






'''simple docstring'''



from __future__ import annotations

from random import random
class UpperCAmelCase_       :




      """simple docstring"""




      def __init__(			self      :		Dict  ,   UpperCAmelCase      :		int | None = None		)	->	Union[str, Any]:


       '''simple docstring'''

       lowercase       : str						=value
       lowercase       : Tuple						=random()
       lowercase       : Node | None						=None
       lowercase       : Node | None						=None






      def __repr__(			self      :		Tuple		)	->	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'''

       lowercase       : Dict						=str(self.value		) + ''' '''
       lowercase       : Optional[Any]						=str(self.left or ''''''		)
       lowercase       : int						=str(self.right or ''''''		)
       return value + left + right





def 				lowercase_					(     __A			:							Node | None       ,   __A			:							int      )							->   tuple[Node | None, Node | None]:



 """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:
   lowercase	,		lowercase       : Optional[Any]						=split(root.left       ,   __A      )
   return left, root
  else:
   lowercase	,		lowercase       : List[str]						=split(root.right       ,   __A      )
   return root, right


def 				lowercase_					(     __A			:							Node | None       ,   __A			:							Node | None      )							->   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:
  lowercase       : Union[str, Any]						=merge(left.right       ,   __A      )
  return left
 else:
  lowercase       : Union[str, Any]						=merge(__A       ,   right.left      )
  return right


def 				lowercase_					(     __A			:							Node | None       ,   __A			:							int      )							->   Node | None:



 """simple docstring"""




 lowercase       : Union[str, Any]						=Node(__A      )
 lowercase	,		lowercase       : Union[str, Any]						=split(__A       ,   __A      )
 return merge(merge(__A       ,   __A      )       ,   __A      )


def 				lowercase_					(     __A			:							Node | None       ,   __A			:							int      )							->   Node | None:



 """simple docstring"""




 lowercase	,		lowercase       : str						=split(__A       ,   value - 1      )
 lowercase	,		lowercase       : Optional[Any]						=split(__A       ,   __A      )
 return merge(__A       ,   __A      )


def 				lowercase_					(     __A			:							Node | None      )							->   None:



 """simple docstring"""




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


def 				lowercase_					(     __A			:							Node | None       ,   __A			:							str      )							->   Node | None:



 """simple docstring"""




 for arg in args.split():
  if arg[0] == "+":
   lowercase       : Tuple						=insert(__A       ,   int(arg[1:]      )      )

  elif arg[0] == "-":
   lowercase       : Optional[int]						=erase(__A       ,   int(arg[1:]      )      )

  else:
   print('''Unknown command'''      )

 return root


def 				lowercase_					(     )							->   None:



 """simple docstring"""




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

 lowercase       : Optional[int]						=input()
 while args != "q":
  lowercase       : Tuple						=interact_treap(__A       ,   __A      )
  print(__A      )
  lowercase       : List[str]						=input()

 print('''good by!'''      )


if __name__ == "__main__":
      import doctest

      doctest.testmod()
      main()











'''simple docstring'''



from __future__ import annotations


def 				lowercase_					(     __A			:							list[list[int]]      )							->   int:



 """simple docstring"""




 for i in range(1       ,   len(matrix[0]      )      ):
  matrix[0][i] += matrix[0][i - 1]

 # preprocessing the first column
 for i in range(1       ,   len(__A      )      ):
  matrix[i][0] += matrix[i - 1][0]

 # updating the path cost for current position
 for i in range(1       ,   len(__A      )      ):
  for j in range(1       ,   len(matrix[0]      )      ):
   matrix[i][j] += min(matrix[i - 1][j]       ,   matrix[i][j - 1]      )

 return matrix[-1][-1]


if __name__ == "__main__":
      import doctest

      doctest.testmod()



