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6 <TITLE>Comparison Between Chess And Go</TITLE>
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12
13 <P ALIGN="CENTER"><STRONG><A NAME="Comparison Between Chess And Go">Comparison Between Chess And Go</A></STRONG></P>
14
15 <P ALIGN="CENTER"><STRONG>&copy; 2008 Milton N. Bradley</STRONG></P>
16
17 <P>Although manifestly quite different, Chess and Go are unquestionably the two finest strategic board games in all of human history. Some prefer one, some the
18 other, and there are a small fortunate number who enjoy and excel at both. So why compare these two exemplars in a manner designed to demonstrate that one
19 is superior to the other? The answer to that important question is at least partially provided by the lead editorial in The New York Times of May 10, 1997
20 entitled "Mind Over Matter", which commented on the then ongoing Chess match between IBM's Deep Blue Computer Program and World Chess Champion
21 Gary Kasparov, in part as follows:</P>
22
23 <P>"No one much cared when computers mastered backgammon and checkers or clobbered lesser Grandmasters in chess. But now that we have sent the greatest
24 chess champion in human history into battle, the prospect of defeat seems unnerving. Still, before mere mortals sink too deeply into despair, it is important to
25 recognize several comforting alibis that may apply here.</P>
26
27 <P>Deep Blue is not thinking the way humans do. It is using its immense number-crunching power to explore millions of moves per second, and applying a set of
28 rules provided by its human masters to pick the strongest. <STRONG>This gives it tremendous powers to play chess, a narrow, circumscribed pursuit that is red
29 meat for high-speed computation but hardly the supreme measure of intelligence its practitioners like to pretend.</STRONG>"</P>
30
31 <P>Deep Blue won its match with human World Chess Champion Kasparov by causing his resignation in Game 6 after only 19 moves, after what had been an
32 even contest to that point. The following is a typical reaction to this event as posted on the web newsgroup rec.games.chess.misc: "Deep Blue won that final
33 game not because of any superiority it had over Kasparov, but because of bizarre opening play by Kasparov.". To my mind that's a sure indication that
34 Kasparov "cracked" psychologically, but whether or not that alone is sufficient to justify characterizing his defeat as "decisive" I leave to the reader's judgment.</P>
35
36 <P>The key thing that's almost certain is that with the inevitable improvements that might have been readily added to its hardware and software in subsequent
37 months had IBM chosen to continue its development, Deep Blue would likely have become indisputably superior. But having satisfied whatever corporate
38 objectives they had, once having achieved that narrow victory IBM "pulled the plug" and disassembled Deep Blue, presumably forever.</P>
39
40 <P>Now it appears that those improvements have come to pass, as explained in the Chess column of The New York Times on Sunday Feb 17, 2008, when Grandmaster Joel Benjamin wrote:
41 “If a computer played perfectly, could any human hope to achieve a draw? Chess engines are still far from perfection, but their advances have been staggering.
42 Deep Blue made history in 1997 by defeating Gary Kasparov in a six-game match. A decade later, no human would dare take on a chess program at even strength. The premier chess engine, Rybka, is estimated at (Elo) 3100, or 300 points higher than any player.
43 Rybka is exploring this dominant relationship with handicap matches against grandmasters. After narrowly losing a match at pawn handicap (the rough equivalent of 2 stones in Go? MB) I agreed to participate in an experiment. Every draw would count as a win for me. After we split 4 games, Rybka streaked to a 6-2 rout.
44 Rybka played Black in all 8 games. Larry Kaufman, co-programmer of Rybka, opined that no human has a chance without first move. Playing White greatly increases the chances for a grandmaster to draw with Rybka....”
