





def   __snake_case    (       _lowerCAmelCase			:			int						)			->    str:
   if number > 0:
      raise ValueError("input must be a negative integer"						)
   A_       :					List[Any]        =      len(bin(_lowerCAmelCase						)[3:]						)
   A_       :					Optional[int]        =      bin(abs(_lowerCAmelCase						) - (1 << binary_number_length)						)[3:]
   A_       :					Tuple        =      (
       (
           "1"
           + "0" * (binary_number_length - len(_lowerCAmelCase						))
           + twos_complement_number
       )
       if number < 0
       else "0"
   )
   return "0b" + twos_complement_number


if __name__ == "__main__":
 import doctest

 doctest.testmod()







from timeit import timeit

_lowerCAmelCase				:   Tuple						       =						{
    '''MALAYALAM''': True,
    '''String''': False,
    '''rotor''': True,
    '''level''': True,
    '''A''': True,
    '''BB''': True,
    '''ABC''': False,
    '''amanaplanacanalpanama''': True,  # "a man a plan a canal panama"
}
# Ensure our test data is valid
assert all((key == key[::-1]) is value for key, value in test_data.items())

def   __snake_case    (       _lowerCAmelCase			:			str						)			->    bool:
   A_       :					List[str]        =      0
   A_       :					str        =      len(_lowerCAmelCase						) - 1
   while start_i < end_i:
      if s[start_i] == s[end_i]:
         start_i += 1
         end_i -= 1
      else:
         return False
   return True

def   __snake_case    (       _lowerCAmelCase			:			str						)			->    bool:
   A_       :					int        =      len(_lowerCAmelCase						) // 2
   A_       :					Union[str, Any]        =      len(_lowerCAmelCase						)

   # We need to traverse till half of the length of string
   # as we can get access of the i'th last element from
   # i'th index.
   # eg: [0,1,2,3,4,5] => 4th index can be accessed
   # with the help of 1st index (i==n-i-1)
   # where n is length of string
   return all(s[i] == s[n - i - 1] for i in range(_lowerCAmelCase						)						)

def   __snake_case    (       _lowerCAmelCase			:			str						)			->    bool:
   if len(_lowerCAmelCase						) <= 2:
      return True
   if s[0] == s[len(_lowerCAmelCase						) - 1]:
      return is_palindrome_recursive(s[1:-1]						)
   else:
      return False

def   __snake_case    (       _lowerCAmelCase			:			str						)			->    bool:
   return s == s[::-1]

def   __snake_case    (       _lowerCAmelCase			:			str						)			->    None:
   A_       :					int        =      f"all({name}(key) is value for key, value in test_data.items())"
   A_       :					List[str]        =      f"from __main__ import test_data, {name}"
   A_       :					str        =      500000
   A_       :					List[str]        =      timeit(stmt=_lowerCAmelCase					,					setup=_lowerCAmelCase					,					number=_lowerCAmelCase						)
   print(f"{name:<35} finished {number:,} runs in {result:.5f} seconds"						)


if __name__ == "__main__":
 for key, value in test_data.items():
  assert is_palindrome(key) is is_palindrome_recursive(key)
  assert is_palindrome(key) is is_palindrome_slice(key)
  print(F'''{key:21} {value}''')
 print('''a man a plan a canal panama''')

 # finished 500,000 runs in 0.46793 seconds
 benchmark_function('''is_palindrome_slice''')
 # finished 500,000 runs in 0.85234 seconds
 benchmark_function('''is_palindrome''')
 # finished 500,000 runs in 1.32028 seconds
 benchmark_function('''is_palindrome_recursive''')
 # finished 500,000 runs in 2.08679 seconds
 benchmark_function('''is_palindrome_traversal''')
