A proposal to correct past players' GS tally

uscwang

Hall of Fame
#1
Here is my list of all time greats after correction for missed opportunities (AO in early days, only 3 pro GS each year) and for lesser weights of close era amateur and pro GS. No correction was made for Sampras, Federer, Nadal, and Djokovic.

1. Ken Rosewall 22
2. Roger Federer 20
3. Pacho Gonzalez 18
4. Rafael Nadal 17
5. Bill Tilden / Novak Djokovic 15
7. Rod Laver / Bjorn Borg / Pete Sampras 14
10. Connors 12
11. Don Budge 11
12. McEnroe 10

Rules:
- GS titles are corrected by a factor (Total possible GS / Actual GS played). Close era pro GS is further corrected by a factor (4 / 3) to account for the fact only 3 pro GS are played each year. The correction is made only for years between the first and last GS Win, and only for systematic missing of GS (e.g. Borg missing AO, but not Nadal missing individual GS).
- A weight of 0.4 is assigned to close era amateur GS, and 0.6 to pro GS. This reflect that they were run in parallel (therefore contemporary greats had more chances to win), amateur GS didn't include the best pro players, pro GS was usually 12-player draw, and that tennis was played by a much smaller pool of players. (This part is obviously debatable and I would like to hear your opinions.)

I felt this can be a start of comparing apples and oranges all as fruits.

Borg:
Open era: 11 wins in 24 GS from 1974 to 1981, missed 7 AO. 11 * (24 + 7) / 24 = 14

Laver:
Close era amateur: 6 wins from 1960 to 62, no missed GS. 6 * 0.4 = 2.4
Close era pro: 8 wins from 1963-67, no missed GS. 8 * (4/3) * 0.6 = 6.4
Open era: 5 wins from 1968-69, no missed. 5 = 5
Total = 14

Rosewall:
Close era amateur: 4 wins from 1953 to 56, missed 2 FO, not corrected. 4 * 0.4 = 1.6
Close era pro: 15 wins in 24 GS from 1957-66, missed 5 AO. 15 * (24 + 5) / 24 * (4 / 3) * 0.6 = 14.5
Open era: 4 wins in 13 GS from 1968-72, missed 6. 4 * (13+6)/13 = 6
Total = 22

Gonzalez:
Close era amateur: 2 wins in 4 GS from 1948 to 49, missed 4. 2 * (4+4)/4 * 0.4 = 1.6
Close era pro: 12 wins in 21 GS from 1950-61, missed 15. 12 * (21 + 15) / 21 * (4 / 3) * 0.6 = 16.5
Open era: no wins.
Total = 18

Tilden:
Close era amateur: 10 wins in 19 GS from 1920 to 30, missed 25. 10 * (19+25)/19 * 0.4 = 9.3
Close era pro: 4 wins in 8 GS from 1931-35, missed 7. 4 * (7+8) / 8 * (4 / 3) * 0.6 = 6
Open era: N/A
Total = 15

Connors:
Open era: 8 wins in 27 GS from 1974 to 83, missed 13. 8 * (27+13)/27 = 12

McEnroe:
Open era: 7 wins in 17 GS from 1979 to 84, missed 7. 7 * (17+7)/17 = 10

Don Budge
Close era amateur: 6 wins in 6 GS from 1937 to 38, missed 2. 6 * (6 + 2)/6 * 0.4 = 3.2
Close era pro: 4 wins in 5 GS from 1939-42, missed 7. 4 * (7+5) / 5 * (4 / 3) * 0.6 = 7.68
Total = 11
 
Last edited:
#3
Here is my list of all time greats after correction for missed opportunities (AO in early days, only 3 pro GS each year) and for lesser weights of close era amateur and pro GS. No correction was made for Sampras, Federer, Nadal, and Djokovic.

1. Ken Rosewall 23
2. Roger Federer 20
3. Pacho Gonzalez 18
4. Rafael Nadal 17
5. Novak Djokovic 15
6. Bill Tilden / Rod Laver / Bjorn Borg / Pete Sampras 14

Rules:
- Each close era amateur GS count as 0.4.
- Each close era pro GS count as 0.6.
- GS titles are corrected by a factor (Total possible GS / Actual GS played). Close era pro GS is further corrected by a factor (4 / 3) to account for the fact only 3 pro GS are played each year. The correction is made only for years between the first and last GS Win, and only for systematic missing of GS (e.g. Borg missing AO, but not Nadal missing individual GS).
- A weight of 0.4 is assigned to close era amateur GS, and 0.6 to pro GS. This reflect that they were run in parallel (therefore contemporary greats had more chances to win) and that tennis was played by a much smaller pool of players. (This part is obviously debatable and I would like to hear your opinions.)