45
46 <P>In sharp contrast, the best computer Go programs are still mired at just beyond an advanced beginner's level, despite the presence for over 15 years of a $1
47 million prize for a program which can defeat a master Go professional, offered by the Ing Chang-Ki Goe (his unique spelling!) Educational Foundation of
48 Taiwan. But no claimants for this impressive prize are even visible on the far horizon after all these years! The many reasons for this disparity are set out in the
49 comparison below, but the most obvious concerns the many orders of magnitude vastly greater size of the "move trees" in Go, which render the massive
50 number-crunching power of Deep Blue and even its potentially vastly more powerful descendants totally impotent in the critical opening and middle phases of
51 the game.</P>
52
53 <P>At least equally important is the fact that, unlike Go, Chess essentially lacks a deep strategic component! To those who may question this assertion,
54 substantiation is provided by the following famous quote: </P>
55
56 <P>"Chess is 99% tactics." -- Richard Teichmann, (1868-1925), a German Grandmaster who for many years lived in England, and one of the strongest attacking
57 players of all time. </P>
58
59 <P>Al Lawrence, former Executive Director of the US Chess Federation said of this quote: "Everyone has always agreed on this point--even before Teichmann,
60 who happened to come up with a snappy way to say it." </P>
61
62 <P>This was validated by Grandmaster Reuben Fine in his book "Chess Marches On", published by Chess Review, 1945, in which he said on page 97:</P>
63
64 <P>"Thirty years ago Teichmann said that chess is 99% tactics. And despite the enormous strides of chess theory since then, his percentage can only be reduced
65 (by) a few points. Many amateurs think that master games are usually decided by some deeply-laid plan covering all possibilities for at least ten moves.. That is
66 what they conceive the grand strategy of tournaments to be. Actually, however, strategical considerations, while quite important, do not cover a range or depth
67 at all comparable to the popular notion. Very often, in fact, sound strategy can dispense with seeing ahead at all, except in a negative or trivial sense. And it is
68 still true that most games, even between the greatest of the great, are decided by tactics or combinations which have little or nothing to do with the fundamental
69 structure of the game."</P>
70
71 <P>Then there is this excerpt from the internet review "NEW CHESSBASE CDs", by Steve Lopez, who said:</P>
72
73 <P>"It's a hoary old clich&eacute; that's been kicked around for three-quarters of a century. But do you know why it's quoted so often? Because Teichmann was right! If
74 Philidor was right in saying that the pawn is the soul of chess, Teichmann was correct in implying that tactics is the heart of the game."</P>
75
76 <P>Some of my master level chess-playing friends have complained that by making this comparison and demonstrating the objective superiority of Go I am
77 denigrating Chess, but this is a misperception. For example, if we compare precious metals and conclude that gold is more valuable than silver, are we
78 denigrating silver? Or just acknowledging objective reality? It's clear that silver has many vital uses as coinage, an electrical conductor, and in jewelry, so it is
79 of importance in industry, commerce and quality of life areas. Under these circumstances our objective appraisal of its position as less valuable than gold
80 should offend no unbiased observer. And the same should hold true for Chess compared with Go, but regrettably it almost invariably does not. Chess is
81 interesting in its own right and has many assets, but when all of its attributes are stacked up against those of Go it necessarily ranks second best! The problem is
82 that most chessplayers refuse to even contemplate that this could be true!</P>
83
84 <P>What most chessplayers share in this regard is that they are so convinced of the superiority of their game that, almost invariably with at best meager knowledge
85 of Go gained almost entirely by hearsay, they dismiss the entire idea without even exhibiting a willingness to find out for themselves. This is the very problem
86 that Chessmaster Edward Lasker and then World Chess Champion Emanuel Lasker encountered in 1905 in Germany, and which is described in the prior
87 section of this web page entitled "How Go Came To America". Maintaining this close-minded posture is any chessplayer's absolute right, of course, but its sad
88 consequence is that it unnecessarily cuts them off from one of life's greatest purely intellectual challenges and pleasures. Perhaps an even worse loss as a result
89 of their narrow perspective, those chessplayers of my acquaintance who <U>have</U> put forth the effort to study Go report that it has improved their chess, so this is
90 yet another detriment that those who display this "head-in-the-sand" attitude sustain. Hopefully those of you who are reading this do not wear those same
91 blinders, and are willing to investigate Go further and then judge for yourselves!</P>
92
93 <P>Finally, there is this perhaps most cogent comment on the comparison between Chess and Go that appeared in an article in The New York Times Metro Section
94 of Thursday February 6, 2003 entitled "Queen, Captured by Mouse", which focused on the then ongoing tied match between Gary Kasparov and the Israeli
95 Chess software program "Deep Junior". That article featured the cogent quote by Dr. Hans Berliner that appears below, whose relevance can only be fully appreciated if you understand
96 Berliner's background and outstanding credentials in the field. These were spelled out in NY Times Bridge columnist Phillip Alder's column on Saturday, Nov 4, 2006 as follows:
97
98 "Hans Berliner, who was well known in chess circles, used to be a top bridge player, but retired from that game some 50 years ago.
