I want to do LDA (linear discriminant analysis) with the Auto dataset of the ISLR package. To start off, I am trying to take the cars with year = 75 and use it as a "test set", where cars of all other years will be used as a "training set". However, it seems that I've made a mess of things. For instance, in my code below, sequentially using the replace function for the values of mpg.year75 just results in everything being set to high:

Auto.df <- ISLR::Auto

train <- Auto.df$year != 75
Auto.df.notyear75 <- Auto.df[train,]
mpg.notyear75 <- Auto.df.notyear75$mpg

Auto.df.year75 <- Auto.df[!train,] # !train chooses subset complementary to train
mpg.year75 <- Auto.df.year75$mpg

Auto.df.notyear75 <- as_tibble(Auto.df.notyear75)
Auto.df.notyear75 <- Auto.df.notyear75 %>%
  dplyr::rename(mpgclass = mpg) %>%
  mutate(mpgclass = case_when(mpgclass < 20 ~'low', 
                         between(mpgclass, 20, 27) ~ 'medium', 
                         TRUE ~ 'high'))
mpg.notyear75 <- replace(mpg.notyear75, mpg.notyear75 < 20, 'low')
mpg.notyear75 <- replace(mpg.notyear75, mpg.notyear75 >= 20 & mpg.notyear75 < 27, 'medium')
mpg.notyear75 <- replace(mpg.notyear75, mpg.notyear75 >= 27, 'high')

Auto.df.year75 <- as_tibble(Auto.df.year75)
Auto.df.year75 <- Auto.df.year75 %>%
  dplyr::rename(mpgclass = mpg) %>%
  mutate(mpgclass = case_when(mpgclass < 20 ~'low', 
                         between(mpgclass, 20, 27) ~ 'medium', 
                         TRUE ~ 'high'))
mpg.year75 <- replace(mpg.year75, mpg.year75 < 20, 'low')
mpg.year75 <- replace(mpg.year75, mpg.year75 >= 20 & mpg.year75 < 27, 'medium')
mpg.year75 <- replace(mpg.year75, mpg.year75 >= 27, 'high')

I then want to apply lda and show the results in a confusion matrix, similar to this:

lda.fit <- lda(mpgclass ~ acceleration   displacement   horsepower   weight, data = Auto.df)
lda.pred <- predict(lda.fit, data = Auto.df)
with(Auto.df, table(lda.pred$class, mpgclass))

How is this done properly (and cleanly, rather than the mish-mash I have above)?

My data is as follows:

structure(list(mpg = c(18, 15, 18, 16, 17, 15, 14, 14, 14, 15, 
15, 14, 15, 14, 24, 22, 18, 21, 27, 26, 25, 24, 25, 26, 21, 10, 
10, 11, 9, 27, 28, 25, 19, 16, 17, 19, 18, 14, 14, 14, 14, 12, 
13, 13, 18, 22, 19, 18, 23, 28, 30, 30, 31, 35, 27, 26, 24, 25, 
23, 20, 21, 13, 14, 15, 14, 17, 11, 13, 12, 13, 19, 15, 13, 13, 
14, 18, 22, 21, 26, 22, 28, 23, 28, 27, 13, 14, 13, 14, 15, 12, 
13, 13, 14, 13, 12, 13, 18, 16, 18, 18, 23, 26, 11, 12, 13, 12, 
18, 20, 21, 22, 18, 19, 21, 26, 15, 16, 29, 24, 20, 19, 15, 24, 
