Compare 1 and 2 which is better? 1: ef adjust_grayscale_values(img: np.ndarray) -> tuple[np.ndarray, int, int]:
    """Adjust the values of a grayscale image."""
    try:
        # Calculate modal white value in the range [250, 255]
        hist_white, bins_white = np.histogram(img[img >= 250], bins=6, range=(250, 256))
        modal_white = int(bins_white[np.argmax(hist_white)])

        # Calculate modal black value in the range [0, 55]
        hist_black, bins_black = np.histogram(img[img < 56], bins=56, range=(0, 56))
        modal_black = int(bins_black[np.argmax(hist_black)])

        # Convert image to float for processing
        adjusted = img.astype(np.float64)

        # Create a mask for extreme original values (0 and 255)
        mask = (img == 0) | (img == 255)

        # Exclude extreme values from the white adjustment
        white_adjust_mask = ~mask

        # Scale image if modal white is not at maximum intensity
        if modal_white != 255:
            adjusted[white_adjust_mask] *= 255.0 / modal_white
            adjusted = np.clip(adjusted, 0, 255)

        # After white value adjustment, identify new extreme values
        new_extremes = (adjusted == 0) | (adjusted == 255)

        # Combine masks to exclude all extreme values from black adjustment
        total_extremes = mask | new_extremes
        black_adjust_mask = ~total_extremes

        # Adjust image based on modal black value
        if modal_black:
            adjusted[black_adjust_mask] = (
                adjusted[black_adjust_mask] - modal_black
            ) * (255.0 / (255 - modal_black))
            adjusted = np.clip(adjusted, 0, 255)

            gamma = 1.0 - (modal_black / 255.0)
            adjusted[black_adjust_mask] = (
                np.power(adjusted[black_adjust_mask] / 255.0, gamma) * 255
            )

        # Round to nearest integer and then convert to uint8
        adjusted = np.rint(adjusted).astype(np.uint8)

        return adjusted, modal_black, modal_white

    except ValueError as e:
        log_error_message(f"Error adjusting values for image: {e}")
        return img, 0, 255 2: 
def create_adjustment_lut(modal_black: int, modal_white: int, gamma: float) -> np.ndarray:
    """Create a lookup table for grayscale value adjustments."""
    lut = np.arange(256, dtype=np.float64)
    
    # White adjustment
    if modal_white != 255:
        lut *= 255.0 / modal_white
    
    # Black adjustment
    if modal_black > 0:
        lut = (lut - modal_black) * (255.0 / (255 - modal_black))
    
    # Gamma correction
    lut = np.power(lut / 255.0, gamma) * 255
    
    return np.clip(np.round(lut), 0, 255).astype(np.uint8)

def adjust_grayscale_values(img: np.ndarray) -> Tuple[np.ndarray, int, int]:
    """Adjust the values of a grayscale image using a LUT."""
    try:
        # Calculate modal white value in the range [250, 255]
        hist_white, bins_white = np.histogram(img[img >= 250], bins=6, range=(250, 256))
        modal_white = int(bins_white[np.argmax(hist_white)])

        # Calculate modal black value in the range [0, 55]
        hist_black, bins_black = np.histogram(img[img < 56], bins=56, range=(0, 56))
        modal_black = int(bins_black[np.argmax(hist_black)])

        # Calculate gamma based on modal black value
        gamma = 1.0 - (modal_black / 255.0)

        # Create the adjustment LUT
        lut = create_adjustment_lut(modal_black, modal_white, gamma)

        # Apply the LUT to the image
        adjusted = lut[img]

        # Preserve original extreme values (0 and 255)
        mask = (img == 0) | (img == 255)
        adjusted[mask] = img[mask]

        return adjusted, modal_black, modal_white

    except ValueError as e:
        log_error_message(f"Error adjusting values for image: {e}")
        return img, 0, 255