99 Berliner won the 1956 Eastern States open Chess Championship ahead of Bobby Fischer. But he gave up tournament chess to become the world's leading correspondence player,
100 winning that world championship, and building a chess-playing computer.
101
102 During the early stages of writing the chess program, Berliner realized that not enough was known about positional evaluation. So he turned to Backgammon. The result was BKG 9.8,
103 the first computer program to beat a World Champion in any game when it won a backgammon match against Luigi Villa in June 1979. This research led, in 1984, to a chess program called HiTech.
104
105 Berliner went on to become a Professor of Computer science at Carnegie Mellon University, from which he retired in 1998 at 69."
106
107 Because Berliner's work on chess led to the development of IBM's Deep Blue and its descendants, it had great impact and relevance when he said:
108
109 "You don't have to be really good anymore to get good results. Chess is winding down.....What's happening with Chess is that it's gradually losing its place as
110 the par excellence of intellectual activity". And he concluded: "Smart people in search of a challenging board game might try a game called Go..."</P>
111
112 <P>Need I really say more? </P>
113
114 <TABLE BORDER="1" WIDTH="100%" CELLPADDING="3">
115 <TR><TD ALIGN="CENTER"><STRONG> Comparison Between Chess And Go</STRONG></TD>
116 <TD VALIGN="TOP"></TD>
117 <TD VALIGN="TOP">
118 <BR WP="BR1"><BR WP="BR2"></TD></TR>
119 <TR><TD> CRITERION</TD>
120 <TD> CHESS</TD>
121 <TD> GO
122
123 <BR WP="BR1"><BR WP="BR2"></TD></TR>
124 <TR><TD> When Invented</TD>
125 <TD> Reputedly About 455 A.D., Probably Much
126 Earlier.</TD>
127 <TD> About 2000 B.C.
128
129 <BR WP="BR1"><BR WP="BR2"></TD></TR>
130 <TR><TD> Where Invented</TD>
131 <TD> Reputedly India, Probably China</TD>
132 <TD> China
133
134 <BR WP="BR1"><BR WP="BR2"></TD></TR>
135 <TR><TD> Suitable For Players</TD>
136 <TD> 3 years and older</TD>
137 <TD> 3 years and older
138
139 <BR WP="BR1"><BR WP="BR2"></TD></TR>
140 <TR><TD> Number of Players</TD>
141 <TD> 2, White and Black</TD>
142 <TD> 2, Black and White
143
144 <BR WP="BR1"><BR WP="BR2"></TD></TR>
145 <TR><TD> Color Selection</TD>
146 <TD> Chosen by Lot</TD>
147 <TD> The weaker player always takes Black. Equal
148 players alternate colors in successive games.
149
150 <BR WP="BR1"><BR WP="BR2"></TD></TR>
151 <TR><TD> First Play (= The Initiative)</TD>
152 <TD> Always White</TD>
153 <TD> Always Black, except that in handicap games
154 Black's handicap stones count as his first move so
155 that White actually makes the first "free" play.
156
157 <BR WP="BR1"><BR WP="BR2"></TD></TR>
158 <TR><TD> Rules of Play</TD>
159 <TD> Complex: Different piece moves, many special
160 rules (e.g. en passant capture, castling, etc.)</TD>
161 <TD> Elegant: Only 2 simple rules govern all play.
162
163 <BR WP="BR1"><BR WP="BR2"></TD></TR>
164 <TR><TD> Scope/Board Size</TD>
165 <TD> Restricted: Only 8 x 8 = 64 squares.</TD>
166 <TD> Immense: 19 x 19 = 361 intersections.
167
168 <BR WP="BR1"><BR WP="BR2"></TD></TR>
169 <TR><TD> Object Of The Game</TD>
170 <TD> Checkmate Opposing King = Total Victory</TD>
171 <TD> Obtain Larger Territory = Greater "market share"
172
173 <BR WP="BR1"><BR WP="BR2"></TD></TR>
174 <TR><TD> Brain Functions Used In Playing (1)</TD>
175 <TD> Almost Entirely Analytical (left brain).</TD>
176 <TD> Fully utilizes/integrates analytic (left brain) and
177 artistic/pattern recognition (right brain) functions.
