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===Current estimates=== This section discusses and attempts to list the best current estimates for the parameters of the Drake equation. <!-- Please state the rationale behind the estimate and a citation to their source. --> ====Rate of star creation in this Galaxy, {{math|''R''<sub>∗</sub>}}==== Calculations in 2010, from [[NASA]] and the [[European Space Agency]] indicate that the rate of star formation in this Galaxy is about {{solar mass|0.68–1.45|link=yes}} of material per year.<ref name=Robitaille>{{cite journal |author1=Robitaille, Thomas P. |author2=Barbara A. Whitney |title=The present-day star formation rate of the Milky Way determined from Spitzer-detected young stellar objects |journal=The Astrophysical Journal Letters |volume=710 |issue=1 |year=2010 |pages=L11 |arxiv=1001.3672 |bibcode=2010ApJ...710L..11R |doi=10.1088/2041-8205/710/1/L11|s2cid=118703635 }}</ref><ref name="The Drake Equation"> {{cite book |last=Wanjek |first=C. |year=2015 |title=The Drake Equation |url=https://books.google.com/books?id=jcnSCQAAQBAJ&q=Robitaille+and+Whitney+came+up+with+a+figure+for+R*+between+0.68+and+1.45&pg=PA45 |publisher=[[Cambridge University Press]] |access-date=2016-09-09 |isbn=9781107073654 }}</ref> To get the number of stars per year, we divide this by the [[initial mass function]] (IMF) for stars, where the average new star's mass is about {{solar mass|0.5}}.<ref>{{cite journal |last1=Kennicutt |first1=Robert C. |last2=Evans |first2=Neal J. |title=Star Formation in the Milky Way and Nearby Galaxies |journal=Annual Review of Astronomy and Astrophysics |date=22 September 2012 |volume=50 |issue=1 |pages=531–608 |arxiv=1204.3552 |bibcode=2012ARA&A..50..531K |doi=10.1146/annurev-astro-081811-125610|s2cid=118667387 }}</ref> This gives a star formation rate of about 1.5–3 stars per year. {{anchor|eta-earth|}} ====Fraction of those stars that have planets, {{math|''f''<sub>p</sub>}}==== Analysis of [[Gravitational microlensing|microlensing]] surveys, in 2012, has found that {{math|''f''<sub>p</sub>}} may approach 1—that is, stars are orbited by planets as a rule, rather than the exception; and that there are one or more bound planets per Milky Way star.<ref name="bbc.co.uk"> {{cite news |last=Palmer |first=J. |date=11 January 2012 |title=Exoplanets are around every star, study suggests |url=https://www.bbc.co.uk/news/science-environment-16515944 |publisher=[[BBC]] |access-date=2012-01-12 }}</ref><ref name="Nature-20120111"> {{cite journal |last=Cassan |first=A. |display-authors=etal |date=11 January 2012 |title=One or more bound planets per Milky Way star from microlensing observations |journal=[[Nature (journal)|Nature]] |volume=481 |issue=7380 |pages=167–169 |arxiv=1202.0903 |bibcode=2012Natur.481..167C |doi=10.1038/nature10684 |pmid=22237108 |s2cid=2614136 }}</ref> ====Average number of planets that might support life per star that has planets, {{math|''n''<sub>e</sub>}}==== In November 2013, astronomers reported, based on [[Kepler space telescope]] data, that there could be as many as 40 billion [[Terrestrial planet|Earth-sized]] [[extrasolar planets|planets]] orbiting in the [[habitable zone]]s of [[sun-like|sun-like stars]] and [[red dwarf stars]] within the [[Milky Way Galaxy]].<ref name="NYT-20131104">{{cite news |last=Overbye |first=Dennis |title=Far-Off Planets Like the Earth Dot the Galaxy |url=https://www.nytimes.com/2013/11/05/science/cosmic-census-finds-billions-of-planets-that-could-be-like-earth.html |archive-url=https://ghostarchive.org/archive/20220101/https://www.nytimes.com/2013/11/05/science/cosmic-census-finds-billions-of-planets-that-could-be-like-earth.html |archive-date=2022-01-01 |url-access=limited |date=4 November 2013 |work=[[The New York Times]] |access-date=5 November 2013 }}{{cbignore}}</ref><ref name="PNAS-20131031">{{cite journal |last1=Petigura |first1=Eric A. |last2=Howard |first2=Andrew W. |last3=Marcy |first3=Geoffrey W. |title=Prevalence of Earth-size planets orbiting Sun-like stars |date=31 October 2013 |journal=[[Proceedings of the National Academy of Sciences of the United States of America]] |doi=10.1073/pnas.1319909110 |arxiv = 1311.6806 |bibcode = 2013PNAS..11019273P |volume=110 |issue=48 |pages=19273–19278 |pmid=24191033 |pmc=3845182|doi-access=free }}</ref> 11 billion of these estimated planets may be orbiting sun-like stars.