PytracingMaze
MOST RECENT VERSION: Pytracing Maze.py
Also, executable for Windows available on itch.io
Simple ray tracing game in Python, based on my ray casting project. As you may have guessed, things started to get a bit heavy for Python, so i had to resort to the Numba library, improving performance by 100x.
First video - 3D ray casting (proto ray tracing): https://www.youtube.com/watch?v=ravnXknUvvQ
Second video - reflections and shadows, attempted optimization: https://www.youtube.com/watch?v=IFmw6HM-uF0
Third video - Proper optimization, textures and spheres: https://www.youtube.com/watch?v=xHk8KCJ-99M
Intro
Rays
The basic approach is to trace rays of light in the reverse direction, starting from the camera and interacting with the environment, with three basic types of rays:
- Vision rays - Initial rays that shoots from the camera and returns the coordinates where it has hit something
- Reflection rays - Secondary rays cast when a vision ray hits a reflective surface, the new direction is the reflection of vision ray in relation to the normal vector of the surface, can have several bounces (reflections inside reflections)
- Shadow rays - Secondary rays that start where the vision ray has hit something and go in the direction of the light
Maps
Maps are defined by grids, with different maps for different features: wall positions, colors, heights, reflectivities, textures and geometry (spheres or prisms). The maps are generated randomly, so each level and each game is a bit different. For that, a random walker algorithm is used, removing some walls from the map while traversing it, giving preference to pre-existing paths carved randomly.
Game logic
The player starts on one side of the map and has the objective of finding a blue floor patch on the opposite side of the map. At each level the size of map gets bigger.
Inputs
Basic inputs are similar to FPS games, with WASD for movement and mouse for orientation, the esc key is reserved for quitters.
Code
The code is a bit messy, following the basic structure:
- Variables initialization
- Generate random map
- Game loop
- Check inputs
- Movement
- Calculate frame (with Numba)
- Pixel loop
- Initialize Vision ray
- Vision Ray loop
- Increment until reaching a surface
- If hit reflective suface, reflect ray direction, else break out
- Check pixel base color
- Initialize Shadow ray
- Shadow Ray loop
- Increment until reaching light or blocked by something
- Store pixel
- Pixel loop
- Draw frame
- Check if reached end of maze
- Game over
- Game loop
Complexity arises from the different branches on block features wich may be combined (reflectivity, geometry, texture).
Variables initialization
Several variables have to be initialized related to: maps, player's position and orientation, light position and additional support variables.
Imports, map and initialization:
def main():
size = 25 # size of the map
posx, posy, posz = (1.5, np.random.uniform(1, size -1), 0.5)
rot, rot_v = (np.pi/4, 0)
lx, ly, lz = (size/2-0.5, size/2-0.5, 1)
mr, mg, mb, maph, mapr, exitx, exity, mapt, maps = maze_generator(int(posx), int(posy), size)
res, res_o = 5, [64, 96, 112, 160, 192, 224, 300, 400] # resolution options - width
width, height, mod, inc, rr, gg, bb = adjust_resol(res_o[res])
running = True
pg.init()
font = pg.font.SysFont("Arial", 18)
screen = pg.display.set_mode((800, 600))
clock = pg.time.Clock()
pg.mouse.set_visible(False)
Main game loop
The main game loop first checks for some user inputs (quit or change resolution), then the frame calculation frame is called (super_fast()), returning the pixel values. The pixel values are processed and displayed, after that the players movement is processed, checking if he has reached the exit and then checkin for new inputs.
