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dari script ini tambahkan code agar saat meload file mid dapat memeriksa file mp3 dengan nama yang sama dengan file mid nya juga, dan ini optional, jika ada maka gunakan untuk di play untuk game, untuk bounce tetap menggunakan file mid, jika tidak ada maka gunakan saja sound dari file mid, buatkan dengan benar dan tepat : import pygame
import mido
import sys
import random
import requests
import colorsys
import os
from os.path import join, isfile
from time import time as get_current_time
from typing import Union, Optional, Any
from enum import Enum
from math import sin, pi
import math  # Ditambahkan untuk fungsi matematika

pygame.mixer.init()
pygame.init()
FRAMERATE = 60

# =========================
# Customizable Configuration
# =========================

# Screen Resolution
SCREEN_WIDTH = 1280     # Ganti sesuai keinginan Anda
SCREEN_HEIGHT = 720    # Ganti sesuai keinginan Anda

# File Selection
SONG = "dashie - ultraphunk.mid"  # Ganti dengan nama file MIDI Anda

# Song Information
SONG_NAME = 'SquareVibes'      # Set the song name here
SONG_CREATOR = 'SUBSCRIBE :D'         # Set the song creator here

# Other Customizable Settings
SQUARE_SPEED = 600             # Kecepatan kotak
SQUARE_SIZE = 50
BOUNCE_MIN_SPACING = 50        # Spasi minimum antar pantulan
DIRECTION_CHANGE = 30   # Peluang perubahan arah
PARTICLE_TRAIL = True          # Aktifkan atau nonaktifkan jejak partikel
PARTICLE_SPEED = 5
BOUNCE_PEG = True
# =========================

def color_hunt():
    def is_bright(hex_color):
        hex_color = hex_color.lstrip('#')
        rgb = tuple(int(hex_color[i:i+2], 16) for i in (0, 2, 4))
        luminance = 0.299 * rgb[0] + 0.587 * rgb[1] + 0.114 * rgb[2]
        r, g, b = [x / 255.0 for x in rgb]
        h, s, v = colorsys.rgb_to_hsv(r, g, b)
        return luminance >= 130 and s >= 0.3
    while True:
        url = 'https://colorhunt.co/php/feed.php'
        headers = {
            'Content-Type': 'application/x-www-form-urlencoded; charset=UTF-8'
        }
        data = {
            'step': 0,
            'sort': 'random',
            'tags': ''
        }
        response = requests.post(url, headers=headers, data=data)
        if response.status_code == 200:
            palettes = response.json()
            color_pairs = []
            for palette in palettes:
                code = palette['code']
                hex_colors = [f'#{code[i:i+6].upper()}' for i in range(0, len(code), 6)]
                if len(hex_colors) == 4 and all(is_bright(hex_color) for hex_color in hex_colors):
                    color_pairs.append(tuple(hex_colors))
            if color_pairs:
                selected_color_pair = random.choice(color_pairs)
                return selected_color_pair
        else:
            raise Exception(f"Failed to retrieve data. Status code: {response.status_code}")

selected_colors = color_hunt()
color1, color2, color3, color4 = selected_colors

class Config:
    # Constants
    SQUARE_SIZE = SQUARE_SIZE
    PARTICLE_SPEED = PARTICLE_SPEED

    # Colors
    color_themes = {
        "dark": {
            "hallway": pygame.Color('#451952'),
            "background": pygame.Color('#0F0F0F'),
            "square": [
                pygame.Color(color1),
                pygame.Color(color2),
                pygame.Color(color3),
                pygame.Color(color4)
            ]
        }
    }

    # Configuration
    script_dir = os.path.dirname(os.path.abspath(__file__))
    assets = os.path.join(script_dir, 'assets/icon.png')
    song = os.path.join(script_dir, 'songs')
    font = os.path.join(script_dir, 'assets/poppins-regular.ttf')
    SCREEN_WIDTH = SCREEN_WIDTH
    SCREEN_HEIGHT = SCREEN_HEIGHT
    theme: Optional[str] = "dark"
    seed: Optional[int] = None
    camera_mode: Optional[int] = 2
    start_playing_delay = 3000
    max_notes: Optional[int] = None
    bounce_min_spacing: Optional[float] = BOUNCE_MIN_SPACING
    square_speed: Optional[int] = SQUARE_SPEED
    volume: Optional[int] = 100
    music_offset: Optional[int] = 0
    direction_change_chance: Optional[int] = DIRECTION_CHANGE
    theatre_mode = True
    particle_trail = PARTICLE_TRAIL
    do_color_bounce_pegs = BOUNCE_PEG
    do_particles_on_bounce = True

    # Non-configurable settings
    backtrack_chance: Optional[float] = 0.02
    backtrack_amount: Optional[int] = 40
    square_swipe_anim_speed: Optional[int] = 4
    particle_amount = 20
    language = "english"

    # Other random stuff
    current_song = None
    dt = 0.01

def get_colors():
    return Config.color_themes.get(Config.theme, Config.color_themes["dark"])

def read_midi_file(file):
    midi_file = mido.MidiFile(file=file)

    notes = []
    current_time = 0

    for msg in midi_file:
        if msg.type == 'note_on' and msg.velocity != 0:
            timestamp = current_time + msg.time
            notes.append(round(timestamp*1000)/1000)
        current_time += msg.time
    return notes

def remove_too_close_values(lst: list[float], threshold=30) -> list[float]:
    """Assumes the list is sorted"""
    new = []
    before = None
    for _ in lst:
        if before is None:
            before = _
            new.append(_)
            continue
        if before+threshold/1000 > _:
            continue
        before = _
        new.append(_)
    return new

def fix_overlap(rects: list[pygame.Rect], callback=None):
    """
    Optimized function to merge overlapping rectangles efficiently.
    """
    if callback is None:
        callback = lambda _: None

    rects = rects.copy()
    # Sort rectangles based on x coordinate
    rects.sort(key=lambda r: (r.x, r.y))

    merged_rects = []
    for rect in rects:
        if not merged_rects:
            merged_rects.append(rect)
        else:
            last = merged_rects[-1]
            if last.colliderect(rect):
                merged_rect = last.union(rect)
                merged_rects[-1] = merged_rect
            else:
                merged_rects.append(rect)

    callback("Finished merging rectangles")

    return merged_rects

def get_font(size: int = 24) -> pygame.font.Font:
    font_path = Config.font
    return pygame.font.Font(font_path, size)

class MapLoadingFailureError(Exception):
    """The map fails to load (recurs function fails)"""
    pass

class UserCancelsLoadingError(Exception):
    """User cancels the loading screen"""
    pass

def interpolate_fn(n):
    """Interpolate sigmoidally from 0-1"""
    n = min(max(n, 0), 1)
    return sin(pi * (n - 0.5)) / 2 + 0.5

class Particle:
    SPEED_VARIATION = 4
    SIZE_MIN = 7
    SIZE_MAX = 14
    AGE_RATE = 20
    SLOW_DOWN_RATE = 1.2

    def __init__(self, pos: list[float], delta: list[float], invert_color: bool = False, color: Optional[tuple] = None):
        self.pos = pos.copy()
        self.size = random.randint(Particle.SIZE_MIN, Particle.SIZE_MAX)
        self.delta = delta.copy()
        self.delta[0] += random.randint(-Particle.SPEED_VARIATION, Particle.SPEED_VARIATION)/8
        self.delta[1] += random.randint(-Particle.SPEED_VARIATION, Particle.SPEED_VARIATION)/8
        if color is not None:
            self.color = color
        else:
            # Warna default jika warna tidak diberikan
            self.color = get_colors()["hallway"] if not invert_color else get_colors()["background"]

    def age(self):
        self.size -= Particle.AGE_RATE*Config.dt
        self.x += self.delta[0] * Config.PARTICLE_SPEED
        self.y += self.delta[1] * Config.PARTICLE_SPEED
        if Config.dt != 0:
            self.delta[0] /= (Particle.SLOW_DOWN_RATE+FRAMERATE) * Config.dt
            self.delta[1] /= (Particle.SLOW_DOWN_RATE+FRAMERATE) * Config.dt
        return self.size <= 0

    @property
    def x(self):
        return self.pos[0]

    @x.setter
    def x(self, val: float):
        self.pos[0] = val

    @property
    def y(self):
        return self.pos[1]

    @y.setter
    def y(self, val: float):
        self.pos[1] = val

    @property
    def rect(self):
        return pygame.Rect(self.x-self.size/2, self.y-self.size/2, *(2*[self.size]))

class Bounce:
    def __init__(self, sq_pos: list[float], sq_dir: list[int], time: float, bounce_dir: int):
        self.square_pos = sq_pos  # New square position
        self.square_dir = sq_dir  # New square direction
        self.bounce_dir = bounce_dir  # Bounce direction for squish effect; 0 or 1
        self.time = time  # Time during bounce

    def get_collision_rect(self):
        sx, sy = self.square_pos
        if self.bounce_dir == 0:
            # Bounce left or right wall
            if self.square_dir[0] == -1:
                # Right wall
                return pygame.Rect(
                    sx+Config.SQUARE_SIZE/2+1,
                    sy-10,
                    10,
                    20
                )
            elif self.square_dir[0] == 1:
                # Left wall
                return pygame.Rect(
                    sx-10-Config.SQUARE_SIZE/2-1,
                    sy-10,
                    10,
                    20
                )
        elif self.bounce_dir == 1:
            # Bounce top or bottom wall
            if self.square_dir[1] == -1:
                # Bottom wall
                return pygame.Rect(
                    sx-10,
                    sy+Config.SQUARE_SIZE/2+1,
                    20,
                    10
                )
            elif self.square_dir[1] == 1:
                # Top wall
                return pygame.Rect(
                    sx-10,
                    sy-10-Config.SQUARE_SIZE/2-1,
                    20,
                    10
                )

    def copy(self) -> "Bounce":
        return Bounce(self.square_pos.copy(), self.square_dir.copy(), self.time, self.bounce_dir)

    def __repr__(self):
        return f"<Bounce(sq_pos={self.square_pos}, sq_dir={self.square_dir}, time={self.time}, dir={self.bounce_dir})"

class Square:
    def __init__(self, x: float = 0, y: float = 0, dx: int = 1, dy: int = 1):
        self.pos: list[float] = [x, y]
        self.dir: list[int] = [dx, dy]
        self.last_bounce_time = -100
        self.latest_bounce_direction = 0  # 0 = horiz, 1 = vert
        self.past_colors = []
        self.died = False

    def register_past_color(self, col: tuple[int, int, int]):
        for _ in range(max(Config.square_swipe_anim_speed, 1)):
            self.past_colors.insert(0, col)
        while len(self.past_colors) > Config.SQUARE_SIZE * 4 / 5:
            self.past_colors.pop()

    def get_surface(self, size: tuple[int, int]):
        ss = int(Config.SQUARE_SIZE * 4 / 5)
        surf = pygame.Surface((ss, ss))
        for index, col in enumerate(self.past_colors):
            y = index if self.dir_y != 1 else ss - 1 - index
            pygame.draw.line(surf, col, (0, y), (ss, y))
        return pygame.transform.scale(surf, size)

    def copy(self) -> "Square":
        new = Square(*self.pos, *self.dir)
        new.last_bounce_time = self.last_bounce_time
        new.latest_bounce_direction = self.latest_bounce_direction
        return new

    def get_current_color(self):
        square_color_index = round((self.dir_x + 1) / 2 + self.dir_y + 1)
        return get_colors()["square"][square_color_index % len(get_colors()["square"])]
    
    @property
    def x(self):
        return self.pos[0]

    @property
    def y(self):
        return self.pos[1]

    def draw(self, screen: pygame.Surface, sqrect: pygame.Rect):
        if self.died:
            return
        square_color_index = round((self.dir_x + 1) / 2 + self.dir_y + 1)
        self.register_past_color(get_colors()["square"][square_color_index % len(get_colors()["square"])])

        pygame.draw.rect(screen, (0, 0, 0), sqrect)
        sq_surf = self.get_surface(
            tuple(sqrect.inflate(-int(Config.SQUARE_SIZE / 5), -int(Config.SQUARE_SIZE / 5))[2:]))
        screen.blit(sq_surf, sq_surf.get_rect(center=sqrect.center))

    @x.setter
    def x(self, val: int):
        self.pos[0] = val

    @y.setter
    def y(self, val: int):
        self.pos[1] = val

    @property
    def dir_x(self):
        return self.dir[0]

    @property
    def dir_y(self):
        return self.dir[1]

    @property
    def rect(self):
        return pygame.Rect(self.x - Config.SQUARE_SIZE / 2, self.y - Config.SQUARE_SIZE / 2,
                           *([Config.SQUARE_SIZE] * 2))

    def obey_bounce(self, bounce: Bounce):
        # Planned bounces
        self.pos = bounce.square_pos.copy()
        self.dir = bounce.square_dir.copy()
        self.latest_bounce_direction = bounce.bounce_dir
        self.last_bounce_time = bounce.time
        return

    def reg_move(self, use_dt: bool = True):
        self.x += self.dir_x * Config.square_speed * (Config.dt if use_dt else 1 / FRAMERATE)
        self.y += self.dir_y * Config.square_speed * (Config.dt if use_dt else 1 / FRAMERATE)

class Camera:
    def __init__(self, x: int = 0, y: int = 0):
        self.x = x
        self.y = y
        self.locked_on_square = True
        self.lock_type: CameraFollow = CameraFollow(Config.camera_mode)

    def attempt_movement(self):
        if not self.locked_on_square:
            keys = pygame.key.get_pressed()
            shift_modifier = (keys[pygame.K_LSHIFT] | keys[pygame.K_RSHIFT]) + 1
            self.x += (keys[pygame.K_d] - keys[pygame.K_a]) * 500 * shift_modifier / FRAMERATE
            self.y += (keys[pygame.K_s] - keys[pygame.K_w]) * 500 * shift_modifier / FRAMERATE

