Match scheduling algorithm and team numbers

[The Lucas]

I was playing around with the scheduler last night and I noticed the same thing. It think Sean from 25 posted it in the Galileo thread as well.

Originally Posted by Joe Ross

One very easy solution would be to to randomize the team list before it is fed into the MatchMaker software.

Looking at regional schedules, I would guess the software already randomize the team list (don't you agree?) Remember we are playing with an evaluation version of the scheduler algorithm with no GUI or anything, not the actual software used by the scorekeeper. Hopefully they don't put them in OPR order (which looks like what you did) since that would lead to conspiracy theories.

Originally Posted by Joe Ross

My hypothesis was that the algorithm was not able to stray far from the initial set of teams because the minimum match separation was too high to allow that. If the minimum match separation was lowered, so should the correlation between the position and the initial list and the times played.

MMS = Minimum Match Separation

MMS 	Correlation
12	-0.88
10	-0.88
8	-0.60
6	-0.17
2	-0.11

When looking at the MatchRater results, MMS of 12 gives good results, and MMS of 10 gives almost perfect results. As a result, I have a feeling that FIRST would chose 10 for the championship. However, that value still has a strong correlation to placement in the team list and times played. It means that team 25 will very likely not play either with or against any rookie teams, but very likely they would play teams 8 and 40. Each individual match schedule is very good at making sure that you don't play the same team twice, it just limits the number of teams you have a chance of playing.

I think this is the real prob is the default MMS is too high and that is what is typically used (I think it was used at FLR and Philly). If you have to play a single team (out of 86) twice (in 7 matches) that is unacceptable and can heavily skew the seedings (which are very imperfect to begin with). Hopefully the scorekeepers will tweak the MMS until there are no repeats.

Originally Posted by Joe Ross

Note that in the grand scheme of things, this is a very small problem. The MatchMaker software is far better then any other scheduler I've seen in FIRST. I just want to make it better.

I like this algorithm and how it approaches the problem. I love how you can tweak all the variables and they released it for us to evaluate (fun and educational). It may not be perfect, but it is a thousand times better than the Algorithm of Doom last year. By this time last year, we had released the first round of matches for each division.

[Joe Ross]

Originally Posted by The Lucas

Looking at regional schedules, I would guess the software already randomize the team list (don't you agree?) Remember we are playing with an evaluation version of the scheduler algorithm with no GUI or anything, not the actual software used by the scorekeeper. Hopefully they don't put them in OPR order (which looks like what you did) since that would lead to conspiracy theories.

I think the software should randomize the list, but I'm pretty sure it doesn't. For Chesapeake, the average team number that 7 (the lowest number team) faced was 716, and the average team number that 2546 faced was 1831.

Originally Posted by The Lucas

I think this is the real prob is the default MMS is too high and that is what is typically used (I think it was used at FLR and Philly). If you have to play a single team (out of 86) twice (in 7 matches) that is unacceptable and can heavily skew the seedings (which are very imperfect to begin with). Hopefully the scorekeepers will tweak the MMS until there are no repeats.

using a MMS of 10 gives an almost perfect schedule for the championship (good enough to fool the person looking at the statistics). It does not fix the problem with the initial team list, however. You need to go down much further to fix it, which is very unlikely to happen.

[The Lucas]

Originally Posted by Joe Ross

I think the software should randomize the list, but I'm pretty sure it doesn't. For Chesapeake, the average team number that 7 (the lowest number team) faced was 716, and the average team number that 2546 faced was 1831.

Ya looking at Philly and GTR again for only the lowest and highest number teams' schedule I do notice it. The schedules look pretty good when you go match to match, but individual team schedules show the trend. Immediately looking at them, they were much better than my schedules so I figured they were randomized. I guess the difference was fair (low) quality of my schedules versus better quality of reagional.

Originally Posted by Joe Ross

using a MMS of 10 gives an almost perfect schedule for the championship (good enough to fool the person looking at the statistics). It does not fix the problem with the initial team list, however. You need to go down much further to fix it, which is very unlikely to happen.

I agree that 10 MMS doesn't fix the initial team order problem, I didnt say it did (I thought they randomized team list). I was just stressing that the more important problem is the default MMS is too high (and is generally being used) and we may see duplicate opponents. Both problems can be easily fixed due to MatchMaker's flexibility. I just hope they realize these problems. Unfortunately, I don't have any championship scorekeeper volunteers on my team anymore (so I can't rant about this stuff at the airport like last year ) Good work as usual Joe.

[waialua359]

i'd like to know how the parameters were setup where, in Chesapeake with a field of 61 teams, we played with team 75 once and against them 3 times in a span of 5 consecutive matches.

[smurfgirl]

I thought something funny was up at the Connecticut Regional- we played with and against mostly rookie and sophomore teams. Team 175, on the other hand, had a notorious match with six 100's-range established (and incredible) teams.

[Phil Mack]

Originally Posted by waialua359

i'd like to know how the parameters were setup where, in Chesapeake.

the short answer is

MatchMaker -t 60 -r 8 -m 8

You can figure this out for any regional you want to.

MatchMaker takes three parameters for generating a schedule: number of teams playing (60), number of rounds to play(8), and minimum match separation for each team(8). (All other parameters that the program accepts are irrelevant to how the matches are scheduled.)

The first parameter must be the number of teams. The second parameter is dictated by the time available to play the matches. The third parameter of minimum match separation is the only one that is left to discretion.

The third parameter can be found by counting how many matches are between teams' matches. The fewest matches between a pair of matches will be that parameter.

Also, the MatchRater program can be applied to schedules available at http://www.usfirst.org/community/frc...ts.aspx?id=430 offering some insight in the scheduling.

It looks like 75 and 359 just got the short end of the stick on this one, given that there were numerous teams that face 24 distinct opponents. This is a case where the parameters chosen were reasonable(maybe not great, but reasonable), but whoever made the schedule probably ran the program in Default (fast and less effective) instead of Good or Best (which really just runs the same algorithm for longer.)

