Jeff Sagarin'stm Indiana High School Basketball ONE-CLASS Sectionals Page
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All Contents Copyright © 2009 Jeff Sagarintm. All Rights
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Last updated: 2009 March 09 Monday 06:23:02.109 Central Standard Time = GMT/UTC-06:00
2009 March 09 Monday 12:23:02.109 Greenwich Mean Time = GMT/UTC
JULIAN DATE= 2454900
This is a very difficult math problem to get the ultimate "perfect" answer - that is, the absolute
minimum distance sum. The technique used is "simulated annealing". I'll be continually running it and trying to improve the answer.
So check here every once in a while to see if it's been updated.
Indiana High School Basketball old-fashioned ONE-CLASS Sectionals
This file and its name were inspired by and are my way of honoring the great novel
by John R. Tunis in 1944 called "Yea! Wildcats!". It was set in Indiana
and was based on Tunis's experiences and observations as he actually lived with
the family of a key player on one of the teams for a whole season. And Bob Hammel's
superb real-life depiction of how it used to be is the non-fiction equivalent of Tunis's work.
The title is "HOOSIERS CLASSIFIED - Indiana's Love Affair with One-Class Basketball",
written in 1997.
The above two books should be required reading for anyone who truly wants to understand what
Indiana High School Basketball and its tournament truly mean. No one who reads them
would ever want the tournament to be anything other than the way it was up thru 1997 -
the ONE CLASS all-comers way with the sectionals set up to have neighboring teams
and let the chips fall where they may!
The 1<=>64 listing of the sectionals is now in roughly NORTH-SOUTH order. The combining of the sectionals
into regionals will be done in the next stage. And the teams are listed within each sectional in that
same NORTH-SOUTH manner. That was done by giving teams their code numbers based on their latitude,
which of course indicates their NORTH-SOUTH positioning.
The goal is to minimize the total mileage - that is, have the teams as close together as possible.
By mileage, I'm referring to the sum of the mileages from the 64 sectionals. The mileage for a
given sectional is the sum of the distances between all possible pairs of teams in a sectional.
In a 6-team sectional there are 6*5 / 2 = 15 possible pairs of teams.
In a 7-team sectional there are 7*6 / 2 = 21 possible pairs of teams.
46 sectionals with 6 teams = 276 teams 46 * 15 = 690 pairs
18 sectionals with 7 teams = 126 teams 18 * 21 = 378 pairs
------------- -----------
402 teams 1068 pairs
And the numbers to the left of each team's name are simply the code numbers used by the program
for each team. They have no other significance. And as mentioned above, these code numbers
are in order of latitude.
Thus for example, in Sectional #3, you'll find Fremont with a code number of 1
which means that it is the most northern school in Indiana. And in Sectional #63 you'll
find South Spencer with a code number of 402 which means it is the most southern school
in the state. Each team's current class is shown just for interest. A=4A, B=3A, C=2A, D=1A
The new mileage is higher than in some earlier versions of several years ago.
That's because more accurate locations are now being used for each high school. In the previous
versions, zipcodes were used to determine each school's location which in turn were used to
create a latitude and longitude. So for example, if two schools were in the same city and
had the same zipcode, this would have had them having zero distance between them, which is
obviously wrong. But now, the actual individual addresses for each school are being used
which gives the precise coordinates of latitude and longitude which can then be used to
determine very accurate estimates for the distances between each pair of schools.
The suggestion here is that the host role of the sectionals would rotate among the teams
so that each team gets to host its sectional every 6(7) years.
