





from binascii import hexlify
from hashlib import shaaaa
from os import urandom

# RFC 3526 - More Modular Exponential (MODP) Diffie-Hellman groups for
# Internet Key Exchange (IKE) https://tools.ietf.org/html/rfc3526

_lowerCAmelCase				:   Optional[Any]						       =						{
    # 1536-bit
    5: {
        '''prime''': int(
            '''FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD1'''
            + '''29024E088A67CC74020BBEA63B139B22514A08798E3404DD'''
            + '''EF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245'''
            + '''E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED'''
            + '''EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3D'''
            + '''C2007CB8A163BF0598DA48361C55D39A69163FA8FD24CF5F'''
            + '''83655D23DCA3AD961C62F356208552BB9ED529077096966D'''
            + '''670C354E4ABC9804F1746C08CA237327FFFFFFFFFFFFFFFF''',
            base=16,
        ),
        '''generator''': 2,
    },
    # 2048-bit
    14: {
        '''prime''': int(
            '''FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD1'''
            + '''29024E088A67CC74020BBEA63B139B22514A08798E3404DD'''
            + '''EF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245'''
            + '''E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED'''
            + '''EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3D'''
            + '''C2007CB8A163BF0598DA48361C55D39A69163FA8FD24CF5F'''
            + '''83655D23DCA3AD961C62F356208552BB9ED529077096966D'''
            + '''670C354E4ABC9804F1746C08CA18217C32905E462E36CE3B'''
            + '''E39E772C180E86039B2783A2EC07A28FB5C55DF06F4C52C9'''
            + '''DE2BCBF6955817183995497CEA956AE515D2261898FA0510'''
            + '''15728E5A8AACAA68FFFFFFFFFFFFFFFF''',
            base=16,
        ),
        '''generator''': 2,
    },
    # 3072-bit
    15: {
        '''prime''': int(
            '''FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD1'''
            + '''29024E088A67CC74020BBEA63B139B22514A08798E3404DD'''
            + '''EF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245'''
            + '''E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED'''
            + '''EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3D'''
            + '''C2007CB8A163BF0598DA48361C55D39A69163FA8FD24CF5F'''
            + '''83655D23DCA3AD961C62F356208552BB9ED529077096966D'''
            + '''670C354E4ABC9804F1746C08CA18217C32905E462E36CE3B'''
            + '''E39E772C180E86039B2783A2EC07A28FB5C55DF06F4C52C9'''
            + '''DE2BCBF6955817183995497CEA956AE515D2261898FA0510'''
            + '''15728E5A8AAAC42DAD33170D04507A33A85521ABDF1CBA64'''
            + '''ECFB850458DBEF0A8AEA71575D060C7DB3970F85A6E1E4C7'''
            + '''ABF5AE8CDB0933D71E8C94E04A25619DCEE3D2261AD2EE6B'''
            + '''F12FFA06D98A0864D87602733EC86A64521F2B18177B200C'''
            + '''BBE117577A615D6C770988C0BAD946E208E24FA074E5AB31'''
            + '''43DB5BFCE0FD108E4B82D120A93AD2CAFFFFFFFFFFFFFFFF''',
            base=16,
        ),
        '''generator''': 2,
    },
    # 4096-bit
    16: {
        '''prime''': int(
            '''FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD1'''
            + '''29024E088A67CC74020BBEA63B139B22514A08798E3404DD'''
            + '''EF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245'''
