from collections import deque
from math import floor
from random import random
from time import time


class      lowerCamelCase    :
  """simple docstring"""







  def __init__(							self       :				Union[str, Any]      )     ->		Dict:
        SCREAMING_SNAKE_CASE_      =     {}







  def       __A   (							self       :				Union[str, Any]     ,   __magic_name__       :				str     ,   __magic_name__       :				List[Any]     ,   __magic_name__       :				Any=1      )     ->		Tuple:
        if self.graph.get(__magic_name__      ):
              if self.graph[u].count([w, v]      ) == 0:
                    self.graph[u].append([w, v]      )
        else:
              SCREAMING_SNAKE_CASE_      =     [[w, v]]
        if not self.graph.get(__magic_name__      ):
              SCREAMING_SNAKE_CASE_      =     []







  def       __A   (							self       :				Any      )     ->		Tuple:
        return list(self.graph      )







  def       __A   (							self       :				int     ,   __magic_name__       :				Any     ,   __magic_name__       :				Dict      )     ->		List[str]:
        if self.graph.get(__magic_name__      ):
              for _ in self.graph[u]:
                    if _[1] == v:
                          self.graph[u].remove(__magic_name__      )







  def       __A   (							self       :				Union[str, Any]     ,   __magic_name__       :				Dict=-2     ,   __magic_name__       :				int=-1      )     ->		int:
        if s == d:
              return []
        SCREAMING_SNAKE_CASE_      =     []
        SCREAMING_SNAKE_CASE_      =     []
        if s == -2:
              SCREAMING_SNAKE_CASE_      =     list(self.graph      )[0]
        stack.append(__magic_name__      )
        visited.append(__magic_name__      )
        SCREAMING_SNAKE_CASE_      =     s

        while True:
              # check if there is any non isolated nodes
              if len(self.graph[s]      ) != 0:
                    SCREAMING_SNAKE_CASE_      =     s
                    for node in self.graph[s]:
                          if visited.count(node[1]      ) < 1:
                                if node[1] == d:
                                      visited.append(__magic_name__      )
                                      return visited
                                else:
                                      stack.append(node[1]      )
                                      visited.append(node[1]      )
                                      SCREAMING_SNAKE_CASE_      =     node[1]
                                      break

            # check if all the children are visited
              if s == ss:
                    stack.pop()
                    if len(__magic_name__      ) != 0:
                          SCREAMING_SNAKE_CASE_      =     stack[len(__magic_name__      ) - 1]
              else:
                    SCREAMING_SNAKE_CASE_      =     ss

              # check if se have reached the starting point
              if len(__magic_name__      ) == 0:
                    return visited







  def       __A   (							self       :				Any     ,   __magic_name__       :				Optional[int]=-1      )     ->		str:
        if c == -1:
              SCREAMING_SNAKE_CASE_      =     floor(random() * 10_000      ) + 10
        for i in range(__magic_name__      ):
              # every vertex has max 100 edges
              for _ in range(floor(random() * 102      ) + 1      ):
                    SCREAMING_SNAKE_CASE_      =     floor(random() * c      ) + 1
                    if n != i:
                          self.add_pair(__magic_name__     ,   __magic_name__     ,   1      )







  def       __A   (							self       :				List[str]     ,   __magic_name__       :				str=-2      )     ->		List[str]:
        SCREAMING_SNAKE_CASE_      =     deque()
        SCREAMING_SNAKE_CASE_      =     []
        if s == -2:
              SCREAMING_SNAKE_CASE_      =     list(self.graph      )[0]
        d.append(__magic_name__      )
        visited.append(__magic_name__      )
        while d:
              SCREAMING_SNAKE_CASE_      =     d.popleft()
              if len(self.graph[s]      ) != 0:
                    for node in self.graph[s]:
                          if visited.count(node[1]      ) < 1:
                                d.append(node[1]      )
                                visited.append(node[1]      )
        return visited







  def       __A   (							self       :				Optional[Any]     ,   __magic_name__       :				List[Any]      )     ->		Tuple:
        SCREAMING_SNAKE_CASE_      =     0
        for x in self.graph:
              for y in self.graph[x]:
                    if y[1] == u:
                          count += 1
        return count







  def       __A   (							self       :				Any     ,   __magic_name__       :				Union[str, Any]      )     ->		List[str]:
        return len(self.graph[u]      )







  def       __A   (							self       :				Optional[int]     ,   __magic_name__       :				Any=-2      )     ->		List[Any]:
        SCREAMING_SNAKE_CASE_      =     []
        SCREAMING_SNAKE_CASE_      =     []
        if s == -2:
              SCREAMING_SNAKE_CASE_      =     list(self.graph      )[0]
        stack.append(__magic_name__      )
        visited.append(__magic_name__      )
        SCREAMING_SNAKE_CASE_      =     s
        SCREAMING_SNAKE_CASE_      =     []

        while True:
              # check if there is any non isolated nodes
              if len(self.graph[s]      ) != 0:
                    SCREAMING_SNAKE_CASE_      =     s
                    for node in self.graph[s]:
                          if visited.count(node[1]      ) < 1:
                                stack.append(node[1]      )
                                visited.append(node[1]      )
                                SCREAMING_SNAKE_CASE_      =     node[1]
                                break

