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Lottery Blackbody RadiationPrev TopicNext Topic
-
Native American Eagle SunMN
United States
Member #21
December 7, 2001
4,811 Posts
OfflineAs we stated in our blog, we were asked a question by CARBOB about how long does it take for all numbers in a Pick 3 type lottery to be picked; both in a single column and overall.
It led to an interesting formula that is very similar to Blackbody Radiation.
We'll start with a simple Pick 1 example.
This can apply to any individual Pick 3 column.
In the Pick 1 selection, we keep track of the number selected at each drawing.
Below is a table showing the Draw, Picked number and the Tracked # Selection.
The example shows on the 24th drawing, all the numbers have been selected.
On the 25th draw, the cycle starts over and the Tracking begins again.
Draw
Pick 1
Tracked # Selection
0
1
2
3
4
5
6
7
8
9
1
3
·
·
·
1
·
·
·
·
·
·
2
4
·
·
·
1
1
·
·
·
·
·
3
1
·
1
·
1
1
·
·
·
·
·
4
4
·
1
·
1
2
·
·
·
·
·
5
1
·
2
·
1
2
·
·
·
·
·
6
1
·
3
·
1
2
·
·
·
·
·
7
1
·
4
·
1
2
·
·
·
·
·
8
6
·
4
·
1
2
·
1
·
·
·
9
9
·
4
·
1
2
·
1
·
·
1
10
2
·
4
1
1
2
·
1
·
·
1
11
8
·
4
1
1
2
·
1
·
1
1
12
2
·
4
2
1
2
·
1
·
1
1
13
2
·
4
3
1
2
·
1
·
1
1
14
3
·
4
3
2
2
·
1
·
1
1
15
0
1
4
3
2
2
·
1
·
1
1
16
8
1
4
3
2
2
·
1
·
2
1
17
1
1
5
3
2
2
·
1
·
2
1
18
8
1
5
3
2
2
·
1
·
3
1
19
9
1
5
3
2
2
·
1
·
3
2
20
2
1
5
4
2
2
·
1
·
3
2
21
9
1
5
4
2
2
·
1
·
3
3
22
4
1
5
4
2
3
·
1
·
3
3
23
5
1
5
4
2
3
1
1
·
3
3
24
7
1
5
4
2
3
1
1
1
3
3
25
8
·
·
·
·
·
·
·
·
1
·
26
1
·
1
·
·
·
·
·
·
1
·
27
6
·
1
·
·
·
·
1
·
1
·
28
3
·
1
·
1
·
·
1
·
1
·
29
0
1
1
·
1
·
·
1
·
1
·
30
1
1
2
·
1
·
·
1
·
1
·
31
2
1
2
1
1
·
·
1
·
1
·
32
9
1
2
1
1
·
·
1
·
1
1
Continues...
The One Over None
I Know... -
Native American Eagle SunMN
United States
Member #21
December 7, 2001
4,811 Posts
OfflineThe next step was to gather a frequency of draws when the cycle ends.
In the previous example, it was the 24th draw.
We ran a simulation for Millions of draws to obtain a Million data set of end draw cycles.
Below is a table of our obtained data for this run.
The table shows there is a minimum of 10 draws; which is to be expected since there are only 10 numbers 0 to 9 that can be selected.
The Peak appears to be at 24 draws.
Next we will look at the graph of the data.