Main game loop
while running:
for event in pg.event.get():
if event.type == pg.QUIT: # quit game by closing window
running = False
if event.type == pg.KEYDOWN:
if event.key == pg.K_ESCAPE: # quit game with esc
running = False
if event.key == ord('q'): # lower resolution
if res > 0 :
res = res-1
width, height, mod, inc, rr, gg, bb = adjust_resol(res_o[res])
if event.key == ord('e'): # higher resolution
if res < len(res_o)-1 :
res = res+1
width, height, mod, inc, rr, gg, bb = adjust_resol(res_o[res])
rr, gg, bb = super_fast(width, height, mod, inc, posx, posy, posz, rot, rot_v, mr, mg, mb, lx, ly, lz, maph, exitx, exity, mapr, mapt, maps, rr, gg, bb)
pixels = np.dstack((rr,gg,bb))
pixels = np.reshape(pixels, (height,width,3))
surf = pg.surfarray.make_surface((np.rot90(pixels*255)).astype('uint8'))
surf = pg.transform.scale(surf, (800, 600))
screen.blit(surf, (0, 0))
fps = font.render(str(round(clock.get_fps(),1)), 1, pg.Color("coral"))
screen.blit(fps,(10,0))
pg.display.update()
# player's movement
if (int(posx) == exitx and int(posy) == exity):
break
pressed_keys = pg.key.get_pressed()
posx, posy, rot, rot_v = movement(pressed_keys,posx, posy, rot, rot_v, maph, clock.tick()/500)
pg.mouse.set_pos([400, 300])
pg.quit() #Exit pygame
Adjust resolution
Support function for easy resolution change
Adjust resolution
def adjust_resol(width):
height = int(0.75*width)
mod = width/64
inc = 0.02/mod
rr = np.random.uniform(0,1,width * height)
gg = np.random.uniform(0,1,width * height)
bb = np.random.uniform(0,1,width * height)
print('Resolution: ', width, height)
return width, height, mod, inc, rr, gg, bb
Setting up a maze map
Firstly, a map is generated with blocks in random locations and random features, except on the edges of the map, where there are always full-height prismatic walls. After that, a random walker tries to reach the opposite side of the map, in the process some blocks are removed to give way. When it reaches the other side, the location is marked as the exit of the maze.
Maze map setup
def maze_generator(x, y, size):
mr = np.random.uniform(0,1, (size,size))
mg = np.random.uniform(0,1, (size,size))
mb = np.random.uniform(0,1, (size,size))
mapr = np.random.choice([0, 0, 0, 0, 1], (size,size))
maps = np.random.choice([0, 0, 0, 0, 1], (size,size))
mapt = np.random.choice([0, 0, 0, 1, 2], (size,size))
maph = np.random.choice([0, 0, 0, 0, 0, 0, 0, .3, .4, .7, .9], (size,size))
maph[0,:], maph[size-1,:], maph[:,0], maph[:,size-1] = (1,1,1,1)
maps[0,:], maps[size-1,:], maps[:,0], maps[:,size-1] = (0,0,0,0)
maph[x][y], mapr[x][y] = (0, 0)
count = 0
while 1:
testx, testy = (x, y)
if np.random.uniform() > 0.5:
testx = testx + np.random.choice([-1, 1])
else:
testy = testy + np.random.choice([-1, 1])
if testx > 0 and testx < size -1 and testy > 0 and testy < size -1:
if maph[testx][testy] == 0 or count > 5:
count = 0
x, y = (testx, testy)
maph[x][y], mapr[x][y] = (0, 0)
if x == size-2:
exitx, exity = (x, y)
break
else:
count = count+1
mapt[np.where(mapr == 1)] = 0
return mr, mg, mb, maph, mapr, exitx, exity, mapt, maps
User inputs for movement
After each frame is drwan, the player's position and orientation are updated according to keyboard and mouse inputs, but the player can only move if the intended new position is not a wall.
Input and movement
def movement(pressed_keys,posx, posy, rot, rot_v, maph, et):
x, y = (posx, posy)
p_mouse = pg.mouse.get_pos()
rot, rot_v = rot - (p_mouse[0]-400)/200, rot_v -(p_mouse[1]-300)/400
rot_v = np.clip(rot_v, -1, 1)
if pressed_keys[pg.K_UP] or pressed_keys[ord('w')]:
x, y = (x + et*np.cos(rot), y + et*np.sin(rot))
if pressed_keys[pg.K_DOWN] or pressed_keys[ord('s')]:
x, y = (x - et*np.cos(rot), y - et*np.sin(rot))
if pressed_keys[pg.K_LEFT] or pressed_keys[ord('a')]:
x, y = (x - et*np.sin(rot), y + et*np.cos(rot))
if pressed_keys[pg.K_RIGHT] or pressed_keys[ord('d')]:
x, y = (x + et*np.sin(rot), y - et*np.cos(rot))
if maph[int(x)][int(y)] == 0:
posx, posy = (x, y)
return posx, posy, rot, rot_v
Casting rays
Rays are cast for each pixel, starting at the players current position with directions spaced uniformly in the pixel grid for a field of view of 60° horizontally and 45° vertically. When a ray hits something a few checks need to be made for height, shape, reflectivity, color and texture. After the base color of the pixel is defined, a new ray is cast from the last known position in the direction of the light to check if there is something directly blocking the light. Shadows are not affected by reflections for simplification.