    @property
    def pos(self):
        return self.x, self.y

    @pos.setter
    def pos(self, val: Union[tuple[int, int], list[int]]):
        self.x, self.y = val

    def offset(self, pos_or_rect: Union[pygame.Rect, tuple[int, int]]) -> Union[pygame.Rect, list[int]]:
        if isinstance(pos_or_rect, pygame.Rect):
            return pos_or_rect.move(-self.x, -self.y)
        else:
            return [pos_or_rect[0]-self.x, pos_or_rect[1]-self.y]

    def apply_parallax(self, pos: tuple[float, float], depth: float) -> list[float]:
        # Parallax factor: nearer stars move faster than distant ones
        parallax_factor = 0.2 + depth * 0.8  # From 0.2 to 1.0
        screen_x = (pos[0] - self.x) * parallax_factor
        screen_y = (pos[1] - self.y) * parallax_factor
        return [screen_x, screen_y]

    def follow(self, square: Square):

        # Square in center
        if self.lock_type == CameraFollow.Center:
            self.pos = [square.x - Config.SCREEN_WIDTH / 2, square.y - Config.SCREEN_HEIGHT / 2]

        # Smooth camera
        if self.lock_type == CameraFollow.Smoothed:
            easing_rate = 3
            self.x = (square.x - Config.SCREEN_WIDTH / 2) * easing_rate * Config.dt + self.x - easing_rate * self.x * Config.dt
            self.y = (square.y - Config.SCREEN_HEIGHT / 2) * easing_rate * Config.dt + self.y - easing_rate * self.y * Config.dt

class CameraFollow(Enum):
    Center = 0  # Center the square
    Smoothed = 2  # Smoothed camera

class Star:
    def __init__(self, pos: tuple[float, float], depth: float):
        self.initial_pos = list(pos)
        self.depth = depth  # between 0 (far) and 1 (near)
        size_min = 0.5
        size_max = 2
        self.size = size_min + (1 - self.depth) * (size_max - size_min)
        self.phase = random.uniform(0, 2 * math.pi)  # Ditambahkan untuk fase acak
        self.brightness = 0  # Akan diperbarui dalam metode update
        self.color = (255, 255, 255)  # Warna default, akan diperbarui

    def update(self, time):
        # Adjust brightness over time to create blinking effect
        blink_speed = 10  # can adjust to get desired speed
        brightness_variation = (math.sin(blink_speed * time + self.phase) + 1) / 2  # Normalize between 0 and 1
        min_brightness = 100
        max_brightness = 255
        self.brightness = min_brightness + brightness_variation * (max_brightness - min_brightness)
        self.color = (int(self.brightness),) * 3  # Update color based on brightness

    def get_screen_pos(self, camera: Camera):
        parallax_factor = 0.2 + self.depth * 0.8  # from 0.2 to 1.0
        screen_x = (self.initial_pos[0] - camera.x) * parallax_factor
        screen_y = (self.initial_pos[1] - camera.y) * parallax_factor
        return [screen_x, screen_y]

class World:
    """It's a cruel world out there"""

    def __init__(self):
        self.future_bounces: list[Bounce] = []
        self.past_bounces: list[Bounce] = []
        self.start_time = 0
        self.time = 0
        self.rectangles: list[pygame.Rect] = []
        self.collision_times: list[float] = []
        self.particles: list[Particle] = []
        self.stars: list[Star] = []
        self.timestamps = []
        self.square = Square()
        self.colors = []
        self.safe_areas: list[pygame.Rect] = []

    def update_time(self) -> None:
        self.time = get_current_time() - self.start_time

    def get_next_bounce(self) -> Bounce:
        """Also pops the bounce from the future_bounces list"""
        self.past_bounces.append(self.future_bounces.pop(0))
        return self.past_bounces[-1]

    def add_bounce_particles(self, sp: list[float], sd: list[float], color: tuple):
        for _ in range(Config.particle_amount):
            new = Particle([sp[0] + random.randint(-10, 10), sp[1] + random.randint(-10, 10)], sd, color=color)
            self.particles.append(new)

    def handle_bouncing(self, square: Square):
        if len(self.future_bounces):
            if (self.time * 1000 + Config.music_offset)/1000 > self.future_bounces[0].time:
                current_bounce = self.get_next_bounce()
                before = square.dir.copy()
                square.obey_bounce(current_bounce)
                changed = square.dir.copy()
                for _ in range(2):
                    if before[_] == changed[_]:
                        changed[_] = 0
                    else:
                        changed[_] = -changed[_]
                if Config.do_particles_on_bounce:
                    square_color = square.get_current_color()
                    self.add_bounce_particles(square.pos, changed, color=square_color)

                # Stop square at end
                if len(self.future_bounces) == 0:
                    square.dir = [0, 0]
                    square.pos = current_bounce.square_pos

    def generate_stars(self):
        self.stars = []
        # Menghitung total area aman
        total_safe_area = sum(area.width * area.height for area in self.safe_areas)
        star_density = 0.0001  # Sesuaikan sesuai kebutuhan
        total_num_stars = int(total_safe_area * star_density)
        min_distance_squared = (20) ** 2  # Menghindari clustering

        # Mendapatkan bounding rectangle dari semua area aman
        min_x = min(area.left for area in self.safe_areas)
        max_x = max(area.right for area in self.safe_areas)
        min_y = min(area.top for area in self.safe_areas)
        max_y = max(area.bottom for area in self.safe_areas)
        bounding_rect = pygame.Rect(min_x, min_y, max_x - min_x, max_y - min_y)

        stars = []
        attempts = 0
        max_attempts = total_num_stars * 10

        while len(stars) < total_num_stars and attempts < max_attempts:
            x = random.uniform(bounding_rect.left, bounding_rect.right)
            y = random.uniform(bounding_rect.top, bounding_rect.bottom)
            point = (x, y)

            # Memastikan titik berada dalam area aman
            inside_safe_area = any(area.collidepoint(point) for area in self.safe_areas)

            if inside_safe_area:
                # Memastikan jarak minimum antar bintang
                if all((star.initial_pos[0] - x) ** 2 + (star.initial_pos[1] - y) ** 2 >= min_distance_squared for star in stars):
                    depth = random.uniform(0, 1)
                    star = Star((x, y), depth)
                    stars.append(star)
            attempts += 1

        self.stars = stars

    def gen_future_bounces(self, _start_notes: list[float], percent_update_callback):
        """Recursive function with optimized overlap checking"""
        total_notes = len(_start_notes)
        max_percent = 0
        path = []
        safe_areas = []
        force_return = 0

        def recurs(
                square: Square,
                notes: list[float],
                bounces_so_far: list[Bounce] = None,
                prev_index_priority=None,
                t: float = 0,
                depth: int = 0
        ) -> Union[list[Bounce], bool]:
            nonlocal force_return, max_percent
            if prev_index_priority is None:
                prev_index_priority = [0, 1]
            if bounces_so_far is None:
                bounces_so_far = []
            if total_notes:
                gone_through_percent = (total_notes-len(notes)) * 100 // total_notes
                while gone_through_percent > max_percent:
                    max_percent += 1
                    if percent_update_callback(f"{max_percent}% done generating map"):
                        raise UserCancelsLoadingError()

            all_bounce_rects = [_bounc.get_collision_rect() for _bounc in bounces_so_far]
            if len(notes) == 0:
                return bounces_so_far

            path_segment_start = len(path)
            start_rect = square.rect.copy()
            while True:
                t += 1/FRAMERATE
                square.reg_move(False)
                path.append(square.rect)
                if t > notes[0]:
                    # No collision (we good)
                    bounce_indexes = prev_index_priority

                    # Randomly change direction every X% of the time
                    if random.random() * 100 < Config.direction_change_chance:
                        bounce_indexes = list(bounce_indexes.__reversed__())

                    # Add safe area
                    safe_areas.append(start_rect.union(square.rect))

                    for direction_to_bounce in bounce_indexes:
                        square.dir[direction_to_bounce] *= -1
                        bounces_so_far.append(Bounce(square.pos.copy(), square.dir.copy(), t, direction_to_bounce))

                        toextend = recurs(
                            square=square.copy(),
                            notes=notes[1:],
                            bounces_so_far=[_b.copy() for _b in bounces_so_far],
                            t=t,
                            prev_index_priority=bounce_indexes.copy(),
                            depth=depth+1
                        )

                        if toextend:
                            return toextend
                        else:
                            bounces_so_far = bounces_so_far[:-1]
                            square.dir[direction_to_bounce] *= -1

                            # Backtrack if necessary
                            if force_return:
                                force_return -= 1
                                while len(path) != path_segment_start:
                                    path.pop()
                                return False

                            continue
                    while len(path) != path_segment_start:
                        path.pop()
                    return False

                othercheck = False
                if len(bounces_so_far):
                    othercheck = bounces_so_far[-1].get_collision_rect().collidelist(path[:-10])+1

                if square.rect.collidelist(all_bounce_rects) != -1 or othercheck:
                    if depth > 200:
                        if random.random() < Config.backtrack_chance:
                            max_percent -= (Config.backtrack_amount * 100 // total_notes) + 1
                            force_return = Config.backtrack_amount

                    while len(path) != path_segment_start:
                        path.pop()
                    return False

        _start_notes = _start_notes[:Config.max_notes] if Config.max_notes is not None else _start_notes

        self.future_bounces = recurs(
            square=self.square.copy(),
            notes=remove_too_close_values(
                [_sn for _sn in _start_notes],
                threshold=Config.bounce_min_spacing
            )
        )

        if self.future_bounces is False:
            raise MapLoadingFailureError("The map failed to generate because of the recursion function. " +
                                         "If the MIDI has too many notes too close, it may not generate. " +
                                         "Maybe try changing the \"bounce min spacing\", \"square speed\", or \"change dir chance\" in the config.")

        if len(self.future_bounces) == 0:
            raise MapLoadingFailureError("Map safe area list is empty. Please report this issue.")

        percent_update_callback("Merging overlapping safe areas")

        # Merging overlapping safe areas more efficiently
        self.safe_areas = fix_overlap(safe_areas, percent_update_callback)

        self.rectangles = [_fb.get_collision_rect() for _fb in self.future_bounces]
        self.collision_times = [_fb.time for _fb in self.future_bounces]

        def gather_colors(num_colors=20):
            colors = []
            while len(colors) < num_colors:
                new_colors = color_hunt()
                rgb_colors = [tuple(int(hex_color[i:i+2], 16) for i in (1, 3, 5)) for hex_color in new_colors]
                colors.extend(rgb_colors)
            return colors[:num_colors]
        collected_colors = gather_colors()
        # Setting random colors for the generated pegs
        self.colors = [random.choice(collected_colors) for _ in self.future_bounces]

        # Generate stars in safe areas
        self.generate_stars()

        return self.safe_areas

class Game:
    def __init__(self):
        self.active = False
        self.notes = []
        self.camera = Camera()
        self.world = World()
        self.safe_areas: list[pygame.Rect] = []
        self.music_has_played = False
        self.offset_happened = False

    def start_song(self, screen: pygame.Surface):
        random.seed(Config.seed)

        # Load song and notes
        with open(Config.current_song.fp, 'rb') as f:
            notes = read_midi_file(file=f)
        notes = sorted([note for note in notes])
        self.notes = notes

        # Other settings
        self.world = World()
        self.music_has_played = False
        self.offset_happened = False
        self.camera.lock_type = CameraFollow(Config.camera_mode)
        screen.fill(get_colors()["background"])
        pygame.display.flip()

        def update_loading_screen(message: str):
            screen.fill(get_colors()["background"], pygame.Rect(0, 0, Config.SCREEN_WIDTH, Config.SCREEN_HEIGHT))
            font_size = int(Config.SCREEN_HEIGHT * 0.05)
            loading_text = get_font(font_size).render(message, True, get_colors()["hallway"])
            text_rect = loading_text.get_rect()
            text_rect.center = (Config.SCREEN_WIDTH // 2, Config.SCREEN_HEIGHT // 2)
            screen.blit(loading_text, text_rect)
            pygame.display.flip()


        try:
            self.safe_areas = self.world.gen_future_bounces(self.notes, update_loading_screen)
            # No need to fix overlap here, as it's handled in gen_future_bounces
        except UserCancelsLoadingError:
            return True
        except MapLoadingFailureError as e:
            return e.args[0] if len(e.args) else "Big error... can't load map :("

        # Display song title and creator with fade-in and fade-out effects
        self.display_song_info(screen)

        self.world.start_time = get_current_time()
        self.world.square.dir = [0, 0]
        if self.world.future_bounces:
            self.world.square.pos = self.world.future_bounces[0].square_pos
        else:
            self.world.square.pos = [Config.SCREEN_WIDTH / 2, Config.SCREEN_HEIGHT / 2]
        return None

    def display_song_info(self, screen):
        # Function to display song title and creator with fade-in and fade-out effects
        display_duration = 5000  # milliseconds
        fade_duration = 1000     # milliseconds for fade-in and fade-out
        start_time = pygame.time.get_ticks()
        elapsed = 0
        font_size = int(Config.SCREEN_HEIGHT * 0.10)
        font_size2 = int(Config.SCREEN_HEIGHT * 0.05)
        
        # Prepare text surfaces with per-pixel alpha
        
        title_surface = get_font(font_size).render(f"{SONG_NAME}", True, color4)
        creator_surface = get_font(font_size2).render(f"{SONG_CREATOR}", True, color4)
        
        # Enable alpha blending
        title_surface = title_surface.convert_alpha()
        creator_surface = creator_surface.convert_alpha()
        
        # Centering the text
        title_rect = title_surface.get_rect(center=(Config.SCREEN_WIDTH // 2, Config.SCREEN_HEIGHT // 2 - font_size))
        creator_rect = creator_surface.get_rect(center=(Config.SCREEN_WIDTH // 2, Config.SCREEN_HEIGHT // 2 + font_size2))
        
        while elapsed < display_duration:
            for event in pygame.event.get():
                if event.type == pygame.QUIT:
                    pygame.quit()
                    sys.exit()
                self.handle_event(event)
            
            elapsed = pygame.time.get_ticks() - start_time
            
            # Calculate alpha value
            if elapsed < fade_duration:
                # Fade-in phase
                alpha = int(255 * (elapsed / fade_duration))
            elif elapsed > display_duration - fade_duration:
                # Fade-out phase
                alpha = int(255 * ((display_duration - elapsed) / fade_duration))
            else:
                # Fully visible
                alpha = 255