Better luck next time.
~Phil

[nuggetsyl]

Thanks for doing the study. I total agree with Joe that this years algorithm is much better then lasts. I am sure first will see this and make the small modification for next years algorithm. The one question i have is you said you did 200 matches yet the first one i see is 1114 and us and the number 210 does that mean i play with them once and against them once????

[Joe Ross]

Originally Posted by nuggetsyl

Thanks for doing the study. I total agree with Joe that this years algorithm is much better then lasts. I am sure first will see this and make the small modification for next years algorithm. The one question i have is you said you did 200 matches yet the first one i see is 1114 and us and the number 210 does that mean i play with them once and against them once????

That means that in at least 10 match schedules, you see 1114 in two separate matches (one with and one against).

As Brian pointed out, when I ran the simulation, I did not sort by team number, so those statistics do not apply to specific team numbers, only specific positions in the team list. 25 probably only has about a 25% chance of seeing 1114 in a match.

[waialua359]

just wanted to point out and add to the fact that in looking at our practice matches tomorrow, only 1 team of the 3 matches for either sides have a 2xxx team. Other than team 1165, we have no team no. larger than ours (other 5 teams on the field).
Interesting to say the least if that is a sign of things to come on the match schedule for friday and saturday.

[BBnum3]

Just to back up what's been discussed here, I just looked at the match schedule for my team (1816) this weekend. Out of 35 alliance partners/opponents, only two have numbers lower than 1212.

[Joe Ross]

In June, the Saxtons released a new version of the MatchMaker software (1.0.3b1). The description is "Here is a beta release of the new version that has an improved algorithm to reduce the clumping effect observed at the Philly regional during week 6." It can be downloaded from the usual place, http://www.idleloop.com/matchmaker/download.php

I've started running the same tests as I did in this thread, but the early results look very good.

I generated schedules for the size from the championship (85 teams, 8 matches, default minimum match separation). I then summed the team numbers of each alliance and plotted them, similar to the picture in this thread.

team_number_sum_102.PNG shows the results from the version run at the championship, and looks very similar to the thread linked above.
team_number_sum_103.PNG shows the results from the new version. It looks much better (less correlated).
team_number_sum_102_Random.PNG shows the results from the older version, with a randomized team list. This looks very similar to the results from the new version, which shows the new version does a good job.

I'll post more as I evaluate further.

[ATannahill]

i downloaded the new version, unzipped it, and opened it. I got a command prompt to flash on the screen then it closed. am i doing it wrong?

[SamC]

Originally Posted by rtfgnow

i downloaded the new version, unzipped it, and opened it. I got a command prompt to flash on the screen then it closed. am i doing it wrong?

From the download site listed above,

Originally Posted by MatchMaker Site

The program is a console application, it has no graphical UI you just run it from the command line (Terminal on Mac OS X or the Command Prompt on Windows).

so for example on windows, extract to c:\MatchMakerWin
then open Command Prompt and use

C:\>cd c:\MatchMakerWin

C:\MatchMakerWin>MatchMaker.exe

You should see a series of examples and such and then be able to use the program.

[Joe Ross]

Originally Posted by Joe Ross

In June, the Saxtons released a new version of the MatchMaker software (1.0.3b1). The description is "Here is a beta release of the new version that has an improved algorithm to reduce the clumping effect observed at the Philly regional during week 6." It can be downloaded from the usual place, http://www.idleloop.com/matchmaker/download.php

I've started running the same tests as I did in this thread, but the early results look very good.

I'll post more as I evaluate further.

Using the same methodology as before, I ran 200 schedules with best setting, 85 teams, 7 matches, and default match separation. The correlation between the distance of teams and the initial list and the chance they play in a match does not correlate, R = -0.05. With the old scheduler, it was -0.88.

