
_lowercase											=    {
    '''a''': '''AAAAA''',
    '''b''': '''AAAAB''',
    '''c''': '''AAABA''',
    '''d''': '''AAABB''',
    '''e''': '''AABAA''',
    '''f''': '''AABAB''',
    '''g''': '''AABBA''',
    '''h''': '''AABBB''',
    '''i''': '''ABAAA''',
    '''j''': '''BBBAA''',
    '''k''': '''ABAAB''',
    '''l''': '''ABABA''',
    '''m''': '''ABABB''',
    '''n''': '''ABBAA''',
    '''o''': '''ABBAB''',
    '''p''': '''ABBBA''',
    '''q''': '''ABBBB''',
    '''r''': '''BAAAA''',
    '''s''': '''BAAAB''',
    '''t''': '''BAABA''',
    '''u''': '''BAABB''',
    '''v''': '''BBBAB''',
    '''w''': '''BABAA''',
    '''x''': '''BABAB''',
    '''y''': '''BABBA''',
    '''z''': '''BABBB''',
    ''' ''': ''' ''',
}


_lowercase											=    {value: key for key, value in encode_dict.items()}
def 							SCREAMING_SNAKE_CASE_	(					UpperCAmelCase_	:     str				)			->						str:
       SCREAMING_SNAKE_CASE_							:				Optional[int]		=''
       for letter in word.lower():
              if letter.isalpha() or letter == " ":
                     encoded += encode_dict[letter]
              else:
                     raise Exception('''encode() accepts only letters of the alphabet and spaces'''				)
       return encoded
def 							SCREAMING_SNAKE_CASE_	(					UpperCAmelCase_	:     str				)			->						str:
       if set(__snake_case				) - {"A", "B", " "} != set():
              raise Exception('''decode() accepts only \'A\', \'B\' and spaces'''				)
       SCREAMING_SNAKE_CASE_							:				str		=''
       for word in coded.split():
              while len(__snake_case				) != 0:
                     decoded += decode_dict[word[:5]]
                     SCREAMING_SNAKE_CASE_							:				Dict		=word[5:]
              decoded += " "
       return decoded.strip()


if __name__ == "__main__":
 from doctest import testmod

 testmod()







'''simple docstring'''




from __future__ import annotations

import math


class 					SCREAMING_SNAKE_CASE       :


     def __init__(		self		,      _UpperCAmelCase):

          '''simple docstring'''






          __A		:					int						=			size
          # approximate the overall size of segment tree with given value
          __A		:					Optional[Any]						=			[0 for i in range(0		,      4 * size)]
          # create array to store lazy update
          __A		:					Optional[Any]						=			[0 for i in range(0		,      4 * size)]
          __A		:					str						=			[0 for i in range(0		,      4 * size)]  # flag for lazy update


     def 				SCREAMING_SNAKE_CASE    (		self		,      _UpperCAmelCase):

          '''simple docstring'''






          return idx * 2


     def 				SCREAMING_SNAKE_CASE    (		self		,      _UpperCAmelCase):

          '''simple docstring'''






          return idx * 2 + 1


     def 				SCREAMING_SNAKE_CASE    (		self		,      _UpperCAmelCase		,      _UpperCAmelCase		,      _UpperCAmelCase		,      _UpperCAmelCase):

          '''simple docstring'''






          if left_element == right_element:
               __A		:					List[Any]						=			a[left_element - 1]
          else:
               __A		:					List[str]						=			(left_element + right_element) // 2
               self.build(self.left(_UpperCAmelCase)		,      _UpperCAmelCase		,      _UpperCAmelCase		,      _UpperCAmelCase)
               self.build(self.right(_UpperCAmelCase)		,      mid + 1		,      _UpperCAmelCase		,      _UpperCAmelCase)
               __A		:					Any						=			max(
                   self.segment_tree[self.left(_UpperCAmelCase)]		,      self.segment_tree[self.right(_UpperCAmelCase)])


     def 				SCREAMING_SNAKE_CASE    (		self		,      _UpperCAmelCase		,      _UpperCAmelCase		,      _UpperCAmelCase		,      _UpperCAmelCase		,      _UpperCAmelCase		,      _UpperCAmelCase):

