The Discovery of the Apollo 12 Lunar Module Impact Site

GoneToPlaid's 11/21/2013 Discovery

The Apollo 12 LM Intrepid's impact site was discovered by GoneToPlaid (me, since I never use my real name online) on the evening of 11/20/2013. I reported my discovery via email on 11/21/2013 to Alan Bean (Apollo 12 LMP), Eric Jones and Ken Glover (editors of the Apollo Lunar Surface Journal), Andrew Chaikin (author and contributor to the ALSJ), and professor Ulrich Lotzmann (ALSJ contributor, discoverer of numerous asteroids, and discoverer of two periodic comets).

My discovery initially remained confidential since I needed to perform further research in order to confirm several of my hypotheses about the remarkably unusual circumstances regarding how this impact site could have possibly been created by the lunar module which the Apollo 12 crew most appropriately named Intrepid. This research involved terrain modeling versus LM trajectory and impact angle from the horizontal, confirmation from Apollo astronauts that the LMs were fully pressurized after being jettisoned from the CMs following ascent and orbital rendezvous, and performing basic physics calculations for what is essentially a pressurized aluminum can traveling at a velocity of over 3700 miles per hour which would rip open and explode within 1 to 5 milliseconds after making contact with the lunar surface. Since I am not a scientist, I had to perform further research during my limited free time. Thus it took me until 04/12/2015 to complete all of my research and to confirm that this really is the Apollo 12 LM Intrepid's lunar impact site. I published this web page about my discovery on 04/15/2015.

My confirmed discovery was once again reported via email on 04/11/2015 to the same parties as above. I then reported my confirmed discovery via email directly to Dr. Mark Robinson (principal investigator for the Lunar Reconnaissance Orbiter mission) on 04/12/2015. Dr. Robinson forwarded my email to on 04/13/2015 to planetary scientist Jeffrey Plescia at John Hopkins University. Jeffrey Plescia formerly worked at the USGS and at JPL. I received an email response from Jeffrey Plescia on 04/15/2015, asking for the impact site coordinates. I replied via email to both Dr. Robinson and Jeffrey Plescia on 04/15/2015. I emailed Dr. Mark Robinson and Jeffrey Plescia with a link to this web page which listed the LM impact site coordinates and which provided direct links for viewing the impact site using the LRO Team's QuickMap web site, and with contact information for the people at NASA who I had also contacted about my discovery . In my email, I asked Jeffrey and the LRO Team to confirm my discovery so that NASA and the LRO Team could issue a press release about the discovery. I never heard back from either of them via email or by phone. I subsequently emailed additional information to Jeffrey Plescia on 04/17/2015, yet I did not receive any reply. Jeffrey Plescia and the LRO Team never followed up my request to confirm my discovery.

As mentioned, on 04/15/2015, I reported my discovery via email to my contacts at NASA, and to the same parties for the 11/20/2013 email. Specifically, I additionally reported my discovery to these people at NASA: "Barry, Bill (HQ-NH000)" bill.barry@nasa.gov, "Ulrich, Bert (HQ-NG000)" bert.ulrich@nasa.gov, "Brown, Fred A. (HQ-NG000)" fred.a.brown@nasa.gov, "Feinberg, Al (HQ-NG000)" al.feinberg@nasa.gov. This same email was also sent to ALSJ contributor David Woods and to former NASA Administrator Michael Griffin. I received enthusiastic responses from David Woods and Michael Griffin. I never received any email responses or phone calls from NASA.

On 07/21/2015, I emailed Stuart Robbins, a research scientist at Southwest Research Institute (SwRI), about the discovery of the Apollo 12 LM impact site. I never received a reply.

Associate Professor Phil Stooke's 05/21/2016 Discovery

Since my emails and this web page's details about my discovery of the Apollo 12 LM impact site were ignored by both NASA and the LRO Team, Phil Stooke correctly is an independent co-discover of the Apollo 12 LM impact site.

Phil Stooke, a professor at the University of Western Ontario (Western University), independently discovered the Apollo 12 LM's impact site. It appears that Phil independently discovered this impact site on or about 05/20/2016. See Phil's post about his independent discovery::

05/20/2016 - Unmanned Spaceflight.com > Earth & Moon > Lunar Exploration > LRO & LCROSS > Post #381

Phil must have discovered the impact site somewhat earlier than the date of his above post since Phil's attachments show that Phil had already performed considerable post-discovery work to document his independent discovery. I will update Phil's independent discovery date once Phil gets back to me with information about his true independent discovery date.