Generic rays
def super_fast(args):
for j in range(height): #vertical loop
rot_j = rot_v + np.deg2rad(24 - j/mod) # vertical rotation
for i in range(width): #horizontal vision loop
rot_i = rot + np.deg2rad(i/mod - 30) # horizontal rotation
x, y, z = (posx, posy, posz) # ray starts at the player's position
sin, cos, sinz = (inc*np.sin(rot_i), inc*np.cos(rot_i)), inc*np.sin(rot_j) # x, y, z increments a.k.a. ray direction
while 1: # ray loop and reflections
x += cos; y += sin; z += sinz # increment ray
if "ray has hit something":
if "is a mirror":
"reflect ray"
else:
break
"check for the color of the block where ray has hit"
if z < 1: # ceiling has no shadows
"calculate new ray direction for shadow ray"
while 1: # shadow ray
x += cos; y += sin; z += sinz # increment ray
if "ray has hit something":
"increase shading"
if "ray has reached ceiling" or "shading threshhold":
break
"store pixel values"
First case: Regular walls with different heights and textures, ceiling and floor
The simplest case is when a ray hits a prismatic wall, that is, the checks for spheres and reflective blocks have failed. Then a base color for the pixel is retrieved and the texture is checked.
Regular walls, ceiling and floor
if z > 1: # ceiling
sh =(abs(np.sin(y+ly)+np.sin(x+lx))+6)/8
if (x-lx)**2 + (y-ly)**2 < 0.1: #light source
c1, c2, c3 = 1, 1, 1
elif int(np.rad2deg(np.arctan((y-ly)/(x-lx)))/6)%2 ==1:
c1, c2, c3 = 0.3*sh, 0.7*sh, 1*sh
else:
c1, c2, c3 = .2*sh, .6*sh, 1*sh
elif z < 0: # floor
if int(x*2)%2 == int(y*2)%2:
c1, c2, c3 = .8,.8,.8
else:
if int(x) == exitx and int(y) == exity: #exit
c1, c2, c3 = 0,0,.6
else:
c1, c2, c3 = .1,.1,.1
elif maph[int(x)][int(y)] > 0: # walls
c1, c2, c3 = mr[int(x)][int(y)], mg[int(x)][int(y)], mg[int(x)][int(y)]
if mapt[int(x)][int(y)]: # textured walls
if y%1 < 0.05 or y%1 > 0.95:
ww = int((x*3)%1*4)
else:
ww = int((y*3)%1*4)
if x%1 < 0.95 and x%1 > 0.05 and y%1 < 0.95 and y%1 > 0.05:
zz = int(x*5%1*6)
else:
zz = int(z*5%1*6)
text = texture[zz][ww]
c1, c2, c3 = c1*text, c2*text, c3*text
else:
c1, c2, c3 = .5,.5,.5 # if all fails
Second case: reflective prismatic walls
Reflective prismatic walls simply invert one of the components of direction of the rays. Surfaces facing up invert the z direction, sufaces facing the y direction (paralell to the xz plane) reflect the y direction and the same for the x direction. For that we can probe the blocks to sense which side of the wall we hit. A shading factor is introduced in reflections, making the darker while limiting the maximum number of reflections when a threshhold is reached. The color of the firs mirror is saved for a tinted mirror effect.
Reflective walls
elif mapr[int(x)][int(y)]: # check reflections
if modr == 1:
cx, cy = int(x), int(y)
modr = modr*0.7
if modr < 0.2:
break
if abs(z-maph[int(x)][int(y)]) < abs(sinz):
sinz = -sinz
elif maph[int(x+cos)][int(y-sin)] == maph[int(x)][int(y)]:
cos = -cos
else:
sin = -sin
Third case: Spheres
Spheres allow for rays to pass through the corners of the walls when the distance to the center of the block is greater than the radius of the sphere. Spheres may also have reflections, the difference is that the new direction of the ray is calculated by reflecting it around the normal of the surface. Spheres can also be textured, but the texture mapping does not consider the curvature of the surface.
