

'''simple docstring'''







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







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


if __name__ == "__main__":
						import doctest

						doctest.testmod()
						__lowerCamelCase		       =    [
						    [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'''







def       UpperCAmelCase__    (      UpperCAmelCase__				)			->			bool:
       return str(UpperCAmelCase__				) == str(UpperCAmelCase__				)[::-1]
def       UpperCAmelCase__    (      UpperCAmelCase__				)			->			int:
       return int(UpperCAmelCase__				) + int(str(UpperCAmelCase__				)[::-1]				)
def       UpperCAmelCase__    (      UpperCAmelCase__ = 1_00_00				)			->			int:
       A_						=      []
       for num in range(1,       UpperCAmelCase__				):
              A_						=      0
              A_						=      num
              while iterations < 50:
                     A_						=      sum_reverse(UpperCAmelCase__				)
                     iterations += 1
                     if is_palindrome(UpperCAmelCase__				):
                            break
              else:
                     lychrel_nums.append(UpperCAmelCase__				)
       return len(UpperCAmelCase__				)


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