'''simple docstring'''



def 				snake_case_      (		SCREAMING_SNAKE_CASE__ = 10**12       ):







  '''simple docstring'''



  _snake_case     		=				1
  _snake_case     		=				0

  _snake_case     		=				1
  _snake_case     		=				1

  while numerator <= 2 * min_total - 1:
    prev_numerator += 2 * numerator
    numerator += 2 * prev_numerator

    prev_denominator += 2 * denominator
    denominator += 2 * prev_denominator

  return (denominator + 1) // 2


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









'''simple docstring'''



def 				snake_case_      (		SCREAMING_SNAKE_CASE__       ):







  '''simple docstring'''



  _snake_case     		=				[0 for i in range(len(SCREAMING_SNAKE_CASE__       )       )]

  # initialize interval's left pointer and right pointer
  _snake_case		,		_snake_case     		=				0, 0

  for i in range(1					,	len(SCREAMING_SNAKE_CASE__       )       ):
    # case when current index is inside the interval
    if i <= right_pointer:
      _snake_case     		=				min(right_pointer - i + 1					,	z_result[i - left_pointer]       )
      _snake_case     		=				min_edge

    while go_next(SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__       ):
      z_result[i] += 1

    # if new index's result gives us more right interval,
    # we've to update left_pointer and right_pointer
    if i + z_result[i] - 1 > right_pointer:
      _snake_case		,		_snake_case     		=				i, i + z_result[i] - 1

  return z_result




def 				snake_case_      (		SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__       ):







  '''simple docstring'''



  return i + z_result[i] < len(SCREAMING_SNAKE_CASE__       ) and s[z_result[i]] == s[i + z_result[i]]




def 				snake_case_      (		SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__       ):







  '''simple docstring'''



  _snake_case     		=				0
  # concatenate 'pattern' and 'input_str' and call z_function
  # with concatenated string
  _snake_case     		=				z_function(pattern + input_str       )

  for val in z_result:
    # if value is greater then length of the pattern string
    # that means this index is starting position of substring
    # which is equal to pattern string
    if val >= len(SCREAMING_SNAKE_CASE__       ):
      answer += 1

  return answer


if __name__ == "__main__":
 import doctest

 doctest.testmod()