I felt this can be a start of comparing apples and oranges all as fruits.

Borg:
Won 11 titles in 24 GS from 1974 to 1981, missed 7 AO. 11 * (24 + 7) / 24 = 14
Great list, you should consider adjusting for slams missed due to injury as well, which would give Pete at least 15, though as high as 20.
 
#4
Here is my list of all time greats after correction for missed opportunities (AO in early days, only 3 pro GS each year) and for lesser weights of close era amateur and pro GS. No correction was made for Sampras, Federer, Nadal, and Djokovic.

1. Ken Rosewall 22
2. Roger Federer 20
3. Pacho Gonzalez 18
4. Rafael Nadal 17
5. Bill Tilden / Novak Djokovic 15
7. Bjorn Borg / Pete Sampras 14
9. Rod Laver 13

Rules:
- GS titles are corrected by a factor (Total possible GS / Actual GS played). Close era pro GS is further corrected by a factor (4 / 3) to account for the fact only 3 pro GS are played each year. The correction is made only for years between the first and last GS Win, and only for systematic missing of GS (e.g. Borg missing AO, but not Nadal missing individual GS).
- A weight of 0.4 is assigned to close era amateur GS, and 0.6 to pro GS. This reflect that they were run in parallel (therefore contemporary greats had more chances to win), amateur GS didn't include the best pro players, pro GS was usually 12-player draw, and that tennis was played by a much smaller pool of players. (This part is obviously debatable and I would like to hear your opinions.)

I felt this can be a start of comparing apples and oranges all as fruits.

Borg:
Open era: 11 wins in 24 GS from 1974 to 1981, missed 7 AO. 11 * (24 + 7) / 24 = 14

Laver:
Close era amateur: 4 wins from 1960 to 62, no missed GS. 4 * 0.4 = 1.6
Close era pro: 8 wins from 1963-67, no missed GS. 8 * (4/3) * 0.6 = 6.4
Open era: 5 wins from 1968-69, no missed. 5
Total = 13

Rosewall:
Close era amateur: 4 wins from 1953 to 56, missed 2 FO, not corrected. 4 * 0.4 = 1.6
Close era pro: 15 wins in 24 GS from 1957-66, missed 5 AO. 15 * (24 + 5) / 24 * (4 / 3) * 0.6 = 14.5
Open era: 4 wins in 13 GS from 1968-69, missed 6. 4 * (13+6)/13 = 6
Total = 22

Gonzalez:
Close era amateur: 2 wins in 4 GS from 1948 to 49, missed 4. 2 * (4+4)/4 * 0.4 = 1.6
Close era pro: 12 wins in 21 GS from 1950-61, missed 15. 12 * (21 + 15) / 21 * (4 / 3) * 0.6 = 16.5
Open era: no wins.
Total = 18

Tilden:
Close era amateur: 10 wins in 19 GS from 1920 to 30, missed 25. 10 * (19+25)/19 * 0.4 = 9.3
Close era pro: 4 wins in 8 GS from 1931-35, missed 7. 4 * (7+8) / 8 * (4 / 3) * 0.6 = 6
Open era: N/A
Total = 15
I think you should not count amateur slams at all, because winning a tournament where the top players don't compete add little to greatness. Think Ferrer and his 13 ATP 500 titles. Doesn't apply to Tilden because I believe at his time the amateur slam had all the best competing in them.

Also your conversation rate for missed tournaments doesn't work. Very unlikely that Rosewall would win all 6 tournaments he didn't enter. Likewise, Gonzalez missed 15 pro slam and yet your calculation give him an additional 16.5 pro slams!

In any case it's nice to see some recognition for past greats!
 

uscwang

Hall of Fame
#6
I think you should not count amateur slams at all, because winning a tournament where the top players don't compete add little to greatness. Think Ferrer and his 13 ATP 500 titles. Doesn't apply to Tilden because I believe at his time the amateur slam had all the best competing in them.

