




from __future__ import annotations

from collections import namedtuple
from dataclasses import dataclass
@dataclass
class       a__   :
						_a							:   int
						_a							:   TreeNode | None =   None
						_a							:   TreeNode | None =   None






UpperCamelCase__         =      namedtuple("""CoinsDistribResult""", """moves excess""")







def      _a				(						SCREAMING_SNAKE_CASE_							:    TreeNode | None					):

					if root is None:
										return 0

					# Validation
					def count_nodes(SCREAMING_SNAKE_CASE_							:    TreeNode | None					) -> int:
										if node is None:
															return 0

										return count_nodes(node.left					) + count_nodes(node.right					) + 1

					def count_coins(SCREAMING_SNAKE_CASE_							:    TreeNode | None					) -> int:
										if node is None:
															return 0

										return count_coins(node.left					) + count_coins(node.right					) + node.data

					if count_nodes(SCREAMING_SNAKE_CASE_					) != count_coins(SCREAMING_SNAKE_CASE_					):
										raise ValueError("The nodes number should be same as the number of coins"					)

					# Main calculation
					def get_distrib(SCREAMING_SNAKE_CASE_							:    TreeNode | None					) -> CoinsDistribResult:

										if node is None:
															return CoinsDistribResult(0				,				1					)

										__lowerCAmelCase       ,							__lowerCAmelCase           =	get_distrib(node.left					)
										__lowerCAmelCase       ,							__lowerCAmelCase           =	get_distrib(node.right					)

										__lowerCAmelCase           =	1 - left_distrib_excess
										__lowerCAmelCase           =	1 - right_distrib_excess

										__lowerCAmelCase           =	(
										    left_distrib_moves
										    + right_distrib_moves
										    + abs(SCREAMING_SNAKE_CASE_					)
										    + abs(SCREAMING_SNAKE_CASE_					)
										)
										__lowerCAmelCase           =	node.data - coins_to_left - coins_to_right

										return CoinsDistribResult(SCREAMING_SNAKE_CASE_				,				SCREAMING_SNAKE_CASE_					)

					return get_distrib(SCREAMING_SNAKE_CASE_					)[0]


if __name__ == "__main__":
					import doctest

					doctest.testmod()










import math







def      _a				(						SCREAMING_SNAKE_CASE_							:    int					):

					if 1 < number < 4:
										# 2 and 3 are primes
										return True
					elif number < 2 or number % 2 == 0 or number % 3 == 0:
										# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
										return False

					# All primes number are in format of 6k +/- 1
					for i in range(5				,				int(math.sqrt(SCREAMING_SNAKE_CASE_					) + 1					)				,				6					):
										if number % i == 0 or number % (i + 2) == 0:
															return False
					return True







def      _a				(						SCREAMING_SNAKE_CASE_							:    int = 1_00_01					):

					try:
										__lowerCAmelCase           =	int(SCREAMING_SNAKE_CASE_					)
					except (TypeError, ValueError):
										raise TypeError("Parameter nth must be int or castable to int."					) from None
					if nth <= 0:
										raise ValueError("Parameter nth must be greater than or equal to one."					)
					__lowerCAmelCase           =	[]
					__lowerCAmelCase           =	2
					while len(SCREAMING_SNAKE_CASE_					) < nth:
										if is_prime(SCREAMING_SNAKE_CASE_					):
															primes.append(SCREAMING_SNAKE_CASE_					)
															num += 1
										else:
															num += 1
					return primes[len(SCREAMING_SNAKE_CASE_					) - 1]


if __name__ == "__main__":
					print(f'''{solution() = }''')