178
179 <BR WP="BR1"><BR WP="BR2"></TD></TR>
180 <TR><TD> Number/kind of Playing Pieces</TD>
181 <TD> 1 King, 1 Queen, 2 ea. Rooks, Knights, &amp; Bishops
182 + 8 Pawns/side.</TD>
183 <TD> An unlimited supply of uniform double-convex
184 lens shaped pieces (called stones) per side.
185
186 <BR WP="BR1"><BR WP="BR2"></TD></TR>
187 <TR><TD> The Moves Of The Pieces</TD>
188 <TD> Each type of piece has its own unique move.</TD>
189 <TD> None. Stones are simply entered on the board
190 one-per-turn on any empty intersection according
191 to the rules of Go, and then are never moved
192 thereafter unless captured (when they are removed
193 from the board).
194
195 <BR WP="BR1"><BR WP="BR2"></TD></TR>
196 <TR><TD> The Starting Lineup.</TD>
197 <TD> Fixed by custom.</TD>
198 <TD> None. The board begins empty and the players
199 enter their stones anywhere that they wish to
200 uniquely structure the board in every game.
201
202 <BR WP="BR1"><BR WP="BR2"></TD></TR>
203 <TR><TD> Captures</TD>
204 <TD> Made one-at-a-time, by moving the capturing
205 piece into the square occupied by the piece being
206 captured.</TD>
207 <TD> Captured singly or en masse, by surrounding the
208 captive(s) so that they are not connected to any
209 adjacent open intersection.
210
211 <BR WP="BR1"><BR WP="BR2"></TD></TR>
212 <TR><TD> The Fate Of Captives.</TD>
213 <TD> Removed from the board (and further play).</TD>
214 <TD> Removed from the board and held as prisoners,
215 which are subtracted from the opponent's score at
216 game's end. Each prisoner is worth one point.
217
218 <BR WP="BR1"><BR WP="BR2"></TD></TR>
219 <TR><TD> Number of possible First Moves.</TD>
220 <TD> 20 White x 20 Black = 400.</TD>
221 <TD> 361 Black x 360 White = 129960, although
222 symmetry reduces this number to an effective
223 32,490.
224
225 <BR WP="BR1"><BR WP="BR2"></TD></TR>
226 <TR><TD> Number of STRONG First Moves</TD>
227 <TD> 8 White x 8 Black = 64</TD>
228 <TD> 32 Black x 31 White = 992
229
230 <BR WP="BR1"><BR WP="BR2"></TD></TR>
231 <TR><TD> The Value Of First Move</TD>
232 <TD> Not precisely evaluated, but often considered
233 sufficient to force a draw and close to enough to
234 confer a winning advantage.</TD>
235 <TD> Most often evaluated at 6 1/2 points (called
236 Komi), which are added to White's final score to
237 compensate for playing second. The extra 1/2 point
238 prevents draws.
239
240 <BR WP="BR1"><BR WP="BR2"></TD></TR>
241 <TR><TD> Estimated Number of Possible Board
242 Configurations</TD>
243 <TD> 10 <SUP>120</SUP></TD>
244 <TD> OMNI Magazine in June, 1991 proposed 10 <SUP>761</SUP>,
245 but most believe that the correct figure is really on
246 the order of 10 <SUP>174.</SUP>
247
248 <BR WP="BR1"><BR WP="BR2"></TD></TR>
249 <TR><TD> Opening "Book"</TD>
250 <TD> Structures the entire board. Any given "book" line
251 is always feasible.</TD>
252 <TD> Structures only a single corner. Integration of the
253 4 corners with the sides and center is governed by
254 general strategic principles and tactical constraints.
255 The feasibility of any given corner sequence
256 depends upon what has already happened as well
257 as the player's strategic plan for the remainder of
258 the game.
259
260 <BR WP="BR1"><BR WP="BR2"></TD></TR>
261 <TR><TD> Handicap System</TD>
262 <TD> No formal system. Giving handicaps of one or
263 more pieces or pawns imprecisely compensates for
264 differences in playing strength, and distorts both
265 tactics and strategy.</TD>
266 <TD> Handicaps consist of allowing Black to place an
267 appropriate number of stones on the board before
268 White's first move. This natural and very precise
269 compensation for playing strength differences is
270 completely consistent with normal play.
