In master, we already remove the King from the mobility area of minor pieces
because the King simply stands in the way of other pieces, and since opponent
cannot capture the King, any piece which "protects" the King cannot recapture.
Similarly, this patch introduces the idea that it is rarely a need for a Queen
to be "protected" by a minor (unless it is attacked only by a Queen, in fact).
We used to have a LoosePiece bonus, and in a similar vein the Queen was excluded
from that penalty.
Idea came when reviewing an old game of Kholmov. He was a very good midgame
player, but in the opening his misplace his Queen (and won in the end :-) :
http://www.chessgames.com/perl/chessgame?gid=1134645
Both white queen moves 10.Qd3 and 13.Qb3 are in the way of some minor piece.
I would prefer to not give a bishop mobility bonus at move 10 for the square d3,
or later a knight mobility bonus at move 13 for the square b3. And the textbook
move is 19.Qe3! which prepares 20.Nb3. This short game sample shows how much a
queen can be "in the way" of minor pieces.
STC
http://tests.stockfishchess.org/tests/view/5ac2c15f0ebc591746423fa3
LLR: 2.96 (-2.94,2.94) [0.00,5.00]
Total: 22066 W: 4561 L: 4330 D: 13175
LTC
http://tests.stockfishchess.org/tests/view/5ac2d6500ebc591746423faf
LLR: 2.96 (-2.94,2.94) [0.00,5.00]
Total: 25871 W: 3953 L: 3738 D: 18180
Closes https://github.com/official-stockfish/Stockfish/pull/1532
Ideas for future work in this area:
• tweak some more mobility areas for other piece type.
• construct a notion of global mobility for the whole piece set.
• bad bishops.
Bench: 4989125
Simplify ThreatBySafePawn evaluation by removing the 'if (weak)' speed
optimization check from threats evaluation. This is a non functional
change as it removes just a speed optimization conditional which was
probably useful before but does no longer provide benefits. This section
section had a few more lines not long ago, with ThreatByHangingPawn and
a loop through the threatened pieces, but now there is not much left.
Passed STC:
LLR: 2.95 (-2.94,2.94) [-3.00,1.00]
Total: 47775 W: 9696 L: 9624 D: 28455
http://tests.stockfishchess.org/tests/view/5ac298910ebc591746423f8b
Closes https://github.com/official-stockfish/Stockfish/pull/1531
Non functional change.
When we reach a position with only two opposite colored bishops and
one pawn on the board, current master would give it a scale factor
of 9/64=0.14 in about one position out of 7200, and a scale factor
of 0.0 in the 7199 others. The patch gives a scale factor of 0.0 in
100% of the cases.
STC:
LLR: 2.96 (-2.94,2.94) [-3.00,1.00]
Total: 55845 W: 11467 L: 11410 D: 32968
http://tests.stockfishchess.org/tests/view/5abc585f0ebc5902926cf15e
LTC:
LLR: 2.95 (-2.94,2.94) [-3.00,1.00]
Total: 11915 W: 1852 L: 1719 D: 8344
http://tests.stockfishchess.org/tests/view/5abc7f750ebc5902926cf18c
We also have exhaustive coverage analysis of this patch effect by
Alain Savard, comparing the perfect evaluation given by the Syzygy
tablebase with the heuristic play after this patch for the set of
all legal positions of the KBPKP endgame with opposite bishops, in
the comments thread for this pull request:
https://github.com/official-stockfish/Stockfish/pull/1520
Alain's conclusion:
> According to this definition and the data, I consider this PR is
> identical to master to "solve for draw" and slightly better than
> master to solve earlier for "wins".
Note: this patch is a side effect of an ongoing effort to improve
the evaluation of positions involving a pair of opposite bishops.
See the GitHub diff of this LTC test which almost passed at sprt[0..5]
for a discussion:
http://tests.stockfishchess.org/tests/view/5ab9030b0ebc5902932cbf93
No functional change (at small bench depths)
We now use per-thread dynamic contempt. This patch has the following
effects:
* for Threads=1: **non-functional**
* for Threads>1:
* with MultiPV=1: **no regression, little to no ELO gain**
* with MultiPV>1: **clear improvement over master**
First, I tried testing at standard MultiPV=1 play with [0,5] bounds.
