如何在pygame中添加残像? [英] How to add afterimages in pygame?
问题描述
由于角色移动是基于网格的,所以角色从一个方格移动到另一个方格时看起来有点奇怪,因为它们只是从一个方格出现到另一个方格.为了让运动感觉更自然,我想添加残影",以便模拟流畅的运动.
示范图片:由于我的代码有字符直接移动到下一个方块上,我不知道如何在两者之间对精灵进行 blit.
if IDO.get_key(pygame.K_RIGHT):如果 PhaseFocus == 0 或 PhaseFocus == 2:网纹 +=1如果 Current_Selected != 0 和 Current_Selected.Phase == 2:如果 Current_Selected.x != Reticlex:Current_Selected.x = Reticlex如果 Current_Selected.x != Reticley:Current_Selected.y = Reticley如果 IDO.get_key(pygame.K_LEFT):如果 PhaseFocus == 0 或 PhaseFocus == 2:网纹 -=1如果 Current_Selected != 0 和 Current_Selected.Phase == 2:如果 Current_Selected.x != Reticlex:Current_Selected.x = Reticlex如果 Current_Selected.x != Reticley:Current_Selected.y = Reticley
当当前选择的角色处于阶段 2(携带)时,他们应该有这些残像.
让我们看看如何做到这一点.
第 1 步:基本设置
我们从一个空的"pygame 游戏开始,像这样:
导入pygame定义主():屏幕 = pygame.display.set_mode((640, 480))时钟 = pygame.time.Clock()为真:事件 = pygame.event.get()对于事件中的 e:如果 e.type == pygame.QUIT:返回screen.fill((30, 30, 30))pygame.display.flip()时钟滴答(60)如果 __name__ == '__main__':主要的()
我们有一个 Clock
、一个游戏循环并处理 QUIT
事件.我总是将来自 event.get()
的事件存储在一个变量中,以防我想再次迭代它们,例如当 Sprite
想要监听事件时.始终每帧只调用一次 event.get()
!
第 2 步:网格
我们想要一个基于网格的游戏,所以让我们画一个网格.此外,我们将一堆 Rect
存储在一个列表中,这样我们就可以轻松查找对象的屏幕坐标.我们希望将对象居中放置在其图块中,因此使用 Rect
类将为我们完成繁琐的工作.
导入pygame瓷砖尺寸 = 32GRID_W, GRID_H = (20, 15)def create_grid():冲浪 = pygame.Surface((TILESIZE * GRID_W, TILESIZE * GRID_H))surf.set_colorkey((2, 2, 2))冲浪.fill((2, 2, 2))网格 = []对于范围内的 y(GRID_H):行 = []对于范围内的 x(GRID_W):r = pygame.Rect(x * TILESIZE, y * TILESIZE, TILESIZE, TILESIZE)line.append(r)pygame.draw.rect(冲浪,pygame.Color('灰色'),r,1)grid.append(行)返回网格,冲浪定义主():screen = pygame.display.set_mode((TILESIZE * GRID_W, TILESIZE * GRID_H))时钟 = pygame.time.Clock()网格,grid_surf = create_grid()为真:事件 = pygame.event.get()对于事件中的 e:如果 e.type == pygame.QUIT:返回screen.fill((30, 30, 30))screen.blit(grid_surf, (0, 0))pygame.display.flip()时钟滴答(60)
<小时>第 3 步:网格上有东西在移动
我们现在创建一个在这个网格上移动的actor.在这种情况下,它是一个简单的 Sprite
,每秒移动一次.
导入pygame随机导入瓷砖尺寸 = 32GRID_W, GRID_H = (20, 15)查找 = 无类演员(pygame.sprite.Sprite):def __init__(self, grid_pos):super().__init__()self.image = pygame.Surface((TILESIZE//2, TILESIZE//2))self.rect = self.image.get_rect()self.pos = pygame.Vector2()self.update_pos(grid_pos)self.image.fill(pygame.Color('dodgerblue'))self.timeout = 1000def update_pos(self, grid_pos):self.grid_pos = grid_posself.rect.center = get_grid_rect(grid_pos).centerself.pos = pygame.Vector2(self.rect.topleft)def move_random(self):d = random.choice([-1, 1])x, y = self.grid_pos如果 random.randint(0, 2):x += d别的:y += dself.update_pos((x, y))定义更新(自我,事件,dt):self.timeout -= dt如果 self.timeout <= 0:self.timeout = 1000self.move_random()def get_grid_rect(pos):x, y = 位置返回查找[y][x]def create_grid():冲浪 = pygame.Surface((TILESIZE * GRID_W, TILESIZE * GRID_H))surf.set_colorkey((2, 2, 2))冲浪.fill((2, 2, 2))网格 = []对于范围内的 y(GRID_H):行 = []对于范围内的 x(GRID_W):r = pygame.Rect(x * TILESIZE, y * TILESIZE, TILESIZE, TILESIZE)line.append(r)pygame.draw.rect(冲浪,pygame.Color('灰色'),r,1)grid.append(行)返回网格,冲浪定义主():screen = pygame.display.set_mode((TILESIZE * GRID_W, TILESIZE * GRID_H))DT,时钟 = 0,pygame.time.Clock()网格,grid_surf = create_grid()全局查找查找 = 网格精灵 = pygame.sprite.Group(Actor((9, 6)))为真:事件 = pygame.event.get()对于事件中的 e:如果 e.type == pygame.QUIT:返回sprites.update(事件,dt)screen.fill((30, 30, 30))screen.blit(grid_surf, (0, 0))sprites.draw(屏幕)pygame.display.flip()dt = 时钟.tick(60)如果 __name__ == '__main__':主要的()
<小时>第 4 步:平滑移动
当我们想要移动时,我们设置一个 target_grid_pos
,而不是总是绘制位于图块中心的 Actor.每一帧,我们都会稍微移动 Actor,直到到达我们的目标图块.我们使用 pygame 的 Vector2
类和它的 lerp
和 distance_to
方法.