Spheres
if maps[int(x)][int(y)]: # check spheres
if ((x-int(x)-0.5)**2 + (y-int(y)-0.5)**2 + (z-int(z)-0.5)**2 < 0.25):
if (mapr[int(x)][int(y)]): # spherical mirror
if (modr == 1):
cx, cy = int(x), int(y)
modr = modr*0.7
if (modr < 0.2):
break
if (abs(maph[int(x)][int(y)] - z) <= abs(sinz)): ## horizontal surface
sinz = -sinz
else:
nx = (x-int(x)-0.5)/0.5; ny = (y-int(y)-0.5)/0.5; nz =(z-0.5)/0.5
dot = 2*(cos*nx + sin*ny + sinz*nz)
cos = (cos - nx*dot); sin = (sin - ny*dot); sinz = (sinz - nz*dot)
x += cos; y += sin; z += sinz # avoid ray being trapped
else:
break
Shadow rays and shading
Before we start the Shadow ray loop, we check if the the shading was affected by reflections to mix the color of the pixel with the color of the mirror. We need to calculate the distance to the light source and new increments in its direction. The shading occurs incrementally, for softer edges, depending on the amount of material that is blocking the light. When a threshhold is reached, the ray is interrupted.
Shading
if modr < 1: # tinted mirrors
c1r, c2r, c3r = mr[cx][cy], mg[cx][cy], mg[cx][cy]
dtol = np.sqrt((x-lx)**2+(y-ly)**2+(lz-1)**2)
modr = modr*(0.6 + 0.4/(dtol+0.001))
if modr > 1:
modr = 1
if z < 1: # shadows
cos, sin, sinz = .05*(lx-x)/dtol, .05*(ly-y)/dtol, .05*(lz-z)/dtol
while 1:
x += cos; y += sin; z += sinz
if maph[int(x)][int(y)]!= 0 and z<= maph[int(x)][int(y)]:
if maps[int(x)][int(y)]: # check spheres
if ((x-int(x)-0.5)**2 + (y-int(y)-0.5)**2 + (z-int(z)-0.5)**2 < 0.25):
modr = modr*0.9
else:
modr = modr*0.9
if modr < 0.3:
break
if z > 1:
break
Optimization
The naive approach with small increments is very inefficient. A much more compelling approach is to take advantage of the grid structure of the map, with a DDA algorithm (Digital differential analyzer), as presented by Lode Vandevenne. Ideally, we would create a grid in the z direction for full optimization with a true voxel space, I'm not doing that. I will simply call the DDA everytime the ray is at an empty cell to find the next non empty one.
DDA
if (maph[int(x)][int(y)] == 0 or (sinz > 0 and not maps[int(x)][int(y)])): ## LoDev DDA for optimization
norm = np.sqrt(cos**2 + sin**2 + sinz**2)
rayDirX, rayDirY, rayDirZ = cos/norm, sin/norm, sinz/norm
mapX, mapY = int(x), int(y)
deltaDistX, deltaDistY, deltaDistZ= abs(1/rayDirX), abs(1/rayDirY), abs(1/rayDirZ)
if (rayDirX < 0):
stepX, sideDistX = -1, (x - mapX) * deltaDistX
else:
stepX, sideDistX = 1, (mapX + 1.0 - x) * deltaDistX
if (rayDirY < 0):
stepY, sideDistY = -1, (y - mapY) * deltaDistY
else:
stepY, sideDistY = 1, (mapY + 1 - y) * deltaDistY
if (rayDirZ < 0):
sideDistZ = z*deltaDistZ;
else:
sideDistZ = (1-z)*deltaDistZ
while (1):
if (sideDistX < sideDistY):
sideDistX += deltaDistX; mapX += stepX
dist = sideDistX; side = 0
else:
sideDistY += deltaDistY; mapY += stepY
dist = sideDistY; side = 1
if (maph[mapX][mapY] > 0):
break
if (side):
dist = dist - deltaDistY
else:
dist = dist - deltaDistX
if (dist > sideDistZ):
dist = sideDistZ
x = x + rayDirX*dist - cos/2
y = y + rayDirY*dist - sin/2
z = z + rayDirZ*dist - sinz/2
## end of LoDev DDA
To use it, we simply inject this code in the ray loop and in the shading loop. This results in a 2 to 3 times increase in performance, not too shabby.