Draws
Pick 1 Tracked # Selection Frequency
0
0
1
0
2
0
3
0
4
0
5
0
6
0
7
0
8
0
9
0
10
344
11
1605
12
4306
13
7962
14
12670
15
19266
16
24277
17
29919
18
34560
19
38797
20
41426
21
43395
22
45105
23
44710
24
45240
25
43409
26
42265
27
40858
28
38108
29
36519
30
34598
31
31914
32
29250
33
27122
34
25506
35
23658
36
21466
37
19721
38
18198
39
16430
40
15337
41
14041
42
12429
43
11339
44
10231
45
8885
46
8500
47
7532
48
6914
49
5965
50
5333
51
4974
52
4461
53
4077
54
3847
55
3361
56
2983
57
2857
58
2536
59
2289
60
1979
61
1828
62
1573
63
1559
64
1076
65
1207
66
974
67
950
68
926
69
787
70
599
71
586
72
548
73
469
74
477
75
416
76
342
77
280
78
299
79
189
80
228
81
208
82
219
83
139
84
184
85
141
86
107
87
144
88
113
89
75
90
76
91
64
92
77
93
104
94
61
95
28
96
54
97
58
98
59
99
32
100
18
101
28
102
26
103
10
104
29
105
20
106
14
107
16
108
10
109
7
110
8
111
7
112
6
113
21
114
4
115
0
116
10
117
3
118
0
119
0
120
10
121
0
122
6
123
0
124
3
125
0
126
0
127
0
128
3
129
0
130
0
131
0
132
0
133
3
134
0
135
0
136
3
137
0
138
0
139
0
140
5
Continues ...
The One Over None
I Know... -
Native American Eagle SunMN
United States
Member #21
December 7, 2001
4,811 Posts
OfflineIn the graph of the Tracked # Selections, we can see the frequency is skewed to the low end and tapers off to the high end.
This graph looks very similar to a natural phenomenon know as Blackbody Radiation.
Below is a graph of the Planck Radiation Formula.
We tried to curve fit this formula to the data, but it did not fit very well.
We had to come up with a different variation that looks nearly the same as the Planck Formula.
Continues ...
The One Over None
I Know... -
Native American Eagle SunMN
United States
Member #21
December 7, 2001
4,811 Posts
OfflineThe formula expression we had to used is as follows.
This expression fit the data far better.
Using the expression we curve fit it and found the values for α, β, γ and δ.
The graph next shows the bar graph and the curve fit probability function.
Continues ...
The One Over None
I Know... -
Native American Eagle SunMN
United States
Member #21
December 7, 2001
4,811 Posts
OfflineThe coefficients for the Pick 1 probability are:
Coefficients
Pick 1
α
-966.93367803712
β
30.6458275075256
γ
-0.165505462399517
δ
-0.105317939314043
These plugged in the probability function gives the following graph.
Continues ...
The One Over None
I Know... -
Quote: Originally posted by JADELottery on Jul 29, 2016
The formula expression we had to used is as follows.
This expression fit the data far better.
Using the expression we curve fit it and found the values for α, β, γ and δ.
The graph next shows the bar graph and the curve fit probability function.
Continues ...
Is this the same or similar as the wave add in you made for excel 2007?
-
Native American Eagle SunMN
United States
Member #21
December 7, 2001
4,811 Posts
OfflineUsing the coefficients and probability function we can now calculate the maximum frequency draws that it takes to draw all the numbers in a single column.
This works out to be about 22.732498 draws.
In addition, here are other points of interest in the data we sampled.
·
Draws
Minimum
10
Peak
22.732498
Mode
24
Median
27
Mean
29.283008
Maximum
140
Continues ...
The One Over None
I Know... -
Native American Eagle SunMN
United States
Member #21
December 7, 2001
4,811 Posts
OfflineQuote: Originally posted by lottologix on Jul 29, 2016
Is this the same or similar as the wave add in you made for excel 2007?
This is something new.
The One Over None
I Know... -
I have been trying to follow your research. So far it has led me to test skip ranges for single digits. this does tell when to best play the number. working with the 2007 add in I found that groups of 5 worked best. I was not having much luck with straight number runs but it did work better with box digit tracking. Are you going to make a new add in for this method? I find this very interesting and appreciate your work on this. I wonder how this formula in this thread would look when applied to digit skips?
Thank you.
-
Quote: Originally posted by JADELottery on Jul 29, 2016
Using the coefficients and probability function we can now calculate the maximum frequency draws that it takes to draw all the numbers in a single column.
This works out to be about 22.732498 draws.
In addition, here are other points of interest in the data we sampled.
