


from __future__ import annotations

from collections import namedtuple
from dataclasses import dataclass







@dataclass
class       lowerCamelCase__   :
     SCREAMING_SNAKE_CASE__      			=			42
     SCREAMING_SNAKE_CASE__      			=			None
     SCREAMING_SNAKE_CASE__      			=			None



UpperCAmelCase__   	=							namedtuple('''CoinsDistribResult''', '''moves excess''')
def 				UpperCAmelCase_					(							__snake_case						)     ->			Any:







 """simple docstring"""


 if root is None:
  return 0

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

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

 def count_coins(__snake_case						) -> int:
  if node is None:
   return 0

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

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

 # Main calculation
 def get_distrib(__snake_case						) -> CoinsDistribResult:

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

  _lowercase							      =get_distrib(node.left						)
  _lowercase							      =get_distrib(node.right						)

  _lowercase							      =1 - left_distrib_excess
  _lowercase							      =1 - right_distrib_excess

  _lowercase							      =(
      left_distrib_moves
      + right_distrib_moves
      + abs(_snake_case						)
      + abs(_snake_case						)
  )
  _lowercase							      =node.data - coins_to_left - coins_to_right

  return CoinsDistribResult(_snake_case     ,						_snake_case						)

 return get_distrib(_snake_case						)[0]


if __name__ == "__main__":
  import doctest

  doctest.testmod()



"""simple docstring"""




import math
import unittest

def lowercase_  (   _snake_case						):
							assert isinstance(_snake_case   ,_snake_case						) and (
							    number >= 0
							), "'number' must been an int and positive"

							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(_snake_case						) + 1						)   ,6						):
														if number % i == 0 or number % (i + 2) == 0:
																					return False
							return True



class 	lowerCAmelCase_						(unittest.TestCase  ):


				"""simple docstring"""



				def 	__magic_name__    (self    )					->		Dict:



											"""simple docstring"""




											self.assertTrue(is_prime(2    )    )
											self.assertTrue(is_prime(3    )    )
											self.assertTrue(is_prime(5    )    )
											self.assertTrue(is_prime(7    )    )
											self.assertTrue(is_prime(11    )    )
											self.assertTrue(is_prime(13    )    )
											self.assertTrue(is_prime(17    )    )
											self.assertTrue(is_prime(19    )    )
											self.assertTrue(is_prime(23    )    )
											self.assertTrue(is_prime(29    )    )



				def 	__magic_name__    (self    )					->		List[Any]:



											"""simple docstring"""




											with self.assertRaises(SCREAMING_SNAKE_CASE__    ):
																		is_prime(-19    )
											self.assertFalse(
											    is_prime(0    )   ,       """Zero doesn't have any positive factors, primes must have exactly two."""   ,       )
											self.assertFalse(
											    is_prime(1    )   ,       """One only has 1 positive factor, primes must have exactly two."""   ,       )
											self.assertFalse(is_prime(2 * 2    )    )
											self.assertFalse(is_prime(2 * 3    )    )
											self.assertFalse(is_prime(3 * 3    )    )
											self.assertFalse(is_prime(3 * 5    )    )
											self.assertFalse(is_prime(3 * 5 * 7    )    )


if __name__ == "__main__":
					unittest.main()




