N <- 1059
n_eth <- 4
n_age <- 3
height <- 
c(74, 66, 64, 63, 64, 62, 73, 72, 72, 68, 68, 65, 66, 68, 68, 70, 64,
73, 62, 63, 67, 66, 72, 63, 64, 72, 77, 64, 64, 72, 68, 64, 67, 65, 64, 65, 65,
67, 68, 60, 65, 62, 72, 67, 70, 68, 71, 71, 73, 68, 66, 69, 63, 62, 64, 67, 71,
60, 66, 66, 65, 70, 62, 72, 67, 68, 70, 62, 63, 66, 70, 68, 70, 66, 68, 70, 61,
64, 69, 64, 67, 69, 67, 68, 63, 71, 64, 68, 68, 66, 77, 67, 62, 67, 61, 64, 62,
63, 68, 64, 72, 64, 61, 74, 70, 71, 63, 64, 62, 70, 71, 71, 67, 64, 67, 62, 68,
62, 68, 74, 68, 62, 66, 68, 60, 68, 72, 66, 68, 68, 69, 64, 65, 61, 72, 66, 68,
70, 71, 71, 68, 60, 63, 68, 64, 68, 61, 68, 66, 70, 71, 65, 66, 70, 66, 61, 72,
74, 67, 66, 62, 72, 65, 60, 62, 66, 64, 65, 73, 69, 64, 67, 62, 63, 67, 68, 72,
70, 70, 67, 63, 66, 66, 71, 67, 76, 69, 65, 62, 62, 62, 61, 65, 72, 72, 64, 71,
72, 66, 65, 62, 66, 67, 64, 63, 67, 68, 64, 66, 65, 65, 72, 68, 74, 63, 64, 68,
67, 67, 73, 65, 77, 68, 62, 64, 67, 70, 62, 63, 62, 69, 64, 69, 59, 66, 62, 75,
63, 65, 70, 68, 69, 72, 64, 63, 73, 75, 65, 66, 66, 64, 66, 64, 63, 73, 72, 72,
64, 64, 68, 69, 60, 76, 72, 62, 62, 71, 74, 65, 63, 67, 63, 65, 65, 63, 70, 68,
67, 65, 69, 68, 66, 71, 64, 74, 62, 65, 66, 67, 73, 76, 63, 63, 70, 71, 65, 63,
64, 64, 67, 66, 68, 65, 67, 73, 63, 71, 73, 65, 59, 70, 72, 66, 70, 69, 68, 74,
67, 64, 67, 70, 64, 62, 68, 72, 63, 69, 64, 71, 64, 61, 68, 68, 64, 66, 62, 65,
66, 72, 70, 62, 71, 70, 64, 63, 65, 71, 62, 68, 76, 64, 66, 63, 63, 70, 68, 70,
69, 63, 65, 69, 68, 66, 65, 70, 70, 66, 68, 68, 70, 65, 64, 65, 77, 70, 64, 64,
64, 64, 63, 58, 62, 64, 64, 62, 64, 66, 69, 64, 71, 68, 68, 62, 63, 69, 67, 64,
70, 69, 69, 69, 60, 66, 67, 66, 70, 64, 60, 68, 73, 72, 64, 67, 71, 73, 70, 70,
71, 66, 75, 60, 72, 75, 60, 73, 65, 67, 69, 64, 70, 68, 62, 64, 68, 64, 73, 73,
69, 68, 71, 66, 66, 70, 66, 63, 75, 67, 63, 69, 71, 62, 65, 72, 65, 63, 64, 72,
64, 70, 65, 64, 64, 67, 73, 73, 65, 64, 67, 67, 74, 63, 74, 74, 63, 62, 62, 67,
69, 73, 63, 67, 69, 71, 72, 64, 64, 74, 62, 65, 60, 69, 61, 65, 66, 70, 72, 64,
71, 73, 64, 68, 64, 66, 67, 64, 64, 62, 69, 63, 72, 75, 70, 69, 64, 72, 69, 71,
59, 68, 77, 70, 69, 63, 73, 66, 72, 72, 69, 67, 66, 67, 68, 65, 62, 69, 70, 66,
66, 66, 72, 69, 66, 69, 60, 65, 62, 67, 67, 68, 66, 74, 65, 68, 66, 65, 62, 73,
62, 70, 58, 68, 67, 70, 63, 66, 65, 61, 61, 67, 73, 71, 64, 67, 62, 67, 69, 66,
66, 66, 66, 72, 64, 65, 72, 71, 64, 64, 67, 75, 66, 67, 71, 68, 67, 71, 63, 61,
65, 67, 65, 66, 67, 74, 74, 66, 69, 66, 74, 72, 66, 67, 65, 65, 68, 64, 64, 63,
69, 67, 60, 62, 72, 67, 66, 66, 60, 65, 72, 64, 64, 64, 66, 73, 74, 65, 63, 63,
66, 70, 66, 63, 63, 69, 73, 68, 64, 63, 70, 64, 66, 72, 64, 67, 66, 71, 71, 71,
74, 75, 72, 66, 65, 72, 60, 64, 65, 65, 62, 73, 68, 66, 71, 73, 61, 63, 64, 67,
63, 73, 66, 70, 68, 67, 74, 64, 60, 59, 75, 64, 71, 63, 67, 69, 70, 66, 74, 65,
64, 68, 66, 69, 60, 75, 64, 63, 64, 63, 67, 66, 65, 63, 66, 64, 71, 71, 72, 70,
74, 68, 74, 75, 68, 63, 72, 64, 63, 66, 61, 73, 65, 62, 68, 68, 63, 63, 68, 64,
70, 70, 72, 69, 63, 63, 63, 73, 69, 70, 65, 72, 62, 72, 73, 68, 66, 60, 65, 63,
64, 71, 67, 63, 65, 63, 65, 74, 67, 68, 65, 64, 68, 65, 72, 66, 64, 72, 64, 67,
68, 64, 66, 65, 70, 70, 66, 66, 74, 62, 66, 65, 71, 66, 67, 61, 66, 72, 69, 64,
63, 60, 70, 73, 65, 64, 72, 67, 69, 71, 66, 63, 71, 72, 68, 72, 66, 66, 65, 71,
74, 70, 64, 69, 63, 68, 73, 63, 71, 65, 65, 71, 70, 68, 66, 64, 66, 70, 64, 71,
64, 63, 66, 68, 62, 69, 64, 64, 69, 74, 68, 67, 72, 73, 64, 68, 63, 71, 64, 60,
66, 59, 63, 66, 65, 64, 66, 66, 73, 72, 74, 65, 71, 68, 70, 64, 59, 68, 68, 69,
69, 75, 69, 72, 68, 72, 63, 69, 63, 72, 65, 73, 69, 69, 61, 73, 67, 63, 62, 65,
72, 67, 65, 72, 64, 68, 68, 76, 63, 68, 72, 64, 68, 61, 67, 63, 60, 74, 62, 72,
65, 62, 71, 71, 70, 67, 62, 63, 61, 72, 63, 66, 64, 66, 68, 60, 61, 64, 66, 66,
67, 68, 66, 69, 69, 71, 74, 69, 72, 64, 72, 63, 70, 66, 62, 64, 69, 64, 67, 72,
65, 63, 70, 64, 68, 66, 70, 66, 64, 70, 74, 66, 62, 66, 62, 69, 68, 72, 64, 72,
74, 66, 68, 62, 71, 63, 71, 72, 72, 68, 64, 70, 66, 67, 68, 64, 65, 70, 71, 62,
71, 74, 64, 70, 64, 70, 74, 74, 66, 71, 69, 60, 64, 64, 72, 69, 67, 65, 68, 74,
65, 71, 64, 69, 64, 72, 63, 65, 72, 65, 64, 71, 62, 66, 64, 68, 66, 66, 66, 66,
63, 68, 70, 63, 70, 72, 75, 62, 68, 68, 70, 73, 62, 64, 73, 66, 70, 70, 72, 64,
72, 68)
earn <- 
c(50000, 60000, 30000, 51000, 9000, 29000, 32000, 2000, 27000, 30000,
12000, 12000, 22000, 17000, 40000, 44000, 7000, 53000, 5000, 14000, 5500, 40000,
34000, 10000, 27000, 50000, 41000, 15000, 25000, 75000, 27000, 12000, 30000,
21000, 27000, 25000, 24000, 32000, 10000, 11000, 18700, 20000, 3500, 13000,
21000, 34000, 17000, 35000, 4000, 14000, 10000, 25000, 16000, 16000, 16500,
3840, 22000, 200, 26000, 2500, 17000, 8000, 10000, 15000, 2400, 30000, 30000,
10000, 5000, 12000, 20000, 20000, 20000, 1200, 700, 20000, 10000, 40000, 60000,
16040, 15000, 10000, 33000, 18000, 15000, 21000, 21000, 37000, 38000, 17000,
32000, 27500, 16500, 25000, 27000, 5000, 70000, 5000, 5000, 20000, 4000, 60000,
5000, 30000, 70000, 50000, 44000, 30000, 10000, 23000, 45000, 15000, 17000,
30000, 27500, 18000, 43000, 32000, 10000, 60000, 21000, 2400, 1000, 27000, 6600,
16000, 90000, 8000, 20000, 15000, 12000, 24000, 20000, 19000, 10000, 40000,
25000, 25000, 25000, 19000, 44000, 15000, 17000, 24000, 23000, 65000, 7000,
40000, 15000, 20000, 20000, 20000, 25000, 49000, 11000, 16000, 35000, 125000,
23000, 17000, 27000, 70000, 35000, 10000, 35000, 15000, 12000, 8000, 35000,
45000, 15000, 24000, 25000, 25000, 20000, 24000, 44000, 69000, 62000, 32000,
20000, 32000, 25000, 170000, 35000, 40000, 33000, 18000, 30000, 26000, 5000,
17000, 32000, 15000, 50000, 8000, 40000, 40000, 32750, 36000, 6000, 12000,
60000, 40000, 43000, 45000, 6000, 20000, 17000, 2000, 65000, 50000, 11000,
35000, 27000, 3500, 42000, 20000, 15000, 10000, 17000, 28000, 15000, 20000,
20000, 10500, 13000, 10000, 3000, 24000, 17000, 11000, 32000, 17000, 3000, 2100,
3192, 17000, 30000, 15000, 24000, 50000, 50000, 20000, 30000, 22000, 27000,
4000, 17500, 16500, 28000, 52000, 15000, 19000, 27000, 15000, 15000, 14500,
24000, 18000, 4000, 700, 27000, 12000, 22000, 30000, 35000, 20000, 32000, 6000,
12000, 10000, 1000, 16000, 25000, 25000, 32000, 35000, 6000, 80000, 20000, 1000,
28000, 26000, 27000, 18000, 2000, 6000, 25000, 12000, 12000, 4000, 26000, 23000,
21000, 25000, 4000, 23900, 35000, 26000, 25000, 23500, 12000, 15000, 3000,
15000, 175000, 1000, 10000, 20000, 35000, 40000, 50000, 1e+05, 35000, 24000,
35000, 30000, 5000, 148000, 30000, 6500, 3000, 40000, 30000, 14000, 15000,
26000, 8000, 24000, 10000, 12000, 50000, 23000, 40000, 6000, 5000, 110000,
41000, 21000, 4000, 25000, 30000, 14000, 6000, 14000, 43000, 25000, 65000,
16000, 20000, 12000, 8000, 16000, 19000, 21000, 43000, 35000, 21000, 5800,
17000, 24000, 11000, 10000, 40000, 40000, 24000, 24000, 20000, 60000, 11000,
5000, 27000, 89000, 40000, 15000, 1000, 22000, 12000, 22000, 40000, 40000,
