





'''simple docstring'''

# Imports
import numpy as np







class __a :





   def __init__(					self				:			Dict				,lowerCamelCase				:			Optional[Any]=None				,lowerCamelCase				:			Dict=None				,lowerCamelCase				:			Optional[int]=None				,lowerCamelCase				:			Tuple=None				,lowerCamelCase				:			int=None    ):

      '''simple docstring'''

      self.set_matricies(red=lowerCamelCase				,green=lowerCamelCase				,blue=lowerCamelCase				,red_edge=lowerCamelCase				,nir=lowerCamelCase    )





   def      UpperCAmelCase__     (					self				:			List[Any]				,lowerCamelCase				:			Optional[int]=None				,lowerCamelCase				:			List[Any]=None				,lowerCamelCase				:			Optional[Any]=None				,lowerCamelCase				:			int=None				,lowerCamelCase				:			Any=None    ):

      '''simple docstring'''

      if red is not None:
         __SCREAMING_SNAKE_CASE      							=       red
      if green is not None:
         __SCREAMING_SNAKE_CASE      							=       green
      if blue is not None:
         __SCREAMING_SNAKE_CASE      							=       blue
      if red_edge is not None:
         __SCREAMING_SNAKE_CASE      							=       red_edge
      if nir is not None:
         __SCREAMING_SNAKE_CASE      							=       nir
      return True





   def      UpperCAmelCase__     (					self				:			List[Any]				,lowerCamelCase				:			List[str]=""				,lowerCamelCase				:			Tuple=None				,lowerCamelCase				:			int=None				,lowerCamelCase				:			Optional[int]=None				,lowerCamelCase				:			List[str]=None				,lowerCamelCase				:			str=None    ):

      '''simple docstring'''

      self.set_matricies(red=lowerCamelCase				,green=lowerCamelCase				,blue=lowerCamelCase				,red_edge=lowerCamelCase				,nir=lowerCamelCase    )
      __SCREAMING_SNAKE_CASE      							=       {
          """ARVI2""": self.arvaa,
          """CCCI""": self.ccci,
          """CVI""": self.cvi,
          """GLI""": self.gli,
          """NDVI""": self.ndvi,
          """BNDVI""": self.bndvi,
          """redEdgeNDVI""": self.red_edge_ndvi,
          """GNDVI""": self.gndvi,
          """GBNDVI""": self.gbndvi,
          """GRNDVI""": self.grndvi,
          """RBNDVI""": self.rbndvi,
          """PNDVI""": self.pndvi,
          """ATSAVI""": self.atsavi,
          """BWDRVI""": self.bwdrvi,
          """CIgreen""": self.ci_green,
          """CIrededge""": self.ci_rededge,
          """CI""": self.ci,
          """CTVI""": self.ctvi,
          """GDVI""": self.gdvi,
          """EVI""": self.evi,
          """GEMI""": self.gemi,
          """GOSAVI""": self.gosavi,
          """GSAVI""": self.gsavi,
          """Hue""": self.hue,
          """IVI""": self.ivi,
          """IPVI""": self.ipvi,
          """I""": self.i,
          """RVI""": self.rvi,
          """MRVI""": self.mrvi,
          """MSAVI""": self.m_savi,
          """NormG""": self.norm_g,
          """NormNIR""": self.norm_nir,
          """NormR""": self.norm_r,
          """NGRDI""": self.ngrdi,
          """RI""": self.ri,
          """S""": self.s,
          """IF""": self._if,
          """DVI""": self.dvi,
          """TVI""": self.tvi,
          """NDRE""": self.ndre,
      }

      try:
         return funcs[index]()
      except KeyError:
         print("""Index not in the list!"""    )
         return False





   def      UpperCAmelCase__     (					self				:			Optional[Any]    ):

      '''simple docstring'''

      return -0.18 + (1.17 * ((self.nir - self.red) / (self.nir + self.red)))





   def      UpperCAmelCase__     (					self				:			Union[str, Any]    ):

      '''simple docstring'''

      return ((self.nir - self.redEdge) / (self.nir + self.redEdge)) / (
          (self.nir - self.red) / (self.nir + self.red)
      )





   def      UpperCAmelCase__     (					self				:			Optional[Any]    ):