Phil realized, just as I did, that there must be an initial point (IP) of contact between the lunar module and the moon's surface. Whether or not this IP would be readily visible was an entirely different question. Yet we both reasonably assumed that some sort of IP contact scar should be visible while backtracking along the centerline and bearing of the debris field and that it should be a simple matter of locating it. Actually, this was not quite so simple since one has to further backtrack along the bearing and centerline of the debris field in order to locate and rule out any other potential IP candidates. Why? Because the local terrain along this centerline is strongly undulating terrain. In any event, both Phil and I independently located the Apollo 12 Intrepid's IP impact scar. And as shown further below and after examining the DEM along the centerline which includes the debris field, the theoretical starting point of the debris field matches very well with the location of the IP which Phil and I independently identified. The IP is readily visible, yet we both had to look carefully for it and confirm that the IP impact scar was real. It took me some time to find it, and it took Phil some time to find it. On 09/12/2016, Phil posted an update about his independent discovery of the Apollo 12 LM IP:

09/12/2016 - Unmanned Spaceflight.com > Earth & Moon > Lunar Exploration > LRO & LCROSS > Post #391

Once again, Phil must have discovered the IP on a somewhat earlier date than his above post since his attachments show post-discovery work.

Discovery of the Apollo 14 LM Impact Site

Phil Stooke discovered the Apollo 14 LM impact site on or about 03/19/2010, a bit over four years before I independently discovered it on 04/18/2015. This is a most remarkable achievement by Phil. See:

03/19/2010 - Unmanned Spaceflight.com > Earth & Moon > Lunar Exploration > LRO & LCROSS > Post #62

There is absolutely no question in my mind that the true Apollo 14 LM impact site has been correctly identified since there is absolutely nothing even remotely nearby the vicinity of the impact site which could be an alternative candidate for the Apollo 14 LM's impact site.

Other Apollo LM Impact Site Candidates

Phil has a possible A15 LM impact site candidate which I need to research and verify. I had previously (and perhaps too quickly) ruled out this possible A15 LM impact site candidate, yet Phil has presented additional evidence which I need to investigate. If this really is the A15 LM impact site and since I initially rejected this potential A15 LM impact site location, then this discovery would be entirely Phil's discovery, with me only serving to confirm his discovery by presenting evidence to confirm his discovery.

I have a strong candidate for the A17 LM impact site. I believe that Phil also has a different candidate for the A17 LM impact site. At this point, it is down to a matter of either proving or disproving each candidate. I hope that Phil and I can work together to confirm any A15 and A17 LM impact site candidates.

The Apollo 12 Lunar Module Impact Site

The Apollo 12 LM Intrepid approached from the east on a bearing of approximately 285° clockwise from lunar north. Thus the Intrepid was traveling in a west-northwesterly direction. This bearing is almost exactly the same bearing on which the Intrepid traveled on during its descent and landing to mark the second time in mankind's history in which human beings landed and set foot on another world. The Intrepid's angle of descent at impact was 3.7° from horizontal and its velocity at impact was 1680 meters per second (3758 miles per hour). That is far faster than the top speed of a Lockheed SR-71 Blackbird yet somewhat less than the top speed of the North American X-15 research aircraft.

Apollo 12 LM Impact Site Data

Object Date Time (UT) Impact Point Latitude Impact Point Longitude Impact Velocity (km/s) Impact Energy (ergs) Angle from Horizontal Bearing (clockwise from North) Furthest Extent of Debris Field from Impact Point Time to Create Debris Field
Toksoz et al., 1974 Data:
Apollo 12 LM 20 November 1969 22:17:17.7 3.94 S 21.20 W 1.68 3.36 x 1016 3.7°      
GoneToPlaid's 2015 Data:
      3.92 S 21.17 W       284.9° 2950 m 1.76 s

LRO Team QuickMap View of the Impact Site

A12 LM Impact Site 0.5 m/pixel (full link) - QuickMap - QuickMap view (link with full URL) showing a 0.5m/pixel close-up view of a fairly small part of the debris field. This view is centered in between the two bright and fresh secondary craters which may have been created by large pieces of the LM Intrepid. A short bit.ly URL which is suitable for use in news articles is: http://bit.ly/1FHnBat

NOTE: To see the entire debris field while viewing either of the above QuickMap links, simply click the minus (-) zoom button twice to zoom out from 0.5 m per pixel to 2 m per pixel. This setting will show the entire impact site and debris field if your computer has a horizontal resolution of 1920 pixels or greater. Laptop users with lower resolution screens will have to click the minus zoom button one additional time in order to see the full extent of the impact site.