Also your conversation rate for missed tournaments doesn't work. Very unlikely that Rosewall would win all 6 tournaments he didn't enter. Likewise, Gonzalez missed 15 pro slam and yet your calculation give him an additional 16.5 pro slams!

In any case it's nice to see some recognition for past greats!
Please read again. That is not how I corrected for missed GS.
 
#8
Look. There's no equivalent and there's no way to force the accomplishments of players into a...

Oh whatever carry on.
Pretty much this.

If you are serious about trying to compare apples and oranges as fruits, the only way to even begin would be by performing an exhaustive analysis into tennis history and evaluating every single year on its own merit and assign what the 4 biggest events were for each season in its own time as majors. Then look at who won all of those events to come up with a major count. Discussions like these are going on in the former pro player's forum if you are interested.
 
#10
I think it's a fun thread and something interesting to think about. My only issue is how Laver ended up with only 13 Slams but I will delve deeper into your formula later when I have more time and see how you got to that.

Edit: I noticed you have Laver down for 4 amateur Slams when he actually had 6.
 
#13
Pretty much this.

If you are serious about trying to compare apples and oranges as fruits, the only way to even begin would be by performing an exhaustive analysis into tennis history and evaluating every single year on its own merit and assign what the 4 biggest events were for each season in its own time as majors. Then look at who won all of those events to come up with a major count. Discussions like these are going on in the former pro player's forum if you are interested.

Yep. A lot of this discussion has happened over the years in FPP, which is the more selective enclave of lunatics on this website. There's not a whole lot of crossover between that cadre of lunatics and our glorious GPPD menagerie of complete nutcases.

If they unite forces then special things could happen.

The key to this happening is Federer's retirement. Murray won't do much to push the needle because it's frikkin' Andy Murray (lol).


(lol)




(lol)
 
#21
Here is my list of all time greats after correction for missed opportunities (AO in early days, only 3 pro GS each year) and for lesser weights of close era amateur and pro GS. No correction was made for Sampras, Federer, Nadal, and Djokovic.

1. Ken Rosewall 22
2. Roger Federer 20
3. Pacho Gonzalez 18
4. Rafael Nadal 17
5. Bill Tilden / Novak Djokovic 15
7. Rod Laver / Bjorn Borg / Pete Sampras 14
10. Connors 12
11. Don Budge 11
12. McEnroe 10

Rules:
- GS titles are corrected by a factor (Total possible GS / Actual GS played). Close era pro GS is further corrected by a factor (4 / 3) to account for the fact only 3 pro GS are played each year. The correction is made only for years between the first and last GS Win, and only for systematic missing of GS (e.g. Borg missing AO, but not Nadal missing individual GS).
- A weight of 0.4 is assigned to close era amateur GS, and 0.6 to pro GS. This reflect that they were run in parallel (therefore contemporary greats had more chances to win), amateur GS didn't include the best pro players, pro GS was usually 12-player draw, and that tennis was played by a much smaller pool of players. (This part is obviously debatable and I would like to hear your opinions.)

I felt this can be a start of comparing apples and oranges all as fruits.

Borg:
Open era: 11 wins in 24 GS from 1974 to 1981, missed 7 AO. 11 * (24 + 7) / 24 = 14

Laver:
Close era amateur: 6 wins from 1960 to 62, no missed GS. 6 * 0.4 = 2.4
Close era pro: 8 wins from 1963-67, no missed GS. 8 * (4/3) * 0.6 = 6.4
Open era: 5 wins from 1968-69, no missed. 5 = 5
Total = 14

Rosewall:
Close era amateur: 4 wins from 1953 to 56, missed 2 FO, not corrected. 4 * 0.4 = 1.6
Close era pro: 15 wins in 24 GS from 1957-66, missed 5 AO. 15 * (24 + 5) / 24 * (4 / 3) * 0.6 = 14.5
Open era: 4 wins in 13 GS from 1968-72, missed 6. 4 * (13+6)/13 = 6
Total = 22

Gonzalez:
Close era amateur: 2 wins in 4 GS from 1948 to 49, missed 4. 2 * (4+4)/4 * 0.4 = 1.6
Close era pro: 12 wins in 21 GS from 1950-61, missed 15. 12 * (21 + 15) / 21 * (4 / 3) * 0.6 = 16.5
Open era: no wins.
Total = 18

