  We present new strong-lensing (SL) mass reconstruction of the six Hubble
Frontier Fields (HFF) clusters with the MAximum-entropy ReconStruction (${\tt
MARS}$) algorithm. ${\tt MARS}$ is a new free-form inversion method, which
suppresses spurious small-scale fluctuations while achieving excellent
convergence in positions of multiple images. For each HFF cluster, we obtain a
model-independent mass distribution from the compilation of the self-consistent
SL data in the literature. With $100-200$ multiple images per cluster, we
reconstruct solutions with small scatters of multiple images in both source
(~0".02) and image planes (~0."05-0.''1), which are lower than the previous
results by a factor of 5-10. An outstanding case is the MACS J0416.1-2403 mass
reconstruction, which is based on the largest high-quality SL dataset where all
236 multiple images/knots have spectroscopic redshifts. Although our solution
is smooth on a large scale, it reveals group/galaxy-scale peaks where the
substructures are required by the data. We find that in general, these mass
peaks are in excellent spatial agreement with the member galaxies, although
${\tt MARS}$ never uses the galaxy distributions as priors. Our study
corroborates the flexibility and accuracy of the ${\tt MARS}$ algorithm and
demonstrates that ${\tt MARS}$ is a powerful tool in the JWST era, when $2-3$
times larger number of multiple image candidates become available for SL mass
reconstruction, and self-consistency within the dataset becomes a critical
issue.
