



from __future__ import annotations

import sys







class      __lowerCAmelCase       :



			def __init__(		self  :    Dict					,						A  :    str					,						A  :    int)  ->       Optional[Any]:



						"""simple docstring"""






						_UpperCAmelCase									=  letter
						_UpperCAmelCase									=  freq
						_UpperCAmelCase									=  {}



			def __repr__(		self  :    Tuple)  ->       str:



						"""simple docstring"""






						return F"{self.letter}:{self.freq}"







class      __lowerCAmelCase       :



			def __init__(		self  :    Optional[int]					,						A  :    int					,						A  :    Letter | TreeNode					,						A  :    Letter | TreeNode)  ->       Tuple:



						"""simple docstring"""






						_UpperCAmelCase									=  freq
						_UpperCAmelCase									=  left
						_UpperCAmelCase									=  right





def 				A      (	_UpperCAmelCase							:  str       )							->					list[Letter]:







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





def 				A      (	_UpperCAmelCase							:  list[Letter]       )							->					Letter | TreeNode:







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





def 				A      (	_UpperCAmelCase							:  Letter | TreeNode				,  _UpperCAmelCase							:  str       )							->					list[Letter]:







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





def 				A      (	_UpperCAmelCase							:  str       )							->					None:







			'''simple docstring'''
			_UpperCAmelCase									=  parse_file(_UpperCAmelCase       )
			_UpperCAmelCase									=  build_tree(_UpperCAmelCase       )
			_UpperCAmelCase									=  {
			    k: v for letter in traverse_tree(_UpperCAmelCase				,  ''       ) for k, v in letter.bitstring.items()
			}
			print(F"Huffman Coding  of {file_path}: "       )
			with open(_UpperCAmelCase       ) as f:
						while True:
									_UpperCAmelCase									=  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])





import sys

sys.set_int_max_str_digits(0)  # type: ignore





def 				A      (	_UpperCAmelCase							:  int       )							->					bool:







			'''simple docstring'''
			_UpperCAmelCase									=  [0] * 11
			_UpperCAmelCase									=  [0] * 11

			# mark last 9 numbers
			for _ in range(9       ):
						_UpperCAmelCase									=  1
						_UpperCAmelCase									=  number // 10
			# flag
			_UpperCAmelCase									=  True

			# check last 9 numbers for pandigitality

			for x in range(9       ):
						if not check_last[x + 1]:
									_UpperCAmelCase									=  False
			if not f:
						return f

			# mark first 9 numbers
			_UpperCAmelCase									=  int(str(_UpperCAmelCase       )[:9]       )

			for _ in range(9       ):
						_UpperCAmelCase									=  1
						_UpperCAmelCase									=  number // 10

			# check first 9 numbers for pandigitality

			for x in range(9       ):
						if not check_front[x + 1]:
									_UpperCAmelCase									=  False
			return f





def 				A      (	_UpperCAmelCase							:  int       )							->					bool:







			'''simple docstring'''
			_UpperCAmelCase									=  [0] * 11

			# mark last 9 numbers
			for _ in range(9       ):
						_UpperCAmelCase									=  1
						_UpperCAmelCase									=  number // 10
			# flag
			_UpperCAmelCase									=  True

			# check last 9 numbers for pandigitality

			for x in range(9       ):
						if not check_last[x + 1]:
									_UpperCAmelCase									=  False
			return f





def 				A      (	)							->					int:







			'''simple docstring'''
			_UpperCAmelCase									=  1
			_UpperCAmelCase									=  1
			_UpperCAmelCase									=  2
			# temporary Fibonacci numbers

			_UpperCAmelCase									=  1
			_UpperCAmelCase									=  1
			_UpperCAmelCase									=  2
			# temporary Fibonacci numbers mod 1e9

			# mod m=1e9, done for fast optimisation
			_UpperCAmelCase									=  [0] * 1_000_000
			_UpperCAmelCase									=  1_000_000_000

			for x in range(1_000_000       ):
						_UpperCAmelCase									=  (aa + ba) % m
						_UpperCAmelCase									=  ba % m
						_UpperCAmelCase									=  ca % m
						if checka(_UpperCAmelCase       ):
									_UpperCAmelCase									=  1

			for x in range(1_000_000       ):
						_UpperCAmelCase									=  a + b
						_UpperCAmelCase									=  b
						_UpperCAmelCase									=  c
						# perform check only if in tocheck
						if tocheck[x + 3] and check(_UpperCAmelCase       ):
									return x + 3  # first 2 already done
			return -1


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