
"""simple docstring"""
import math
def 				a__   (   a   :				int		):

  """simple docstring"""







  _snake_case     :						Union[str, Any]						=   math.loga(math.sqrt(4 * positive_integer + 1		) / 2 + 1 / 2		)

  return exponent == int(a_		)
def 				a__   (   a   :				float = 1 / 12_345		):

  """simple docstring"""







  _snake_case     :						Any						=   0
  _snake_case     :						str						=   0

  _snake_case     :						Optional[Any]						=   3
  while True:
    _snake_case     :						Optional[int]						=   (integer**2 - 1) / 4
    # if candidate is an integer, then there is a partition for k
    if partition_candidate == int(a_		):
      _snake_case     :						Union[str, Any]						=   int(a_		)
      total_partitions += 1
      if check_partition_perfect(a_		):
        perfect_partitions += 1
    if perfect_partitions > 0:
      if perfect_partitions / total_partitions < max_proportion:
        return int(a_		)
    integer += 1


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



"""simple docstring"""
from __future__ import annotations






class      _UpperCAmelCase				:
    def __init__(    self						,    snake_case_						,    snake_case_     ):
      _snake_case			,					_snake_case     :						Dict						=   text, pattern
      _snake_case			,					_snake_case     :						int						=   len(snake_case_     ), len(snake_case_     )
    def 					lowerCamelCase__	(    self						,    snake_case_     ):

      for i in range(self.patLen - 1						,    -1						,    -1     ):
        if char == self.pattern[i]:
          return i
      return -1
    def 					lowerCamelCase__	(    self						,    snake_case_     ):

      for i in range(self.patLen - 1						,    -1						,    -1     ):
        if self.pattern[i] != self.text[current_pos + i]:
          return current_pos + i
      return -1


    def 					lowerCamelCase__	(    self     ):
      # searches pattern in text and returns index positions
      _snake_case     :						List[str]						=   []
      for i in range(self.textLen - self.patLen + 1     ):
        _snake_case     :						Union[str, Any]						=   self.mismatch_in_text(snake_case_     )
        if mismatch_index == -1:
          positions.append(snake_case_     )
        else:
          _snake_case     :						Tuple						=   self.match_in_pattern(self.text[mismatch_index]     )
          _snake_case     :						Tuple						=   (
              mismatch_index - match_index
          )  # shifting index lgtm [py/multiple-definition]
      return positions


_a      :			List[Any]					=							"""ABAABA"""
_a      :			str					=							"""AB"""
_a      :			List[Any]					=							BoyerMooreSearch(text, pattern)
_a      :			Any					=							bms.bad_character_heuristic()

if len(positions) == 0:
    print("""No match found""")
else:
    print("""Pattern found in following positions: """)
    print(positions)