<ref name="LATimes-20131104">{{cite news |last=Khan |first=Amina |title=Milky Way may host billions of Earth-size planets |url=http://www.latimes.com/science/la-sci-earth-like-planets-20131105,0,2673237.story |date=4 November 2013 |work=[[Los Angeles Times]] |access-date=5 November 2013 }}</ref> Since there are about 100 billion stars in the galaxy, this implies {{math|''f''<sub>p</sub> · ''n''<sub>e</sub>}} is roughly 0.4. The nearest planet in the habitable zone is [[Proxima Centauri b]], which is as close as about 4.2 light-years away. The consensus at the Green Bank meeting was that {{math|''n''<sub>e</sub>}} had a minimum value between 3 and 5. Dutch science journalist [[Govert Schilling]] has opined that this is optimistic.<ref name=schilling2011 /> Even if planets are in the [[habitable zone]], the number of planets with the right proportion of elements is difficult to estimate.<ref name="Trimble">{{cite journal |last=Trimble |first=V. |year=1997 |title=Origin of the biologically important elements |journal=[[Origins of Life and Evolution of the Biosphere]] |volume=27 |issue=1–3 |pages=3–21 |doi=10.1023/A:1006561811750 |pmid=9150565 |bibcode=1997OLEB...27....3T |s2cid=7612499 }}</ref> Brad Gibson, Yeshe Fenner, and Charley Lineweaver determined that about 10% of [[star system]]s in the Milky Way Galaxy are hospitable to life, by having heavy elements, being far from [[supernova]]e and being stable for a sufficient time.<ref> {{cite journal |last1=Lineweaver |first1=C. H. |last2=Fenner |first2=Y. |last3=Gibson |first3=B. K. |year=2004 |title=The Galactic Habitable Zone and the Age Distribution of Complex Life in the Milky Way |journal=[[Science (journal)|Science]] |volume=303 |issue=5654 |pages= 59–62 |arxiv=astro-ph/0401024 |bibcode=2004Sci...303...59L |doi=10.1126/science.1092322 |pmid=14704421 |s2cid=18140737 }}</ref> The discovery of numerous [[gas giant]]s in close orbit with their stars has introduced doubt that life-supporting planets commonly survive the formation of their stellar systems. So-called [[hot Jupiter]]s may migrate from distant orbits to near orbits, in the process disrupting the orbits of habitable planets. On the other hand, the variety of [[star system]]s that might have habitable zones is not just limited to solar-type stars and Earth-sized planets. It is now estimated that even tidally locked planets close to [[red dwarf]] stars [[habitability of red dwarf systems|might have habitable zones]],<ref> {{cite journal |last1=Dressing |first1=C. D. |last2=Charbonneau |first2=D. |year=2013 |title=The Occurrence Rate of Small Planets around Small Stars |journal=[[The Astrophysical Journal]] |volume=767 |issue= 1|page=95 |arxiv=1302.1647 |bibcode=2013ApJ...767...95D |doi=10.1088/0004-637X/767/1/95 |s2cid=29441006 }}</ref> although the flaring behavior of these stars might speak against this.<ref>{{cite web|title=Red Dwarf Stars Could Leave Habitable Earth-Like Planets Vulnerable to Radiation|url=http://scitechdaily.com/red-dwarf-stars-could-leave-habitable-earth-like-planets-vulnerable-to-radiation/|website=SciTech Daily|access-date=22 September 2015|date=2 July 2013}}</ref> The possibility of life on [[natural satellite|moons]] of gas giants (such as [[Jupiter]]'s moon [[Europa (moon)|Europa]], or [[Saturn]]'s moons [[Titan (moon)|Titan]] and [[Enceladus]]) adds further uncertainty to this figure.<ref>{{cite journal |last1=Heller |first1=René |last2=Barnes |first2=Rory |title=Constraints on the Habitability of Extrasolar Moons |journal=Proceedings of the International Astronomical Union |date=29 April 2014 |volume=8 |issue=S293 |pages=159–164 |arxiv=1210.5172 |bibcode=2014IAUS..293..159H |doi=10.1017/S1743921313012738|s2cid=92988047 }}</ref> The authors of the [[rare Earth hypothesis]] propose a number of additional constraints on habitability for planets, including being in galactic zones with suitably low radiation, high star metallicity, and low enough density to avoid excessive asteroid bombardment. They also propose that it is necessary to have a planetary system with large gas giants which provide bombardment protection without a [[hot Jupiter]]; and a planet with [[plate tectonic]]s, a large moon that creates tidal pools, and moderate [[axial tilt]] to generate seasonal variation.