Here are the full results

	1114	103	330	217	40	254	494	25	1717	121	469	1629	234	148	343	65	2046	176	1540	195	88	70	291	1450	2468	2062	716	1503	1816	932	48	384	694	1089	1983	316	548	2165	1676	364	84	1366	134	1023	2487	180	812	2237	2638	425	2340	894	1319	2549	612	2564	597	980	2437	1038	8	302	457	1138	1739	399	1758	2599	2023	115	1885	1296	1212	2423	1390	839	226	168	2354	1254	1523	2621	1576	509	1595
1114	0	83	80	87	83	83	72	95	85	83	73	86	80	83	77	90	105	73	81	88	83	76	95	82	76	81	87	105	94	78	73	87	86	82	81	80	66	84	80	83	75	82	79	84	95	89	97	94	87	93	61	85	78	70	84	80	81	80	79	87	86	79	84	84	75	87	80	80	86	80	83	87	100	81	90	89	91	75	73	71	76	91	85	85	71
103	83	0	85	86	77	75	69	77	90	82	80	83	84	88	72	72	86	88	69	83	91	90	93	79	79	84	86	94	91	86	74	75	73	64	69	76	82	93	75	83	83	90	88	78	71	88	95	88	90	74	87	87	73	92	83	82	73	79	73	82	89	93	81	103	84	85	88	87	96	85	78	71	85	82	104	87	87	77	93	104	79	78	85	74	98
330	80	85	0	84	89	94	69	97	89	83	84	83	95	96	85	78	86	71	96	79	83	93	95	94	75	82	84	81	93	78	86	89	92	78	84	88	86	83	71	94	85	79	85	81	74	98	77	75	80	75	72	91	84	86	98	86	89	92	76	95	77	71	73	66	89	66	72	81	88	80	79	83	71	79	80	83	92	89	88	76	95	60	79	71	77
217	87	86	84	0	84	69	91	95	96	81	87	80	73	72	85	79	94	82	81	81	81	91	81	90	77	83	75	74	91	90	74	89	82	79	79	94	93	93	88	79	83	91	78	97	91	85	76	86	80	83	75	81	76	79	89	73	81	79	91	93	79	84	93	92	85	85	86	76	75	82	63	71	81	80	90	90	76	81	81	75	93	76	80	90	89
40	83	77	89	84	0	81	78	90	74	83	89	88	83	75	97	86	75	85	77	90	92	78	72	78	82	67	75	75	73	81	89	92	98	83	98	85	92	85	81	85	83	84	90	73	86	94	82	74	85	78	77	78	85	84	76	99	95	91	88	81	91	98	79	83	59	71	79	79	99	84	74	87	96	72	71	69	83	83	82	86	86	81	90	86	74
254	83	75	94	69	81	0	75	74	76	94	81	92	95	80	91	104	77	92	85	70	92	93	88	85	88	86	77	89	85	83	68	80	88	76	85	91	83	84	89	86	96	90	84	94	80	75	74	81	89	86	72	81	86	88	81	80	81	85	86	80	83	88	72	84	90	81	83	78	83	89	89	75	75	72	83	84	72	87	83	77	103	74	76	91	85
494	72	69	69	91	78	75	0	96	81	87	95	74	82	85	73	90	91	79	72	83	88	90	83	90	88	82	82	87	95	88	77	83	83	101	89	74	88	71	89	91	78	77	82	77	71	79	60	72	97	79	89	74	85	85	93	80	84	78	77	88	91	85	77	98	76	106	86	90	81	77	84	88	95	83	86	82	81	88	77	89	90	82	82	97	78
25	95	77	97	95	90	74	96	0	75	71	87	80	81	90	93	75	88	76	83	80	78	79	97	91	82	73	86	75	79	91	78	72	71	90	82	69	75	95	76	96	82	70	92	91	88	81	79	99	86	86	95	86	78	82	97	85	91	73	75	80	79	86	77	85	99	71	91	89	77	75	89	79	86	83	80	75	89	76	84	81	89	87	79	80	85
1717	85	90	89	96	74	76	81	75	0	78	95	78	81	75	91	88	83	100	89	80	95	81	74	82	89	75	86	81	93	92	82	87	75	82	82	77	83	74	78	87	83	75	81	82	90	81	77	76	91	82	78	76	79	90	90	84	91	74	80	87	95	95	91	74	95	85	77	84	76	77	90	94	88	79	71	86	80	97	75	82	95	74	87	68	89
121	83	82	83	81	83	94	87	71	78	0	77	75	77	86	81	84	84	86	89	69	86	73	89	79	75	94	81	73	75	88	76	88	82	85	86	76	93	74	78	92	83	72	92	79	75	77	83	90	97	68	71	87	101	85	70	89	85	77	97	101	87	83	69	78	78	92	89	90	90	87	79	83	80	89	77	93	87	86	83	90	90	83	73	80	77
469	73	80	84	87	89	81	95	87	95	77	0	79	84	94	83	69	79	71	90	88	81	81	90	79	80	77	87	77	74	90	83	82	104	80	78	98	91	70	94	76	83	79	102	83	79	87	77	87	84	87	81	84	92	77	81	83	69	88	80	92	79	86	89	77	74	82	71	69	90	86	92	83	103	80	67	85	74	85	85	86	89	81	78	85	77
1629	86	83	83	80	88	92	74	80	78	75	79	0	85	75	93	61	68	67	89	87	71	81	92	85	88	85	76	86	84	88	90	81	87	64	69	87	88	81	85	79	70	87	98	105	87	86	82	74	83	91	97	89	97	76	78	82	75	80	86	97	89	90	80	72	68	87	70	88	86	96	76	94	79	83	80	88	82	95	69	80	68	88	91	81	90
234	80	84	95	73	83	95	82	81	81	77	84	85	0	90	86	103	71	86	64	91	78	84	91	82	84	73	94	81	79	73	94	83	80	79	96	81	89	98	70	96	83	73	96	75	82	93	79	81	78	84	87	85	84	73	86	78	78	79	78	90	69	86	88	71	88	91	91	64	75	85	90	82	86	74	84	73	96	89	85	89	86	82	89	77	82
148	83	88	96	72	75	80	85	90	75	86	94	75	90	0	88	83	82	77	78	95	81	91	87	83	91	84	73	86	87	88	88	92	89	81	80	83	72	79	74	100	80	81	76	82	90	91	77	72	98	88	101	85	85	92	82	79	72	95	78	72	83	69	84	87	85	99	84	76	92	85	71	81	66	78	77	82	82	81	79	77	74	77	90	76	78
