from __future__ import annotations

import sys





class 					__snake_case    :




					def __init__(  self       ,			__UpperCamelCase       ,			__UpperCamelCase						)	->    List[Any]:



									'''simple docstring'''







									snake_case__   :      str   				= letter
									snake_case__   :      int   				= freq
									snake_case__   :      dict[str, str]   				= {}




					def __repr__(  self						)	->    int:



									'''simple docstring'''







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





class 					__snake_case    :




					def __init__(  self       ,			__UpperCamelCase       ,			__UpperCamelCase       ,			__UpperCamelCase						)	->    str:



									'''simple docstring'''







									snake_case__   :      int   				= freq
									snake_case__   :      Letter | TreeNode   				= left
									snake_case__   :      Letter | TreeNode   				= right




def 					UpperCamelCase__		(							A__       )  ->   list[Letter]:
				snake_case__   :      dict[str, int]   				= {}
				with open(__UpperCAmelCase       ) as f:
								while True:
												snake_case__   :      Tuple   				= f.read(1       )
												if not c:
																break
												snake_case__   :      str   				= chars[c] + 1 if c in chars else 1
				return sorted((Letter(__UpperCAmelCase     ,					__UpperCAmelCase       ) for c, f in chars.items())     ,					key=lambda A__       : x.freq       )
def 					UpperCamelCase__		(							A__       )  ->   Letter | TreeNode:
				snake_case__   :      list[Letter | TreeNode]   				= letters  # type: ignore
				while len(__UpperCAmelCase       ) > 1:
								snake_case__   :      Optional[Any]   				= response.pop(0       )
								snake_case__   :      Optional[Any]   				= response.pop(0       )
								snake_case__   :      Optional[int]   				= left.freq + right.freq
								snake_case__   :      int   				= TreeNode(__UpperCAmelCase     ,					__UpperCAmelCase     ,					__UpperCAmelCase       )
								response.append(__UpperCAmelCase       )
								response.sort(key=lambda A__       : x.freq       )
				return response[0]
def 					UpperCamelCase__		(							A__     ,					A__       )  ->   list[Letter]:
				if isinstance(__UpperCAmelCase     ,					__UpperCAmelCase       ):
								snake_case__   :      Union[str, Any]   				= bitstring
								return [root]
				snake_case__   :      TreeNode   				= root  # type: ignore
				snake_case__   :      List[str]   				= []
				letters += traverse_tree(treenode.left     ,					bitstring + '0'       )
				letters += traverse_tree(treenode.right     ,					bitstring + '1'       )
				return letters
def 					UpperCamelCase__		(							A__       )  ->   None:
				snake_case__   :      Optional[Any]   				= parse_file(__UpperCAmelCase       )
				snake_case__   :      List[Any]   				= build_tree(__UpperCAmelCase       )
				snake_case__   :      Optional[int]   				= {
				    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:
												snake_case__   :      Tuple   				= 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])



'''simple docstring'''
import math







def 				__UpperCamelCase (					__UpperCAmelCase  :					str			)							->	Optional[int]:
  lowercase				:							Tuple									=   0
  if n % 2 == 0:
    count += 1
    while n % 2 == 0:
      lowercase				:							Optional[int]									=   int(n / 2			)
    # the n input value must be odd so that
    # we can skip one element (ie i += 2)

  lowercase				:							Dict									=   3

  while i <= int(math.sqrt(__UpperCAmelCase			)			):
    if n % i == 0:
      count += 1
      while n % i == 0:
        lowercase				:							Dict									=   int(n / i			)
    lowercase				:							List[Any]									=   i + 2

  # this condition checks the prime
  # number n is greater than 2

  if n > 2:
    count += 1
  return count


if __name__ == "__main__":
 _A		:      List[Any]						   =5_1_2_4_2_1_8_3
 print(f"""The number of distinct prime factors is/are {exact_prime_factor_count(n)}""")
 print(f"""The value of log(log(n)) is {math.log(math.log(n)):.4f}""")