导入pygame随机导入瓷砖尺寸 = 32GRID_W, GRID_H = (20, 15)查找 = 无类演员(pygame.sprite.Sprite):def __init__(self, grid_pos):super().__init__()self.image = pygame.Surface((TILESIZE//2, TILESIZE//2))self.rect = self.image.get_rect()self.pos = pygame.Vector2()self.update_pos(grid_pos)self.image.fill(pygame.Color('dodgerblue'))self.timeout = 1000def update_pos(self, grid_pos):#self.target_pos = 无self.target_grid_pos = 无self.grid_pos = grid_posself.rect.center = get_grid_rect(grid_pos).centerself.pos = pygame.Vector2(self.rect.center)def move_random(self):d = random.choice([-1, 1])x, y = self.grid_pos如果 random.randint(0, 2):x += d别的:y += dself.target_pos = pygame.Vector2(get_grid_rect((x, y)).center)self.target_grid_pos = (x, y)定义更新(自我,事件,dt):self.timeout -= dt如果 self.timeout <= 0:self.timeout = 1000self.move_random()如果 self.target_grid_pos:self.pos = self.pos.lerp(self.target_pos, 0.1)如果 self.pos.distance_to(self.target_pos) <1:self.update_pos(self.target_grid_pos)self.rect.center = self.posdef get_grid_rect(pos):x, y = 位置返回查找[y][x]def create_grid():冲浪 = pygame.Surface((TILESIZE * GRID_W, TILESIZE * GRID_H))surf.set_colorkey((2, 2, 2))冲浪.fill((2, 2, 2))网格 = []对于范围内的 y(GRID_H):行 = []对于范围内的 x(GRID_W):r = pygame.Rect(x * TILESIZE, y * TILESIZE, TILESIZE, TILESIZE)line.append(r)pygame.draw.rect(冲浪,pygame.Color('灰色'),r,1)grid.append(行)返回网格,冲浪定义主():screen = pygame.display.set_mode((TILESIZE * GRID_W, TILESIZE * GRID_H))DT,时钟 = 0,pygame.time.Clock()网格,grid_surf = create_grid()全局查找查找 = 网格精灵 = pygame.sprite.Group(Actor((9, 6)))为真:事件 = pygame.event.get()对于事件中的 e:如果 e.type == pygame.QUIT:返回sprites.update(事件,dt)screen.fill((30, 30, 30))screen.blit(grid_surf, (0, 0))sprites.draw(屏幕)pygame.display.flip()dt = 时钟.tick(60)如果 __name__ == '__main__':主要的()
<小时>第五步:添加效果
每 300 毫秒,我们创建一个 Actor 图像的副本,在 Actor 的位置对其进行 blit,并确保在 200 毫秒后将其删除.在真实游戏中,您可能希望缓存图像或使用预渲染的图像.
我将 Group
切换为 LayeredUpdates
以便我们可以确保原始图像始终绘制在阴影"上方.
我还添加了一个图像(来自
Since character movement is grid based, characters look a bit odd when going from square to square as they just appear from one square onto another. To make the movement feel more natural, I wanted to add "afterimages" so that there would be a simulation of smooth movement.
Demonstrational image: Since my code has characters moving directly onto the next square, I don't know how to blit sprites in between.
if IDO.get_key(pygame.K_RIGHT):
if PhaseFocus == 0 or PhaseFocus == 2:
Reticlex +=1
if Currently_Selected != 0 and Currently_Selected.Phase == 2:
if Currently_Selected.x != Reticlex:
Currently_Selected.x = Reticlex
if Currently_Selected.x != Reticley:
Currently_Selected.y = Reticley
if IDO.get_key(pygame.K_LEFT):
if PhaseFocus == 0 or PhaseFocus == 2:
Reticlex -=1
if Currently_Selected != 0 and Currently_Selected.Phase == 2:
if Currently_Selected.x != Reticlex:
Currently_Selected.x = Reticlex
if Currently_Selected.x != Reticley:
Currently_Selected.y = Reticley
When the currently selected character is in Phase 2 (carried around) they should have these afterimages.
Let's see how we can do this.
Step 1: Basic setup
We start with an "empty" pygame game, like this:
import pygame
def main():
screen = pygame.display.set_mode((640, 480))
clock = pygame.time.Clock()
while True:
events = pygame.event.get()
for e in events:
if e.type == pygame.QUIT:
return
screen.fill((30, 30, 30))
pygame.display.flip()
clock.tick(60)
if __name__ == '__main__':
main()
We have a Clock
, a single game loop and handle the QUIT
event. I always store the events from event.get()
in a variable in case I want to iterate over them again, e.g. when a Sprite
wants to listen for an event. Always call event.get()
only once per frame!