343	77	72	85	85	97	91	73	93	91	81	83	93	86	88	0	87	85	74	63	91	98	79	77	96	90	79	86	88	91	89	88	91	79	85	84	88	76	69	92	89	69	85	78	89	72	76	85	68	96	83	76	85	84	97	86	89	85	78	72	95	71	86	85	88	90	80	89	86	63	102	68	74	74	88	82	74	66	83	73	90	80	94	91	71	80
65	90	72	78	79	86	104	90	75	88	84	69	61	103	83	87	0	87	86	97	92	93	74	76	94	82	79	79	77	73	82	69	79	82	73	75	76	83	79	87	81	88	75	73	83	85	76	85	83	85	99	90	81	84	82	91	86	79	92	91	95	92	84	86	75	92	84	79	94	79	80	82	84	85	79	70	80	106	95	71	88	80	80	79	88	81
2046	105	86	86	94	75	77	91	88	83	84	79	68	71	82	85	87	0	92	83	83	79	81	82	85	84	77	73	93	83	87	80	83	91	78	84	77	97	73	75	61	75	88	78	90	86	80	83	75	90	85	84	62	81	101	94	81	89	81	84	83	81	82	79	92	98	77	75	70	79	75	105	93	82	91	83	72	87	84	89	89	101	71	71	88	94
176	73	88	71	82	85	92	79	76	100	86	71	67	86	77	74	86	92	0	88	73	92	72	77	72	83	88	86	78	82	76	90	90	82	76	81	95	78	88	93	73	80	66	87	94	75	84	73	92	88	78	84	94	82	79	99	83	89	95	87	86	87	74	85	82	85	81	99	90	89	74	92	93	82	84	84	78	87	77	77	80	87	89	79	77	85
1540	81	69	96	81	77	85	72	83	89	89	90	89	64	78	63	97	83	88	0	72	71	83	84	88	78	85	76	84	84	87	69	80	91	89	85	86	82	94	84	86	73	74	81	84	97	75	88	73	83	82	81	105	80	92	85	90	104	86	95	82	90	79	89	96	96	93	84	80	86	76	86	79	77	90	97	76	69	81	84	78	71	84	81	92	84
195	88	83	79	81	90	70	83	80	80	69	88	87	91	95	91	92	83	73	72	0	76	93	85	98	90	77	90	79	83	90	84	81	69	81	75	87	84	75	70	67	75	91	85	86	80	82	95	75	83	73	72	94	80	88	75	88	84	95	76	80	94	84	68	81	81	80	88	95	83	80	93	86	89	96	65	85	84	84	81	81	95	91	86	78	76
88	83	91	83	81	92	92	88	78	95	86	81	71	78	81	98	93	79	92	71	76	0	77	88	83	87	88	84	81	96	75	87	76	85	88	74	70	88	75	80	79	80	82	88	79	83	85	69	86	69	71	94	79	95	65	76	82	83	93	82	72	92	80	77	74	89	89	86	72	88	80	88	88	96	76	109	88	81	90	78	87	77	81	90	97	74
70	76	90	93	91	78	93	90	79	81	73	81	81	84	91	79	74	81	72	83	93	77	0	91	94	86	71	92	86	87	85	81	89	80	81	83	94	76	83	102	101	87	81	81	76	91	95	77	83	75	90	82	74	91	81	87	82	88	73	91	75	75	87	81	86	74	84	66	86	74	62	78	69	84	76	90	100	73	79	76	88	86	73	91	81	89
291	95	93	95	81	72	88	83	97	74	89	90	92	91	87	77	76	82	77	84	85	88	91	0	82	86	73	81	71	89	82	97	89	85	89	81	74	94	86	81	75	76	89	65	76	83	89	84	81	73	67	94	87	88	76	85	74	90	96	87	80	77	80	90	78	85	75	78	74	58	90	91	77	93	84	83	78	89	70	88	89	87	88	81	77	88
1450	82	79	94	90	78	85	90	91	82	79	79	85	82	83	96	94	85	72	88	98	83	94	82	0	51	100	84	79	93	75	83	85	75	88	87	78	96	77	90	77	89	81	77	67	91	79	95	75	88	69	73	87	77	91	74	81	97	98	91	72	96	60	85	93	91	72	89	85	80	79	92	91	80	95	85	92	84	80	67	86	78	65	68	91	90
2468	76	79	75	77	82	88	88	82	89	75	80	88	84	91	90	82	84	83	78	90	87	86	86	51	0	81	78	84	83	79	93	91	78	84	76	87	85	81	85	89	105	94	91	80	93	86	90	81	82	80	97	82	60	86	82	74	85	80	65	97	89	74	83	96	79	89	76	77	77	83	84	85	81	92	83	91	93	85	74	83	81	81	68	71	90
2062	81	84	82	83	67	86	82	73	75	94	77	85	73	84	79	79	77	88	85	77	88	71	73	100	81	0	80	84	86	83	92	71	75	68	84	73	74	81	99	90	81	91	71	89	86	82	86	84	73	77	85	90	84	87	104	71	79	93	81	79	78	92	103	82	93	79	88	88	88	88	83	85	79	86	101	82	70	74	87	88	86	82	80	94	87
716	87	86	84	75	75	77	82	86	86	81	87	76	94	73	86	79	73	86	76	90	84	92	81	84	78	80	0	92	70	84	92	78	72	73	78	87	83	95	86	80	76	68	75	78	76	83	83	88	82	87	97	76	86	73	86	85	79	79	82	87	93	75	85	70	93	88	96	78	78	97	96	96	81	88	78	79	82	86	101	76	89	88	81	82	90
1503	105	94	81	74	75	89	87	75	81	73	77	86	81	86	88	77	93	78	84	79	81	86	71	79	84	84	92	0	67	87	91	79	89	107	95	82	90	83	80	89	97	82	85	98	82	83	83	83	75	88	78	76	86	87	75	76	89	80	75	71	79	88	93	73	84	81	96	75	88	83	81	74	82	82	90	94	93	72	64	97	80	89	74	94	76
1816	94	91	93	91	73	85	95	79	93	75	74	84	79	87	91	73	83	82	84	83	96	87	89	93	83	86	70	67	0	64	85	80	83	73	93	90	91	79	82	81	85	103	83	82	90	93	90	80	65	81	83	74	80	90	74	80	87	71	73	76	84	93	83	80	69	85	83	101	85	77	94	90	76	86	94	84	73	84	84	89	89	86	85	82	93