          '''simple docstring'''






          if self.flag[idx] is True:
               __A		:					Optional[Any]						=			self.lazy[idx]
               __A		:					Optional[Any]						=			False
               if left_element != right_element:
                    __A		:					List[Any]						=			self.lazy[idx]
                    __A		:					Dict						=			self.lazy[idx]
                    __A		:					Tuple						=			True
                    __A		:					Union[str, Any]						=			True

          if right_element < a or left_element > b:
               return True
          if left_element >= a and right_element <= b:
               __A		:					Optional[int]						=			val
               if left_element != right_element:
                    __A		:					Tuple						=			val
                    __A		:					Any						=			val
                    __A		:					Tuple						=			True
                    __A		:					Union[str, Any]						=			True
               return True
          __A		:					str						=			(left_element + right_element) // 2
          self.update(self.left(_UpperCAmelCase)		,      _UpperCAmelCase		,      _UpperCAmelCase		,      _UpperCAmelCase		,      _UpperCAmelCase		,      _UpperCAmelCase)
          self.update(self.right(_UpperCAmelCase)		,      mid + 1		,      _UpperCAmelCase		,      _UpperCAmelCase		,      _UpperCAmelCase		,      _UpperCAmelCase)
          __A		:					int						=			max(
              self.segment_tree[self.left(_UpperCAmelCase)]		,      self.segment_tree[self.right(_UpperCAmelCase)])
          return True


     def 				SCREAMING_SNAKE_CASE    (		self		,      _UpperCAmelCase		,      _UpperCAmelCase		,      _UpperCAmelCase		,      _UpperCAmelCase		,      _UpperCAmelCase):

          '''simple docstring'''






          if self.flag[idx] is True:
               __A		:					Union[str, Any]						=			self.lazy[idx]
               __A		:					List[str]						=			False
               if left_element != right_element:
                    __A		:					Union[str, Any]						=			self.lazy[idx]
                    __A		:					Optional[int]						=			self.lazy[idx]
                    __A		:					str						=			True
                    __A		:					Union[str, Any]						=			True
          if right_element < a or left_element > b:
               return -math.inf
          if left_element >= a and right_element <= b:
               return self.segment_tree[idx]
          __A		:					Any						=			(left_element + right_element) // 2
          __A		:					int						=			self.query(self.left(_UpperCAmelCase)		,      _UpperCAmelCase		,      _UpperCAmelCase		,      _UpperCAmelCase		,      _UpperCAmelCase)
          __A		:					Union[str, Any]						=			self.query(self.right(_UpperCAmelCase)		,      mid + 1		,      _UpperCAmelCase		,      _UpperCAmelCase		,      _UpperCAmelCase)
          return max(_UpperCAmelCase		,      _UpperCAmelCase)


     def __str__(		self):

          '''simple docstring'''






          return str([self.query(1		,      1		,      self.size		,      _UpperCAmelCase		,      _UpperCAmelCase) for i in range(1		,      self.size + 1)])


if __name__ == "__main__":
  lowercase__       : Union[str, Any]         =       [1, 2, -4, 7, 3, -5, 6, 11, -20, 9, 14, 15, 5, 2, -8]
  lowercase__       : str         =       15
  lowercase__       : List[Any]         =       SegmentTree(size)
  segt.build(1, 1, size, A)
  print(segt.query(1, 1, size, 4, 6))
  print(segt.query(1, 1, size, 7, 11))
  print(segt.query(1, 1, size, 7, 12))
  segt.update(1, 1, size, 1, 3, 1_11)
  print(segt.query(1, 1, size, 1, 15))
  segt.update(1, 1, size, 7, 8, 2_35)
  print(segt)