"""simple docstring"""

import itertools


def    lowerCAmelCase			(__UpperCamelCase							:    int = 1_0_0_0_0_0_0			):
							"""simple docstring"""


							__UpperCamelCase							=[1]

							for i in itertools.count(len(__UpperCamelCase			)			):
														__UpperCamelCase							=0
														for j in itertools.count(1			):
																					__UpperCamelCase							=-1 if j % 2 == 0 else +1
																					__UpperCamelCase							=(j * j * 3 - j) // 2
																					if index > i:
																												break
																					item += partitions[i - index] * sign
																					item %= number
																					index += j
																					if index > i:
																												break
																					item += partitions[i - index] * sign
																					item %= number

														if item == 0:
																					return i
														partitions.append(__UpperCamelCase			)

							return 0


if __name__ == "__main__":
				import doctest

				doctest.testmod()

				print(f'''{solution() = }''')




"""simple docstring"""

def    lowerCAmelCase			(__UpperCamelCase							:    int							,					__UpperCamelCase							:    int			):
							"""simple docstring"""


							return (input_a, input_a).count(0			) % 2


def    lowerCAmelCase			():
							"""simple docstring"""


							assert xor_gate(0							,					0			) == 0
							assert xor_gate(0							,					1			) == 1
							assert xor_gate(1							,					0			) == 1
							assert xor_gate(1							,					1			) == 0


if __name__ == "__main__":
				print(xor_gate(0, 0))
				print(xor_gate(0, 1))