35000, 7000, 14000, 15000, 6000, 11000, 10000, 20000, 38000, 29000, 20000, 8000,
36000, 1500, 42000, 25000, 13000, 30000, 7000, 31000, 15000, 50000, 5000, 600,
14000, 40000, 24000, 22000, 20000, 20112, 41000, 13000, 60000, 24000, 38000,
3000, 13000, 5000, 20000, 22000, 28000, 22000, 30000, 30000, 30000, 26000,
22000, 25000, 11000, 13000, 10000, 12000, 7000, 57000, 36000, 29000, 8000, 3000,
20000, 33000, 16000, 8000, 32000, 14500, 13000, 7000, 12000, 19000, 9000, 20000,
55000, 10000, 13000, 20000, 30000, 12000, 26000, 12500, 8000, 15000, 65000,
25000, 8000, 15000, 12000, 35000, 40000, 29000, 15000, 20000, 3000, 1000, 8000,
5000, 25000, 20000, 30000, 12000, 10000, 16000, 45000, 40000, 19000, 17600,
30000, 18000, 25000, 6000, 70000, 15000, 25000, 35000, 18000, 28000, 15000,
22000, 35000, 18000, 35000, 16400, 22000, 30000, 17000, 25000, 10000, 40000,
12500, 35000, 105000, 1e+05, 21000, 10000, 33000, 26000, 18000, 15000, 5000,
60000, 28000, 42000, 2000, 20000, 28000, 10000, 31000, 17000, 16000, 35000,
3000, 16000, 35000, 27000, 25000, 40000, 45000, 14000, 25000, 40000, 34000,
40000, 35000, 12000, 30000, 23000, 2000, 20000, 10000, 60000, 12000, 25000,
8000, 2000, 18600, 20000, 1e+05, 50000, 27000, 1000, 18000, 17000, 14000, 33000,
23000, 10000, 22000, 13000, 33000, 36000, 10000, 6000, 12000, 10000, 21000,
26000, 22000, 23000, 20000, 10000, 7000, 15000, 26000, 10000, 3000, 27000,
28000, 15000, 55000, 20000, 8500, 30000, 20000, 25000, 3000, 16000, 10000,
15000, 28000, 31500, 95000, 38000, 30000, 35900, 12000, 10000, 45000, 40000,
21500, 14000, 38000, 1000, 15000, 24000, 4500, 18000, 14000, 10000, 9500, 6000,
2500, 40000, 25000, 28000, 33000, 4000, 4100, 32000, 13000, 8000, 17000, 18000,
12000, 7000, 1200, 14000, 17000, 30000, 25000, 22000, 15000, 20000, 9000, 17000,
1800, 18000, 25000, 20000, 75000, 3500, 30000, 1000, 9000, 11000, 12000, 30000,
19000, 9000, 30000, 9000, 15000, 8000, 33000, 12000, 18000, 30000, 12500, 10000,
21000, 21000, 5000, 22000, 30000, 123000, 8000, 2000, 7600, 10000, 35000, 15000,
4000, 16000, 200, 23000, 16000, 6000, 600, 28000, 15000, 15000, 25000, 15000,
40000, 30000, 5000, 35000, 16000, 28000, 20000, 21000, 17000, 24000, 40000,
8000, 19000, 5000, 24000, 5000, 33000, 24000, 6000, 90000, 57000, 13800, 30000,
15000, 31000, 33000, 30000, 12000, 5000, 21000, 28000, 12000, 19000, 6000, 5300,
15000, 17000, 1700, 5400, 10000, 35000, 28000, 42000, 45000, 55000, 36000,
25000, 19000, 38000, 15000, 96000, 11000, 9000, 5000, 50000, 6000, 1e+05, 16500,
32000, 30000, 10000, 15000, 26000, 17000, 22000, 10000, 50000, 20000, 400,
16000, 14000, 5000, 40000, 5000, 25000, 12000, 58000, 18000, 1000, 21000, 11000,
13000, 25000, 600, 25000, 36000, 15000, 3500, 19005, 62000, 25000, 50000, 40000,
26000, 22000, 21000, 30000, 27000, 4000, 45000, 18000, 6000, 14000, 35000,
15000, 12000, 1000, 32000, 1500, 3000, 35000, 70000, 21000, 50000, 15000, 9000,
10000, 30000, 16000, 20000, 1e+05, 10000, 35000, 7000, 8000, 11000, 25000,
25000, 30000, 48000, 17000, 26000, 10000, 60000, 22000, 24000, 20000, 7000,
30000, 23000, 20000, 3000, 30000, 12000, 40000, 15000, 36000, 10000, 13000,
10000, 30000, 23000, 28000, 20000, 25000, 25000, 18000, 16000, 45000, 12000,
2000, 10000, 14000, 15000, 10000, 1200, 15000, 10000, 2000, 4000, 10000, 1500,
18000, 4000, 28000, 10000, 3000, 12000, 19000, 36000, 7000, 35000, 40000, 15000,
8000, 25000, 28000, 22000, 21500, 3000, 23000, 16000, 15000, 53000, 26000, 4000,
10000, 43000, 17000, 4000, 50000, 55000, 28000, 5000, 18000, 21000, 12000,
33000, 50000, 16000, 35000, 25000, 20000, 18000, 25000, 40000, 14000, 12000,
25000, 38000, 14000, 15000, 17000, 18000, 70000, 30000, 8000, 30000, 27000,
47000, 12000, 24000, 13000, 80000, 5000, 25000, 28000, 8000, 10000, 9000, 20000,
20000, 28000, 265, 26000, 27000, 14000, 32000, 10000, 7000, 28000, 60000, 12000,
15000, 26000, 26000, 18720, 80000, 48000, 18000, 35000, 5000, 9000, 30000,
80000, 35000, 12000, 2e+05, 4000, 2000, 2000, 15000, 1500, 28000, 9000, 60000,
1200, 1400, 7000, 21000, 44000, 29000, 3000, 12000, 20000, 37000, 8000, 35000,
25000, 18000, 30000, 12000, 18000, 20000, 31000, 6000, 12000, 13000, 26000,
15000, 30000, 2000, 5000, 53000, 2000, 25000, 5000, 21000, 17000, 12000, 42000,
21000, 25000, 3000, 4000, 20000, 52000, 60000, 15000, 90000, 2000, 16000, 24000,
15000, 42000, 10000, 17000, 30000, 32000, 36000, 10000, 20000, 24000, 17000,
23000, 25000, 50000, 20000, 30000, 7000, 30000, 3000, 20000, 40000, 16000,
11000, 16000, 18000, 12000, 4000, 60000, 43000, 31000, 50000, 27000, 30000,
12000, 20000, 25000, 3000, 110000, 58000, 10000, 19000, 8000, 60000, 6000)
y <- 
c(10.8197782844103, 11.0020998412042, 10.3089526606443, 10.8395809117065,
9.10497985631836, 10.2750511089686, 10.3734911817819, 7.60090245954208,
10.2035921449865, 10.3089526606443, 9.39266192877014, 9.39266192877014,
9.99879773234045, 9.74096862303835, 10.5966347330961, 10.6919449129004,
8.85366542803745, 10.8780471925343, 8.51719319141624, 9.5468126085974,
8.61250337122056, 10.5966347330961, 10.4341158035983, 9.21034037197618,
10.2035921449865, 10.8197782844103, 10.6213273456864, 9.61580548008435,
10.1266311038503, 11.2252433925184, 10.2035921449865, 9.39266192877014,
10.3089526606443, 9.95227771670556, 10.2035921449865, 10.1266311038503,
10.0858091093301, 10.3734911817819, 9.21034037197618, 9.30565055178051,
9.83627880284268, 9.90348755253613, 8.1605182474775, 9.47270463644367,
9.95227771670556, 10.4341158035983, 9.74096862303835, 10.4631033404715,
8.29404964010203, 9.5468126085974, 9.21034037197618, 10.1266311038503,
9.68034400122192, 9.68034400122192, 9.71111565988867, 8.25322764558177,
9.99879773234045, 5.29831736654804, 10.1658518170036, 7.82404601085629,
9.74096862303835, 8.98719682066197, 9.21034037197618, 9.61580548008435,
7.78322401633604, 10.3089526606443, 10.3089526606443, 9.21034037197618,
8.51719319141624, 9.39266192877014, 9.90348755253613, 9.90348755253613,
9.90348755253613, 7.09007683577609, 6.5510803350434, 9.90348755253613,
9.21034037197618, 10.5966347330961, 11.0020998412042, 9.68284088142051,
9.61580548008435, 9.21034037197618, 10.4042628404486, 9.7981270368783,
9.61580548008435, 9.95227771670556, 9.95227771670556, 10.5186731916264,
10.5453414387085, 9.74096862303835, 10.3734911817819, 10.2219412836547,
9.71111565988867, 10.1266311038503, 10.2035921449865, 8.51719319141624,
11.1562505210315, 8.51719319141624, 8.51719319141624, 9.90348755253613,
8.29404964010203, 11.0020998412042, 8.51719319141624, 10.3089526606443,
11.1562505210315, 10.8197782844103, 10.6919449129004, 10.3089526606443,
9.21034037197618, 10.0432494949113, 10.7144177687525, 9.61580548008435,
9.74096862303835, 10.3089526606443, 10.2219412836547, 9.7981270368783,
10.6689553946757, 10.3734911817819, 9.21034037197618, 11.0020998412042,
9.95227771670556, 7.78322401633604, 6.90775527898214, 10.2035921449865,
8.79482492801452, 9.68034400122192, 11.4075649493124, 8.98719682066197,