This yielded 2 yellow and 1 red test:
5+0.05, Threads=5:
LLR: -2.96 (-2.94,2.94) [0.00,5.00]
Total: 82689 W: 16439 L: 16190 D: 50060
http://tests.stockfishchess.org/tests/view/5aa93a5a0ebc5902952892e6
5+0.05, Threads=8:
LLR: -2.96 (-2.94,2.94) [0.00,5.00]
Total: 27164 W: 4974 L: 4983 D: 17207
http://tests.stockfishchess.org/tests/view/5ab2639b0ebc5902a6fbefd5
5+0.5, Threads=16:
LLR: -2.97 (-2.94,2.94) [0.00,5.00]
Total: 41396 W: 7127 L: 7082 D: 27187
http://tests.stockfishchess.org/tests/view/5ab124220ebc59029516cb62
Then, I tested with Skill Level=17 (implicitly MutliPV=4), showing
a clear improvement:
5+0.05, Threads=5:
LLR: 2.96 (-2.94,2.94) [0.00,5.00]
Total: 3498 W: 1316 L: 1135 D: 1047
http://tests.stockfishchess.org/tests/view/5ab4b6580ebc5902932aeca2
Next, I tested the patch with MultiPV=1 again, this time checking for
non-regression ([-3, 1]):
5+0.5, Threads=5:
LLR: 2.96 (-2.94,2.94) [-3.00,1.00]
Total: 65575 W: 12786 L: 12745 D: 40044
http://tests.stockfishchess.org/tests/view/5ab4e8500ebc5902932aecb3
Finally, I ran some tests with fixed number of games, checking if
reverting dynamic contempt gains more elo with Skill Level=17 (i.e.
MultiPV) than applying the "prevScore" fix and this patch. These tests
showed, that this patch gains 15 ELO when playing with Skill Level=17:
5+0.05, Threads=3, "revert dynamic contempt" vs. "WITHOUT this patch":
ELO: -11.43 +-4.1 (95%) LOS: 0.0%
Total: 20000 W: 7085 L: 7743 D: 5172
http://tests.stockfishchess.org/tests/view/5ab636450ebc590295d88536
5+0.05, Threads=3, "revert dynamic contempt" vs. "WITH this patch":
ELO: -26.42 +-4.1 (95%) LOS: 0.0%
Total: 20000 W: 6661 L: 8179 D: 5160
http://tests.stockfishchess.org/tests/view/5ab62e680ebc590295d88524
---
***FAQ***
**Why should this be commited?**
I believe that the gain for multi-thread MultiPV search is a sufficient
justification for this otherwise neutral change. I also believe this
implementation of dynamic contempt is more logical, although this may
be just my opinion.
**Why is per-thread contempt better at MultiPV?**
A likely explanation for the gain in MultiPV mode is that during
search each thread independently switches between rootMoves and via
the shared contempt score skews each other's evaluation.
**Why were the tests done with Skill Level=17?**
This was originally suggested by @Hanamuke and the idea is that with
Skill Level Stockfish sometimes plays also moves it thinks are slightly
sub-optimal and thus the quality of all moves offered by the MultiPV
search is checked by the test.
**Why are the ELO differences so huge?**
This is most likely because of the nature of Skill Level mode --
since it slower and weaker than normal mode, bugs in evaluation have
much greater effect.
---
Closes https://github.com/official-stockfish/Stockfish/pull/1515.
No functional change -- in single thread mode.
Make kingRing always eight squares, extending the bitboard to the
F file if the king is on the H file, and to the C file if the king
is on the A file. This may deal with cases where Stockfish (like
many other engines) would shift the king around on the back rank
like g1h1, not because there is some imminent threat, but because
it makes king safety look a little better just because the king ring
had a smaller area.
STC:
LLR: 2.96 (-2.94,2.94) [0.00,5.00]
Total: 34000 W: 7167 L: 6877 D: 19956
http://tests.stockfishchess.org/tests/view/5ab8216d0ebc5902932cbe64
LTC:
LLR: 2.96 (-2.94,2.94) [0.00,5.00]
Total: 22574 W: 3576 L: 3370 D: 15628
http://tests.stockfishchess.org/tests/view/5ab84e6a0ebc5902932cbe72
How to continue from there?
This patch probably makes it easier to tune the king safety evaluation,
because the new regularity of the king ring size will make the king
safety function more continuous.
