






def   SCREAMING_SNAKE_CASE_				(				__magic_name__   :    int      ,     __magic_name__   :    int      ,     __magic_name__   :    int   )						->     Dict:






	"""simple docstring"""



	if power < 0:
		return -1
	base %= mod
	UpperCamelCase	:Any		=      1

	while power > 0:
		if power & 1:
			UpperCamelCase	:Union[str, Any]		=      (result * base) % mod
		UpperCamelCase	:Optional[Any]		=      power >> 1
		UpperCamelCase	:Optional[Any]		=      (base * base) % mod

	return result

def   SCREAMING_SNAKE_CASE_				(				)						->     Tuple:






	"""simple docstring"""



	print(modular_exponential(3      ,     200      ,     13   )   )


if __name__ == "__main__":
	import doctest

	doctest.testmod()

	main()








from __future__ import annotations

from abc import abstractmethod
from collections.abc import Iterable
from typing import Generic, Protocol, TypeVar

class        _SCREAMING_SNAKE_CASE			(     _a ):





	@abstractmethod
	def __lt__(						self							:   T					,    __lowerCamelCase							:   T      ):
		pass





	@abstractmethod
	def __gt__(						self							:   T					,    __lowerCamelCase							:   T      ):
		pass





	@abstractmethod
	def __eq__(						self							:   T					,    __lowerCamelCase							:   object      ):
		pass
UpperCAmelCase_					:		str           = TypeVar('''T''', bound=Comparable)

class        _SCREAMING_SNAKE_CASE			(     Generic[T] ):





	def __init__(						self							:   Dict      ):
		UpperCamelCase	:list[T]		=      []
		UpperCamelCase	:int		=      0





	def __repr__(						self							:   List[str]      ):
		return str(self.h      )





	def 		_A					(						self							:   Tuple					,    __lowerCamelCase							:   int      ):
		if child_idx > 0:
			return (child_idx - 1) // 2
		return None





	def 		_A					(						self							:   List[str]					,    __lowerCamelCase							:   int      ):
		UpperCamelCase	:Optional[int]		=      2 * parent_idx + 1
		if left_child_index < self.heap_size:
			return left_child_index
		return None





	def 		_A					(						self							:   List[str]					,    __lowerCamelCase							:   int      ):
		UpperCamelCase	:Optional[Any]		=      2 * parent_idx + 2
		if right_child_index < self.heap_size:
			return right_child_index
		return None





	def 		_A					(						self							:   Tuple					,    __lowerCamelCase							:   int      ):
		if index < self.heap_size:
			UpperCamelCase	:int		=      index
			UpperCamelCase	:Dict		=      self.left_child_idx(__lowerCamelCase      )
			UpperCamelCase	:Any		=      self.right_child_idx(__lowerCamelCase      )
			# check which child is larger than its parent
			if left_child is not None and self.h[left_child] > self.h[violation]:
				UpperCamelCase	:Dict		=      left_child
			if right_child is not None and self.h[right_child] > self.h[violation]:
				UpperCamelCase	:Dict		=      right_child
			# if violation indeed exists
			if violation != index:
				# swap to fix the violation
				UpperCamelCase	, UpperCamelCase	:Optional[int]		=      self.h[index], self.h[violation]
				# fix the subsequent violation recursively if any
				self.max_heapify(__lowerCamelCase      )





	def 		_A					(						self							:   Any					,    __lowerCamelCase							:   Iterable[T]      ):
		UpperCamelCase	:Optional[Any]		=      list(__lowerCamelCase      )
		UpperCamelCase	:int		=      len(self.h      )
		if self.heap_size > 1:
			# max_heapify from right to left but exclude leaves (last level)
			for i in range(self.heap_size // 2 - 1					,    -1					,    -1      ):
				self.max_heapify(__lowerCamelCase      )





	def 		_A					(						self							:   Optional[int]      ):
		if self.heap_size >= 2:
			UpperCamelCase	:List[str]		=      self.h[0]
			UpperCamelCase	:str		=      self.h.pop(-1      )
			self.heap_size -= 1
			self.max_heapify(0      )
			return me
		elif self.heap_size == 1:
			self.heap_size -= 1
			return self.h.pop(-1      )
		else:
			raise Exception("""Empty heap"""      )





	def 		_A					(						self							:   Optional[Any]					,    __lowerCamelCase							:   T      ):
		self.h.append(__lowerCamelCase      )
		UpperCamelCase	:Any		=      (self.heap_size - 1) // 2
		self.heap_size += 1
		while idx >= 0:
			self.max_heapify(__lowerCamelCase      )
			UpperCamelCase	:List[str]		=      (idx - 1) // 2





	def 		_A					(						self							:   int      ):
		UpperCamelCase	:int		=      self.heap_size
		for j in range(size - 1					,    0					,    -1      ):
			UpperCamelCase	, UpperCamelCase	:Any		=      self.h[j], self.h[0]
			self.heap_size -= 1
			self.max_heapify(0      )
		UpperCamelCase	:List[str]		=      size


if __name__ == "__main__":
	import doctest

	# run doc test
	doctest.testmod()

	# demo
	for unsorted in [
	    [0],
	    [2],
	    [3, 5],
	    [5, 3],
	    [5, 5],
	    [0, 0, 0, 0],
	    [1, 1, 1, 1],
	    [2, 2, 3, 5],
	    [0, 2, 2, 3, 5],
	    [2, 5, 3, 0, 2, 3, 0, 3],
	    [6, 1, 2, 7, 9, 3, 4, 5, 10, 8],
	    [1_03, 9, 1, 7, 11, 15, 25, 2_01, 2_09, 1_07, 5],
	    [-45, -2, -5],
	]:
		print(F'''unsorted array: {unsorted}''')

		UpperCAmelCase_					:		Heap[int]           = Heap()
		heap.build_max_heap(unsorted)
		print(F'''after build heap: {heap}''')

		print(F'''max value: {heap.extract_max()}''')
		print(F'''after max value removed: {heap}''')

		heap.insert(1_00)
		print(F'''after new value 100 inserted: {heap}''')

		heap.heap_sort()
		print(F'''heap-sorted array: {heap}\n''')
