






'''simple docstring'''



from __future__ import annotations

from functools import lru_cache
from math import ceil

SCREAMING_SNAKE_CASE						=	100

SCREAMING_SNAKE_CASE						=	set(range(3, NUM_PRIMES, 2))
primes.add(2)
SCREAMING_SNAKE_CASE						=	42

for prime in range(3, ceil(NUM_PRIMES**0.5), 2):
      if prime not in primes:
            continue
      primes.difference_update(set(range(prime * prime, NUM_PRIMES, prime)))


@lru_cache(maxsize=1_0_0			)
def 							lowercase_				(    __A :       int			)       ->      set[int]:



 """simple docstring"""




 if number_to_partition < 0:
  return set()
 elif number_to_partition == 0:
  return {1}

 lowercase					:   set[int]				  =set()
 lowercase					:   int
 lowercase					:   int

 for prime in primes:
  if prime > number_to_partition:
   continue
  for sub in partition(number_to_partition - prime			):
   ret.add(sub * prime			)

 return ret


def 							lowercase_				(    __A :       int = 5_0_0_0			)       ->      int | None:



 """simple docstring"""




 for number_to_partition in range(1					,      __A			):
  if len(partition(__A			)			) > number_unique_partitions:
   return number_to_partition
 return None


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











'''simple docstring'''



from __future__ import annotations

import math


def 							lowercase_				(    __A :       float					,      __A :       int			)       ->      float:



 """simple docstring"""




 lowercase					:   str				  =u
 for i in range(1					,      __A			):
  lowercase					:   Any				  =temp * (u - i)
 return temp


def 							lowercase_				(    )       ->      None:



 """simple docstring"""




 lowercase					:   List[str]				  =int(input('''enter the numbers of values: '''			)			)
 lowercase					:   list[list[float]]				  =[]
 for _ in range(__A			):
  y.append([]			)
 for i in range(__A			):
  for j in range(__A			):
   y[i].append(__A			)
   lowercase					:   List[Any]				  =0

 print('''enter the values of parameters in a list: '''			)
 lowercase					:   Optional[int]				  =list(map(__A					,      input().split()			)			)

 print('''enter the values of corresponding parameters: '''			)
 for i in range(__A			):
  lowercase					:   str				  =float(input()			)

 lowercase					:   int				  =int(input('''enter the value to interpolate: '''			)			)
 lowercase					:   Union[str, Any]				  =(value - x[0]) / (x[1] - x[0])

 # for calculating forward difference table

 for i in range(1					,      __A			):
  for j in range(n - i			):
   lowercase					:   str				  =y[j + 1][i - 1] - y[j][i - 1]

 lowercase					:   Any				  =y[0][0]
 for i in range(1					,      __A			):
  summ += (ucal(__A					,      __A			) * y[0][i]) / math.factorial(__A			)

 print(F'the value at {value} is {summ}'			)


if __name__ == "__main__":
      main()