<ref name="RareEarth">{{cite book |last1=Ward |first1=Peter D. |last2=Brownlee |first2=Donald |title=Rare Earth: Why Complex Life is Uncommon in the Universe |publisher=Copernicus Books (Springer Verlag) |date=2000 |isbn=0-387-98701-0 }}</ref> ====Fraction of the above that actually go on to develop life, {{math|''f''<sub>l</sub>}}==== Geological evidence from the Earth suggests that {{math|''f''<sub>l</sub>}} may be high; life on Earth appears to have begun around the same time as favorable conditions arose, suggesting that [[abiogenesis]] may be relatively common once conditions are right. However, this evidence only looks at the Earth (a single model planet), and contains [[anthropic bias]], as the planet of study was not chosen randomly, but by the living organisms that already inhabit it (ourselves). From a classical [[hypothesis testing]] standpoint, without assuming that the underlying distribution of {{math|''f''<sub>l</sub>}} is the same for all planets in the Milky Way, there are zero [[degrees of freedom (statistics)|degrees of freedom]], permitting no valid estimates to be made. If life (or evidence of past life) were to be found on [[life on Mars|Mars]], [[Europa (moon)|Europa]], [[Enceladus]] or [[Titan (moon)|Titan]] that developed independently from life on Earth it would imply a value for {{math|''f''<sub>l</sub>}} close to 1. While this would raise the number of degrees of freedom from zero to one, there would remain a great deal of uncertainty on any estimate due to the small sample size, and the chance they are not really independent. Countering this argument is that there is no evidence for abiogenesis occurring more than once on the Earth—that is, all terrestrial life stems from a common origin. If abiogenesis were more common it would be speculated to have occurred more than once on the Earth. Scientists have searched for this by looking for [[bacteria]] that are unrelated to other life on Earth, but none have been found yet.<ref> {{cite journal |last=Davies |first=P. |year=2007 |title=Are Aliens Among Us? |journal=[[Scientific American]] |volume=297 |issue=6 |pages=62–69 |doi=10.1038/scientificamerican1207-62 |bibcode = 2007SciAm.297f..62D }}</ref> It is also possible that life arose more than once, but that other branches were out-competed, or died in mass extinctions, or were lost in other ways. Biochemists [[Francis Crick]] and [[Leslie Orgel]] laid special emphasis on this uncertainty: "At the moment we have no means at all of knowing" whether we are "likely to be alone in the galaxy (Universe)" or whether "the galaxy may be pullulating with life of many different forms."<ref> {{cite journal |last1=Crick |first1=F. H. C. |last2=Orgel |first2=L. E. |year=1973 |title=Directed Panspermia |url=http://profiles.nlm.nih.gov/ps/access/SCBCCP.pdf |archive-url=https://web.archive.org/web/20111029060655/http://profiles.nlm.nih.gov/ps/access/SCBCCP.pdf |archive-date=2011-10-29 |url-status=live |journal=[[Icarus (journal)|Icarus]] |volume=19 |issue=3 |pages=341–346 |bibcode=1973Icar...19..341C |doi=10.1016/0019-1035(73)90110-3 }}</ref> As an alternative to abiogenesis on Earth, they proposed the hypothesis of [[directed panspermia]], which states that Earth life began with "microorganisms sent here deliberately by a technological society on another planet, by means of a special long-range unmanned spaceship". In 2020, a paper by scholars at the [[University of Nottingham]] proposed an "Astrobiological Copernican" principle, based on the [[Principle of Mediocrity]], and speculated that "intelligent life would form on other [Earth-like] planets like it has on Earth, so within a few billion years life would automatically form as a natural part of evolution". In the authors' framework, {{math|''f''<sub>l</sub>}}, {{math|''f''<sub>i</sub>}}, and {{math|''f''<sub>c</sub>}} are all set to a probability of 1 (certainty). Their resultant calculation concludes there are more than thirty current technological civilizations in the galaxy (disregarding error bars).