·
Draws
Minimum
10
Peak
22.732498
Mode
24
Median
27
Mean
29.283008
Maximum
140
Continues ...
I'd suggest to set the maximum to 140 to lifetime of the game.
-
Native American Eagle SunMN
United States
Member #21
December 7, 2001
4,811 Posts
OfflineWe expanded this tracking to all the Pick 3 numbers and were excited to find the same formula worked for the Pick 3 overall tracking.
Below is an example of the tracking.
In this example, we can see all the numbers are picked by draw 8.
Then the cycle starts over and the next complete selection is at draw 18 or 10 draws to select all numbers.
Draw
Pick 3
Tracked # Selection
A
B
C
0
1
2
3
4
5
6
7
8
9
1
2
6
8
·
·
1
·
·
·
1
·
1
·
2
0
1
6
1
1
1
·
·
·
2
·
1
·
3
6
4
0
2
1
1
·
1
·
3
·
1
·
4
0
0
8
4
1
1
·
1
·
3
·
2
·
5
5
5
6
4
1
1
·
1
2
4
·
2
·
6
1
5
1
4
3
1
·
1
3
4
·
2
·
7
9
7
2
4
3
2
·
1
3
4
1
2
1
8
0
3
4
5
3
2
1
2
3
4
1
2
1
9
0
9
2
1
·
1
·
·
·
·
·
·
1
10
6
3
8
1
·
1
1
·
·
1
·
1
1
11
9
0
9
2
·
1
1
·
·
1
·
1
3
12
6
7
5
2
·
1
1
·
1
2
1
1
3
13
9
3
6
2
·
1
2
·
1
3
1
1
4
14
3
6
2
2
·
2
3
·
1
4
1
1
4
15
4
5
9
2
·
2
3
1
2
4
1
1
5
16
8
4
7
2
·
2
3
2
2
4
2
2
5
17
8
3
6
2
·
2
4
2
2
5
2
3
5
18
9
1
2
2
1
3
4
2
2
5
2
3
6
19
0
3
5
1
·
·
1
·
1
·
·
·
·
20
4
1
6
1
1
·
1
1
1
1
·
·
·
21
3
8
7
1
1
·
2
1
1
1
1
1
·
22
6
6
9
1
1
·
2
1
1
3
1
1
1
23
3
5
4
1
1
·
3
2
2
3
1
1
1
24
2
9
2
1
1
2
3
2
2
3
1
1
2
25
0
0
8
2
·
·
·
·
·
·
·
1
·
26
0
1
5
3
1
·
·
·
1
·
·
1
·
27
8
3
2
3
1
1
1
·
1
·
·
2
·
28
3
3
4
3
1
1
3
1
1
·
·
2
·
29
8
6
0
4
1
1
3
1
1
1
·
3
·
30
3
7
0
5
1
1
4
1
1
1
1
3
·
31
2
3
3
5
1
2
6
1
1
1
1
3
·
32
6
7
7
5
1
2
6
1
1
2
3
3
·
Continues ...
The One Over None
I Know... -
Native American Eagle SunMN
United States
Member #21
December 7, 2001
4,811 Posts
OfflineKnowing this formula works for Pick 3, we completed it for Pick 1 to Pick 5.
Below is a table of the frequency data we sampled.