20, 11, 20, 19, 15, 31, 26, 32, 25, 16, 16, 18, 16, 13, 14, 14, 
14, 29, 26, 26, 31, 32, 28, 24, 26, 24, 26, 31, 19, 18, 15, 15, 
16, 15, 16, 14, 17, 16, 15, 18, 21, 20, 13, 29, 23, 20, 23, 24, 
25, 24, 18, 29, 19, 23, 23, 22, 25, 33, 28, 25, 25, 26, 27, 17.5, 
16, 15.5, 14.5, 22, 22, 24, 22.5, 29, 24.5, 29, 33, 20, 18, 18.5, 
17.5, 29.5, 32, 28, 26.5, 20, 13, 19, 19, 16.5, 16.5, 13, 13, 
13, 31.5, 30, 36, 25.5, 33.5, 17.5, 17, 15.5, 15, 17.5, 20.5, 
19, 18.5, 16, 15.5, 15.5, 16, 29, 24.5, 26, 25.5, 30.5, 33.5, 
30, 30.5, 22, 21.5, 21.5, 43.1, 36.1, 32.8, 39.4, 36.1, 19.9, 
19.4, 20.2, 19.2, 20.5, 20.2, 25.1, 20.5, 19.4, 20.6, 20.8, 18.6, 
18.1, 19.2, 17.7, 18.1, 17.5, 30, 27.5, 27.2, 30.9, 21.1, 23.2, 
23.8, 23.9, 20.3, 17, 21.6, 16.2, 31.5, 29.5, 21.5, 19.8, 22.3, 
20.2, 20.6, 17, 17.6, 16.5, 18.2, 16.9, 15.5, 19.2, 18.5, 31.9, 
34.1, 35.7, 27.4, 25.4, 23, 27.2, 23.9, 34.2, 34.5, 31.8, 37.3, 
28.4, 28.8, 26.8, 33.5, 41.5, 38.1, 32.1, 37.2, 28, 26.4, 24.3, 
19.1, 34.3, 29.8, 31.3, 37, 32.2, 46.6, 27.9, 40.8, 44.3, 43.4, 
36.4, 30, 44.6, 33.8, 29.8, 32.7, 23.7, 35, 32.4, 27.2, 26.6, 
25.8, 23.5, 30, 39.1, 39, 35.1, 32.3, 37, 37.7, 34.1, 34.7, 34.4, 
29.9, 33, 33.7, 32.4, 32.9, 31.6, 28.1, 30.7, 25.4, 24.2, 22.4, 
26.6, 20.2, 17.6, 28, 27, 34, 31, 29, 27, 24, 36, 37, 31, 38, 
36, 36, 36, 34, 38, 32, 38, 25, 38, 26, 22, 32, 36, 27, 27, 44, 
32, 28, 31), cylinders = c(8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 
8, 8, 4, 6, 6, 6, 4, 4, 4, 4, 4, 4, 6, 8, 8, 8, 8, 4, 4, 4, 6, 
6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 8, 6, 4, 6, 6, 4, 4, 4, 4, 4, 4, 
4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 
4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 
6, 6, 6, 6, 6, 4, 8, 8, 8, 8, 6, 4, 4, 4, 3, 4, 6, 4, 8, 8, 4, 
4, 4, 4, 8, 4, 6, 8, 6, 6, 6, 4, 4, 4, 4, 6, 6, 6, 8, 8, 8, 8, 
8, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 8, 8, 8, 8, 6, 
6, 6, 6, 6, 8, 8, 4, 4, 6, 4, 4, 4, 4, 6, 4, 6, 4, 4, 4, 4, 4, 
4, 4, 4, 4, 4, 8, 8, 8, 8, 6, 6, 6, 6, 4, 4, 4, 4, 6, 6, 6, 6, 
4, 4, 4, 4, 4, 8, 4, 6, 6, 8, 8, 8, 8, 4, 4, 4, 4, 4, 8, 8, 8, 
8, 6, 6, 6, 6, 8, 8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 6, 4, 3, 4, 
4, 4, 4, 4, 8, 8, 8, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 8, 6, 8, 8, 
4, 4, 4, 4, 4, 4, 4, 4, 5, 6, 4, 6, 4, 4, 6, 6, 4, 6, 6, 8, 8, 
8, 8, 8, 8, 8, 8, 4, 4, 4, 4, 5, 8, 4, 8, 4, 4, 4, 4, 4, 6, 6, 
4, 4, 4, 4, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 4, 
4, 4, 4, 6, 3, 4, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 
4, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 8, 6, 6, 4, 4, 4, 4, 4, 4, 4, 