total miles=11684.1294 total pairs=1068
average miles between pairs of teams=10.94
Further Explanation
____________________________________________________________________________________________________
SECTIONAL# 1 total miles=86 average distance between teams=4 pairs=21 teams=7
20 Mish. Marian B $
16 Mishawaka A $
15 SB Adams A $
2 SB Clay A $
18 SB Riley A $
6 SB St. Joseph's B $
13 SB Washington A $
____________________________________________________________________________________________________
SECTIONAL# 2 total miles=75 average distance between teams=5 pairs=15 teams=6
24 Concord A $
8 Elk. Central A $
17 Elk. Christian D $
5 Elk. Memorial A $
23 Jimtown C $
11 Penn A $
____________________________________________________________________________________________________
SECTIONAL# 3 total miles=88 average distance between teams=4 pairs=21 teams=7
21 East Chicago A $
12 Hamm. Clark B $
36 Hamm. Gavit B $
26 Hamm. Noll C $
29 Hammond B $
40 Munster A $
9 Whiting D $
____________________________________________________________________________________________________
SECTIONAL# 4 total miles=188 average distance between teams=13 pairs=15 teams=6
30 LaPorte A $
4 MC Marquette D $
10 Michigan City A $
7 New Prairie B $
58 S. Central (UM) D $
45 Westville D $
____________________________________________________________________________________________________
SECTIONAL# 5 total miles=221 average distance between teams=15 pairs=15 teams=6
69 Central Noble C $
62 East Noble A $
3 Howe Military D $
19 Lakeland B $
22 Prairie Hts. C $
27 Westview C $
____________________________________________________________________________________________________
SECTIONAL# 6 total miles=82 average distance between teams=4 pairs=21 teams=7
31 Bowman Academy D $
42 Calumet B $
38 Gary Roosevelt B $
32 Gary West A $
47 Griffith B $
34 Hamm. Morton A $
43 Highland A $
____________________________________________________________________________________________________
SECTIONAL# 7 total miles=95 average distance between teams=5 pairs=21 teams=7
51 Andrean B $
46 Gary Wallace B $
28 Gary Wirt B $
49 Hobart A $
37 Lake Station C $
52 Merrillville A $
39 River Forest C $
____________________________________________________________________________________________________
SECTIONAL# 8 total miles=158 average distance between teams=11 pairs=15 teams=6
44 Bethany Christian D $
50 Fairfield C $
35 Goshen A $
60 NorthWood B $
14 Northridge A $
66 Wawasee B $
____________________________________________________________________________________________________
SECTIONAL# 9 total miles=217 average distance between teams=14 pairs=15 teams=6
25 Angola B $
67 DeKalb A $
63 Eastside C $
1 Fremont C $
73 Garrett C $
48 Hamilton D $
____________________________________________________________________________________________________
SECTIONAL#10 total miles=123 average distance between teams=8 pairs=15 teams=6
33 Chesterton A $
70 Morgan Twp. D $
41 Portage A $
53 Valparaiso A $
54 Washington Twp. D $
55 Wheeler C $
____________________________________________________________________________________________________
SECTIONAL#11 total miles=203 average distance between teams=14 pairs=15 teams=6
61 Bremen C $
59 Glenn B $
56 LaVille C $
71 Oregon-Davis D $
74 Plymouth B $
79 Triton D $
____________________________________________________________________________________________________
SECTIONAL#12 total miles=162 average distance between teams=11 pairs=15 teams=6
68 Boone Grove C $
65 Crown Point A $
72 Hanover Cent. C $
77 Hebron C $
57 Lake Central A $
80 Lowell A $
____________________________________________________________________________________________________
SECTIONAL#13 total miles=285 average distance between teams=19 pairs=15 teams=6
83 Churubusco C $
91 Columbia City B $
113 Manchester C $
84 Warsaw A $
64 West Noble B $
101 Whitko B $
____________________________________________________________________________________________________
SECTIONAL#14 total miles=252 average distance between teams=17 pairs=15 teams=6
81 Knox B $
78 Kouts D $
76 LaCrosse D $
88 North Judson C $
114 West Central D $
107 Winamac C $
____________________________________________________________________________________________________
SECTIONAL#15 total miles=182 average distance between teams=12 pairs=15 teams=6
82 Argos D $
102 Caston D $
85 Culver C $
86 Culver Military B $
104 Rochester B $
95 Tipp. Valley B $
____________________________________________________________________________________________________
SECTIONAL#16 total miles=76 average distance between teams=4 pairs=21 teams=7
89 Carroll (FW) A $
96 FW Concordia B $
93 FW Dwenger B $
100 FW Keystone D $
99 FW North A $
92 FW Northrop A $
97 FW Snider A $
____________________________________________________________________________________________________
SECTIONAL#17 total miles=169 average distance between teams=11 pairs=15 teams=6
98 FW Blackhawk D $