One Million Tracked # Selections 0-9
Draws
Pick 1
Pick 2
Pick 3
Pick 4
Pick 5
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3995
3
0
0
0
24378
173281
4
0
0
14907
148658
301168
5
0
629
73153
220812
232686
6
0
8813
131099
199469
137767
7
0
29338
153688
147390
74468
8
0
55532
145563
98287
38103
9
0
76909
123660
62752
19275
10
344
91148
96463
38486
9677
11
1605
95825
73743
23778
4769
12
4306
93583
53976
14387
2403
13
7962
86657
38879
8607
1229
14
12670
76938
27920
5262
585
15
19266
67279
19803
3085
291
16
24277
57428
13978
1881
147
17
29919
48065
9847
1120
75
18
34560
39763
6899
659
36
19
38797
32691
5012
412
15
20
41426
26565
3379
247
15
21
43395
21883
2446
140
13
22
45105
17873
1615
82
0
23
44710
14162
1207
41
1
24
45240
11759
805
25
1
25
43409
9422
601
17
0
26
42265
7546
395
8
0
27
40858
6082
293
9
0
28
38108
4787
207
1
0
29
36519
3939
134
3
0
30
34598
3066
110
0
0
31
31914
2464
65
1
0
32
29250
1950
37
2
0
33
27122
1609
32
0
0
34
25506
1254
21
1
0
35
23658
1006
18
0
0
36
21466
854
11
0
0
37
19721
632
7
0
0
38
18198
519
5
0
0
39
16430
372
5
0
0
40
15337
335
8
0
0
41
14041
258
3
0
0
42
12429
209
1
0
0
43
11339
157
0
0
0
44
10231
126
2
0
0
45
8885
124
0
0
0
46
8500
91
1
0
0
47
7532
65
1
0
0
48
6914
50
0
0
0
49
5965
57
0
0
0
50
5333
36
0
0
0
51
4974
35
1
0
0
52
4461
25
0
0
0
53
4077
21
0
0
0
54
3847
15
0
0
0
55
3361
10
0
0
0
56
2983
14
0
0
0
57
2857
2
0
0
0
58
2536
2
0
0
0
59
2289
7
0
0
0
60
1979
2
0
0
0
61
1828
4
0
0
0
62
1573
5
0
0
0
63
1559
2
0
0
0
64
1076
0
0
0
0
65
1207
0
0
0
0
66
974
2
0
0
0
67
950
0
0
0
0
68
926
1
0
0
0
69
787
0
0
0
0
70
599
2
0
0
0
71
586
0
0
0
0
72
548
0
0
0
0
73
469
1
0
0
0
74
477
0
0
0
0
75
416
0
0
0
0
76
342
0
0
0
0
77
280
0
0
0
0
78
299
0
0
0
0
79
189
0
0
0
0
80
228
0
0
0
0
81
208
0
0
0
0
82
219
0
0
0
0
83
139
0
0
0
0
84
184
0
0
0
0
85
141
0
0
0
0
86
107
0
0
0
0
87
144
0
0
0
0
88
113
0
0
0
0
89
75
0
0
0
0
90
76
0
0
0
0
91
64
0
0
0
0
92
77
0
0
0
0
93
104
0
0
0
0
94
61
0
0
0
0
95
28
0
0
0
0
96
54
0
0
0
0
97
58
0
0
0
0
98
59
0
0
0
0
99
32
0
0
0
0
100
18
0
0
0
0
101
28
0
0
0
0
102
26
0
0
0
0
103
10
0
0
0
0
104
29
0
0
0
0
105
20
0
0
0
0
106
14
0
0
0
0
107
16
0
0
0
0
108
10
0
0
0
0
109
7
0
0
0
0
110
8
0
0
0
0
111
7
0
0
0
0
112
6
0
0
0
0
113
21
0
0
0
0
114
4
0
0
0
0
115
0
0
0
0
0
116
10
0
0
0
0
117
3
0
0
0
0
118
0
0
0
0
0
119
0
0
0
0
0
120
10
0
0
0
0
121
0
0
0
0
0
122
6
0
0
0
0
123
0
0
0
0
0
124
3
0
0
0
0
125
0
0
0
0
0
126
0
0
0
0
0
127
0
0
0
0
0
128
3
0
0
0
0
129
0
0
0
0
0
130
0
0
0
0
0
131
0
0
0
0
0
132
0
0
0
0
0
133
3
0
0
0
0
134
0
0
0
0
0
135
0
0
0
0
0
136
3
0
0
0
0
137
0
0
0
0
0
138
0
0
0
0
0
139
0
0
0
0
0
140
5
0
0
0
0
Continues ...
The One Over None
I Know... -
Native American Eagle SunMN
United States
Member #21
December 7, 2001
4,811 Posts
OfflineThe coefficients worked out to the following.
