/home/huypn168/BARC/images/49754_train.png /home/huypn168/BARC/images/49754_test.png
You are an world-class visual puzzle solver who are extremely good at spotting patterns and solving puzzles. You are also an expert Python programmer who can write code to solve puzzles."

You will be given a visual puzzle of input grid and output grid, your data include the samples (input-output pairs) of the hidden pattern in the puzzle in form of images and the test input grid image. Your job is to solve the puzzle by writing a Python function that takes in the input grid and returns the output grid.

We first define a common library that contains the functions that you can use to solve the Puzzle.
Here is the common library function signature and docstring that you can use to solve the problem (skipping the implementation for brevity):

([{'name': 'Color', 'docstring': "Enum for colors\n\nColor.BLACK, Color.BLUE, Color.RED, Color.GREEN, Color.YELLOW, Color.GREY, Color.PINK, Color.ORANGE, Color.TEAL, Color.MAROON\n\nUse Color.ALL_COLORS for `set` of all possible colors\nUse Color.NOT_BLACK for `set` of all colors except black\n\nColors are strings (NOT integers), so you CAN'T do math/arithmetic/indexing on them.\n(The exception is Color.BLACK, which is 0)"}, {'name': 'Symmetry', 'docstring': 'Symmetry transformations, which transformed the 2D grid in ways that preserve visual structure.\nReturned by `detect_rotational_symmetry`, `detect_translational_symmetry`, `detect_mirror_symmetry`.'}, {'name': 'TranslationalSymmetry', 'docstring': 'Translation symmetry transformation, which repeatedly translates by a fixed vector\n\nExample usage:\n# Create a translational symmetry that translates by (dx, dy)\nsymmetry = TranslationalSymmetry(translate_x=dx, translate_y=dy)\n# example of using orbit to tile the entire canvas\nfor x, y in np.argwhere(input_grid != Color.BLACK):\n    # Compute orbit on to the target grid, which is typically the output\n    symmetric_points = orbit(output_grid, x, y, [symmetry])\n    for x, y in symmetric_points:\n        output_grid[x, y] = input_grid[x, y]'}, {'name': 'MirrorSymmetry', 'docstring': 'Mirror symmetry transformation, which flips horizontally and/or vertically\n\nExample usage:\nsymmetry = MirrorSymmetry(mirror_x=x if "horizontal" else None, mirror_y=y if "vertical" else None)\n\n# Flip mirrored_object over the symmetry and draw to the output\nfor x, y in np.argwhere(mirrored_object != background):\n    x2, y2 = symmetry.apply(x, y)\n    output_grid[x2, y2] = mirrored_object[x, y]'}], [{'name': 'flood_fill', 'docstring': 'Fill the connected region that contains the point (x, y) with the specified color.\n\nconnectivity: 4 or 8, for 4-way or 8-way connectivity. 8-way counts diagonals as connected, 4-way only counts cardinal directions as connected.', 'signature': 'def flood_fill(grid, x, y, color, connectivity=4)'}, {'name': 'draw_line', 'docstring': 'Draws a line starting at (x, y) extending to (end_x, end_y) or of the specified length in the specified direction\nDirection should be a vector with elements -1, 0, or 1.\nIf length is None, then the line will continue until it hits the edge of the grid.\n\nstop_at_color: optional list of colors that the line should stop at. If the line hits a pixel of one of these colors, it will stop.\n\nReturns the endpoint of the line.\n\nExample:\n# blue diagonal line from (0, 0) to (2, 2)\nstop_x, stop_y = draw_line(grid, 0, 0, length=3, color=blue, direction=(1, 1))\ndraw_line(grid, 0, 0, end_x=2, end_y=2, color=blue)\nassert (stop_x, stop_y) == (2, 2)', 'signature': 'def draw_line(grid, x, y, end_x=None, end_y=None, length=None, direction=None, color=None, stop_at_color=[])'}, {'name': 'find_connected_components', 'docstring': 'Find the connected components in the grid. Returns a list of connected components, where each connected component is a numpy array.\n\nconnectivity: 4 or 8, for 4-way or 8-way connectivity.\nmonochromatic: if True, each connected component is assumed to have only one color. If False, each connected component can include multiple colors.', 'signature': 'def find_connected_components( grid, background=Color.BLACK, connectivity=4, monochromatic=True )'}, {'name': 'randomly_scatter_points', 'docstring': 'Randomly scatter points of the specified color in the grid with specified density.\n\nExample usage:\nrandomly_scatter_points(grid, color=a_color, density=0.5, background=background_color)', 'signature': 'def randomly_scatter_points(grid, color, density=0.5, background=Color.BLACK)'}, {'name': 'scale_pattern', 'docstring': 'Scales the pattern by the specified factor.', 'signature': 'def scale_pattern(pattern, scale_factor)'}, {'name': 'scale_sprite', 'docstring': 'Scales the sprite by the specified factor.