Tilden:
Close era amateur: 10 wins in 19 GS from 1920 to 30, missed 25. 10 * (19+25)/19 * 0.4 = 9.3
Close era pro: 4 wins in 8 GS from 1931-35, missed 7. 4 * (7+8) / 8 * (4 / 3) * 0.6 = 6
Open era: N/A
Total = 15

Connors:
Open era: 8 wins in 27 GS from 1974 to 83, missed 13. 8 * (27+13)/27 = 12

McEnroe:
Open era: 7 wins in 17 GS from 1979 to 84, missed 7. 7 * (17+7)/17 = 10

Don Budge
Close era amateur: 6 wins in 6 GS from 1937 to 38, missed 2. 6 * (6 + 2)/6 * 0.4 = 3.2
Close era pro: 4 wins in 5 GS from 1939-42, missed 7. 4 * (7+5) / 5 * (4 / 3) * 0.6 = 7.68
Total = 11
I like effort to interpret all the various eras but the result does not seem good to me. For several reasons.

To measure the great champions of all time only on the majors seems to me silly. And the more time passes, the more it seems silly.

There are too many tournaments to play, as essential as
- the big tournament editions won by Pro players (Madison Square Garden, Melbourne, Los Angeles, Geneva ...)
- Key Byscayne's Lipton of the 80s,
- Grand Slam Cup,
- Masters GP,
- current Indian Wells and Miami,
- Tennis Champions Classic (1970-71),
- big WCT tournaments of the early 70s,
- Ampol Series '59,
- WCT Finals to Dallas (especially the early years),
- the most important Open tournaments on hc (Las Vegas, Palm Springs and Los Angeles),
- all the top tournaments indoor (Philadelphia, Memphis, Tokyo, Wembley ..),
- big tournaments not ATP-sanctioned,
- big tournaments on clay (Indianapolis, Boston, Washington, Bournemouth, Rome and Montecarlo),
- and still the World Series (or World Tour) that Kramer and Gonzalez won repeatedly.

The exercise you did is a good exercise in style but if your intent is to trace what has happened in the past can not be limited to slam tournaments that in most of the history did not count as top tournaments (the same Wimbledon in the Pro years it was worth little, because it was amateurs).
 

uscwang

Hall of Fame
#22
I like effort to interpret all the various eras but the result does not seem good to me. For several reasons.

To measure the great champions of all time only on the majors seems to me silly. And the more time passes, the more it seems silly.

There are too many tournaments to play, as essential as
- the big tournament editions won by Pro players (Madison Square Garden, Melbourne, Los Angeles, Geneva ...)
- Key Byscayne's Lipton of the 80s,
- Grand Slam Cup,
- Masters GP,
- current Indian Wells and Miami,
- Tennis Champions Classic (1970-71),
- big WCT tournaments of the early 70s,
- Ampol Series '59,
- WCT Finals to Dallas (especially the early years),
- the most important Open tournaments on hc (Las Vegas, Palm Springs and Los Angeles),
- all the top tournaments indoor (Philadelphia, Memphis, Tokyo, Wembley ..),
- big tournaments not ATP-sanctioned,
- big tournaments on clay (Indianapolis, Boston, Washington, Bournemouth, Rome and Montecarlo),
- and still the World Series (or World Tour) that Kramer and Gonzalez won repeatedly.

The exercise you did is a good exercise in style but if your intent is to trace what has happened in the past can not be limited to slam tournaments that in most of the history did not count as top tournaments (the same Wimbledon in the Pro years it was worth little, because it was amateurs).
Thanks for the insight. But it is also true that GS is in the center of tennis discussion today. That's why i think it better to give close era amateur and pro GS weights relative to open era GS, rather than considering other important tournaments back then that may not even exist today.
 

thrust

Hall of Fame
#23
Here is my list of all time greats after correction for missed opportunities (AO in early days, only 3 pro GS each year) and for lesser weights of close era amateur and pro GS. No correction was made for Sampras, Federer, Nadal, and Djokovic.