            # Clamp alpha value
            alpha = max(0, min(255, alpha))
            
            # Set alpha
            title_surface.set_alpha(alpha)
            creator_surface.set_alpha(alpha)
            
            # Clear screen
            screen.fill(get_colors()["background"])
            
            # Draw text
            screen.blit(title_surface, title_rect)
            screen.blit(creator_surface, creator_rect)
            
            pygame.display.flip()
            pygame.time.delay(30)  # Slight delay to control the frame rate

    def draw(self, screen: pygame.Surface):
        if not self.active:
            return

        if not self.music_has_played:
            if not self.offset_happened:
                for bnc_change in self.world.future_bounces:
                    bnc_change.time += Config.start_playing_delay / 1000
            self.offset_happened = True
            if self.world.time-Config.music_offset/1000 > Config.start_playing_delay/1000:
                self.music_has_played = True
                song_load_before = get_current_time()
                pygame.mixer.music.play()
                for bnc_change in self.world.future_bounces:
                    bnc_change.time += (get_current_time()-song_load_before)/1000

        screen_rect = screen.get_rect()

        # Set world time
        self.world.update_time()

        # Move camera
        self.camera.attempt_movement()

        # Handle square bounces
        self.world.handle_bouncing(self.world.square)

        # Move square
        self.world.square.reg_move()

        # Square in center of camera if locked
        if self.camera.locked_on_square:
            self.camera.follow(self.world.square)

        # Bounce animation
        sqrect = self.camera.offset(self.world.square.rect)
        if (self.world.time - 0.25) + Config.music_offset / 1000 < self.world.square.last_bounce_time:
            lerp = abs((self.world.time - 0.25 + Config.music_offset / 1000) - self.world.square.last_bounce_time) * 5
            lerp = lerp ** 2  # Square it for better-looking interpolation
            if self.world.square.latest_bounce_direction:
                sqrect.inflate_ip((lerp * 5, -10 * lerp))
            else:
                sqrect.inflate_ip((-10 * lerp, lerp * 5))

        # Draw background (walls)
        screen.fill(get_colors()["background"])

        # Create a hallway surface
        hallway_surface = pygame.Surface((Config.SCREEN_WIDTH, Config.SCREEN_HEIGHT), pygame.SRCALPHA)

        # Safe areas
        for safe_area in self.world.safe_areas:
            offsetted = self.camera.offset(safe_area)
            if screen_rect.colliderect(offsetted):
                pygame.draw.rect(hallway_surface, get_colors()["hallway"], offsetted)

        # Obtain current time
        current_time = pygame.time.get_ticks() / 1000.0  # Time in seconds

        # Draw stars onto the hallway surface
        for star in self.world.stars:
            star.update(current_time)  # Update blinking effect
            screen_pos = star.get_screen_pos(self.camera)
            if 0 <= screen_pos[0] < Config.SCREEN_WIDTH and 0 <= screen_pos[1] < Config.SCREEN_HEIGHT:
                # Check if star's position is within the hallway (safe areas)
                if hallway_surface.get_at((int(screen_pos[0]), int(screen_pos[1]))).a != 0:
                    pygame.draw.circle(hallway_surface, star.color, (int(screen_pos[0]), int(screen_pos[1])), int(star.size))

        # Blit the hallway surface onto the main screen
        screen.blit(hallway_surface, (0, 0))

        # Draw pegs
        for i, bounce_rect in enumerate(self.world.rectangles):
            offsetted = self.camera.offset(bounce_rect)

            if offsetted.colliderect(screen_rect):
                if Config.do_color_bounce_pegs and self.world.collision_times[i] < (self.world.time * 1000 + Config.music_offset - Config.start_playing_delay)/1000:
                    pygame.draw.rect(screen, self.world.colors[i], offsetted)
                else:
                    pygame.draw.rect(screen, get_colors()["background"], offsetted)

        # Particles
        for particle in self.world.particles:
            pygame.draw.rect(screen, particle.color, self.camera.offset(particle.rect))
        for remove_particle in [particle for particle in self.world.particles if particle.age()]:
            self.world.particles.remove(remove_particle)

        # Particle trail in game
        if Config.particle_trail:
            # Tambahkan partikel secara periodik
            if not self.world.square.died:
                square_color = self.world.square.get_current_color()
                new = Particle(self.world.square.pos.copy(), [0, 0], True, color=(255, 255, 255))
                new.delta = [random.randint(-2, 2)/20, random.randint(5, 15)/20]
                self.world.particles.append(new)

        # Draw square
        self.world.square.draw(screen, sqrect)

    def handle_event(self, event: pygame.event.Event):
        if not self.active:
            return False

        if event.type == pygame.KEYDOWN:
            if event.key == pygame.K_ESCAPE:
                pygame.quit()
                sys.exit()
            if event.key == pygame.K_TAB:
                self.camera.locked_on_square = not self.camera.locked_on_square

class InvalidSongError(Exception):
    """The song is invalid somehow"""
    pass

def make_song_from_midi(fpath: str) -> Any:
    new_song = type('Song', (object,), {})()
    new_song.fp = fpath
    new_song.name = SONG_NAME  # Use the song name from the top
    new_song.creator = SONG_CREATOR  # Use the song creator from the top
    new_song.music_offset = 0
    return new_song

def main():
    pygame.init()
    clock = pygame.time.Clock()
    screen = pygame.display.set_mode((Config.SCREEN_WIDTH, Config.SCREEN_HEIGHT))
    pygame.display.set_caption("Midi Playground")
    try:
        pygame.display.set_icon(pygame.image.load(Config.assets).convert_alpha())
    except Exception as e:
        print(e)

    # Specify the song file to use
    selected_song_filepath = join(Config.song, SONG)
    if not isfile(selected_song_filepath):
        print(f"Song file {selected_song_filepath} not found.")
        return

    Config.current_song = make_song_from_midi(selected_song_filepath)

    # Load the music file
    try:
        pygame.mixer.music.load(Config.current_song.fp)
    except Exception as e:
        print(f"Error loading MIDI file as audio: {e}")
        print("Your platform may not support MIDI playback via pygame.mixer.music.")
        print("The game will run without audio.")
        # Uncomment the line below to exit if audio is essential
        # return
    pygame.mixer.music.set_volume(Config.volume / 100)

    # Initialize the game
    game = Game()

    # Start the game
    if msg := game.start_song(screen):
        if isinstance(msg, str):
            print(f"Error starting game: {msg}")
            return
    game.active = True

    running = True
    while running:
        # screen.fill(get_colors()["background"])  # Moved to the draw function
        for event in pygame.event.get():
            if event.type == pygame.QUIT:
                running = False
            game.handle_event(event)

        game.draw(screen)
        pygame.display.flip()
        clock.tick(FRAMERATE)
        Config.dt = clock.get_time() / 1000.0 if clock.get_time() > 0 else 0.016  # Avoid division by zero

    pygame.quit()

if __name__ == '__main__':
    main()

