,51,58,101,104,167,215],"S^3"],
[[1,27,52,58,92,96,101,167,215],"S^3"],
[[1,31,130,142,156,170,194],"S^3"],
[[1,31,130,146,153,179,193],"S^3"],
[[1,31,130,146,162,195],"S^3"],
[[1,31,131,133,154,156,196],"S^3"],
[[1,31,133,135,142,194],"S^3"],
[[1,31,133,135,151,170,196],"S^3"],
[[1,31,134,137,147,175,187,196,230],"S^2xS^1"],
[[1,31,142,153,156,170,172,187,194],"S^2xS^1"],
[[1,31,142,153,156,170,176,194],"L(3,1)"],
[[1,31,142,156,160,165,242],"S^2~S^1"],
[[1,31,142,156,161,170,194,243],"L(8,3)"],
[[1,31,142,163,180],"S^3"],
[[1,31,142,165,194,240],"S^2~S^1"],
[[1,31,142,169,237,239,240],"S^2~S^1"],
[[1,31,143,179,209,212,217,235],"RP^2xS^1"],
[[1,31,146,153,161,179,193,243],"L(8,3)"],
[[1,31,146,153,162,172,187,195],"S^2xS^1"],
[[1,31,146,153,162,176,195],"L(3,1)"],
[[1,31,146,156,162,242],"S^2~S^1"],
[[1,31,146,160,162,194,240],"S^2~S^1"],
[[1,31,146,161,162,195,243],"L(8,3)"],
[[1,31,146,172,179,187,193],"S^2xS^1"],
[[1,31,146,173,179,224],"S^2~S^1"],
[[1,31,146,176,179,193],"L(3,1)"],
[[1,31,146,181,183,187,192,193],"S^2xS^1"],
[[1,31,146,196,226],"S^2~S^1"],
[[1,31,152,212,217,218,235],"RP^2xS^1"],
[[1,31,152,214,215,218,224,225,243],"S^3/Q28"],
[[1,31,152,215,217,218,224,228],"RP^2xS^1"],
[[1,31,152,221,226,227],"S^2~S^1"],
[[1,31,152,222,237,239,240],"RP^2xS^1"],
[[2,3,18,146,172,179,187,193],"S^2xS^1"],
[[2,3,18,146,173,179,224],"S^2~S^1"],
[[2,3,18,146,176,179,193],"L(3,1)"],
[[2,3,18,146,181,183,187,192,193],"S^2xS^1"],
[[2,3,18,146,196,226],"S^2~S^1"],
[[2,3,18,147,173,175,187,188,196],"S^2xS^1"],
[[2,3,18,149,172,173,187,196],"S^2xS^1"],
[[2,3,18,149,173,176,196],"L(3,1)"],
[[2,3,18,149,193,196,224],"S^2~S^1"],
[[2,3,18,152,221,226,227],"S^2~S^1"],
[[2,3,21,48,131,221,226,227],"S^2~S^1"],
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