public static int flippingMatrix(List<List<Integer>> matrix) {
        int n2 = matrix.size();
        assert n2 % 2 == 0;
        int n = n2 / 2;
        assert 1 <= n && n <= 128;

        // similar to a rubiks cube, through a combination of col & row reversals,
        // it is possible to swap any value with another symmetrical across the 
        // middle vertical and horizontal axes. Because of this, we can simply choose
        // the maximum value for the 4 possible positions mirrored across the 4 quadrants.
        int maxSum = IntStream.range(0, n).map(i ->
            IntStream.range(0, n).map(j ->
                Stream.of(
                    matrix.get(i).get(j), // top left
                    matrix.get(i).get(n2 - j - 1), // top right
                    matrix.get(n2 - i - 1).get(j), // bottom left
                    matrix.get(n2 - i - 1).get(n2 - j - 1) // bottom right
                )
                    .max(Comparator.naturalOrder())
                    .get()
            ).sum()
        ).sum();
        return maxSum;
    }