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6, 6, 4, 6, 4, 4, 4, 4, 4, 4, 
4, 4), displacement = c(307, 350, 318, 304, 302, 429, 454, 440, 
455, 390, 383, 340, 400, 455, 113, 198, 199, 200, 97, 97, 110, 
107, 104, 121, 199, 360, 307, 318, 304, 97, 140, 113, 232, 225, 
250, 250, 232, 350, 400, 351, 318, 383, 400, 400, 258, 140, 250, 
250, 122, 116, 79, 88, 71, 72, 97, 91, 113, 97.5, 97, 140, 122, 
350, 400, 318, 351, 304, 429, 350, 350, 400, 70, 304, 307, 302, 
318, 121, 121, 120, 96, 122, 97, 120, 98, 97, 350, 304, 350, 
302, 318, 429, 400, 351, 318, 440, 455, 360, 225, 250, 232, 250, 
198, 97, 400, 400, 360, 350, 232, 97, 140, 108, 70, 122, 155, 
98, 350, 400, 68, 116, 114, 121, 318, 121, 156, 350, 198, 232, 
250, 79, 122, 71, 140, 250, 258, 225, 302, 350, 318, 302, 304, 
98, 79, 97, 76, 83, 90, 90, 116, 120, 108, 79, 225, 250, 250, 
250, 400, 350, 318, 351, 231, 250, 258, 225, 231, 262, 302, 97, 
140, 232, 140, 134, 90, 119, 171, 90, 232, 115, 120, 121, 121, 
91, 107, 116, 140, 98, 101, 305, 318, 304, 351, 225, 250, 200, 
232, 85, 98, 90, 91, 225, 250, 250, 258, 97, 85, 97, 140, 130, 
318, 120, 156, 168, 350, 350, 302, 318, 98, 111, 79, 122, 85, 
305, 260, 318, 302, 250, 231, 225, 250, 400, 350, 400, 351, 97, 
151, 97, 140, 98, 98, 97, 97, 146, 121, 80, 90, 98, 78, 85, 91, 
260, 318, 302, 231, 200, 200, 140, 225, 232, 231, 200, 225, 258, 
305, 231, 302, 318, 98, 134, 119, 105, 134, 156, 151, 119, 131, 
163, 121, 163, 89, 98, 231, 200, 140, 232, 225, 305, 302, 351, 
318, 350, 351, 267, 360, 89, 86, 98, 121, 183, 350, 141, 260, 
105, 105, 85, 91, 151, 173, 173, 151, 98, 89, 98, 86, 151, 140, 
151, 225, 97, 134, 120, 119, 108, 86, 156, 85, 90, 90, 121, 146, 
91, 97, 89, 168, 70, 122, 107, 135, 151, 156, 173, 135, 79, 86, 
81, 97, 85, 89, 91, 105, 98, 98, 105, 107, 108, 119, 120, 141, 
145, 168, 146, 231, 350, 200, 225, 112, 112, 112, 112, 135, 151, 
140, 105, 91, 91, 105, 98, 120, 107, 108, 91, 91, 91, 181, 262, 
156, 232, 144, 135, 151, 140, 97, 135, 120, 119), horsepower = c(130, 
165, 150, 150, 140, 198, 220, 215, 225, 190, 170, 160, 150, 225, 
95, 95, 97, 85, 88, 46, 87, 90, 95, 113, 90, 215, 200, 210, 193, 
88, 90, 95, 100, 105, 100, 88, 100, 165, 175, 153, 150, 180, 
170, 175, 110, 72, 100, 88, 86, 90, 70, 76, 65, 69, 60, 70, 95, 
80, 54, 90, 86, 165, 175, 150, 153, 150, 208, 155, 160, 190, 
97, 150, 130, 140, 150, 112, 76, 87, 69, 86, 92, 97, 80, 88, 
175, 150, 145, 137, 150, 198, 150, 158, 150, 215, 225, 175, 105, 
100, 100, 88, 95, 46, 150, 167, 170, 180, 100, 88, 72, 94, 90, 
85, 107, 90, 145, 230, 49, 75, 91, 112, 150, 110, 122, 180, 95, 
