


"""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"""


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


      lowerCamelCase__           =		[False] * len(_a							)
      lowerCamelCase__           =		[]
      queue.append(_a							)
      lowerCamelCase__           =		True

      while queue:
            lowerCamelCase__           =		queue.pop(0							)
            for ind in range(len(graph[u]							)							):
                  if visited[ind] is False and graph[u][ind] > 0:
                        queue.append(_a							)
                        lowerCamelCase__           =		True
                        lowerCamelCase__           =		u

      return visited[t]



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


      lowerCamelCase__           =		[-1] * (len(_a							))
      lowerCamelCase__           =		0
      while bfs(_a		,   _a		,   _a		,   _a							):
            lowerCamelCase__           =		float('Inf'							)
            lowerCamelCase__           =		sink

            while s != source:
                  # Find the minimum value in select path
                  lowerCamelCase__           =		min(_a		,   graph[parent[s]][s]							)
                  lowerCamelCase__           =		parent[s]

            max_flow += path_flow
            lowerCamelCase__           =		sink

            while v != source:
                  lowerCamelCase__           =		parent[v]
                  graph[u][v] -= path_flow
                  graph[v][u] += path_flow
                  lowerCamelCase__           =		parent[v]
      return max_flow


_snake_case          =							[
    [0, 16, 13, 0, 0, 0],
    [0, 0, 10, 12, 0, 0],
    [0, 4, 0, 0, 14, 0],
    [0, 0, 9, 0, 0, 20],
    [0, 0, 0, 7, 0, 4],
    [0, 0, 0, 0, 0, 0],
]

_snake_case      ,					_snake_case          =							0, 5






print(ford_fulkerson(graph, source, sink))