            # check if all the children are visited
              if s == ss:
                    sorted_nodes.append(stack.pop()      )
                    if len(__magic_name__      ) != 0:
                          SCREAMING_SNAKE_CASE_      =     stack[len(__magic_name__      ) - 1]
              else:
                    SCREAMING_SNAKE_CASE_      =     ss

              # check if se have reached the starting point
              if len(__magic_name__      ) == 0:
                    return sorted_nodes







  def       __A   (							self       :				Tuple      )     ->		List[Any]:
        SCREAMING_SNAKE_CASE_      =     []
        SCREAMING_SNAKE_CASE_      =     []
        SCREAMING_SNAKE_CASE_      =     list(self.graph      )[0]
        stack.append(__magic_name__      )
        visited.append(__magic_name__      )
        SCREAMING_SNAKE_CASE_      =     -2
        SCREAMING_SNAKE_CASE_      =     []
        SCREAMING_SNAKE_CASE_      =     s
        SCREAMING_SNAKE_CASE_      =     False
        SCREAMING_SNAKE_CASE_      =     set()

        while True:
              # check if there is any non isolated nodes
              if len(self.graph[s]      ) != 0:
                    SCREAMING_SNAKE_CASE_      =     s
                    for node in self.graph[s]:
                          if (
                              visited.count(node[1]      ) > 0
                              and node[1] != parent
                              and indirect_parents.count(node[1]      ) > 0
                              and not on_the_way_back
                          ):
                                SCREAMING_SNAKE_CASE_      =     len(__magic_name__      ) - 1
                                while len_stack >= 0:
                                      if stack[len_stack] == node[1]:
                                            anticipating_nodes.add(node[1]      )
                                            break
                                      else:
                                            anticipating_nodes.add(stack[len_stack]      )
                                            len_stack -= 1
                          if visited.count(node[1]      ) < 1:
                                stack.append(node[1]      )
                                visited.append(node[1]      )
                                SCREAMING_SNAKE_CASE_      =     node[1]
                                break

            # check if all the children are visited
              if s == ss:
                    stack.pop()
                    SCREAMING_SNAKE_CASE_      =     True
                    if len(__magic_name__      ) != 0:
                          SCREAMING_SNAKE_CASE_      =     stack[len(__magic_name__      ) - 1]
              else:
                    SCREAMING_SNAKE_CASE_      =     False
                    indirect_parents.append(__magic_name__      )
                    SCREAMING_SNAKE_CASE_      =     s
                    SCREAMING_SNAKE_CASE_      =     ss

              # check if se have reached the starting point
              if len(__magic_name__      ) == 0:
                    return list(__magic_name__      )







  def       __A   (							self       :				int      )     ->		Tuple:
        SCREAMING_SNAKE_CASE_      =     []
        SCREAMING_SNAKE_CASE_      =     []
        SCREAMING_SNAKE_CASE_      =     list(self.graph      )[0]
        stack.append(__magic_name__      )
        visited.append(__magic_name__      )
        SCREAMING_SNAKE_CASE_      =     -2
        SCREAMING_SNAKE_CASE_      =     []
        SCREAMING_SNAKE_CASE_      =     s
        SCREAMING_SNAKE_CASE_      =     False
        SCREAMING_SNAKE_CASE_      =     set()

        while True:
              # check if there is any non isolated nodes
              if len(self.graph[s]      ) != 0:
                    SCREAMING_SNAKE_CASE_      =     s
                    for node in self.graph[s]:
                          if (
                              visited.count(node[1]      ) > 0
                              and node[1] != parent
                              and indirect_parents.count(node[1]      ) > 0
                              and not on_the_way_back
                          ):
                                SCREAMING_SNAKE_CASE_      =     len(__magic_name__      ) - 1
                                while len_stack_minus_one >= 0:
                                      if stack[len_stack_minus_one] == node[1]:
                                            anticipating_nodes.add(node[1]      )
                                            break
                                      else:
                                            return True
                          if visited.count(node[1]      ) < 1:
                                stack.append(node[1]      )
                                visited.append(node[1]      )
                                SCREAMING_SNAKE_CASE_      =     node[1]
                                break