One Million Tracked # Selections 0-9
Coefficients
Pick 1
Pick 2
Pick 3
Pick 4
Pick 5
α
-966.93367803712
-288.229657414759
-112.848634704551
-60.9196072763659
-45.5856415845385
β
30.6458275075256
26.4269626065139
12.9474585211997
8.68322021541142
11.5743576972091
γ
-0.165505462399517
-0.00183622361668888
1.05332367290803
1.76921742869347
1.45813918513947
δ
-0.105317939314043
-0.212279140684865
-0.354411199971372
-0.522830929386791
-0.679029762719017
Continues ...
The One Over None
I Know... -
Native American Eagle SunMN
United States
Member #21
December 7, 2001
4,811 Posts
OfflineHere are the points of interest for Pick 1 to Pick 5.
·
Draws
Pick 1
Pick 2
Pick 3
Pick 4
Pick 5
Minimum
10
5
4
3
2
Peak
22.732498
11.031043
7.202824
5.261479
4.031870
Mode
24
11
7
5
4
Median
27
13
8
6
5
Mean
29.283008
14.131397
9.047672
6.483503
4.933889
Maximum
140
73
51
34
24
Continues ...
The One Over None
I Know... -
Native American Eagle SunMN
United States
Member #21
December 7, 2001
4,811 Posts
OfflineThis formula is not restricted to just Daily Pick games.
We applied it to Mega Millions and Powerball.
Below is a tracked # selection data sample run for both.
One Million Tracked # Selections
Draws
Mega Millions
Powerball
P5
MM
P5
PB
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
4
0
0
0
0
5
0
0
0
0
6
0
0
0
0
7
0
0
0
0
8
0
0
0
0
9
0
0
0
0
10
0
0
0
0
11
0
0
0
0
12
0
0
0
0
13
0
0
0
0
14
0
0
0
0
15
0
6
0
0
16
0
21
0
0
17
0
53
0
0
18
0
168
0
0
19
0
470
0
0
20
0
982
0
0
21
0
1671
0
0
22
0
2511
0
0
23
0
4031
0
0
24
0
5264
0
0
25
0
7190
0
0
26
0
8643
3
0
27
0
11155
8
0
28
0
12608
11
0
29
0
15605
32
0
30
0
17408
61
0
31
8
19214
106
0
32
8
20884
245
0
33
25
22715
425
0
34
88
23963
747
0
35
134
25091
1133
12
36
285
26388
1786
0
37
366
27319
2575
36
38
718
27779
3702
24
39
1006
27975
4729
70
40
1581
28542
6435
146
41
2064
28161
7556
127
42
2869
28541
9333
321
43
3732
28112
11083
302
44
4865
27377
13536
442
45
6270
27127
15633
537
46
7434
25827
16868
1030
47
8842
25596
18930
913
48
10051
24616
21102
1338
49
12102
23820
22873
1356
50
13269
22724
23745
1891
51
15383
21957
25158
1978
52
16758
21502
26565
2566
53
18215
20001
27424
2995
54
20223
19208
27559
3253
55
20613
17998
28846
3931
56
22067
17909
28569
4051
57
23735
17046
28395
5022
58
24333
15877
28384
5282
59
24971
15429
27849
5979
60
25600
13804
26908
6655
61
26338
13253
27360
7002
62
25844
12853
26291
7782
63
26228
11885
25557
8786
64
26364
11389
24957
9426
65
25300
10759
24921
9427
66
25959
10012
23606
10125
67
25278
9633
21904
10666
68
25136