<ref>{{cite journal |last1=Westby |first1=Tom |last2=Conselice |first2=Christopher J. |title=The Astrobiological Copernican Weak and Strong Limits for Intelligent Life |journal=The Astrophysical Journal |date=15 June 2020 |volume=896 |issue=1 |pages=58 |doi=10.3847/1538-4357/ab8225|arxiv=2004.03968 |bibcode=2020ApJ...896...58W |s2cid=215415788 |doi-access=free }}</ref><ref>{{cite news |last1=Davis |first1=Nicola |title=Scientists say most likely number of contactable alien civilisations is 36 |url=https://www.theguardian.com/science/2020/jun/15/scientists-say-most-likely-number-of-contactable-alien-civilisations-is-36 |access-date=19 June 2020 |work=The Guardian |date=15 June 2020}}</ref> ====Fraction of the above that develops intelligent life, {{math|''f''<sub>i</sub>}}==== This value remains particularly controversial. Those who favor a low value, such as the biologist [[Ernst Mayr]], point out that of the billions of species that have existed on Earth, only one has become intelligent and from this, infer a tiny value for {{math|''f''<sub>i</sub>}}.<ref name="Ernst Mayr on SETI"> {{cite web |title = Ernst Mayr on SETI |url = http://www.planetary.org/explore/topics/search_for_life/seti/mayr.html |publisher = [[The Planetary Society]] |url-status = dead |archive-url = https://web.archive.org/web/20101206171624/http://www.planetary.org/explore/topics/search_for_life/seti/mayr.html |archive-date = 6 December 2010 |df = dmy-all }}</ref> Likewise, the Rare Earth hypothesis, notwithstanding their low value for {{math|''n''<sub>e</sub>}} above, also think a low value for {{math|''f''<sub>i</sub>}} dominates the analysis.<ref>Rare Earth, p. xviii.: "We believe that life in the form of microbes or their equivalents is very common in the universe, perhaps more common than even Drake or Sagan envisioned. However, ''complex'' life—animals and higher plants—is likely to be far more rare than commonly assumed."</ref> Those who favor higher values note the generally increasing complexity of life over time, concluding that the appearance of intelligence is almost inevitable,<ref name="acampbell.ukfsn.org"> {{cite web |last = Campbell |first = A. |date = 13 March 2005 |title = Review of ''Life's Solution'' by Simon Conway Morris |url = http://www.acampbell.ukfsn.org/bookreviews/r/morris.html |url-status = dead |archive-url = https://web.archive.org/web/20110716063324/http://www.acampbell.ukfsn.org/bookreviews/r/morris.html |archive-date = 16 July 2011 |df = dmy-all }}</ref><ref> {{cite book |last=Bonner |first=J. T. |year=1988 |title=The evolution of complexity by means of natural selection |url=https://archive.org/details/evolutionofcompl0000bonn |url-access=registration |publisher=[[Princeton University Press]] |isbn=0-691-08494-7 }}</ref> implying an {{math|''f''<sub>i</sub>}} approaching 1. Skeptics point out that the large spread of values in this factor and others make all estimates unreliable. (See [[#Criticism|Criticism]]). In addition, while it appears that life developed soon after the formation of Earth, the [[Cambrian explosion]], in which a large variety of multicellular life forms came into being, occurred a considerable amount of time after the formation of Earth, which suggests the possibility that special conditions were necessary. Some scenarios such as the [[snowball Earth]] or research into [[extinction events]] have raised the possibility that life on Earth is relatively fragile. Research on any past [[life on Mars]] is relevant since a discovery that life did form on Mars but ceased to exist might raise the estimate of {{math|''f''<sub>l</sub>}} but would indicate that in half the known cases, intelligent life did not develop. Estimates of {{math|''f''<sub>i</sub>}} have been affected by discoveries that the Solar System's orbit is circular in the galaxy, at such a distance that it remains out of the spiral arms for tens of millions of years (evading radiation from [[nova]]e). Also, Earth's large moon may aid the evolution of life by [[Rare Earth hypothesis#A large moon|stabilizing the planet's axis of rotation]]. There has been quantitative work to begin to define <math>f_\mathrm{l} \cdot f_\mathrm{i}</math>. One example is a Bayesian analysis published in 2020. In the conclusion, the author cautions that this study applies to Earth's conditions. In Bayesian terms, the study favors the formation of intelligence on a planet with identical conditions to Earth but does not do so with high confidence.