1. Ken Rosewall 22
2. Roger Federer 20
3. Pacho Gonzalez 18
4. Rafael Nadal 17
5. Bill Tilden / Novak Djokovic 15
7. Rod Laver / Bjorn Borg / Pete Sampras 14
10. Connors 12
11. Don Budge 11
12. McEnroe 10

Rules:
- GS titles are corrected by a factor (Total possible GS / Actual GS played). Close era pro GS is further corrected by a factor (4 / 3) to account for the fact only 3 pro GS are played each year. The correction is made only for years between the first and last GS Win, and only for systematic missing of GS (e.g. Borg missing AO, but not Nadal missing individual GS).
- A weight of 0.4 is assigned to close era amateur GS, and 0.6 to pro GS. This reflect that they were run in parallel (therefore contemporary greats had more chances to win), amateur GS didn't include the best pro players, pro GS was usually 12-player draw, and that tennis was played by a much smaller pool of players. (This part is obviously debatable and I would like to hear your opinions.)

I felt this can be a start of comparing apples and oranges all as fruits.

Borg:
Open era: 11 wins in 24 GS from 1974 to 1981, missed 7 AO. 11 * (24 + 7) / 24 = 14

Laver:
Close era amateur: 6 wins from 1960 to 62, no missed GS. 6 * 0.4 = 2.4
Close era pro: 8 wins from 1963-67, no missed GS. 8 * (4/3) * 0.6 = 6.4
Open era: 5 wins from 1968-69, no missed. 5 = 5
Total = 14

Rosewall:
Close era amateur: 4 wins from 1953 to 56, missed 2 FO, not corrected. 4 * 0.4 = 1.6
Close era pro: 15 wins in 24 GS from 1957-66, missed 5 AO. 15 * (24 + 5) / 24 * (4 / 3) * 0.6 = 14.5
Open era: 4 wins in 13 GS from 1968-72, missed 6. 4 * (13+6)/13 = 6
Total = 22

Gonzalez:
Close era amateur: 2 wins in 4 GS from 1948 to 49, missed 4. 2 * (4+4)/4 * 0.4 = 1.6
Close era pro: 12 wins in 21 GS from 1950-61, missed 15. 12 * (21 + 15) / 21 * (4 / 3) * 0.6 = 16.5
Open era: no wins.
Total = 18

Tilden:
Close era amateur: 10 wins in 19 GS from 1920 to 30, missed 25. 10 * (19+25)/19 * 0.4 = 9.3
Close era pro: 4 wins in 8 GS from 1931-35, missed 7. 4 * (7+8) / 8 * (4 / 3) * 0.6 = 6
Open era: N/A
Total = 15

Connors:
Open era: 8 wins in 27 GS from 1974 to 83, missed 13. 8 * (27+13)/27 = 12

McEnroe:
Open era: 7 wins in 17 GS from 1979 to 84, missed 7. 7 * (17+7)/17 = 10

Don Budge
Close era amateur: 6 wins in 6 GS from 1937 to 38, missed 2. 6 * (6 + 2)/6 * 0.4 = 3.2
Close era pro: 4 wins in 5 GS from 1939-42, missed 7. 4 * (7+5) / 5 * (4 / 3) * 0.6 = 7.68
Total = 11
GOOD LIST!
 
#24
Yep. A lot of this discussion has happened over the years in FPP, which is the more selective enclave of lunatics on this website. There's not a whole lot of crossover between that cadre of lunatics and our glorious GPPD menagerie of complete nutcases.

If they unite forces then special things could happen.

The key to this happening is Federer's retirement. Murray won't do much to push the needle because it's frikkin' Andy Murray (lol).


(lol)




(lol)
Generally I find discussion about the current big 3 over in FPP (in the broader spectrum of GOAT list discussions) to usually be more reasoned and logical than having the same conversations on GPPD due to less people having a major bias towards 1 of the 3 players. However, there are still similar biases shown in discussions between former players with other former players (i.e Rosewall for example) and as such I imagine when Federer retires, the legion of his fans on GPPD will just go over and do the same over there in regards to Federer vs Laver/Rosewall/Gonzales/Tilden discussions. (And tbh it will wind up even worse for them because there is MAJOR push back on Fed being the GOAT over there compared to that group of 4, whereas Fed is at least recognized by most as the OE GOAT for GPPD purposes).
 
#25
Here is my list of all time greats after correction for missed opportunities (AO in early days, only 3 pro GS each year) and for lesser weights of close era amateur and pro GS. No correction was made for Sampras, Federer, Nadal, and Djokovic.