932	78	86	78	90	81	83	88	91	92	88	90	88	73	88	89	82	87	76	87	90	75	85	82	75	79	83	84	87	64	0	85	74	88	83	82	79	85	81	81	74	89	71	92	79	72	83	91	84	89	80	87	79	89	75	70	79	93	85	92	83	86	84	78	76	95	89	75	75	84	85	85	91	96	97	86	61	88	81	96	86	85	84	88	83	78
48	73	74	86	74	89	68	77	78	82	76	83	90	94	88	88	69	80	90	69	84	87	81	97	83	93	92	92	91	85	85	0	88	85	86	91	83	88	79	94	77	88	83	76	88	87	91	87	83	79	82	74	78	82	72	80	98	93	81	79	80	77	91	90	79	84	69	85	78	80	81	77	97	77	87	90	76	75	85	81	87	82	95	92	86	79
384	87	75	89	89	92	80	83	72	87	88	82	81	83	92	91	79	83	90	80	81	76	89	89	85	91	71	78	79	80	74	88	0	84	81	79	77	78	78	83	80	98	76	80	86	102	84	86	76	87	84	81	76	75	80	86	97	79	86	88	83	89	78	94	87	76	67	78	88	85	83	83	83	88	96	82	74	84	98	82	88	86	80	67	75	85
694	86	73	92	82	98	88	83	71	75	82	104	87	80	89	79	82	91	82	91	69	85	80	85	75	78	75	72	89	83	88	85	84	0	80	90	80	89	83	72	74	74	85	104	73	79	89	91	86	81	71	69	74	82	86	95	86	82	87	93	100	87	82	90	76	82	73	82	87	82	74	84	81	90	75	85	79	94	84	66	78	80	81	99	87	79
1089	82	64	78	79	83	76	101	90	82	85	80	64	79	81	85	73	78	76	89	81	88	81	89	88	84	68	73	107	73	83	86	81	80	0	93	93	84	91	79	84	86	89	75	84	89	101	81	96	85	78	87	93	74	72	71	83	97	74	85	96	87	92	96	84	85	89	97	71	70	80	79	82	92	76	90	80	87	75	81	81	75	81	92	98	88
1983	81	69	84	79	98	85	89	82	82	86	78	69	96	80	84	75	84	81	85	75	74	83	81	87	76	84	78	95	93	82	91	79	90	93	0	84	73	101	81	96	90	84	78	81	94	81	64	88	77	84	59	88	76	91	92	81	79	83	89	83	82	96	75	70	87	76	84	93	83	87	72	68	88	72	79	98	78	85	69	82	89	82	95	83	77
316	80	76	88	94	85	91	74	69	77	76	98	87	81	83	88	76	77	95	86	87	70	94	74	78	87	73	87	82	90	79	83	77	80	93	84	0	86	76	95	76	91	79	89	95	84	78	84	77	77	75	89	88	89	94	82	89	85	94	85	88	80	78	66	69	85	68	91	78	96	85	84	84	69	74	78	100	82	82	93	83	98	82	79	72	90
548	66	82	86	93	92	83	88	75	83	93	91	88	89	72	76	83	97	78	82	84	88	76	94	96	85	74	83	90	91	85	88	78	89	84	73	86	0	83	78	74	87	82	73	75	75	66	84	78	73	92	100	80	95	83	89	71	85	92	75	82	73	87	77	93	77	84	86	70	83	76	79	82	85	87	77	82	87	86	85	89	85	95	99	82	81
2165	84	93	83	93	85	84	71	95	74	74	70	81	98	79	69	79	73	88	94	75	75	83	86	77	81	81	95	83	79	81	79	78	83	91	101	76	83	0	76	84	66	86	79	102	97	83	77	87	85	79	85	84	97	92	72	79	79	80	83	76	76	84	82	84	65	73	61	77	67	95	79	91	82	91	101	96	98	74	85	86	85	74	88	88	86
1676	80	75	71	88	81	89	89	76	78	78	94	85	70	74	92	87	75	93	84	70	80	102	81	90	85	99	86	80	82	81	94	83	72	79	81	95	78	76	0	77	76	93	85	79	82	74	90	88	91	96	88	84	90	78	81	80	79	73	84	76	81	84	84	86	89	90	72	87	92	90	78	92	84	91	78	97	89	76	81	82	88	78	78	90	96
364	83	83	94	79	85	86	91	96	87	92	76	79	96	100	89	81	61	73	86	67	79	101	75	77	89	90	80	89	81	74	77	80	74	84	96	76	74	84	77	0	77	80	82	88	84	81	75	87	70	92	77	90	85	94	85	95	71	92	80	104	83	87	88	80	76	70	83	81	83	81	70	85	79	93	98	86	75	84	74	91	66	60	75	87	95
84	75	83	85	83	83	96	78	82	83	83	83	70	83	80	69	88	75	80	73	75	80	87	76	89	105	81	76	97	85	89	88	98	74	86	90	91	87	66	76	77	0	82	83	81	90	80	88	87	77	88	76	88	96	75	75	93	79	83	94	66	64	94	86	95	78	76	98	85	78	88	75	87	71	75	85	83	95	83	83	85	77	86	82	89	86
1366	82	90	79	91	84	90	77	70	75	72	79	87	73	81	85	75	88	66	74	91	82	81	89	81	94	91	68	82	103	71	83	76	85	89	84	79	82	86	93	80	82	0	79	89	87	78	79	90	77	72	82	84	65	87	86	94	65	81	80	79	82	85	81	85	112	72	79	88	100	84	89	83	72	83	96	81	81	91	79	103	80	81	85	86	73
134	79	88	85	78	90	84	82	92	81	92	102	98	96	76	78	73	78	87	81	85	88	81	65	77	91	71	75	85	83	92	76	80	104	75	78	89	73	79	85	82	83	79	0	89	89	80	83	93	86	72	81	96	92	75	90	90	86	78	74	92	73	78	90	81	88	89	94	108	95	81	90	89	76	89	81	60	97	69	73	78	72	75	99	72	86
1023	84	78	81	97	73	94	77	91	82	79	83	105	75	82	89	83	90	94	84	86	79	76	76	67	80	89	78	98	82	79	88	86	73	84	81	95	75	102	79	88	81	89	89	0	82	77	80	78	89	79	75	86	76	84	64	77	84	85	79	77	87	86	74	96	92	90	76	85	80	86	88	89	85	76	80	76	89	96	92	78	89	87	82	81	87
