


import heapq




def      UpperCamelCase     (   _a		)       ->				Tuple:
     '''simple docstring'''





     lowercase_							:Optional[Any]			     =							[]

     # for each node and his adjacency list add them and the rank of the node to queue
     # using heapq module the queue will be filled like a Priority Queue
     # heapq works with a min priority queue, so I used -1*len(v) to build it
     for key, value in graph.items():
          # O(log(n))
          heapq.heappush(_a							,		[-1 * len(_a		), (key, value)]		)

     # chosen_vertices = set of chosen vertices
     lowercase_							:int			     =							set()

     # while queue isn't empty and there are still edges
     #   (queue[0][0] is the rank of the node with max rank)
     while queue and queue[0][0] != 0:
          # extract vertex with max rank from queue and add it to chosen_vertices
          lowercase_							:List[Any]			     =							heapq.heappop(_a		)[1][0]
          chosen_vertices.add(_a		)

          # Remove all arcs adjacent to argmax
          for elem in queue:
               # if v haven't adjacent node, skip
               if elem[0] == 0:
                    continue
               # if argmax is reachable from elem
               # remove argmax from elem's adjacent list and update his rank
               if argmax in elem[1][1]:
                    lowercase_							:List[str]			     =							elem[1][1].index(_a		)
                    del elem[1][1][index]
                    elem[0] += 1
                    # re-order the queue
          heapq.heapify(_a		)
     return chosen_vertices


if __name__ == "__main__":
   import doctest

   doctest.testmod()

   SCREAMING_SNAKE_CASE							:		List[str]       =					{0: [1, 3], 1: [0, 3], 2: [0, 3, 4], 3: [0, 1, 2], 4: [2, 3]}
   print(f"Minimum vertex cover:\n{greedy_min_vertex_cover(graph)}")


"""simple docstring"""


from __future__ import annotations

import typing
from collections import Counter






def      __UpperCAmelCase       (      lowercase		):







  """simple docstring"""
  _UpperCAmelCase    			=   Counter()
  for base in range(1 ,max_perimeter + 1		):
    for perpendicular in range(lowercase ,max_perimeter + 1		):
      _UpperCAmelCase    			=   (base * base + perpendicular * perpendicular) ** 0.5
      if hypotenuse == int(lowercase		):
        _UpperCAmelCase    			=   int(base + perpendicular + hypotenuse		)
        if perimeter > max_perimeter:
          continue
        triplets[perimeter] += 1
  return triplets






def      __UpperCAmelCase       (      lowercase = 10_00		):







  """simple docstring"""
  _UpperCAmelCase    			=   pythagorean_triple(lowercase		)
  return triplets.most_common(1		)[0][0]


if __name__ == "__main__":
    print(F'''Perimeter {solution()} has maximum solutions''')
