





'''simple docstring'''



def 				_lowerCAmelCase  (			lowerCamelCase_     :					int = 1_0_0_0_0_0_0			):
			__lowercase			  =							limit + 1
			__lowercase			  =							[0] * limit
			for first_term in range(1						,    lowerCamelCase_			):
						for n in range(lowerCamelCase_						,    lowerCamelCase_						,    lowerCamelCase_			):
									__lowercase			  =							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

			__lowercase			  =							sum(1 for x in frequency[1:limit] if x == 1_0			)

			return count


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












'''simple docstring'''



import numpy as np




def 				_lowerCAmelCase  (			lowerCamelCase_     :					np.array			):
			return 1 / (1 + np.exp(-vector			))




def 				_lowerCAmelCase  (			lowerCamelCase_     :					np.array			):
			return vector * sigmoid(1.7_02 * vector			)


if __name__ == "__main__":
	import doctest

	doctest.testmod()