116 Heritage B $
75 Lakewood Park Chr. D $
87 Leo B $
103 New Haven B $
94 Woodlan C $
____________________________________________________________________________________________________
SECTIONAL#18 total miles=99 average distance between teams=5 pairs=21 teams=7
105 FW Canterbury D $
111 FW Elmhurst B $
110 FW Luers C $
106 FW South A $
115 FW Wayne B $
112 Harding B $
108 Homestead A $
____________________________________________________________________________________________________
SECTIONAL#19 total miles=339 average distance between teams=23 pairs=15 teams=6
142 Benton Central B $
90 Kank. Valley B $
109 North Newton C $
117 Rensselaer B $
125 South Newton D $
133 Tri-County D $
____________________________________________________________________________________________________
SECTIONAL#20 total miles=183 average distance between teams=12 pairs=15 teams=6
118 Huntington North A $
122 Northfield C $
140 Oak Hill C $
132 Southwood C $
126 Wabash C $
130 White's D $
____________________________________________________________________________________________________
SECTIONAL#21 total miles=208 average distance between teams=14 pairs=15 teams=6
129 Adams Central C $
123 Bellmont B $
134 Bluffton C $
124 Norwell B $
138 South Adams C $
139 Southern Wells D $
____________________________________________________________________________________________________
SECTIONAL#22 total miles=255 average distance between teams=17 pairs=15 teams=6
143 Carroll (Flora) C $
141 Delphi C $
136 Frontier D $
119 North White D $
120 Pioneer D $
131 Twin Lakes B $
____________________________________________________________________________________________________
SECTIONAL#23 total miles=196 average distance between teams=13 pairs=15 teams=6
135 Cass C $
128 Logansport A $
137 Maconaquah B $
121 North Miami C $
146 Northwestern B $
127 Peru B $
____________________________________________________________________________________________________
SECTIONAL#24 total miles=152 average distance between teams=10 pairs=15 teams=6
157 Blackford B $
144 Eastbrook B $
147 Lakeview Chr. D $
160 Madison-Grant C $
145 Marion A $
149 Mississinewa C $
____________________________________________________________________________________________________
SECTIONAL#25 total miles=126 average distance between teams=8 pairs=15 teams=6
148 Harrison (WL) A $
159 Lafayette Cent. Catholic D $
158 Lafayette Jeff A $
162 McCutcheon A $
155 Rossville D $
152 W. Lafayette B $
____________________________________________________________________________________________________
SECTIONAL#26 total miles=148 average distance between teams=10 pairs=15 teams=6
150 Eastern (Gtwn.) C $
151 Kokomo A $
153 Taylor C $
170 Tipton C $
161 Tri-Central D $
156 Western B $
____________________________________________________________________________________________________
SECTIONAL#27 total miles=167 average distance between teams=11 pairs=15 teams=6
172 Alexandria C $
185 And. Highland A $
188 Daleville D $
165 Elwood C $
173 Frankton C $
168 Wes-Del D $
____________________________________________________________________________________________________
SECTIONAL#28 total miles=140 average distance between teams=7 pairs=21 teams=7
190 Cowan D $
169 Delta B $
176 Muncie Burris C $
175 Muncie Central A $
182 Muncie South B $
180 Wapahani C $
178 Yorktown B $
____________________________________________________________________________________________________
SECTIONAL#29 total miles=218 average distance between teams=15 pairs=15 teams=6
164 Clinton Central C $
171 Clinton Prairie D $
166 Frankfort B $
196 Lebanon B $
184 Sheridan C $
195 Western Boone B $
____________________________________________________________________________________________________
SECTIONAL#30 total miles=265 average distance between teams=18 pairs=15 teams=6
167 Attica D $
200 Crawfordsville B $
189 Fountain Cent. C $
187 N. Montgomery B $
163 Seeger C $
186 Southmont B $
____________________________________________________________________________________________________
SECTIONAL#31 total miles=258 average distance between teams=17 pairs=15 teams=6
154 Jay County A $
177 Monroe Cent. D $
211 Northeastern C $
198 Rand. Southern D $
174 Union City D $
179 Winchester C $
____________________________________________________________________________________________________
SECTIONAL#32 total miles=177 average distance between teams=8 pairs=21 teams=7
205 Carmel A $
206 Fishers A $
201 Guerin Catholic C $
181 Hamilton Hts. B $
207 Hamilton SE A $
197 Noblesville A $
194 Westfield A $
____________________________________________________________________________________________________
SECTIONAL#33 total miles=156 average distance between teams=10 pairs=15 teams=6
192 Anderson A $
193 Lapel C $
191 Liberty Christian School D $
216 Mt. Vernon (Fort.) B $
204 Pendleton Hts. A $
202 Shenandoah C $