1. Ken Rosewall 22
2. Roger Federer 20
3. Pacho Gonzalez 18
4. Rafael Nadal 17
5. Bill Tilden / Novak Djokovic 15
7. Rod Laver / Bjorn Borg / Pete Sampras 14
10. Connors 12
11. Don Budge 11
12. McEnroe 10

Rules:
- GS titles are corrected by a factor (Total possible GS / Actual GS played). Close era pro GS is further corrected by a factor (4 / 3) to account for the fact only 3 pro GS are played each year. The correction is made only for years between the first and last GS Win, and only for systematic missing of GS (e.g. Borg missing AO, but not Nadal missing individual GS).
- A weight of 0.4 is assigned to close era amateur GS, and 0.6 to pro GS. This reflect that they were run in parallel (therefore contemporary greats had more chances to win), amateur GS didn't include the best pro players, pro GS was usually 12-player draw, and that tennis was played by a much smaller pool of players. (This part is obviously debatable and I would like to hear your opinions.)

I felt this can be a start of comparing apples and oranges all as fruits.

Borg:
Open era: 11 wins in 24 GS from 1974 to 1981, missed 7 AO. 11 * (24 + 7) / 24 = 14

Laver:
Close era amateur: 6 wins from 1960 to 62, no missed GS. 6 * 0.4 = 2.4
Close era pro: 8 wins from 1963-67, no missed GS. 8 * (4/3) * 0.6 = 6.4
Open era: 5 wins from 1968-69, no missed. 5 = 5
Total = 14

Rosewall:
Close era amateur: 4 wins from 1953 to 56, missed 2 FO, not corrected. 4 * 0.4 = 1.6
Close era pro: 15 wins in 24 GS from 1957-66, missed 5 AO. 15 * (24 + 5) / 24 * (4 / 3) * 0.6 = 14.5
Open era: 4 wins in 13 GS from 1968-72, missed 6. 4 * (13+6)/13 = 6
Total = 22

Gonzalez:
Close era amateur: 2 wins in 4 GS from 1948 to 49, missed 4. 2 * (4+4)/4 * 0.4 = 1.6
Close era pro: 12 wins in 21 GS from 1950-61, missed 15. 12 * (21 + 15) / 21 * (4 / 3) * 0.6 = 16.5
Open era: no wins.
Total = 18

Tilden:
Close era amateur: 10 wins in 19 GS from 1920 to 30, missed 25. 10 * (19+25)/19 * 0.4 = 9.3
Close era pro: 4 wins in 8 GS from 1931-35, missed 7. 4 * (7+8) / 8 * (4 / 3) * 0.6 = 6
Open era: N/A
Total = 15

Connors:
Open era: 8 wins in 27 GS from 1974 to 83, missed 13. 8 * (27+13)/27 = 12

McEnroe:
Open era: 7 wins in 17 GS from 1979 to 84, missed 7. 7 * (17+7)/17 = 10

Don Budge
Close era amateur: 6 wins in 6 GS from 1937 to 38, missed 2. 6 * (6 + 2)/6 * 0.4 = 3.2
Close era pro: 4 wins in 5 GS from 1939-42, missed 7. 4 * (7+5) / 5 * (4 / 3) * 0.6 = 7.68
Total = 11
Interesting approach. Do you think though that that Amateurs pre-1930 were lesser than the pro's? Hence, is the 0.4 weighting appropriate for that time? There were very few pro's and only a few pro tournaments. Most people viewed Tilden as THE player of the 1920's and would expect him during that period to beat any pro of that era in a H2H battle.
 
#28
Thanks for the insight. But it is also true that GS is in the center of tennis discussion today. That's why i think it better to give close era amateur and pro GS weights relative to open era GS, rather than considering other important tournaments back then that may not even exist today.
It is doubtful that the old pros had a well defined GS series.

The most important events of the late 1950's were the TOC events from 1957 to 1959, which were completely dominated by the top two pros of that era,

Gonzales and Hoad.

Neither player did well at Wembley or RG during that stretch, but gave their best efforts for the six TOC events.
 
#29
Fun thought experiment. I've always wondered what the records would be like if the pro tour was counted, but given that there were 3 pro majors and much smaller draws, it seemed impossible to convert. Clearly still is, but this approximation gives us some insight as to the best players at the time.
 
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