




def 	lowerCAmelCase_	(     lowerCamelCase:				int  )    ->	int:


      '''simple docstring'''




      return n * (2 * n - 1)

def 	lowerCAmelCase_	(     lowerCamelCase:				int  )    ->	bool:


      '''simple docstring'''




      lowerCamelCase__					     = (1 + 24 * n) ** 0.5
      return ((1 + root) / 6) % 1 == 0

def 	lowerCAmelCase_	(     lowerCamelCase:				int = 1_44  )    ->	int:


      '''simple docstring'''




      lowerCamelCase__					     = start
      lowerCamelCase__					     = hexagonal_num(lowerCamelCase  )
      while not is_pentagonal(lowerCamelCase  ):
            n += 1
            lowerCamelCase__					     = hexagonal_num(lowerCamelCase  )
      return num


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





from __future__ import annotations

import sys






class 	A	:
     """simple docstring"""

     def __init__(			self     :      str		,     A__     :      str		,     A__     :      int	) ->				str:
           lowerCamelCase__					     = letter
           lowerCamelCase__					     = freq
           lowerCamelCase__					     = {}




     def __repr__(			self     :      Any	) ->				str:
           return F"""{self.letter}:{self.freq}"""






class 	A	:
     """simple docstring"""

     def __init__(			self     :      Optional[Any]		,     A__     :      int		,     A__     :      Letter | TreeNode		,     A__     :      Letter | TreeNode	) ->				Any:
           lowerCamelCase__					     = freq
           lowerCamelCase__					     = left
           lowerCamelCase__					     = right

def 	lowerCAmelCase_	(     lowerCamelCase:				str  )    ->	list[Letter]:


      '''simple docstring'''




      lowerCamelCase__					     = {}
      with open(lowerCamelCase  ) as f:
            while True:
                  lowerCamelCase__					     = f.read(1  )
                  if not c:
                        break
                  lowerCamelCase__					     = chars[c] + 1 if c in chars else 1
      return sorted((Letter(lowerCamelCase   , lowerCamelCase  ) for c, f in chars.items())   , key=lambda lowerCamelCase  : x.freq  )

def 	lowerCAmelCase_	(     lowerCamelCase:				list[Letter]  )    ->	Letter | TreeNode:


      '''simple docstring'''




      lowerCamelCase__					     = letters  # type: ignore
      while len(lowerCamelCase  ) > 1:
            lowerCamelCase__					     = response.pop(0  )
            lowerCamelCase__					     = response.pop(0  )
            lowerCamelCase__					     = left.freq + right.freq
            lowerCamelCase__					     = TreeNode(lowerCamelCase   , lowerCamelCase   , lowerCamelCase  )
            response.append(lowerCamelCase  )
            response.sort(key=lambda lowerCamelCase  : x.freq  )
      return response[0]

def 	lowerCAmelCase_	(     lowerCamelCase:				Letter | TreeNode   , lowerCamelCase:				str  )    ->	list[Letter]:


      '''simple docstring'''




      if isinstance(lowerCamelCase   , lowerCamelCase  ):
            lowerCamelCase__					     = bitstring
            return [root]
      lowerCamelCase__					     = root  # type: ignore
      lowerCamelCase__					     = []
      letters += traverse_tree(treenode.left   , bitstring + '0'  )
      letters += traverse_tree(treenode.right   , bitstring + '1'  )
      return letters

def 	lowerCAmelCase_	(     lowerCamelCase:				str  )    ->	None:


      '''simple docstring'''




      lowerCamelCase__					     = parse_file(lowerCamelCase  )
      lowerCamelCase__					     = build_tree(lowerCamelCase  )
      lowerCamelCase__					     = {
          k: v for letter in traverse_tree(lowerCamelCase   , ''  ) for k, v in letter.bitstring.items()
      }
      print(f"""Huffman Coding  of {file_path}: """  )
      with open(lowerCamelCase  ) as f:
            while True:
                  lowerCamelCase__					     = f.read(1  )
                  if not c:
                        break
                  print(letters[c]   , end=' '  )
      print()


if __name__ == "__main__":
      # pass the file path to the huffman function
      huffman(sys.argv[1])