____________________________________________________________________________________________________
SECTIONAL#34 total miles=108 average distance between teams=5 pairs=21 teams=7
215 Brebeuf B $
223 I. Broad Ripple A $
214 N. Central(Indpls.) A $
219 Park Tudor C $
220 Pike A $
209 University D $
208 Zionsville A $
____________________________________________________________________________________________________
SECTIONAL#35 total miles=173 average distance between teams=12 pairs=15 teams=6
203 Blue River D $
238 Cambridge City C $
212 Hagerstown C $
213 New Castle A $
231 Tri D $
199 Union (Modoc) D $
____________________________________________________________________________________________________
SECTIONAL#36 total miles=86 average distance between teams=4 pairs=21 teams=7
218 Heritage Christian C $
228 I. Arlington A $
226 I. Cathedral A $
224 I. Chatard B $
225 Lawr. Central A $
217 Lawr. North A $
246 Warren Central A $
____________________________________________________________________________________________________
SECTIONAL#37 total miles=242 average distance between teams=16 pairs=15 teams=6
183 Covington D $
210 N. Vermillion D $
249 Riverton Parke D $
255 Rockville D $
265 S. Vermillion B $
227 Turkey Run D $
____________________________________________________________________________________________________
SECTIONAL#38 total miles=120 average distance between teams=8 pairs=15 teams=6
259 Avon A $
251 Ben Davis A $
221 Bethesda Christian School D $
232 Brownsburg A $
244 Covenant Chr.(Indpls.) C $
222 Tri-West C $
____________________________________________________________________________________________________
SECTIONAL#39 total miles=68 average distance between teams=3 pairs=21 teams=7
250 I. Attucks D $
253 I. Metropolitan D $
237 I. Northwest B $
240 I. Ritter C $
257 I. Washington C $
229 International D $
243 Speedway C $
____________________________________________________________________________________________________
SECTIONAL#40 total miles=81 average distance between teams=4 pairs=21 teams=7
241 Fall Creek D $
254 I. Howe B $
260 I. Manual A $
248 I. Scecina C $
252 I. Tech A $
233 I. Tindley D $
230 Indiana Deaf D $
____________________________________________________________________________________________________
SECTIONAL#41 total miles=171 average distance between teams=11 pairs=15 teams=6
235 Eastern Hancock C $
245 Greenfield A $
242 Knightstown C $
269 Morristown D $
256 Morton Mem. D $
276 Rushville B $
____________________________________________________________________________________________________
SECTIONAL#42 total miles=227 average distance between teams=15 pairs=15 teams=6
239 Centerville C $
274 Connersville A $
293 Franklin Co. B $
236 Richmond A $
234 Seton Catholic D $
275 Union County C $
____________________________________________________________________________________________________
SECTIONAL#43 total miles=157 average distance between teams=7 pairs=21 teams=7
262 Beech Grove B $
268 Franklin Cent. A $
267 I. Lutheran D $
264 I. Roncalli B $
261 New Palestine B $
270 Southport A $
278 Triton Central C $
____________________________________________________________________________________________________
SECTIONAL#44 total miles=204 average distance between teams=14 pairs=15 teams=6
271 Cascade C $
285 Cloverdale C $
258 Danville B $
273 Greencastle B $
247 North Putnam C $
281 South Putnam C $
____________________________________________________________________________________________________
SECTIONAL#45 total miles=174 average distance between teams=12 pairs=15 teams=6
266 Decatur Central A $
292 Eminence D $
296 Martinsville A $
282 Monrovia C $
277 Mooresville A $
263 Plainfield A $
____________________________________________________________________________________________________
SECTIONAL#46 total miles=164 average distance between teams=8 pairs=21 teams=7
283 Center Grove A $
289 Franklin A $
280 Greenwood A $
279 Greenwood Christian D $
298 Indian Creek C $
272 Perry Meridian A $
284 Whiteland A $
____________________________________________________________________________________________________
SECTIONAL#47 total miles=278 average distance between teams=13 pairs=21 teams=7
306 Clay City D $
309 N. Central (Farm.) D $
287 Northview A $
297 TH Holy Cross D $
288 TH North A $
295 TH South A $
290 West Vigo B $
____________________________________________________________________________________________________
SECTIONAL#48 total miles=273 average distance between teams=13 pairs=21 teams=7
314 Columbus East A $
310 Columbus North A $
301 Edinburgh D $
304 Hauser C $
286 Shelbyville B $
294 So'western (Shel.) D $
291 Waldron D $
____________________________________________________________________________________________________
SECTIONAL#49 total miles=207 average distance between teams=14 pairs=15 teams=6
303 Batesville B $
302 Greensburg B $
317 Jac-Cen-Del D $
299 North Decatur C $
300 Oldenburg Academy D $
312 South Decatur D $