100, 100, 67, 80, 65, 75, 100, 110, 105, 140, 150, 150, 140, 
150, 83, 67, 78, 52, 61, 75, 75, 75, 97, 93, 67, 95, 105, 72, 
72, 170, 145, 150, 148, 110, 105, 110, 95, 110, 110, 129, 75, 
83, 100, 78, 96, 71, 97, 97, 70, 90, 95, 88, 98, 115, 53, 86, 
81, 92, 79, 83, 140, 150, 120, 152, 100, 105, 81, 90, 52, 60, 
70, 53, 100, 78, 110, 95, 71, 70, 75, 72, 102, 150, 88, 108, 
120, 180, 145, 130, 150, 68, 80, 58, 96, 70, 145, 110, 145, 130, 
110, 105, 100, 98, 180, 170, 190, 149, 78, 88, 75, 89, 63, 83, 
67, 78, 97, 110, 110, 48, 66, 52, 70, 60, 110, 140, 139, 105, 
95, 85, 88, 100, 90, 105, 85, 110, 120, 145, 165, 139, 140, 68, 
95, 97, 75, 95, 105, 85, 97, 103, 125, 115, 133, 71, 68, 115, 
85, 88, 90, 110, 130, 129, 138, 135, 155, 142, 125, 150, 71, 
65, 80, 80, 77, 125, 71, 90, 70, 70, 65, 69, 90, 115, 115, 90, 
76, 60, 70, 65, 90, 88, 90, 90, 78, 90, 75, 92, 75, 65, 105, 
65, 48, 48, 67, 67, 67, 67, 62, 132, 100, 88, 72, 84, 84, 92, 
110, 84, 58, 64, 60, 67, 65, 62, 68, 63, 65, 65, 74, 75, 75, 
100, 74, 80, 76, 116, 120, 110, 105, 88, 85, 88, 88, 88, 85, 
84, 90, 92, 74, 68, 68, 63, 70, 88, 75, 70, 67, 67, 67, 110, 
85, 92, 112, 96, 84, 90, 86, 52, 84, 79, 82), weight = c(3504, 
3693, 3436, 3433, 3449, 4341, 4354, 4312, 4425, 3850, 3563, 3609, 
3761, 3086, 2372, 2833, 2774, 2587, 2130, 1835, 2672, 2430, 2375, 
2234, 2648, 4615, 4376, 4382, 4732, 2130, 2264, 2228, 2634, 3439, 
3329, 3302, 3288, 4209, 4464, 4154, 4096, 4955, 4746, 5140, 2962, 
2408, 3282, 3139, 2220, 2123, 2074, 2065, 1773, 1613, 1834, 1955, 
2278, 2126, 2254, 2408, 2226, 4274, 4385, 4135, 4129, 3672, 4633, 
4502, 4456, 4422, 2330, 3892, 4098, 4294, 4077, 2933, 2511, 2979, 
2189, 2395, 2288, 2506, 2164, 2100, 4100, 3672, 3988, 4042, 3777, 
4952, 4464, 4363, 4237, 4735, 4951, 3821, 3121, 3278, 2945, 3021, 
2904, 1950, 4997, 4906, 4654, 4499, 2789, 2279, 2401, 2379, 2124, 
2310, 2472, 2265, 4082, 4278, 1867, 2158, 2582, 2868, 3399, 2660, 
2807, 3664, 3102, 2901, 3336, 1950, 2451, 1836, 2542, 3781, 3632, 
3613, 4141, 4699, 4457, 4638, 4257, 2219, 1963, 2300, 1649, 2003, 
2125, 2108, 2246, 2489, 2391, 2000, 3264, 3459, 3432, 3158, 4668, 
4440, 4498, 4657, 3907, 3897, 3730, 3785, 3039, 3221, 3169, 2171, 
2639, 2914, 2592, 2702, 2223, 2545, 2984, 1937, 3211, 2694, 2957, 
2945, 2671, 1795, 2464, 2220, 2572, 2255, 2202, 4215, 4190, 3962, 
4215, 3233, 3353, 3012, 3085, 2035, 2164, 1937, 1795, 3651, 3574, 
3645, 3193, 1825, 1990, 2155, 2565, 3150, 3940, 3270, 2930, 3820, 
4380, 4055, 3870, 3755, 2045, 2155, 1825, 2300, 1945, 3880, 4060, 
4140, 4295, 3520, 3425, 3630, 3525, 4220, 4165, 4325, 4335, 1940, 
