

"""simple docstring"""






def 	lowercase      (   __UpperCamelCase = "The quick brown fox jumps over the lazy dog"      ,   ) ->      bool:
 __magic_name__     =      set()

 # Replace all the whitespace in our sentence
 __magic_name__     =      input_str.replace(''' '''      ,   ''''''						)
 for alpha in input_str:
  if "a" <= alpha.lower() <= "z":
   frequency.add(alpha.lower()						)
 return len(__UpperCamelCase						) == 26





def 	lowercase      (   __UpperCamelCase = "The quick brown fox jumps over the lazy dog"      ,   ) ->      bool:
 __magic_name__     =      [False] * 26
 for char in input_str:
  if char.islower():
   __magic_name__     =      True
  elif char.isupper():
   __magic_name__     =      True
 return all(__UpperCamelCase						)





def 	lowercase      (   __UpperCamelCase = "The quick brown fox jumps over the lazy dog"      ,   ) ->      bool:
 return len({char for char in input_str.lower() if char.isalpha()}						) == 26





def 	lowercase      (   ) ->      None:
 from timeit import timeit

 __magic_name__     =      '''from __main__ import is_pangram, is_pangram_faster, is_pangram_fastest'''
 print(timeit('''is_pangram()'''      ,   setup=__UpperCamelCase						)						)
 print(timeit('''is_pangram_faster()'''      ,   setup=__UpperCamelCase						)						)
 print(timeit('''is_pangram_fastest()'''      ,   setup=__UpperCamelCase						)						)
 # 5.348480500048026, 2.6477354579837993, 1.8470395830227062
 # 5.036091582966037, 2.644472333951853,  1.8869528750656173


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 benchmark()




"""simple docstring"""






from __future__ import annotations

from sys import maxsize
from typing import Generic, TypeVar

__lowerCamelCase										=		TypeVar("T")





def 	lowercase      (   __UpperCamelCase						) ->      int:
 return (position - 1) // 2





def 	lowercase      (   __UpperCamelCase						) ->      int:
 return (2 * position) + 1





def 	lowercase      (   __UpperCamelCase						) ->      int:
 return (2 * position) + 2
class        _lowercase					(     Generic[T]     ):







     def __init__(      self       ):
      __magic_name__     =      []
      __magic_name__     =      {}
      __magic_name__     =      0







     def __len__(      self       ):
      return self.elements







     def __repr__(      self       ):
      return str(self.heap       )







     def 	lowerCAmelCase__    (      self       ):
      # Check if the priority queue is empty
      return self.elements == 0







     def 	lowerCAmelCase__    (      self ,						UpperCamelCase_ ,						UpperCamelCase_       ):
      # Add an element with given priority to the queue
      self.heap.append((elem, weight)       )
      __magic_name__     =      self.elements
      self.elements += 1
      self._bubble_up(UpperCamelCase_       )







     def 	lowerCAmelCase__    (      self       ):
      # Remove and return the element with lowest weight (highest priority)
      if self.elements > 1:
       self._swap_nodes(0 ,						self.elements - 1       )
      __magic_name__   ,						__magic_name__     =      self.heap.pop()
      del self.position_map[elem]
      self.elements -= 1
      if self.elements > 0:
       __magic_name__   ,						__magic_name__     =      self.heap[0]
       self._bubble_down(UpperCamelCase_       )
      return elem







     def 	lowerCAmelCase__    (      self ,						UpperCamelCase_ ,						UpperCamelCase_       ):
      # Update the weight of the given key
      __magic_name__     =      self.position_map[elem]
      __magic_name__     =      (elem, weight)
      if position > 0:
       __magic_name__     =      get_parent_position(UpperCamelCase_       )
       __magic_name__   ,						__magic_name__     =      self.heap[parent_position]
       if parent_weight > weight:
        self._bubble_up(UpperCamelCase_       )
       else:
        self._bubble_down(UpperCamelCase_       )
      else:
       self._bubble_down(UpperCamelCase_       )







     def 	lowerCAmelCase__    (      self ,						UpperCamelCase_       ):
      # Place a node at the proper position (upward movement) [to be used internally
      # only]
      __magic_name__     =      self.position_map[elem]
      if curr_pos == 0:
       return None
      __magic_name__     =      get_parent_position(UpperCamelCase_       )
      __magic_name__   ,						__magic_name__     =      self.heap[curr_pos]
      __magic_name__   ,						__magic_name__     =      self.heap[parent_position]
      if parent_weight > weight:
       self._swap_nodes(UpperCamelCase_ ,						UpperCamelCase_       )
       return self._bubble_up(UpperCamelCase_       )
      return None