\n\nExample usage:\nscaled_sprite = scale_sprite(sprite, factor=3)\noriginal_width, original_height = sprite.shape\nscaled_width, scaled_height = scaled_sprite.shape\nassert scaled_width == original_width * 3 and scaled_height == original_height * 3', 'signature': 'def scale_sprite(sprite, factor)'}, {'name': 'blit', 'docstring': 'Copies the sprite into the grid at the specified location. Modifies the grid in place.\n\nbackground: color treated as transparent. If specified, only copies the non-background pixels of the sprite.', 'signature': 'def blit(grid, sprite, x=0, y=0, background=None)'}, {'name': 'blit_object', 'docstring': 'Draws an object onto the grid using its current location.\n\nExample usage:\nblit_object(output_grid, an_object, background=background_color)', 'signature': 'def blit_object(grid, obj, background=Color.BLACK)'}, {'name': 'blit_sprite', 'docstring': 'Draws a sprite onto the grid at the specified location.\n\nExample usage:\nblit_sprite(output_grid, the_sprite, x=x, y=y, background=background_color)', 'signature': 'def blit_sprite(grid, sprite, x, y, background=Color.BLACK)'}, {'name': 'bounding_box', 'docstring': 'Find the bounding box of the non-background pixels in the grid.\nReturns a tuple (x, y, width, height) of the bounding box.\n\nExample usage:\nobjects = find_connected_components(input_grid, monochromatic=True, background=Color.BLACK, connectivity=8)\nteal_object = [ obj for obj in objects if np.any(obj == Color.TEAL) ][0]\nteal_x, teal_y, teal_w, teal_h = bounding_box(teal_object)', 'signature': 'def bounding_box(grid, background=Color.BLACK)'}, {'name': 'bounding_box_mask', 'docstring': 'Find the bounding box of the non-background pixels in the grid.\nReturns a mask of the bounding box.\n\nExample usage:\nobjects = find_connected_components(input_grid, monochromatic=True, background=Color.BLACK, connectivity=8)\nteal_object = [ obj for obj in objects if np.any(obj == Color.TEAL) ][0]\nteal_bounding_box_mask = bounding_box_mask(teal_object)\n# teal_bounding_box_mask[x, y] is true if and only if (x, y) is in the bounding box of the teal object', 'signature': 'def bounding_box_mask(grid, background=Color.BLACK)'}, {'name': 'object_position', 'docstring': '(x,y) position of the provided object. By default, the upper left corner.\n\nanchor: "upper left", "upper right", "lower left", "lower right", "center", "upper center", "lower center", "left center", "right center"\n\nExample usage:\nx, y = object_position(obj, background=background_color, anchor="upper left")\nmiddle_x, middle_y = object_position(obj, background=background_color, anchor="center")', 'signature': 'def object_position(obj, background=Color.BLACK, anchor="upper left")'}, {'name': 'object_colors', 'docstring': 'Returns a list of colors in the object.\n\nExample usage:\ncolors = object_colors(obj, background=background_color)', 'signature': 'def object_colors(obj, background=Color.BLACK)'}, {'name': 'crop', 'docstring': 'Crop the grid to the smallest bounding box that contains all non-background pixels.\n\nExample usage:\n# Extract a sprite from an object\nsprite = crop(an_object, background=background_color)', 'signature': 'def crop(grid, background=Color.BLACK)'}, {'name': 'translate', 'docstring': 'Translate by the vector (x, y). Fills in the new pixels with the background color.\n\nExample usage:\nred_object = ... # extract some object\nshifted_red_object = translate(red_object, x=1, y=1)\nblit_object(output_grid, shifted_red_object, background=background_color)', 'signature': 'def translate(obj, x, y, background=Color.BLACK)'}, {'name': 'collision', 'docstring': 'Check if object1 and object2 collide when object1 is at (x1, y1) and object2 is at (x2, y2).\n\nExample usage:\n\n# Check if a sprite can be placed onto a grid at (X,Y)\ncollision(object1=output_grid, object2=a_sprite, x2=X, y2=Y)\n\n# Check if two objects collide\ncollision(object1=object1, object2=object2, x1=X1, y1=Y1, x2=X2, y2=Y2)', 'signature': 'def collision( _=None, object1=None, object2=None, x1=0, y1=0, x2=0, y2=0, background=Color.BLACK )'}, {'name': 'contact', 'docstring': 'Check if object1 and object2 touch each other (have contact) when object1 is at (x1, y1) and object2 is at (x2, y2).\nThey are touching each other if they share a border, or if they overlap. Collision implies contact, but contact does not imply collision.\n\nconnectivity: 4 or 8, for 4-way or 8-way connectivity. (8-way counts diagonals as touching, 4-way only counts cardinal directions as touching)\n\nExample usage:\n\n# Check if a sprite touches anything if it were to be placed at (X,Y)\ncontact(object1=output_grid, object2=a_sprite, x2=X, y2=Y)\n\n# Check if two objects touch each other\ncontact(object1=object1, object2=object2)', 'signature': 'def contact( _=None, object1=None, object2=None, x1=0, y1=0, x2=0, y2=0, background=Color.BLACK, connectivity=4, )'}, {'name': 'randomly_spaced_indices', 'docstring': 'Generate randomly-spaced indices guaranteed to not be adjacent.