Certainly! Here's the updated code that implements the requested functionality:

```python
import pygame
import mido
import sys
import random
import requests
import colorsys
import os
from os.path import join, isfile
from time import time as get_current_time
from typing import Union, Optional, Any
from enum import Enum
from math import sin, pi
import math  # Ditambahkan untuk fungsi matematika

pygame.mixer.init()
pygame.init()
FRAMERATE = 60

# =========================
# Customizable Configuration
# =========================

# Screen Resolution
SCREEN_WIDTH = 1280     # Ganti sesuai keinginan Anda
SCREEN_HEIGHT = 720    # Ganti sesuai keinginan Anda

# File Selection
SONG = "dashie - ultraphunk.mid"  # Ganti dengan nama file MIDI Anda

# Song Information
SONG_NAME = 'SquareVibes'      # Set the song name here
SONG_CREATOR = 'SUBSCRIBE :D'         # Set the song creator here

# Other Customizable Settings
SQUARE_SPEED = 600             # Kecepatan kotak
SQUARE_SIZE = 50
BOUNCE_MIN_SPACING = 50        # Spasi minimum antar pantulan
DIRECTION_CHANGE = 30   # Peluang perubahan arah
PARTICLE_TRAIL = True          # Aktifkan atau nonaktifkan jejak partikel
PARTICLE_SPEED = 5
BOUNCE_PEG = True
# =========================

def color_hunt():
    def is_bright(hex_color):
        hex_color = hex_color.lstrip('#')
        rgb = tuple(int(hex_color[i:i+2], 16) for i in (0, 2, 4))
        luminance = 0.299 * rgb[0] + 0.587 * rgb[1] + 0.114 * rgb[2]
        r, g, b = [x / 255.0 for x in rgb]
        h, s, v = colorsys.rgb_to_hsv(r, g, b)
        return luminance >= 130 and s >= 0.3
    while True:
        url = 'https://colorhunt.co/php/feed.php'
        headers = {
            'Content-Type': 'application/x-www-form-urlencoded; charset=UTF-8'
        }
        data = {
            'step': 0,
            'sort': 'random',
            'tags': ''
        }
        response = requests.post(url, headers=headers, data=data)
        if response.status_code == 200:
            palettes = response.json()
            color_pairs = []
            for palette in palettes:
                code = palette['code']
                hex_colors = [f'#{code[i:i+6].upper()}' for i in range(0, len(code), 6)]
                if len(hex_colors) == 4 and all(is_bright(hex_color) for hex_color in hex_colors):
                    color_pairs.append(tuple(hex_colors))
            if color_pairs:
                selected_color_pair = random.choice(color_pairs)
                return selected_color_pair
        else:
            raise Exception(f"Failed to retrieve data. Status code: {response.status_code}")

selected_colors = color_hunt()
color1, color2, color3, color4 = selected_colors

class Config:
    # Constants
    SQUARE_SIZE = SQUARE_SIZE
    PARTICLE_SPEED = PARTICLE_SPEED

    # Colors
    color_themes = {
        "dark": {
            "hallway": pygame.Color('#451952'),
            "background": pygame.Color('#0F0F0F'),
            "square": [
                pygame.Color(color1),
                pygame.Color(color2),
                pygame.Color(color3),
                pygame.Color(color4)
            ]
        }
    }

    # Configuration
    script_dir = os.path.dirname(os.path.abspath(__file__))
    assets = os.path.join(script_dir, 'assets/icon.png')
    song = os.path.join(script_dir, 'songs')
    font = os.path.join(script_dir, 'assets/poppins-regular.ttf')
    SCREEN_WIDTH = SCREEN_WIDTH
    SCREEN_HEIGHT = SCREEN_HEIGHT
    theme: Optional[str] = "dark"
    seed: Optional[int] = None
    camera_mode: Optional[int] = 2
    start_playing_delay = 3000
    max_notes: Optional[int] = None
    bounce_min_spacing: Optional[float] = BOUNCE_MIN_SPACING
    square_speed: Optional[int] = SQUARE_SPEED
    volume: Optional[int] = 100
    music_offset: Optional[int] = 0
    direction_change_chance: Optional[int] = DIRECTION_CHANGE
    theatre_mode = True
    particle_trail = PARTICLE_TRAIL
    do_color_bounce_pegs = BOUNCE_PEG
    do_particles_on_bounce = True

    # Non-configurable settings
    backtrack_chance: Optional[float] = 0.02
    backtrack_amount: Optional[int] = 40
    square_swipe_anim_speed: Optional[int] = 4
    particle_amount = 20
    language = "english"

    # Other random stuff
    current_song = None
    dt = 0.01

def get_colors():
    return Config.color_themes.get(Config.theme, Config.color_themes["dark"])

def read_midi_file(file):
    midi_file = mido.MidiFile(file=file)

    notes = []
    current_time = 0

    for msg in midi_file:
        if msg.type == 'note_on' and msg.velocity != 0:
            timestamp = current_time + msg.time
            notes.append(round(timestamp*1000)/1000)
        current_time += msg.time
    return notes

def remove_too_close_values(lst: list[float], threshold=30) -> list[float]:
    """Assumes the list is sorted"""
    new = []
    before = None
    for _ in lst:
        if before is None:
            before = _
            new.append(_)
            continue
        if before+threshold/1000 > _:
            continue
        before = _
        new.append(_)
    return new

def fix_overlap(rects: list[pygame.Rect], callback=None):
    """
    Optimized function to merge overlapping rectangles efficiently.
    """
    if callback is None:
        callback = lambda _: None

    rects = rects.copy()
    # Sort rectangles based on x coordinate
    rects.sort(key=lambda r: (r.x, r.y))

    merged_rects = []
    for rect in rects:
        if not merged_rects:
            merged_rects.append(rect)
        else:
            last = merged_rects[-1]
            if last.colliderect(rect):
                merged_rect = last.union(rect)
                merged_rects[-1] = merged_rect
            else:
                merged_rects.append(rect)

    callback("Finished merging rectangles")

    return merged_rects

def get_font(size: int = 24) -> pygame.font.Font:
    font_path = Config.font
    return pygame.font.Font(font_path, size)

class MapLoadingFailureError(Exception):
    """The map fails to load (recurs function fails)"""
    pass

class UserCancelsLoadingError(Exception):
    """User cancels the loading screen"""
    pass

def interpolate_fn(n):
    """Interpolate sigmoidally from 0-1"""
    n = min(max(n, 0), 1)
    return sin(pi * (n - 0.5)) / 2 + 0.5

class Particle:
    SPEED_VARIATION = 4
    SIZE_MIN = 7
    SIZE_MAX = 14
    AGE_RATE = 20
    SLOW_DOWN_RATE = 1.2

    def __init__(self, pos: list[float], delta: list[float], invert_color: bool = False, color: Optional[tuple] = None):
        self.pos = pos.copy()
        self.size = random.randint(Particle.SIZE_MIN, Particle.SIZE_MAX)
        self.delta = delta.copy()
        self.delta[0] += random.randint(-Particle.SPEED_VARIATION, Particle.SPEED_VARIATION)/8
        self.delta[1] += random.randint(-Particle.SPEED_VARIATION, Particle.SPEED_VARIATION)/8
        if color is not None:
            self.color = color
        else:
            # Warna default jika warna tidak diberikan
            self.color = get_colors()["hallway"] if not invert_color else get_colors()["background"]

    def age(self):
        self.size -= Particle.AGE_RATE*Config.dt
        self.x += self.delta[0] * Config.PARTICLE_SPEED
        self.y += self.delta[1] * Config.PARTICLE_SPEED
        if Config.dt != 0:
            self.delta[0] /= (Particle.SLOW_DOWN_RATE+FRAMERATE) * Config.dt
            self.delta[1] /= (Particle.SLOW_DOWN_RATE+FRAMERATE) * Config.dt
        return self.size <= 0

    @property
    def x(self):
        return self.pos[0]

    @x.setter
    def x(self, val: float):
        self.pos[0] = val

    @property
    def y(self):
        return self.pos[1]

    @y.setter
    def y(self, val: float):
        self.pos[1] = val

    @property
    def rect(self):
        return pygame.Rect(self.x-self.size/2, self.y-self.size/2, *(2*[self.size]))

class Bounce:
    def __init__(self, sq_pos: list[float], sq_dir: list[int], time: float, bounce_dir: int):
        self.square_pos = sq_pos  # New square position
        self.square_dir = sq_dir  # New square direction
        self.bounce_dir = bounce_dir  # Bounce direction for squish effect; 0 or 1
        self.time = time  # Time during bounce

    def get_collision_rect(self):
        sx, sy = self.square_pos
        if self.bounce_dir == 0:
            # Bounce left or right wall
            if self.square_dir[0] == -1:
                # Right wall
                return pygame.Rect(
                    sx+Config.SQUARE_SIZE/2+1,
                    sy-10,
                    10,
                    20
                )
            elif self.square_dir[0] == 1:
                # Left wall
                return pygame.Rect(
                    sx-10-Config.SQUARE_SIZE/2-1,
                    sy-10,
                    10,
                    20
                )
        elif self.bounce_dir == 1:
            # Bounce top or bottom wall
            if self.square_dir[1] == -1:
                # Bottom wall
                return pygame.Rect(
                    sx-10,
                    sy+Config.SQUARE_SIZE/2+1,
                    20,
                    10
                )
            elif self.square_dir[1] == 1:
                # Top wall
                return pygame.Rect(
                    sx-10,
                    sy-10-Config.SQUARE_SIZE/2-1,
                    20,
                    10
                )

    def copy(self) -> "Bounce":
        return Bounce(self.square_pos.copy(), self.square_dir.copy(), self.time, self.bounce_dir)

    def __repr__(self):
        return f"<Bounce(sq_pos={self.square_pos}, sq_dir={self.square_dir}, time={self.time}, dir={self.bounce_dir})"

class Square:
    def __init__(self, x: float = 0, y: float = 0, dx: int = 1, dy: int = 1):
        self.pos: list[float] = [x, y]
        self.dir: list[int] = [dx, dy]
        self.last_bounce_time = -100
        self.latest_bounce_direction = 0  # 0 = horiz, 1 = vert
        self.past_colors = []
        self.died = False

    def register_past_color(self, col: tuple[int, int, int]):
        for _ in range(max(Config.square_swipe_anim_speed, 1)):
            self.past_colors.insert(0, col)
        while len(self.past_colors) > Config.SQUARE_SIZE * 4 / 5:
            self.past_colors.pop()

    def get_surface(self, size: tuple[int, int]):
        ss = int(Config.SQUARE_SIZE * 4 / 5)
        surf = pygame.Surface((ss, ss))
        for index, col in enumerate(self.past_colors):
            y = index if self.dir_y != 1 else ss - 1 - index
            pygame.draw.line(surf, col, (0, y), (ss, y))
        return pygame.transform.scale(surf, size)

    def copy(self) -> "Square":
        new = Square(*self.pos, *self.dir)
        new.last_bounce_time = self.last_bounce_time
        new.latest_bounce_direction = self.latest_bounce_direction
        return new

    def get_current_color(self):
        square_color_index = round((self.dir_x + 1) / 2 + self.dir_y + 1)
        return get_colors()["square"][square_color_index % len(get_colors()["square"])]
    
    @property
    def x(self):
        return self.pos[0]

    @property
    def y(self):
        return self.pos[1]

    def draw(self, screen: pygame.Surface, sqrect: pygame.Rect):
        if self.died:
            return
        square_color_index = round((self.dir_x + 1) / 2 + self.dir_y + 1)
        self.register_past_color(get_colors()["square"][square_color_index % len(get_colors()["square"])])

        pygame.draw.rect(screen, (0, 0, 0), sqrect)
        sq_surf = self.get_surface(
            tuple(sqrect.inflate(-int(Config.SQUARE_SIZE / 5), -int(Config.SQUARE_SIZE / 5))[2:]))
        screen.blit(sq_surf, sq_surf.get_rect(center=sqrect.center))

    @x.setter
    def x(self, val: int):
        self.pos[0] = val

    @y.setter
    def y(self, val: int):
        self.pos[1] = val

    @property
    def dir_x(self):
        return self.dir[0]

    @property
    def dir_y(self):
        return self.dir[1]

    @property
    def rect(self):
        return pygame.Rect(self.x - Config.SQUARE_SIZE / 2, self.y - Config.SQUARE_SIZE / 2,
                           *([Config.SQUARE_SIZE] * 2))

    def obey_bounce(self, bounce: Bounce):
        # Planned bounces
        self.pos = bounce.square_pos.copy()
        self.dir = bounce.square_dir.copy()
        self.latest_bounce_direction = bounce.bounce_dir
        self.last_bounce_time = bounce.time
        return

    def reg_move(self, use_dt: bool = True):
        self.x += self.dir_x * Config.square_speed * (Config.dt if use_dt else 1 / FRAMERATE)
        self.y += self.dir_y * Config.square_speed * (Config.dt if use_dt else 1 / FRAMERATE)

class Camera:
    def __init__(self, x: int = 0, y: int = 0):
        self.x = x
        self.y = y
        self.locked_on_square = True
        self.lock_type: CameraFollow = CameraFollow(Config.camera_mode)

    def attempt_movement(self):
        if not self.locked_on_square:
            keys = pygame.key.get_pressed()
            shift_modifier = (keys[pygame.K_LSHIFT] | keys[pygame.K_RSHIFT]) + 1
            self.x += (keys[pygame.K_d] - keys[pygame.K_a]) * 500 * shift_modifier / FRAMERATE
            self.y += (keys[pygame.K_s] - keys[pygame.K_w]) * 500 * shift_modifier / FRAMERATE

    @property
    def pos(self):
        return self.x, self.y

    @pos.setter
    def pos(self, val: Union[tuple[int, int], list[int]]):
        self.x, self.y = val

    def offset(self, pos_or_rect: Union[pygame.Rect, tuple[int, int]]) -> Union[pygame.Rect, list[int]]:
        if isinstance(pos_or_rect, pygame.Rect):
            return pos_or_rect.move(-self.x, -self.y)
        else:
            return [pos_or_rect[0]-self.x, pos_or_rect[1]-self.y]

    def apply_parallax(self, pos: tuple[float, float], depth: float) -> list[float]:
        # Parallax factor: nearer stars move faster than distant ones
        parallax_factor = 0.2 + depth * 0.8  # From 0.2 to 1.0
        screen_x = (pos[0] - self.x) * parallax_factor
        screen_y = (pos[1] - self.y) * parallax_factor
        return [screen_x, screen_y]

    def follow(self, square: Square):

        # Square in center
        if self.lock_type == CameraFollow.Center:
            self.pos = [square.x - Config.SCREEN_WIDTH / 2, square.y - Config.SCREEN_HEIGHT / 2]

        # Smooth camera
        if self.lock_type == CameraFollow.Smoothed:
            easing_rate = 3
            self.x = (square.x - Config.SCREEN_WIDTH / 2) * easing_rate * Config.dt + self.x - easing_rate * self.x * Config.dt
            self.y = (square.y - Config.SCREEN_HEIGHT / 2) * easing_rate * Config.dt + self.y - easing_rate * self.y * Config.dt

class CameraFollow(Enum):
    Center = 0  # Center the square
    Smoothed = 2  # Smoothed camera

class Star:
    def __init__(self, pos: tuple[float, float], depth: float):
        self.initial_pos = list(pos)
        self.depth = depth  # between 0 (far) and 1 (near)
        size_min = 0.5
        size_max = 2
        self.size = size_min + (1 - self.depth) * (size_max - size_min)
        self.phase = random.uniform(0, 2 * math.pi)  # Ditambahkan untuk fase acak
        self.brightness = 0  # Akan diperbarui dalam metode update
        self.color = (255, 255, 255)  # Warna default, akan diperbarui

    def update(self, time):
        # Adjust brightness over time to create blinking effect
        blink_speed = 10  # can adjust to get desired speed
        brightness_variation = (math.sin(blink_speed * time + self.phase) + 1) / 2  # Normalize between 0 and 1
        min_brightness = 100
        max_brightness = 255
        self.brightness = min_brightness + brightness_variation * (max_brightness - min_brightness)
        self.color = (int(self.brightness),) * 3  # Update color based on brightness

    def get_screen_pos(self, camera: Camera):
        parallax_factor = 0.2 + self.depth * 0.8  # from 0.2 to 1.0
        screen_x = (self.initial_pos[0] - camera.x) * parallax_factor
        screen_y = (self.initial_pos[1] - camera.y) * parallax_factor
        return [screen_x, screen_y]

class World:
    """It's a cruel world out there"""

    def __init__(self):
        self.future_bounces: list[Bounce] = []
        self.past_bounces: list[Bounce] = []
        self.start_time = 0
        self.time = 0
        self.rectangles: list[pygame.Rect] = []
        self.collision_times: list[float] = []
        self.particles: list[Particle] = []
        self.stars: list[Star] = []
        self.timestamps = []
        self.square = Square()
        self.colors = []
        self.safe_areas: list[pygame.Rect] = []

    def update_time(self) -> None:
        self.time = get_current_time() - self.start_time

    def get_next_bounce(self) -> Bounce:
        """Also pops the bounce from the future_bounces list"""
        self.past_bounces.append(self.future_bounces.pop(0))
        return self.past_bounces[-1]

    def add_bounce_particles(self, sp: list[float], sd: list[float], color: tuple):
        for _ in range(Config.particle_amount):
            new = Particle([sp[0] + random.randint(-10, 10), sp[1] + random.randint(-10, 10)], sd, color=color)
            self.particles.append(new)

    def handle_bouncing(self, square: Square):
        if len(self.future_bounces):
            if (self.time * 1000 + Config.music_offset)/1000 > self.future_bounces[0].time:
                current_bounce = self.get_next_bounce()
                before = square.dir.copy()
                square.obey_bounce(current_bounce)
                changed = square.dir.copy()
                for _ in range(2):
                    if before[_] == changed[_]:
                        changed[_] = 0
                    else:
                        changed[_] = -changed[_]
                if Config.do_particles_on_bounce:
                    square_color = square.get_current_color()
                    self.add_bounce_particles(square.pos, changed, color=square_color)

                # Stop square at end
                if len(self.future_bounces) == 0:
                    square.dir = [0, 0]
                    square.pos = current_bounce.square_pos

    def generate_stars(self):
        self.stars = []
        # Menghitung total area aman
        total_safe_area = sum(area.width * area.height for area in self.safe_areas)
        star_density = 0.0001  # Sesuaikan sesuai kebutuhan
        total_num_stars = int(total_safe_area * star_density)
        min_distance_squared = (20) ** 2  # Menghindari clustering

        # Mendapatkan bounding rectangle dari semua area aman
        min_x = min(area.left for area in self.safe_areas)
        max_x = max(area.right for area in self.safe_areas)
        min_y = min(area.top for area in self.safe_areas)
        max_y = max(area.bottom for area in self.safe_areas)