            # check if all the children are visited
              if s == ss:
                    stack.pop()
                    SCREAMING_SNAKE_CASE_      =     True
                    if len(__magic_name__      ) != 0:
                          SCREAMING_SNAKE_CASE_      =     stack[len(__magic_name__      ) - 1]
              else:
                    SCREAMING_SNAKE_CASE_      =     False
                    indirect_parents.append(__magic_name__      )
                    SCREAMING_SNAKE_CASE_      =     s
                    SCREAMING_SNAKE_CASE_      =     ss

              # check if se have reached the starting point
              if len(__magic_name__      ) == 0:
                    return False







  def       __A   (							self       :				Optional[int]     ,   __magic_name__       :				Tuple=-2     ,   __magic_name__       :				List[Any]=-1      )     ->		Any:
        SCREAMING_SNAKE_CASE_      =     time()
        self.dfs(__magic_name__     ,   __magic_name__      )
        SCREAMING_SNAKE_CASE_      =     time()
        return end - begin







  def       __A   (							self       :				Dict     ,   __magic_name__       :				List[str]=-2      )     ->		Any:
        SCREAMING_SNAKE_CASE_      =     time()
        self.bfs(__magic_name__      )
        SCREAMING_SNAKE_CASE_      =     time()
        return end - begin



class      lowerCamelCase    :
  """simple docstring"""







  def __init__(							self       :				Tuple      )     ->		Tuple:
        SCREAMING_SNAKE_CASE_      =     {}







  def       __A   (							self       :				int     ,   __magic_name__       :				List[Any]     ,   __magic_name__       :				Any     ,   __magic_name__       :				Tuple=1      )     ->		Tuple:
        # check if the u exists
        if self.graph.get(__magic_name__      ):
              # if there already is a edge
              if self.graph[u].count([w, v]      ) == 0:
                    self.graph[u].append([w, v]      )
        else:
              # if u does not exist
              SCREAMING_SNAKE_CASE_      =     [[w, v]]
        # add the other way
        if self.graph.get(__magic_name__      ):
              # if there already is a edge
              if self.graph[v].count([w, u]      ) == 0:
                    self.graph[v].append([w, u]      )
        else:
              # if u does not exist
              SCREAMING_SNAKE_CASE_      =     [[w, u]]







  def       __A   (							self       :				Dict     ,   __magic_name__       :				Union[str, Any]     ,   __magic_name__       :				List[Any]      )     ->		Tuple:
        if self.graph.get(__magic_name__      ):
              for _ in self.graph[u]:
                    if _[1] == v:
                          self.graph[u].remove(__magic_name__      )
        # the other way round
        if self.graph.get(__magic_name__      ):
              for _ in self.graph[v]:
                    if _[1] == u:
                          self.graph[v].remove(__magic_name__      )







  def       __A   (							self       :				Any     ,   __magic_name__       :				str=-2     ,   __magic_name__       :				Tuple=-1      )     ->		int:
        if s == d:
              return []
        SCREAMING_SNAKE_CASE_      =     []
        SCREAMING_SNAKE_CASE_      =     []
        if s == -2:
              SCREAMING_SNAKE_CASE_      =     list(self.graph      )[0]
        stack.append(__magic_name__      )
        visited.append(__magic_name__      )
        SCREAMING_SNAKE_CASE_      =     s

        while True:
              # check if there is any non isolated nodes
              if len(self.graph[s]      ) != 0:
                    SCREAMING_SNAKE_CASE_      =     s
                    for node in self.graph[s]:
                          if visited.count(node[1]      ) < 1:
                                if node[1] == d:
                                      visited.append(__magic_name__      )
                                      return visited
                                else:
                                      stack.append(node[1]      )
                                      visited.append(node[1]      )
                                      SCREAMING_SNAKE_CASE_      =     node[1]
                                      break

            # check if all the children are visited
              if s == ss:
                    stack.pop()
                    if len(__magic_name__      ) != 0:
                          SCREAMING_SNAKE_CASE_      =     stack[len(__magic_name__      ) - 1]
              else:
                    SCREAMING_SNAKE_CASE_      =     ss