2740, 2265, 2755, 2051, 2075, 1985, 2190, 2815, 2600, 2720, 1985, 
1800, 1985, 2070, 1800, 3365, 3735, 3570, 3535, 3155, 2965, 2720, 
3430, 3210, 3380, 3070, 3620, 3410, 3425, 3445, 3205, 4080, 2155, 
2560, 2300, 2230, 2515, 2745, 2855, 2405, 2830, 3140, 2795, 3410, 
1990, 2135, 3245, 2990, 2890, 3265, 3360, 3840, 3725, 3955, 3830, 
4360, 4054, 3605, 3940, 1925, 1975, 1915, 2670, 3530, 3900, 3190, 
3420, 2200, 2150, 2020, 2130, 2670, 2595, 2700, 2556, 2144, 1968, 
2120, 2019, 2678, 2870, 3003, 3381, 2188, 2711, 2542, 2434, 2265, 
2110, 2800, 2110, 2085, 2335, 2950, 3250, 1850, 2145, 1845, 2910, 
2420, 2500, 2290, 2490, 2635, 2620, 2725, 2385, 1755, 1875, 1760, 
2065, 1975, 2050, 1985, 2215, 2045, 2380, 2190, 2210, 2350, 2615, 
2635, 3230, 3160, 2900, 2930, 3415, 3725, 3060, 3465, 2605, 2640, 
2395, 2575, 2525, 2735, 2865, 1980, 2025, 1970, 2125, 2125, 2160, 
2205, 2245, 1965, 1965, 1995, 2945, 3015, 2585, 2835, 2665, 2370, 
2950, 2790, 2130, 2295, 2625, 2720), acceleration = c(12, 11.5, 
11, 12, 10.5, 10, 9, 8.5, 10, 8.5, 10, 8, 9.5, 10, 15, 15.5, 
15.5, 16, 14.5, 20.5, 17.5, 14.5, 17.5, 12.5, 15, 14, 15, 13.5, 
18.5, 14.5, 15.5, 14, 13, 15.5, 15.5, 15.5, 15.5, 12, 11.5, 13.5, 
13, 11.5, 12, 12, 13.5, 19, 15, 14.5, 14, 14, 19.5, 14.5, 19, 
18, 19, 20.5, 15.5, 17, 23.5, 19.5, 16.5, 12, 12, 13.5, 13, 11.5, 
11, 13.5, 13.5, 12.5, 13.5, 12.5, 14, 16, 14, 14.5, 18, 19.5, 
18, 16, 17, 14.5, 15, 16.5, 13, 11.5, 13, 14.5, 12.5, 11.5, 12, 
13, 14.5, 11, 11, 11, 16.5, 18, 16, 16.5, 16, 21, 14, 12.5, 13, 
12.5, 15, 19, 19.5, 16.5, 13.5, 18.5, 14, 15.5, 13, 9.5, 19.5, 
15.5, 14, 15.5, 11, 14, 13.5, 11, 16.5, 16, 17, 19, 16.5, 21, 
17, 17, 18, 16.5, 14, 14.5, 13.5, 16, 15.5, 16.5, 15.5, 14.5, 
16.5, 19, 14.5, 15.5, 14, 15, 15.5, 16, 16, 16, 21, 19.5, 11.5, 
14, 14.5, 13.5, 21, 18.5, 19, 19, 15, 13.5, 12, 16, 17, 16, 18.5, 
13.5, 16.5, 17, 14.5, 14, 17, 15, 17, 14.5, 13.5, 17.5, 15.5, 
16.9, 14.9, 17.7, 15.3, 13, 13, 13.9, 12.8, 15.4, 14.5, 17.6, 
17.6, 22.2, 22.1, 14.2, 17.4, 17.7, 21, 16.2, 17.8, 12.2, 17, 
16.4, 13.6, 15.7, 13.2, 21.9, 15.5, 16.7, 12.1, 12, 15, 14, 18.5, 
14.8, 18.6, 15.5, 16.8, 12.5, 19, 13.7, 14.9, 16.4, 16.9, 17.7, 
19, 11.1, 11.4, 12.2, 14.5, 14.5, 16, 18.2, 15.8, 17, 15.9, 16.4, 
14.1, 14.5, 12.8, 13.5, 21.5, 14.4, 19.4, 18.6, 16.4, 15.5, 13.2, 
12.8, 19.2, 18.2, 15.8, 15.4, 17.2, 17.2, 15.8, 16.7, 18.7, 15.1, 
13.2, 13.4, 11.2, 13.7, 16.5, 14.2, 14.7, 14.5, 14.8, 16.7, 17.6, 
14.9, 15.9, 13.6, 15.7, 15.8, 14.9, 16.6, 15.4, 18.2, 17.3, 18.2, 
16.6, 15.4, 13.4, 13.2, 15.2, 14.9, 14.3, 15, 13, 14, 15.2, 14.4, 