        bounding_rect = pygame.Rect(min_x, min_y, max_x - min_x, max_y - min_y)

        stars = []
        attempts = 0
        max_attempts = total_num_stars * 10

        while len(stars) < total_num_stars and attempts < max_attempts:
            x = random.uniform(bounding_rect.left, bounding_rect.right)
            y = random.uniform(bounding_rect.top, bounding_rect.bottom)
            point = (x, y)

            # Memastikan titik berada dalam area aman
            inside_safe_area = any(area.collidepoint(point) for area in self.safe_areas)

            if inside_safe_area:
                # Memastikan jarak minimum antar bintang
                if all((star.initial_pos[0] - x) ** 2 + (star.initial_pos[1] - y) ** 2 >= min_distance_squared for star in stars):
                    depth = random.uniform(0, 1)
                    star = Star((x, y), depth)
                    stars.append(star)
            attempts += 1

        self.stars = stars

    def gen_future_bounces(self, _start_notes: list[float], percent_update_callback):
        """Recursive function with optimized overlap checking"""
        total_notes = len(_start_notes)
        max_percent = 0
        path = []
        safe_areas = []
        force_return = 0

        def recurs(
                square: Square,
                notes: list[float],
                bounces_so_far: list[Bounce] = None,
                prev_index_priority=None,
                t: float = 0,
                depth: int = 0
        ) -> Union[list[Bounce], bool]:
            nonlocal force_return, max_percent
            if prev_index_priority is None:
                prev_index_priority = [0, 1]
            if bounces_so_far is None:
                bounces_so_far = []
            if total_notes:
                gone_through_percent = (total_notes-len(notes)) * 100 // total_notes
                while gone_through_percent > max_percent:
                    max_percent += 1
                    if percent_update_callback(f"{max_percent}% done generating map"):
                        raise UserCancelsLoadingError()

            all_bounce_rects = [_bounc.get_collision_rect() for _bounc in bounces_so_far]
            if len(notes) == 0:
                return bounces_so_far

            path_segment_start = len(path)
            start_rect = square.rect.copy()
            while True:
                t += 1/FRAMERATE
                square.reg_move(False)
                path.append(square.rect)
                if t > notes[0]:
                    # No collision (we good)
                    bounce_indexes = prev_index_priority

                    # Randomly change direction every X% of the time
                    if random.random() * 100 < Config.direction_change_chance:
                        bounce_indexes = list(bounce_indexes.__reversed__())

                    # Add safe area
                    safe_areas.append(start_rect.union(square.rect))

                    for direction_to_bounce in bounce_indexes:
                        square.dir[direction_to_bounce] *= -1
                        bounces_so_far.append(Bounce(square.pos.copy(), square.dir.copy(), t, direction_to_bounce))

                        toextend = recurs(
                            square=square.copy(),
                            notes=notes[1:],
                            bounces_so_far=[_b.copy() for _b in bounces_so_far],
                            t=t,
                            prev_index_priority=bounce_indexes.copy(),
                            depth=depth+1
                        )

                        if toextend:
                            return toextend
                        else:
                            bounces_so_far = bounces_so_far[:-1]
                            square.dir[direction_to_bounce] *= -1

                            # Backtrack if necessary
                            if force_return:
                                force_return -= 1
                                while len(path) != path_segment_start:
                                    path.pop()
                                return False

                            continue
                    while len(path) != path_segment_start:
                        path.pop()
                    return False

                othercheck = False
                if len(bounces_so_far):
                    othercheck = bounces_so_far[-1].get_collision_rect().collidelist(path[:-10])+1

                if square.rect.collidelist(all_bounce_rects) != -1 or othercheck:
                    if depth > 200:
                        if random.random() < Config.backtrack_chance:
                            max_percent -= (Config.backtrack_amount * 100 // total_notes) + 1
                            force_return = Config.backtrack_amount

                    while len(path) != path_segment_start:
                        path.pop()
                    return False

        _start_notes = _start_notes[:Config.max_notes] if Config.max_notes is not None else _start_notes

        self.future_bounces = recurs(
            square=self.square.copy(),
            notes=remove_too_close_values(
                [_sn for _sn in _start_notes],
                threshold=Config.bounce_min_spacing
            )
        )

        if self.future_bounces is False:
            raise MapLoadingFailureError("The map failed to generate because of the recursion function. " +
                                         "If the MIDI has too many notes too close, it may not generate. " +
                                         "Maybe try changing the \"bounce min spacing\", \"square speed\", or \"change dir chance\" in the config.")

        if len(self.future_bounces) == 0:
            raise MapLoadingFailureError("Map safe area list is empty. Please report this issue.")

        percent_update_callback("Merging overlapping safe areas")

        # Merging overlapping safe areas more efficiently
        self.safe_areas = fix_overlap(safe_areas, percent_update_callback)

        self.rectangles = [_fb.get_collision_rect() for _fb in self.future_bounces]
        self.collision_times = [_fb.time for _fb in self.future_bounces]

        def gather_colors(num_colors=20):
            colors = []
            while len(colors) < num_colors:
                new_colors = color_hunt()
                rgb_colors = [tuple(int(hex_color[i:i+2], 16) for i in (1, 3, 5)) for hex_color in new_colors]
                colors.extend(rgb_colors)
            return colors[:num_colors]
        collected_colors = gather_colors()
        # Setting random colors for the generated pegs
        self.colors = [random.choice(collected_colors) for _ in self.future_bounces]

        # Generate stars in safe areas
        self.generate_stars()

        return self.safe_areas

class Game:
    def __init__(self):
        self.active = False
        self.notes = []
        self.camera = Camera()
        self.world = World()
        self.safe_areas: list[pygame.Rect] = []
        self.music_has_played = False
        self.offset_happened = False

    def start_song(self, screen: pygame.Surface):
        random.seed(Config.seed)

        # Load song and notes
        with open(Config.current_song.fp, 'rb') as f:
            notes = read_midi_file(file=f)
        notes = sorted([note for note in notes])
        self.notes = notes

        # Other settings
        self.world = World()
        self.music_has_played = False
        self.offset_happened = False
        self.camera.lock_type = CameraFollow(Config.camera_mode)
        screen.fill(get_colors()["background"])
        pygame.display.flip()

        def update_loading_screen(message: str):
            screen.fill(get_colors()["background"], pygame.Rect(0, 0, Config.SCREEN_WIDTH, Config.SCREEN_HEIGHT))
            font_size = int(Config.SCREEN_HEIGHT * 0.05)
            loading_text = get_font(font_size).render(message, True, get_colors()["hallway"])
            text_rect = loading_text.get_rect()
            text_rect.center = (Config.SCREEN_WIDTH // 2, Config.SCREEN_HEIGHT // 2)
            screen.blit(loading_text, text_rect)
            pygame.display.flip()


        try:
            self.safe_areas = self.world.gen_future_bounces(self.notes, update_loading_screen)
            # No need to fix overlap here, as it's handled in gen_future_bounces
        except UserCancelsLoadingError:
            return True
        except MapLoadingFailureError as e:
            return e.args[0] if len(e.args) else "Big error... can't load map :("

        # Display song title and creator with fade-in and fade-out effects
        self.display_song_info(screen)

        self.world.start_time = get_current_time()
        self.world.square.dir = [0, 0]
        if self.world.future_bounces:
            self.world.square.pos = self.world.future_bounces[0].square_pos
        else:
            self.world.square.pos = [Config.SCREEN_WIDTH / 2, Config.SCREEN_HEIGHT / 2]
        return None

    def display_song_info(self, screen):
        # Function to display song title and creator with fade-in and fade-out effects
        display_duration = 5000  # milliseconds
        fade_duration = 1000     # milliseconds for fade-in and fade-out
        start_time = pygame.time.get_ticks()
        elapsed = 0
        font_size = int(Config.SCREEN_HEIGHT * 0.10)
        font_size2 = int(Config.SCREEN_HEIGHT * 0.05)
        
        # Prepare text surfaces with per-pixel alpha
        
        title_surface = get_font(font_size).render(f"{SONG_NAME}", True, color4)
        creator_surface = get_font(font_size2).render(f"{SONG_CREATOR}", True, color4)
        
        # Enable alpha blending
        title_surface = title_surface.convert_alpha()
        creator_surface = creator_surface.convert_alpha()
        
        # Centering the text
        title_rect = title_surface.get_rect(center=(Config.SCREEN_WIDTH // 2, Config.SCREEN_HEIGHT // 2 - font_size))
        creator_rect = creator_surface.get_rect(center=(Config.SCREEN_WIDTH // 2, Config.SCREEN_HEIGHT // 2 + font_size2))
        
        while elapsed < display_duration:
            for event in pygame.event.get():
                if event.type == pygame.QUIT:
                    pygame.quit()
                    sys.exit()
                self.handle_event(event)
            
            elapsed = pygame.time.get_ticks() - start_time
            
            # Calculate alpha value
            if elapsed < fade_duration:
                # Fade-in phase
                alpha = int(255 * (elapsed / fade_duration))
            elif elapsed > display_duration - fade_duration:
                # Fade-out phase
                alpha = int(255 * ((display_duration - elapsed) / fade_duration))
            else:
                # Fully visible
                alpha = 255

            # Clamp alpha value
            alpha = max(0, min(255, alpha))
            
            # Set alpha
            title_surface.set_alpha(alpha)
            creator_surface.set_alpha(alpha)
            
            # Clear screen
            screen.fill(get_colors()["background"])
            
            # Draw text
            screen.blit(title_surface, title_rect)
            screen.blit(creator_surface, creator_rect)
            
            pygame.display.flip()
            pygame.time.delay(30)  # Slight delay to control the frame rate

    def draw(self, screen: pygame.Surface):
        if not self.active:
            return

        if not self.music_has_played:
            if not self.offset_happened:
                for bnc_change in self.world.future_bounces:
                    bnc_change.time += Config.start_playing_delay / 1000
            self.offset_happened = True
            if self.world.time-Config.music_offset/1000 > Config.start_playing_delay/1000:
                self.music_has_played = True
                song_load_before = get_current_time()
                pygame.mixer.music.play()
                for bnc_change in self.world.future_bounces:
                    bnc_change.time += (get_current_time()-song_load_before)/1000

        screen_rect = screen.get_rect()

        # Set world time
        self.world.update_time()

        # Move camera
        self.camera.attempt_movement()

        # Handle square bounces
        self.world.handle_bouncing(self.world.square)

        # Move square
        self.world.square.reg_move()

        # Square in center of camera if locked
        if self.camera.locked_on_square:
            self.camera.follow(self.world.square)

        # Bounce animation
        sqrect = self.camera.offset(self.world.square.rect)
        if (self.world.time - 0.25) + Config.music_offset / 1000 < self.world.square.last_bounce_time:
            lerp = abs((self.world.time - 0.25 + Config.music_offset / 1000) - self.world.square.last_bounce_time) * 5
            lerp = lerp ** 2  # Square it for better-looking interpolation
            if self.world.square.latest_bounce_direction:
                sqrect.inflate_ip((lerp * 5, -10 * lerp))
            else:
                sqrect.inflate_ip((-10 * lerp, lerp * 5))

        # Draw background (walls)
        screen.fill(get_colors()["background"])

        # Create a hallway surface
        hallway_surface = pygame.Surface((Config.SCREEN_WIDTH, Config.SCREEN_HEIGHT), pygame.SRCALPHA)

        # Safe areas
        for safe_area in self.world.safe_areas:
            offsetted = self.camera.offset(safe_area)
            if screen_rect.colliderect(offsetted):
                pygame.draw.rect(hallway_surface, get_colors()["hallway"], offsetted)

        # Obtain current time
        current_time = pygame.time.get_ticks() / 1000.0  # Time in seconds

        # Draw stars onto the hallway surface
        for star in self.world.stars:
            star.update(current_time)  # Update blinking effect
            screen_pos = star.get_screen_pos(self.camera)
            if 0 <= screen_pos[0] < Config.SCREEN_WIDTH and 0 <= screen_pos[1] < Config.SCREEN_HEIGHT:
                # Check if star's position is within the hallway (safe areas)
                if hallway_surface.get_at((int(screen_pos[0]), int(screen_pos[1]))).a != 0:
                    pygame.draw.circle(hallway_surface, star.color, (int(screen_pos[0]), int(screen_pos[1])), int(star.size))

        # Blit the hallway surface onto the main screen
        screen.blit(hallway_surface, (0, 0))

        # Draw pegs
        for i, bounce_rect in enumerate(self.world.rectangles):
            offsetted = self.camera.offset(bounce_rect)

            if offsetted.collidescreen_rect):
                if Config.do_color_bounce_pegs and self.world.collision_times[i] < (self.world.time * 1000 + Config.music_offset - Config.start_playing_delay)/1000:
                    pygame.draw.rect(screen, self.world.colors[i], offsetted)
                else:
                    pygame.draw.rect(screen, get_colors()["background"], offsetted)

        # Particles
        for particle in self.world.particles:
            pygame.draw.rect(screen, particle.color, self.camera.offset(particle.rect))
        for remove_particle in [particle for particle in self.world.particles if particle.age()]:
            self.world.particles.remove(remove_particle)

        # Particle trail in game
        if Config.particle_trail:
            # Tambahkan partikel secara periodik
            if not self.world.square.died:
                square_color = self.world.square.get_current_color()
                new = Particle(self.world.square.pos.copy(), [0, 0], True, color=(255, 255, 255))
                new.delta = [random.randint(-2, 2)/20, random.randint(5, 15)/20]
                self.world.particles.append(new)

        # Draw square
        self.world.square.draw(screen, sqrect)

    def handle_event(self, event: pygame.event.Event):
        if not self.active:
            return False

        if event.type == pygame.KEYDOWN:
            if event.key == pygame.K_ESCAPE:
                pygame.quit()
                sys.exit()
            if event.key == pygame.K_TAB:
                self.camera.locked_on_square = not self.camera.locked_on_square

class InvalidSongError(Exception):
    """The song is invalid somehow"""
    pass

def make_song_from_midi(fpath: str, audio_fp: Optional[str] = None) -> Any:
    new_song = type('Song', (object,), {})()
    new_song.fp = fpath    # MIDI file path
    new_song.audio_fp = audio_fp if audio_fp else fpath    # Audio file path, default to fpath
    new_song.name = SONG_NAME  # Use the song name from the top
    new_song.creator = SONG_CREATOR  # Use the song creator from the top
    new_song.music_offset = 0
    return new_song

def main():
    pygame.init()
    clock = pygame.time.Clock()
    screen = pygame.display.set_mode((Config.SCREEN_WIDTH, Config.SCREEN_HEIGHT))
    pygame.display.set_caption("Midi Playground")
    try:
        pygame.display.set_icon(pygame.image.load(Config.assets).convert_alpha())
    except Exception as e:
        print(e)

    # Specify the song file to use
    selected_song_filepath = join(Config.song, SONG)
    if not isfile(selected_song_filepath):
        print(f"Song file {selected_song_filepath} not found.")
        return

    # Get the base file name without extension
    base_name = os.path.splitext(SONG)[0]

    # Check for corresponding MP3 file
    mp3_song_name = base_name + '.mp3'
    mp3_filepath = join(Config.song, mp3_song_name)

    if isfile(mp3_filepath):
        audio_fp = mp3_filepath
    else:
        audio_fp = selected_song_filepath

    Config.current_song = make_song_from_midi(selected_song_filepath, audio_fp=audio_fp)

    # Load the music file
    try:
        pygame.mixer.music.load(Config.current_song.audio_fp)
    except Exception as e:
        print(f"Error loading audio file: {e}")
        print("The game will run without audio.")
        # Uncomment the line below to exit if audio is essential
        # return
    pygame.mixer.music.set_volume(Config.volume / 100)

    # Initialize the game
    game = Game()

    # Start the game
    if msg := game.start_song(screen):
        if isinstance(msg, str):
            print(f"Error starting game: {msg}")
            return
    game.active = True

    running = True
    while running:
        # screen.fill(get_colors()["background"])  # Moved to the draw function
        for event in pygame.event.get():
            if event.type == pygame.QUIT:
                running = False
            game.handle_event(event)

        game.draw(screen)
        pygame.display.flip()
        clock.tick(FRAMERATE)
        Config.dt = clock.get_time() / 1000.0 if clock.get_time() > 0 else 0.016  # Avoid division by zero

    pygame.quit()

if __name__ == '__main__':
    main()
```