2487	95	71	74	91	86	80	71	88	90	75	79	87	82	90	72	85	86	75	97	80	83	91	83	91	93	86	76	82	90	72	87	102	79	89	94	84	75	97	82	84	90	87	89	82	0	82	87	75	88	70	75	86	81	90	81	73	90	93	79	89	84	80	77	87	76	72	88	86	78	79	75	64	77	62	84	75	88	76	80	79	82	84	77	90	79
180	89	88	98	85	94	75	79	81	81	77	87	86	93	91	76	76	80	84	75	82	85	95	89	79	86	82	83	83	93	83	91	84	89	101	81	78	66	83	74	81	80	78	80	77	82	0	90	97	88	78	73	73	77	77	83	92	98	87	89	80	77	83	81	82	72	83	86	82	90	78	81	71	100	88	70	101	78	83	87	85	85	78	89	82	91
812	97	95	77	76	82	74	60	79	77	83	77	82	79	77	85	85	83	73	88	95	69	77	84	95	90	86	83	83	90	91	87	86	91	81	64	84	84	77	90	75	88	79	83	80	87	90	0	81	76	84	104	83	68	83	82	88	83	84	79	80	90	72	92	91	88	90	88	85	71	68	99	88	88	94	93	88	74	82	88	86	70	80	74	88	75
2237	94	88	75	86	74	81	72	99	76	90	87	74	81	72	68	83	75	92	73	75	86	83	81	75	81	84	88	83	80	84	83	76	86	96	88	77	78	87	88	87	87	90	93	78	75	97	81	0	77	82	78	86	79	71	69	90	86	71	91	94	77	90	91	82	90	86	79	79	83	88	89	80	92	78	79	89	102	80	85	91	89	74	80	79	87
2638	87	90	80	80	85	89	97	86	91	97	84	83	78	98	96	85	90	88	83	83	69	75	73	88	82	73	82	75	65	89	79	87	81	85	77	77	73	85	91	70	77	77	86	89	88	88	76	77	0	85	84	89	103	76	79	81	107	85	83	92	81	96	78	85	74	91	70	87	104	86	77	86	71	86	77	90	87	81	81	74	89	71	89	91	95
425	93	74	75	83	78	86	79	86	82	68	87	91	84	88	83	99	85	78	82	73	71	90	67	69	80	77	87	88	81	80	82	84	71	78	84	75	92	79	96	92	88	72	72	79	70	78	84	82	85	0	85	79	82	79	97	91	87	83	86	85	104	90	62	80	81	99	90	80	86	69	98	85	70	89	78	79	77	80	79	88	70	91	99	82	83
2340	61	87	72	75	77	72	89	95	78	71	81	97	87	101	76	90	84	84	81	72	94	82	94	73	97	85	97	78	83	87	74	81	69	87	59	89	100	85	88	77	76	82	81	75	75	73	104	78	84	85	0	85	90	88	80	82	89	79	78	91	91	82	81	73	87	91	95	91	84	79	66	83	76	87	81	73	82	74	79	90	78	98	101	92	77
894	85	87	91	81	78	81	74	86	76	87	84	89	85	85	85	81	62	94	105	94	79	74	87	87	82	90	76	76	74	79	78	76	74	93	88	88	80	84	84	90	88	84	96	86	86	73	83	86	89	79	85	0	77	84	81	88	93	99	76	74	94	92	100	81	84	90	79	71	86	76	64	78	62	72	78	97	96	67	81	71	67	80	80	84	99
1319	78	73	84	76	85	86	85	78	79	101	92	97	84	85	84	84	81	82	80	80	95	91	88	77	60	84	86	86	80	89	82	75	82	74	76	89	95	97	90	85	96	65	92	76	81	77	68	79	103	82	90	77	0	78	81	99	82	83	88	81	74	85	90	72	104	77	98	85	90	73	77	98	84	82	77	80	81	96	82	78	85	83	73	72	71
2549	70	92	86	79	84	88	85	82	90	85	77	76	73	92	97	82	101	79	92	88	65	81	76	91	86	87	73	87	90	75	72	80	86	72	91	94	83	92	78	94	75	87	75	84	90	77	83	71	76	79	88	84	78	0	96	86	87	82	87	86	76	81	81	87	82	77	80	79	95	74	91	72	88	91	93	78	83	87	79	78	83	88	79	63	93
612	84	83	98	89	76	81	93	97	90	70	81	78	86	82	86	91	94	99	85	75	76	87	85	74	82	104	86	75	74	70	80	86	95	71	92	82	89	72	81	85	75	86	90	64	81	83	82	69	79	97	80	81	81	96	0	87	88	86	89	91	88	80	81	89	71	87	79	74	77	82	92	72	88	85	81	76	83	79	97	77	79	80	79	83	77
2564	80	82	86	73	99	80	80	85	84	89	83	82	78	79	89	86	81	83	90	88	82	82	74	81	74	71	85	76	80	79	98	97	86	83	81	89	71	79	80	95	93	94	90	77	73	92	88	90	81	91	82	88	99	86	87	0	96	85	74	76	80	76	84	76	73	87	88	90	94	84	96	97	76	80	71	77	80	83	84	85	74	73	82	61	77
597	81	73	89	81	95	81	84	91	91	85	69	75	78	72	85	79	89	89	104	84	83	88	90	97	85	79	79	89	87	93	93	79	82	97	79	85	85	79	79	71	79	65	86	84	90	98	83	86	107	87	89	93	82	87	88	96	0	90	93	77	88	77	80	73	85	76	78	82	87	77	77	81	70	83	64	79	74	76	84	92	80	78	77	88	75
980	80	79	92	79	91	85	78	73	74	77	88	80	79	95	78	92	81	95	86	95	93	73	96	98	80	93	79	80	71	85	81	86	87	74	83	94	92	80	73	92	83	81	78	85	93	87	84	71	85	83	79	99	83	82	86	85	90	0	82	66	80	78	86	70	93	90	80	79	78	86	84	82	103	77	77	84	67	77	78	85	82	84	97	86	78
2437	79	73	76	91	88	86	77	75	80	97	80	86	78	78	72	91	84	87	95	76	82	91	87	91	65	81	82	75	73	92	79	88	93	85	89	85	75	83	84	80	94	80	74	79	79	89	79	91	83	86	78	76	88	87	89	74	93	82	0	90	92	95	75	80	84	86	77	87	84	75	101	78	98	94	93	82	75	87	79	85	84	86	76	79	63
