code: def cartesian(arrays, out=None):
      
  
      arrays = [np.asarray(x) for x in arrays]
      dtype = arrays[0].dtype
  
      n = np.prod([x.size for x in arrays])
      if out is None:
          out = np.zeros([n, len(arrays)], dtype=dtype)
  
      m = n // arrays[0].size
      out[:,0] = np.repeat(arrays[0], m)
      if arrays[1:]:
          cartesian(arrays[1:], out=out[0:m,1:])
          for j in range(1, arrays[0].size):
              out[j*m:(j+1)*m,1:] = out[0:m,1:]
      return out
docs: Generate a cartesian product of input arrays.
  
      Parameters
      ----------
      arrays : list of array-like
          1-D arrays to form the cartesian product of.
      out : ndarray
          Array to place the cartesian product in.
  
      Returns
      -------
      out : ndarray
          2-D array of shape (M, len(arrays)) containing cartesian products
          formed of input arrays.
  
      Examples
      --------
      >>> cartesian(([1, 2, 3], [4, 5], [6, 7]))
      array([[1, 4, 6],
             [1, 4, 7],
             [1, 5, 6],
             [1, 5, 7],
             [2, 4, 6],
             [2, 4, 7],
             [2, 5, 6],
             [2, 5, 7],
             [3, 4, 6],
             [3, 4, 7],
             [3, 5, 6],
             [3, 5, 7]])