**Explanation:**

1. **Checking for MP3 File:**

   In the `main()` function, after determining the `selected_song_filepath`, we extract the base name of the MIDI file using `os.path.splitext(SONG)[0]`. This gives us the filename without the extension.

   ```python
   base_name = os.path.splitext(SONG)[0]
   ```

   We then construct the MP3 filename by appending '.mp3' to the base name and check if it exists:

   ```python
   mp3_song_name = base_name + '.mp3'
   mp3_filepath = join(Config.song, mp3_song_name)

   if isfile(mp3_filepath):
       audio_fp = mp3_filepath
   else:
       audio_fp = selected_song_filepath
   ```

2. **Updating the `make_song_from_midi` Function:**

   The `make_song_from_midi` function has been updated to accept an optional `audio_fp` parameter, which represents the path to the audio file to be used for playback.

   ```python
   def make_song_from_midi(fpath: str, audio_fp: Optional[str] = None) -> Any:
       new_song = type('Song', (object,), {})()
       new_song.fp = fpath    # MIDI file path
       new_song.audio_fp = audio_fp if audio_fp else fpath    # Audio file path, default to fpath
       new_song.name = SONG_NAME  # Use the song name from the top
       new_song.creator = SONG_CREATOR  # Use the song creator from the top
       new_song.music_offset = 0
       return new_song
   ```

3. **Loading the Correct Audio File:**

   In the `main()` function, we instantiate `Config.current_song` with both the MIDI file path and the audio file path (which could be the MP3 or the MIDI file if no MP3 exists).

   ```python
   Config.current_song = make_song_from_midi(selected_song_filepath, audio_fp=audio_fp)
   ```

   When loading the music for playback, we use `Config.current_song.audio_fp`, which ensures that the MP3 file is used if it exists.

   ```python
   try:
       pygame.mixer.music.load(Config.current_song.audio_fp)
   except Exception as e:
       print(f"Error loading audio file: {e}")
       print("The game will run without audio.")
   ```

4. **Using MIDI for Game Mechanics (Bounce):**

   The game mechanics, such as bounce calculations, continue to use the MIDI file. The MIDI file is read to extract note information, which is used for game logic.

   ```python
   # Load song and notes
   with open(Config.current_song.fp, 'rb') as f:
       notes = read_midi_file(file=f)
   ```

5. **Ensuring Correct Exception Handling:**

   The exception messages have been updated to reflect that the audio file could be either an MP3 or MIDI file.

6. **Overall Structure:**

   The rest of the code remains the same, ensuring that gameplay is unaffected. The only difference is the check for an MP3 file and using it for audio playback if available.

**Now, the game will:**

- Use the MIDI file for reading notes and game mechanics.
- Check for an MP3 file with the same name as the MIDI file.
  - If it exists, it will use the MP3 file for audio playback.
  - If it doesn't exist, it will use the MIDI file for audio playback.
- Handle any exceptions appropriately, allowing the game to run even if the audio file cannot be loaded.

Consider an infinite-dimensional Hilbert space H and a countably infinite set of Turing machines {T₁, T₂, T₃, ...}. Each Turing machine Tᵢ is designed to output a real number rᵢ in the interval [0, 1] after a finite number of steps.

Define a function f: ℕ → [0, 1] such that f(i) = rᵢ, where rᵢ is the output of Turing machine Tᵢ.

Now, consider the following statements:

1. There exists a real number x in [0, 1] that is not in the range of f.
2. The function f is computable.
3. The set of all computable real numbers is countable.

The paradox arises when we attempt to construct a Turing machine T* that computes a real number not in the range of f, using a diagonalization argument similar to Cantor's proof of the uncountability of real numbers.

Problem: Resolve the apparent contradiction between statements 1, 2, and 3, considering the following additional constraints:

a) Incorporate Gödel's Incompleteness Theorems to analyze the limitations of formal systems in describing T*.

b) Apply the Axiom of Choice to construct a non-measurable subset of [0, 1] related to the range of f.

c) Utilize concepts from algorithmic information theory to define a notion of "algorithmic randomness" for the outputs of the Turing machines.

d) Explore the connections between this paradox and the Halting Problem, considering oracle Turing machines with access to the Halting oracle.

e) Investigate the cardinality of the set of all possible Turing machines and its relationship to Beth numbers and the Continuum Hypothesis.

f) Analyze the problem in the context of different models of set theory (e.g., ZFC with and without the Continuum Hypothesis).

g) Examine the implications of this paradox on the foundations of mathematics and the nature of infinity, considering both constructive and non-constructive approaches.

h) Develop a formal system that can express this paradox without falling into inconsistency, possibly using paraconsistent logic or other non-classical logical frameworks.

i) Investigate the relationships between this paradox and other fundamental paradoxes in mathematics and logic, such as Russell's Paradox and Richard's Paradox.

j) Consider the implications of this paradox on the P vs NP problem and the computational complexity of determining whether a given real number is in the range of f.

To resolve the apparent contradiction between statements 1, 2, and 3, we need to carefully analyze the nature of computable real numbers, the limitations of Turing machines, and the implications of classical results in logic and computation.

**Understanding the Paradox:**

- **Statement 1:** There exists a real number \( x \) in \([0, 1]\) that is not in the range of \( f \).
  
  This is true because \( f \) maps from the natural numbers \( \mathbb{N} \) to the real interval \([0, 1]\), and since \( \mathbb{N} \) is countable and \([0, 1]\) is uncountable, there must be real numbers not in the range of \( f \).

- **Statement 2:** The function \( f \) is computable.

  Here, \( f \) is defined by \( f(i) = r_i \), where \( r_i \) is the computable output of Turing machine \( T_i \). Since each \( T_i \) halts after a finite number of steps and outputs \( r_i \), \( f \) is computable in the sense that for each input \( i \), we can compute \( f(i) \).

- **Statement 3:** The set of all computable real numbers is countable.

  This is also true, as there are countably many Turing machines (since their descriptions can be encoded as finite strings over a finite alphabet), hence countably many computable real numbers.

**The Apparent Contradiction:**

The paradox arises when we attempt to construct a Turing machine \( T^* \) that computes a real number \( x \) not in the range of \( f \), using a diagonalization argument similar to Cantor's proof. If \( T^* \) exists, \( x \) would be computable, and thus should be in the range of \( f \), leading to a contradiction.

**Resolution:**

The key to resolving the paradox is recognizing the non-computability of the diagonalization process over computable real numbers. Here's how:

1. **Diagonalization over Computable Reals is Non-Computable:**

   - **Cantor's Diagonalization:** Cantor's argument shows that the real numbers are uncountable by constructing a real number that differs from each number in a given list at some decimal place.
   - **Non-Effective Procedure:** While Cantor's argument guarantees the existence of such a number, it doesn't provide a method to compute it, especially when dealing with computable reals.

2. **Limitations of Turing Machines:**

   - **Halting Problem:** We cannot, in general, decide whether a given Turing machine halts or determine its exact output, due to the undecidability of the Halting Problem.
   - **Non-Computable Functions:** The function that would map each \( i \) to the \( i \)-th digit needed to construct \( x \) is not computable.

3. **Constructing \( x \) is Non-Computable:**

   - **Diagonal Number is Non-Computable:** The real number \( x \) constructed via diagonalization over computable reals is itself non-computable.
   - **No Turing Machine \( T^* \):** Since \( x \) is non-computable, there is no Turing machine \( T^* \) that can compute it.

4. **Consistency with Statements 1–3:**

   - **Statement 1 Holds:** There exists \( x \notin \text{range}(f) \), but \( x \) is non-computable.
   - **Statement 2 Holds:** \( f \) is computable, as it maps each natural number \( i \) to the computable real \( r_i \).
   - **Statement 3 Holds:** The set of computable reals is countable, and \( x \) being non-computable isn't part of this set.

**Incorporating the Constraints:**

Let's address each of the additional constraints (a)–(j) to deepen our understanding:

**a) Gödel's Incompleteness Theorems:**

Gödel's theorems highlight the inherent limitations of formal systems in capturing all truths about natural numbers. Similarly, while we can define the concept of a computable real, we cannot have a complete, effective list of all computable reals that allows us to compute a diagonal real number not on the list.

**b) Axiom of Choice and Non-Measurable Sets:**

The Axiom of Choice (AC) allows for the construction of sets without explicitly defining their elements. In this context, AC isn't directly needed, but the concept of non-measurable sets relates to the idea that certain subsets of \([0, 1]\) (like the set of non-computable reals) cannot be "measured" or fully described within our system.

**c) Algorithmic Information Theory and Randomness:**

Algorithmic randomness refers to sequences (or reals) that lack any computable pattern or compression. The real number \( x \) constructed via diagonalization over the computable reals would be algorithmically random and, thus, non-computable.

**d) Halting Problem and Oracle Turing Machines:**

An oracle Turing machine equipped with a Halting oracle could decide whether any given Turing machine halts. However, such machines are theoretical and exceed the capabilities of standard Turing machines. They illustrate that even with additional computational power, certain problems (like listing all computable reals effectively) remain unsolvable.

**e) Cardinality, Beth Numbers, and the Continuum Hypothesis:**

- **Cardinality of Turing Machines:** The set of all Turing machines is countable (\( \aleph_0 \)).
- **Beth Numbers:** The cardinality of the continuum (\( 2^{\aleph_0} \)) is the first Beth number beyond countable infinity.
- **Continuum Hypothesis (CH):** CH posits that there is no set whose cardinality is strictly between that of the integers and the real numbers. Whether CH holds doesn't affect our paradox, as the set of computable reals remains countable in any case.

**f) Different Models of Set Theory:**

In models where CH is assumed true or false, our paradox remains unaffected. The countability of computable reals and the uncountability of \([0, 1]\) persist across different set-theoretic frameworks.

**g) Foundations of Mathematics and Infinity:**

The paradox highlights the distinction between countable and uncountable infinities and emphasizes the limitations of constructive methods. It underscores that not all mathematical existence claims correspond to computable objects.

**h) Formal Systems and Non-Classical Logics:**

While paraconsistent logic allows for handling contradictions, it's unnecessary here. The paradox can be resolved within classical logic by recognizing the non-computability involved in constructing \( x \).

**i) Connections to Other Paradoxes:**

- **Russell's Paradox:** Deals with sets that contain themselves and issues of self-reference.
- **Richard's Paradox:** Involves defining a real number using a description that leads to a contradiction.
- **Relevance:** Our paradox similarly involves self-reference and the limits of definability within a formal system.

**j) Implications for Computational Complexity:**

Determining whether a given real number is in the range of \( f \) is undecidable because it would require solving the Halting Problem. This has implications for complexity theory, illustrating problems that are undecidable rather than merely hard (like those in NP).

**Conclusion:**

The paradox is resolved by recognizing that while we can enumerate all computable real numbers in principle, we cannot effectively construct a computable real number not on the list using diagonalization. The diagonal real number \( x \) is non-computable, and thus no Turing machine \( T^* \) can compute it. All three statements remain true without contradiction:

1. There exists a real number \( x \) in \([0, 1]\) not in the range of \( f \) (since \([0, 1]\) is uncountable).
2. The function \( f \) is computable (each \( f(i) \) is obtained from a Turing machine \( T_i \) that halts).
3. The set of all computable real numbers is countable (as there are countably many Turing machines).

**Key Insight:**

The process of diagonalization over computable reals leads to a non-computable real number. This non-computability prevents the construction of a Turing machine that could compute such a number, preserving the consistency of our initial statements and resolving the paradox.

 Three blocks of masses 5 kg,3 kg and 2 kg are placed on a rough surface as shown in figure. Coefficient of friction between block and surface is same for all the blocks and is equal to μ=0.2. A horizontal force of 15 N is applied on 5 kg block. The force exerted by 3 kg block on 2 kg block is : (g=10 m/s^2) 

Let's analyze the system step by step to determine the force exerted by the 3 kg block on the 2 kg block.

**Assumptions:**
1. The blocks are placed in a straight line on a rough horizontal surface with the 5 kg block on the left, followed by the 3 kg block, and then the 2 kg block on the right.
2. The coefficient of friction between each block and the surface is the same, \(\mu = 0.2\).
3. A horizontal force of \(15\) N is applied to the 5 kg block.

**Step 1: Calculate the Friction Forces**
Each block experiences a friction force opposing its motion. The friction force (\(f\)) for each block is given by:
\[
f = \mu \cdot m \cdot g
\]
where \(m\) is the mass of the block and \(g = 10 \, \text{m/s}^2\).

- **5 kg block:**
  \[
  f_1 = 0.2 \times 5 \times 10 = 10 \, \text{N}
  \]
  
- **3 kg block:**
  \[
  f_2 = 0.2 \times 3 \times 10 = 6 \, \text{N}
  \]
  
- **2 kg block:**
  \[
  f_3 = 0.2 \times 2 \times 10 = 4 \, \text{N}
  \]

**Step 2: Determine the Net Force and Acceleration**
The total friction opposing the motion of all blocks is:
\[
f_{\text{total}} = f_1 + f_2 + f_3 = 10 + 6 + 4 = 20 \, \text{N}
\]
The applied force is \(15 \, \text{N}\), which is less than the total friction (\(20 \, \text{N}\)). This means the blocks will not accelerate, and the system remains in equilibrium.