Google Moon KMZ File for the Impact Site

A12_LM_Impact_Site.kmz — 63 MB KMZ file of the impact site for use in Google Moon. Since this KMZ file is rather large, you may wish to right-click on the link to download and save the file. After the KMZ file has been downloaded to a location on you computer, you can then open the downloaded file in Google Moon.

Videos of Apollo 12 Lunar Module Intrepid's Lunar Impact Site

The best way to see the extent of the impact site is to watch either of the following MP4 videos. Both are identical except that the HQ version has higher fidelity. In the following video, what you are looking for are the dark streaks from impact debris which appear to converge towards the distant horizon. You will note that the dark streaks do not actually converge on a vanishing point located at the center of the distant horizon. Why? Because the dark streaks are the result of an outwardly spreading fan of debris material, rather than all of the dark streaks being aligned along parallel lines. Videos are credit NASA/GSFC/ASU/Google/GoneToPlaid.

Video of Apollo 12 Lunar Module Impact Site (HQ version)

Video of Apollo 12 Lunar Module Impact Site (lower quality YouTube version)

Plotting Error in the Apollo 12 Mission Report Image for the A12 Landing and Impact Sites

I have discovered that the Figure 5-2 image NASA-S-70-570 on page 93 (Section 5, page 11) within the Apollo 12 Mission Report contains an erroneously overlaid plot of the Apollo 12 landing site location and the Apollo 12 LM impact site location. See below. I aligned a crop of Lunar Orbiter IV image 4125_h3 to the overlaid NASA-S-70-570 image from the Apollo 12 Mission Report . I then plotted the actual LM landing and impact site locations in yellow. The originally plotted LM landing and impact site locations and their trajectories were highlighted in blue. The original plot was then translated to align with the actual landing site location. With the original plotting error in NASA-S-70-570 now corrected, you can see that the NASA's computed position for the Intrepid's impact site very closely matches the actual impact site location. See images below.

NASA-S-70-570 and Lunar Orbiter IV Image 4125_h3
A. Crop of LO image 4125_h3. B. NASA-S-70-570 overlaid on LO image 4125_h3. C. Actual locations versus plotted locations in NASA-S-70-570 image.
     
D. Actual locations versus plotted locations overlaid on LO image 4125_h3. E. Plotted locations shifted to align with the actual Apollo 12 landing site location on LO image 4125_h3.. F. Plotted locations shifted to align with the actual Apollo 12 landing site in NASA-S-70-570 image.
Enhanced LRO Images of the Apollo 12 Lunar Module Intrepid's Impact Site
NOTE: I am still examining and processing additional LRO images of the impact site. Additional LRO images will be added soon. Processed and enhanced LRO images are credit NASA/GSFC/ASU/GoneToPlaid.
LRO Image M129431676LCRC. North is up.
Labeled and enhanced version of the calibrated image of the impact site. Image scale: 1 meter per pixel.
Note: Use your web browser's scrollbars to pan around the following images
Labeled and enhanced version of the calibrated image of the impact site. Image scale: 0.5 meters per pixel.
Enhanced Version of the calibrated image of the impact site. Clean with no labels. Image scale: 0.5 meters per pixel.
Calibrated image of the impact site. Image scale: 0.5 meters per pixel.
Google Moon Views of the Apollo 12 Lunar Module Intrepid's Impact Site
Processed and enhanced LRO images which I overlaid onto Google Moon are credit NASA/GSFC/ASU/Google/GoneToPlaid.
LRO Image M129431676LCRC overlaid onto Google Moon. This Google Moon perspective view of the overlaid LRO image looks down range along the LM crash site debris fan.
LRO Image M129431676LCRC overlaid onto Google Moon. This Google Moon perspective view of the overlaid LRO image looks back (up range) along the LM crash site debris fan. This view shows the most obvious portions of the debris fan rather than the full extent of the crash site.