____________________________________________________________________________________________________
SECTIONAL#50 total miles=227 average distance between teams=15 pairs=15 teams=6
313 Blgtn. North A $
316 Blgtn. South A $
311 Brown County B $
325 Eastern Greene C $
308 Edgewood B $
305 Owen Valley B $
____________________________________________________________________________________________________
SECTIONAL#51 total miles=226 average distance between teams=15 pairs=15 teams=6
307 East Central A $
320 Lawrenceburg C $
318 Milan D $
331 Rising Sun D $
322 South Dearborn B $
323 South Ripley C $
____________________________________________________________________________________________________
SECTIONAL#52 total miles=281 average distance between teams=13 pairs=21 teams=7
327 Bloomfield C $
324 Linton C $
334 North Daviess D $
315 Shakamak D $
319 Sullivan B $
321 Union (Dugger) D $
326 White River Valley D $
____________________________________________________________________________________________________
SECTIONAL#53 total miles=203 average distance between teams=14 pairs=15 teams=6
341 Austin C $
332 Brownstown C $
337 Crothersville D $
335 Medora D $
330 Seymour A $
329 Trinity Lutheran D $
____________________________________________________________________________________________________
SECTIONAL#54 total miles=269 average distance between teams=18 pairs=15 teams=6
328 Jennings Co. A $
338 Madison B $
339 Madison Shawe Memorial D $
356 New Washington D $
343 So'western (Han.) C $
340 Switzerland Co. C $
____________________________________________________________________________________________________
SECTIONAL#55 total miles=192 average distance between teams=13 pairs=15 teams=6
336 North Knox C $
348 South Knox C $
346 Vin. Rivet D $
350 Vincennes B $
351 Washington B $
352 Washington Cath. D $
____________________________________________________________________________________________________
SECTIONAL#56 total miles=221 average distance between teams=15 pairs=15 teams=6
333 Bedford NL A $
342 Mitchell B $
349 Orleans D $
358 Paoli C $
357 Springs Valley D $
355 W. Washington C $
____________________________________________________________________________________________________
SECTIONAL#57 total miles=216 average distance between teams=14 pairs=15 teams=6
361 Borden D $
362 Charlestown B $
360 Eastern (Pekin) C $
359 Henryville D $
354 Salem B $
344 Scottsburg B $
____________________________________________________________________________________________________
SECTIONAL#58 total miles=248 average distance between teams=17 pairs=15 teams=6
353 Barr-Reeve D $
367 Jasper B $
345 Loogootee D $
363 NE Dubois D $
347 Shoals D $
378 Southridge B $
____________________________________________________________________________________________________
SECTIONAL#59 total miles=119 average distance between teams=6 pairs=21 teams=7
372 Christian Academy(NewAlbany) D $
376 Clarksville C $
374 Jeffersonville A $
377 New Albany A $
375 Providence C $
364 Rock Creek Chr. D $
366 Silver Creek B $
____________________________________________________________________________________________________
SECTIONAL#60 total miles=244 average distance between teams=16 pairs=15 teams=6
389 Boonville B $
379 Gibson Southern B $
365 Pike Central B $
368 Princeton B $
383 Tecumseh D $
370 Wood Memorial D $
____________________________________________________________________________________________________
SECTIONAL#61 total miles=213 average distance between teams=14 pairs=15 teams=6
382 Corydon B $
371 Crawford Co. B $
369 Floyd Central A $
380 Lanesville D $
373 North Harrison B $
388 S. Central (Eliz.) D $
____________________________________________________________________________________________________
SECTIONAL#62 total miles=200 average distance between teams=13 pairs=15 teams=6
390 Ev. Central A $
393 Ev. Mater Dei C $
396 Ev. Reitz A $
400 Mt. Vernon (Posey) B $
385 New Harmony D $
384 North Posey C $
____________________________________________________________________________________________________
SECTIONAL#63 total miles=279 average distance between teams=19 pairs=15 teams=6
401 Cannelton D $
381 Forest Park C $
387 Heritage Hills B $
386 Perry Central C $
402 South Spencer C $
399 Tell City C $
____________________________________________________________________________________________________
SECTIONAL#64 total miles=67 average distance between teams=4 pairs=15 teams=6
394 Castle A $
398 Ev. Bosse B $
391 Ev. Day D $
395 Ev. Harrison A $
397 Ev. Memorial B $
392 Ev. North A $
____________________________________________________________________________________________________
Explanation of Data
It's really hard to get the exact solution other than literally
checking every possible combination but with 402 Indiana high school(347 in NCAA division I) teams,
you can see that the factorial issue soon makes that impossible
on even the best PC's and in fact for even the fastest super-computers.