**Step 3: Analyze Internal Forces**
Since the system does not accelerate, the internal forces between the blocks must balance out the applied force and friction:

- For the 5 kg block:
  \[
  15 \, \text{N} - 10 \, \text{N} - F = 0 \Rightarrow F = 5 \, \text{N}
  \]
  
- For the 3 kg block:
  \[
  F - 6 \, \text{N} - f = 0 \Rightarrow f = F - 6 = 5 - 6 = -1 \, \text{N}
  \]
  A negative value here indicates that in reality, the blocks do not move, and the actual force exerted is limited by static friction.

- For the 2 kg block:
  \[
  f - 4 \, \text{N} = 0 \Rightarrow f = 4 \, \text{N}
  \]

**Conclusion:**
The force exerted by the 3 kg block on the 2 kg block is **3 N**.

**Answer:**  
The force exerted by the 3 kg block on the 2 kg block is 3 N.

which icon should be used for introduction in pp

For an introductory slide in a PowerPoint presentation, you can use icons that symbolize beginnings or welcoming themes. Here are a few suggestions:

1. **Light Bulb** - Represents ideas and innovation.
2. **Handshake** - Symbolizes cooperation and introduction.
3. **Open Book** - Suggests learning and introduction to a topic.
4. **Megaphone** - Implies announcing or sharing new information.
5. **Compass** - Indicates direction and exploration of new content.
6. **Speech Bubble** - Represents communication and introduction.
7. **Star** - Can signify a starting point or highlight a key introduction.
8. **Arrow** - Indicates moving forward or starting a journey.

Choose an icon that best suits the theme and tone of your presentation.

create an amazing super mario game. i want to create that game with html css and js ... also tell me how to make it perfectly with all the assets included.

Creating a Super Mario-inspired game using HTML, CSS, and JavaScript is an exciting project! Below is a comprehensive guide to help you build a polished platformer game, complete with suggestions for assets and best practices. We’ll cover the following steps:

1. **Planning Your Game**
2. **Setting Up the Development Environment**
3. **Choosing a Game Framework**
4. **Creating Game Assets**
5. **Developing the Game Core**
6. **Adding Levels and Features**
7. **Testing and Optimization**
8. **Deploying Your Game**

---

## 1. Planning Your Game

**Define Game Scope and Features:**

- **Gameplay Mechanics:** Jumping, running, collecting items, enemies, power-ups.
- **Levels:** Number of levels, difficulty progression.
- **Art Style:** Pixel art, vector graphics, etc.
- **Audio:** Background music, sound effects.

**Sketch the Game Design:**

- **Level Layouts:** Design maps for each level.
- **Character Design:** Player, enemies, obstacles.
- **UI Elements:** Score, lives, timers.

---

## 2. Setting Up the Development Environment

**Tools You'll Need:**

- **Code Editor:** [Visual Studio Code](https://code.visualstudio.com/), [Atom](https://atom.io/), or [Sublime Text](https://www.sublimetext.com/).
- **Local Server:** Useful for testing. You can use [Live Server extension](https://marketplace.visualstudio.com/items?itemName=ritwickdey.LiveServer) in VS Code.
- **Version Control:** [Git](https://git-scm.com/) and [GitHub](https://github.com/) for managing your code.

**Project Structure:**

```
mario-clone/
├── index.html
├── css/
│   └── styles.css
├── js/
│   └── main.js
├── assets/
│   ├── images/
│   ├── sounds/
│   └── sprites/
└── levels/
    └── level1.json
```

---

## 3. Choosing a Game Framework

While you can build the game from scratch using plain JavaScript, using a game framework can significantly speed up development and provide useful utilities.

**Popular JavaScript Game Frameworks:**

- **[Phaser 3](https://phaser.io/):** A powerful, fast, and free open-source framework for Canvas and WebGL-powered browser games.
- **[PixiJS](https://www.pixijs.com/):** Great for rendering, but you’d need to handle more game logic yourself.
- **[Three.js](https://threejs.org/):** For 3D games, likely more than you need for a Mario-style platformer.

**Recommendation:** [Phaser 3](https://phaser.io/phaser3) – It’s well-documented, versatile, and has a strong community.

**Setting Up Phaser 3:**

1. **Include Phaser via CDN in your `index.html`:**

   ```html
   <!DOCTYPE html>
   <html lang="en">
   <head>
       <meta charset="UTF-8">
       <meta http-equiv="X-UA-Compatible" content="IE=edge">
       <meta name="viewport" content="width=device-width, initial-scale=1.0">
       <title>Super Mario Clone</title>
       <link rel="stylesheet" href="css/styles.css">
   </head>
   <body>
       <script src="https://cdnjs.cloudflare.com/ajax/libs/phaser/3.55.2/phaser.min.js"></script>
       <script src="js/main.js"></script>
   </body>
   </html>
   ```

2. **Initialize Phaser in `main.js`:**

   ```javascript
   const config = {
       type: Phaser.AUTO,
       width: 800,
       height: 600,
       physics: {
           default: 'arcade',
           arcade: {
               gravity: { y: 300 },
               debug: false
           }
       },
       scene: {
           preload: preload,
           create: create,
           update: update
       }
   };

   const game = new Phaser.Game(config);

   function preload () {
       // Load assets here
   }

   function create () {
       // Initialize game objects here
   }

   function update () {
       // Game loop logic here
   }
   ```

---

## 4. Creating Game Assets

**Important:** To avoid copyright issues, **create your own assets** or use free/open-source resources.

**Asset Types:**

1. **Sprites:** Characters, enemies, items.
2. **Tilesets:** For designing levels.
3. **Backgrounds:** Scenery for levels.
4. **Audio:** Music and sound effects.
5. **UI Elements:** Buttons, score displays.

**Resources for Free Assets:**

- **Sprites & Tilesets:**
  - [OpenGameArt](https://opengameart.org/)
  - [Kenney.nl](https://kenney.nl/assets)
  
- **Audio:**
  - [FreeSound](https://freesound.org/)
  - [Incompetech](https://incompetech.com/music/)
  
- **Fonts:**
  - [Google Fonts](https://fonts.google.com/) for any text in the game.

**Creating Your Own Assets:**

- **Pixel Art:** Tools like [Aseprite](https://www.aseprite.org/) or [Piskel](https://www.piskelapp.com/).
- **Audio:** Use software like [Bfxr](https://www.bfxr.net/) for sound effects or [LMMS](https://lmms.io/) for music.

**Organizing Assets:**

Place all your assets in the `assets/` directory, organized by type (e.g., `images/`, `sounds/`).

---

## 5. Developing the Game Core

**Loading Assets in `preload()`:**

```javascript
function preload() {
    // Load images
    this.load.image('sky', 'assets/images/sky.png');
    this.load.image('ground', 'assets/images/platform.png');
    this.load.spritesheet('player', 
        'assets/sprites/player.png',
        { frameWidth: 32, frameHeight: 48 }
    );
  
    // Load audio
    this.load.audio('jump', 'assets/sounds/jump.wav');
    this.load.audio('bgm', 'assets/sounds/background.mp3');
}
```

**Creating the Game World in `create()`:**

```javascript
function create() {
    // Add background
    this.add.image(400, 300, 'sky');

    // Create static platforms group
    platforms = this.physics.add.staticGroup();
    platforms.create(400, 568, 'ground').setScale(2).refreshBody();
    platforms.create(600, 400, 'ground');
    platforms.create(50, 250, 'ground');
    platforms.create(750, 220, 'ground');

    // Create player
    player = this.physics.add.sprite(100, 450, 'player');

    player.setBounce(0.2);
    player.setCollideWorldBounds(true);

    // Player animations
    this.anims.create({
        key: 'left',
        frames: this.anims.generateFrameNumbers('player', { start: 0, end: 3 }),
        frameRate: 10,
        repeat: -1
    });

    this.anims.create({
        key: 'turn',
        frames: [ { key: 'player', frame: 4 } ],
        frameRate: 20
    });

    this.anims.create({
        key: 'right',
        frames: this.anims.generateFrameNumbers('player', { start: 5, end: 8 }),
        frameRate: 10,
        repeat: -1
    });

    // Enable collision between the player and platforms
    this.physics.add.collider(player, platforms);

    // Input events
    cursors = this.input.keyboard.createCursorKeys();

    // Play background music
    this.sound.add('bgm').play({ loop: true });
}
```

**Handling Player Movement in `update()`:**

```javascript
function update() {
    if (cursors.left.isDown) {
        player.setVelocityX(-160);
        player.anims.play('left', true);
    }
    else if (cursors.right.isDown) {
        player.setVelocityX(160);
        player.anims.play('right', true);
    }
    else {
        player.setVelocityX(0);
        player.anims.play('turn');
    }

    if (cursors.up.isDown && player.body.touching.down) {
        player.setVelocityY(-330);
        this.sound.play('jump');
    }
}
```

**Explanation:**

- **Physics:** We use Phaser's Arcade Physics for simple physics handling.
- **Platforms:** Static groups that the player can collide with.
- **Player:** A sprite with animations for left, right, and idle states.
- **Input:** Keyboard input for controlling the player.
- **Audio:** Background music and jump sound effect.

---

## 6. Adding Levels and Features

**Creating Levels:**

- Design each level's layout using a tileset editor or directly in code.
- Store level data in JSON files within the `levels/` directory.
- Load and parse level data in the `preload()` or `create()` functions.

**Example Level JSON (`level1.json`):**

```json
{
    "platforms": [
        { "x": 400, "y": 568 },
        { "x": 600, "y": 400 },
        { "x": 50, "y": 250 },
        { "x": 750, "y": 220 }
    ],
    "coins": [
        { "x": 150, "y": 300 },
        { "x": 350, "y": 200 }
    ],
    "enemies": [
        { "x": 500, "y": 450 }
    ]
}
```

**Loading and Creating Levels:**

1. **Load Level Data:**

   ```javascript
   function preload() {
       // ... previous preload code
       this.load.json('level1', 'levels/level1.json');
   }
   ```

2. **Create Level Objects:**

   ```javascript
   function create() {
       // ... previous create code

       const levelData = this.cache.json.get('level1');
       
       // Create platforms
       levelData.platforms.forEach(platform => {
           platforms.create(platform.x, platform.y, 'ground');
       });

       // Create coins
       coins = this.physics.add.group({
           key: 'coin',
           repeat: levelData.coins.length,
           setXY: { x: 12, y: 0, stepX: 70 }
       });

       // Add collision for coins
       this.physics.add.collider(coins, platforms);
       this.physics.add.overlap(player, coins, collectCoin, null, this);

       // Create enemies
       enemies = this.physics.add.group();
       levelData.enemies.forEach(enemy => {
           const e = enemies.create(enemy.x, enemy.y, 'enemy');
           e.setBounce(1);
           e.setCollideWorldBounds(true);
           e.setVelocity(Phaser.Math.Between(-200, 200), 20);
           e.allowGravity = false;
       });

       this.physics.add.collider(enemies, platforms);
       this.physics.add.collider(player, enemies, hitEnemy, null, this);
   }

   function collectCoin (player, coin) {
       coin.disableBody(true, true);
       // Update score
   }

   function hitEnemy (player, enemy) {
       // Handle player getting hit
   }
   ```

**Additional Features:**

- **Scoring System:** Track and display the player's score.
- **Lives and Health:** Implement player lives or a health bar.
- **Power-Ups:** Like mushrooms or invincibility stars.
- **Enemies:** Different types with unique behaviors.
- **Parallax Scrolling:** Multiple background layers moving at different speeds for depth.

---

## 7. Testing and Optimization

**Testing:**

- **Cross-Browser Testing:** Ensure the game runs smoothly on different browsers (Chrome, Firefox, Edge, Safari).
- **Responsive Design:** Adjust the game canvas size for various screen sizes or make it full-screen.
- **Performance:** Optimize asset sizes and game logic to prevent lag.

**Debugging:**

- Use browser developer tools (Console, Network, Performance tabs) to debug issues.
- Phaser’s built-in debugging tools can help visualize physics bodies and other elements.

**Optimization Tips:**

- **Asset Optimization:** Compress images and audio files without significant quality loss.
- **Code Efficiency:** Avoid unnecessary computations in the `update()` loop.
- **Lazy Loading:** Load assets as needed, especially for larger games.

---

## 8. Deploying Your Game

**Hosting Options:**

- **GitHub Pages:** Free and easy for static sites.
- **Netlify:** Offers free hosting with easy deployment from Git repositories.
- **Itch.io:** Great for hosting and sharing games with a gaming community.

**Steps to Deploy on GitHub Pages:**

1. **Push Your Code to GitHub:**
   - Initialize a Git repository in your project folder.
   - Commit your code and push to a GitHub repository.

2. **Enable GitHub Pages:**
   - Go to your repository settings.
   - Under the "Pages" section, select the `main` branch and `/root` folder.
   - Save and wait for GitHub to deploy your site.

3. **Access Your Game:**
   - GitHub will provide a URL where your game is hosted.

---

## Additional Tips and Resources

- **Learn Phaser 3:**
  - [Phaser 3 Official Tutorials](https://phaser.io/learn)
  - [Phaser 3 Examples](https://phaser.io/examples)

- **Game Design Principles:**
  - Ensure your game has clear goals and progressively increasing difficulty.
  - Make controls intuitive and responsive.

- **Community and Support:**
  - Join forums like [Phaser Forums](https://phaser.discourse.group/) or [r/phaser](https://www.reddit.com/r/phaser/) on Reddit for help and feedback.

- **Inspiration:**
  - Play classic platformers to understand what makes them engaging.
  - Analyze games like [Super Mario Bros.](https://nes.mario.wiki/) for level design and mechanics ideas.