            + '''E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED'''
            + '''EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3D'''
            + '''C2007CB8A163BF0598DA48361C55D39A69163FA8FD24CF5F'''
            + '''83655D23DCA3AD961C62F356208552BB9ED529077096966D'''
            + '''670C354E4ABC9804F1746C08CA18217C32905E462E36CE3B'''
            + '''E39E772C180E86039B2783A2EC07A28FB5C55DF06F4C52C9'''
            + '''DE2BCBF6955817183995497CEA956AE515D2261898FA0510'''
            + '''15728E5A8AAAC42DAD33170D04507A33A85521ABDF1CBA64'''
            + '''ECFB850458DBEF0A8AEA71575D060C7DB3970F85A6E1E4C7'''
            + '''ABF5AE8CDB0933D71E8C94E04A25619DCEE3D2261AD2EE6B'''
            + '''F12FFA06D98A0864D87602733EC86A64521F2B18177B200C'''
            + '''BBE117577A615D6C770988C0BAD946E208E24FA074E5AB31'''
            + '''43DB5BFCE0FD108E4B82D120A92108011A723C12A787E6D7'''
            + '''88719A10BDBA5B2699C327186AF4E23C1A946834B6150BDA'''
            + '''2583E9CA2AD44CE8DBBBC2DB04DE8EF92E8EFC141FBECAA6'''
            + '''287C59474E6BC05D99B2964FA090C3A2233BA186515BE7ED'''
            + '''1F612970CEE2D7AFB81BDD762170481CD0069127D5B05AA9'''
            + '''93B4EA988D8FDDC186FFB7DC90A6C08F4DF435C934063199'''
            + '''FFFFFFFFFFFFFFFF''',
            base=16,
        ),
        '''generator''': 2,
    },
    # 6144-bit
    17: {
        '''prime''': int(
            '''FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD129024E08'''
            + '''8A67CC74020BBEA63B139B22514A08798E3404DDEF9519B3CD3A431B'''
            + '''302B0A6DF25F14374FE1356D6D51C245E485B576625E7EC6F44C42E9'''
            + '''A637ED6B0BFF5CB6F406B7EDEE386BFB5A899FA5AE9F24117C4B1FE6'''
            + '''49286651ECE45B3DC2007CB8A163BF0598DA48361C55D39A69163FA8'''
            + '''FD24CF5F83655D23DCA3AD961C62F356208552BB9ED529077096966D'''
            + '''670C354E4ABC9804F1746C08CA18217C32905E462E36CE3BE39E772C'''
            + '''180E86039B2783A2EC07A28FB5C55DF06F4C52C9DE2BCBF695581718'''
            + '''3995497CEA956AE515D2261898FA051015728E5A8AAAC42DAD33170D'''
            + '''04507A33A85521ABDF1CBA64ECFB850458DBEF0A8AEA71575D060C7D'''
            + '''B3970F85A6E1E4C7ABF5AE8CDB0933D71E8C94E04A25619DCEE3D226'''
            + '''1AD2EE6BF12FFA06D98A0864D87602733EC86A64521F2B18177B200C'''
            + '''BBE117577A615D6C770988C0BAD946E208E24FA074E5AB3143DB5BFC'''
            + '''E0FD108E4B82D120A92108011A723C12A787E6D788719A10BDBA5B26'''
            + '''99C327186AF4E23C1A946834B6150BDA2583E9CA2AD44CE8DBBBC2DB'''
            + '''04DE8EF92E8EFC141FBECAA6287C59474E6BC05D99B2964FA090C3A2'''
            + '''233BA186515BE7ED1F612970CEE2D7AFB81BDD762170481CD0069127'''
            + '''D5B05AA993B4EA988D8FDDC186FFB7DC90A6C08F4DF435C934028492'''
            + '''36C3FAB4D27C7026C1D4DCB2602646DEC9751E763DBA37BDF8FF9406'''
            + '''AD9E530EE5DB382F413001AEB06A53ED9027D831179727B0865A8918'''
            + '''DA3EDBEBCF9B14ED44CE6CBACED4BB1BDB7F1447E6CC254B33205151'''
            + '''2BD7AF426FB8F401378CD2BF5983CA01C64B92ECF032EA15D1721D03'''
            + '''F482D7CE6E74FEF6D55E702F46980C82B5A84031900B1C9E59E7C97F'''
            + '''BEC7E8F323A97A7E36CC88BE0F1D45B7FF585AC54BD407B22B4154AA'''
            + '''CC8F6D7EBF48E1D814CC5ED20F8037E0A79715EEF29BE32806A1D58B'''
