



"""simple docstring"""




from __future__ import annotations

import math

def 						__snake_case						(				SCREAMING_SNAKE_CASE__     :						float						,  SCREAMING_SNAKE_CASE__     :						int    )  ->       float:





     '''simple docstring'''

     _UpperCAmelCase      :     int        =   u
     for i in range(1						,  SCREAMING_SNAKE_CASE__    ):
          _UpperCAmelCase      :     Tuple        =   temp * (u - i)
     return temp

def 						__snake_case						(				)  ->       None:





     '''simple docstring'''

     _UpperCAmelCase      :     Optional[int]        =   int(input("enter the numbers of values: "    )    )
     _UpperCAmelCase      :     list[list[float]]        =   []
     for _ in range(SCREAMING_SNAKE_CASE__    ):
          y.append([]    )
     for i in range(SCREAMING_SNAKE_CASE__    ):
          for j in range(SCREAMING_SNAKE_CASE__    ):
               y[i].append(SCREAMING_SNAKE_CASE__    )
               _UpperCAmelCase      :     List[Any]        =   0

     print("enter the values of parameters in a list: "    )
     _UpperCAmelCase      :     int        =   list(map(SCREAMING_SNAKE_CASE__						,  input().split()    )    )

     print("enter the values of corresponding parameters: "    )
     for i in range(SCREAMING_SNAKE_CASE__    ):
          _UpperCAmelCase      :     Any        =   float(input()    )

     _UpperCAmelCase      :     Optional[Any]        =   int(input("enter the value to interpolate: "    )    )
     _UpperCAmelCase      :     str        =   (value - x[0]) / (x[1] - x[0])

     # for calculating forward difference table

     for i in range(1						,  SCREAMING_SNAKE_CASE__    ):
          for j in range(n - i    ):
               _UpperCAmelCase      :     Dict        =   y[j + 1][i - 1] - y[j][i - 1]

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

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


if __name__ == "__main__":
 main()





"""simple docstring"""




from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_sentencepiece_available


_lowerCAmelCase    : Union[str, Any]							=							{}

try:
 if not is_sentencepiece_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 _lowerCAmelCase    : Optional[Any]							=							["GPTSw3Tokenizer"]


if TYPE_CHECKING:
 try:
  if not is_sentencepiece_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .tokenization_gpt_swa import GPTSwaTokenizer

else:
 import sys

 _lowerCAmelCase    : List[Any]							=							_LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)
