


"""simple docstring"""






def    A_ ( _lowerCAmelCase  :       int,  _lowerCAmelCase  :       int,  _lowerCAmelCase  :       int							):






     """simple docstring"""

     if common_ratio == 1:
          # Formula for sum if common ratio is 1
          return num_of_terms * first_term

     # Formula for finding sum of n terms of a GeometricProgression
     return (first_term / (1 - common_ratio)) * (1 - common_ratio**num_of_terms)



"""simple docstring"""






def    A_ ( _lowerCAmelCase  :       list[list[int]]							):






     """simple docstring"""

     _a     						=					[list(_lowerCAmelCase							) for row in matrix]
     if matrix and isinstance(_lowerCAmelCase,  _lowerCAmelCase							):
          if isinstance(matrix[0],  _lowerCAmelCase							):
               _a     						=					0
               for row in matrix:
                    if prev_len == 0:
                         _a     						=					len(_lowerCAmelCase							)
                         _a     						=					True
                    else:
                         _a     						=					prev_len == len(_lowerCAmelCase							)
          else:
               _a     						=					True
     else:
          _a     						=					False

     return result
def    A_ ( _lowerCAmelCase  :       list[list[int]]							):






     """simple docstring"""

     if check_matrix(_lowerCAmelCase							) and len(_lowerCAmelCase							) > 0:
          _a     						=					[list(_lowerCAmelCase							) for row in a]
          _a     						=					len(_lowerCAmelCase							)
          if isinstance(a[0],  _lowerCAmelCase							):
               _a     						=					len(a[0]							)
          else:
               for dat in a:
                    print(_lowerCAmelCase							)
               return

          # horizotal printing increasing
          for i in range(0,  _lowerCAmelCase							):
               print(a[0][i]							)
          # vertical printing down
          for i in range(1,  _lowerCAmelCase							):
               print(a[i][mat_col - 1]							)
          # horizotal printing decreasing
          if mat_row > 1:
               for i in range(mat_col - 2,  -1,  -1							):
                    print(a[mat_row - 1][i]							)
        # vertical printing up
          for i in range(mat_row - 2,  0,  -1							):
               print(a[i][0]							)
          _a     						=					[row[1 : mat_col - 1] for row in a[1 : mat_row - 1]]
          if len(_lowerCAmelCase							) > 0:
               spiral_print_clockwise(_lowerCAmelCase							)
          else:
               return
     else:
          print('''Not a valid matrix'''							)
          return
def    A_ ( _lowerCAmelCase  :       list[list]							):






     """simple docstring"""

     if matrix:
          return list(matrix.pop(0							)							) + spiral_traversal(list(zip(*_lowerCAmelCase							)							)[::-1]							)
     else:
          return []


# driver code
if __name__ == "__main__":
   import doctest

   doctest.testmod()

   __snake_case												=							[[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]]
   spiral_print_clockwise(a)