            + '''B7C5DA76F550AA3D8A1FBFF0EB19CCB1A313D55CDA56C9EC2EF29632'''
            + '''387FE8D76E3C0468043E8F663F4860EE12BF2D5B0B7474D6E694F91E'''
            + '''6DCC4024FFFFFFFFFFFFFFFF''',
            base=16,
        ),
        '''generator''': 2,
    },
    # 8192-bit
    18: {
        '''prime''': int(
            '''FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD1'''
            + '''29024E088A67CC74020BBEA63B139B22514A08798E3404DD'''
            + '''EF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245'''
            + '''E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED'''
            + '''EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3D'''
            + '''C2007CB8A163BF0598DA48361C55D39A69163FA8FD24CF5F'''
            + '''83655D23DCA3AD961C62F356208552BB9ED529077096966D'''
            + '''670C354E4ABC9804F1746C08CA18217C32905E462E36CE3B'''
            + '''E39E772C180E86039B2783A2EC07A28FB5C55DF06F4C52C9'''
            + '''DE2BCBF6955817183995497CEA956AE515D2261898FA0510'''
            + '''15728E5A8AAAC42DAD33170D04507A33A85521ABDF1CBA64'''
            + '''ECFB850458DBEF0A8AEA71575D060C7DB3970F85A6E1E4C7'''
            + '''ABF5AE8CDB0933D71E8C94E04A25619DCEE3D2261AD2EE6B'''
            + '''F12FFA06D98A0864D87602733EC86A64521F2B18177B200C'''
            + '''BBE117577A615D6C770988C0BAD946E208E24FA074E5AB31'''
            + '''43DB5BFCE0FD108E4B82D120A92108011A723C12A787E6D7'''
            + '''88719A10BDBA5B2699C327186AF4E23C1A946834B6150BDA'''
            + '''2583E9CA2AD44CE8DBBBC2DB04DE8EF92E8EFC141FBECAA6'''
            + '''287C59474E6BC05D99B2964FA090C3A2233BA186515BE7ED'''
            + '''1F612970CEE2D7AFB81BDD762170481CD0069127D5B05AA9'''
            + '''93B4EA988D8FDDC186FFB7DC90A6C08F4DF435C934028492'''
            + '''36C3FAB4D27C7026C1D4DCB2602646DEC9751E763DBA37BD'''
            + '''F8FF9406AD9E530EE5DB382F413001AEB06A53ED9027D831'''
            + '''179727B0865A8918DA3EDBEBCF9B14ED44CE6CBACED4BB1B'''
            + '''DB7F1447E6CC254B332051512BD7AF426FB8F401378CD2BF'''
            + '''5983CA01C64B92ECF032EA15D1721D03F482D7CE6E74FEF6'''
            + '''D55E702F46980C82B5A84031900B1C9E59E7C97FBEC7E8F3'''
            + '''23A97A7E36CC88BE0F1D45B7FF585AC54BD407B22B4154AA'''
            + '''CC8F6D7EBF48E1D814CC5ED20F8037E0A79715EEF29BE328'''
            + '''06A1D58BB7C5DA76F550AA3D8A1FBFF0EB19CCB1A313D55C'''
            + '''DA56C9EC2EF29632387FE8D76E3C0468043E8F663F4860EE'''
            + '''12BF2D5B0B7474D6E694F91E6DBE115974A3926F12FEE5E4'''
            + '''38777CB6A932DF8CD8BEC4D073B931BA3BC832B68D9DD300'''
            + '''741FA7BF8AFC47ED2576F6936BA424663AAB639C5AE4F568'''
            + '''3423B4742BF1C978238F16CBE39D652DE3FDB8BEFC848AD9'''
            + '''22222E04A4037C0713EB57A81A23F0C73473FC646CEA306B'''
            + '''4BCBC8862F8385DDFA9D4B7FA2C087E879683303ED5BDD3A'''
            + '''062B3CF5B3A278A66D2A13F83F44F82DDF310EE074AB6A36'''
            + '''4597E899A0255DC164F31CC50846851DF9AB48195DED7EA1'''
            + '''B1D510BD7EE74D73FAF36BC31ECFA268359046F4EB879F92'''
            + '''4009438B481C6CD7889A002ED5EE382BC9190DA6FC026E47'''
            + '''9558E4475677E9AA9E3050E2765694DFC81F56E880B96E71'''
            + '''60C980DD98EDD3DFFFFFFFFFFFFFFFFF''',
            base=16,
        ),
        '''generator''': 2,
    },
}