Closes https://github.com/official-stockfish/Stockfish/pull/1512
Bench: 5934103
To more clearly distinguish them from "const" local variables, this patch
defines compile-time local constants as constexpr. This is consistent with
the definition of PvNode as constexpr in search() and qsearch(). It also
makes the code more robust, since the compiler will now check that those
constants are indeed compile-time constants.
We can go even one step further and define all the evaluation and search
compile-time constants as constexpr.
In generate_castling() I replaced "K" with "step", since K was incorrectly
capitalised (in the Chess960 case).
In timeman.cpp I had to make the non-local constants MaxRatio and StealRatio
constepxr, since otherwise gcc would complain when calculating TMaxRatio and
TStealRatio. (Strangely, I did not have to make Is64Bit constexpr even though
it is used in ucioption.cpp in the calculation of constexpr MaxHashMB.)
I have renamed PieceCount to pieceCount in material.h, since the values of
the array are not compile-time constants.
Some compile-time constants in tbprobe.cpp were overlooked. Sides and MaxFile
are not compile-time constants, so were renamed to sides and maxFile.
Non-functional change.
Implements renaming suggestions by Marco Costalba, Günther Demetz,
Gontran Lemaire, Ronald de Man, Stéphane Nicolet, Alain Savard,
Joost VandeVondele, Jerry Donald Watson, Mike Whiteley, xoto10,
and I hope that I haven't forgotten anybody.
Perpetual renaming thread for suggestions:
https://github.com/official-stockfish/Stockfish/issues/1426
No functional change.
King and pawn endgames are typically decisive, and a small
advantage is often sufficient to win. Therefore we now take
this into account when computing the initiative adjustment.
This idea came from a series of patches by Gian-Carlo Pascutto.
STC:
LLR: 2.95 (-2.94,2.94) [0.00,5.00]
Total: 48770 W: 10203 L: 9845 D: 28722
http://tests.stockfishchess.org/tests/view/5aa58cce0ebc59029780ff8d
LTC:
LLR: 2.96 (-2.94,2.94) [0.00,5.00]
Total: 22252 W: 3572 L: 3366 D: 15314
http://tests.stockfishchess.org/tests/view/5aa5b27c0ebc59029780ffad
Ideas for future developement:
- There have been a number of changes to the initiative
calculation lately. Perhaps the coefficients could be
tuned again.
- It may be possible to add special knowledge for other
endgames in the initiative calculation.
Closes https://github.com/official-stockfish/Stockfish/pull/1481
Bench: 5750110
"Loose pieces drop, in blitz keep everything protected"
Adding a small S(2,2) bonus for knights, bishops, rooks, and
queens that are "connected" to each other (in the sense that
they are under attack by our own pieces) apparently is a good
thing. It probably helps the pieces work together a bit better.
STC
LLR: 2.96 (-2.94,2.94) [0.00,5.00]
Total: 12317 W: 2655 L: 2467 D: 7195
http://tests.stockfishchess.org/tests/view/5aa2d86b0ebc590297cb6474
LTC
LLR: 2.96 (-2.94,2.94) [0.00,5.00]
Total: 35725 W: 5516 L: 5263 D: 24946
http://tests.stockfishchess.org/tests/view/5aa2fc6f0ebc590297cb64a8
How to continue from there (by Stefan Geschwentner)?
• First we should identify all other eval terms which have an overlap
with new connectivity bonus (like the outpost bonus). A simple way
would be subtract the connectivity bonus from them and look if this
better, or use a SPSA session for these terms.
• Tuning Connectivity himself with SPSA seems not so promising because
of the small range which is useful. Here manual testing changes of
Connectivity like +-1 seems better.
• The eg value is more important because in endgame the position gets
more open and so attacks on pieces are easier. Another important point
is that when defending/fortress-like positions each defending piece
needs a protection, otherwise attacks on them can break defense.
Closes https://github.com/official-stockfish/Stockfish/pull/1474
Bench: 5318575
Allow a potential slider threat from a square currently occupied
by a harmless attacker, just as the recent "knight on queen" patch.
Also from not completely safe squares, use the mobilityArea instead
of excluding all pawns for both SlidersOnQueen and KnightOnQueen
We now compute the potential sliders threat on queen only if opponent
has one queen.