9.90348755253613, 9.61580548008435, 9.39266192877014, 10.0858091093301,
9.90348755253613, 9.85219425814858, 9.21034037197618, 10.5966347330961,
10.1266311038503, 10.1266311038503, 10.1266311038503, 9.85219425814858,
10.6919449129004, 9.61580548008435, 9.74096862303835, 10.0858091093301,
10.0432494949113, 11.0821425488778, 8.85366542803745, 10.5966347330961,
9.61580548008435, 9.90348755253613, 9.90348755253613, 9.90348755253613,
10.1266311038503, 10.7995755770928, 9.30565055178051, 9.68034400122192,
10.4631033404715, 11.7360690162844, 10.0432494949113, 9.74096862303835,
10.2035921449865, 11.1562505210315, 10.4631033404715, 9.21034037197618,
10.4631033404715, 9.61580548008435, 9.39266192877014, 8.98719682066197,
10.4631033404715, 10.7144177687525, 9.61580548008435, 10.0858091093301,
10.1266311038503, 10.1266311038503, 9.90348755253613, 10.0858091093301,
10.6919449129004, 11.1418617835794, 11.0348896640272, 10.3734911817819,
9.90348755253613, 10.3734911817819, 10.1266311038503, 12.0435537160324,
10.4631033404715, 10.5966347330961, 10.4042628404486, 9.7981270368783,
10.3089526606443, 10.1658518170036, 8.51719319141624, 9.74096862303835,
10.3734911817819, 9.61580548008435, 10.8197782844103, 8.98719682066197,
10.5966347330961, 10.5966347330961, 10.3966582410634, 10.4912742174382,
8.69951474821019, 9.39266192877014, 11.0020998412042, 10.5966347330961,
10.6689553946757, 10.7144177687525, 8.69951474821019, 9.90348755253613,
9.74096862303835, 7.60090245954208, 11.0821425488778, 10.8197782844103,
9.30565055178051, 10.4631033404715, 10.2035921449865, 8.1605182474775,
10.6454248972655, 9.90348755253613, 9.61580548008435, 9.21034037197618,
9.74096862303835, 10.2399597891573, 9.61580548008435, 9.90348755253613,
9.90348755253613, 9.25913053614561, 9.47270463644367, 9.21034037197618,
8.00636756765025, 10.0858091093301, 9.74096862303835, 9.30565055178051,
10.3734911817819, 9.74096862303835, 8.00636756765025, 7.64969262371151,
8.0684029585697, 9.74096862303835, 10.3089526606443, 9.61580548008435,
10.0858091093301, 10.8197782844103, 10.8197782844103, 9.90348755253613,
10.3089526606443, 9.99879773234045, 10.2035921449865, 8.29404964010203,
9.76995615991161, 9.71111565988867, 10.2399597891573, 10.8589989975636,
9.61580548008435, 9.85219425814858, 10.2035921449865, 9.61580548008435,
9.61580548008435, 9.58190392840867, 10.0858091093301, 9.7981270368783,
8.29404964010203, 6.5510803350434, 10.2035921449865, 9.39266192877014,
9.99879773234045, 10.3089526606443, 10.4631033404715, 9.90348755253613,
10.3734911817819, 8.69951474821019, 9.39266192877014, 9.21034037197618,
6.90775527898214, 9.68034400122192, 10.1266311038503, 10.1266311038503,
10.3734911817819, 10.4631033404715, 8.69951474821019, 11.289781913656,
9.90348755253613, 6.90775527898214, 10.2399597891573, 10.1658518170036,
10.2035921449865, 9.7981270368783, 7.60090245954208, 8.69951474821019,
10.1266311038503, 9.39266192877014, 9.39266192877014, 8.29404964010203,
10.1658518170036, 10.0432494949113, 9.95227771670556, 10.1266311038503,
8.29404964010203, 10.0816337379196, 10.4631033404715, 10.1658518170036,
10.1266311038503, 10.0647557001323, 9.39266192877014, 9.61580548008435,
8.00636756765025, 9.61580548008435, 12.0725412529057, 6.90775527898214,
9.21034037197618, 9.90348755253613, 10.4631033404715, 10.5966347330961,
10.8197782844103, 11.5129254649702, 10.4631033404715, 10.0858091093301,
10.4631033404715, 10.3089526606443, 8.51719319141624, 11.9049675527463,
10.3089526606443, 8.77955745588373, 8.00636756765025, 10.5966347330961,
10.3089526606443, 9.5468126085974, 9.61580548008435, 10.1658518170036,
8.98719682066197, 10.0858091093301, 9.21034037197618, 9.39266192877014,
10.8197782844103, 10.0432494949113, 10.5966347330961, 8.69951474821019,
8.51719319141624, 11.6082356447746, 10.6213273456864, 9.95227771670556,
8.29404964010203, 10.1266311038503, 10.3089526606443, 9.5468126085974,
8.69951474821019, 9.5468126085974, 10.6689553946757, 10.1266311038503,
11.0821425488778, 9.68034400122192, 9.90348755253613, 9.39266192877014,
8.98719682066197, 9.68034400122192, 9.85219425814858, 9.95227771670556,
10.6689553946757, 10.4631033404715, 9.95227771670556, 8.66561319653451,
9.74096862303835, 10.0858091093301, 9.30565055178051, 9.21034037197618,
10.5966347330961, 10.5966347330961, 10.0858091093301, 10.0858091093301,
9.90348755253613, 11.0020998412042, 9.30565055178051, 8.51719319141624,
10.2035921449865, 11.3963916487143, 10.5966347330961, 9.61580548008435,
6.90775527898214, 9.99879773234045, 9.39266192877014, 9.99879773234045,
10.5966347330961, 10.5966347330961, 10.4631033404715, 8.85366542803745,
9.5468126085974, 9.61580548008435, 8.69951474821019, 9.30565055178051,
9.21034037197618, 9.90348755253613, 10.5453414387085, 10.2750511089686,
9.90348755253613, 8.98719682066197, 10.4912742174382, 7.3132203870903,
10.6454248972655, 10.1266311038503, 9.47270463644367, 10.3089526606443,
8.85366542803745, 10.3417424834673, 9.61580548008435, 10.8197782844103,
8.51719319141624, 6.39692965521615, 9.5468126085974, 10.5966347330961,
10.0858091093301, 9.99879773234045, 9.90348755253613, 9.90907193083003,
10.6213273456864, 9.47270463644367, 11.0020998412042, 10.0858091093301,
10.5453414387085, 8.00636756765025, 9.47270463644367, 8.51719319141624,
9.90348755253613, 9.99879773234045, 10.2399597891573, 9.99879773234045,
10.3089526606443, 10.3089526606443, 10.3089526606443, 10.1658518170036,
9.99879773234045, 10.1266311038503, 9.30565055178051, 9.47270463644367,
9.21034037197618, 9.39266192877014, 8.85366542803745, 10.9508065468167,
10.4912742174382, 10.2750511089686, 8.98719682066197, 8.00636756765025,
9.90348755253613, 10.4042628404486, 9.68034400122192, 8.98719682066197,
10.3734911817819, 9.58190392840867, 9.47270463644367, 8.85366542803745,
9.39266192877014, 9.85219425814858, 9.10497985631836, 9.90348755253613,
10.9150884642146, 9.21034037197618, 9.47270463644367, 9.90348755253613,
10.3089526606443, 9.39266192877014, 10.1658518170036, 9.43348392329039,
8.98719682066197, 9.61580548008435, 11.0821425488778, 10.1266311038503,
8.98719682066197, 9.61580548008435, 9.39266192877014, 10.4631033404715,
10.5966347330961, 10.2750511089686, 9.61580548008435, 9.90348755253613,
8.00636756765025, 6.90775527898214, 8.98719682066197, 8.51719319141624,
10.1266311038503, 9.90348755253613, 10.3089526606443, 9.39266192877014,
9.21034037197618, 9.68034400122192, 10.7144177687525, 10.5966347330961,
9.85219425814858, 9.77565418102624, 10.3089526606443, 9.7981270368783,
10.1266311038503, 8.69951474821019, 11.1562505210315, 9.61580548008435,
10.1266311038503, 10.4631033404715, 9.7981270368783, 10.2399597891573,
9.61580548008435, 9.99879773234045, 10.4631033404715, 9.7981270368783,
10.4631033404715, 9.70503661381229, 9.99879773234045, 10.3089526606443,
9.74096862303835, 10.1266311038503, 9.21034037197618, 10.5966347330961,
9.43348392329039, 10.4631033404715, 11.5617156291397, 11.5129254649702,