Step 2: A grid
We want a grid based game, so let's draw a grid. Also, we store a bunch of Rect
s in a list so it will be easy for us to lookup the screen coordinates of an object. We want to center objects in their tile, so using the Rect
class will do the dirty work for us.
import pygame
TILESIZE = 32
GRID_W, GRID_H = (20, 15)
def create_grid():
surf = pygame.Surface((TILESIZE * GRID_W, TILESIZE * GRID_H))
surf.set_colorkey((2, 2, 2))
surf.fill((2, 2, 2))
grid = []
for y in range(GRID_H):
line = []
for x in range(GRID_W):
r = pygame.Rect(x * TILESIZE, y * TILESIZE, TILESIZE, TILESIZE)
line.append(r)
pygame.draw.rect(surf, pygame.Color('grey'), r, 1)
grid.append(line)
return grid, surf
def main():
screen = pygame.display.set_mode((TILESIZE * GRID_W, TILESIZE * GRID_H))
clock = pygame.time.Clock()
grid, grid_surf = create_grid()
while True:
events = pygame.event.get()
for e in events:
if e.type == pygame.QUIT:
return
screen.fill((30, 30, 30))
screen.blit(grid_surf, (0, 0))
pygame.display.flip()
clock.tick(60)
Step 3: Something's moving on the grid
We now create an actor that travels on this grid. In this case it's a simple Sprite
that moves every second.
import pygame
import random
TILESIZE = 32
GRID_W, GRID_H = (20, 15)
LOOKUP = None
class Actor(pygame.sprite.Sprite):
def __init__(self, grid_pos):
super().__init__()
self.image = pygame.Surface((TILESIZE // 2, TILESIZE // 2))
self.rect = self.image.get_rect()
self.pos = pygame.Vector2()
self.update_pos(grid_pos)
self.image.fill(pygame.Color('dodgerblue'))
self.timeout = 1000
def update_pos(self, grid_pos):
self.grid_pos = grid_pos
self.rect.center = get_grid_rect(grid_pos).center
self.pos = pygame.Vector2(self.rect.topleft)
def move_random(self):
d = random.choice([-1, 1])
x, y = self.grid_pos
if random.randint(0, 2):
x += d
else:
y += d
self.update_pos((x, y))
def update(self, events, dt):
self.timeout -= dt
if self.timeout <= 0:
self.timeout = 1000
self.move_random()
def get_grid_rect(pos):
x, y = pos
return LOOKUP[y][x]
def create_grid():
surf = pygame.Surface((TILESIZE * GRID_W, TILESIZE * GRID_H))
surf.set_colorkey((2, 2, 2))
surf.fill((2, 2, 2))
grid = []
for y in range(GRID_H):
line = []
for x in range(GRID_W):
r = pygame.Rect(x * TILESIZE, y * TILESIZE, TILESIZE, TILESIZE)
line.append(r)
pygame.draw.rect(surf, pygame.Color('grey'), r, 1)
grid.append(line)
return grid, surf
def main():
screen = pygame.display.set_mode((TILESIZE * GRID_W, TILESIZE * GRID_H))
dt, clock = 0, pygame.time.Clock()
grid, grid_surf = create_grid()
global LOOKUP
LOOKUP = grid
sprites = pygame.sprite.Group(Actor((9, 6)))
while True:
events = pygame.event.get()
for e in events:
if e.type == pygame.QUIT:
return
sprites.update(events, dt)
screen.fill((30, 30, 30))
screen.blit(grid_surf, (0, 0))
sprites.draw(screen)
pygame.display.flip()
dt = clock.tick(60)
if __name__ == '__main__':
main()
Step 4: Smooth movement
Instead of always drawing the Actor that the center of the tiles, we set a target_grid_pos
when we want to move. Each frame, we move the Actor a little bit until we reached our target tile. We use pygame's Vector2
class and it's lerp
and distance_to
methods.