Run as SPRT [0,4] since it is some kind of simplification but maybe
not clearly one.
STC:
http://tests.stockfishchess.org/tests/view/5aa1ddf10ebc590297cb63d8
LLR: 2.95 (-2.94,2.94) [0.00,4.00]
Total: 22997 W: 4817 L: 4570 D: 13610
LTC:
http://tests.stockfishchess.org/tests/view/5aa1fe6b0ebc590297cb63e5
LLR: 2.95 (-2.94,2.94) [0.00,4.00]
Total: 11926 W: 1891 L: 1705 D: 8330
After this patch is committed, we may try to:
• re-introduce some "threat by queen" bonus to make Stockfish's queen
more aggressive (attacking aspect)
• introduce a concept of "queen overload" to force the opponent queen
into passivity and protecting duties (defensive aspect)
• more generally, re-tune the queen mobility array since patches in the
last three months have affected a lot the location/activity of queens.
Closes https://github.com/official-stockfish/Stockfish/pull/1473
bench: 5788691
We give a S(21,11) bonus for knight threats on the next moves
against enemy queen. The threats are from squares which are
"not strongly protected" and which may be empty, contain enemy
pieces or even one of our piece at the moment (N,B,Q,R) -- hence
be two-steps threats in the later case because we will have to
move our piece and *then* attack the enemy queen with the knight.
STC: http://tests.stockfishchess.org/tests/view/5a9e442e0ebc590297cb6162
LLR: 2.96 (-2.94,2.94) [0.00,5.00]
Total: 35129 W: 7346 L: 7052 D: 20731
LTC: http://tests.stockfishchess.org/tests/view/5a9e6e620ebc590297cb617f
LLR: 2.96 (-2.94,2.94) [0.00,5.00]
Total: 42442 W: 6695 L: 6414 D: 29333
How to continue from there?
• Trying to refine the threat condition ("not strongly protected")
• Trying the two-steps idea for bishops or rooks threats against queen
Bench: 6051247
Similar removal of superposition code trick as in the
"Simplify tropism computation" patch. This simplification
of the space() function will allow us to specify space
masks which can reach into enemy territory.
passed STC:
LLR: 3.38 (-2.94,2.94) [-3.00,1.00]
Total: 184630 W: 40581 L: 40758 D: 103291
http://tests.stockfishchess.org/tests/view/5a8433360ebc590297cc80c5
passed LTC:
LLR: 2.95 (-2.94,2.94) [-3.00,1.00]
Total: 231799 W: 37647 L: 37858 D: 156294
http://tests.stockfishchess.org/tests/view/5a96a34a0ebc590297cc8cfd
No functional change.
The current master applies Eval::Tempo even to leaves evaluated
as draw by some of the static evaluation functions of endgame.cpp
(for instance KNN vs K or stalemates in KP vs K). This results in
some lines being reported as +0.07 or -0.07 when the terminal
position has reached such endgames (0.07 being about the value
of a tempo for Stockfish).
This patch does not apply Eval::tempo to these positions. This leads
to more nodes being evaluated as VALUE_DRAW during search, giving more
opportunities for cut-offs in alpha-beta.
STC:
LLR: 2.96 (-2.94,2.94) [0.00,4.00]
Total: 52602 W: 11776 L: 11403 D: 29423
http://tests.stockfishchess.org/tests/view/5a8cb8f60ebc590297cc8546
LTC:
LLR: 2.97 (-2.94,2.94) [0.00,4.00]
Total: 156613 W: 26820 L: 26158 D: 103635
http://tests.stockfishchess.org/tests/view/5a8f452d0ebc590297cc865a
Bench: 4924749
To compute dicovered check or pinned pieces we use some bitwise
operators that are not really needed because already accounted for
at the caller site.
For instance in evaluation we compute:
pos.pinned_pieces(Us) & s
Where pinned_pieces() is:
st->blockersForKing[c] & pieces(c)
So in this case the & operator with pieces(c) is useless,
given the outer '& s'.
There are many places where we can use the naked blockersForKing[]
instead of the full pinned_pieces() or discovered_check_candidates().
This path is simpler than original and gives around 1% speed up for me.
Also tested for speed by mstembera and snicolet (neutral in both cases).
No functional change.
This is one of the most difficult to understand but also
most important and speed critical functions of SF.
