




from __future__ import annotations

from collections import deque
from enum import Enum
from math import atana, degrees
from sys import maxsize
class      _UpperCamelCase (			lowerCAmelCase						):
      UpperCAmelCase_            =						1
      UpperCAmelCase_            =						2
      UpperCAmelCase_            =						3
      def __repr__(     self				:Union[str, Any] )       ->     Optional[int]:
       return f'''{self.__class__.__name__}.{self.name}'''



def   lowerCAmelCase						(						_lowerCAmelCase							:				tuple[int, int]  ,							_lowerCAmelCase							:				int  ,							_lowerCAmelCase							:				int		):




 """simple docstring"""







 UpperCAmelCase__	,	UpperCAmelCase__								=  point
 return degrees(atana(y - miny  ,							x - minx		)		)



def   lowerCAmelCase						(						_lowerCAmelCase							:				tuple[int, int]  ,							_lowerCAmelCase							:				tuple[int, int]  ,							_lowerCAmelCase							:				tuple[int, int]		):




 """simple docstring"""







 UpperCAmelCase__	,	UpperCAmelCase__								=  starting
 UpperCAmelCase__	,	UpperCAmelCase__								=  via
 UpperCAmelCase__	,	UpperCAmelCase__								=  target
 UpperCAmelCase__								=  degrees(atana(ya - ya  ,							xa - xa		)		)
 via_angle %= 360
 UpperCAmelCase__								=  degrees(atana(ya - ya  ,							xa - xa		)		)
 target_angle %= 360
 # t-
 #  \ \
 #   \ v
 #    \|
 #     s
 # via_angle is always lower than target_angle, if direction is left.
 # If they are same, it means they are on a same line of convex hull.
 if target_angle > via_angle:
  return Direction.left
 elif target_angle == via_angle:
  return Direction.straight
 else:
  return Direction.right



def   lowerCAmelCase						(						_lowerCAmelCase							:				list[tuple[int, int]]		):




 """simple docstring"""







 if len(_lowerCAmelCase		) <= 2:
  # There is no convex hull
  raise ValueError("graham_scan: argument must contain more than 3 points."		)
 if len(_lowerCAmelCase		) == 3:
  return points
 # find the lowest and the most left point
 UpperCAmelCase__								=  0
 UpperCAmelCase__	,	UpperCAmelCase__								=  maxsize, maxsize
 for i, point in enumerate(_lowerCAmelCase		):
  UpperCAmelCase__								=  point[0]
  UpperCAmelCase__								=  point[1]
  if y < miny:
   UpperCAmelCase__								=  y
   UpperCAmelCase__								=  x
   UpperCAmelCase__								=  i
  if y == miny and x < minx:
   UpperCAmelCase__								=  x
   UpperCAmelCase__								=  i

    # remove the lowest and the most left point from points for preparing for sort
 points.pop(_lowerCAmelCase		)

 UpperCAmelCase__								=  sorted(_lowerCAmelCase  ,							key=lambda _lowerCAmelCase		: angle_comparer(_lowerCAmelCase  ,							_lowerCAmelCase  ,							_lowerCAmelCase		)		)
 # This insert actually costs complexity,
 # and you should instead add (minx, miny) into stack later.
 # I'm using insert just for easy understanding.
 sorted_points.insert(0  ,							(minx, miny)		)

 UpperCAmelCase__								=  deque()
 stack.append(sorted_points[0]		)
 stack.append(sorted_points[1]		)
 stack.append(sorted_points[2]		)
 # In any ways, the first 3 points line are towards left.
 # Because we sort them the angle from minx, miny.
 UpperCAmelCase__								=  Direction.left

 for i in range(3  ,							len(_lowerCAmelCase		)		):
  while True:
   UpperCAmelCase__								=  stack[-2]
   UpperCAmelCase__								=  stack[-1]
   UpperCAmelCase__								=  sorted_points[i]
   UpperCAmelCase__								=  check_direction(_lowerCAmelCase  ,							_lowerCAmelCase  ,							_lowerCAmelCase		)

   if next_direction == Direction.left:
    UpperCAmelCase__								=  Direction.left
    break
   if next_direction == Direction.straight:
    if current_direction == Direction.left:
     # We keep current_direction as left.
     # Because if the straight line keeps as straight,
     # we want to know if this straight line is towards left.
     break
    elif current_direction == Direction.right:
     # If the straight line is towards right,
     # every previous points on those straigh line is not convex hull.
     stack.pop()
   if next_direction == Direction.right:
    stack.pop()
  stack.append(sorted_points[i]		)
 return list(_lowerCAmelCase		)











def   lowerCAmelCase						(						_lowerCAmelCase							:				int  ,							_lowerCAmelCase							:				int		):




 """simple docstring"""







 if a < b:
  return gcd(_lowerCAmelCase  ,							_lowerCAmelCase		)
 if a % b == 0:
  return b
 return gcd(_lowerCAmelCase  ,							a % b		)



def   lowerCAmelCase						(						_lowerCAmelCase							:				int  ,							_lowerCAmelCase							:				int  ,							_lowerCAmelCase							:				int		):




 """simple docstring"""







 if y == 0:
  return 1
 UpperCAmelCase__								=  power(_lowerCAmelCase  ,							y // 2  ,							_lowerCAmelCase		) % mod
 UpperCAmelCase__								=  (temp * temp) % mod
 if y % 2 == 1:
  UpperCAmelCase__								=  (temp * x) % mod
 return temp



def   lowerCAmelCase						(						_lowerCAmelCase							:				int		):




 """simple docstring"""







 UpperCAmelCase__								=  2
 while b < n:
  if gcd(_lowerCAmelCase  ,							_lowerCAmelCase		) == 1 and power(_lowerCAmelCase  ,							n - 1  ,							_lowerCAmelCase		) != 1:
   return False
  b += 1
 return True


if __name__ == "__main__":
  _lowerCAmelCase  :				Dict						=				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.''')