     def 	lowerCAmelCase__    (      self ,						UpperCamelCase_       ):
      # Place a node at the proper position (downward movement) [to be used
      # internally only]
      __magic_name__     =      self.position_map[elem]
      __magic_name__   ,						__magic_name__     =      self.heap[curr_pos]
      __magic_name__     =      get_child_left_position(UpperCamelCase_       )
      __magic_name__     =      get_child_right_position(UpperCamelCase_       )
      if child_left_position < self.elements and child_right_position < self.elements:
       __magic_name__   ,						__magic_name__     =      self.heap[child_left_position]
       __magic_name__   ,						__magic_name__     =      self.heap[child_right_position]
       if child_right_weight < child_left_weight and child_right_weight < weight:
        self._swap_nodes(UpperCamelCase_ ,						UpperCamelCase_       )
        return self._bubble_down(UpperCamelCase_       )
      if child_left_position < self.elements:
       __magic_name__   ,						__magic_name__     =      self.heap[child_left_position]
       if child_left_weight < weight:
        self._swap_nodes(UpperCamelCase_ ,						UpperCamelCase_       )
        return self._bubble_down(UpperCamelCase_       )
      else:
       return None
      if child_right_position < self.elements:
       __magic_name__   ,						__magic_name__     =      self.heap[child_right_position]
       if child_right_weight < weight:
        self._swap_nodes(UpperCamelCase_ ,						UpperCamelCase_       )
        return self._bubble_down(UpperCamelCase_       )
      return None







     def 	lowerCAmelCase__    (      self ,						UpperCamelCase_ ,						UpperCamelCase_       ):
      # Swap the nodes at the given positions
      __magic_name__     =      self.heap[nodea_pos][0]
      __magic_name__     =      self.heap[nodea_pos][0]
      __magic_name__   ,						__magic_name__     =      (
          self.heap[nodea_pos],
          self.heap[nodea_pos],
      )
      __magic_name__     =      nodea_pos
      __magic_name__     =      nodea_pos


class        _lowercase					(     Generic[T]     ):







     def __init__(      self       ):
      __magic_name__     =      {}
      __magic_name__     =      0







     def __repr__(      self       ):
      return str(self.connections       )







     def __len__(      self       ):
      return self.nodes







     def 	lowerCAmelCase__    (      self ,						UpperCamelCase_       ):
      # Add a node in the graph if it is not in the graph
      if node not in self.connections:
       __magic_name__     =      {}
       self.nodes += 1







     def 	lowerCAmelCase__    (      self ,						UpperCamelCase_ ,						UpperCamelCase_ ,						UpperCamelCase_       ):
      # Add an edge between 2 nodes in the graph
      self.add_node(UpperCamelCase_       )
      self.add_node(UpperCamelCase_       )
      __magic_name__     =      weight
      __magic_name__     =      weight





def 	lowercase      (   __UpperCamelCase      ,   ) ->      tuple[dict[T, int], dict[T, T | None]]:
 __magic_name__     =      {node: maxsize for node in graph.connections}
 __magic_name__     =      {node: None for node in graph.connections}

 __magic_name__     =      MinPriorityQueue()
 for node, weight in dist.items():
  priority_queue.push(__UpperCamelCase      ,   __UpperCamelCase						)

 if priority_queue.is_empty():
  return dist, parent

 # initialization
 __magic_name__     =      priority_queue.extract_min()
 __magic_name__     =      0
 for neighbour in graph.connections[node]:
  if dist[neighbour] > dist[node] + graph.connections[node][neighbour]:
   __magic_name__     =      dist[node] + graph.connections[node][neighbour]
   priority_queue.update_key(__UpperCamelCase      ,   dist[neighbour]						)
   __magic_name__     =      node

    # running prim's algorithm
 while not priority_queue.is_empty():
  __magic_name__     =      priority_queue.extract_min()
  for neighbour in graph.connections[node]:
   if dist[neighbour] > dist[node] + graph.connections[node][neighbour]:
    __magic_name__     =      dist[node] + graph.connections[node][neighbour]
    priority_queue.update_key(__UpperCamelCase      ,   dist[neighbour]						)
    __magic_name__     =      node
 return dist, parent

