莫名错误'str' object is not callable

[luo591]

源码如下
def collatz(number):
if number % 2 == 0:
number = number // 2
print(str(number))
return number
elif number % 2 == 1:
number = 3 * number + 1
print(str(number))
return number
while True:
print('tpye a number.')
input = input()
if collatz(int(input)) != 1:
continue

程序运行后，显示如下
Python 3.6.2rc1 (heads/3.6:268e1fb, Jun 17 2017, 19:01:44) [MSC v.1900 64 bit (AMD64)] on win32
Type "copyright", "credits" or "license()" for more information.
>>>
============ RESTART: C:/Users/Administrator/Documents/defcoll.py ============
tpye a number.
7
22
tpye a number.
Traceback (most recent call last):
File "C:/Users/Administrator/Documents/defcoll.py", line 12, in <module>
input = input()
TypeError: 'str' object is not callable
>>>

为何第一遍程序运行没问题，第二遍就出问题了？？
求指教

[A102350004]

遇到了一样的问题，楼主解决了么？