class        __magic_name__	:





     """simple docstring"""



     def __init__(				self							:List[str]      ,   snake_case							:int = 14	):





        '''simple docstring'''




        if group not in primes:
           raise ValueError("Unsupported Group"	)
        A_       :					List[str]        =      primes[group]["prime"]
        A_       :					Tuple        =      primes[group]["generator"]

        A_       :					Optional[Any]        =      int(hexlify(urandom(32	)	)      ,   base=16	)



     def     SCREAMING_SNAKE_CASE		(				self							:Optional[Any]	):





        '''simple docstring'''




        return hex(self.__private_key	)[2:]



     def     SCREAMING_SNAKE_CASE		(				self							:List[str]	):





        '''simple docstring'''




        A_       :					Tuple        =      pow(self.generator      ,   self.__private_key      ,   self.prime	)
        return hex(snake_case	)[2:]



     def     SCREAMING_SNAKE_CASE		(				self							:List[str]      ,   snake_case							:int	):





        '''simple docstring'''




        return (
            2 <= key <= self.prime - 2
            and pow(snake_case      ,   (self.prime - 1) // 2      ,   self.prime	) == 1
        )



     def     SCREAMING_SNAKE_CASE		(				self							:Tuple      ,   snake_case							:str	):





        '''simple docstring'''




        A_       :					Optional[int]        =      int(snake_case      ,   base=16	)
        if not self.is_valid_public_key(snake_case	):
           raise ValueError("Invalid public key"	)
        A_       :					int        =      pow(snake_case      ,   self.__private_key      ,   self.prime	)
        return shaaaa(str(snake_case	).encode()	).hexdigest()



     @staticmethod
     def     SCREAMING_SNAKE_CASE		(				snake_case							:int      ,   snake_case							:int	):





        '''simple docstring'''




        return (
            2 <= remote_public_key_str <= prime - 2
            and pow(snake_case      ,   (prime - 1) // 2      ,   snake_case	) == 1
        )





     @staticmethod
     def     SCREAMING_SNAKE_CASE		(				snake_case							:str      ,   snake_case							:str      ,   snake_case							:int = 14	):





        '''simple docstring'''




        A_       :					List[str]        =      int(snake_case      ,   base=16	)
        A_       :					Optional[Any]        =      int(snake_case      ,   base=16	)
        A_       :					int        =      primes[group]["prime"]
        if not DiffieHellman.is_valid_public_key_static(snake_case      ,   snake_case	):
           raise ValueError("Invalid public key"	)
        A_       :					str        =      pow(snake_case      ,   snake_case      ,   snake_case	)
        return shaaaa(str(snake_case	).encode()	).hexdigest()


if __name__ == "__main__":
 import doctest

 doctest.testmod()







from __future__ import annotations

import math
import random
from typing import Any


class        __magic_name__	:





     """simple docstring"""



     def __init__(				self							:Tuple	):





        '''simple docstring'''




        A_       :					list[Any]        =      []
        A_       :					int        =      0
        A_       :					int        =      0



     def     SCREAMING_SNAKE_CASE		(				self							:List[Any]	):





        '''simple docstring'''




        return self.head == self.tail



     def     SCREAMING_SNAKE_CASE		(				self							:Optional[Any]      ,   snake_case							:Any	):





        '''simple docstring'''




        self.data.append(snake_case	)
        A_       :					int        =      self.tail + 1



     def     SCREAMING_SNAKE_CASE		(				self							:str	):





        '''simple docstring'''




        A_       :					int        =      self.data[self.head]
        A_       :					Tuple        =      self.head + 1
        return ret



     def     SCREAMING_SNAKE_CASE		(				self							:Optional[int]	):





        '''simple docstring'''




        return self.tail - self.head





     def     SCREAMING_SNAKE_CASE		(				self							:Any	):





        '''simple docstring'''




        print(self.data	)
        print("**************"	)
        print(self.data[self.head : self.tail]	)




class        __magic_name__	:





     """simple docstring"""



     def __init__(				self							:Any      ,   snake_case							:Any	):





        '''simple docstring'''




        A_       :					Any        =      data
        A_       :					MyNode | None        =      None
        A_       :					MyNode | None        =      None
        A_       :					int        =      1



     def     SCREAMING_SNAKE_CASE		(				self							:List[str]	):





        '''simple docstring'''




        return self.data



     def     SCREAMING_SNAKE_CASE		(				self							:Dict	):





        '''simple docstring'''




        return self.left



     def     SCREAMING_SNAKE_CASE		(				self							:Any	):





        '''simple docstring'''




        return self.right



     def     SCREAMING_SNAKE_CASE		(				self							:List[Any]	):





        '''simple docstring'''




        return self.height



     def     SCREAMING_SNAKE_CASE		(				self							:List[str]      ,   snake_case							:Any	):





        '''simple docstring'''




        A_       :					Optional[int]        =      data



     def     SCREAMING_SNAKE_CASE		(				self							:Optional[int]      ,   snake_case							:MyNode | None	):





        '''simple docstring'''




        A_       :					Tuple        =      node



     def     SCREAMING_SNAKE_CASE		(				self							:str      ,   snake_case							:MyNode | None	):





        '''simple docstring'''




