


'''simple docstring'''




__lowercase	:   Any   		=					float("""inf""")





class _snake_case :
							"""simple docstring"""





							def __init__( self      ,					__A						)  ->List[str]:



											"""simple docstring"""







											__lowerCamelCase		:   Optional[Any]           =       [0] * n
											__lowerCamelCase		:   Any           =       [0] * n
											__lowerCamelCase		:   int           =       [0] * n
											__lowerCamelCase		:   int           =       [[] for _ in range(__A						)]







							def 		__SCREAMING_SNAKE_CASE( self      ,					__A      ,					__A      ,					__A      ,					__A=0						)  ->int:



											"""simple docstring"""







											self.adj[a].append([b, len(self.adj[b]						), c, 0]						)
											self.adj[b].append([a, len(self.adj[a]						) - 1, rcap, 0]						)







							def 		__SCREAMING_SNAKE_CASE( self      ,					__A      ,					__A      ,					__A						)  ->Dict:



											"""simple docstring"""







											if vertex == sink or not flow:
															return flow

											for i in range(self.ptr[vertex]      ,					len(self.adj[vertex]						)						):
															__lowerCamelCase		:   List[str]           =       self.adj[vertex][i]
															if self.lvl[e[0]] == self.lvl[vertex] + 1:
																			__lowerCamelCase		:   Any           =       self.depth_first_search(e[0]      ,					__A      ,					min(__A      ,					e[2] - e[3]						)						)
																			if p:
																							self.adj[vertex][i][3] += p
																							self.adj[e[0]][e[1]][3] -= p
																							return p
															__lowerCamelCase		:   Any           =       self.ptr[vertex] + 1
											return 0







							def 		__SCREAMING_SNAKE_CASE( self      ,					__A      ,					__A						)  ->int:



											"""simple docstring"""







											__lowerCamelCase    ,       __lowerCamelCase		:   Optional[int]           =       0, source
											for l in range(31						):  # noqa: E741  l = 30 maybe faster for random data
															while True:
																			__lowerCamelCase    ,       __lowerCamelCase		:   int           =       [0] * len(self.q						), [0] * len(self.q						)
																			__lowerCamelCase    ,       __lowerCamelCase    ,       __lowerCamelCase		:   List[str]           =       0, 1, 1
																			while qi < qe and not self.lvl[sink]:
																							__lowerCamelCase		:   int           =       self.q[qi]
																							qi += 1
																							for e in self.adj[v]:
																											if not self.lvl[e[0]] and (e[2] - e[3]) >> (30 - l):
																															__lowerCamelCase		:   Union[str, Any]           =       e[0]
																															qe += 1
																															__lowerCamelCase		:   Tuple           =       self.lvl[v] + 1

																			__lowerCamelCase		:   int           =       self.depth_first_search(__A      ,					__A      ,					__A						)
																			while p:
																							flow += p
																							__lowerCamelCase		:   Any           =       self.depth_first_search(__A      ,					__A      ,					__A						)

																			if not self.lvl[sink]:
																							break

											return flow
__lowercase	:   Optional[int]   		=					Dinic(10)
__lowercase	:   Dict   		=					0
__lowercase	:   List[Any]   		=					9
for vertex in range(1, 5):
				graph.add_edge(source, vertex, 1)
for vertex in range(5, 9):
				graph.add_edge(vertex, sink, 1)
for vertex in range(1, 5):
				graph.add_edge(vertex, vertex + 4, 1)

# Now we can know that is the maximum flow(source -> sink)
print(graph.max_flow(source, sink))









'''simple docstring'''




from collections import Counter
from functools import total_ordering

from data_structures.heap.heap import Heap





@total_ordering
class _snake_case :
							"""simple docstring"""





							def __init__( self      ,					__A      ,					__A						)  ->None:



											"""simple docstring"""







											__lowerCamelCase		:   List[Any]           =       word
											__lowerCamelCase		:   Optional[Any]           =       count







							def __eq__( self      ,					__A						)  ->bool:



											"""simple docstring"""







											if not isinstance(__A      ,					__A						):
															return NotImplemented
											return self.count == other.count







							def __lt__( self      ,					__A						)  ->bool:



											"""simple docstring"""







											if not isinstance(__A      ,					__A						):
															return NotImplemented
											return self.count < other.count





def 				a_							(    lowercase				,    lowercase     )      ->list[str]:






				'''simple docstring'''

				__lowerCamelCase		:   Heap[WordCount]           =       Heap()
				__lowerCamelCase		:   int           =       Counter(lowercase     )
				heap.build_max_heap(
				    [WordCount(lowercase				,    lowercase     ) for word, count in count_by_word.items()]     )
				return [heap.extract_max().word for _ in range(min(lowercase				,    len(lowercase     )     )     )]


if __name__ == "__main__":
				import doctest

				doctest.testmod()