\nUseful for generating random dividers.\n\npadding: guaranteed empty space in between indices\nborder_size: guaranteed empty space at the border\n\nExample usage:\nx_indices = randomly_spaced_indices(grid.shape[0], num_dividers, border_size=1, padding=2) # make sure each region is at least 2 pixels wide\nfor x in x_indices:\n    grid[x, :] = divider_color', 'signature': 'def randomly_spaced_indices(max_len, n_indices, border_size=1, padding=1)'}, {'name': 'check_between_objects', 'docstring': 'Check if a pixel is between two objects.\n\npadding: minimum distance from the edge of the objects\n\nExample usage:\nif check_between_objects(obj1, obj2, x, y, padding=1, background=background_color):\n    # do something', 'signature': 'def check_between_objects(obj1, obj2, x, y, padding = 0, background=Color.BLACK)'}, {'name': 'random_free_location_for_sprite', 'docstring': 'Find a random free location for the sprite in the grid\nReturns a tuple (x, y) of the top-left corner of the sprite in the grid, which can be passed to `blit_sprite`\n\nborder_size: minimum distance from the edge of the grid\nbackground: color treated as transparent\npadding: if non-zero, the sprite will be padded with a non-background color before checking for collision\npadding_connectivity: 4 or 8, for 4-way or 8-way connectivity when padding the sprite\n\nExample usage:\nx, y = random_free_location_for_sprite(grid, sprite, padding=1, padding_connectivity=8, border_size=1, background=Color.BLACK) # find the location, using generous padding\nassert not collision(object1=grid, object2=sprite, x2=x, y2=y)\nblit_sprite(grid, sprite, x, y)\n\nIf no free location can be found, raises a ValueError.', 'signature': 'def random_free_location_for_sprite( grid, sprite, background=Color.BLACK, border_size=0, padding=0, padding_connectivity=8, )'}, {'name': 'object_interior', 'docstring': "Computes the interior of the object (including edges)\n\nreturns a new grid of `bool` where True indicates that the pixel is part of the object's interior.\n\nExample usage:\ninterior = object_interior(obj, background=Color.BLACK)\nfor x, y in np.argwhere(interior):\n    # x,y is either inside the object or at least on its edge", 'signature': 'def object_interior(grid, background=Color.BLACK)'}, {'name': 'object_boundary', 'docstring': "Computes the boundary of the object (excluding interior)\n\nreturns a new grid of `bool` where True indicates that the pixel is part of the object's boundary.\n\nExample usage:\nboundary = object_boundary(obj, background=Color.BLACK)\nassert np.all(obj[boundary] != Color.BLACK)", 'signature': 'def object_boundary(grid, background=Color.BLACK)'}, {'name': 'object_neighbors', 'docstring': "Computes a mask of the points that neighbor or border the object, but are not part of the object.\n\nreturns a new grid of `bool` where True indicates that the pixel is part of the object's border neighbors5.\n\nExample usage:\nneighbors = object_neighbors(obj, background=Color.BLACK)\nassert np.all(obj[neighbors] == Color.BLACK)", 'signature': 'def object_neighbors(grid, background=Color.BLACK, connectivity=4)'}, {'name': 'orbit', 'docstring': 'Compute the orbit of the point (x, y) under the symmetry transformations `symmetries`.\nThe orbit is the set of points that the point (x, y) maps to after applying the symmetry transformations different numbers of times.\nReturns a list of points in the orbit.\n\nExample:\nsymmetries = detect_rotational_symmetry(input_grid)\nfor x, y in np.argwhere(input_grid != Color.BLACK):\n    # Compute orbit on to the target grid, which is typically the output\n    symmetric_points = orbit(output_grid, x, y, symmetries)\n    # ... now we do something with them like copy colors or infer missing colors', 'signature': 'def orbit(grid, x, y, symmetries)'}, {'name': 'detect_translational_symmetry', 'docstring': 'Finds translational symmetries in a grid.\nSatisfies: grid[x, y] == grid[x + translate_x, y + translate_y] for all x, y, as long as neither pixel is in `ignore_colors`, and as long as x,y is not background.\n\nReturns a list of Symmetry objects, each representing a different translational symmetry.\n\nExample:\nsymmetries = detect_translational_symmetry(grid, ignore_colors=[occluder_color], background=background_color)\nfor x, y in np.argwhere(grid != occluder_color & grid != background_color):\n    # Compute orbit on to the target grid\n    # When copying to an output, this is usually the output grid\n    symmetric_points = orbit(grid, x, y, symmetries)\n    for x, y in symmetric_points:\n        assert grid[x, y] == grid[x, y] or grid[x, y] == occluder_color', 'signature': 'def detect_translational_symmetry(grid, ignore_colors=[Color.BLACK], background=None)'}, {'name': 'submit', 'docstring': 'Submit the output grid to the problem\nargs: \n    output_grid: numpy array of shape (n, m)', 'signature': 'def submit(output_grid)'}, {'name': 'detect_mirror_symmetry', 'docstring': "Returns list of mirror symmetries.