        A_       :					str        =      node





     def     SCREAMING_SNAKE_CASE		(				self							:Tuple      ,   snake_case							:int	):





        '''simple docstring'''




        A_       :					Optional[int]        =      height




def   __snake_case    (       _lowerCAmelCase			:			MyNode | None						)			->    int:
   if node is None:
      return 0
   return node.get_height()

def   __snake_case    (       _lowerCAmelCase			:			int					,					_lowerCAmelCase			:			int						)			->    int:
   if a > b:
      return a
   return b

def   __snake_case    (       _lowerCAmelCase			:			MyNode						)			->    MyNode:
   print("left rotation node:"					,					node.get_data()						)
   A_       :					Optional[int]        =      node.get_left()
   assert ret is not None
   node.set_left(ret.get_right()						)
   ret.set_right(_lowerCAmelCase						)
   A_       :					Any        =      my_max(get_height(node.get_right()						)					,					get_height(node.get_left()						)						) + 1
   node.set_height(_lowerCAmelCase						)
   A_       :					List[str]        =      my_max(get_height(ret.get_right()						)					,					get_height(ret.get_left()						)						) + 1
   ret.set_height(_lowerCAmelCase						)
   return ret

def   __snake_case    (       _lowerCAmelCase			:			MyNode						)			->    MyNode:
   print("right rotation node:"					,					node.get_data()						)
   A_       :					Union[str, Any]        =      node.get_right()
   assert ret is not None
   node.set_right(ret.get_left()						)
   ret.set_left(_lowerCAmelCase						)
   A_       :					int        =      my_max(get_height(node.get_right()						)					,					get_height(node.get_left()						)						) + 1
   node.set_height(_lowerCAmelCase						)
   A_       :					Dict        =      my_max(get_height(ret.get_right()						)					,					get_height(ret.get_left()						)						) + 1
   ret.set_height(_lowerCAmelCase						)
   return ret

def   __snake_case    (       _lowerCAmelCase			:			MyNode						)			->    MyNode:
   A_       :					List[Any]        =      node.get_left()
   assert left_child is not None
   node.set_left(left_rotation(_lowerCAmelCase						)						)
   return right_rotation(_lowerCAmelCase						)

def   __snake_case    (       _lowerCAmelCase			:			MyNode						)			->    MyNode:
   A_       :					List[Any]        =      node.get_right()
   assert right_child is not None
   node.set_right(right_rotation(_lowerCAmelCase						)						)
   return left_rotation(_lowerCAmelCase						)

def   __snake_case    (       _lowerCAmelCase			:			MyNode | None					,					_lowerCAmelCase			:			Any						)			->    MyNode | None:
   if node is None:
      return MyNode(_lowerCAmelCase						)
   if data < node.get_data():
      node.set_left(insert_node(node.get_left()					,					_lowerCAmelCase						)						)
      if (
          get_height(node.get_left()						) - get_height(node.get_right()						) == 2
      ):  # an unbalance detected
         A_       :					Any        =      node.get_left()
         assert left_child is not None
         if (
             data < left_child.get_data()
         ):  # new node is the left child of the left child
            A_       :					Optional[int]        =      right_rotation(_lowerCAmelCase						)
         else:
            A_       :					int        =      lr_rotation(_lowerCAmelCase						)
   else:
      node.set_right(insert_node(node.get_right()					,					_lowerCAmelCase						)						)
      if get_height(node.get_right()						) - get_height(node.get_left()						) == 2:
         A_       :					Dict        =      node.get_right()
         assert right_child is not None
         if data < right_child.get_data():
            A_       :					Optional[Any]        =      rl_rotation(_lowerCAmelCase						)
         else:
            A_       :					Dict        =      left_rotation(_lowerCAmelCase						)
   A_       :					Optional[int]        =      my_max(get_height(node.get_right()						)					,					get_height(node.get_left()						)						) + 1
   node.set_height(_lowerCAmelCase						)
   return node

def   __snake_case    (       _lowerCAmelCase			:			MyNode						)			->    Any:
   while True:
      A_       :					Any        =      root.get_right()
      if right_child is None:
         break
      A_       :					Optional[Any]        =      right_child
   return root.get_data()

def   __snake_case    (       _lowerCAmelCase			:			MyNode						)			->    Any:
   while True:
      A_       :					Optional[Any]        =      root.get_left()
      if left_child is None:
         break
      A_       :					int        =      left_child
   return root.get_data()