Where exactly did the LM Intrepid make its initial contact with the lunar surface?

This is a question which has perplexed me since I previously was unable to find any blatantly an obvious point of initial contact further back along my carefully plotted centerline throughout the length of the entire debris field. I would expect to find an obvious and very fresh crater at the Intrepid's initial point of contact with the lunar surface. The debris field itself gives us some clues since the debris field is very long and has a rather narrow fan pattern. Had the Intrepid impacted the lunar surface at a steeper angle relative to the lunar surface, then an obvious crater would have been created with ejecta being strewn throughout a much wider fan of secondary debris. Yet this is not what is seen when looking at the debris field. This lead me to suspect that part of the Intrepid must have just barely grazed the lunar surface at a very shallow angle. Assuming that this is what did indeed occur, the part of the Intrepid which grazed the lunar surface would instantly disintegrate and send shrapnel like a shotgun blast upward and into the LM's pressurized hull. The result would be a virtually instantaneous explosive decompression of the LM's hull.

So for the moment let's assume that the above scenario is what actually occurred. The LM was pressurized with pure oxygen. At 20° Celsius, oxygen molecules have an average speed of 478 meters per second. The LM's speed at impact was 1680 meters per second. Assuming that the oxygen was able to act with 100% efficiency in terms of accelerating the LM's hull fragments, then a 32° wide fan of debris would have been created. But of course this is impossible since this requires the hull fragments to have zero inertia and for the oxygen molecules to have 100% efficiency at imparting their average speed to the hull fragments. Just winging it, I figured that the oxygen would act upon the exploding hull fragments with only 50% efficiency. This results in a 16° wide debris fan. The measured angular width of the actual debris fan is a bit less than this and seems to converge at a point near the west side of an apparent ridge which is located to the east of the debris field.

The above scenario is only a hypothesis for the observed angular width and convergence of the debris fan, and for the lack of any obvious initial impact crater. The above scenario requires the LM to initially barely graze the lunar surface. This in turn also requires the local slope of the lunar surface, within a distance of only a tens of meters downrange of the initial impact point, to become greater than the descent slope of the LM at the point where the LM grazed the lunar surface such that there is a void beneath the LM and its fan of exploding hull fragments as the LM's debris fan traveled and impacted further downrange. In other words, this scenario requires the LM to graze the lunar surface at or very near the westward side of a lunar ridge.

My crash scenario would appear to be extremely unlikely. However unlikely, let's see if there is evidence for the above scenario. For an answer, we will have to look at the Lunar Reconnaissance Orbiter's GLD100 DTM data. After examining the following, you will see that the GLD100 DTM evidence not only supports this scenario, but also appears to impose an upper limit on the trajectory angle of an object which could have created the observed debris field. This upper limit is exactly the same 3.7° angle from horizontal at which the LM Intrepid struck the lunar surface. The eastward convergence of the debris field fan proves that whatever created the debris field impacted from the east and not the west. So in other words, the LRO GLD100 DTM for the debris field appears to be the smoking gun which proves that this is indeed the Apollo 12 Intrepid's lunar impact site. See the images below.

The LRO GLD100 elevation plot along the centerline of the debris field is shown. Also shown is the LM's descent slope and the calculated beginning of the debris field. The calculate beginning of the debris field assumes that the LM barely grazed the lunar terrain near the right end of the green centerline of the debris field.
 
As you can see, the actual beginning of the debris field is very close to the theoretical starting point for the debris field.

The above GLD100 data appears to support my crash scenario. But my crash scenario falls apart if I can't find signs of the Intrepid's initial point of contact with the lunar surface in the area predicted by the GLD100 data plot, and additionally find signs that the LM's pressurized hull exploded immediately above the surface a few milliseconds later and only a few meters downrange of this initial point of contact. Is anything like this visible in LRO images? The answer is YES, as shown below.

The LRO GLD100 data predicts that the LM's initial contact point with the lunar surface should be within the yellow ellipse.
 
My enhanced version of LRO image M129431676LCRC shows something at the predicted location based on the GLD100 data. Image scale of the linked image is 0.25 meters per pixel. The thin dark streak might have been created by a LM appendage striking the lunar surface. The streak's bearing appears to be correct, yet this is far from solid evidence to support my crash scenario. Perhaps another LRO image will show something far more conclusive...
 