import pygame
import random
TILESIZE = 32
GRID_W, GRID_H = (20, 15)
LOOKUP = None
class Actor(pygame.sprite.Sprite):
def __init__(self, grid_pos):
super().__init__()
self.image = pygame.Surface((TILESIZE // 2, TILESIZE // 2))
self.rect = self.image.get_rect()
self.pos = pygame.Vector2()
self.update_pos(grid_pos)
self.image.fill(pygame.Color('dodgerblue'))
self.timeout = 1000
def update_pos(self, grid_pos):#
self.target_pos = None
self.target_grid_pos = None
self.grid_pos = grid_pos
self.rect.center = get_grid_rect(grid_pos).center
self.pos = pygame.Vector2(self.rect.center)
def move_random(self):
d = random.choice([-1, 1])
x, y = self.grid_pos
if random.randint(0, 2):
x += d
else:
y += d
self.target_pos = pygame.Vector2(get_grid_rect((x, y)).center)
self.target_grid_pos = (x, y)
def update(self, events, dt):
self.timeout -= dt
if self.timeout <= 0:
self.timeout = 1000
self.move_random()
if self.target_grid_pos:
self.pos = self.pos.lerp(self.target_pos, 0.1)
if self.pos.distance_to(self.target_pos) < 1:
self.update_pos(self.target_grid_pos)
self.rect.center = self.pos
def get_grid_rect(pos):
x, y = pos
return LOOKUP[y][x]
def create_grid():
surf = pygame.Surface((TILESIZE * GRID_W, TILESIZE * GRID_H))
surf.set_colorkey((2, 2, 2))
surf.fill((2, 2, 2))
grid = []
for y in range(GRID_H):
line = []
for x in range(GRID_W):
r = pygame.Rect(x * TILESIZE, y * TILESIZE, TILESIZE, TILESIZE)
line.append(r)
pygame.draw.rect(surf, pygame.Color('grey'), r, 1)
grid.append(line)
return grid, surf
def main():
screen = pygame.display.set_mode((TILESIZE * GRID_W, TILESIZE * GRID_H))
dt, clock = 0, pygame.time.Clock()
grid, grid_surf = create_grid()
global LOOKUP
LOOKUP = grid
sprites = pygame.sprite.Group(Actor((9, 6)))
while True:
events = pygame.event.get()
for e in events:
if e.type == pygame.QUIT:
return
sprites.update(events, dt)
screen.fill((30, 30, 30))
screen.blit(grid_surf, (0, 0))
sprites.draw(screen)
pygame.display.flip()
dt = clock.tick(60)
if __name__ == '__main__':
main()
Step 5: Adding the effect
Every 300 ms, we create a copy of the Actor's image, blit it at the Actor's position, and make sure to delete it after 200ms. In a real game, you probably want to cache the images or use pre-rendered ones.
I switched the Group
for LayeredUpdates
so we can make sure the original images is always drawn above the "shadows".
I also added an image (from rltiles) instead of a simple rect so it looks nicer in this demo.
import pygame
import random
import gzip
import base64
TILESIZE = 64
GRID_W, GRID_H = (10, 7)
LOOKUP = None
class Shadow(pygame.sprite.Sprite):
def __init__(self, source):
super().__init__()
self._layer = 5
self.image = source.image.copy().convert_alpha()
self.image.fill((0, 0, 200, 100), special_flags=pygame.BLEND_ADD)
self.rect = source.rect.copy()
self.timeout = 200
