

'''simple docstring'''






import math
from collections.abc import Iterator
from itertools import takewhile


def 		_A     (    A__      ):






 """simple docstring"""



 if 1 < number < 4:
  # 2 and 3 are primes
  return True
 elif number < 2 or number % 2 == 0 or number % 3 == 0:
  # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
  return False

 # All primes number are in format of 6k +/- 1
 for i in range(5     ,				int(math.sqrt(A__      ) + 1      )     ,				6      ):
  if number % i == 0 or number % (i + 2) == 0:
   return False
 return True


def 		_A     (    ):






 """simple docstring"""



 __lowercase							  = 2
 while True:
  if is_prime(A__      ):
   yield num
  num += 1


def 		_A     (    A__ = 2000000      ):






 """simple docstring"""



 return sum(takewhile(lambda A__      : x < n     ,				prime_generator()      )      )


if __name__ == "__main__":
 print(f'{solution() = }')






'''simple docstring'''






# using dfs for finding eulerian path traversal




def     snake_case_					(     lowerCAmelCase_       ,   lowerCAmelCase_       ,   lowerCAmelCase_       ,   lowerCAmelCase_=None		)->		List[str]:





       '''simple docstring'''


       _UpperCAmelCase  :						Any			     = (path or []) + [u]
       for v in graph[u]:
              if visited_edge[u][v] is False:
                     _UpperCAmelCase     ,_UpperCAmelCase  :						Tuple			     = True, True
                     _UpperCAmelCase  :						List[Any]			     = dfs(lowerCAmelCase_       ,   lowerCAmelCase_       ,   lowerCAmelCase_       ,   lowerCAmelCase_		)
       return path




def     snake_case_					(     lowerCAmelCase_       ,   lowerCAmelCase_		)->		Optional[int]:





       '''simple docstring'''


       _UpperCAmelCase  :						Optional[Any]			     = 0
       _UpperCAmelCase  :						Optional[int]			     = -1
       for i in range(lowerCAmelCase_		):
              if i not in graph.keys():
                     continue
              if len(graph[i]		) % 2 == 1:
                     odd_degree_nodes += 1
                     _UpperCAmelCase  :						Optional[int]			     = i
       if odd_degree_nodes == 0:
              return 1, odd_node
       if odd_degree_nodes == 2:
              return 2, odd_node
       return 3, odd_node




def     snake_case_					(     lowerCAmelCase_       ,   lowerCAmelCase_		)->		List[Any]:





       '''simple docstring'''


       _UpperCAmelCase  :						str			     = [[False for _ in range(max_node + 1		)] for _ in range(max_node + 1		)]
       _UpperCAmelCase     ,_UpperCAmelCase  :						int			     = check_circuit_or_path(lowerCAmelCase_       ,   lowerCAmelCase_		)
       if check == 3:
              print("""graph is not Eulerian"""		)
              print("""no path"""		)
              return
       _UpperCAmelCase  :						Dict			     = 1
       if check == 2:
              _UpperCAmelCase  :						Dict			     = odd_node
              print("""graph has a Euler path"""		)
       if check == 1:
              print("""graph has a Euler cycle"""		)
       _UpperCAmelCase  :						Dict			     = dfs(lowerCAmelCase_       ,   lowerCAmelCase_       ,   lowerCAmelCase_		)
       print(lowerCAmelCase_		)




def     snake_case_					(     )->		Union[str, Any]:





       '''simple docstring'''


       _UpperCAmelCase  :						Any			     = {1: [2, 3, 4], 2: [1, 3], 3: [1, 2], 4: [1, 5], 5: [4]}
       _UpperCAmelCase  :						int			     = {1: [2, 3, 4, 5], 2: [1, 3], 3: [1, 2], 4: [1, 5], 5: [1, 4]}
       _UpperCAmelCase  :						Tuple			     = {1: [2, 3, 4], 2: [1, 3, 4], 3: [1, 2], 4: [1, 2, 5], 5: [4]}
       _UpperCAmelCase  :						List[Any]			     = {1: [2, 3], 2: [1, 3], 3: [1, 2]}
       _UpperCAmelCase  :						List[str]			     = {
           1: [],
           2: []
           # all degree is zero
       }
       _UpperCAmelCase  :						Union[str, Any]			     = 10
       check_euler(lowerCAmelCase_       ,   lowerCAmelCase_		)
       check_euler(lowerCAmelCase_       ,   lowerCAmelCase_		)
       check_euler(lowerCAmelCase_       ,   lowerCAmelCase_		)
       check_euler(lowerCAmelCase_       ,   lowerCAmelCase_		)
       check_euler(lowerCAmelCase_       ,   lowerCAmelCase_		)


if __name__ == "__main__":
   main()