def   __snake_case    (       _lowerCAmelCase			:			MyNode					,					_lowerCAmelCase			:			Any						)			->    MyNode | None:
   A_       :					Optional[int]        =      root.get_left()
   A_       :					Dict        =      root.get_right()
   if root.get_data() == data:
      if left_child is not None and right_child is not None:
         A_       :					int        =      get_left_most(_lowerCAmelCase						)
         root.set_data(_lowerCAmelCase						)
         root.set_right(del_node(_lowerCAmelCase					,					_lowerCAmelCase						)						)
      elif left_child is not None:
         A_       :					Tuple        =      left_child
      elif right_child is not None:
         A_       :					Any        =      right_child
      else:
         return None
   elif root.get_data() > data:
      if left_child is None:
         print("No such data"						)
         return root
      else:
         root.set_left(del_node(_lowerCAmelCase					,					_lowerCAmelCase						)						)
   else:  # root.get_data() < data
      if right_child is None:
         return root
      else:
         root.set_right(del_node(_lowerCAmelCase					,					_lowerCAmelCase						)						)

   if get_height(_lowerCAmelCase						) - get_height(_lowerCAmelCase						) == 2:
      assert right_child is not None
      if get_height(right_child.get_right()						) > get_height(right_child.get_left()						):
         A_       :					Dict        =      left_rotation(_lowerCAmelCase						)
      else:
         A_       :					List[Any]        =      rl_rotation(_lowerCAmelCase						)
   elif get_height(_lowerCAmelCase						) - get_height(_lowerCAmelCase						) == -2:
      assert left_child is not None
      if get_height(left_child.get_left()						) > get_height(left_child.get_right()						):
         A_       :					Optional[Any]        =      right_rotation(_lowerCAmelCase						)
      else:
         A_       :					Tuple        =      lr_rotation(_lowerCAmelCase						)
   A_       :					List[str]        =      my_max(get_height(root.get_right()						)					,					get_height(root.get_left()						)						) + 1
   root.set_height(_lowerCAmelCase						)
   return root


class        __magic_name__	:





     """simple docstring"""



     def __init__(				self							:List[str]	):





        '''simple docstring'''




        A_       :					MyNode | None        =      None



     def     SCREAMING_SNAKE_CASE		(				self							:List[Any]	):





        '''simple docstring'''




        return get_height(self.root	)



     def     SCREAMING_SNAKE_CASE		(				self							:str      ,   snake_case							:Any	):





        '''simple docstring'''




        print("insert:" + str(snake_case	)	)
        A_       :					List[Any]        =      insert_node(self.root      ,   snake_case	)



     def     SCREAMING_SNAKE_CASE		(				self							:Optional[Any]      ,   snake_case							:Any	):





        '''simple docstring'''




        print("delete:" + str(snake_case	)	)
        if self.root is None:
           print("Tree is empty!"	)
           return
        A_       :					Dict        =      del_node(self.root      ,   snake_case	)





     def __str__(				self							:Optional[int]      ,   ):  # a level traversale, gives a more intuitive look on the tree





        '''simple docstring'''




        A_       :					Optional[Any]        =      ""
        A_       :					Optional[int]        =      MyQueue()
        q.push(self.root	)
        A_       :					Optional[int]        =      self.get_height()
        if layer == 0:
           return output
        A_       :					Dict        =      0
        while not q.is_empty():
           A_       :					Optional[int]        =      q.pop()
           A_       :					Union[str, Any]        =      " " * int(math.pow(2      ,   layer - 1	)	)
           output += space
           if node is None:
              output += "*"
              q.push(snake_case	)
              q.push(snake_case	)
           else:
              output += str(node.get_data()	)
              q.push(node.get_left()	)
              q.push(node.get_right()	)
           output += space
           A_       :					str        =      cnt + 1
           for i in range(100	):
              if cnt == math.pow(2      ,   snake_case	) - 1:
                 A_       :					int        =      layer - 1
                 if layer == 0:
                    output += "\n*************************************"
                    return output
                 output += "\n"
                 break
        output += "\n*************************************"
        return output




def   __snake_case    (       )			->    None:
   import doctest

   doctest.testmod()


if __name__ == "__main__":
 _test()
 _lowerCAmelCase				:   int						       =						AVLtree()
 _lowerCAmelCase				:   Optional[int]						       =						list(range(10))
 random.shuffle(lst)
 for i in lst:
  t.insert(i)
  print(str(t))
 random.shuffle(lst)
 for i in lst:
  t.del_node(i)
  print(str(t))
