code: 
  '''simple docstring'''
  def       _UpperCamelCase	(					)     ->       int:
  
  
  		'''simple docstring'''
  
  
  		for a in range(300 ):
  				for b in range(a + 1   ,					400 ):
  						for c in range(b + 1   ,					500 ):
  								if (a + b + c) == 1000 and (a**2) + (b**2) == (c**2):
  										return a * b * c
  
  		return -1
  
  
  
  
  def       _UpperCamelCase	(					)     ->       int:
  
  
  		'''simple docstring'''
  
  
  		for a in range(300 ):
  				for b in range(400 ):
  						snake_case     :					Dict     =	1000 - a - b
  						if a < b < c and (a**2) + (b**2) == (c**2):
  								return a * b * c
  
  		return -1
  
  
  
  
  def       _UpperCamelCase	(					)     ->       None:
  
  
  		'''simple docstring'''
  
  
  		import timeit
  
  		print(
  		    timeit.timeit('''solution()'''   ,					setup='''from __main__ import solution'''   ,					number=1000 ) )
  		print(
  		    timeit.timeit(
  		        '''solution_fast()'''   ,					setup='''from __main__ import solution_fast'''   ,					number=1000 ) )
  
  
  if __name__ == "__main__":
  						print(f"{solution() = }")
  
  
  
style_context: 
  '''simple docstring'''
  import numpy as np
  
  
  
  
  def       _UpperCamelCase	(					SCREAMING_SNAKE_CASE__ )     ->       Optional[Any]:
  
  
  		'''simple docstring'''
  
  
  		snake_case ,snake_case     :					str     =	a.shape
  		snake_case     :					Union[str, Any]     =	min(SCREAMING_SNAKE_CASE__   ,					SCREAMING_SNAKE_CASE__ )
  		snake_case     :					List[Any]     =	np.eye(SCREAMING_SNAKE_CASE__ )
  		snake_case     :					Union[str, Any]     =	a.copy()
  
  		for k in range(t - 1 ):
  				# select a column of modified matrix A':
  				snake_case     :					Union[str, Any]     =	r[k:, [k]]
  				# construct first basis vector
  				snake_case     :					str     =	np.zeros_like(SCREAMING_SNAKE_CASE__ )
  				snake_case     :					List[str]     =	1.0
  				# determine scaling factor
  				snake_case     :					int     =	np.linalg.norm(SCREAMING_SNAKE_CASE__ )
  				# construct vector v for Householder reflection
  				snake_case     :					Optional[int]     =	x + np.sign(x[0] ) * alpha * ea
  				v /= np.linalg.norm(SCREAMING_SNAKE_CASE__ )
  
  				# construct the Householder matrix
  				snake_case     :					Tuple     =	np.eye(m - k ) - 2.0 * v @ v.T
  				# pad with ones and zeros as necessary
  				snake_case     :					int     =	np.block([[np.eye(SCREAMING_SNAKE_CASE__ ), np.zeros((k, m - k) )], [np.zeros((m - k, k) ), q_k]] )
  
  				snake_case     :					int     =	q @ q_k.T
  				snake_case     :					Dict     =	q_k @ r
  
  		return q, r
  
  
  if __name__ == "__main__":
  						import doctest
  
  						doctest.testmod()
  
  
  