9.95227771670556, 9.21034037197618, 10.4042628404486, 10.1658518170036,
9.7981270368783, 9.61580548008435, 8.51719319141624, 11.0020998412042,
10.2399597891573, 10.6454248972655, 7.60090245954208, 9.90348755253613,
10.2399597891573, 9.21034037197618, 10.3417424834673, 9.74096862303835,
9.68034400122192, 10.4631033404715, 8.00636756765025, 9.68034400122192,
10.4631033404715, 10.2035921449865, 10.1266311038503, 10.5966347330961,
10.7144177687525, 9.5468126085974, 10.1266311038503, 10.5966347330961,
10.4341158035983, 10.5966347330961, 10.4631033404715, 9.39266192877014,
10.3089526606443, 10.0432494949113, 7.60090245954208, 9.90348755253613,
9.21034037197618, 11.0020998412042, 9.39266192877014, 10.1266311038503,
8.98719682066197, 7.60090245954208, 9.83091685970129, 9.90348755253613,
11.5129254649702, 10.8197782844103, 10.2035921449865, 6.90775527898214,
9.7981270368783, 9.74096862303835, 9.5468126085974, 10.4042628404486,
10.0432494949113, 9.21034037197618, 9.99879773234045, 9.47270463644367,
10.4042628404486, 10.4912742174382, 9.21034037197618, 8.69951474821019,
9.39266192877014, 9.21034037197618, 9.95227771670556, 10.1658518170036,
9.99879773234045, 10.0432494949113, 9.90348755253613, 9.21034037197618,
8.85366542803745, 9.61580548008435, 10.1658518170036, 9.21034037197618,
8.00636756765025, 10.2035921449865, 10.2399597891573, 9.61580548008435,
10.9150884642146, 9.90348755253613, 9.04782144247841, 10.3089526606443,
9.90348755253613, 10.1266311038503, 8.00636756765025, 9.68034400122192,
9.21034037197618, 9.61580548008435, 10.2399597891573, 10.3577428248137,
11.4616321705827, 10.5453414387085, 10.3089526606443, 10.4884925744764,
9.39266192877014, 9.21034037197618, 10.7144177687525, 10.5966347330961,
9.97580821411575, 9.5468126085974, 10.5453414387085, 6.90775527898214,
9.61580548008435, 10.0858091093301, 8.41183267575841, 9.7981270368783,
9.5468126085974, 9.21034037197618, 9.15904707758863, 8.69951474821019,
7.82404601085629, 10.5966347330961, 10.1266311038503, 10.2399597891573,
10.4042628404486, 8.29404964010203, 8.3187422526924, 10.3734911817819,
9.47270463644367, 8.98719682066197, 9.74096862303835, 9.7981270368783,
9.39266192877014, 8.85366542803745, 7.09007683577609, 9.5468126085974,
9.74096862303835, 10.3089526606443, 10.1266311038503, 9.99879773234045,
9.61580548008435, 9.90348755253613, 9.10497985631836, 9.74096862303835,
7.49554194388426, 9.7981270368783, 10.1266311038503, 9.90348755253613,
11.2252433925184, 8.1605182474775, 10.3089526606443, 6.90775527898214,
9.10497985631836, 9.30565055178051, 9.39266192877014, 10.3089526606443,
9.85219425814858, 9.10497985631836, 10.3089526606443, 9.10497985631836,
9.61580548008435, 8.98719682066197, 10.4042628404486, 9.39266192877014,
9.7981270368783, 10.3089526606443, 9.43348392329039, 9.21034037197618,
9.95227771670556, 9.95227771670556, 8.51719319141624, 9.99879773234045,
10.3089526606443, 11.7199396343546, 8.98719682066197, 7.60090245954208,
8.93590352627442, 9.21034037197618, 10.4631033404715, 9.61580548008435,
8.29404964010203, 9.68034400122192, 5.29831736654804, 10.0432494949113,
9.68034400122192, 8.69951474821019, 6.39692965521615, 10.2399597891573,
9.61580548008435, 9.61580548008435, 10.1266311038503, 9.61580548008435,
10.5966347330961, 10.3089526606443, 8.51719319141624, 10.4631033404715,
9.68034400122192, 10.2399597891573, 9.90348755253613, 9.95227771670556,
9.74096862303835, 10.0858091093301, 10.5966347330961, 8.98719682066197,
9.85219425814858, 8.51719319141624, 10.0858091093301, 8.51719319141624,
10.4042628404486, 10.0858091093301, 8.69951474821019, 11.4075649493124,
10.9508065468167, 9.5324238711453, 10.3089526606443, 9.61580548008435,
10.3417424834673, 10.4042628404486, 10.3089526606443, 9.39266192877014,
8.51719319141624, 9.95227771670556, 10.2399597891573, 9.39266192877014,
9.85219425814858, 8.69951474821019, 8.57546209954021, 9.61580548008435,
9.74096862303835, 7.43838353004431, 8.59415423255237, 9.21034037197618,
10.4631033404715, 10.2399597891573, 10.6454248972655, 10.7144177687525,
10.9150884642146, 10.4912742174382, 10.1266311038503, 9.85219425814858,
10.5453414387085, 9.61580548008435, 11.47210347045, 9.30565055178051,
9.10497985631836, 8.51719319141624, 10.8197782844103, 8.69951474821019,
11.5129254649702, 9.71111565988867, 10.3734911817819, 10.3089526606443,
9.21034037197618, 9.61580548008435, 10.1658518170036, 9.74096862303835,
9.99879773234045, 9.21034037197618, 10.8197782844103, 9.90348755253613,
5.99146454710798, 9.68034400122192, 9.5468126085974, 8.51719319141624,
10.5966347330961, 8.51719319141624, 10.1266311038503, 9.39266192877014,
10.9681982895286, 9.7981270368783, 6.90775527898214, 9.95227771670556,
9.30565055178051, 9.47270463644367, 10.1266311038503, 6.39692965521615,
10.1266311038503, 10.4912742174382, 9.61580548008435, 8.1605182474775,
9.85245738142335, 11.0348896640272, 10.1266311038503, 10.8197782844103,
10.5966347330961, 10.1658518170036, 9.99879773234045, 9.95227771670556,
10.3089526606443, 10.2035921449865, 8.29404964010203, 10.7144177687525,
9.7981270368783, 8.69951474821019, 9.5468126085974, 10.4631033404715,
9.61580548008435, 9.39266192877014, 6.90775527898214, 10.3734911817819,
7.3132203870903, 8.00636756765025, 10.4631033404715, 11.1562505210315,
9.95227771670556, 10.8197782844103, 9.61580548008435, 9.10497985631836,
9.21034037197618, 10.3089526606443, 9.68034400122192, 9.90348755253613,
11.5129254649702, 9.21034037197618, 10.4631033404715, 8.85366542803745,
8.98719682066197, 9.30565055178051, 10.1266311038503, 10.1266311038503,
10.3089526606443, 10.77895628989, 9.74096862303835, 10.1658518170036,
9.21034037197618, 11.0020998412042, 9.99879773234045, 10.0858091093301,
9.90348755253613, 8.85366542803745, 10.3089526606443, 10.0432494949113,
9.90348755253613, 8.00636756765025, 10.3089526606443, 9.39266192877014,
10.5966347330961, 9.61580548008435, 10.4912742174382, 9.21034037197618,
9.47270463644367, 9.21034037197618, 10.3089526606443, 10.0432494949113,
10.2399597891573, 9.90348755253613, 10.1266311038503, 10.1266311038503,
9.7981270368783, 9.68034400122192, 10.7144177687525, 9.39266192877014,
7.60090245954208, 9.21034037197618, 9.5468126085974, 9.61580548008435,
9.21034037197618, 7.09007683577609, 9.61580548008435, 9.21034037197618,
7.60090245954208, 8.29404964010203, 9.21034037197618, 7.3132203870903,
9.7981270368783, 8.29404964010203, 10.2399597891573, 9.21034037197618,
8.00636756765025, 9.39266192877014, 9.85219425814858, 10.4912742174382,
8.85366542803745, 10.4631033404715, 10.5966347330961, 9.61580548008435,
8.98719682066197, 10.1266311038503, 10.2399597891573, 9.99879773234045,
9.97580821411575, 8.00636756765025, 10.0432494949113, 9.68034400122192,
9.61580548008435, 10.8780471925343, 10.1658518170036, 8.29404964010203,
9.21034037197618, 10.6689553946757, 9.74096862303835, 8.29404964010203,
10.8197782844103, 10.9150884642146, 10.2399597891573, 8.51719319141624,
9.7981270368783, 9.95227771670556, 9.39266192877014, 10.4042628404486,