              # check if se have reached the starting point
              if len(__magic_name__      ) == 0:
                    return visited







  def       __A   (							self       :				Dict     ,   __magic_name__       :				int=-1      )     ->		int:
        if c == -1:
              SCREAMING_SNAKE_CASE_      =     floor(random() * 10_000      ) + 10
        for i in range(__magic_name__      ):
              # every vertex has max 100 edges
              for _ in range(floor(random() * 102      ) + 1      ):
                    SCREAMING_SNAKE_CASE_      =     floor(random() * c      ) + 1
                    if n != i:
                          self.add_pair(__magic_name__     ,   __magic_name__     ,   1      )







  def       __A   (							self       :				Union[str, Any]     ,   __magic_name__       :				Optional[Any]=-2      )     ->		List[Any]:
        SCREAMING_SNAKE_CASE_      =     deque()
        SCREAMING_SNAKE_CASE_      =     []
        if s == -2:
              SCREAMING_SNAKE_CASE_      =     list(self.graph      )[0]
        d.append(__magic_name__      )
        visited.append(__magic_name__      )
        while d:
              SCREAMING_SNAKE_CASE_      =     d.popleft()
              if len(self.graph[s]      ) != 0:
                    for node in self.graph[s]:
                          if visited.count(node[1]      ) < 1:
                                d.append(node[1]      )
                                visited.append(node[1]      )
        return visited







  def       __A   (							self       :				List[str]     ,   __magic_name__       :				Union[str, Any]      )     ->		Optional[Any]:
        return len(self.graph[u]      )







  def       __A   (							self       :				List[str]      )     ->		Dict:
        SCREAMING_SNAKE_CASE_      =     []
        SCREAMING_SNAKE_CASE_      =     []
        SCREAMING_SNAKE_CASE_      =     list(self.graph      )[0]
        stack.append(__magic_name__      )
        visited.append(__magic_name__      )
        SCREAMING_SNAKE_CASE_      =     -2
        SCREAMING_SNAKE_CASE_      =     []
        SCREAMING_SNAKE_CASE_      =     s
        SCREAMING_SNAKE_CASE_      =     False
        SCREAMING_SNAKE_CASE_      =     set()

        while True:
              # check if there is any non isolated nodes
              if len(self.graph[s]      ) != 0:
                    SCREAMING_SNAKE_CASE_      =     s
                    for node in self.graph[s]:
                          if (
                              visited.count(node[1]      ) > 0
                              and node[1] != parent
                              and indirect_parents.count(node[1]      ) > 0
                              and not on_the_way_back
                          ):
                                SCREAMING_SNAKE_CASE_      =     len(__magic_name__      ) - 1
                                while len_stack >= 0:
                                      if stack[len_stack] == node[1]:
                                            anticipating_nodes.add(node[1]      )
                                            break
                                      else:
                                            anticipating_nodes.add(stack[len_stack]      )
                                            len_stack -= 1
                          if visited.count(node[1]      ) < 1:
                                stack.append(node[1]      )
                                visited.append(node[1]      )
                                SCREAMING_SNAKE_CASE_      =     node[1]
                                break

            # check if all the children are visited
              if s == ss:
                    stack.pop()
                    SCREAMING_SNAKE_CASE_      =     True
                    if len(__magic_name__      ) != 0:
                          SCREAMING_SNAKE_CASE_      =     stack[len(__magic_name__      ) - 1]
              else:
                    SCREAMING_SNAKE_CASE_      =     False
                    indirect_parents.append(__magic_name__      )
                    SCREAMING_SNAKE_CASE_      =     s
                    SCREAMING_SNAKE_CASE_      =     ss

              # check if se have reached the starting point
              if len(__magic_name__      ) == 0:
                    return list(__magic_name__      )







  def       __A   (							self       :				str      )     ->		Any:
        SCREAMING_SNAKE_CASE_      =     []
        SCREAMING_SNAKE_CASE_      =     []
        SCREAMING_SNAKE_CASE_      =     list(self.graph      )[0]
        stack.append(__magic_name__      )
        visited.append(__magic_name__      )
        SCREAMING_SNAKE_CASE_      =     -2
        SCREAMING_SNAKE_CASE_      =     []
        SCREAMING_SNAKE_CASE_      =     s
        SCREAMING_SNAKE_CASE_      =     False
        SCREAMING_SNAKE_CASE_      =     set()

        while True:
              # check if there is any non isolated nodes
              if len(self.graph[s]      ) != 0:
                    SCREAMING_SNAKE_CASE_      =     s
                    for node in self.graph[s]:
                          if (
                              visited.count(node[1]      ) > 0
                              and node[1] != parent
                              and indirect_parents.count(node[1]      ) > 0
                              and not on_the_way_back
                          ):
                                SCREAMING_SNAKE_CASE_      =     len(__magic_name__      ) - 1
                                while len_stack_minus_one >= 0:
                                      if stack[len_stack_minus_one] == node[1]:
                                            anticipating_nodes.add(node[1]      )
                                            break
                                      else:
                                            return True
                          if visited.count(node[1]      ) < 1:
                                stack.append(node[1]      )
                                visited.append(node[1]      )
                                SCREAMING_SNAKE_CASE_      =     node[1]
                                break