8838
22117
11952
69
24567
8398
20746
11962
70
24367
8143
19513
12203
71
23037
7349
18453
13058
72
22396
6791
18200
13282
73
21372
6413
16654
13705
74
20769
6228
16193
13050
75
19621
5888
15325
14416
76
19264
5298
14519
14426
77
17935
5123
13719
14956
78
17884
4603
12327
15210
79
16991
4450
12096
15250
80
15732
4117
10988
15151
81
15975
3858
10298
15340
82
14931
3754
9727
15700
83
14226
3311
8978
15412
84
12918
3115
8675
15023
85
12416
2772
8106
15243
86
11848
2732
7546
15816
87
11129
2532
7212
15356
88
9995
2440
6760
15153
89
9565
2329
6324
15671
90
9433
2022
5665
14222
91
8685
1988
5360
14353
92
8218
1776
4952
14211
93
7697
1704
4703
14911
94
7062
1496
4690
14660
95
6969
1548
4195
13699
96
6370
1311
3707
13853
97
5987
1413
3382
14235
98
5797
1246
3186
13164
99
5257
1212
3193
13521
100
4945
1039
2844
12957
101
4526
1019
2460
12246
102
4364
816
2358
12244
103
4094
839
2268
11867
104
3910
909
2212
12305
105
3768
730
1983
11564
106
3467
703
1842
10381
107
3026
593
1728
11491
108
3069
590
1727
11378
109
2771
609
1401
10832
110
2482
509
1390
10758
111
2252
455
1268
9948
112
1951
450
1072
9738
113
2022
439
1190
9189
114
2089
414
1063
9481
115
2115
441
859
8957
116
1844
350
913
8550
117
1715
263
741
8031
118
1524
331
759
8612
119
1491
320
673
7686
120
1272
233
628
7515
121
1216
266
549
7193
122
1230
279
491
7464
123
1201
240
572
6885
124
1024
183
483
6659
125
1012
162
425
6443
126
849
204
381
6716
127
832
121
401
5940
128
787
129
327
5677
129
628
139
329
5766
130
724
119
287
5523
131
707
109
256
5600
132
588
138
295
5587
133
466
100
230
5199
134
501
85
176
4683
135
425
147
324
4842
136
389
91
129
4488
137
429
60
142
4078
138
394
110
191
4237
139
331
109
137
4063
140
313
92
131
3840
141
266
58
177
3827
142
250
68
70
3524
143
292
47
87
3441
144
306
32
118
3258
145
262
24
92
3446
146
229
31
103
3044
147
152
41
134
3051
148
233
28
106
2744
149
203
31
77
2585
150
204
13
103
2792
151
170
37
71
2739
152
164
21
72
2628
153
163
25
43
2037
154
155
45
81
2307
155
131
22
45
2511
156
98
10
22
2286
157
48
13
33
2255
158
96
21
36
1909
159
94
17
44
1965
160
84
20
30
1939
161
66
25
26
1702
162
80
5
19
1677
163
71
16
30
1575
164
80
13
27
1482
165
62
12
11
1424
166
50
4
28
1646
167
76
13
22
1490
168
44
0
10
1326
169
67
4
4
1340
170
40
2
17
1303
171
25
16
17
1276
172
27
0
23
1284
173
42
4
6
1140
174
21
0
7
1192
175
36
4
6
1026
176
24
0
17
928
177
35
2
7
984
178
30
4
6
918
179
33
6
8
831
180
23
15
22
777
181
21
4
9
696
182
5
4
12
747
183
16
2
0
809
184
12
0
7
867
185
20
0
10
947
186
28
4
0
670
187
7