10.8197782844103, 9.68034400122192, 10.4631033404715, 10.1266311038503,
9.90348755253613, 9.7981270368783, 10.1266311038503, 10.5966347330961,
9.5468126085974, 9.39266192877014, 10.1266311038503, 10.5453414387085,
9.5468126085974, 9.61580548008435, 9.74096862303835, 9.7981270368783,
11.1562505210315, 10.3089526606443, 8.98719682066197, 10.3089526606443,
10.2035921449865, 10.7579028806922, 9.39266192877014, 10.0858091093301,
9.47270463644367, 11.289781913656, 8.51719319141624, 10.1266311038503,
10.2399597891573, 8.98719682066197, 9.21034037197618, 9.10497985631836,
9.90348755253613, 9.90348755253613, 10.2399597891573, 5.57972982598622,
10.1658518170036, 10.2035921449865, 9.5468126085974, 10.3734911817819,
9.21034037197618, 8.85366542803745, 10.2399597891573, 11.0020998412042,
9.39266192877014, 9.61580548008435, 10.1658518170036, 10.1658518170036,
9.83734775003158, 11.289781913656, 10.77895628989, 9.7981270368783,
10.4631033404715, 8.51719319141624, 9.10497985631836, 10.3089526606443,
11.289781913656, 10.4631033404715, 9.39266192877014, 12.2060726455302,
8.29404964010203, 7.60090245954208, 7.60090245954208, 9.61580548008435,
7.3132203870903, 10.2399597891573, 9.10497985631836, 11.0020998412042,
7.09007683577609, 7.24422751560335, 8.85366542803745, 9.95227771670556,
10.6919449129004, 10.2750511089686, 8.00636756765025, 9.39266192877014,
9.90348755253613, 10.5186731916264, 8.98719682066197, 10.4631033404715,
10.1266311038503, 9.7981270368783, 10.3089526606443, 9.39266192877014,
9.7981270368783, 9.90348755253613, 10.3417424834673, 8.69951474821019,
9.39266192877014, 9.47270463644367, 10.1658518170036, 9.61580548008435,
10.3089526606443, 7.60090245954208, 8.51719319141624, 10.8780471925343,
7.60090245954208, 10.1266311038503, 8.51719319141624, 9.95227771670556,
9.74096862303835, 9.39266192877014, 10.6454248972655, 9.95227771670556,
10.1266311038503, 8.00636756765025, 8.29404964010203, 9.90348755253613,
10.8589989975636, 11.0020998412042, 9.61580548008435, 11.4075649493124,
7.60090245954208, 9.68034400122192, 10.0858091093301, 9.61580548008435,
10.6454248972655, 9.21034037197618, 9.74096862303835, 10.3089526606443,
10.3734911817819, 10.4912742174382, 9.21034037197618, 9.90348755253613,
10.0858091093301, 9.74096862303835, 10.0432494949113, 10.1266311038503,
10.8197782844103, 9.90348755253613, 10.3089526606443, 8.85366542803745,
10.3089526606443, 8.00636756765025, 9.90348755253613, 10.5966347330961,
9.68034400122192, 9.30565055178051, 9.68034400122192, 9.7981270368783,
9.39266192877014, 8.29404964010203, 11.0020998412042, 10.6689553946757,
10.3417424834673, 10.8197782844103, 10.2035921449865, 10.3089526606443,
9.39266192877014, 9.90348755253613, 10.1266311038503, 8.00636756765025,
11.6082356447746, 10.9681982895286, 9.21034037197618, 9.85219425814858,
8.98719682066197, 11.0020998412042, 8.69951474821019)
x <- 
c(74, 66, 64, 63, 64, 62, 73, 72, 72, 68, 68, 65, 66, 68, 68, 70, 64, 73,
62, 63, 67, 66, 72, 63, 64, 72, 77, 64, 64, 72, 68, 64, 67, 65, 64, 65, 65, 67,
68, 60, 65, 62, 72, 67, 70, 68, 71, 71, 73, 68, 66, 69, 63, 62, 64, 67, 71, 60,
66, 66, 65, 70, 62, 72, 67, 68, 70, 62, 63, 66, 70, 68, 70, 66, 68, 70, 61, 64,
69, 64, 67, 69, 67, 68, 63, 71, 64, 68, 68, 66, 77, 67, 62, 67, 61, 64, 62, 63,
68, 64, 72, 64, 61, 74, 70, 71, 63, 64, 62, 70, 71, 71, 67, 64, 67, 62, 68, 62,
68, 74, 68, 62, 66, 68, 60, 68, 72, 66, 68, 68, 69, 64, 65, 61, 72, 66, 68, 70,
71, 71, 68, 60, 63, 68, 64, 68, 61, 68, 66, 70, 71, 65, 66, 70, 66, 61, 72, 74,
67, 66, 62, 72, 65, 60, 62, 66, 64, 65, 73, 69, 64, 67, 62, 63, 67, 68, 72, 70,
70, 67, 63, 66, 66, 71, 67, 76, 69, 65, 62, 62, 62, 61, 65, 72, 72, 64, 71, 72,
66, 65, 62, 66, 67, 64, 63, 67, 68, 64, 66, 65, 65, 72, 68, 74, 63, 64, 68, 67,
67, 73, 65, 77, 68, 62, 64, 67, 70, 62, 63, 62, 69, 64, 69, 59, 66, 62, 75, 63,
65, 70, 68, 69, 72, 64, 63, 73, 75, 65, 66, 66, 64, 66, 64, 63, 73, 72, 72, 64,
64, 68, 69, 60, 76, 72, 62, 62, 71, 74, 65, 63, 67, 63, 65, 65, 63, 70, 68, 67,
65, 69, 68, 66, 71, 64, 74, 62, 65, 66, 67, 73, 76, 63, 63, 70, 71, 65, 63, 64,
64, 67, 66, 68, 65, 67, 73, 63, 71, 73, 65, 59, 70, 72, 66, 70, 69, 68, 74, 67,
64, 67, 70, 64, 62, 68, 72, 63, 69, 64, 71, 64, 61, 68, 68, 64, 66, 62, 65, 66,
72, 70, 62, 71, 70, 64, 63, 65, 71, 62, 68, 76, 64, 66, 63, 63, 70, 68, 70, 69,
63, 65, 69, 68, 66, 65, 70, 70, 66, 68, 68, 70, 65, 64, 65, 77, 70, 64, 64, 64,
64, 63, 58, 62, 64, 64, 62, 64, 66, 69, 64, 71, 68, 68, 62, 63, 69, 67, 64, 70,
69, 69, 69, 60, 66, 67, 66, 70, 64, 60, 68, 73, 72, 64, 67, 71, 73, 70, 70, 71,
66, 75, 60, 72, 75, 60, 73, 65, 67, 69, 64, 70, 68, 62, 64, 68, 64, 73, 73, 69,
68, 71, 66, 66, 70, 66, 63, 75, 67, 63, 69, 71, 62, 65, 72, 65, 63, 64, 72, 64,
70, 65, 64, 64, 67, 73, 73, 65, 64, 67, 67, 74, 63, 74, 74, 63, 62, 62, 67, 69,
73, 63, 67, 69, 71, 72, 64, 64, 74, 62, 65, 60, 69, 61, 65, 66, 70, 72, 64, 71,
73, 64, 68, 64, 66, 67, 64, 64, 62, 69, 63, 72, 75, 70, 69, 64, 72, 69, 71, 59,
68, 77, 70, 69, 63, 73, 66, 72, 72, 69, 67, 66, 67, 68, 65, 62, 69, 70, 66, 66,
66, 72, 69, 66, 69, 60, 65, 62, 67, 67, 68, 66, 74, 65, 68, 66, 65, 62, 73, 62,
70, 58, 68, 67, 70, 63, 66, 65, 61, 61, 67, 73, 71, 64, 67, 62, 67, 69, 66, 66,
66, 66, 72, 64, 65, 72, 71, 64, 64, 67, 75, 66, 67, 71, 68, 67, 71, 63, 61, 65,
67, 65, 66, 67, 74, 74, 66, 69, 66, 74, 72, 66, 67, 65, 65, 68, 64, 64, 63, 69,
67, 60, 62, 72, 67, 66, 66, 60, 65, 72, 64, 64, 64, 66, 73, 74, 65, 63, 63, 66,
70, 66, 63, 63, 69, 73, 68, 64, 63, 70, 64, 66, 72, 64, 67, 66, 71, 71, 71, 74,
75, 72, 66, 65, 72, 60, 64, 65, 65, 62, 73, 68, 66, 71, 73, 61, 63, 64, 67, 63,
73, 66, 70, 68, 67, 74, 64, 60, 59, 75, 64, 71, 63, 67, 69, 70, 66, 74, 65, 64,
68, 66, 69, 60, 75, 64, 63, 64, 63, 67, 66, 65, 63, 66, 64, 71, 71, 72, 70, 74,
68, 74, 75, 68, 63, 72, 64, 63, 66, 61, 73, 65, 62, 68, 68, 63, 63, 68, 64, 70,
70, 72, 69, 63, 63, 63, 73, 69, 70, 65, 72, 62, 72, 73, 68, 66, 60, 65, 63, 64,
71, 67, 63, 65, 63, 65, 74, 67, 68, 65, 64, 68, 65, 72, 66, 64, 72, 64, 67, 68,
64, 66, 65, 70, 70, 66, 66, 74, 62, 66, 65, 71, 66, 67, 61, 66, 72, 69, 64, 63,
60, 70, 73, 65, 64, 72, 67, 69, 71, 66, 63, 71, 72, 68, 72, 66, 66, 65, 71, 74,
70, 64, 69, 63, 68, 73, 63, 71, 65, 65, 71, 70, 68, 66, 64, 66, 70, 64, 71, 64,
63, 66, 68, 62, 69, 64, 64, 69, 74, 68, 67, 72, 73, 64, 68, 63, 71, 64, 60, 66,
59, 63, 66, 65, 64, 66, 66, 73, 72, 74, 65, 71, 68, 70, 64, 59, 68, 68, 69, 69,
75, 69, 72, 68, 72, 63, 69, 63, 72, 65, 73, 69, 69, 61, 73, 67, 63, 62, 65, 72,
67, 65, 72, 64, 68, 68, 76, 63, 68, 72, 64, 68, 61, 67, 63, 60, 74, 62, 72, 65,
62, 71, 71, 70, 67, 62, 63, 61, 72, 63, 66, 64, 66, 68, 60, 61, 64, 66, 66, 67,
68, 66, 69, 69, 71, 74, 69, 72, 64, 72, 63, 70, 66, 62, 64, 69, 64, 67, 72, 65,
63, 70, 64, 68, 66, 70, 66, 64, 70, 74, 66, 62, 66, 62, 69, 68, 72, 64, 72, 74,
66, 68, 62, 71, 63, 71, 72, 72, 68, 64, 70, 66, 67, 68, 64, 65, 70, 71, 62, 71,