      '''simple docstring'''

      return self.nir * (self.red / (self.green**2))





   def      UpperCAmelCase__     (					self				:			Dict    ):

      '''simple docstring'''

      return (2 * self.green - self.red - self.blue) / (
          2 * self.green + self.red + self.blue
      )





   def      UpperCAmelCase__     (					self				:			Tuple    ):

      '''simple docstring'''

      return (self.nir - self.red) / (self.nir + self.red)





   def      UpperCAmelCase__     (					self				:			Union[str, Any]    ):

      '''simple docstring'''

      return (self.nir - self.blue) / (self.nir + self.blue)





   def      UpperCAmelCase__     (					self				:			Any    ):

      '''simple docstring'''

      return (self.redEdge - self.red) / (self.redEdge + self.red)





   def      UpperCAmelCase__     (					self				:			Optional[Any]    ):

      '''simple docstring'''

      return (self.nir - self.green) / (self.nir + self.green)





   def      UpperCAmelCase__     (					self				:			Optional[int]    ):

      '''simple docstring'''

      return (self.nir - (self.green + self.blue)) / (
          self.nir + (self.green + self.blue)
      )





   def      UpperCAmelCase__     (					self				:			Any    ):

      '''simple docstring'''

      return (self.nir - (self.green + self.red)) / (
          self.nir + (self.green + self.red)
      )





   def      UpperCAmelCase__     (					self				:			Any    ):

      '''simple docstring'''

      return (self.nir - (self.blue + self.red)) / (self.nir + (self.blue + self.red))





   def      UpperCAmelCase__     (					self				:			str    ):

      '''simple docstring'''

      return (self.nir - (self.green + self.red + self.blue)) / (
          self.nir + (self.green + self.red + self.blue)
      )





   def      UpperCAmelCase__     (					self				:			List[str]				,lowerCamelCase				:			List[str]=0.08				,lowerCamelCase				:			Dict=1.22				,lowerCamelCase				:			int=0.03    ):

      '''simple docstring'''

      return a * (
          (self.nir - a * self.red - b)
          / (a * self.nir + self.red - a * b + x * (1 + a**2))
      )





   def      UpperCAmelCase__     (					self				:			int    ):

      '''simple docstring'''

      return (0.1 * self.nir - self.blue) / (0.1 * self.nir + self.blue)





   def      UpperCAmelCase__     (					self				:			List[Any]    ):

      '''simple docstring'''

      return (self.nir / self.green) - 1





   def      UpperCAmelCase__     (					self				:			Union[str, Any]    ):

      '''simple docstring'''

      return (self.nir / self.redEdge) - 1





   def      UpperCAmelCase__     (					self				:			Any    ):

      '''simple docstring'''

      return (self.red - self.blue) / self.red





   def      UpperCAmelCase__     (					self				:			str    ):

      '''simple docstring'''

      __SCREAMING_SNAKE_CASE      							=       self.ndvi()
      return ((ndvi + 0.5) / (abs(ndvi + 0.5    ))) * (abs(ndvi + 0.5    ) ** (1 / 2))





   def      UpperCAmelCase__     (					self				:			Optional[Any]    ):

      '''simple docstring'''

      return self.nir - self.green





   def      UpperCAmelCase__     (					self				:			str    ):

      '''simple docstring'''

      return 2.5 * (
          (self.nir - self.red) / (self.nir + 6 * self.red - 7.5 * self.blue + 1)
      )





   def      UpperCAmelCase__     (					self				:			Union[str, Any]    ):

      '''simple docstring'''

      __SCREAMING_SNAKE_CASE      							=       (2 * (self.nir**2 - self.red**2) + 1.5 * self.nir + 0.5 * self.red) / (
          self.nir + self.red + 0.5
      )
      return n * (1 - 0.25 * n) - (self.red - 0.125) / (1 - self.red)





   def      UpperCAmelCase__     (					self				:			Dict				,lowerCamelCase				:			Union[str, Any]=0.16    ):

      '''simple docstring'''

      return (self.nir - self.green) / (self.nir + self.green + y)





   def      UpperCAmelCase__     (					self				:			Tuple				,lowerCamelCase				:			Optional[int]=0.5    ):

      '''simple docstring'''

      return ((self.nir - self.green) / (self.nir + self.green + n)) * (1 + n)





   def      UpperCAmelCase__     (					self				:			List[Any]    ):

