private int manhattanDistancePlusReversalPenalty(PuzzleState goal) {
        int distance = manhattanDistance(goal);
        for (int i = 0; i <= 7; ++i) {
            for (int j = i + 1; j <= 7; ++j) {
                if (board[i] == goal.board[j] && board[j] == goal.board[i]) distance += 2;
            }
        }
        return distance;
    }