My enhanced version of another LRO image, image M122353240LCRC, clearly shows a spreading fan of dark steaks along the correct bearing. Image scale of the linked image is 0.25 meters per pixel. The fan's angular width is about twice as large as predicted. All of the craters within the ellipse appear to be preexisting craters, yet it appears that the exploding LM freshened the largest crater and threw some rim material westward in a fan with one bright streak which is on the same bearing as the LM's deorbit track.

LRO Team QuickMap View of the Intrepid's Initial Point of Contact with the Lunar Surface

A12 LM Initial Contact Point at 0.5 m/pixel (full link) - QuickMap - QuickMap view (link with full URL) showing a 0.5m/pixel close-up view of the Apollo 12 lunar module Intrepid's initial point (IP) of contact with the lunar surface. This QuickMap view is precisely centered on the IP. A short bit.ly URL which is suitable for use in news articles is: http://bit.ly/1FSI5gt

Alternatively, following is a labeled QuickMap screen capture of the Intrepid's initial point of contact with the lunar surface.

QuickMap 0.5 m/pixel close-up of the Intrepid's Initial contact Point (IP) with the lunar surface.

The GLD100 data for the location shown in the above image indicates that the slope of the terrain at this initial contact point location and along the same bearing as the debris field is approximately -2.6°. The LM's descent angle at impact was -3.7°, for a difference of only 1.1°. Roughly 1 degree is an extraordinarily shallow impact angle. I theorize that this extremely shallow impact angle allowed the pressurized LM to explode rather than burrowing into the terrain and creating an impact crater.

So there you have it. The evidence which I presented above would appear to validate my scenario for exactly how and where the Intrepid impacted the lunar surface.

Links to LRO NAC and WAC Images of the Impact Site

NOTES:

1. The raw LRO NAC images may be flipped, mirrored, or rotated 180° depending on the orientation of the LRO (flying front end first or tail end first) and on whether the LRO was on the ascending or descending node of its orbit.

2. The vertical image scale doesn't match the horizontal image scale. This is because the LRO NACs are push broom cameras and as such, must have a small amount of terrain overlap as the image is acquired image row by image row. Otherwise small lunar surface details wouldn't be seen if they were in a dead space between each image row.

Region of interest:

Lower-Left corner (lon, lat) = (-21.26559, -3.93712)
Upper-Right corner (lon, lat) = (-21.15769, -3.88330)

Projected extent (in cartographic coordinates):
width (km) = 3.27
height (km) = 1.63
perimeter (km) = 9.81
area (sq. km) = 5.34
 

LROC NAC images within ROI (23 records):

Image ID Orbit # Image Start Time Incidence Angle Emission Angle
M107013893LC 910 2009-09-08 01:50:25 24.097 1.751
M107013893RC 910 2009-09-08 01:50:25 24.268 1.175
M109372514RC 1252 2009-10-05 09:00:47 3.93 1.137
M109372514LC 1252 2009-10-05 09:00:47 3.873 1.689
M114091363RC 1947 2009-11-28 23:48:16 57.774 0.921
M122353240RC 3164 2010-03-04 14:46:13 25.512 1.13
M122353240LC 3164 2010-03-04 14:46:13 25.445 1.692
M129431676LC 4207 2010-05-25 13:00:08 55.879 1.685
M129431676RC 4207 2010-05-25 13:00:08 55.946 1.135
M155376303RC 8031 2011-03-21 19:50:35 6.869 1.133
M155376303LC 8031 2011-03-21 19:50:35 6.829 1.688
M181308988LC 11832 2012-01-15 23:22:01 64.786 1.751
M183667860RC 12162 2012-02-12 06:36:33 37.013 1.174
M193096305RC 13481 2012-05-31 09:37:18 72.621 1.294
M1129624731LC 18609 2013-07-28 04:24:23 42.984 1.764
M1134338206LC 19272 2013-09-20 17:42:19 11.306 1.734
M1142581814RC 20431 2013-12-25 03:35:47 70.741 1.172
M1144935363LC 20762 2014-01-21 09:21:35 42.216 1.741
M1152001036RC 21755 2014-04-13 04:02:49 42.368 1.177
M1154357246LC 22086 2014-05-10 10:32:59 69.383 1.744
M1169665200LC 24238 2014-11-03 14:45:33 66.511 1.73
M1180257335RC 25728 2015-03-06 05:01:08 16.169 1.179
M1180257335LC 25728 2015-03-06 05:01:08 16.015 1.736
 