      '''simple docstring'''

      return np.arctan(
          ((2 * self.red - self.green - self.blue) / 30.5) * (self.green - self.blue)    )





   def      UpperCAmelCase__     (					self				:			List[str]				,lowerCamelCase				:			List[Any]=None				,lowerCamelCase				:			Union[str, Any]=None    ):

      '''simple docstring'''

      return (self.nir - b) / (a * self.red)





   def      UpperCAmelCase__     (					self				:			str    ):

      '''simple docstring'''

      return (self.nir / ((self.nir + self.red) / 2)) * (self.ndvi() + 1)





   def      UpperCAmelCase__     (					self				:			Tuple    ):

      '''simple docstring'''

      return (self.red + self.green + self.blue) / 30.5





   def      UpperCAmelCase__     (					self				:			List[Any]    ):

      '''simple docstring'''

      return self.nir / self.red





   def      UpperCAmelCase__     (					self				:			Union[str, Any]    ):

      '''simple docstring'''

      return (self.rvi() - 1) / (self.rvi() + 1)





   def      UpperCAmelCase__     (					self				:			str    ):

      '''simple docstring'''

      return (
          (2 * self.nir + 1)
          - ((2 * self.nir + 1) ** 2 - 8 * (self.nir - self.red)) ** (1 / 2)
      ) / 2





   def      UpperCAmelCase__     (					self				:			List[str]    ):

      '''simple docstring'''

      return self.green / (self.nir + self.red + self.green)





   def      UpperCAmelCase__     (					self				:			List[str]    ):

      '''simple docstring'''

      return self.nir / (self.nir + self.red + self.green)





   def      UpperCAmelCase__     (					self				:			int    ):

      '''simple docstring'''

      return self.red / (self.nir + self.red + self.green)





   def      UpperCAmelCase__     (					self				:			Any    ):

      '''simple docstring'''

      return (self.green - self.red) / (self.green + self.red)





   def      UpperCAmelCase__     (					self				:			Union[str, Any]    ):

      '''simple docstring'''

      return (self.red - self.green) / (self.red + self.green)





   def      UpperCAmelCase__     (					self				:			Union[str, Any]    ):

      '''simple docstring'''

      __SCREAMING_SNAKE_CASE      							=       np.max([np.max(self.red    ), np.max(self.green    ), np.max(self.blue    )]    )
      __SCREAMING_SNAKE_CASE      							=       np.min([np.min(self.red    ), np.min(self.green    ), np.min(self.blue    )]    )
      return (max_value - min_value) / max_value





   def      UpperCAmelCase__     (					self				:			Any    ):

      '''simple docstring'''

      return (2 * self.red - self.green - self.blue) / (self.green - self.blue)





   def      UpperCAmelCase__     (					self				:			List[str]    ):

      '''simple docstring'''

      return self.nir / self.red





   def      UpperCAmelCase__     (					self				:			Any    ):

      '''simple docstring'''

      return (self.ndvi() + 0.5) ** (1 / 2)





   def      UpperCAmelCase__     (					self				:			Optional[int]    ):

      '''simple docstring'''

      return (self.nir - self.redEdge) / (self.nir + self.redEdge)












'''simple docstring'''

from __future__ import annotations

from collections.abc import Callable

a        =						list[list[float | int]]

def 						__magic_name__       (							__UpperCAmelCase							,	__UpperCAmelCase      )						->					Matrix:

   '''simple docstring'''







   __SCREAMING_SNAKE_CASE      							=       len(__UpperCAmelCase      )
   __SCREAMING_SNAKE_CASE      							=       [[0 for _ in range(size + 1      )] for _ in range(__UpperCAmelCase      )]
   __SCREAMING_SNAKE_CASE      							=       42
   __SCREAMING_SNAKE_CASE      							=       42
   __SCREAMING_SNAKE_CASE      							=       42
   __SCREAMING_SNAKE_CASE      							=       42
   __SCREAMING_SNAKE_CASE      							=       42
   __SCREAMING_SNAKE_CASE      							=       42

   for row in range(__UpperCAmelCase      ):
      for col in range(__UpperCAmelCase      ):
         __SCREAMING_SNAKE_CASE      							=       matrix[row][col]

