
from __future__ import annotations

from decimal import Decimal

from numpy import array

def 		UpperCamelCase	(      lowercase_   )		->	Any:


  '''simple docstring'''






  lowercase__  :   Any    		=      Decimal

  # Check if the provided matrix has 2 rows and 2 columns
  # since this implementation only works for 2x2 matrices
  if len(lowercase_   ) == 2 and len(matrix[0]   ) == 2 and len(matrix[1]   ) == 2:
    # Calculate the determinant of the matrix
    lowercase__  :   str    		=      float(
        d(matrix[0][0]   ) * d(matrix[1][1]   ) - d(matrix[1][0]   ) * d(matrix[0][1]   )   )
    if determinant == 0:
      raise ValueError("""This matrix has no inverse."""   )

    # Creates a copy of the matrix with swapped positions of the elements
    lowercase__  :   str    		=      [[0.0, 0.0], [0.0, 0.0]]
    lowercase__		,    lowercase__  :   List[str]    		=      matrix[1][1], matrix[0][0]
    lowercase__		,    lowercase__  :   List[str]    		=      -matrix[1][0], -matrix[0][1]

    # Calculate the inverse of the matrix
    return [
        [(float(d(lowercase_   )   ) / determinant) or 0.0 for n in row] for row in swapped_matrix
    ]
  elif (
      len(lowercase_   ) == 3
      and len(matrix[0]   ) == 3
      and len(matrix[1]   ) == 3
      and len(matrix[2]   ) == 3
  ):
    # Calculate the determinant of the matrix using Sarrus rule
    lowercase__  :   List[Any]    		=      float(
        (
            (d(matrix[0][0]   ) * d(matrix[1][1]   ) * d(matrix[2][2]   ))
            + (d(matrix[0][1]   ) * d(matrix[1][2]   ) * d(matrix[2][0]   ))
            + (d(matrix[0][2]   ) * d(matrix[1][0]   ) * d(matrix[2][1]   ))
        )
        - (
            (d(matrix[0][2]   ) * d(matrix[1][1]   ) * d(matrix[2][0]   ))
            + (d(matrix[0][1]   ) * d(matrix[1][0]   ) * d(matrix[2][2]   ))
            + (d(matrix[0][0]   ) * d(matrix[1][2]   ) * d(matrix[2][1]   ))
        )   )
    if determinant == 0:
      raise ValueError("""This matrix has no inverse."""   )

    # Creating cofactor matrix
    lowercase__  :   int    		=      [
        [d(0.0   ), d(0.0   ), d(0.0   )],
        [d(0.0   ), d(0.0   ), d(0.0   )],
        [d(0.0   ), d(0.0   ), d(0.0   )],
    ]
    lowercase__  :   int    		=      (d(matrix[1][1]   ) * d(matrix[2][2]   )) - (
        d(matrix[1][2]   ) * d(matrix[2][1]   )
    )
    lowercase__  :   List[Any]    		=      -(
        (d(matrix[1][0]   ) * d(matrix[2][2]   )) - (d(matrix[1][2]   ) * d(matrix[2][0]   ))
    )
    lowercase__  :   Dict    		=      (d(matrix[1][0]   ) * d(matrix[2][1]   )) - (
        d(matrix[1][1]   ) * d(matrix[2][0]   )
    )
    lowercase__  :   int    		=      -(
        (d(matrix[0][1]   ) * d(matrix[2][2]   )) - (d(matrix[0][2]   ) * d(matrix[2][1]   ))
    )
    lowercase__  :   Any    		=      (d(matrix[0][0]   ) * d(matrix[2][2]   )) - (
        d(matrix[0][2]   ) * d(matrix[2][0]   )
    )
    lowercase__  :   int    		=      -(
        (d(matrix[0][0]   ) * d(matrix[2][1]   )) - (d(matrix[0][1]   ) * d(matrix[2][0]   ))
    )
    lowercase__  :   Dict    		=      (d(matrix[0][1]   ) * d(matrix[1][2]   )) - (
        d(matrix[0][2]   ) * d(matrix[1][1]   )
    )
    lowercase__  :   str    		=      -(
        (d(matrix[0][0]   ) * d(matrix[1][2]   )) - (d(matrix[0][2]   ) * d(matrix[1][0]   ))
    )
    lowercase__  :   str    		=      (d(matrix[0][0]   ) * d(matrix[1][1]   )) - (
        d(matrix[0][1]   ) * d(matrix[1][0]   )
    )

    # Transpose the cofactor matrix (Adjoint matrix)
    lowercase__  :   int    		=      array(lowercase_   )
    for i in range(3   ):
      for j in range(3   ):
        lowercase__  :   Tuple    		=      cofactor_matrix[j][i]

        # Inverse of the matrix using the formula (1/determinant) * adjoint matrix
    lowercase__  :   Dict    		=      array(lowercase_   )
    for i in range(3   ):
      for j in range(3   ):
        inverse_matrix[i][j] /= d(lowercase_   )

        # Calculate the inverse of the matrix
    return [[float(d(lowercase_   )   ) or 0.0 for n in row] for row in inverse_matrix]
  raise ValueError("""Please provide a matrix of size 2x2 or 3x3."""   )








lowerCamelCase__    :		str          =   [
    [0, 1_6, 1_3, 0, 0, 0],
    [0, 0, 1_0, 1_2, 0, 0],
    [0, 4, 0, 0, 1_4, 0],
    [0, 0, 9, 0, 0, 2_0],
    [0, 0, 0, 7, 0, 4],
    [0, 0, 0, 0, 0, 0],
]

def 		UpperCamelCase	(      lowercase_ , lowercase_ , lowercase_ , lowercase_   )		->	str:


  '''simple docstring'''






  lowercase__  :   Any    		=      [False] * len(lowercase_   )
  lowercase__  :   List[Any]    		=      [s]
  lowercase__  :   int    		=      True

  while queue:
    lowercase__  :   Dict    		=      queue.pop(0   )
    for ind in range(len(graph[u]   )   ):
      if visited[ind] is False and graph[u][ind] > 0:
        queue.append(lowercase_   )
        lowercase__  :   Optional[Any]    		=      True
        lowercase__  :   int    		=      u

  return visited[t]

def 		UpperCamelCase	(      lowercase_ , lowercase_ , lowercase_   )		->	int:


  '''simple docstring'''






  lowercase__  :   Optional[int]    		=      [-1] * (len(lowercase_   ))
  lowercase__  :   Optional[Any]    		=      0
  lowercase__  :   List[Any]    		=      []
  lowercase__  :   Optional[Any]    		=      [i[:] for i in graph]  # Record original cut, copy.
  while bfs(lowercase_ , lowercase_ , lowercase_ , lowercase_   ):
    lowercase__  :   Optional[int]    		=      float("""Inf"""   )
    lowercase__  :   Tuple    		=      sink

    while s != source:
      # Find the minimum value in select path
      lowercase__  :   List[str]    		=      min(lowercase_ , graph[parent[s]][s]   )
      lowercase__  :   List[str]    		=      parent[s]

    max_flow += path_flow
    lowercase__  :   str    		=      sink

    while v != source:
      lowercase__  :   int    		=      parent[v]
      graph[u][v] -= path_flow
      graph[v][u] += path_flow
      lowercase__  :   Union[str, Any]    		=      parent[v]

  for i in range(len(lowercase_   )   ):
    for j in range(len(graph[0]   )   ):
      if graph[i][j] == 0 and temp[i][j] > 0:
        res.append((i, j)   )

  return res


if __name__ == "__main__":
     print(mincut(test_graph, source=0, sink=5))