\nSatisfies: grid[x, y] == grid[2*mirror_x - x, 2*mirror_y - y] for all x, y, as long as neither pixel is in `ignore_colors`\n\nExample:\nsymmetries = detect_mirror_symmetry(grid, ignore_colors=[Color.RED], background=Color.BLACK) # ignore_color: In case parts of the object have been removed and occluded by red\nfor x, y in np.argwhere(grid != Color.BLACK & grid != Color.RED): # Everywhere that isn't background and isn't occluded\n    for sym in symmetries:\n        symmetric_x, symmetric_y = sym.apply(x, y)\n        assert grid[symmetric_x, symmetric_y] == grid[x, y] or grid[symmetric_x, symmetric_y] == Color.RED\n\nIf the grid has both horizontal and vertical mirror symmetries, the returned list will contain two elements.", 'signature': 'def detect_mirror_symmetry(grid, ignore_colors=[Color.BLACK], background=None)'}, {'name': 'detect_rotational_symmetry', 'docstring': 'Finds rotational symmetry in a grid, or returns None if no symmetry is possible.\nSatisfies: grid[x, y] == grid[y - rotate_center_y + rotate_center_x, -x + rotate_center_y + rotate_center_x] # clockwise\n           grid[x, y] == grid[-y + rotate_center_y + rotate_center_x, x - rotate_center_y + rotate_center_x] # counterclockwise\n           for all x, y, as long as neither pixel is in `ignore_colors`, and as long as x, y is not `background`.\n\nExample:\nsym = detect_rotational_symmetry(grid, ignore_colors=[Color.GREEN], background=Color.BLACK) # ignore_color: In case parts of the object have been removed and occluded by black\nfor x, y in np.argwhere(grid != Color.GREEN):\n    rotated_x, rotated_y = sym.apply(x, y, iters=1) # +1 clockwise, -1 counterclockwise\n    assert grid[rotated_x, rotated_y] == grid[x, y] or grid[rotated_x, rotated_y] == Color.GREEN or grid[x, y] == Color.BLACK\nprint(sym.center_x, sym.center_y) # In case these are needed, they are floats', 'signature': 'def detect_rotational_symmetry(grid, ignore_colors=[Color.BLACK], background=None)'}, {'name': 'create_grid_visualization', 'docstring': 'Create a visualization of grid(s) and return PIL image.\n\nArgs:\n    input_grid (List[List[int]]): The input grid\n    output_grid (List[List[int]]): The output grid\n    example_title (str, optional): The title of the example. Defaults to "Output Test Grid".', 'signature': 'def create_grid_visualization(input_grid, output_grid, example_title="Output Test Grid")'}, {'name': 'is_contiguous', 'docstring': 'Check if an array is contiguous.\n\nbackground: Color that counts as transparent (default: Color.BLACK)\nconnectivity: 4 or 8, for 4-way (only cardinal directions) or 8-way connectivity (also diagonals) (default: 4)\n\nReturns True/False', 'signature': 'def is_contiguous(bitmask, background=Color.BLACK, connectivity=4)'}, {'name': 'random_sprite', 'docstring': "Generate a sprite (an object), represented as a numpy array.\n\nn, m: dimensions of the sprite. If these are lists, then a random value will be chosen from the list.\nsymmetry: optional type of symmetry to apply to the sprite. Can be 'horizontal', 'vertical', 'diagonal', 'radial', 'mirror', 'not_symmetric'. If None, a random symmetry type will be chosen.\ncolor_palette: optional list of colors to use in the sprite. If None, a random color palette will be chosen.\n\nReturns an (n,m) NumPy array representing the sprite.", 'signature': 'def random_sprite(n, m, density=0.5, symmetry=None, color_palette=None, connectivity=4, background=Color.BLACK)'}, {'name': 'detect_objects', 'docstring': 'Detects and extracts objects from the grid that satisfy custom specification.\n\npredicate: a function that takes a candidate object as input and returns True if it counts as an object\nbackground: color treated as transparent\nmonochromatic: if True, each object is assumed to have only one color. If False, each object can include multiple colors.\nconnectivity: 4 or 8, for 4-way or 8-way connectivity. If None, the connectivity is determined automatically.\nallowed_dimensions: a list of tuples (n, m) specifying the allowed dimensions of the objects. If None, objects of any size are allowed.\ncolors: a list of colors that the objects are allowed to have. If None, objects of any color are allowed.\ncan_overlap: if True, objects can overlap. If False, objects cannot overlap.\n\nReturns a list of objects, where each object is a numpy array.', 'signature': 'def detect_objects(grid, _=None, predicate=None, background=Color.BLACK, monochromatic=False, connectivity=None, allowed_dimensions=None, colors=None, can_overlap=False)'}])

