
'''simple docstring'''

def __A  (    lowerCAmelCase_       ):
     if not isinstance(lowerCAmelCase_ ,       lowerCAmelCase_       ):
          _UpperCAmelCase					:  Tuple         =    f"Input value of [number={number}] must be an integer"
          raise TypeError(lowerCAmelCase_       )
     if number < 0 or number % 2 == 1:
          return False
     _UpperCAmelCase					:  Any         =    int(number**0.5       )
     return number == number_sqrt * (number_sqrt + 1)


if __name__ == "__main__":
   import doctest

   doctest.testmod()




'''simple docstring'''

from itertools import combinations, product







def __A  (    lowerCAmelCase_ ,       lowerCAmelCase_ ,       lowerCAmelCase_ ,       lowerCAmelCase_       ):
     if xa == ya == 0 or xa == ya == 0:
          return False
     _UpperCAmelCase					:  Any         =    xa * xa + ya * ya
     _UpperCAmelCase					:  Any         =    xa * xa + ya * ya
     _UpperCAmelCase					:  Tuple         =    (xa - xa) * (xa - xa) + (ya - ya) * (ya - ya)
     return (
         a_square + b_square == c_square
         or a_square + c_square == b_square
         or b_square + c_square == a_square
     )







def __A  (    lowerCAmelCase_ = 50       ):
     return sum(
         1
         for pta, pta in combinations(product(range(limit + 1       ) ,       repeat=2       ) ,       2       )
         if is_right(*lowerCAmelCase_ ,       *lowerCAmelCase_       )       )


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