def update(self, events, dt):
self.timeout -= dt
if self.timeout <= 0:
self.kill()
class Actor(pygame.sprite.Sprite):
def __init__(self, grid_pos):
super().__init__()
self._layer = 10
data, size = gzip.decompress(base64.b64decode(HYDRA)), (64, 64)
self.image = pygame.image.fromstring(data, size, "RGB")
self.image.set_colorkey((71, 108, 108))
self.rect = self.image.get_rect()
self.pos = pygame.Vector2()
self.update_pos(grid_pos)
self.timeout = 1000
self.shadow_timeout = 100
def update_pos(self, grid_pos):#
self.target_pos = None
self.target_grid_pos = None
self.grid_pos = grid_pos
self.rect.center = get_grid_rect(grid_pos).center
self.pos = pygame.Vector2(self.rect.center)
def move_random(self):
d = random.choice([-1, 1])
x, y = self.grid_pos
if random.randint(0, 2):
x += d
else:
y += d
self.target_pos = pygame.Vector2(get_grid_rect((x, y)).center)
self.target_grid_pos = (x, y)
def update(self, events, dt):
self.timeout -= dt
if self.timeout <= 0:
self.timeout = 1000
self.move_random()
if self.target_grid_pos:
self.shadow_timeout -= dt
if self.shadow_timeout <= 0:
self.shadow_timeout = 100
self.groups()[0].add(Shadow(self))
self.pos = self.pos.lerp(self.target_pos, 0.1)
if self.pos.distance_to(self.target_pos) < 1:
self.update_pos(self.target_grid_pos)
self.rect.center = self.pos
def get_grid_rect(pos):
x, y = pos
return LOOKUP[y][x]
def create_grid():
surf = pygame.Surface((TILESIZE * GRID_W, TILESIZE * GRID_H))
surf.set_colorkey((2, 2, 2))
surf.fill((2, 2, 2))
grid = []
for y in range(GRID_H):
line = []
for x in range(GRID_W):
r = pygame.Rect(x * TILESIZE, y * TILESIZE, TILESIZE, TILESIZE)
line.append(r)
pygame.draw.rect(surf, pygame.Color('grey'), r, 1)
grid.append(line)
return grid, surf
def main():
screen = pygame.display.set_mode((TILESIZE * GRID_W, TILESIZE * GRID_H))
dt, clock = 0, pygame.time.Clock()
grid, grid_surf = create_grid()
global LOOKUP
LOOKUP = grid
sprites = pygame.sprite.LayeredUpdates(Actor((4, 3)))
while True:
events = pygame.event.get()
for e in events:
if e.type == pygame.QUIT:
return
sprites.update(events, dt)
screen.fill((30, 30, 30))
screen.blit(grid_surf, (0, 0))
sprites.draw(screen)
pygame.display.flip()
dt = clock.tick(60)
HYDRA = 'H4sIAEVFLF0C/+16Z2xk15Xmea8CK5LFKrJYOeecc85VJItkkaxizjl0ZOeWWq2WrNCSW61kW5IlB8lKli3ZLdnWjlfQAl57vTuDhWeA3QHs/THwzGCwwGLmhweY/bXnkrJ2VyPbrVYL2B9LHBSq2Y/vfffc757zffe+6t5e9YuL3d3y9nZhbQ2jsrNT2d3949dXDq/Pr64eXV/eIn+b21jLHtvKHdvMra8W19cq23/6Pnct9vcz8wvuXN6VzmQXFhHSHxkpfpa3d9Kzc85U2lMoFlZX0zOzzlxW20yrrrXV903qinFPqZRfWq4dO/ZFoMW0FDc2MgsLmfn50uYmfkfMvtFBZS4gS3sCY0OZufnS1tan/+3eHv5Jem7O06zL0l5VLhSeHPMWSwqziZ82sR+rs24O8YdcqmI42Grmlpbw4rs5C0e3wmzPzTtjSXsknltcSk5N20IRadbDP5nlnsnJU15HMom//yh7n3j6/n5qesaaSkgLXu65gmA/o4i6FUqtuL+PG9XRDxTh22P004P8YxlZzOmIJlJzc3cz83t7hfX15My0u1mTl4IDJb93dBCnXqFU88I65oNl+mtN3kxAVg15m/XUzExxfb3yf98BBxVvjavdDl7SwLhRZ3y5zm37