            # check if all the children are visited
              if s == ss:
                    stack.pop()
                    SCREAMING_SNAKE_CASE_      =     True
                    if len(__magic_name__      ) != 0:
                          SCREAMING_SNAKE_CASE_      =     stack[len(__magic_name__      ) - 1]
              else:
                    SCREAMING_SNAKE_CASE_      =     False
                    indirect_parents.append(__magic_name__      )
                    SCREAMING_SNAKE_CASE_      =     s
                    SCREAMING_SNAKE_CASE_      =     ss

              # check if se have reached the starting point
              if len(__magic_name__      ) == 0:
                    return False







  def       __A   (							self       :				Any      )     ->		List[str]:
        return list(self.graph      )







  def       __A   (							self       :				Union[str, Any]     ,   __magic_name__       :				Any=-2     ,   __magic_name__       :				Optional[Any]=-1      )     ->		Union[str, Any]:
        SCREAMING_SNAKE_CASE_      =     time()
        self.dfs(__magic_name__     ,   __magic_name__      )
        SCREAMING_SNAKE_CASE_      =     time()
        return end - begin







  def       __A   (							self       :				Any     ,   __magic_name__       :				Any=-2      )     ->		Union[str, Any]:
        SCREAMING_SNAKE_CASE_      =     time()
        self.bfs(__magic_name__      )
        SCREAMING_SNAKE_CASE_      =     time()
        return end - begin



from itertools import product

from cva import COLOR_BGR2GRAY, cvtColor, imread, imshow, waitKey
from numpy import dot, exp, mgrid, pi, ravel, square, uinta, zeros


def    a__       (						__UpperCamelCase   ,					__UpperCamelCase ):
      SCREAMING_SNAKE_CASE_      =     k_size // 2
      SCREAMING_SNAKE_CASE_   ,       SCREAMING_SNAKE_CASE_      =     mgrid[0 - center : k_size - center, 0 - center : k_size - center]
      SCREAMING_SNAKE_CASE_      =     1 / (2 * pi * sigma) * exp(-(square(__UpperCamelCase ) + square(__UpperCamelCase )) / (2 * square(__UpperCamelCase )) )
      return g


def    a__       (						__UpperCamelCase   ,					__UpperCamelCase   ,					__UpperCamelCase ):
      SCREAMING_SNAKE_CASE_   ,       SCREAMING_SNAKE_CASE_      =     image.shape[0], image.shape[1]
      # dst image height and width
      SCREAMING_SNAKE_CASE_      =     height - k_size + 1
      SCREAMING_SNAKE_CASE_      =     width - k_size + 1

      # im2col, turn the k_size*k_size pixels into a row and np.vstack all rows
      SCREAMING_SNAKE_CASE_      =     zeros((dst_height * dst_width, k_size * k_size) )
      SCREAMING_SNAKE_CASE_      =     0
      for i, j in product(range(__UpperCamelCase )   ,					range(__UpperCamelCase ) ):
            SCREAMING_SNAKE_CASE_      =     ravel(image[i : i + k_size, j : j + k_size] )
            SCREAMING_SNAKE_CASE_      =     window
            row += 1

      #  turn the kernel into shape(k*k, 1)
      SCREAMING_SNAKE_CASE_      =     gen_gaussian_kernel(__UpperCamelCase   ,					__UpperCamelCase )
      SCREAMING_SNAKE_CASE_      =     ravel(__UpperCamelCase )

      # reshape and get the dst image
      SCREAMING_SNAKE_CASE_      =     dot(__UpperCamelCase   ,					__UpperCamelCase ).reshape(__UpperCamelCase   ,					__UpperCamelCase ).astype(__UpperCamelCase )

      return dst


if __name__ == "__main__":
      # read original image
      A   :     Tuple       =				imread(r"../image_data/lena.jpg")
      # turn image in gray scale value
      A   :     Optional[int]       =				cvtColor(img, COLOR_BGR2GRAY)

      # get values with two different mask size
      A   :     Tuple       =				gaussian_filter(gray, 3, sigma=1)
      A   :     Optional[int]       =				gaussian_filter(gray, 5, sigma=0.8)

      # show result images
      imshow("gaussian filter with 3x3 mask", gaussianaxa)
      imshow("gaussian filter with 5x5 mask", gaussianaxa)
      waitKey()


