




'''simple docstring'''


def  _SCREAMING_SNAKE_CASE     (      UpperCamelCase__    :					int ,    UpperCamelCase__    :					list				):




     """simple docstring"""


     _enforce_args(UpperCamelCase__ ,    UpperCamelCase__				)
     if n == 0:
          return 0
     a_     :							Dict     						=  float("""-inf"""				)
     for i in range(1 ,    n + 1				):
          a_     :							str     						=  max(
              UpperCamelCase__ ,    prices[i - 1] + naive_cut_rod_recursive(n - i ,    UpperCamelCase__				)				)

     return max_revue



def  _SCREAMING_SNAKE_CASE     (      UpperCamelCase__    :					int ,    UpperCamelCase__    :					list				):




     """simple docstring"""


     _enforce_args(UpperCamelCase__ ,    UpperCamelCase__				)
     a_     :							Union[str, Any]     						=  [float("""-inf"""				) for _ in range(n + 1				)]
     return _top_down_cut_rod_recursive(UpperCamelCase__ ,    UpperCamelCase__ ,    UpperCamelCase__				)



def  _SCREAMING_SNAKE_CASE     (      UpperCamelCase__    :					int ,    UpperCamelCase__    :					list ,    UpperCamelCase__    :					list				):




     """simple docstring"""


     if max_rev[n] >= 0:
          return max_rev[n]
     elif n == 0:
          return 0
     else:
          a_     :							Tuple     						=  float("""-inf"""				)
          for i in range(1 ,    n + 1				):
               a_     :							List[str]     						=  max(
                   UpperCamelCase__ ,    prices[i - 1] + _top_down_cut_rod_recursive(n - i ,    UpperCamelCase__ ,    UpperCamelCase__				) ,    )

          a_     :							str     						=  max_revenue

     return max_rev[n]



def  _SCREAMING_SNAKE_CASE     (      UpperCamelCase__    :					int ,    UpperCamelCase__    :					list				):




     """simple docstring"""


     _enforce_args(UpperCamelCase__ ,    UpperCamelCase__				)

     # length(max_rev) = n + 1, to accommodate for the revenue obtainable from a rod of
     # length 0.
     a_     :							Tuple     						=  [float("""-inf"""				) for _ in range(n + 1				)]
     a_     :							Dict     						=  0

     for i in range(1 ,    n + 1				):
          a_     :							Optional[int]     						=  max_rev[i]
          for j in range(1 ,    i + 1				):
               a_     :							Optional[int]     						=  max(UpperCamelCase__ ,    prices[j - 1] + max_rev[i - j]				)

          a_     :							Tuple     						=  max_revenue_i

     return max_rev[n]



def  _SCREAMING_SNAKE_CASE     (      UpperCamelCase__    :					int ,    UpperCamelCase__    :					list				):




     """simple docstring"""


     if n < 0:
          a_     :							Optional[Any]     						=  F"n must be greater than or equal to 0. Got n = {n}"
          raise ValueError(UpperCamelCase__				)

     if n > len(UpperCamelCase__				):
          a_     :							Optional[Any]     						=  (
              """Each integral piece of rod must have a corresponding price. """
              F"Got n = {n} but length of prices = {len(UpperCamelCase__				)}"
          )
          raise ValueError(UpperCamelCase__				)



def  _SCREAMING_SNAKE_CASE     (      ):




     """simple docstring"""


     a_     :							Dict     						=  [6, 10, 12, 15, 20, 23]
     a_     :							int     						=  len(UpperCamelCase__				)

     # the best revenue comes from cutting the rod into 6 pieces, each
     # of length 1 resulting in a revenue of 6 * 6 = 36.
     a_     :							Optional[int]     						=  36

     a_     :							int     						=  top_down_cut_rod(UpperCamelCase__ ,    UpperCamelCase__				)
     a_     :							Optional[int]     						=  bottom_up_cut_rod(UpperCamelCase__ ,    UpperCamelCase__				)
     a_     :							Union[str, Any]     						=  naive_cut_rod_recursive(UpperCamelCase__ ,    UpperCamelCase__				)

     assert expected_max_revenue == max_rev_top_down
     assert max_rev_top_down == max_rev_bottom_up
     assert max_rev_bottom_up == max_rev_naive


if __name__ == "__main__":
 main()






'''simple docstring'''


def  _SCREAMING_SNAKE_CASE     (      UpperCamelCase__    :					list[int] ,    UpperCamelCase__    :					str				):




     """simple docstring"""


     a_     :							Tuple     						=  int(UpperCamelCase__				)

     # Initialize Result
     a_     :							Tuple     						=  []

     # Traverse through all denomination
     for denomination in reversed(UpperCamelCase__				):
          # Find denominations
          while int(UpperCamelCase__				) >= int(UpperCamelCase__				):
               total_value -= int(UpperCamelCase__				)
               answer.append(UpperCamelCase__				)  # Append the "answers" array

     return answer


# Driver Code
if __name__ == "__main__":
 lowerCAmelCase_      :  List[str]				     =  []
 lowerCAmelCase_      :  Union[str, Any]				     =  '0'

 if (
     input('Do you want to enter your denominations ? (yY/n): ').strip().lower()
     == "y"
 ):
  lowerCAmelCase_      :  str				     =  int(input('Enter the number of denominations you want to add: ').strip())

  for i in range(0, n):
   denominations.append(int(input(f"Denomination {i}: ").strip()))
  lowerCAmelCase_      :  Union[str, Any]				     =  input('Enter the change you want to make in Indian Currency: ').strip()
 else:
  # All denominations of Indian Currency if user does not enter
  lowerCAmelCase_      :  List[Any]				     =  [1, 2, 5, 10, 20, 50, 100, 500, 2000]
  lowerCAmelCase_      :  str				     =  input('Enter the change you want to make: ').strip()

 if int(value) == 0 or int(value) < 0:
  print('The total value cannot be zero or negative.')

 else:
  print(f"Following is minimal change for {value}: ")
  lowerCAmelCase_      :  Optional[int]				     =  find_minimum_change(denominations, value)
  # Print result
  for i in range(len(answer)):
   print(answer[i], end=' ')