hV5Nt7KfH9LSV/Lw+jj8ZI71YJnvUmpN1kSnU9vfv1v48enJzpQ5GulLO7gX8pwLhf6Ec0ClEgt7eAENA5/+6jj99RHuuXxf1GaNRFPT09WPOXw4EbXjx+MTkyqnnRvR0g+X4eUW9fI4+0RC4FYJXCrGPTmC/6cLrIcqfLtcqzfj4+rHj98t/Hir6FhLaTFzgkr68Sr1fJM95+MFNd1iEQKgL2TgzUl8OuNGjeOSq02WxMRE7cSJj5mTX11LdKZwjcv0Or5Vzp73E8K8OUk90WDNBdnTfupmA77XhndnGNerXWXLQMjubpQxCTiPdwt/bLylstt4bgXzQpb6epN6aYR1Ji3waviY/3tzBP+PZhmP1bgBtdphj463cPWRComxvY3/NAR8/WpVr1zarernu1VdIw64N8d4usZ7ocF/dYR+uw0/mIY3JqmnGtSZJKflkYZs1lAkNTt7d/CfOBEbH1dbrXxNH2fUxbyQhm+MwBMN5nKEuRKhnh6CtzvwzjT9RJ016uhLOW3lLF6fX1nJraxER8csuYTIp+tyyZA8vIyJW7OzV0PwUEX13WrtP+Wr/7ko/uEIvDqB+OHrTXisTC/6BA6V2myNdzqfHzzmEDMZHhtVOW0CuVhgU3ArVupsmvlUVfjKkPD7LcatDvyQZA+eHYR7M+wpr9hnNDjd0VYrMt7SeF2ioJHZsMKsm9oKUfdk4bkmhRe/NVP49/nX/lbz1q+lmddCvBdq9A+n4LUJuFFlLPi6XRqt1Z6Ymvr8+LOLi8H6oLGU7B0KsMfdXbN+9rE4PF7Tfa+88JfxuV8l1O804Nvj8GabTMrjZXopwHcoB6RycyhoyMd6cnZ2wwYzblj2wUYA7knDW20y3q+NDd8K/vzve/72H5lP/lLRej/Y/8EEhfP43DBjK9zt1Wotts+DnxD4sN1HMfMGoyBmYJ5Lw3da8M4UvD8HP1ks/3nxP/yT5Bd/I6i84mM9UaV+0CGr4IkacynAcyhFAmGPtI/v1zI3w3AiBusBmHDAkBmW/fDNUXhpBI4lazcMH/wX3r/8T/iHf2a+/vdq1y+b9HvTSCT6TFIYNmistli7fWfd6gg5Zt5bLutKse5WkLkVpe4vwPNHVJ+Cp4eq3w388u8E/+N39Mu/kq596NZ+OEr/YApeHGHsxXhetVDex0kbGZNu2AzCqg8m7VAzQtkA43a4mIb783AmabjkmrmhuPiq9NQHlvFfJPr/HSlB8J1xeKjEXgiKSm59OnKH+Hd2cmur4daY0mPjF6w0In+mAQ+X4HqZTME3RuF0Knfd/O5fCP7pd9Rv/pH7+t+pQ/9xkPHeFLw+wbiQ4SWNfKzqywE4HYPVw8yXDXRO21U2cIctFHJpKwhnk7gcGCMW5qSNeTVLf6NJwGMVQvxfHYIHS8yVoMChvLNum1lYdBXyynRAMBtmIG1wYX5liOC/Lwf35+BKFs6mFec9jfuUq8/K5t511n6WkX44Sb03gwuQerTM2Awzpjywfpj5MRtUjZDTSuqmxIIntRUULXth3kNWxKgVSgbIGqDuhI0YPN8k4JFd3x7DT8alLN+rvjNVmex0tF63wKdlYm96tgHPD2NZgMsZ5n5EsBkUbgaYJ2L0up/TNPImzNwLsa5nazQ2oHc68EoLvjYEj1XgUhrWAjBuQ4Ssgl5Y1Nub1uF579ByQDrhZNTMVEpLJdSQ1kJcAwEtlO1wkIbHq/DcELyG1WASexk3a7wDnYbVPjU1pXHY+U4F6exfHYSnagTPglcwZvPPuYMLnp62E4YtUNBDUg8ZK3SC8NQgqgj41ihqA1JLkW9LPiji/2p6y4bYpL00YgtGNSa7TGSW8vT9PJWkyyqlYmoyBTULVKyQtsJCCG7W4Y0JcpPrVcas57MyB1t2embGM1gdyHq7Gnb6Sg4eLcOFVNdmcGDK5Wha04PWSNkkjmkY+Oi0BhJaCOogZ4XdOHypTKiLC+T7HTJlK35u3SRvWpxNa2HImstb7T6rxmZV26xyvV4sFvMVYpZTRuMUDCJ+M9iUkLGQ+zxaIYzFgZxPfmbmTE1ZAsG+kIW3EaeuFeDBAi406DhlbWdjKzi97A+E1Ep1n0gu5pikVFRFSgr2ppoNkmaY8MFjVXh5jLDoyTq9E1YteFvHIyOzHq9XaXaag7UKqm7UZp5CQSZTdvf0CKS9XZYB5BJkteCWgUsJHi2M++DhCukmzzQ+q87EpqnU6Dh2KQNFwotNUsqORyVjNs+wZWzG02n7vRGHXGeQiMQCqZhtG6DTOkKkugVsCgjrYC0CD5RI9p5t0PdklceiY5vhWs2ilvXK9Ob4ZBsrGwps50hVUvEK/JruAYlAImLbZHRYCUlcCEpQ9YNfB6sReKiMnfqz4ic6R2/kOeWkW31tGPH3nUlk1vzFIas/pLV7LcFK0VMqyky6bnmfcKCXa5QSImWQRUrwYvY0MOqG+wrwwjASgHeQ1KQMGuOAeKBX6bKhCIm320a/v6/qYz9aZR2kBWEdEbEKCcchp6tmKBvJfdwKiBth0o+puBP8ut/jf47gV19Mz5yKt1sOi1neK1PakglbsyQZDQlSpm5FX7eoB4nEDCgppHFYDTrMngam/XBPHvGjtObZFXyDjFsw942FLdWsPRrvVyq4eTP1YpN6rtm1GRUkjEKNVKjuY8d0jLyB1ISiEap2aszDWAndUf4NPIeMeSYFXxmEawXNPZmFq7mZ5YDdpewWivqU8t6cg3W9xrqU48cM3ZJegbKPa5fTdTNgRFTgURACDLrhUo55KimwKlBzYjFkP1oXlVx9KoUIPWPKSD+CrXCcemWcdW+eH9SKJL0i