74, 64, 70, 64, 70, 74, 74, 66, 71, 69, 60, 64, 64, 72, 69, 67, 65, 68, 74, 65,
71, 64, 69, 64, 72, 63, 65, 72, 65, 64, 71, 62, 66, 64, 68, 66, 66, 66, 66, 63,
68, 70, 63, 70, 72, 75, 62, 68, 68, 70, 73, 62, 64, 73, 66, 70, 70, 72, 64, 72,
68)
x_centered <- 
c(6.93201133144476, -1.06798866855524, -3.06798866855524,
-4.06798866855524, -3.06798866855524, -5.06798866855524, 5.93201133144476,
4.93201133144476, 4.93201133144476, 0.932011331444755, 0.932011331444755,
-2.06798866855524, -1.06798866855524, 0.932011331444755, 0.932011331444755,
2.93201133144476, -3.06798866855524, 5.93201133144476, -5.06798866855524,
-4.06798866855524, -0.0679886685552447, -1.06798866855524, 4.93201133144476,
-4.06798866855524, -3.06798866855524, 4.93201133144476, 9.93201133144476,
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-7.06798866855524, -2.06798866855524, -5.06798866855524, 4.93201133144476,
-0.0679886685552447, 2.93201133144476, 0.932011331444755, 3.93201133144476,
3.93201133144476, 5.93201133144476, 0.932011331444755, -1.06798866855524,
1.93201133144476, -4.06798866855524, -5.06798866855524, -3.06798866855524,
-0.0679886685552447, 3.93201133144476, -7.06798866855524, -1.06798866855524,
-1.06798866855524, -2.06798866855524, 2.93201133144476, -5.06798866855524,
4.93201133144476, -0.0679886685552447, 0.932011331444755, 2.93201133144476,
-5.06798866855524, -4.06798866855524, -1.06798866855524, 2.93201133144476,
0.932011331444755, 2.93201133144476, -1.06798866855524, 0.932011331444755,
2.93201133144476, -6.06798866855524, -3.06798866855524, 1.93201133144476,
-3.06798866855524, -0.0679886685552447, 1.93201133144476, -0.0679886685552447,
0.932011331444755, -4.06798866855524, 3.93201133144476, -3.06798866855524,
0.932011331444755, 0.932011331444755, -1.06798866855524, 9.93201133144476,
-0.0679886685552447, -5.06798866855524, -0.0679886685552447, -6.06798866855524,
-3.06798866855524, -5.06798866855524, -4.06798866855524, 0.932011331444755,
-3.06798866855524, 4.93201133144476, -3.06798866855524, -6.06798866855524,
6.93201133144476, 2.93201133144476, 3.93201133144476, -4.06798866855524,
-3.06798866855524, -5.06798866855524, 2.93201133144476, 3.93201133144476,
3.93201133144476, -0.0679886685552447, -3.06798866855524, -0.0679886685552447,
-5.06798866855524, 0.932011331444755, -5.06798866855524, 0.932011331444755,
6.93201133144476, 0.932011331444755, -5.06798866855524, -1.06798866855524,
0.932011331444755, -7.06798866855524, 0.932011331444755, 4.93201133144476,
-1.06798866855524, 0.932011331444755, 0.932011331444755, 1.93201133144476,
-3.06798866855524, -2.06798866855524, -6.06798866855524, 4.93201133144476,
-1.06798866855524, 0.932011331444755, 2.93201133144476, 3.93201133144476,
3.93201133144476, 0.932011331444755, -7.06798866855524, -4.06798866855524,
0.932011331444755, -3.06798866855524, 0.932011331444755, -6.06798866855524,
0.932011331444755, -1.06798866855524, 2.93201133144476, 3.93201133144476,
-2.06798866855524, -1.06798866855524, 2.93201133144476, -1.06798866855524,
-6.06798866855524, 4.93201133144476, 6.93201133144476, -0.0679886685552447,
-1.06798866855524, -5.06798866855524, 4.93201133144476, -2.06798866855524,
-7.06798866855524, -5.06798866855524, -1.06798866855524, -3.06798866855524,
-2.06798866855524, 5.93201133144476, 1.93201133144476, -3.06798866855524,
-0.0679886685552447, -5.06798866855524, -4.06798866855524, -0.0679886685552447,
0.932011331444755, 4.93201133144476, 2.93201133144476, 2.93201133144476,
-0.0679886685552447, -4.06798866855524, -1.06798866855524, -1.06798866855524,
3.93201133144476, -0.0679886685552447, 8.93201133144476, 1.93201133144476,
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-6.06798866855524, -2.06798866855524, 4.93201133144476, 4.93201133144476,
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4.93201133144476, 0.932011331444755, 6.93201133144476, -4.06798866855524,
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2.93201133144476, 0.932011331444755, 1.93201133144476, 4.93201133144476,
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-1.06798866855524, -3.06798866855524, -4.06798866855524, 5.93201133144476,
4.93201133144476, 4.93201133144476, -3.06798866855524, -3.06798866855524,
0.932011331444755, 1.93201133144476, -7.06798866855524, 8.93201133144476,
4.93201133144476, -5.06798866855524, -5.06798866855524, 3.93201133144476,
6.93201133144476, -2.06798866855524, -4.06798866855524, -0.0679886685552447,
-4.06798866855524, -2.06798866855524, -2.06798866855524, -4.06798866855524,
2.93201133144476, 0.932011331444755, -0.0679886685552447, -2.06798866855524,
1.93201133144476, 0.932011331444755, -1.06798866855524, 3.93201133144476,
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5.93201133144476, -2.06798866855524, -8.06798866855524, 2.93201133144476,
4.93201133144476, -1.06798866855524, 2.93201133144476, 1.93201133144476,
0.932011331444755, 6.93201133144476, -0.0679886685552447, -3.06798866855524,
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0.932011331444755, 4.93201133144476, -4.06798866855524, 1.93201133144476,
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0.932011331444755, 0.932011331444755, -3.06798866855524, -1.06798866855524,
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2.93201133144476, -5.06798866855524, 3.93201133144476, 2.93201133144476,
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1.93201133144476, -3.06798866855524, 3.93201133144476, 0.932011331444755,
0.932011331444755, -5.06798866855524, -4.06798866855524, 1.93201133144476,
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5.93201133144476, 5.93201133144476, 1.93201133144476, 0.932011331444755,
3.93201133144476, -1.06798866855524, -1.06798866855524, 2.93201133144476,
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5.93201133144476, 5.93201133144476, -2.06798866855524, -3.06798866855524,
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6.93201133144476, 6.93201133144476, -4.06798866855524, -5.06798866855524,
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1.93201133144476, -4.06798866855524, 4.93201133144476, 7.93201133144476,
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1.93201133144476, -0.0679886685552447, -1.06798866855524, -0.0679886685552447,
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6.93201133144476, -1.06798866855524, 1.93201133144476, -1.06798866855524,
6.93201133144476, 4.93201133144476, -1.06798866855524, -0.0679886685552447,
-2.06798866855524, -2.06798866855524, 0.932011331444755, -3.06798866855524,
-3.06798866855524, -4.06798866855524, 1.93201133144476, -0.0679886685552447,
-7.06798866855524, -5.06798866855524, 4.93201133144476, -0.0679886685552447,
-1.06798866855524, -1.06798866855524, -7.06798866855524, -2.06798866855524,
4.93201133144476, -3.06798866855524, -3.06798866855524, -3.06798866855524,
-1.06798866855524, 5.93201133144476, 6.93201133144476, -2.06798866855524,
-4.06798866855524, -4.06798866855524, -1.06798866855524, 2.93201133144476,
