






'''simple docstring'''




from __future__ import annotations

import math







class       __lowercase					:

	def __init__(      self   :						Dict  ,					UpperCAmelCase_   :						int):
			UpperCamelCase__				:					Dict					=					size
			# approximate the overall size of segment tree with given value
			UpperCamelCase__				:					Any					=					[0 for i in range(0  ,					4 * size)]
			# create array to store lazy update
			UpperCamelCase__				:					Tuple					=					[0 for i in range(0  ,					4 * size)]
			UpperCamelCase__				:					List[str]					=					[0 for i in range(0  ,					4 * size)]  # flag for lazy update

	def      __UpperCamelCase							(      self   :						Dict  ,					UpperCAmelCase_   :						int):
			return idx * 2

	def      __UpperCamelCase							(      self   :						Tuple  ,					UpperCAmelCase_   :						int):
			return idx * 2 + 1

	def      __UpperCamelCase							(      self   :						List[Any]  ,					UpperCAmelCase_   :						int  ,					UpperCAmelCase_   :						int  ,					UpperCAmelCase_   :						int  ,					UpperCAmelCase_   :						list[int]):
			if left_element == right_element:
					UpperCamelCase__				:					Optional[int]					=					a[left_element - 1]
			else:
					UpperCamelCase__				:					str					=					(left_element + right_element) // 2
					self.build(self.left(UpperCAmelCase_)  ,					UpperCAmelCase_  ,					UpperCAmelCase_  ,					UpperCAmelCase_)
					self.build(self.right(UpperCAmelCase_)  ,					mid + 1  ,					UpperCAmelCase_  ,					UpperCAmelCase_)
					UpperCamelCase__				:					int					=					max(
					    self.segment_tree[self.left(UpperCAmelCase_)]  ,					self.segment_tree[self.right(UpperCAmelCase_)])

	def      __UpperCamelCase							(      self   :						List[Any]  ,					UpperCAmelCase_   :						int  ,					UpperCAmelCase_   :						int  ,					UpperCAmelCase_   :						int  ,					UpperCAmelCase_   :						int  ,					UpperCAmelCase_   :						int  ,					UpperCAmelCase_   :						int):
			if self.flag[idx] is True:
					UpperCamelCase__				:					Union[str, Any]					=					self.lazy[idx]
					UpperCamelCase__				:					List[Any]					=					False
					if left_element != right_element:
							UpperCamelCase__				:					List[Any]					=					self.lazy[idx]
							UpperCamelCase__				:					str					=					self.lazy[idx]
							UpperCamelCase__				:					int					=					True
							UpperCamelCase__				:					int					=					True

			if right_element < a or left_element > b:
					return True
			if left_element >= a and right_element <= b:
					UpperCamelCase__				:					str					=					val
					if left_element != right_element:
							UpperCamelCase__				:					List[Any]					=					val
							UpperCamelCase__				:					Tuple					=					val
							UpperCamelCase__				:					Union[str, Any]					=					True
							UpperCamelCase__				:					int					=					True
					return True
			UpperCamelCase__				:					Union[str, Any]					=					(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_)
			UpperCamelCase__				:					Union[str, Any]					=					max(
			    self.segment_tree[self.left(UpperCAmelCase_)]  ,					self.segment_tree[self.right(UpperCAmelCase_)])
			return True

	def      __UpperCamelCase							(      self   :						int  ,					UpperCAmelCase_   :						int  ,					UpperCAmelCase_   :						int  ,					UpperCAmelCase_   :						int  ,					UpperCAmelCase_   :						int  ,					UpperCAmelCase_   :						int):
			if self.flag[idx] is True:
					UpperCamelCase__				:					Union[str, Any]					=					self.lazy[idx]
					UpperCamelCase__				:					Optional[int]					=					False
					if left_element != right_element:
							UpperCamelCase__				:					Dict					=					self.lazy[idx]
							UpperCamelCase__				:					Optional[Any]					=					self.lazy[idx]
							UpperCamelCase__				:					Dict					=					True
							UpperCamelCase__				:					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]
			UpperCamelCase__				:					Union[str, Any]					=					(left_element + right_element) // 2
			UpperCamelCase__				:					int					=					self.query(self.left(UpperCAmelCase_)  ,					UpperCAmelCase_  ,					UpperCAmelCase_  ,					UpperCAmelCase_  ,					UpperCAmelCase_)
			UpperCamelCase__				:					List[Any]					=					self.query(self.right(UpperCAmelCase_)  ,					mid + 1  ,					UpperCAmelCase_  ,					UpperCAmelCase_  ,					UpperCAmelCase_)
			return max(UpperCAmelCase_  ,					UpperCAmelCase_)





