


"""simple docstring"""



def     __lowerCAmelCase		(		lowercase    :    list[list[int]]		,				lowercase    :    int		,				lowercase    :    int		,				lowercase    :    list[int]					)      ->		bool:


    """simple docstring"""





    if graph[path[curr_ind - 1]][next_ver] == 0:
        return False

    # 2. Validate that next vertex is not already in path
    return not any(vertex == next_ver for vertex in path					)







def     __lowerCAmelCase		(		lowercase    :    list[list[int]]		,				lowercase    :    list[int]		,				lowercase    :    int					)      ->		bool:


    """simple docstring"""





    if curr_ind == len(lowercase					):
        # return whether path exists between current and starting vertices
        return graph[path[curr_ind - 1]][path[0]] == 1

    # Recursive Step
    for next_ver in range(0		,				len(lowercase					)					):
        if valid_connection(lowercase		,				lowercase		,				lowercase		,				lowercase					):
            # Insert current vertex  into path as next transition
            snake_case       : int    =       next_ver
            # Validate created path
            if util_hamilton_cycle(lowercase		,				lowercase		,				curr_ind + 1					):
                return True
            # Backtrack
            snake_case       : str    =       -1
    return False







def     __lowerCAmelCase		(		lowercase    :    list[list[int]]		,				lowercase    :    int = 0					)      ->		list[int]:


    """simple docstring"""





    snake_case       : List[Any]    =       [-1] * (len(lowercase					) + 1)
    # initialize start and end of path with starting index
    snake_case       : Dict    =       start_index
    # evaluate and if we find answer return path either return empty array
    return path if util_hamilton_cycle(lowercase		,				lowercase		,				1					) else []









"""simple docstring"""



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







def     __lowerCAmelCase		(		lowercase    :    int					)      ->		bool:


    """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(lowercase					) + 1					)		,				6					):
        if number % i == 0 or number % (i + 2) == 0:
            return False
    return True







def     __lowerCAmelCase		(		)      ->		Iterator[int]:


    """simple docstring"""





    snake_case       : Optional[int]    =       2
    while True:
        if is_prime(lowercase					):
            yield num
        num += 1







def     __lowerCAmelCase		(		lowercase    :    int = 200_0000					)      ->		int:


    """simple docstring"""





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


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