-1.06798866855524, -4.06798866855524, -4.06798866855524, 1.93201133144476,
5.93201133144476, 0.932011331444755, -3.06798866855524, -4.06798866855524,
2.93201133144476, -3.06798866855524, -1.06798866855524, 4.93201133144476,
-3.06798866855524, -0.0679886685552447, -1.06798866855524, 3.93201133144476,
3.93201133144476, 3.93201133144476, 6.93201133144476, 7.93201133144476,
4.93201133144476, -1.06798866855524, -2.06798866855524, 4.93201133144476,
-7.06798866855524, -3.06798866855524, -2.06798866855524, -2.06798866855524,
-5.06798866855524, 5.93201133144476, 0.932011331444755, -1.06798866855524,
3.93201133144476, 5.93201133144476, -6.06798866855524, -4.06798866855524,
-3.06798866855524, -0.0679886685552447, -4.06798866855524, 5.93201133144476,
-1.06798866855524, 2.93201133144476, 0.932011331444755, -0.0679886685552447,
6.93201133144476, -3.06798866855524, -7.06798866855524, -8.06798866855524,
7.93201133144476, -3.06798866855524, 3.93201133144476, -4.06798866855524,
-0.0679886685552447, 1.93201133144476, 2.93201133144476, -1.06798866855524,
6.93201133144476, -2.06798866855524, -3.06798866855524, 0.932011331444755,
-1.06798866855524, 1.93201133144476, -7.06798866855524, 7.93201133144476,
-3.06798866855524, -4.06798866855524, -3.06798866855524, -4.06798866855524,
-0.0679886685552447, -1.06798866855524, -2.06798866855524, -4.06798866855524,
-1.06798866855524, -3.06798866855524, 3.93201133144476, 3.93201133144476,
4.93201133144476, 2.93201133144476, 6.93201133144476, 0.932011331444755,
6.93201133144476, 7.93201133144476, 0.932011331444755, -4.06798866855524,
4.93201133144476, -3.06798866855524, -4.06798866855524, -1.06798866855524,
-6.06798866855524, 5.93201133144476, -2.06798866855524, -5.06798866855524,
0.932011331444755, 0.932011331444755, -4.06798866855524, -4.06798866855524,
0.932011331444755, -3.06798866855524, 2.93201133144476, 2.93201133144476,
4.93201133144476, 1.93201133144476, -4.06798866855524, -4.06798866855524,
-4.06798866855524, 5.93201133144476, 1.93201133144476, 2.93201133144476,
-2.06798866855524, 4.93201133144476, -5.06798866855524, 4.93201133144476,
5.93201133144476, 0.932011331444755, -1.06798866855524, -7.06798866855524,
-2.06798866855524, -4.06798866855524, -3.06798866855524, 3.93201133144476,
-0.0679886685552447, -4.06798866855524, -2.06798866855524, -4.06798866855524,
-2.06798866855524, 6.93201133144476, -0.0679886685552447, 0.932011331444755,
-2.06798866855524, -3.06798866855524, 0.932011331444755, -2.06798866855524,
4.93201133144476, -1.06798866855524, -3.06798866855524, 4.93201133144476,
-3.06798866855524, -0.0679886685552447, 0.932011331444755, -3.06798866855524,
-1.06798866855524, -2.06798866855524, 2.93201133144476, 2.93201133144476,
-1.06798866855524, -1.06798866855524, 6.93201133144476, -5.06798866855524,
-1.06798866855524, -2.06798866855524, 3.93201133144476, -1.06798866855524,
-0.0679886685552447, -6.06798866855524, -1.06798866855524, 4.93201133144476,
1.93201133144476, -3.06798866855524, -4.06798866855524, -7.06798866855524,
2.93201133144476, 5.93201133144476, -2.06798866855524, -3.06798866855524,
4.93201133144476, -0.0679886685552447, 1.93201133144476, 3.93201133144476,
-1.06798866855524, -4.06798866855524, 3.93201133144476, 4.93201133144476,
0.932011331444755, 4.93201133144476, -1.06798866855524, -1.06798866855524,
-2.06798866855524, 3.93201133144476, 6.93201133144476, 2.93201133144476,
-3.06798866855524, 1.93201133144476, -4.06798866855524, 0.932011331444755,
5.93201133144476, -4.06798866855524, 3.93201133144476, -2.06798866855524,
-2.06798866855524, 3.93201133144476, 2.93201133144476, 0.932011331444755,
-1.06798866855524, -3.06798866855524, -1.06798866855524, 2.93201133144476,
-3.06798866855524, 3.93201133144476, -3.06798866855524, -4.06798866855524,
-1.06798866855524, 0.932011331444755, -5.06798866855524, 1.93201133144476,
-3.06798866855524, -3.06798866855524, 1.93201133144476, 6.93201133144476,
0.932011331444755, -0.0679886685552447, 4.93201133144476, 5.93201133144476,
-3.06798866855524, 0.932011331444755, -4.06798866855524, 3.93201133144476,
-3.06798866855524, -7.06798866855524, -1.06798866855524, -8.06798866855524,
-4.06798866855524, -1.06798866855524, -2.06798866855524, -3.06798866855524,
-1.06798866855524, -1.06798866855524, 5.93201133144476, 4.93201133144476,
6.93201133144476, -2.06798866855524, 3.93201133144476, 0.932011331444755,
2.93201133144476, -3.06798866855524, -8.06798866855524, 0.932011331444755,
0.932011331444755, 1.93201133144476, 1.93201133144476, 7.93201133144476,
1.93201133144476, 4.93201133144476, 0.932011331444755, 4.93201133144476,
-4.06798866855524, 1.93201133144476, -4.06798866855524, 4.93201133144476,
-2.06798866855524, 5.93201133144476, 1.93201133144476, 1.93201133144476,
-6.06798866855524, 5.93201133144476, -0.0679886685552447, -4.06798866855524,
-5.06798866855524, -2.06798866855524, 4.93201133144476, -0.0679886685552447,
-2.06798866855524, 4.93201133144476, -3.06798866855524, 0.932011331444755,
0.932011331444755, 8.93201133144476, -4.06798866855524, 0.932011331444755,
4.93201133144476, -3.06798866855524, 0.932011331444755, -6.06798866855524,
-0.0679886685552447, -4.06798866855524, -7.06798866855524, 6.93201133144476,
-5.06798866855524, 4.93201133144476, -2.06798866855524, -5.06798866855524,
3.93201133144476, 3.93201133144476, 2.93201133144476, -0.0679886685552447,
-5.06798866855524, -4.06798866855524, -6.06798866855524, 4.93201133144476,
-4.06798866855524, -1.06798866855524, -3.06798866855524, -1.06798866855524,
0.932011331444755, -7.06798866855524, -6.06798866855524, -3.06798866855524,
-1.06798866855524, -1.06798866855524, -0.0679886685552447, 0.932011331444755,
-1.06798866855524, 1.93201133144476, 1.93201133144476, 3.93201133144476,
6.93201133144476, 1.93201133144476, 4.93201133144476, -3.06798866855524,
4.93201133144476, -4.06798866855524, 2.93201133144476, -1.06798866855524,
-5.06798866855524, -3.06798866855524, 1.93201133144476, -3.06798866855524,
-0.0679886685552447, 4.93201133144476, -2.06798866855524, -4.06798866855524,
2.93201133144476, -3.06798866855524, 0.932011331444755, -1.06798866855524,
2.93201133144476, -1.06798866855524, -3.06798866855524, 2.93201133144476,
6.93201133144476, -1.06798866855524, -5.06798866855524, -1.06798866855524,
-5.06798866855524, 1.93201133144476, 0.932011331444755, 4.93201133144476,
-3.06798866855524, 4.93201133144476, 6.93201133144476, -1.06798866855524,
0.932011331444755, -5.06798866855524, 3.93201133144476, -4.06798866855524,
3.93201133144476, 4.93201133144476, 4.93201133144476, 0.932011331444755,
-3.06798866855524, 2.93201133144476, -1.06798866855524, -0.0679886685552447,
0.932011331444755, -3.06798866855524, -2.06798866855524, 2.93201133144476,
3.93201133144476, -5.06798866855524, 3.93201133144476, 6.93201133144476,
-3.06798866855524, 2.93201133144476, -3.06798866855524, 2.93201133144476,
6.93201133144476, 6.93201133144476, -1.06798866855524, 3.93201133144476,
