






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






def 			lowerCamelCase_    (		_lowerCamelCase							):
 if not list_of_ints:
  return []

 if min(_lowerCamelCase							) < 0:
  raise ValueError('All numbers must be positive'							)

 lowerCamelCase__	:     Dict								=		max(len(bin(_lowerCamelCase							)[2:]							) for x in list_of_ints							)
 return _msd_radix_sort(_lowerCamelCase     ,  _lowerCamelCase							)






def 			lowerCamelCase_    (		_lowerCamelCase     ,  _lowerCamelCase							):
 if bit_position == 0 or len(_lowerCamelCase							) in [0, 1]:
  return list_of_ints

 lowerCamelCase__	:     List[str]								=		[]
 lowerCamelCase__	:     Dict								=		[]
 # Split numbers based on bit at bit_position from the right
 for number in list_of_ints:
  if (number >> (bit_position - 1)) & 1:
   # number has a one at bit bit_position
   ones.append(_lowerCamelCase							)
  else:
   # number has a zero at bit bit_position
   zeros.append(_lowerCamelCase							)

    # recursively split both lists further
 lowerCamelCase__	:     str								=		_msd_radix_sort(_lowerCamelCase     ,  bit_position - 1							)
 lowerCamelCase__	:     Optional[Any]								=		_msd_radix_sort(_lowerCamelCase     ,  bit_position - 1							)

 # recombine lists
 lowerCamelCase__	:     List[str]								=		zeros
 res.extend(_lowerCamelCase							)

 return res






def 			lowerCamelCase_    (		_lowerCamelCase							):
 lowerCamelCase__	:     int								=		len(_lowerCamelCase							)
 if not list_of_ints or length == 1:
  return

 if min(_lowerCamelCase							) < 0:
  raise ValueError('All numbers must be positive'							)

 lowerCamelCase__	:     str								=		max(len(bin(_lowerCamelCase							)[2:]							) for x in list_of_ints							)
 _msd_radix_sort_inplace(_lowerCamelCase     ,  _lowerCamelCase     ,  0     ,  _lowerCamelCase							)






def 			lowerCamelCase_    (		_lowerCamelCase     ,  _lowerCamelCase     ,  _lowerCamelCase     ,  _lowerCamelCase							):
 if bit_position == 0 or end_index - begin_index <= 1:
  return

 bit_position -= 1

 lowerCamelCase__	:     Dict								=		begin_index
 lowerCamelCase__	:     Tuple								=		end_index - 1
 while i <= j:
  lowerCamelCase__	:     Dict								=		False
  if not (list_of_ints[i] >> bit_position) & 1:
   # found zero at the beginning
   i += 1
   lowerCamelCase__	:     Any								=		True
  if (list_of_ints[j] >> bit_position) & 1:
   # found one at the end
   j -= 1
   lowerCamelCase__	:     Tuple								=		True

  if changed:
   continue

  lowerCamelCase__							,	lowerCamelCase__	:     Dict								=		list_of_ints[j], list_of_ints[i]
  j -= 1
  if j != i:
   i += 1

 _msd_radix_sort_inplace(_lowerCamelCase     ,  _lowerCamelCase     ,  _lowerCamelCase     ,  _lowerCamelCase							)
 _msd_radix_sort_inplace(_lowerCamelCase     ,  _lowerCamelCase     ,  _lowerCamelCase     ,  _lowerCamelCase							)


if __name__ == "__main__":
      import doctest

      doctest.testmod()









"""simple docstring"""
class 						a_ :







      '''simple docstring'''

      def __init__(self,	lowerCamelCase_   ):

       '''simple docstring'''



       lowerCamelCase__	:     Dict								=		data
       lowerCamelCase__	:     BinaryTreeNode | None								=		None
       lowerCamelCase__	:     BinaryTreeNode | None								=		None






def 			lowerCamelCase_    (		_lowerCamelCase     ,  _lowerCamelCase							):
 if node is None:
  lowerCamelCase__	:     List[str]								=		BinaryTreeNode(_lowerCamelCase							)
  return node

 # binary search tree is not empty,
 # so we will insert it into the tree
 # if new_value is less than value of data in node,
 #  add it to left subtree and proceed recursively
 if new_value < node.data:
  lowerCamelCase__	:     str								=		insert(node.left_child     ,  _lowerCamelCase							)
 else:
  # if new_value is greater than value of data in node,
  #  add it to right subtree and proceed recursively
  lowerCamelCase__	:     str								=		insert(node.right_child     ,  _lowerCamelCase							)
 return node






def 			lowerCamelCase_    (		_lowerCamelCase							):  # if node is None,return
 if node:
  lowerCamelCase__	:     Any								=		inorder(node.left_child							)
  lowerCamelCase__	:     Tuple								=		[*inorder_array, node.data]
  lowerCamelCase__	:     List[Any]								=		inorder_array + inorder(node.right_child							)
 else:
  lowerCamelCase__	:     Any								=		[]
 return inorder_array






def 			lowerCamelCase_    (		):
 lowerCamelCase__	:     Tuple								=		insert(_lowerCamelCase     ,  15							)
 insert(_lowerCamelCase     ,  10							)
 insert(_lowerCamelCase     ,  25							)
 insert(_lowerCamelCase     ,  6							)
 insert(_lowerCamelCase     ,  14							)
 insert(_lowerCamelCase     ,  20							)
 insert(_lowerCamelCase     ,  60							)
 return root






def 			lowerCamelCase_    (		):
 # main function
 lowerCamelCase__	:     List[Any]								=		make_tree()
 print('Printing values of binary search tree in Inorder Traversal.'							)
 inorder(_lowerCamelCase							)


if __name__ == "__main__":
      import doctest

      doctest.testmod()
      main()

