


'''simple docstring'''



def   lowerCamelCase							(_SCREAMING_SNAKE_CASE				:       Union[str, Any]						,				_SCREAMING_SNAKE_CASE				:       Optional[Any]						,				_SCREAMING_SNAKE_CASE				:       List[str]						,				_SCREAMING_SNAKE_CASE				:       Any       ):

					# 1. Validate that path exists between current and next vertices
					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							(_SCREAMING_SNAKE_CASE				:       int						,				_SCREAMING_SNAKE_CASE				:       Union[str, Any]						,				_SCREAMING_SNAKE_CASE				:       str       ):

					# Base Case
					if curr_ind == len(__SCREAMING_SNAKE_CASE       ):
										# 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(__SCREAMING_SNAKE_CASE       )       ):
										if valid_connection(__SCREAMING_SNAKE_CASE						,				__SCREAMING_SNAKE_CASE						,				__SCREAMING_SNAKE_CASE						,				__SCREAMING_SNAKE_CASE       ):
															# Insert current vertex  into path as next transition
															__a      :	List[str]    =  next_ver
															# Validate created path
															if util_hamilton_cycle(__SCREAMING_SNAKE_CASE						,				__SCREAMING_SNAKE_CASE						,				curr_ind + 1       ):
																				return True
															# Backtrack
															__a      :	List[Any]    =  -1
					return False






def   lowerCamelCase							(_SCREAMING_SNAKE_CASE				:       Union[str, Any]						,				_SCREAMING_SNAKE_CASE				:       Optional[int] = 0       ):
					__a      :	Any    =  [-1] * (len(__SCREAMING_SNAKE_CASE       ) + 1)
					# initialize start and end of path with starting index
					__a      :	Union[str, Any]    =  start_index
					# evaluate and if we find answer return path either return empty array
					return path if util_hamilton_cycle(__SCREAMING_SNAKE_CASE						,				__SCREAMING_SNAKE_CASE						,				1       ) else []







'''simple docstring'''



def   lowerCamelCase							(_SCREAMING_SNAKE_CASE				:       int						,				_SCREAMING_SNAKE_CASE				:       int       ):
					if not isinstance(_SCREAMING_SNAKE_CASE						,				_SCREAMING_SNAKE_CASE       ):
										raise ValueError('iterations must be defined as integers'       )
					if not isinstance(_SCREAMING_SNAKE_CASE						,				_SCREAMING_SNAKE_CASE       ) or not number >= 1:
										raise ValueError(
										    'starting number must be\n                         and integer and be more than 0'       )
					if not iterations >= 1:
										raise ValueError('Iterations must be done more than 0 times to play FizzBuzz'       )

					__a      :	Dict    =  ''
					while number <= iterations:
										if number % 3 == 0:
															out += "Fizz"
										if number % 5 == 0:
															out += "Buzz"
										if 0 not in (number % 3, number % 5):
															out += str(_SCREAMING_SNAKE_CASE       )

										# print(out)
										number += 1
										out += " "
					return out


if __name__ == "__main__":
	import doctest

	doctest.testmod()



