I have this code for solving eight queens problem. There are 92 solutions but there are only 12 unique solutions by rotating/inverting. I cant seem to figure out how to make the program show only 12 unique solutions. Can someone help me getting that code?

```
#include <iostream>
using namespace std;
class ChessBoard {
public:
ChessBoard(); // 8 x 8 chessboard;
ChessBoard(int); // n x n chessboard;
void findSolutions();
private:
const bool available;
const int squares, norm;
bool *column, *leftDiagonal, *rightDiagonal;
int *positionInRow, howMany;
void putQueen(int);
void printBoard(ostream&);
void initializeBoard();
};
ChessBoard::ChessBoard() : available(true), squares(8), norm(squares-1) {
cout <<"squares: " << squares << endl;
initializeBoard();
}
ChessBoard::ChessBoard(int n) : available(true), squares(n), norm(squares-1) {
cout <<"squares: " << squares << endl;
initializeBoard();
}
void ChessBoard::initializeBoard() {
register int i;
column = new bool[squares];
positionInRow = new int[squares];
leftDiagonal = new bool[squares*2 - 1];
rightDiagonal = new bool[squares*2 - 1];
for (i = 0; i < squares; i++)
positionInRow[i] = -1;
for (i = 0; i < squares; i++)
column[i] = available;
for (i = 0; i < squares*2 - 1; i++)
leftDiagonal[i] = rightDiagonal[i] = available;
howMany = 0;
}
void ChessBoard::printBoard(ostream& out)
{
cout << "Solution # " <<howMany<< endl;
for (int row = 0; row < squares; row++)
{
out << "(" << row <<" , " << positionInRow[row] << ")\n";
}
cout << endl;
}
void ChessBoard::putQueen(int row) {
for (int col = 0; col < squares; col++)
if (column[col] == available &&
leftDiagonal [row+col] == available &&
rightDiagonal[row-col+norm] == available) {
positionInRow[row] = col;
column[col] = !available;
leftDiagonal[row+col] = !available;
rightDiagonal[row-col+norm] = !available;
if (row < squares-1)
putQueen(row+1);
else
{
howMany++;
printBoard(cout);
}
column[col] = available;
leftDiagonal[row+col] = available;
rightDiagonal[row-col+norm] = available;
}
}
void ChessBoard::findSolutions() {
putQueen(0);
cout << howMany << " solutions found.\n";
}
int main() {
ChessBoard board;
board.findSolutions();
system("pause");
return 0;
}
```