0
8
609
188
4
2
4
507
189
6
3
0
770
190
18
9
4
436
191
7
4
8
523
192
0
0
0
541
193
4
10
4
504
194
4
0
5
473
195
16
0
0
589
196
5
0
0
353
197
0
0
0
567
198
6
0
3
546
199
0
0
0
321
200
3
0
5
459
201
8
2
4
322
202
0
0
0
237
203
0
0
0
318
204
4
0
3
243
205
0
0
0
366
206
4
0
0
345
207
4
0
0
309
208
4
0
0
375
209
4
0
3
252
210
3
0
0
365
211
0
0
0
159
212
5
0
0
259
213
0
0
0
255
214
8
0
0
176
215
10
0
0
207
216
0
0
0
208
217
0
0
0
232
218
0
0
0
326
219
0
0
0
191
220
0
0
0
156
221
0
0
0
118
222
0
0
0
252
223
4
0
0
169
224
0
0
0
156
225
0
0
0
237
226
0
0
0
179
227
0
0
0
144
228
5
0
0
69
229
0
0
0
196
230
0
0
0
94
231
0
0
0
117
232
0
0
0
82
233
0
0
0
108
234
0
0
0
61
235
5
0
0
84
236
0
0
0
164
237
0
0
0
149
238
0
0
0
120
239
0
0
0
135
240
0
0
0
143
241
0
0
0
127
242
0
0
0
25
243
0
0
0
83
244
0
0
0
47
245
0
2
0
58
246
0
0
0
58
247
0
0
0
71
248
0
0
0
109
249
0
0
0
59
250
0
0
0
24
251
0
0
0
24
252
0
0
0
33
253
0
0
0
49
254
0
0
0
48
255
0
0
0
49
256
0
0
0
38
257
0
0
0
35
258
0
0
0
35
259
0
0
0
84
260
0
0
0
48
261
0
0
0
37
262
0
0
0
37
263
0
0
0
12
264
0
0
0
92
265
0
0
0
58
266
0
0
0
24
267
0
0
0
23
268
0
0
0
35
269
0
0
0
23
270
0
0
0
12
271
0
0
0
23
272
0
0
0
0
273
0
0
0
24
274
0
0
0
11
275
0
0
0
12
276
0
0
0
35
277
0
0
0
23
278
0
0
0
12
279
0
0
0
23
280
0
0
0
12
281
0
0
0
21
282
0
0
0
0
283
0
0
0
0
284
0
0
0
25
285
0
0
0
12
286
0
0
0
37
287
0
0
0
0
288
0
0
0
23
289
0
0
0
45
290
0
0
0
12
291
0
0
0
0
292
0
0
0
25
293
0
0
0
24
294
0
0
0
12
295
0
0
0
0
296
0
0
0
12
297
0
0
0
12
298
0
0
0
0
299
0
0
0
11
300
0
0
0
11
301
0
0
0
0
302
0
0
0
0
303
0
0
0
0
304
0
0
0
25
305
0
0
0
0
306
0
0
0
11
307
0
0
0
12
308
0
0
0
11
309
0
0
0
0
310
0
0
0
24
311
0
0
0
12
312
0
0
0
0
313
0
0
0
0
314
0
0
0
13
315
0
0
0
12
316
0
0
0
0
317
0
0
0
0
318
0
0
0
13
319
0
0
0
0
320
0
0
0
0
321
0
0
0
0
322
0
0
0
0
323
0
0
0
0
324
0
0
0
0
325
0
0
0
0
326
0
0
0
0
327
0
0
0
12
328
0
0
0
13
329
0
0
0
0
330
0
0
0
0
331
0
0
0
0
332
0
0
0
0
333
0
0
0
0
334
0
0
0
0
335
0
0
0
12
336
0
0
0
0
337
0
0
0
0
338
0
0
0
11
339
0
0
0
12
340
0
0
0
0
341
0
0
0
0
342
0
0
0
0
343
0
0
0
0
344
0
0
0
0
345
0
0
0
0
346
0
0
0
0
347
0
0
0
0
348
0
0
0
0
349
0
0
0
0
350
0
0
0
12
351
0
0
0
0
352
0
0
0
0
353
0
0
0
0
354
0
0
0
0
355
0
0
0
0
356
0
0
0
0
357
0
0
0
0
358
0
0
0
0
359
0
0
0
0
360
0
0
0
0
361
0
0
0
0
362
0
0
0
0
363
0
0
0
0
364
0
0
0
0
365
0
0
0
0
366
0
0
0
0
367
0
0
0
0
368
0
0
0
0
369
0
0
0
0
370
0
0
0
0
371
0
0
0
0
372
0
0
0
0
373
0
0
0
0
374
0
0
0
0
375
0
0
0
0
376
0
0
0
0
377
0
0
0
0
378
0
0
0
12
Continues ...
The One Over None
I Know...