<ref name="Kipping2020"> {{cite journal |last1=Kipping |first1=David |date=18 May 2020 |title=An objective Bayesian analysis of life's early start and our late arrival |journal=[[Proceedings of the National Academy of Sciences]] |volume=117 |issue=22 |pages=11995–12003 |doi=10.1073/pnas.1921655117|pmid=32424083 |pmc=7275750 |arxiv=2005.09008 |bibcode=2020PNAS..11711995K |doi-access=free }}</ref><ref name="ColumbiaPR"> {{cite web |author1=Columbia University |title=New study estimates the odds of life and intelligence emerging beyond our planet |url=https://phys.org/news/2020-05-odds-life-intelligence-emerging-planet.html |website=Phys.org |access-date=23 May 2020}} </ref> Planetary scientist [[Pascal Lee]] of the [[SETI Institute]] proposes that this fraction is very low (0.0002). He based this estimate on how long it took Earth to develop intelligent life (1 million years since ''[[Homo erectus]]'' evolved, compared to 4.6 billion years since Earth formed).<ref>{{Cite web|last=Lee|first=Pascal|title=N~1: Alone in the Milky Way, Mt Tam|website=[[YouTube]]|date=24 October 2020 |url=https://www.youtube.com/watch?v=cuJDkIUuDBg| archive-url=https://ghostarchive.org/varchive/youtube/20211211/cuJDkIUuDBg| archive-date=2021-12-11|url-status=live}}{{cbignore}}</ref><ref>{{Cite web |last=Lee |first=Pascal |title=N~1: Alone in the Milky Way – Kalamazoo Astronomical Society |url=https://www.youtube.com/watch?v=wj5nmgoQr50 |url-status=live |archive-url=https://web.archive.org/web/20210315085249/https://www.youtube.com/watch?v=wj5nmgoQr50 |archive-date=2021-03-15 |website=[[YouTube]]|date=6 March 2021 }}</ref> ====Fraction of the above revealing their existence via signal release into space, {{math|''f''<sub>c</sub>}}==== For deliberate communication, the one example we have (the Earth) does not do much explicit communication, though there are [[Active SETI|some efforts]] covering only a tiny fraction of the stars that might look for human presence. (See [[Arecibo message]], for example). There is [[Fermi paradox#They choose not to interact with us|considerable speculation]] why an extraterrestrial civilization might exist but choose not to communicate. However, deliberate communication is not required, and calculations indicate that current or near-future Earth-level technology might well be detectable to civilizations not too much more advanced than present day humans.<ref> {{cite journal |last1=Forgan |first1=D. |last2=Elvis |first2=M. |year=2011 |title=Extrasolar Asteroid Mining as Forensic Evidence for Extraterrestrial Intelligence |journal=[[International Journal of Astrobiology]] |volume=10 |issue=4 |pages=307–313 |arxiv=1103.5369 |bibcode=2011IJAsB..10..307F |doi=10.1017/S1473550411000127 |s2cid=119111392 }}</ref> By this standard, the Earth is a communicating civilization. Another question is what percentage of civilizations in the galaxy are close enough for us to detect, assuming that they send out signals. For example, existing Earth radio telescopes could only detect Earth radio transmissions from roughly a light year away.<ref>{{cite journal |title=The Search for Extraterrestrial Intelligence (SETI) |journal=Annual Review of Astronomy and Astrophysics |first=Jill C. |last=Tarter |author-link=Jill Tarter |volume=39 |pages=511–548 |date=September 2001 |doi=10.1146/annurev.astro.39.1.511 |bibcode=2001ARA&A..39..511T|s2cid=261531924 }}</ref> ====Lifetime of such a civilization wherein it communicates its signals into space, {{math|''L''}}==== [[Michael Shermer]] estimated {{math|''L''}} as 420 years, based on the duration of sixty historical Earthly civilizations.