1.93201133144476, -7.06798866855524, -3.06798866855524, -3.06798866855524,
4.93201133144476, 1.93201133144476, -0.0679886685552447, -2.06798866855524,
0.932011331444755, 6.93201133144476, -2.06798866855524, 3.93201133144476,
-3.06798866855524, 1.93201133144476, -3.06798866855524, 4.93201133144476,
-4.06798866855524, -2.06798866855524, 4.93201133144476, -2.06798866855524,
-3.06798866855524, 3.93201133144476, -5.06798866855524, -1.06798866855524,
-3.06798866855524, 0.932011331444755, -1.06798866855524, -1.06798866855524,
-1.06798866855524, -1.06798866855524, -4.06798866855524, 0.932011331444755,
2.93201133144476, -4.06798866855524, 2.93201133144476, 4.93201133144476,
7.93201133144476, -5.06798866855524, 0.932011331444755, 0.932011331444755,
2.93201133144476, 5.93201133144476, -5.06798866855524, -3.06798866855524,
5.93201133144476, -1.06798866855524, 2.93201133144476, 2.93201133144476,
4.93201133144476, -3.06798866855524, 4.93201133144476, 0.932011331444755)
age <- 
c(2, 3, 1, 2, 1, 2, 2, 1, 1, 1, 1, 3, 2, 3, 1, 2, 3, 2, 3, 1, 1, 2, 2,
2, 3, 2, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 2, 1, 1, 1, 1, 1, 1, 3, 2, 2, 1, 1, 1, 3,
3, 1, 1, 1, 2, 3, 2, 3, 1, 1, 2, 1, 2, 2, 2, 1, 1, 2, 1, 3, 3, 2, 1, 1, 1, 1, 1,
3, 3, 1, 1, 1, 2, 1, 2, 1, 2, 2, 2, 2, 1, 3, 2, 2, 2, 1, 2, 2, 1, 1, 1, 2, 1, 2,
2, 2, 2, 2, 2, 2, 3, 1, 1, 1, 1, 3, 2, 2, 3, 2, 3, 1, 1, 1, 1, 2, 1, 2, 1, 1, 3,
2, 2, 2, 2, 1, 3, 1, 1, 3, 2, 2, 2, 3, 2, 2, 3, 3, 2, 1, 3, 2, 2, 2, 3, 2, 2, 2,
2, 1, 2, 1, 2, 3, 2, 2, 2, 3, 3, 3, 1, 3, 1, 3, 1, 1, 2, 2, 2, 1, 1, 2, 3, 2, 1,
2, 1, 1, 2, 1, 1, 1, 1, 1, 3, 2, 3, 2, 1, 2, 3, 1, 3, 2, 2, 1, 2, 2, 1, 1, 1, 2,
2, 1, 1, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 3, 2, 1, 2, 2, 2, 1, 2, 1, 1, 1, 1,
1, 2, 3, 3, 2, 3, 2, 1, 2, 1, 1, 2, 3, 1, 1, 1, 3, 1, 3, 1, 2, 3, 2, 2, 2, 2, 2,
3, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 3, 2, 3, 1, 3, 1, 2,
2, 1, 3, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 3, 2, 1, 1, 3, 3, 1, 2, 2, 3, 2, 2,
1, 1, 2, 2, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 3, 2, 2, 1,
1, 2, 1, 2, 1, 1, 1, 1, 2, 2, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 1, 1, 3, 2, 2, 1, 2,
1, 1, 1, 3, 2, 1, 3, 2, 3, 1, 2, 3, 1, 2, 1, 2, 2, 3, 2, 3, 3, 2, 1, 1, 1, 3, 1,
2, 2, 2, 1, 1, 3, 2, 2, 1, 2, 2, 2, 3, 1, 1, 2, 1, 1, 1, 2, 1, 3, 2, 2, 1, 1, 2,
1, 1, 1, 3, 2, 2, 3, 2, 2, 1, 1, 1, 2, 3, 1, 2, 1, 1, 1, 1, 2, 3, 3, 2, 2, 2, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 3, 1, 1, 1, 1, 3, 1, 2, 1, 1,
1, 3, 3, 1, 1, 2, 2, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 3, 1, 2, 3, 2, 3,
2, 2, 2, 3, 3, 1, 1, 2, 3, 1, 2, 2, 2, 1, 1, 2, 3, 1, 2, 2, 2, 1, 2, 2, 1, 1, 2,
2, 1, 2, 2, 2, 1, 1, 3, 2, 2, 1, 1, 3, 2, 2, 3, 1, 1, 1, 1, 2, 2, 2, 3, 1, 1, 2,
2, 1, 2, 1, 1, 1, 2, 1, 3, 2, 2, 2, 1, 3, 3, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1,
2, 1, 1, 1, 1, 2, 2, 1, 2, 2, 3, 2, 2, 2, 1, 1, 2, 3, 1, 3, 3, 1, 1, 2, 1, 3, 1,
1, 1, 1, 3, 2, 2, 3, 2, 3, 1, 1, 3, 1, 2, 1, 1, 2, 1, 1, 2, 2, 3, 1, 1, 1, 1, 1,
2, 2, 2, 2, 2, 2, 1, 1, 1, 3, 3, 2, 3, 3, 1, 1, 1, 1, 2, 1, 2, 3, 1, 2, 2, 1, 3,
2, 1, 3, 2, 1, 3, 1, 2, 3, 1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 1, 2, 3, 1, 1, 1, 2,
2, 1, 2, 3, 2, 1, 2, 1, 2, 1, 1, 1, 1, 3, 2, 3, 2, 2, 1, 2, 3, 2, 1, 3, 2, 1, 2,
2, 3, 1, 2, 1, 1, 1, 2, 2, 2, 3, 3, 1, 1, 1, 3, 2, 1, 2, 1, 1, 3, 2, 1, 2, 2, 2,
2, 1, 3, 3, 3, 2, 3, 2, 1, 3, 3, 1, 1, 3, 2, 3, 1, 1, 1, 2, 3, 2, 2, 2, 1, 1, 1,
3, 1, 3, 2, 3, 3, 1, 2, 2, 3, 1, 2, 2, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1,
1, 2, 1, 2, 1, 3, 3, 2, 3, 1, 1, 3, 2, 2, 2, 1, 2, 1, 3, 3, 1, 1, 2, 1, 2, 1, 2,
1, 2, 1, 2, 1, 2, 3, 2, 1, 2, 1, 3, 1, 1, 3, 2, 1, 2, 2, 1, 1, 2, 1, 2, 3, 3, 3,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 1, 2, 1, 2, 3, 2, 2, 1, 1, 1, 2, 1, 1, 1,
1, 3, 3, 1, 2, 2, 3, 2, 2, 2, 3, 1, 3, 3, 3, 3, 2, 1, 2, 1, 1, 2, 2, 1, 3, 1, 2,
1, 3, 2, 3, 3, 1, 1, 2, 1, 1, 2, 2, 1, 3, 2, 1, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1,
1, 2, 3, 3, 3, 1, 1, 2, 2, 2, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 3,
1, 3, 2, 1, 3, 2, 1, 1, 1, 1, 3, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 1, 1, 1, 1, 2, 1,
1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 3, 3, 2, 2, 3, 1, 3, 1, 1, 2, 2, 2, 1, 2, 1,
1, 1, 1, 1, 2, 1, 3, 1, 1, 2, 1, 1, 2, 3, 2, 3, 2, 1, 1, 1, 2, 2, 2, 2, 1, 3, 1,
1, 2, 1, 2, 3, 2, 1, 1, 3, 1)
eth <- 
c(3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 3, 3, 3, 3, 3,
1, 3, 3, 3, 3, 3, 3, 3, 3, 1, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 1, 3, 3, 3, 3, 3, 3,
3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2,
3, 3, 3, 1, 3, 3, 3, 3, 3, 1, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 1, 1, 1, 3, 4, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 4, 3, 3, 3, 3, 1, 1, 4, 3, 3, 3,
1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 3, 1, 3, 3, 3, 3, 3, 1, 1, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 1, 1, 3, 3,
3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 3, 3, 3, 3, 3, 3, 3, 1, 1,
1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 3, 3, 3, 3, 1, 1, 1, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 1, 3, 2, 3, 3, 3, 3, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 3,
1, 1, 3, 3, 1, 1, 4, 3, 1, 3, 3, 3, 1, 3, 3, 3, 3, 3, 3, 3, 3, 1, 3, 1, 1, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 1, 3, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 1, 2, 3, 3,
3, 3, 3, 3, 3, 3, 2, 3, 3, 2, 4, 3, 1, 3, 3, 3, 3, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 1, 2, 2, 3, 1, 3, 1, 1, 3, 2, 1, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 3, 3, 1, 4, 1, 1, 1, 3, 3, 3, 3, 1, 1, 3, 3,
3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 1, 3, 3, 3,
3, 3, 3, 3, 2, 3, 3, 1, 3, 3, 3, 3, 3, 1, 1, 3, 3, 1, 3, 3, 3, 3, 2, 3, 3, 3, 2,
3, 3, 3, 3, 3, 3, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 1, 1, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3,
3, 3, 3, 1, 3, 3, 3, 3, 3, 3, 3, 3, 1, 3, 3, 3, 2, 1, 3, 2, 3, 3, 3, 1, 1, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 1, 3, 3, 3, 2, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 3, 1, 3, 1, 3, 4,
3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 3, 3, 3, 3, 3, 3, 3, 3, 1, 3, 1, 3, 1, 3, 3, 3, 3,
3, 1, 1, 3, 3, 3, 3, 3, 3, 3, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 3, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 3, 3, 2, 3, 2, 3,
4, 3, 3, 4, 2, 3, 3, 3, 3, 3, 2, 3, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 2, 3, 3, 3, 3, 3, 3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 2, 1, 3, 3, 4, 1, 3, 2, 3, 3, 3, 3, 3, 3, 3, 2, 3, 2, 3, 3, 3,
3, 2, 3, 3, 3, 1, 2, 1, 2, 3, 4, 2, 4, 3, 1, 2, 3, 1, 3, 2, 3, 3, 3, 1, 3, 3, 4,
3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 3, 3, 2, 3, 3, 2,
2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 3, 3, 3, 3, 3, 3, 1,
3, 4, 2, 4, 3, 3, 3, 3, 3, 3)