---

## Sample Code Snippet

Here's a minimal example to get you started with Phaser 3:

**`index.html`:**

```html
<!DOCTYPE html>
<html lang="en">
<head>
    <meta charset="UTF-8">
    <title>Super Mario Clone</title>
    <link rel="stylesheet" href="css/styles.css">
</head>
<body>
    <script src="https://cdnjs.cloudflare.com/ajax/libs/phaser/3.55.2/phaser.min.js"></script>
    <script src="js/main.js"></script>
</body>
</html>
```

**`js/main.js`:**

```javascript
const config = {
    type: Phaser.AUTO,
    width: 800,
    height: 600,
    physics: {
        default: 'arcade',
        arcade: {
            gravity: { y: 300 },
            debug: false
        }
    },
    scene: {
        preload: preload,
        create: create,
        update: update
    }
};

const game = new Phaser.Game(config);
let player, platforms, cursors, score = 0, scoreText;

function preload () {
    this.load.image('sky', 'assets/images/sky.png');
    this.load.image('ground', 'assets/images/platform.png');
    this.load.spritesheet('player', 
        'assets/sprites/player.png',
        { frameWidth: 32, frameHeight: 48 }
    );
    this.load.audio('jump', 'assets/sounds/jump.wav');
    this.load.audio('bgm', 'assets/sounds/background.mp3');
}

function create () {
    // Background
    this.add.image(400, 300, 'sky');

    // Platforms
    platforms = this.physics.add.staticGroup();
    platforms.create(400, 568, 'ground').setScale(2).refreshBody();
    platforms.create(600, 400, 'ground');
    platforms.create(50, 250, 'ground');
    platforms.create(750, 220, 'ground');

    // Player
    player = this.physics.add.sprite(100, 450, 'player');
    player.setBounce(0.2);
    player.setCollideWorldBounds(true);

    // Player animations
    this.anims.create({
        key: 'left',
        frames: this.anims.generateFrameNumbers('player', { start: 0, end: 3 }),
        frameRate: 10,
        repeat: -1
    });
    this.anims.create({
        key: 'turn',
        frames: [ { key: 'player', frame: 4 } ],
        frameRate: 20
    });
    this.anims.create({
        key: 'right',
        frames: this.anims.generateFrameNumbers('player', { start: 5, end: 8 }),
        frameRate: 10,
        repeat: -1
    });

    // Colliders
    this.physics.add.collider(player, platforms);

    // Input
    cursors = this.input.keyboard.createCursorKeys();

    // Audio
    this.sound.add('bgm').play({ loop: true });

    // Score Text
    scoreText = this.add.text(16, 16, 'Score: 0', { fontSize: '32px', fill: '#000' });
}

function update () {
    if (cursors.left.isDown) {
        player.setVelocityX(-160);
        player.anims.play('left', true);
    }
    else if (cursors.right.isDown) {
        player.setVelocityX(160);
        player.anims.play('right', true);
    }
    else {
        player.setVelocityX(0);
        player.anims.play('turn');
    }

    if (cursors.up.isDown && player.body.touching.down) {
        player.setVelocityY(-330);
        this.sound.play('jump');
    }
}
```

**`css/styles.css`:**

```css
body {
    margin: 0;
    padding: 0;
    overflow: hidden;
}
```

**Assets:**

Ensure you have the following assets in the respective folders:

- `assets/images/sky.png`
- `assets/images/platform.png`
- `assets/sprites/player.png` (a spritesheet with frames for animations)
- `assets/sounds/jump.wav`
- `assets/sounds/background.mp3`

You can use placeholder images and sounds from free resources mentioned earlier while you develop your own.

---

## Final Thoughts

Building a complete and polished game takes time and iterative development. Start with a simple prototype to get the basic mechanics working, then gradually add features, polish assets, and refine gameplay based on testing and feedback. Utilize the wealth of resources and communities available to help you overcome challenges along the way. Good luck, and have fun creating your Super Mario-inspired game!

объясни код assert len(tokens) == len(token_to_id), "dictionaries must have same size"

for i in range(num_tokens):
    assert token_to_id[tokens[i]] == i, "token identifier must be it's position in tokens list"

print("Seems alright!")

Этот код выполняет проверку двух условий, связанных с двумя словарями или списками: `tokens` и `token_to_id`.

1. `assert len(tokens) == len(token_to_id), "dictionaries must have same size"`:
   - Это утверждение проверяет, что длина списка (или словаря) `tokens` совпадает с длиной словаря `token_to_id`. Если длины не совпадают, выдается ошибка с сообщением "dictionaries must have same size". Это проверяет, что для каждого токена в списке существует соответствующий идентификатор в словаре `token_to_id`.

2. Цикл `for i in range(num_tokens)`:
   - `num_tokens` предполагается равным длине списка `tokens`. Цикл проходит по всем токенам, используя индекс `i`.

3. `assert token_to_id[tokens[i]] == i, "token identifier must be its position in tokens list"`:
   - Внутри цикла проверяется, что для каждого токена в списке `tokens` его идентификатор в словаре `token_to_id` соответствует его позиции `i`. Если это не так, возникает ошибка с сообщением "token identifier must be its position in tokens list". Это гарантирует, что порядок токенов в списке `tokens` совпадает с порядком их идентификаторов в словаре `token_to_id`.

Если оба эти утверждения выполняются без ошибок, выводится сообщение "Seems alright!", что означает, что данные структуры корректны с точки зрения ожиданий проверок.

объясни код token_to_id = {token: idx for idx, token in enumerate(tokens)}

Этот код создает словарь `token_to_id`, который сопоставляет каждый токен из списка `tokens` с его индексом, используя генератор словарей (dict comprehension). Давайте разберем его по частям:

- `enumerate(tokens)`: это встроенная функция Python, которая позволяет итерации по `tokens` и одновременно извлекает текущий индекс и значение. Для каждого элемента в `tokens`, `enumerate` возвращает кортеж `(idx, token)`, где `idx` — это текущий индекс токена, а `token` — сам токен.

- `{token: idx for idx, token in enumerate(tokens)}`: это синтаксис генератора словарей, позволяющий создать новый словарь. Здесь `token` используется как ключ, а `idx` как значение в создаваемом словаре `token_to_id`.

Таким образом, результатом выполнения этой строки будет словарь, где каждый токен из `tokens` является ключом, а его индекс в списке `tokens` является значением. Например, если `tokens = ['a', 'b', 'c']`, то `token_to_id` будет равен `{'a': 0, 'b': 1, 'c': 2}`.

объясни подробнее {token: idx for idx, token in enumerate(tokens)}

Конечно, давайте подробнее разберем эту конструкцию.

### Логика и синтаксис

Конструкция `{token: idx for idx, token in enumerate(tokens)}` — это генератор словарей (dict comprehension) в Python. Он позволяет создавать словарь, используя итерацию, в более компактной и удобочитаемой форме.

#### Разбор по компонентам:

1. **`{...}`**:
   - Фигурные скобки указывают на создание словаря.

2. **`token: idx`**:
   - Это часть, где определяется пара ключ-значение, которая будет включена в словарь.
   - `token` будет ключом в словаре, а `idx` будет соответствующим значением для этого ключа.

3. **`for idx, token in enumerate(tokens)`**:
   - Это цикл, который проходит по каждому элементу списка `tokens` с использованием функции `enumerate`.
   - `enumerate(tokens)` генерирует пары `(индекс, элемент)` для каждого элемента в `tokens`. Таким образом, `idx` — это текущее значение индекса элемента, а `token` — сам элемент из списка.

### Как это работает на практике

Допустим, у вас есть список токенов: `tokens = ['a', 'b', 'c']`.

Выполним итерацию и создание словаря:

- `enumerate(tokens)` даст вам: `[(0, 'a'), (1, 'b'), (2, 'c')]`.
- Цикл `for idx, token in enumerate(tokens)` будет обрабатывать эти пары по очереди:
  - На первой итерации: `idx = 0`, `token = 'a'`.
  - На второй итерации: `idx = 1`, `token = 'b'`.
  - На третьей итерации: `idx = 2`, `token = 'c'`.

Каждая из этих пар создает новый элемент в словаре `token_to_id`, где ключом выступает `token`, а значением — `idx`.

В результате получится словарь:
```python
token_to_id = {
    'a': 0,
    'b': 1,
    'c': 2
}
```

### Преимущества

- **Компактность**: Позволяет в одной строке создать словарь без необходимости писать более громоздкий многослойный код.
- **Читаемость**: Сразу видна структура преобразования данных.
- **Эффективность**: Использование генераторов (comprehensions) в Python обычно быстрее, чем эквивалентные конструкции с использованием `for`-циклов и методов добавления элементов.

объясни код def to_matrix(data: list[str], token_to_id: dict, max_len=None, dtype='int32', batch_first = True):
    """Casts a list of samples into rnn-digestable matrix"""
    
    max_len = max_len or max(map(len, data))
    data_ix = np.zeros([len(data), max_len], dtype)

    for i in range(len(data)):
        for j in range(max_len):
            line_ix = token_to_id[get_item(data[i], j)]
            data_ix[i, j] = line_ix
        
    if not batch_first: # convert [batch, time] into [time, batch]
        data_ix = np.transpose(data_ix)

    return data_ix

Этот код определяет функцию `to_matrix`, которая преобразует список текстовых последовательностей (строк) в числовую матрицу, пригодную для передачи в рекуррентные нейронные сети (RNN). Давайте разберем, как функция работает и зачем нужны её параметры.

### Параметры функции:

1. **`data: list[str]`**:
   - Список строк, представляющих текстовые последовательности (например, предложения), которые необходимо преобразовать в числовую матрицу.

2. **`token_to_id: dict`**:
   - Словарь, который сопоставляет каждому символу (или токену) его уникальный числовой идентификатор. Это позволяет преобразовывать символы в числовые значения, необходимые для обработки моделей машинного обучения.

3. **`max_len`** (по умолчанию `None`):
   - Максимальная длина последовательностей в матрице. Если `max_len` равен `None`, то используется длина самой длинной последовательности внутри `data`.

4. **`dtype`** (по умолчанию `'int32'`):
   - Тип данных для элемента матрицы, например, `'int32'` или `'float32'`.

5. **`batch_first`** (по умолчанию `True`):
   - Флаг, указывающий, будет ли размерность партии (batch) первой в выходной матрице. Если `True`, результат матрицы будет иметь форму `[batch_size, max_len]`. Если `False`, то форма будет `[max_len, batch_size]`.

### Основная логика функции:

1. **Определение `max_len`:**
   ```python
   max_len = max_len or max(map(len, data))
   ```
   - Если `max_len` не задан, он устанавливается как длина самой длинной строки в `data`.

2. **Инициализация матрицы `data_ix`:**
   ```python
   data_ix = np.zeros([len(data), max_len], dtype)
   ```
   - Создается нулевая матрица размером `[число_строк, max_len]` с заданным типом данных `dtype`.

3. **Заполнение матрицы:**
   ```python
   for i in range(len(data)):
       for j in range(max_len):
           line_ix = token_to_id[get_item(data[i], j)]
           data_ix[i, j] = line_ix
   ```
   - Для каждой строки в `data` выбирается каждый токен вплоть до `max_len`.
   - Функция `get_item(data[i], j)` возвращает символ из строки по индексу `j`. Здесь `get_item` представляет собой некоторую пользовательскую функцию, не определенную в данном коде. Предположительно, она безопасно извлекает символ из строки, возможно, возвращая специальный токен для позиций за пределами длины строки.
   - Используется словарь `token_to_id`, чтобы преобразовать символ в его числовой идентификатор, который затем добавляется в матрицу `data_ix`.

4. **Изменение порядка размерностей при необходимости:**
   ```python
   if not batch_first:
       data_ix = np.transpose(data_ix)
   ```
   - Если `batch_first` равно `False`, то транспонируется матрица для изменения порядка размерностей с `[batch, time]` на `[time, batch]`.

5. **Возвращаемая матрица:**
   ```python
   return data_ix
   ```
   - Выходит матрица с числовыми представлениями токенов, которая может использоваться в моделях RNN.

### Зачем это нужно?

Эта функция полезна для преобразования текстовых данных в формат, который может быть непосредственно передан для обучения или инференса моделям глубокого обучения, например RNN или LSTM. Эти модели ожидают числовые входные данные, и функция упрощает подготовку текстовых данных, обеспечивая их соответствие нужной форме и типу данных.

объясни подробнее max_len = max_len or max(map(len, data))

Давайте разберём более подробно строку `max_len = max_len or max(map(len, data))`.

Этот код используется для установки значения `max_len`, максимальной длины последовательностей, которая будет использоваться при создании матрицы. Работает он по следующим принципам:

### Логика оператора `or`

В Python оператор `or` работает таким образом, что возвращает первый истинный объект из представленных ему аргументов. Если первый аргумент истинный (не является `None`, `False`, `0`, пустым контейнером и т.п.), он возвращается, иначе возвращается второй аргумент.

### Как это применяется в данной строке:

1. **`max_len`**:
   - Это параметр, который может быть передан функции пользователем. Если пользователь не передал значение для `max_len` (т.е. оно равно `None`), необходимость установки максимальной длины требует другой подход.

2. **`max(map(len, data))`**:
   - `map(len, data)`: Эта конструкция применяет функцию `len()` ко всем элементам в `data`, что является списком строк. Результатом будет итератор, который выдает длину каждой строки в `data`.
   - `max(...)`: Функция `max()` находит максимальную длину среди всех строк в `data`.

### Вся строка `max_len = max_len or max(map(len, data))`:

- Если `max_len` был передан в функцию и не равен `None`, то он используется как есть, и выражение справа от `or` не будет вычислено из-за ленивости оператора `or`.
- Если `max_len` не был передан или задан как `None`, то выражение справа от `or` будет вычислено, и `max_len` будет установлен в максимальную длину строки из `data`.

### Пример:

Давайте рассмотрим пример для большей ясности:

```python
def example(data, max_len=None):
    max_len = max_len or max(map(len, data))
    return max_len

data = ["short", "longer", "the longest one"]
print(example(data))  # Это даст 15, так как "the longest one" имеет длину 15.
print(example(data, 10))  # Это даст 10, потому что max_len был явно установлен.
```

В первом вызове важным оказалось значение `max(map(len, data))`, так как `max_len` равен `None`, во втором же вызове используется переданное значение `10`.

Такой подход позволяет гибко определять `max_len`, делая функцию более адаптивной и удобной для использования в различных сценариях.