Complete ray function super_fast()
When we put everything together we get an enormous function, it's ugly, but it's super fast =).
Complete function
@njit(fastmath=True)
def super_fast(width, height, mod, inc, posx, posy, posz, rot, rot_v, mr, mg, mb, lx, ly, lz, maph, exitx, exity, mapr, mapt, maps, pr, pg, pb):
texture=[[ .95, .99, .97, .8], # brick wall
[ .97, .95, .96, .85],
[.8, .85, .8, .8],
[ .93, .8, .98, .96],
[ .99, .8, .97, .95],
[.8, .85, .8, .8]]
idx = 0
for j in range(height): #vertical loop
rot_j = rot_v + np.deg2rad(24 - j/mod)
for i in range(width): #horizontal vision loop
rot_i = rot + np.deg2rad(i/mod - 30)
x, y, z = (posx, posy, posz)
sin, cos, = (inc*np.sin(rot_i), inc*np.cos(rot_i))
sinz = inc*np.sin(rot_j)
modr = 1
cx, cy, c1r, c2r, c3r = 1, 1, 1, 1, 1
while 1:
if (maph[int(x)][int(y)] == 0 or (sinz > 0 and not maps[int(x)][int(y)])): ## LoDev DDA for optimization
norm = np.sqrt(cos**2 + sin**2 + sinz**2)
rayDirX, rayDirY, rayDirZ = cos/norm, sin/norm, sinz/norm
mapX, mapY = int(x), int(y)
deltaDistX, deltaDistY, deltaDistZ= abs(1/rayDirX), abs(1/rayDirY), abs(1/rayDirZ)
if (rayDirX < 0):
stepX, sideDistX = -1, (x - mapX) * deltaDistX
else:
stepX, sideDistX = 1, (mapX + 1.0 - x) * deltaDistX
if (rayDirY < 0):
stepY, sideDistY = -1, (y - mapY) * deltaDistY
else:
stepY, sideDistY = 1, (mapY + 1 - y) * deltaDistY
if (rayDirZ < 0):
sideDistZ = z*deltaDistZ;
else:
sideDistZ = (1-z)*deltaDistZ
while (1):
if (sideDistX < sideDistY):
sideDistX += deltaDistX; mapX += stepX
dist = sideDistX; side = 0
else:
sideDistY += deltaDistY; mapY += stepY
dist = sideDistY; side = 1
if (maph[mapX][mapY] > 0):
break
if (side):
dist = dist - deltaDistY
else:
dist = dist - deltaDistX
if (dist > sideDistZ):
dist = sideDistZ
x = x + rayDirX*dist - cos/2
y = y + rayDirY*dist - sin/2
z = z + rayDirZ*dist - sinz/2
## end of LoDev DDA
x += cos; y += sin; z += sinz
if (z > 1 or z < 0): # check ceiling and floor
break
if maph[int(x)][int(y)] > z: # check walls
if maps[int(x)][int(y)]: # check spheres
if ((x-int(x)-0.5)**2 + (y-int(y)-0.5)**2 + (z-int(z)-0.5)**2 < 0.25):
if (mapr[int(x)][int(y)]): # spherical mirror
if (modr == 1):
cx, cy = int(x), int(y)
modr = modr*0.7
if (modr < 0.2):
break
if (abs(maph[int(x)][int(y)] - z) <= abs(sinz)): ## horizontal surface
sinz = -sinz
else:
nx = (x-int(x)-0.5)/0.5; ny = (y-int(y)-0.5)/0.5; nz =(z-0.5)/0.5
dot = 2*(cos*nx + sin*ny + sinz*nz)
cos = (cos - nx*dot); sin = (sin - ny*dot); sinz = (sinz - nz*dot)
x += cos; y += sin; z += sinz
else:
break
elif mapr[int(x)][int(y)]: # check reflections
if modr == 1:
cx, cy = int(x), int(y)
modr = modr*0.7
if modr < 0.2:
break
if abs(z-maph[int(x)][int(y)]) < abs(sinz):
sinz = -sinz