1038	87	82	95	93	81	80	88	80	87	101	92	97	90	72	95	95	83	86	82	80	72	75	80	72	97	79	87	71	76	83	80	83	100	96	83	88	82	76	76	104	66	79	92	77	89	80	80	94	92	85	91	74	81	86	91	76	77	66	90	0	93	66	80	84	79	90	73	93	92	94	83	85	81	62	80	78	87	74	81	78	83	75	82	74	86
8	86	89	77	79	91	83	91	79	95	87	79	89	69	83	71	92	81	87	90	94	92	75	77	96	89	78	93	79	84	86	77	89	87	87	82	80	73	76	81	83	64	82	73	87	84	77	90	77	81	104	91	94	74	76	88	80	88	80	92	93	0	75	84	94	83	83	83	76	91	78	92	85	91	72	100	84	79	89	87	73	82	84	78	97	69
302	79	93	71	84	98	88	85	86	95	83	86	90	86	69	86	84	82	74	79	84	80	87	80	60	74	92	75	88	93	84	91	78	82	92	96	78	87	84	84	87	94	85	78	86	80	83	72	90	96	90	82	92	85	81	80	76	77	78	95	66	75	0	82	89	74	83	78	76	89	90	83	84	77	72	76	90	89	90	83	81	87	79	71	72	90
457	84	81	73	93	79	72	77	77	91	69	89	80	88	84	85	86	79	85	89	68	77	81	90	85	83	103	85	93	83	78	90	94	90	96	75	66	77	82	84	88	86	81	90	74	77	81	92	91	78	62	81	100	90	81	81	84	80	86	75	80	84	82	0	92	86	76	78	97	89	70	86	90	87	89	92	98	81	84	90	70	83	91	85	87	64
1138	84	103	66	92	83	84	98	85	74	78	77	72	71	87	88	75	92	82	96	81	74	86	78	93	96	82	70	73	80	76	79	87	76	84	70	69	93	84	86	80	95	85	81	96	87	82	91	82	85	80	73	81	72	87	89	76	73	70	80	84	94	89	92	0	78	74	83	77	84	82	75	81	87	79	78	77	83	89	69	91	80	84	88	79	94
1739	75	84	89	85	59	90	76	99	95	78	74	68	88	85	90	92	98	85	96	81	89	74	85	91	79	93	93	84	69	95	84	76	82	85	87	85	77	65	89	76	78	112	88	92	76	72	88	90	74	81	87	84	104	82	71	73	85	93	84	79	83	74	86	78	0	83	84	92	80	74	81	84	79	81	80	78	78	88	100	91	83	77	68	96	64
399	87	85	66	85	71	81	106	71	85	92	82	87	91	99	80	84	77	81	93	80	89	84	75	72	89	79	88	81	85	89	69	67	73	89	76	68	84	73	90	70	76	72	89	90	72	83	90	86	91	99	91	90	77	77	87	87	76	90	86	90	83	83	76	74	83	0	84	82	84	86	87	82	84	86	69	84	78	96	95	73	85	86	103	69	111
1758	80	88	72	86	79	83	86	91	77	89	71	70	91	84	89	79	75	99	84	88	86	66	78	89	76	88	96	96	83	75	85	78	82	97	84	91	86	61	72	83	98	79	94	76	88	86	88	79	70	90	95	79	98	80	79	88	78	80	77	73	83	78	78	83	84	84	0	88	73	74	72	99	73	79	106	77	86	88	82	85	73	88	98	88	78
2599	80	87	81	76	79	78	90	89	84	90	69	88	64	76	86	94	70	90	80	95	72	86	74	85	77	88	78	75	101	75	78	88	87	71	93	78	70	77	87	81	85	88	108	85	86	82	85	79	87	80	91	71	85	79	74	90	82	79	87	93	76	76	97	77	92	82	88	0	77	91	89	84	75	84	86	95	84	82	93	66	73	80	89	87	79
2023	86	96	88	75	99	83	81	77	76	90	90	86	75	92	63	79	79	89	86	83	88	74	58	80	77	88	78	88	85	84	80	85	82	70	83	96	83	67	92	83	78	100	95	80	78	90	71	83	104	86	84	86	90	95	77	94	87	78	84	92	91	89	89	84	80	84	73	77	0	75	100	78	77	71	99	82	74	83	92	69	66	90	82	90	74
115	80	85	80	82	84	89	77	75	77	87	86	96	85	85	102	80	75	74	76	80	80	62	90	79	83	88	97	83	77	85	81	83	74	80	87	85	76	95	90	81	88	84	81	86	79	78	68	88	86	69	79	76	73	74	82	84	77	86	75	94	78	90	70	82	74	86	74	91	75	0	89	72	85	82	86	90	82	83	100	82	90	89	88	82	97
1885	83	78	79	63	74	89	84	89	90	79	92	76	90	71	68	82	105	92	86	93	88	78	91	92	84	83	96	81	94	85	77	83	84	79	72	84	79	79	78	70	75	89	90	88	75	81	99	89	77	98	66	64	77	91	92	96	77	84	101	83	92	83	86	75	81	87	72	89	100	89	0	79	102	92	71	75	80	91	75	74	77	84	74	74	71
1296	87	71	83	71	87	75	88	79	94	83	83	94	82	81	74	84	93	93	79	86	88	69	77	91	85	85	96	74	90	91	97	83	81	82	68	84	82	91	92	85	87	83	89	89	64	71	88	80	86	85	83	78	98	72	72	97	81	82	78	85	85	84	90	81	84	82	99	84	78	72	79	0	76	84	76	84	68	93	94	92	78	97	77	84	88
1212	100	85	71	81	96	75	95	86	88	80	103	79	86	66	74	85	82	82	77	89	96	84	93	80	81	79	81	82	76	96	77	88	90	92	88	69	85	82	84	79	71	72	76	85	77	100	88	92	71	70	76	62	84	88	88	76	70	103	98	81	91	77	87	87	79	84	73	75	77	85	102	76	0	84	79	72	77	87	85	88	89	84	74	85	83
2423	81	82	79	80	72	72	83	83	79	89	80	83	74	78	88	79	91	84	90	96	76	76	84	95	92	86	88	82	86	97	87	96	75	76	72	74	87	91	91	93	75	83	89	76	62	88	94	78	86	89	87	72	82	91	85	80	83	77	94	62	72	72	89	79	81	86	79	84	71	82	92	84	84	0	98	56	99	84	84	90	87	97	106	87	92

