from __future__ import annotations

from random import random

class    snake_case       :




  def __init__(   self  :						Any  ,			a_  :						int | None = None					)->							str:




       """simple docstring"""
       SCREAMING_SNAKE_CASE__					:					Tuple      =		value
       SCREAMING_SNAKE_CASE__					:					Optional[Any]      =		random()
       SCREAMING_SNAKE_CASE__					:					Node | None      =		None
       SCREAMING_SNAKE_CASE__					:					Node | None      =		None




  def __repr__(   self  :						int					)->							str:




       """simple docstring"""
       from pprint import pformat

       if self.left is None and self.right is None:
            return F'''\'{self.value}: {self.prior:.5}\''''
       else:
            return pformat(
                {F'''{self.value}: {self.prior:.5}''': (self.left, self.right)}  ,			indent=1					)




  def __str__(   self  :						Tuple					)->							str:




       """simple docstring"""
       SCREAMING_SNAKE_CASE__					:					List[Any]      =		str(self.value					) + ' '
       SCREAMING_SNAKE_CASE__					:					str      =		str(self.left or ''					)
       SCREAMING_SNAKE_CASE__					:					Any      =		str(self.right or ''					)
       return value + left + right







def      _a					(   lowercase__	:      Node | None  ,	lowercase__	:      int			):







     '''simple docstring'''


     if root is None:  # None tree is split into 2 Nones
          return None, None
     elif root.value is None:
          return None, None
     else:
          if value < root.value:
               SCREAMING_SNAKE_CASE__      ,				SCREAMING_SNAKE_CASE__					:					List[Any]      =		split(root.left  ,	lowercase__			)
               return left, root
          else:
               SCREAMING_SNAKE_CASE__      ,				SCREAMING_SNAKE_CASE__					:					Union[str, Any]      =		split(root.right  ,	lowercase__			)
               return root, right







def      _a					(   lowercase__	:      Node | None  ,	lowercase__	:      Node | None			):







     '''simple docstring'''


     if (not left) or (not right):  # If one node is None, return the other
          return left or right
     elif left.prior < right.prior:
          SCREAMING_SNAKE_CASE__					:					Any      =		merge(left.right  ,	lowercase__			)
          return left
     else:
          SCREAMING_SNAKE_CASE__					:					Optional[int]      =		merge(lowercase__  ,	right.left			)
          return right







def      _a					(   lowercase__	:      Node | None  ,	lowercase__	:      int			):







     '''simple docstring'''


     SCREAMING_SNAKE_CASE__					:					Any      =		Node(lowercase__			)
     SCREAMING_SNAKE_CASE__      ,				SCREAMING_SNAKE_CASE__					:					int      =		split(lowercase__  ,	lowercase__			)
     return merge(merge(lowercase__  ,	lowercase__			)  ,	lowercase__			)







def      _a					(   lowercase__	:      Node | None  ,	lowercase__	:      int			):







     '''simple docstring'''


     SCREAMING_SNAKE_CASE__      ,				SCREAMING_SNAKE_CASE__					:					List[Any]      =		split(lowercase__  ,	value - 1			)
     SCREAMING_SNAKE_CASE__      ,				SCREAMING_SNAKE_CASE__					:					Tuple      =		split(lowercase__  ,	lowercase__			)
     return merge(lowercase__  ,	lowercase__			)







def      _a					(   lowercase__	:      Node | None			):







     '''simple docstring'''


     if not root:  # None
          return
     else:
          inorder(root.left			)
          print(root.value  ,	end=','			)
          inorder(root.right			)







def      _a					(   lowercase__	:      Node | None  ,	lowercase__	:      str			):







     '''simple docstring'''


     for arg in args.split():
          if arg[0] == "+":
               SCREAMING_SNAKE_CASE__					:					List[Any]      =		insert(lowercase__  ,	int(arg[1:]			)			)

          elif arg[0] == "-":
               SCREAMING_SNAKE_CASE__					:					Any      =		erase(lowercase__  ,	int(arg[1:]			)			)

          else:
               print('Unknown command'			)

     return root







def      _a					(   ):







     '''simple docstring'''


     SCREAMING_SNAKE_CASE__					:					Optional[int]      =		None
     print(
         'enter numbers to create a tree, + value to add value into treap, '
         '- value to erase all nodes with value. \'q\' to quit. '			)

     SCREAMING_SNAKE_CASE__					:					List[str]      =		input()
     while args != "q":
          SCREAMING_SNAKE_CASE__					:					Tuple      =		interact_treap(lowercase__  ,	lowercase__			)
          print(lowercase__			)
          SCREAMING_SNAKE_CASE__					:					List[str]      =		input()

     print('good by!'			)


if __name__ == "__main__":
      import doctest

      doctest.testmod()
      main()








'''simple docstring'''





SCREAMING_SNAKE_CASE__          =  256
# Modulus to hash a string
SCREAMING_SNAKE_CASE__          =  100_0003




def 							lowerCamelCase	(					_snake_case	:    str  ,_snake_case	:    str							):





    '''simple docstring'''


    lowercase__									=    len(_snake_case							)
    lowercase__									=    len(_snake_case							)
    if p_len > t_len:
        return False

    lowercase__									=    0
    lowercase__									=    0
    lowercase__									=    1

    # Calculating the hash of pattern and substring of text
    for i in range(_snake_case							):
        lowercase__									=    (ord(pattern[i]							) + p_hash * alphabet_size) % modulus
        lowercase__									=    (ord(text[i]							) + text_hash * alphabet_size) % modulus
        if i == p_len - 1:
            continue
        lowercase__									=    (modulus_power * alphabet_size) % modulus

    for i in range(0  ,t_len - p_len + 1							):
        if text_hash == p_hash and text[i : i + p_len] == pattern:
            return True
        if i == t_len - p_len:
            continue
        # Calculate the https://en.wikipedia.org/wiki/Rolling_hash
        lowercase__									=    (
            (text_hash - ord(text[i]							) * modulus_power) * alphabet_size
            + ord(text[i + p_len]							)
        ) % modulus
    return False




def 							lowerCamelCase	(					):





    '''simple docstring'''


    lowercase__									=    "abc1abc12"
    lowercase__									=    "alskfjaldsabc1abc1abc12k23adsfabcabc"
    lowercase__									=    "alskfjaldsk23adsfabcabc"
    assert rabin_karp(_snake_case  ,_snake_case							) and not rabin_karp(_snake_case  ,_snake_case							)

    # Test 2)
    lowercase__									=    "ABABX"
    lowercase__									=    "ABABZABABYABABX"
    assert rabin_karp(_snake_case  ,_snake_case							)

    # Test 3)
    lowercase__									=    "AAAB"
    lowercase__									=    "ABAAAAAB"
    assert rabin_karp(_snake_case  ,_snake_case							)

    # Test 4)
    lowercase__									=    "abcdabcy"
    lowercase__									=    "abcxabcdabxabcdabcdabcy"
    assert rabin_karp(_snake_case  ,_snake_case							)

    # Test 5)
    lowercase__									=    "Lü"
    lowercase__									=    "Lüsai"
    assert rabin_karp(_snake_case  ,_snake_case							)
    lowercase__									=    "Lue"
    assert not rabin_karp(_snake_case  ,_snake_case							)
    print("Success."							)


if __name__ == "__main__":
 test_rabin_karp()




