



"""simple docstring"""


def  _lowerCAmelCase      (   lowercase_						):
						UpperCAmelCase             = current_set.copy()
						for row_index, row in enumerate(lowercase_						):
												UpperCAmelCase             = row[0]
												for column_index, column in enumerate(lowercase_						):
																		if magnitude == 0:
																								UpperCAmelCase             = column
																								continue
																		UpperCAmelCase             = column / magnitude
    # Subtract to cancel term
						UpperCAmelCase             = current_set[0]
						UpperCAmelCase             = [first_row]
						UpperCAmelCase             = current_set[1::]
						for row in current_set:
												UpperCAmelCase             = []
												# If first term is 0, it is already in form we want, so we preserve it
												if row[0] == 0:
																		final_set.append(lowercase_						)
																		continue
												for column_index in range(len(lowercase_						)						):
																		temp_row.append(first_row[column_index] - row[column_index]						)
												final_set.append(lowercase_						)
						# Create next recursion iteration set
						if len(final_set[0]						) != 3:
												UpperCAmelCase             = final_set[0]
												UpperCAmelCase             = []
												UpperCAmelCase             = []
												for row in final_set[1::]:
																		current_first_column.append(row[0]						)
																		next_iteration.append(row[1::]						)
												UpperCAmelCase             = simplify(lowercase_						)
												for i in range(len(lowercase_						)						):
																		resultant[i].insert(0		,	current_first_column[i]						)
												resultant.insert(0		,	lowercase_						)
												UpperCAmelCase             = resultant
						return final_set

def  _lowerCAmelCase      (   lowercase_						):
						if len(lowercase_						) == 0:
												raise IndexError('solve_simultaneous() requires n lists of length n+1'						)
						UpperCAmelCase             = len(lowercase_						) + 1
						if any(len(lowercase_						) != _length for item in equations						):
												raise IndexError('solve_simultaneous() requires n lists of length n+1'						)
						for row in equations:
												if any(not isinstance(lowercase_		,	(int, float)						) for column in row						):
																		raise ValueError('solve_simultaneous() requires lists of integers'						)
						if len(lowercase_						) == 1:
												return [equations[0][-1] / equations[0][0]]
						UpperCAmelCase             = equations.copy()
						if any(0 in row for row in data_set						):
												UpperCAmelCase             = data_set.copy()
												UpperCAmelCase             = []
												for row_index, row in enumerate(lowercase_						):
																		if 0 not in row:
																								UpperCAmelCase             = data_set.pop(lowercase_						)
																								break
												if not full_row:
																		raise ValueError('solve_simultaneous() requires at least 1 full equation'						)
												data_set.insert(0		,	lowercase_						)
						UpperCAmelCase             = data_set.copy()
						UpperCAmelCase             = simplify(lowercase_						)
						UpperCAmelCase             = simplified[::-1]
						UpperCAmelCase             = []
						for row in simplified:
												UpperCAmelCase             = row[-1]
												if not solutions:
																		if row[-2] == 0:
																								solutions.append(0						)
																								continue
																		solutions.append(current_solution / row[-2]						)
																		continue
												UpperCAmelCase             = row.copy()[: len(lowercase_						) - 1 :]
												while temp_row[0] == 0:
																		temp_row.pop(0						)
												if len(lowercase_						) == 0:
																		solutions.append(0						)
																		continue
												UpperCAmelCase             = temp_row[1::]
												UpperCAmelCase             = temp_row[::-1]
												for column_index, column in enumerate(lowercase_						):
																		current_solution -= column * solutions[column_index]
												solutions.append(lowercase_						)
						UpperCAmelCase             = []
						for item in solutions:
												final.append(float(round(lowercase_		,	5						)						)						)
						return final[::-1]


if __name__ == "__main__":
				import doctest

				doctest.testmod()
				snake_case_				     =       [
				    [2, 1, 1, 1, 1, 4],
				    [1, 2, 1, 1, 1, 5],
				    [1, 1, 2, 1, 1, 6],
				    [1, 1, 1, 2, 1, 7],
				    [1, 1, 1, 1, 2, 8],
				]
				print(solve_simultaneous(eq))
				print(solve_simultaneous([[4, 2]]))










'''simple docstring'''





import math






class __A			:



 '''simple docstring'''







 def __init__(self ,   A=0       )    ->     Dict:  # a graph with Node 0,1,...,N-1


      """simple docstring"""



      _a      =  n
      _a      =  [
          [math.inf for j in range(0 ,   A       )] for i in range(0 ,   A       )
      ]  # adjacency matrix for weight
      _a      =  [
          [math.inf for j in range(0 ,   A       )] for i in range(0 ,   A       )
      ]  # dp[i][j] stores minimum distance from i to j



 def 					a__  (self ,   A ,   A ,   A       )    ->     Tuple:


      """simple docstring"""



      _a      =  w



 def 					a__  (self       )    ->     List[Any]:


      """simple docstring"""



      for k in range(0 ,   self.n       ):
           for i in range(0 ,   self.n       ):
                for j in range(0 ,   self.n       ):
                     _a      =  min(self.dp[i][j] ,   self.dp[i][k] + self.dp[k][j]       )



 def 					a__  (self ,   A ,   A       )    ->     str:


      """simple docstring"""



      return self.dp[u][v]


if __name__ == "__main__":
  lowercase_		       =  Graph(5)
  graph.add_edge(0, 2, 9)
  graph.add_edge(0, 4, 10)
  graph.add_edge(1, 3, 5)
  graph.add_edge(2, 3, 7)
  graph.add_edge(3, 0, 10)
  graph.add_edge(3, 1, 2)
  graph.add_edge(3, 2, 1)
  graph.add_edge(3, 4, 6)
  graph.add_edge(4, 1, 3)
  graph.add_edge(4, 2, 4)
  graph.add_edge(4, 3, 9)
  graph.floyd_warshall()
  graph.show_min(1, 4)
  graph.show_min(0, 3)