elif maph[int(x+cos)][int(y-sin)] == maph[int(x)][int(y)]:
cos = -cos
else:
sin = -sin
else:
break
if z > 1: # ceiling
sh =(abs(np.sin(y+ly)+np.sin(x+lx))+6)/8
if (x-lx)**2 + (y-ly)**2 < 0.1: #light source
c1, c2, c3 = 1, 1, 1
elif int(np.rad2deg(np.arctan((y-ly)/(x-lx)))/6)%2 ==1:
c1, c2, c3 = 0.3*sh, 0.7*sh, 1*sh
else:
c1, c2, c3 = .2*sh, .6*sh, 1*sh
elif z < 0: # floor
if int(x*2)%2 == int(y*2)%2:
c1, c2, c3 = .8,.8,.8
else:
if int(x) == exitx and int(y) == exity: #exit
c1, c2, c3 = 0,0,.6
else:
c1, c2, c3 = .1,.1,.1
elif maph[int(x)][int(y)] > 0: # walls
c1, c2, c3 = mr[int(x)][int(y)], mg[int(x)][int(y)], mg[int(x)][int(y)]
if mapt[int(x)][int(y)]: # textured walls
if y%1 < 0.05 or y%1 > 0.95:
ww = int((x*3)%1*4)
else:
ww = int((y*3)%1*4)
if x%1 < 0.95 and x%1 > 0.05 and y%1 < 0.95 and y%1 > 0.05:
zz = int(x*5%1*6)
else:
zz = int(z*5%1*6)
text = texture[zz][ww]
c1, c2, c3 = c1*text, c2*text, c3*text
else:
c1, c2, c3 = .5,.5,.5 # if all fails
if modr < 1:
c1r, c2r, c3r = mr[cx][cy], mg[cx][cy], mg[cx][cy]
dtol = np.sqrt((x-lx)**2+(y-ly)**2+(lz-1)**2)
modr = modr*(0.6 + 0.4/(dtol+0.001))
if modr > 1:
modr = 1
if z < 1: # shadows
cos, sin, sinz = .05*(lx-x)/dtol, .05*(ly-y)/dtol, .05*(lz-z)/dtol
while 1:
if maph[int(x)][int(y)] < z and not maps[int(x)][int(y)]: ## LoDev DDA for optimization
norm = np.sqrt(cos**2 + sin**2 + sinz**2)
rayDirX, rayDirY, rayDirZ = cos/norm, sin/norm, sinz/norm
mapX, mapY = int(x), int(y)
deltaDistX, deltaDistY, deltaDistZ= abs(1/rayDirX), abs(1/rayDirY), abs(1/rayDirZ)
if (rayDirX < 0):
stepX, sideDistX = -1, (x - mapX) * deltaDistX
else:
stepX, sideDistX = 1, (mapX + 1.0 - x) * deltaDistX
if (rayDirY < 0):
stepY, sideDistY = -1, (y - mapY) * deltaDistY
else:
stepY, sideDistY = 1, (mapY + 1 - y) * deltaDistY
if (rayDirZ < 0):
sideDistZ = z*deltaDistZ;
else:
sideDistZ = (1-z)*deltaDistZ
while (1):
if (sideDistX < sideDistY):
sideDistX += deltaDistX; mapX += stepX
dist = sideDistX; side = 0
else:
sideDistY += deltaDistY; mapY += stepY
dist = sideDistY; side = 1
if (maph[mapX][mapY] > 0):
break
if (side):
dist = dist - deltaDistY
else:
dist = dist - deltaDistX
if (dist > sideDistZ):
dist = sideDistZ
x = x + rayDirX*dist - cos/2
y = y + rayDirY*dist - sin/2
z = z + rayDirZ*dist - sinz/2
## end of LoDev DDA
x += cos; y += sin; z += sinz
if maph[int(x)][int(y)]!= 0 and z<= maph[int(x)][int(y)]:
if maps[int(x)][int(y)]: # check spheres
if ((x-int(x)-0.5)**2 + (y-int(y)-0.5)**2 + (z-int(z)-0.5)**2 < 0.25):
modr = modr*0.9
else:
modr = modr*0.9
if modr < 0.3:
break
if z > 1:
break
pr[idx] = modr*np.sqrt(c1*c1r)
pg[idx] = modr*np.sqrt(c2*c2r)
pb[idx] = modr*np.sqrt(c3*c3r)
idx += 1
return pr, pg, pb
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