This patch rewrites some part of it to hopefully
make it clearer and drop some redundant variables
in the process.
Same speed than master (or even a bit more).
Thanks to Chris Cain for useful feedback.
No functional change.
Where variable names are explicitly incorrect, I feel morally obligated to at least
suggest an alternative. There are many, but these two are especially egregious.
No functional change.
As far as can tell, semiopenFiles are set if there is a pawn anywhere on
the file. The removed condition would be true even if the pawns were very
advanced, which doesn't make sense if we're looking for a trapped rook.
Seems the engine fairs better with this removed. My guess s that the
condition that mobility is 3 or less does this well enough.
Begs the question whether this is a mobility issue alone... not sure.
Should I do LTC test?
STC
LLR: 2.95 (-2.94,2.94) [-3.00,1.00]
Total: 13377 W: 3009 L: 2871 D: 7497
http://tests.stockfishchess.org/tests/view/5a855be40ebc590297cc8166
Passed LTC
LLR: 2.95 (-2.94,2.94) [-3.00,1.00]
Total: 16288 W: 2813 L: 2685 D: 10790
http://tests.stockfishchess.org/tests/view/5a8575a80ebc590297cc817e
Bench: 5006365
Make contempt dependent on the current score of the root position.
The idea is that we now use a linear formula like the following to decide
on the contempt to use during a search :
contempt = x + y * eval
where x is the base contempt set by the user in the "Contempt" UCI option,
and y * eval is the dynamic part which adapts itself to the estimation of
the evaluation of the root position returned by the search. In this patch,
we use x = 18 centipawns by default, and the y * eval correction can go
from -20 centipawns if the root eval is less than -2.0 pawns, up to +20
centipawns when the root eval is more than 2.0 pawns.
To summarize, the new contempt goes from -0.02 to 0.38 pawns, depending if
Stockfish is losing or winning, with an average value of 0.18 pawns by default.
STC:
LLR: 2.95 (-2.94,2.94) [0.00,5.00]
Total: 110052 W: 24614 L: 23938 D: 61500
http://tests.stockfishchess.org/tests/view/5a72e6020ebc590f2c86ea20
LTC:
LLR: 2.97 (-2.94,2.94) [0.00,5.00]
Total: 16470 W: 2896 L: 2705 D: 10869
http://tests.stockfishchess.org/tests/view/5a76c5b90ebc5902971a9830
A second match at LTC was organised against the current master:
ELO: 1.45 +-2.9 (95%) LOS: 84.0%
Total: 19369 W: 3350 L: 3269 D: 12750
http://tests.stockfishchess.org/tests/view/5a7acf980ebc5902971a9a2e
Finally, we checked that there is no apparent problem with multithreading,
despite the fact that some threads might have a slightly different contempt
level that the main thread.
Match of this version against master, both using 5 threads, time control 30+0.3:
ELO: 2.18 +-3.2 (95%) LOS: 90.8%
Total: 14840 W: 2502 L: 2409 D: 9929
http://tests.stockfishchess.org/tests/view/5a7bf3e80ebc5902971a9aa2
Include suggestions from Marco Costalba, Aram Tumanian, Ronald de Man, etc.
Bench: 5207156
The 'eval' debugging command in Terminal did not initialize the Eval::Contempt
variable, leading to random output during debugging sessions (normal search
was unaffected by the bug).
Example of session where the two 'eval' commands should give the same output,
but did not:
./stockfish
position startpos
d
eval
go depth 20
d
eval
The bug is fixed by initializing Eval::Contempt to SCORE_ZERO in Eval::trace
No functional change.
Current master can yield different staticEvals depending on the path
used to reach the position. The reason for this is that the evaluation after a
null move is always computed subtracting 2 * Eval::Tempo, while this is not
the case for lazy or specialized evals. This patch always adds tempo to evals,
which doesn't affect playing strength:
LTC
LLR: 2.96 (-2.94,2.94) [-3.00,1.00]
Total: 59911 W: 7616 L: 7545 D: 44750
STC
LLR: 2.95 (-2.94,2.94) [-3.00,1.00]
Total: 104947 W: 18897 L: 18919 D: 67131
Fixes issue #1335
Bench: 5208264
Simplify the other check penalty computation. Compared to current master,
a) it uses a 143 kingDanger penalty instead of S(10, 10) for the "otherCheck"
(credits to ElbertoOne for finding a suitable kingDanger range to replace the score
and to Guardian for showing this could also be a neutral change at LTC).