15, 20.1, 17.4, 24.8, 22.2, 13.2, 14.9, 19.2, 14.7, 16, 11.3, 
12.9, 13.2, 14.7, 18.8, 15.5, 16.4, 16.5, 18.1, 20.1, 18.7, 15.8, 
15.5, 17.5, 15, 15.2, 17.9, 14.4, 19.2, 21.7, 23.7, 19.9, 21.8, 
13.8, 18, 15.3, 11.4, 12.5, 15.1, 17, 15.7, 16.4, 14.4, 12.6, 
12.9, 16.9, 16.4, 16.1, 17.8, 19.4, 17.3, 16, 14.9, 16.2, 20.7, 
14.2, 14.4, 16.8, 14.8, 18.3, 20.4, 19.6, 12.6, 13.8, 15.8, 19, 
17.1, 16.6, 19.6, 18.6, 18, 16.2, 16, 18, 16.4, 15.3, 18.2, 17.6, 
14.7, 17.3, 14.5, 14.5, 16.9, 15, 15.7, 16.2, 16.4, 17, 14.5, 
14.7, 13.9, 13, 17.3, 15.6, 24.6, 11.6, 18.6, 19.4), year = c(70, 
70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 
70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 71, 71, 71, 71, 
71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 
71, 71, 71, 71, 71, 71, 71, 72, 72, 72, 72, 72, 72, 72, 72, 72, 
72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 
72, 72, 72, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 
73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 
73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 74, 74, 74, 74, 74, 
74, 74, 74, 74, 74, 74, 74, 74, 74, 74, 74, 74, 74, 74, 74, 74, 
74, 74, 74, 74, 74, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 
75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 
75, 75, 75, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 
76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 
76, 76, 76, 76, 76, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 
77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 
77, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 
78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 
78, 78, 78, 78, 78, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 
79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 
79, 79, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 
80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 81, 81, 81, 
81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 
81, 81, 81, 81, 81, 81, 81, 81, 81, 82, 82, 82, 82, 82, 82, 82, 
82, 82, 82, 82, 82, 82, 82, 82, 82, 82, 82, 82, 82, 82, 82, 82, 
82, 82, 82, 82, 82, 82, 82), origin = c(1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 
1, 3, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
2, 2, 2, 3, 3, 2, 1, 3, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
3, 1, 1, 1, 1, 2, 2, 2, 2, 1, 3, 3, 1, 3, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 3, 3, 1, 
1, 2, 1, 1, 2, 2, 2, 2, 1, 2, 3, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 1, 2, 2, 3, 3, 2, 1, 1, 1, 1, 
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