<instructions>
- Initially test out your hypothesis, ideas or visualize the output grid produced by the your hypothesized induced function that potentially induces the pattern in the puzzle by outputting code in <code> tags to execute code.
- Observes the images and think VERY HARD about the patterns, concepts and puzzle.
- During your iteration output code in <code> tags to execute code which will be run in a jupyter notebook environment.
- Your final function, output code in <final_code> tags, you must submit the output grid in format of a list of lists using the `submit` function, do not to print anything else inside your final solution, it will affect the evaluation.
- Within <final_code>, provide only the final output grid without any further output.
- The test input grid is always defined in advanced with `test_input_grid` variable. No need to define it again in your code, just use it.
- always uses `create_grid_visualization` function to visualize the output grid.
- Your code should be very skillful in terms of numpy manipulation code and utilizes the common library functions as much as possible.
- Output in the following format:

<thinking>Your thoughts on the next step</thinking>
<code>The python code you want to execute</code>
<final_code>The final code you want to submit, but compulsory to output if you are on your final turn </final_code>

Here is samples image of input grid and output grid <image> and the test input grid <image>. Now solve this puzzle.
user
from common import *

import numpy as np
from typing import *

# concepts:
# reflection, color change

# description:
# In the input you will see a grid with a colored pattern. 
# To make the output, reflect the pattern over the vertical axis (left to right) and change its color to blue.

def main(input_grid):
    # Plan:
    # 1. Find the connected components (colored patterns) in the input grid.
    # 2. For each component, reflect it over the vertical axis.
    # 3. Change the color of each reflected pattern to blue.
    
    # Find connected components (colored objects)
    components = find_connected_components(input_grid, monochromatic=False, background=Color.BLACK)
    
    # Create an output grid initialized to the background color
    output_grid = np.full_like(input_grid, Color.BLACK)

    for component in components:
        # Get the positions of the component
        x, y = object_position(component, background=Color.BLACK)
        component_width, component_height = component.shape
        
        # Change the color of the component to blue
        component[component != Color.BLACK] = Color.BLUE
        
        # Reflect over the vertical axis
        reflected_component = np.fliplr(component)

        # Blit the reflected component to the output grid at the same position
        blit_sprite(output_grid, reflected_component, x, y, background=Color.BLACK)

    return output_grid

def generate_input():
    # Generate the background grid
    width, height = np.random.randint(5, 15, size=2)
    grid = np.zeros((width, height), dtype=int)

    # Randomly choose the number of components
    num_components = np.random.randint(1, 5)
    colors = np.random.choice(Color.NOT_BLACK, size=num_components, replace=False)

    for color in colors:
        # Create a random sprite for each color
        sprite_width = np.random.randint(1, 4)
        sprite_height = np.random.randint(1, 4)
        sprite = random_sprite(n=sprite_width, m=sprite_height, color_palette=[color], density=0.7)
        
        # Find a free location for this sprite on the grid
        try:
            x, y = random_free_location_for_sprite(grid, sprite, padding=1)
            blit_sprite(grid, sprite, x, y)
        except ValueError:
            # If no location found, skip this color
            continue
    
    return grid