


"""simple docstring"""


from __future__ import annotations

from collections.abc import Callable

_snake_case          =							list[list[float | int]]



def   snake_case						(				_a:     Matrix		,   _a:     Matrix							)->		Matrix:
      '''simple docstring'''


      lowerCamelCase__           =		len(_a							)
      lowerCamelCase__           =		[[0 for _ in range(size + 1							)] for _ in range(_a							)]
      lowerCamelCase__           =		42
      lowerCamelCase__           =		42
      lowerCamelCase__           =		42
      lowerCamelCase__           =		42
      lowerCamelCase__           =		42
      lowerCamelCase__           =		42

      for row in range(_a							):
            for col in range(_a							):
                  lowerCamelCase__           =		matrix[row][col]

            lowerCamelCase__           =		vector[row][0]

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

            for rowa in range(row + 1		,   _a							):
                  lowerCamelCase__           =		augmented[rowa][col] / augmented[row][col]
                  lowerCamelCase__           =		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		,   _a							):
            for row in range(_a							):
                  lowerCamelCase__           =		augmented[row][col] / augmented[col][col]
                  for cola in range(_a		,   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(_a							)
      ]



def   snake_case						(				_a:     list[int]							)->		Callable[[int], int]:
      '''simple docstring'''


      lowerCamelCase__           =		len(_a							)
      lowerCamelCase__           =		[[0 for _ in range(_a							)] for _ in range(_a							)]
      lowerCamelCase__           =		[[0] for _ in range(_a							)]
      lowerCamelCase__           =		42
      lowerCamelCase__           =		42
      lowerCamelCase__           =		42
      lowerCamelCase__           =		42

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

      lowerCamelCase__           =		solve(_a		,   _a							)

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

      return interpolated_func



def   snake_case						(				_a:     int							)->		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   snake_case						(				_a:     Callable[[int], int] = question_function		,   _a:     int = 10							)->		int:
      '''simple docstring'''


      lowerCamelCase__           =		[func(_a							) for x_val in range(1		,   order + 1							)]

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

      lowerCamelCase__           =		0
      lowerCamelCase__           =		42
      lowerCamelCase__           =		42

      for poly in polynomials:
            lowerCamelCase__           =		1
            while func(_a							) == poly(_a							):
                  x_val += 1

            ret += poly(_a							)

      return ret


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







"""simple docstring"""


# A Bipartite Graph is a graph whose vertices can be divided into two independent sets,
# U and V such that every edge (u, v) either connects a vertex from U to V or a vertex
# from V to U. In other words, for every edge (u, v), either u belongs to U and v to V,
# or u belongs to V and v to U. We can also say that there is no edge that connects
# vertices of same set.



def   snake_case						(				_a:     Optional[Any]							)->		Union[str, Any]:
      '''simple docstring'''


      lowerCamelCase__           =		[False] * len(_a							)
      lowerCamelCase__           =		[-1] * len(_a							)

      def dfs(_a:     Any		,   _a:     Optional[int]							):
            lowerCamelCase__           =		True
            lowerCamelCase__           =		c
            for u in graph[v]:
                  if not visited[u]:
                        dfs(_a		,   1 - c							)

      for i in range(len(_a							)							):
            if not visited[i]:
                  dfs(_a		,   0							)

      for i in range(len(_a							)							):
            for j in graph[i]:
                  if color[i] == color[j]:
                        return False

      return True


# Adjacency list of graph
_snake_case          =							{0: [1, 3], 1: [0, 2], 2: [1, 3], 3: [0, 2], 4: []}






print(check_bipartite_dfs(graph))