1390	90	104	80	90	71	83	86	80	71	77	67	80	84	77	82	70	83	84	97	65	109	90	83	85	83	101	78	90	94	86	90	82	85	90	79	78	77	101	78	98	85	96	81	80	84	70	93	79	77	78	81	78	77	93	81	71	64	77	93	80	100	76	92	78	80	69	106	86	99	86	71	76	79	98	0	69	80	80	83	86	73	80	89	80	78
839	89	87	83	90	69	84	82	75	86	93	85	88	73	82	74	80	72	78	76	85	88	100	78	92	91	82	79	94	84	61	76	74	79	80	98	100	82	96	97	86	83	81	60	76	75	101	88	89	90	79	73	97	80	78	76	77	79	84	82	78	84	90	98	77	78	84	77	95	82	90	75	84	72	56	69	0	77	84	83	75	97	102	78	75	94
226	91	87	92	76	83	72	81	89	80	87	74	82	96	82	66	106	87	87	69	84	81	73	89	84	93	70	82	93	73	88	75	84	94	87	78	82	87	98	89	75	95	81	97	89	88	78	74	102	87	77	82	96	81	83	83	80	74	67	75	87	79	89	81	83	78	78	86	84	74	82	80	68	77	99	80	77	0	85	80	97	92	91	78	84	81
168	75	77	89	81	83	87	88	76	97	86	85	95	89	81	83	95	84	77	81	84	90	79	70	80	85	74	86	72	84	81	85	98	84	75	85	82	86	74	76	84	83	91	69	96	76	83	82	80	81	80	74	67	96	87	79	83	76	77	87	74	89	90	84	89	88	96	88	82	83	83	91	93	87	84	80	84	85	0	88	75	99	85	73	77	78
2354	73	93	88	81	82	83	77	84	75	83	85	69	85	79	73	71	89	77	84	81	78	76	88	67	74	87	101	64	84	96	81	82	66	81	69	93	85	85	81	74	83	79	73	92	80	87	88	85	81	79	79	81	82	79	97	84	84	78	79	81	87	83	90	69	100	95	82	93	92	100	75	94	85	84	83	83	80	88	0	69	93	99	75	86	85
1254	71	104	76	75	86	77	89	81	82	90	86	80	89	77	90	88	89	80	78	81	87	88	89	86	83	88	76	97	89	86	87	88	78	81	82	83	89	86	82	91	85	103	78	78	79	85	86	91	74	88	90	71	78	78	77	85	92	85	85	78	73	81	70	91	91	73	85	66	69	82	74	92	88	90	86	75	97	75	69	0	78	82	87	77	93
1523	76	79	95	93	86	103	90	89	95	90	89	68	86	74	80	80	101	87	71	95	77	86	87	78	81	86	89	80	89	85	82	86	80	75	89	98	85	85	88	66	77	80	72	89	82	85	70	89	89	70	78	67	85	83	79	74	80	82	84	83	82	87	83	80	83	85	73	73	66	90	77	78	89	87	73	97	92	99	93	78	0	76	82	105	70
2621	91	78	60	76	81	74	82	87	74	83	81	88	82	77	94	80	71	89	84	91	81	73	88	65	81	82	88	89	86	84	95	80	81	81	82	82	95	74	78	60	86	81	75	87	84	78	80	74	71	91	98	80	83	88	80	73	78	84	86	75	84	79	91	84	77	86	88	80	90	89	84	97	84	97	80	102	91	85	99	82	76	0	84	98	88
1576	85	85	79	80	90	76	82	79	87	73	78	91	89	90	91	79	71	79	81	86	90	91	81	68	68	80	81	74	85	88	92	67	99	92	95	79	99	88	78	75	82	85	99	82	77	89	74	80	89	99	101	80	73	79	79	82	77	97	76	82	78	71	85	88	68	103	98	89	82	88	74	77	74	106	89	78	78	73	75	87	82	84	0	77	78
509	85	74	71	90	86	91	97	80	68	80	85	81	77	76	71	88	88	77	92	78	97	81	77	91	71	94	82	94	82	83	86	75	87	98	83	72	82	88	90	87	89	86	72	81	90	82	88	79	91	82	92	84	72	63	83	61	88	86	79	74	97	72	87	79	96	69	88	87	90	82	74	84	85	87	80	75	84	77	86	77	105	98	77	0	87
1595	71	98	77	89	74	85	78	85	89	77	77	90	82	78	80	81	94	85	84	76	74	89	88	90	90	87	90	76	93	78	79	85	79	88	77	90	81	86	96	95	86	73	86	87	79	91	75	87	95	83	77	99	71	93	77	77	75	78	63	86	69	90	64	94	64	111	78	79	74	97	71	88	83	92	78	94	81	78	85	93	70	88	78	87	0

I think it's safe to say that this problem has been solved.