LROC WAC images within ROI (limited to 50 records):

Image ID Orbit # Image Start Time Incidence Angle Emission Angle
M109372456CC 1252 2009-10-05 08:59:48 4.904 1.135
M119984904MC 2815 2010-02-05 04:53:56 52.837 1.142
M119991702MC 2816 2010-02-05 06:47:14 52.725 1.144
M119998469MC 2817 2010-02-05 08:40:01 52.703 1.146
M120012060MC 2819 2010-02-05 12:26:32 52.983 19.875
M122353236CC 3164 2010-03-04 14:46:08 24.948 1.135
M124715008CC 3512 2010-03-31 22:49:00 2.799 1.133
M127070152CC 3859 2010-04-28 05:01:25 29.256 1.135
M129431657CC 4207 2010-05-25 12:59:49 55.761 1.138
M131786096CC 4554 2010-06-21 19:00:28 81.99 1.129
M131792890CC 4555 2010-06-21 20:53:42 82.067 1.129
M132963269CC 4728 2010-07-05 10:00:01 84.161 1.133
M132970064CC 4729 2010-07-05 11:53:16 84.464 15.053
M135324541CC 5076 2010-08-01 17:54:33 57.939 3.336
M135331334CC 5077 2010-08-01 19:47:47 57.769 1.14
M137679013CC 5423 2010-08-28 23:55:45 31.459 1.137
M137685809CC 5424 2010-08-29 01:49:01 31.357 1.14
M140040052CC 5771 2010-09-25 07:46:24 4.864 1.136
M140046847CC 5772 2010-09-25 09:39:40 4.649 1.138
M142401333CC 6119 2010-10-22 15:41:05 22.585 1.133
M142408125CC 6120 2010-10-22 17:34:17 22.647 1.13
M144755430CC 6466 2010-11-18 21:36:02 50.11 1.136
M144762224CC 6467 2010-11-18 23:29:16 50.183 1.138
M147116059CC 6814 2010-12-16 05:19:51 78.062 1.137
M147122830CC 6815 2010-12-16 07:12:42 78.142 1.136
M150660005CC 7336 2011-01-26 05:45:37 60.306 1.142
M153021093CC 7684 2011-02-22 13:37:05 33.037 1.141
M155376255CC 8031 2011-03-21 19:49:47 4.89 1.133
M157730157CC 8378 2011-04-18 01:41:29 22.92 1.135
M157736918CC 8379 2011-04-18 03:34:11 23.083 1.135
M160091535CC 8726 2011-05-15 09:37:47 49.759 1.137
M160098387CC 8727 2011-05-15 11:31:59 49.867 1.138
M162446181CC 9073 2011-06-11 15:41:53 76.27 1.141
M162452974CC 9074 2011-06-11 17:35:06 76.343 1.142
M165978596CC 9594 2011-07-22 12:55:28 64.864 1.139
M165985372CC 9595 2011-07-22 14:48:24 64.706 1.141
M168340057CC 9942 2011-08-18 20:53:09 36.713 1.132
M170694773CC 10289 2011-09-15 02:58:25 10.161 1.139
M170701693CC 10290 2011-09-15 04:53:45 11.2 1.138
M173056952CC 10637 2011-10-12 11:08:04 17.662 0.974
M175414889CC 10985 2011-11-08 18:07:01 45.018 1.124
M177772047CC 11334 2011-12-06 00:52:59 72.979 1.135
M181294074CC 11830 2012-01-15 19:13:26 66.12 1.17
M181301232CC 11831 2012-01-15 21:12:44 65.979 1.171
M181308359CC 11832 2012-01-15 23:11:31 66.055 1.171
M181315517CC 11833 2012-01-16 01:10:49 65.908 1.168
M181322672CC 11834 2012-01-16 03:10:04 65.777 1.169
M183653419CC 12160 2012-02-12 02:35:51 37.138 1.183
M183660575CC 12161 2012-02-12 04:35:07 37.007 1.16
M183667702CC 12162 2012-02-12 06:33:54 37.064 1.184
 
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