	def __str__(      self   :						List[str]):
			return str([self.query(1  ,					1  ,					self.size  ,					UpperCAmelCase_  ,					UpperCAmelCase_) for i in range(1  ,					self.size + 1)])


if __name__ == "__main__":
		lowerCAmelCase__          =						[1, 2, -4, 7, 3, -5, 6, 11, -20, 9, 14, 15, 5, 2, -8]
		lowerCAmelCase__          =						15
		lowerCAmelCase__          =						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, 111)
		print(segt.query(1, 1, size, 1, 15))
		segt.update(1, 1, size, 7, 8, 235)
		print(segt)












'''simple docstring'''




import os
import random
import sys

from . import cryptomath_module as cryptomath
from . import rabin_miller

lowerCAmelCase__          =						3







def       __UpperCAmelCase						(  lowerCamelCase_)							->     int:
		print('Generating primitive root of p')
		while True:
				UpperCamelCase__				:					Any					=					random.randrange(3     ,      lowerCamelCase_)
				if pow(lowerCamelCase_     ,      2     ,      lowerCamelCase_) == 1:
						continue
				if pow(lowerCamelCase_     ,      lowerCamelCase_     ,      lowerCamelCase_) == 1:
						continue
				return g







def       __UpperCAmelCase						(  lowerCamelCase_)							->     tuple[tuple[int, int, int, int], tuple[int, int]]:
		print('Generating prime p...')
		UpperCamelCase__				:					List[str]					=					rabin_miller.generate_large_prime(lowerCamelCase_)  # select large prime number.
		UpperCamelCase__				:					Any					=					primitive_root(lowerCamelCase_)  # one primitive root on modulo p.
		UpperCamelCase__				:					Union[str, Any]					=					random.randrange(3     ,      lowerCamelCase_)  # private_key -> have to be greater than 2 for safety.
		UpperCamelCase__				:					Dict					=					cryptomath.find_mod_inverse(pow(lowerCamelCase_     ,      lowerCamelCase_     ,      lowerCamelCase_)     ,      lowerCamelCase_)

		UpperCamelCase__				:					List[Any]					=					(key_size, e_a, e_a, p)
		UpperCamelCase__				:					Optional[Any]					=					(key_size, d)

		return public_key, private_key







def       __UpperCAmelCase						(  lowerCamelCase_     ,      lowerCamelCase_)							->     None:
		if os.path.exists(f'{name}_pubkey.txt') or os.path.exists(f'{name}_privkey.txt'):
				print('\nWARNING:')
				print(
				    f'"{name}_pubkey.txt" or "{name}_privkey.txt" already exists. \n'
				    'Use a different name or delete these files and re-run this program.')
				sys.exit()

		UpperCamelCase__,	UpperCamelCase__				:					Union[str, Any]					=					generate_key(lowerCamelCase_)
		print(f'\nWriting public key to file {name}_pubkey.txt...')
		with open(f'{name}_pubkey.txt'     ,      'w') as fo:
				fo.write(f'{public_key[0]},{public_key[1]},{public_key[2]},{public_key[3]}')

		print(f'Writing private key to file {name}_privkey.txt...')
		with open(f'{name}_privkey.txt'     ,      'w') as fo:
				fo.write(f'{private_key[0]},{private_key[1]}')







def       __UpperCAmelCase						(  )							->     None:
		print('Making key files...')
		make_key_files('elgamal'     ,      2_048)
		print('Key files generation successful')


if __name__ == "__main__":
		main()




