




from __future__ import annotations

import sys
class      a__       :






						def __init__(  self						,     _A						,     _A     ):




											"""simple docstring"""



											__lowerCAmelCase							  =			letter
											__lowerCAmelCase							  =			freq
											__lowerCAmelCase							  =			{}






						def __repr__(  self     ):




											"""simple docstring"""



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






class      a__       :






						def __init__(  self						,     _A						,     _A						,     _A     ):




											"""simple docstring"""



											__lowerCAmelCase							  =			freq
											__lowerCAmelCase							  =			left
											__lowerCAmelCase							  =			right







def       _a (		SCREAMING_SNAKE_CASE_				:							str	):
					__lowerCAmelCase							  =			{}
					with open(SCREAMING_SNAKE_CASE_	) 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(SCREAMING_SNAKE_CASE_ , SCREAMING_SNAKE_CASE_	) for c, f in chars.items()) , key=lambda SCREAMING_SNAKE_CASE_	: x.freq	)







def       _a (		SCREAMING_SNAKE_CASE_				:							list[Letter]	):
					__lowerCAmelCase							  =			letters  # type: ignore
					while len(SCREAMING_SNAKE_CASE_	) > 1:
										__lowerCAmelCase							  =			response.pop(0	)
										__lowerCAmelCase							  =			response.pop(0	)
										__lowerCAmelCase							  =			left.freq + right.freq
										__lowerCAmelCase							  =			TreeNode(SCREAMING_SNAKE_CASE_ , SCREAMING_SNAKE_CASE_ , SCREAMING_SNAKE_CASE_	)
										response.append(SCREAMING_SNAKE_CASE_	)
										response.sort(key=lambda SCREAMING_SNAKE_CASE_	: x.freq	)
					return response[0]







def       _a (		SCREAMING_SNAKE_CASE_				:							Letter | TreeNode , SCREAMING_SNAKE_CASE_				:							str	):
					if isinstance(SCREAMING_SNAKE_CASE_ , SCREAMING_SNAKE_CASE_	):
										__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       _a (		SCREAMING_SNAKE_CASE_				:							str	):
					__lowerCAmelCase							  =			parse_file(SCREAMING_SNAKE_CASE_	)
					__lowerCAmelCase							  =			build_tree(SCREAMING_SNAKE_CASE_	)
					__lowerCAmelCase							  =			{
					    k: v for letter in traverse_tree(SCREAMING_SNAKE_CASE_ , ""	) for k, v in letter.bitstring.items()
					}
					print(F"""Huffman Coding  of {file_path}: """	)
					with open(SCREAMING_SNAKE_CASE_	) 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])










def       _a (		SCREAMING_SNAKE_CASE_				:							int , SCREAMING_SNAKE_CASE_				:							int	):
					if a < b:
										return gcd(SCREAMING_SNAKE_CASE_ , SCREAMING_SNAKE_CASE_	)
					if a % b == 0:
										return b
					return gcd(SCREAMING_SNAKE_CASE_ , a % b	)







def       _a (		SCREAMING_SNAKE_CASE_				:							int , SCREAMING_SNAKE_CASE_				:							int , SCREAMING_SNAKE_CASE_				:							int	):
					if y == 0:
										return 1
					__lowerCAmelCase							  =			power(SCREAMING_SNAKE_CASE_ , y // 2 , SCREAMING_SNAKE_CASE_	) % mod
					__lowerCAmelCase							  =			(temp * temp) % mod
					if y % 2 == 1:
										__lowerCAmelCase							  =			(temp * x) % mod
					return temp







def       _a (		SCREAMING_SNAKE_CASE_				:							int	):
					__lowerCAmelCase							  =			2
					while b < n:
										if gcd(SCREAMING_SNAKE_CASE_ , SCREAMING_SNAKE_CASE_	) == 1 and power(SCREAMING_SNAKE_CASE_ , n - 1 , SCREAMING_SNAKE_CASE_	) != 1:
															return False
										b += 1
					return True


if __name__ == "__main__":
					UpperCamelCase__            =     int(input("""Enter number: """).strip())
					if is_carmichael_number(number):
										print(f'''{number} is a Carmichael Number.''')
					else:
										print(f'''{number} is not a Carmichael Number.''')




