


"""simple docstring"""






import math



def 			A__		(					_UpperCAmelCase    :      int	)							->	bool:

	'''simple docstring'''


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



def 			A__		(					_UpperCAmelCase    :      int = 60_08_51_47_51_43	)							->	int:

	'''simple docstring'''


	try:
		snake_case__  :						List[Any]		=      int(_UpperCAmelCase	)
	except (TypeError, ValueError):
		raise TypeError("Parameter n must be int or castable to int."	)
	if n <= 0:
		raise ValueError("Parameter n must be greater than or equal to one."	)
	snake_case__  :						int		=      0
	if is_prime(_UpperCAmelCase	):
		return n
	while n % 2 == 0:
		n //= 2
	if is_prime(_UpperCAmelCase	):
		return n
	for i in range(3				,    int(math.sqrt(_UpperCAmelCase	)	) + 1				,    2	):
		if n % i == 0:
			if is_prime(n // i	):
				snake_case__  :						int		=      n // i
				break
			elif is_prime(_UpperCAmelCase	):
				snake_case__  :						List[Any]		=      i
	return max_number


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







"""simple docstring"""
from __future__ import annotations

import random

# Adjacency list representation of this graph:
# https://en.wikipedia.org/wiki/File:Single_run_of_Karger%E2%80%99s_Mincut_algorithm.svg
_a   :      List[str]       =				{
    """1""": ["""2""", """3""", """4""", """5"""],
    """2""": ["""1""", """3""", """4""", """5"""],
    """3""": ["""1""", """2""", """4""", """5""", """10"""],
    """4""": ["""1""", """2""", """3""", """5""", """6"""],
    """5""": ["""1""", """2""", """3""", """4""", """7"""],
    """6""": ["""7""", """8""", """9""", """10""", """4"""],
    """7""": ["""6""", """8""", """9""", """10""", """5"""],
    """8""": ["""6""", """7""", """9""", """10"""],
    """9""": ["""6""", """7""", """8""", """10"""],
    """10""": ["""6""", """7""", """8""", """9""", """3"""],
}
def 					a__ ( a :					dict[str, list[str]]		):

  """simple docstring"""







  _snake_case  :    List[Any]            = {node: {node} for node in graph}

  _snake_case  :    str            = {node: graph[node][:] for node in graph}

  while len(a		) > 2:
    # Choose a random edge.
    _snake_case  :    str            = random.choice(list(graph_copy.keys()		)		)
    _snake_case  :    Union[str, Any]            = random.choice(graph_copy[u]		)

    # Contract edge (u, v) to new node uv
    _snake_case  :    Union[str, Any]            = u + v
    _snake_case  :    Union[str, Any]            = list(set(graph_copy[u] + graph_copy[v]		)		)
    uv_neighbors.remove(a		)
    uv_neighbors.remove(a		)
    _snake_case  :    Union[str, Any]            = uv_neighbors
    for neighbor in uv_neighbors:
      graph_copy[neighbor].append(a		)

    _snake_case  :    Dict            = set(contracted_nodes[u].union(contracted_nodes[v]		)		)

    # Remove nodes u and v.
    del graph_copy[u]
    del graph_copy[v]
    for neighbor in uv_neighbors:
      if u in graph_copy[neighbor]:
        graph_copy[neighbor].remove(a		)
      if v in graph_copy[neighbor]:
        graph_copy[neighbor].remove(a		)

    # Find cutset.
  _snake_case  :    List[Any]            = [contracted_nodes[node] for node in graph_copy]
  return {
      (node, neighbor)
      for node in groups[0]
      for neighbor in graph[node]
      if neighbor in groups[1]
  }


if __name__ == "__main__":
    print(partition_graph(TEST_GRAPH))