271
272 <BR WP="BR1"><BR WP="BR2"></TD></TR>
273 <TR><TD> Military Analogy</TD>
274 <TD> A single battle.</TD>
275 <TD> An entire multi-front war.
276
277 <BR WP="BR1"><BR WP="BR2"></TD></TR>
278 <TR><TD> The Nature of Play</TD>
279 <TD> Primarily tactical, with only a modest strategic
280 component.</TD>
281 <TD> Profoundly strategic, but with incisive, complex,
282 integral tactics.
283
284 <BR WP="BR1"><BR WP="BR2"></TD></TR>
285 <TR><TD> The Nature Of The Opening</TD>
286 <TD> Primarily a struggle for development, center
287 control, and maneuvering space, with subsidiary
288 objectives of pawn structure, king safety, and
289 material.</TD>
290 <TD> Each side establishes a series of delicate
291 balances/tradeoffs between the conflicting yet
292 complementary objectives of territorial acquisition,
293 "influence", making "shape", maintaining center
294 access, and attack and defense.
295
296 <BR WP="BR1"><BR WP="BR2"></TD></TR>
297 <TR><TD> The Nature Of The Middle Game</TD>
298 <TD> Mainly tactical piece maneuvering to attempt to
299 attain a winning material advantage or to mount a
300 successful mating attack, often involving real
301 and/or pseudo sacrifices, but also with strategic
302 elements involving piece mobility, center control
303 and pawn structure.</TD>
304 <TD> Features deep strategic planning implemented via
305 incisive tactics involving feints, diversions,
306 invasions, pincer and multi-purpose attacks,, often
307 involving both real and pseudo sacrifices.
308
309 <BR WP="BR1"><BR WP="BR2"></TD></TR>
310 <TR><TD> The Nature Of The Endgame</TD>
311 <TD> Piece and pawn maneuvers to force and/or
312 consolidate a winning material advantage, promote
313 a pawn, or force mate. "Endgame" moves always
314 occur at the physical end of the game.</TD>
315 <TD> Final consolidation of territorial borders between
316 safe opposing armies. Although these sequences
317 typically involve only a few points each,
318 maintenance of the initiative throughout a
319 sequence of such plays can readily result in the
320 gain of enough points to decide the game. Because
321 of the immense board size, local "endgame"
322 sequences frequently occur at almost every stage
323 of the game.
324
325 <BR WP="BR1"><BR WP="BR2"></TD></TR>
326 <TR><TD> How Victory Is Decided. (2)</TD>
327 <TD> Checkmate, resignation, or time. Draws are
328 possible by agreement, stalemate, repetition of
329 position, or perpetual check.</TD>
330 <TD> Higher final score, resignation, or time. No draws
331 are possible because repetition of any full board
332 position is prohibited, and because of the extra half
333 point given to White as part of his compensation
334 for Black's first move advantage.
335
336 <BR WP="BR1"><BR WP="BR2"></TD></TR>
337 <TR><TD> Business/Strategic Planning Analogy</TD>
338 <TD> Emphasis on short term profits. Minimal attention
339 to automation, Quality Control, and investment in
340 capital equipment/plant modernization.</TD>
341 <TD> Emphasis on long term planning, including
342 automation, Quality control, and investment in
343 capital equipment/plant modernization.
344
345 <BR WP="BR1"><BR WP="BR2"></TD></TR>
346 <TR><TD> Countries Using This Kind Of Thinking In Their
347 Business/Political Decision Making.</TD>
348 <TD> US, Western Democracies, Russia, and Eastern
349 European Nations.</TD>
350 <TD> Japan, Taiwan, South Korea, Hong Kong,
351 Singapore.
352
353 <BR WP="BR1"><BR WP="BR2"></TD></TR>
354 <TR><TD> Strength Of computer Programs</TD>
355 <TD> Grandmaster Level</TD>
356 <TD> Intermediate (5-8 Kyu) level
357
358 <BR WP="BR1"><BR WP="BR2"></TD></TR>
359 <TR><TD> Reasons For Computer Program Performance</TD>
360 <TD> Restricted scope makes application of "standard"
361 techniques such as heuristic search, etc. feasible
362 even on microcomputers.</TD>
363 <TD> Immense scale makes the application of
364 "standard" techniques infeasible even on
365 supercomputers. Requires a real breakthrough in
366 Artificial Intelligence which has not yet been
367 achieved.
