procedure BackTrackingSymmetric;
var
  Queen, Col, Row: integer;
begin;
  for Queen:=0 to QueenCount-2 do QueenColRow[Queen].QueenRow:=Queen+1;   //symmetric
  QueenColRow[QueenCount-1].QueenRow:=0;                                  //symmetric

  Queen:=QueenCount-1;
  with QueenColRow[Queen] do begin;
    Col:=BoardSize-1;
    Row:=QueenRow;
    end;
  while true do begin;
    while Col>=0 do begin;
      if CountCol[Col] or CountDiagP[Col+Row] or CountDiagM[Col-Row]=0 then begin;
        CountCol[Col]:=1;
        CountDiagP[Col+Row]:=1;
        CountDiagM[Col-Row]:=1;
        QueenColRow[Queen].QueenCol:=Col;
        if Queen>0 then begin;
          dec(Queen);
          if Row=0 then begin;
            Row:=BoardSize-1-Col; if Col>Row then Col:=Row else dec(Col); //symmetric
            end
          else Col:=BoardSize-1;
          Row:=QueenColRow[Queen].QueenRow;
          continue;
          end;
        CountSymmetricSolution;                                           //symmetric
        //exit; //comment this statement to calculate all solutions
        CountCol[Col]:=0;
        CountDiagP[Col+Row]:=0;
        CountDiagM[Col-Row]:=0;
        end;
      dec(Col);
      end;
    inc(Queen);
    if Queen>=QueenCount then break;
    with QueenColRow[Queen] do begin;
      Col:=QueenCol;
      Row:=QueenRow;
      end;
    CountCol[Col]:=0;
    CountDiagP[Col+Row]:=0;
    CountDiagM[Col-Row]:=0;
    dec(Col);
    end;
  end;

procedure CountSymmetricSolution;
var
  i, SymCount: integer;
begin;
  if SolutionCount=0 then ShowFirstSolution;
  if BoardSize>1
  then if QueenColRow[BoardSize-1].QueenCol
        + QueenColRow[BoardSize-2].QueenCol
        <>BoardSize-1
       then SymCount:=4
       else SymCount:=2
  else SymCount:=1;
  inc(SolutionCount, SymCount);
  for i:=0 to BoardSize-2 do //excluding big digonals
    if (CountDiagP[i]=CountDiagP[i+BoardSize])
    or (CountDiagM[i+1]=CountDiagM[i+1-BoardSize]) then exit;
  if ModularCount=0 then ShowFirstSolution;
  inc(ModularCount, SymCount);
  end;