


from __future__ import annotations

from dataclasses import dataclass






@dataclass
class    UpperCAmelCase__	:



				"""simple docstring"""






				UpperCAmelCase__						:		float
				UpperCAmelCase__						:		TreeNode | None              =  None
				UpperCAmelCase__						:		TreeNode | None              =  None

def 						_UpperCAmelCase    (      SCREAMING_SNAKE_CASE__      : Union[str, Any]    ):



					def is_valid_tree(SCREAMING_SNAKE_CASE__      : Optional[Any]    ) -> bool:
										if node is None:
															return True

										if not isinstance(A__      ,					A__    ):
															return False

										try:
															float(node.data    )
										except (TypeError, ValueError):
															return False

										return is_valid_tree(node.left    ) and is_valid_tree(node.right    )

					if not is_valid_tree(A__    ):
										raise ValueError(
										    'Each node should be type of TreeNode and data should be float.'    )

					def is_binary_search_tree_recursive_check(
					    SCREAMING_SNAKE_CASE__      : Union[str, Any]      ,					SCREAMING_SNAKE_CASE__      : List[str]      ,					SCREAMING_SNAKE_CASE__      : List[str]    ) -> bool:

										if node is None:
															return True

										return (
										    left_bound < node.data < right_bound
										    and is_binary_search_tree_recursive_check(node.left      ,					A__      ,					node.data    )
										    and is_binary_search_tree_recursive_check(
										        node.right      ,					node.data      ,					A__    )
										)

					return is_binary_search_tree_recursive_check(A__      ,					-float('inf'    )      ,					float('inf'    )    )


if __name__ == "__main__":
			import doctest

			doctest.testmod()









from __future__ import annotations

def 						_UpperCAmelCase    (      SCREAMING_SNAKE_CASE__      : int      ,					SCREAMING_SNAKE_CASE__      : int    ):
     if b == 0:
          return (1, 0)
     ((__UpperCamelCase)							,				(__UpperCamelCase))   							=extended_euclid(SCREAMING_SNAKE_CASE__      ,					a % b    )
     __UpperCamelCase   							=a // b
     return (y, x - k * y)

def 						_UpperCAmelCase    (      SCREAMING_SNAKE_CASE__      : int      ,					SCREAMING_SNAKE_CASE__      : int      ,					SCREAMING_SNAKE_CASE__      : int      ,					SCREAMING_SNAKE_CASE__      : int    ):
     ((__UpperCamelCase)							,				(__UpperCamelCase))   							=extended_euclid(SCREAMING_SNAKE_CASE__      ,					SCREAMING_SNAKE_CASE__    )
     __UpperCamelCase   							=na * na
     __UpperCamelCase   							=ra * x * na + ra * y * na
     return (n % m + m) % m

def 						_UpperCAmelCase    (      SCREAMING_SNAKE_CASE__      : int      ,					SCREAMING_SNAKE_CASE__      : int    ):
     ((__UpperCamelCase)							,				(__UpperCamelCase))   							=extended_euclid(SCREAMING_SNAKE_CASE__      ,					SCREAMING_SNAKE_CASE__    )
     if b < 0:
          __UpperCamelCase   							=(b % n + n) % n
     return b

def 						_UpperCAmelCase    (      SCREAMING_SNAKE_CASE__      : int      ,					SCREAMING_SNAKE_CASE__      : int      ,					SCREAMING_SNAKE_CASE__      : int      ,					SCREAMING_SNAKE_CASE__      : int    ):
     __UpperCamelCase							,				__UpperCamelCase   							=invert_modulo(SCREAMING_SNAKE_CASE__      ,					SCREAMING_SNAKE_CASE__    ), invert_modulo(SCREAMING_SNAKE_CASE__      ,					SCREAMING_SNAKE_CASE__    )
     __UpperCamelCase   							=na * na
     __UpperCamelCase   							=ra * x * na + ra * y * na
     return (n % m + m) % m


if __name__ == "__main__":
   from doctest import testmod

   testmod(name='chinese_remainder_theorem', verbose=True)
   testmod(name='chinese_remainder_theorem2', verbose=True)
   testmod(name='invert_modulo', verbose=True)
   testmod(name='extended_euclid', verbose=True)