<ref name="Why ET Hasn’t Called"> {{cite journal |last=Shermer |first=M. |date=August 2002 |title=Why ET Hasn't Called |url=http://www.michaelshermer.com/2002/08/why-et-hasnt-called/ |journal=[[Scientific American]] |volume=287 |issue=2 |page=21 |bibcode=2002SciAm.287b..33S |doi=10.1038/scientificamerican0802-33 }}</ref> Using 28 civilizations more recent than the Roman Empire, he calculates a figure of 304 years for "modern" civilizations. It could also be argued from Michael Shermer's results that the fall of most of these civilizations was followed by later civilizations that carried on the technologies, so it is doubtful that they are separate civilizations in the context of the Drake equation. In the expanded version, including ''reappearance number'', this lack of specificity in defining single civilizations does not matter for the result, since such a civilization turnover could be described as an increase in the ''reappearance number'' rather than increase in {{math|''L''}}, stating that a civilization reappears in the form of the succeeding cultures. Furthermore, since none could communicate over interstellar space, the method of comparing with historical civilizations could be regarded as invalid. [[David Grinspoon]] has argued that once a civilization has developed enough, it might overcome all threats to its survival. It will then last for an indefinite period of time, making the value for {{math|''L''}} potentially billions of years. If this is the case, then he proposes that the Milky Way Galaxy may have been steadily accumulating advanced civilizations since it formed.<ref name="David Grinspoon 2004"> {{cite book |last=Grinspoon |first=D. |year=2004 |title=Lonely Planets }}</ref> He proposes that the last factor {{math|''L''}} be replaced with {{math|''f''<sub>IC</sub> · ''T''}}, where {{math|''f''<sub>IC</sub>}} is the fraction of communicating civilizations that become "immortal" (in the sense that they simply do not die out), and {{math|''T''}} representing the length of time during which this process has been going on. This has the advantage that {{math|''T''}} would be a relatively easy-to-discover number, as it would simply be some fraction of the age of the universe. It has also been hypothesized that once a civilization has learned of a more advanced one, its longevity could increase because it can learn from the experiences of the other.<ref name="GoldsmithOwen"> {{Cite book |last1=Goldsmith |first1=D. |last2=Owen |first2=T. |year=1992 |title=The Search for Life in the Universe |edition=2nd |page=415 |publisher=[[Addison-Wesley]] |isbn=1-891389-16-5 }}</ref> The astronomer [[Carl Sagan]] speculated that all of the terms, except for the lifetime of a civilization, are relatively high and the determining factor in whether there are large or small numbers of civilizations in the universe is the civilization lifetime, or in other words, the ability of technological civilizations to avoid self-destruction. In Sagan's case, the Drake equation was a strong motivating factor for his interest in environmental issues and his efforts to warn against the dangers of [[nuclear warfare]]. Paleobiologist [[Olev Vinn]] suggests that the lifetime of most technological civilizations is brief due to inherited behavior patterns present in all intelligent organisms. These behaviors, incompatible with civilized conditions, inevitably lead to self-destruction soon after the emergence of advanced technologies.<ref name=vinn2024>{{cite journal|last=Vinn|first=O.|date=2024|title=Potential incompatibility of inherited behavior patterns with civilization: Implications for Fermi paradox|journal=Science Progress|volume=107|issue=3|pages=1–6|doi=10.1177/00368504241272491|pmid= 39105260|s2cid= |doi-access=free|pmc=11307330}}</ref> An intelligent civilization might not be organic, as some have suggested that [[artificial general intelligence]] may replace humanity.<ref>{{cite news |author=Sulleyman |first=Aatif |date=2 November 2017 |title=Stephen Hawking warns artificial intelligence 'may replace humans altogether' |work=independent.co.uk |url=https://www.independent.co.uk/life-style/gadgets-and-tech/news/stephen-hawking-artificial-intelligence-fears-ai-will-replace-humans-virus-life-a8034341.html}}</ref>
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