1QDfq2EgFdcC1NkUaycmTJrvBL/ByLMNMHej8HAR9iPi07HY0/XY+YwmqBVyBN29In5cTz1Rp74yzDqd5oy6u7JGdlxLNSxkIVQNZBSjLqrjZ077uFWrEEdXMFPPDOKiZp1Mcss2oV6KLpLG4oB66cezjCcbgrhRKleafH51zC9ImJllE2fS0zsZ0uUid4gfKbEUgIMEtOwovajXxlk3G/ycuUcgJAkPaxn35UmR+fEcvDJOLkOFgE22ZqImHdQxHHiJeTHDj+hFEnFvjwiZRq5/cwI1KvN6jR/Vc3Mm6kFiweC9GcbNhiBl1thsqPYDgw250SAU9fTKBrQeV7zTvtP8y5h7MXiI5B/Op1DwUC+N4kRzJ71Cp1IQ0TGwL3yHOFbSqvCCScRv6q6bHdMu65xXMukRNQOmcsqdy2MYKsmeYR9zI0w9UqGerLPPZ1jXimTgqAO/16GeHmSvhHrLHkM6ak+nXLkchrtQCA0PowO6U/7LmQcpUgav5kh8uUoU73fbjKcavIaDV7DQmD3sU+/PE999IUlPuzhDFt2gud5xFqsWk0Ojcbnik5Olzc382pqvOShzmji4PI/H2F+ti2+N9fy0zXh/lqg1NCyoN+4vMOd9ApNM73Gj7a383jR91i2go/qv0hm4ZiljKwLX8kS3z7lh3g3HCSuwK1HXyvBojTwX1Q5qHvTCV3PiE9HMbrg05QpFVJ6g1V/IxMYnCiurmbl5VyKlrEUFuyl4pMJ+qen8N5WL/9Wz8+d+2csleHGMuJ5XW7jQ0HPxDVKd25Wena3d6c5DbX8/0emYfAGJx8Bp+2iUvkMWaJhgwg5bIVSevBfqxnfrpg+Gee9OwPfbqJbhhSb9UEl2LjW8F21OeB1eo8nvCzTq2GcTUx3vSEMWd/HmQzRC/fF81/cnCh9mfvoP/e/+RtJ+w6F/pcC9NUlYdKPKXAkITAN6tzs9c+f4qx/pn1lPozIQdnS5FXRYRcA/UIAXR6k3xx0f1O/7tevqX9n038oRufvWFFmD18uCnbClYA6kPNHhur9StfiDWqNVa7XJcj7umRyNV/7ZArwzw7lZqr7o+At0Pf/M+NVvOQ/+pdXxs2G4NY9JYO7HDvG7MrPz9ZMnP2UH7/aisLaemprxDFUHiv6usoVuu+BsAr41Bm9P02+MJ97P3vrtwM9/K9y5ZfK/kRL+ZBJuzSKpiGN1q1QWU6BScTXKAyk3L6QTpM0czPzzI4Rm30V3P8S6lAjcb3vmx73v/5Xgw7/pufbXDvvPm/DePNk8vJzl5EzyuMc/WM/MzRU3NiqfXTnXjh9LTs1YfcH+qJ13rkC/MALfPBRjKGifG6av5VJPOT/4jfB3/0L9+r93PfnXRscv8OmLxDMepNBwifv7FUpNX8rF3U4gqeibderIkqAoRctzkKDOJXoOAu59bfx+U/qNsP39qvDfTh0W4RaWCPpknD/mlbpNtnCU7Px8pv3D3d3i+kaqPeUcLPdlnMwpN4XiB8vL9zpE0j/dgKt56kTUccn68NuS93/F/9lve67/N5v9lyPwo0V8On2tyK3ZuC4FVyNhlc3Ul4qktmB1/ckc8VMoYjeCsOiF7RDx7yUzDDphKwmPDsLrOIPTBP8LTXhukLkd5ur61Hpzot2+zV30o32G4uZmfKpjCoX66gHOlRKFDvfFEeJc7svCqRi9F6H2o9TpOP9UwLpnCF0wRL4etLxT5v9ZB340RwopSp1zaXotxBh30AgVbfKrE2STBGlzo0pdSDI2gowpFzVihYoR8jpI6SGoJwrt4TJxiyiV0bC83WHek+M5lRqzJTYxcZv1EyttYW0tOt6yDhbENR97O0Yyho9+ug5XMnAiylr19046RFNOFppZzGH10CvNh+FKCb6DIKfglTGitNGw3KzBvRm4JwMP5sl3bBnoPQ8S3I2AasWvatkFMQ3tlRGdjK4HlWrOAoshuJyHZw69261pGmtswdTvNTvKOWwfCOx28o+GyxgK9qbt7PtK9EuH9hkJcyEFe2H6TEK8HfKOWu1lYzdaFfR6OR0kteDVwLAbHijDN0cITiTA21NkmTw/RD1UYp5OsHHg92aZZxLMtlMxastPu/KDVo1TzTPIGChTiwYYs0PVChEDVBxwJU/4g8+9XkGmsUsWictg9gfQKdwOfqz5anS7Xg2NmhNb7SMlksNTcfZOuG89aJ/3VCbsiZJRgs/1qojdRqkc1UMBba8fTqXhiQZZpG91iPN6vNx9OeM4FY8ci3iORx0bQcekw1szJbL6eMLqjPk1QZ/QrWXirYbNRCc7lSQVk144yJBZeKoODxXoWY/QodRYbLez//kRfruNb5LRTRsx3Ss+sj9zJiE4EXOPWkuDJjRMpSHbgEsDejlENWQnquOCmhUsKoia4GIOcNZwyeDYj0UM26G5g+TZM8mVjcDMgmduwVuqmDUaicpiiYyOIlGVFrNAL6XReybVEJSDbQCMCsjZ4IEiIeG3RumDlDCo19ze/u3/xm8coIesaLphNwwHceQP+2RM2rQ4ysbqoDkxbJM0HdByw6yHKApsaiR7CvCoYdAF23G4UScJfKQkPhELjruKGWMspguFNOGw1mqVdQs5Uq0uMjaWW17x1+v6WKjbrmb6ETY6Xx0xXAEtDLlgPwlfGULXIwzqbh9/cnpG7/P22DQsTCnm/3Sc8OdiGhcv1bKLS/pQRhsYscn3I7wrWcHljOB4VNCyc/I6OqoElwwscoib4VwGbtRQ8rH24wKfulcgEIl6joLH4wFAj0zmrddzq6vpxUVfo64ymLqdalbNAliUEshMBVhVUHPCtSL7dEocsRhdnuT09