In fact, for the Indiana High Schools, based on there being 46 sectionals with 6 teams and 18 sectionals with 7 teams,
I think it would be:
402!
____________________________________
(6!)^46 * (7!)^18
And the natural logarithm of the answer is 1556.3926512477 and thus the logbase10 of the answer is 675.9327401116
which means the number of possible combinations is 10^675.9327401116 which is an amazingly large number!
It would be actually be an exact integer, but I don't have access to a computer that can handle such large integers.
I think only the latest "super computers" can.
For college basketball with 357 teams with 27 sectionals with 5 teams and 37 sectionals with 6 teams, it would be:
357!
____________________________________ = 10^596.0757525196 which is also a number beyond the capacity to
(5!)^27 * (6!)^37 simply "try all the possibilities".
NOTE: I originally had underestimated these quantities by having (incorrectly) an additional factor of 64! in the denominators.
An observant reader named Loren Maxwell alerted me to this and so it's been corrected.
Remember, there are 31.5576 million seconds in an average year or ˜ 3.16 * 10^7 seconds.
Thus for even a super-computer to check every possibility in one-year, it would have to evaluate
more than 10^668 possibilities per second for the high schools and more than 10^588 per second for the colleges.
So the simulated annealing technique is used to avoid the impossible task of literally checking every possibility.
It was first developed in the early 1950s at Los Alamos by guys like Edward Teller when they
(Metropolis, N.; Rosenbluth, A. W.; Rosenbluth, M.; Teller, A. H.; and Teller, E.
"Equation of State Calculations by Fast Computing Machines." J. Chem. Phys. 21, 1087-1092, 1953. )
were working on the hydrogen bomb. I was in my early oughts then
and so was only consulting with them on an informal basis :-) (just kidding!) at that time.
http://scienze-como.uninsubria.it/bressanini/montecarlo-history/index.html
> Equation of State Calculations by Fast Computing Machines
> N. Metropolis, A.W.Rosenbluth, M.N.Rosenbluth, A.H.Teller and E. Teller 1953
> The Journal of Chemical Physics, 21, 1087 (1953)
> THE paper. Probably THE most important algorithm of the 20th century, often called the M(RT)2 algorith from the names of the authors.
(the paper begins in the middle of page 1087)
The exact same technique could be used to redistrict
for congressional and state districts if you were to treat each
voter as a "team". And each district would end up with very close to the
same number of voters and those voters would all be close to each other
geographically. No more ludicrously shaped districts created totally for the
purpose of giving an advantage to the party drawing the lines.
Of course you'd need to use the supercomputers at the major universities
because even using simulated annealing would take a very long time with
several million "teams(voters)" in each state :-D
But the neat thing about this is that each party could have a mathematician
who liked them run the program and they'd either both get the same answer,
or the one with the lower total distance would have the better answer.
The fact that this would literally "take politics out of the equation", is probably
the reason that it wouldn't be adopted; each party would worry that an honest
redistricting could take away "their" safe seats.
Enjoy!
Jeff Sagarin
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