This makes our king safety model more consistent and simpler.
b) it might also score more than one "otherCheck" penalty for a given piece type instead of just one
c) it might score many pinned penalties instead of just one.
d) It also remove 3 conditionals and uses simpler expressions.
So it was tested as a SPRT[-3, 1]
Passed STC
http://tests.stockfishchess.org/tests/view/5a2b560b0ebc590ccbb8ba6b
LLR: 2.96 (-2.94,2.94) [-3.00,1.00]
Total: 11705 W: 2217 L: 2080 D: 7408
And LTC
http://tests.stockfishchess.org/tests/view/5a2bfd0d0ebc590ccbb8bab0
LLR: 2.94 (-2.94,2.94) [-3.00,1.00]
Total: 26812 W: 3575 L: 3463 D: 19774
Trying to improve on b) another attempt was made to score also the
"otherchecks" for piece types which had some safe checks, but this
failed STC http://tests.stockfishchess.org/tests/view/5a2c79e60ebc590ccbb8badd
bench: 5149133
* A better contempt implementation for Stockfish
The round 2 of TCEC season 10 demonstrated the benefit of having a nice contempt implementation: it gives the strongest programs in the tournament the ability to slow down the game when they feel the position is slightly worse, prefering to stay in a complicated (even if slightly risky) middle game rather than simplifying by force into a drawn endgame.
The current contempt implementation of Stockfish is inadequate, and this patch is an attempt to provide a better one.
Passed STC non-regression test against master:
LLR: 2.95 (-2.94,2.94) [-3.00,1.00]
Total: 83360 W: 15089 L: 15075 D: 53196
http://tests.stockfishchess.org/tests/view/5a1bf2de0ebc590ccbb8b370
This contempt implementation is showing promising results in certains situations. For instance, it obtained a nice +30 Elo gain when playing with contempt=40 against Stockfish 7, compared to current master:
• master against SF 7 (20000 games at LTC): +121.2 Elo
• this patch with contempt=40 (20000 games at LTC): +154.11 Elo
This was the result of real cooperative work from the Stockfish team, with key ideas coming from Stefan Geschwentner (locutus2) and Chris Cain (ceebo) while most of the community helped with feedback and computer time.
In this commit the bench is unchanged by default, but you can test at home with the new contempt in the UCI options. The style of play will change a lot when using contempt different of zero (I repeat: not done in this version by default, however)!
The Stockfish team is still deliberating over the best default contempt value in self-play and the best contempt modeling strategy, to help users choosing a contempt value when playing against much weaker programs. These informations will be given in future commits when available :-)
Bench: 5051254
* Remove the prefetch
No functional change.
Currently the NORTH/WEST/SOUTH/EAST values are of type Square, but conceptually they are not squares but directions. This patch separates these values into a Direction enum and overloads addition and subtraction to allow adding a Square to a Direction (to get a new Square).
I have also slightly trimmed the possible overloadings to improve type safety. For example, it would normally not make sense to add a Color to a Color or a Piece to a Piece, or to multiply or divide them by an integer. It would also normally not make sense to add a Square to a Square.
This is a non-functional change.
The new "weak" expression helps simplify the safe check calculations for rooks or minors, (but the end result for all the safe checks is the exactly the same as in current master)
The only functional change is for the "outer king ring" (for example, squares f3 g3 h3 when white king is on g1). In current master, there was a 191 penalty if any of these was not defended at all.
With this pr, there is this 191 penalty if any of these is not defended at all or is only defended by a white queen.
Tested as a simplification
STC
http://tests.stockfishchess.org/tests/view/59fb03d80ebc590ccbb89fee
LLR: 2.96 (-2.94,2.94) [-3.00,1.00]
Total: 66167 W: 12015 L: 11971 D: 42181
(against master (Update Copyright year inMakefile))
LTC
http://tests.stockfishchess.org/tests/view/5a0106ae0ebc590ccbb8a55f
LLR: 2.96 (-2.94,2.94) [-3.00,1.00]
Total: 15790 W: 2095 L: 1968 D: 11727
(against master (Handle BxN trade as good capture when history scor))
same as #1296 but rebased on latest master
bench: 5109559