O3UH5SImBlLPt3rN3VlDNS8h6i1vTCZiK2QaM4dKBtKI9bB49HmtfzIlezIxdTofiS25BON24nd8ykpt7Ira+JUrNyGgxPWsPuFTAaDxWIfBYPBQPxsLrdPo1E67Eq73RAIeIslczbRGzQzw0qqekjIzSi9GGQN2SUlj62Wj7Va+dXV26z/KHTRLJgC/r6AGWFQbSfZ4tsIwImYcDtoblqKLfvKbujMpdTBBRJnzydbx6OytQCM2KiwimmQ8GS9PEkPX9LTJeTRTAL4kz8UReNImEwcmNRgQNKiVjcEA70uXVfZSs956bMp7nJEErZaImHUfuXt7T92oPyvz3bX15PtKUcp3+cysLxyetQOa36sZsxVP7/jtE+7Wiu+va3Q9mHsboWG1gPSVT80bV0OOVcsZHO6MOcMmkFTNPypH7FKhdxArZWYbNsLWYnHxHHIOCG1NOt1NyqpzuHJ12fRD0ezUNndw7RYIpF+l4lXsNLjdoocOgQxlBvB4c3gzmZoa4sEDqGxGezfCcK4k2eR8Xl85qfm/PCH2dUl7OvrVShEcvlR6AOB1Pz80S49PtEciSitZqXVgv4rvbBwhOfO9GdpYyMzv+Cr1+R+GyeoYqwcuuALKc351PT55OXzqfOHcel8sn0+KbuUggU/z6YQdHEx838IP65cZz4fnZyMtFrhVgs/kzMzqFg+2rHc2EjNzGK3xUDl+YdO8G9z/5C8ITA7723UZDEXJ2ukTyXIWcPljPpccup84vL55PnDwC+diykZWsv9WFfBxNP3s5D29Kczp1+nS05NDR4c1E+cOIpPaDP8Z/34cYyj39/BmwMfH3fG2pOmcEgStHA7fvp0Ah4rU4+UGKfi6k3kT2BnK7i5GdzYDK6vByp74T7UGBfT9G6ENebEIXRxOTRFfQz7aLXi54DRiJX8Lp5Hfyp+FEvxsXFbNS/OuZhNG3X8cP/hRpX/SEl3kEjthGd3Qvu74Z2d0OJWsLbkda0HBMcOdycuZRibYYFTyRPyGb+fAhaHI1Yq5WYzgrckEsjqL+6tEsw81s9oe1Lv8YizDvaJJFwvEdpczaNzVF3NjV1KHzuXPDhHmH/6XHL6RMyIRWnJS2H92Y3AyThz0c+3ybkCHsk/1kkmE1erp1pNzc2hE8kuLZW3tr6gt3rwtvmVlVCzaconRRkHu+WmcME+XCTb/qhnvlxVXs0398JrKz6M+TX/8KovNO/txqY56SBbW5sh5oSzK6nnyEWsLjZmnsPnD5hM9mwWKwypgXfvNYz/o06SnB8FVrBku6N1OYVuNWM1BLhgN0Mow+DLZXipicJe9EA+MOko5LX5vDZY0EnyWjqtgaCMbLidiDG2IjyvSsDH+sn8uLYHR0Yq+/tfRMLxnrnlZV+1Zk+lbImEPZnET0M8LErYWBUzhebuVBwup4kBQQ+FcTXffzKWmXaNjlpHRqzphqkvo4WYCsIKcph7Oo74+S6lkC/gcrksFusIf2h0FNl+t/AftYnC+np+ZRXBR8Zbaq+zVyPvUQ+INAMitVTgUDKG7eR8fDUAJ2NE/9+sEv6fS6IEGlj2FaddnY6z3XYWh60yBO+XkSGMWvFieitMXkQZkHTLJdzebqQ/ipzw2NhdrDaYiuzhW2pGt8/kD2hifmHDze54WKtB9kqQNe1lzHhhLwIXkvBA/qNzwzkPOXdGFp2K85f95ozR61V5PEqLUyHR97PN/VRECQ0zim1qK8yc8bIn3MwJDzNjZPQKZQZzdGKi/vH7M58vsLDkFpf8I0OKOJoaVbdTw48ZmIsBIo8fr5BFei4F+1GsISTbXyqQT9T2yO1pF6wSeF0tZ49FLhaLenu7RaLubrGIr+mj0YUhf2bcKC2o41H22Zj4QkixbNH5exwBfWS4ihNdOuywnzOwNTtiCUXax1+J0QdJxnqYRpLjCkWRj+X9SvbwlNZOzvfbDmJMlrzkN+sBtOrUuJMZN3LMSp5YwuEIWEw2i8kSdAsFhgG6ZiYDRDu/5qd2gv2n3JUrytmLPas7zJFWty9utMbT6bvxDlu0M6lyOzDn2CXhS0UiZnZCsOAlj96PYIbpsomBOieiYoRVjKCSAMPpwNnZDHLHrdpYv80ldDr5Oh1XKGQxaCaXz+Uqxay0ntGwoF+jB63MYYtiXDO8KFhaZW5s0I0GS28UDBjMsYmJz48/PN/py3sZGT2MWEjGxm3E7yB16yb8QhcNHLuMvNWjlPAVEr5U1BXS0DsRuDeLWZUumYfXhGvrjJ1tutlkGQxcNovLwkLJZXMVveQMWi/F4Ov7xSax0SZw2HkuJ0+jYQsE2L+UuIrvCn5JwccMqmivjOGRMbxyhk/O8H8ULEs/RyLkszl8DrenR6RUaaUhG3fCRy34WKM2+Yi6ucBbW6d3dxA/02DgcPndIqm0T6VW6I1qk0Xz+1CbrAqjTX4YUp1JotZqPJ678vZUbKqtCrh7tDKhWtqtGfhECGQSjpDPYrPZHI5EqfSWK+56RRZx8W2KHoui3yIz2sU2p8jpFun0gp5eXs+AzJHLYXlBbIk/EPF2G6VyYmamcDfevkvPzTszWaPXZ3B7jB7vJ0LndCotFpRYMrPZGImgyiLv9CbTeofT6PYY3F6d26t1+TBUNqfCatWHQsnDnVWsyX8y7k793NrKraxkFxYyCwvZxcVPBP4Sq0QSVdbcXGZpCS8m9XZ5+V9fnJ6fxyszi4vFu/tm7/+P/7fjfwE2vbH0ADAAAA=='
if __name__ == '__main__':
main()
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