vector<int> backtrackLegalSolution(vector<int> board, int row){
// Solution we want: {1, 3, 5, 7, 0, 0, 0, 0}
            if(row != 0){
                // Can only move to the right, trying other combinations to the left does not work, we are always moving towards the right.
                for(int col = findLastPosition(board)[1]; col < board.size() + 1; col++){
                    cout << " this is the column : " << col << "\n";
                    cout << "this is the row : " << row << "\n";
                    vector<int> newBoard = board;
                    newBoard[row] = col;
                    if(isLegalPosition(newBoard)){
                        cout << "This backtracking board is found!\n";
                        printBoard(newBoard);
                        return newBoard;
                    }
                }
                // TODO: Need to figure out here what to do when there has been a path already traveled.
                vector<int> newBoard = board;
                newBoard[row] = 0;
                backtrackLegalSolution(newBoard, row - 1);
            }
            else{
                if(findLastPosition(board)[1] == board.size()){
                    cout << "if the board is in the last one, no more, end it";
                    cout << "stop the function, this is the base case???";
                    return {0};
                }
                else{
                    cout << "otherwise, the next position in the first row is the current position + 1, unless it is at the edge.";
                    vector<int> newBoard = board;
                    newBoard[0] = findLastPosition(board)[1] + 1;
                    cout << "new board!";
                    return newBoard;
                }
            }
            return {0};
    };