


'''simple docstring'''

# A Bipartite Graph is a graph whose vertices can be divided into two independent sets,
# U and V such that every edge (u, v) either connects a vertex from U to V or a vertex
# from V to U. In other words, for every edge (u, v), either u belongs to U and v to V,
# or u belongs to V and v to U. We can also say that there is no edge that connects
# vertices of same set.

def _SCREAMING_SNAKE_CASE (A			)			->			Any:






       """simple docstring"""







       lowercase__      =					[False] * len(A			)
       lowercase__      =					[-1] * len(A			)

       def dfs(A    ,					A			):
              lowercase__      =					True
              lowercase__      =					c
              for u in graph[v]:
                     if not visited[u]:
                            dfs(A    ,					1 - c			)

       for i in range(len(A			)			):
              if not visited[i]:
                     dfs(A    ,					0			)

       for i in range(len(A			)			):
              for j in graph[i]:
                     if color[i] == color[j]:
                            return False

       return True


# Adjacency list of graph
lowerCamelCase				:  Optional[Any]    		=      {0: [1, 3], 1: [0, 2], 2: [1, 3], 3: [0, 2], 4: []}

print(check_bipartite_dfs(graph))








'''simple docstring'''

from __future__ import annotations

lowerCamelCase				:  List[str]    		=      []

def _SCREAMING_SNAKE_CASE (A    ,					A    ,					A			)			->			bool:






       """simple docstring"""







       for i in range(len(A			)			):
              if board[row][i] == 1:
                     return False
       for i in range(len(A			)			):
              if board[i][column] == 1:
                     return False
       for i, j in zip(range(A    ,					-1    ,					-1			)    ,					range(A    ,					-1    ,					-1			)			):
              if board[i][j] == 1:
                     return False
       for i, j in zip(range(A    ,					-1    ,					-1			)    ,					range(A    ,					len(A			)			)			):
              if board[i][j] == 1:
                     return False
       return True

def _SCREAMING_SNAKE_CASE (A    ,					A			)			->			bool:






       """simple docstring"""







       if row >= len(A			):
              solution.append(A			)
              printboard(A			)
              print()
              return True
       for i in range(len(A			)			):
              if is_safe(A    ,					A    ,					A			):
                     lowercase__      =					1
                     solve(A    ,					row + 1			)
                     lowercase__      =					0
       return False

def _SCREAMING_SNAKE_CASE (A			)			->			None:






       """simple docstring"""







       for i in range(len(A			)			):
              for j in range(len(A			)			):
                     if board[i][j] == 1:
                            print('''Q'''    ,					end=''' '''			)
                     else:
                            print('''.'''    ,					end=''' '''			)
              print()


# n=int(input("The no. of queens"))
lowerCamelCase				:  Optional[Any]    		=      8
lowerCamelCase				:  Optional[int]    		=      [[0 for i in range(n)] for j in range(n)]
solve(board, 0)

print('The total no. of solutions are :', len(solution))