368 </TD></TR></TABLE>
369
370 <BR WP="BR1"><BR WP="BR2">
371
372 <P><STRONG>Notes</STRONG></P>
373
374 <P>(1) It has been my experience that most chessplayers strongly dispute the contention that chess is primarily a left brain function while Go integrates both left and
375 right brain, and absent any research studies specifically designed to explore this issue it was formerly impossible to definitively resolve it. But now at last one
376 such a study has been performed, with conclusions that substantiate the contention, as follows:</P>
377
378 <P><STRONG>Cognitive Brain Research 1 (2002) </STRONG></P>
379
380 <P><STRONG>Research report </STRONG></P>
381
382 <P><STRONG>A functional MRI study of high-level cognition </STRONG></P>
383
384 <P><STRONG>II. The game of GO </STRONG></P>
385
386 <P>Xiangchuan Chen , Daren Zhang , Xiaochu Zhang , Zhihao Li , Xiaomei Meng , </P>
387
388 <P>* Sheng He , Xiaoping Hu </P>
389
390 <P>Department of Neurobiology and Biophysics ,University of Science and Technology of China , Hefei , Anhui , 230027, PR China </P>
391
392 <P>Hospital of Anhui Medical University , Hefei , Anhui , 230027, PR China </P>
393
394 <P>Department of Psychology ,University of Minnesota , Minneapolis ,MN 55455, USA </P>
395
396 <P>Center for Magnetic Resonance Research ,University of Minnesota , 2021 Sixth Street SE , Minneapolis ,MN 55455, USA </P>
397
398 <P>Accepted 26 July 2002 </P>
399
400 <P><STRONG>Abstract</STRONG> </P>
401
402 <P>GO is a board game thought to be different from chess in many aspects, most significantly in that GO emphasizes global strategy more than local battle, a
403 property very difficult for computer programs to emulate. To investigate the neural basis of GO, functional magnetic resonance imaging (fMRI) was used to
404 measure brain activities of subjects engaged in playing GO. Enhanced activations were observed in many cortical areas, such as dorsal prefrontal, parietal,
405 occipital, posterior temporal, and primary somatosensory and motor areas. </P>
406
407 <P>Quantitative analysis indicated a modest degree of stronger activation in right parietal area than in left. This type of right hemisphere lateralization differs from
408 the modest left hemisphere lateralization observed during chess playing.</P>
409
410 <p> </p>
411
412 <p>(2) At first blush, the idea of a draw is superficially appealing! After all, if two opponents are really almost exactly equal in strength, why should the result of
413 their encounter be that one gets a full point and the other gets nothing? Especially if no obviously egregious errors have been made, it seems fairer that they split the
414 point evenly. But upon deeper introspection, that idea begins to fall apart. And this is something that most chessplayers implicitly acknowledge, but then act as though
415 they were either oblivious to or deliberately choose to ignore as less than significant. That this attitude is at best mistaken was made abundantly clear by Robert Byrne,
416 the distinguished New York Times chess columnist, in his regular weekly column of Sunday, March 28, 2004 when he said:
417
418 <p>“Vladimir Kramnik of Russia, the world champion, won the Super GM Tournament in Linares, Spain, held from Feb. 19 to March 5. He scored 7-5 in the elite seven-entrant
419 double-round-robin invitational event. Peter Leko and Garry Kasparov tied for second with 61/2 -51/2. It is the greatest satisfaction in the game to be No.1 in a tourney
420 where everyone is at the top of the world rankings. That having been said, this competition had only nine decisive encounters. All the rest were draws.”
421
422 <p>Translating Byrne’s statement a bit to make clearer the point he’s making, we see that of a total of 84 games contested a full 89% resulted in a draw! And how many of
423 those were actually infamous “grandmaster draws”, in which the opponents, wary of each other’s skills and unwilling to risk a loss, really only “go through the motions”
424 for a few desultory moves and then quickly agree to a face saving draw, isn’t revealed. The fact that Byrne even explicitly pointed this out is, I believe, ample proof
425 that even among the most ardent chess lovers this remains a serious intrinsic flaw that greatly diminishes both the game’s integrity and the satisfaction its players derive
426 from it.</p>
427
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