


'''simple docstring'''






def 							UpperCamelCase_     (       A__   :  int = 1_00_00_00   ):
  '''simple docstring'''





  lowerCAmelCase_     : str     =  limit + 1
  lowerCAmelCase_     : Union[str, Any]     =  [0] * limit
  for first_term in range(1				,       A__   ):
    for n in range(A__				,       A__				,       A__   ):
      lowerCAmelCase_     : Dict     =  first_term + n / first_term
      if common_difference % 4:  # d must be divisble by 4
        continue
      else:
        common_difference /= 4
        if (
            first_term > common_difference
            and first_term < 4 * common_difference
        ):  # since x,y,z are positive integers
          frequency[n] += 1  # so z>0 and a>d ,also 4d<a

  lowerCAmelCase_     : Optional[Any]     =  sum(1 for x in frequency[1:limit] if x == 10   )

  return count


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







'''simple docstring'''






from __future__ import annotations

import numpy as np







def 							UpperCamelCase_     (       A__   :  np.ndarray   ):
  '''simple docstring'''





  lowerCAmelCase_,				lowerCAmelCase_     : List[str]     =  np.shape(A__   )
  if rows != columns:
    lowerCAmelCase_     : List[str]     =  (
        """'table' has to be of square shaped array but got a """
        f'{rows}x{columns} array:\n{table}'
    )
    raise ValueError(A__   )

  lowerCAmelCase_     : Optional[int]     =  np.zeros((rows, columns)   )
  lowerCAmelCase_     : Tuple     =  np.zeros((rows, columns)   )
  for i in range(A__   ):
    for j in range(A__   ):
      lowerCAmelCase_     : str     =  sum(lower[i][k] * upper[k][j] for k in range(A__   )   )
      if upper[j][j] == 0:
        raise ArithmeticError("""No LU decomposition exists"""   )
      lowerCAmelCase_     : Union[str, Any]     =  (table[i][j] - total) / upper[j][j]
    lowerCAmelCase_     : Dict     =  1
    for j in range(A__				,       A__   ):
      lowerCAmelCase_     : str     =  sum(lower[i][k] * upper[k][j] for k in range(A__   )   )
      lowerCAmelCase_     : List[str]     =  table[i][j] - total
  return lower, upper


if __name__ == "__main__":
  import doctest

  doctest.testmod()