      __SCREAMING_SNAKE_CASE      							=       vector[row][0]

   __SCREAMING_SNAKE_CASE      							=       0
   __SCREAMING_SNAKE_CASE      							=       0
   while row < size and col < size:
      # pivoting
      __SCREAMING_SNAKE_CASE      							=       max((abs(augmented[rowa][col]      ), rowa) for rowa in range(__UpperCAmelCase							,	__UpperCAmelCase      )      )[
          1
      ]
      if augmented[pivot_row][col] == 0:
         col += 1
         continue
      else:
         __SCREAMING_SNAKE_CASE							,     __SCREAMING_SNAKE_CASE      							=       augmented[pivot_row], augmented[row]

      for rowa in range(row + 1							,	__UpperCAmelCase      ):
         __SCREAMING_SNAKE_CASE      							=       augmented[rowa][col] / augmented[row][col]
         __SCREAMING_SNAKE_CASE      							=       0
         for cola in range(col + 1							,	size + 1      ):
            augmented[rowa][cola] -= augmented[row][cola] * ratio

      row += 1
      col += 1

   # back substitution
   for col in range(1							,	__UpperCAmelCase      ):
      for row in range(__UpperCAmelCase      ):
         __SCREAMING_SNAKE_CASE      							=       augmented[row][col] / augmented[col][col]
         for cola in range(__UpperCAmelCase							,	size + 1      ):
            augmented[row][cola] -= augmented[col][cola] * ratio

    # round to get rid of numbers like 2.000000000000004
   return [
       [round(augmented[row][size] / augmented[row][row]							,	10      )] for row in range(__UpperCAmelCase      )
   ]

def 						__magic_name__       (							__UpperCAmelCase      )						->					Callable[[int], int]:

   '''simple docstring'''







   __SCREAMING_SNAKE_CASE      							=       len(__UpperCAmelCase      )
   __SCREAMING_SNAKE_CASE      							=       [[0 for _ in range(__UpperCAmelCase      )] for _ in range(__UpperCAmelCase      )]
   __SCREAMING_SNAKE_CASE      							=       [[0] for _ in range(__UpperCAmelCase      )]
   __SCREAMING_SNAKE_CASE      							=       42
   __SCREAMING_SNAKE_CASE      							=       42
   __SCREAMING_SNAKE_CASE      							=       42
   __SCREAMING_SNAKE_CASE      							=       42

   for x_val, y_val in enumerate(__UpperCAmelCase      ):
      for col in range(__UpperCAmelCase      ):
         __SCREAMING_SNAKE_CASE      							=       (x_val + 1) ** (size - col - 1)
      __SCREAMING_SNAKE_CASE      							=       y_val

   __SCREAMING_SNAKE_CASE      							=       solve(__UpperCAmelCase							,	__UpperCAmelCase      )

   def interpolated_func(__UpperCAmelCase      ) -> int:
      return sum(
          round(coeffs[x_val][0]      ) * (var ** (size - x_val - 1))
          for x_val in range(__UpperCAmelCase      )      )

   return interpolated_func

def 						__magic_name__       (							__UpperCAmelCase      )						->					int:

   '''simple docstring'''







   return (
       1
       - variable
       + variable**2
       - variable**3
       + variable**4
       - variable**5
       + variable**6
       - variable**7
       + variable**8
       - variable**9
       + variable**10
   )

def 						__magic_name__       (							__UpperCAmelCase = question_function							,	__UpperCAmelCase = 10      )						->					int:

   '''simple docstring'''







   __SCREAMING_SNAKE_CASE      							=       [func(__UpperCAmelCase      ) for x_val in range(1							,	order + 1      )]

   __SCREAMING_SNAKE_CASE      							=       [
       interpolate(data_points[:max_coeff]      ) for max_coeff in range(1							,	order + 1      )
   ]

   __SCREAMING_SNAKE_CASE      							=       0
   __SCREAMING_SNAKE_CASE      							=       42
   __SCREAMING_SNAKE_CASE      							=       42

   for poly in polynomials:
      __SCREAMING_SNAKE_CASE      							=       1
      while func(__UpperCAmelCase      ) == poly(__UpperCAmelCase      ):
         x_val += 1

      ret += poly(__UpperCAmelCase      )

   return ret


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





