2021 Day 12

Author

Nathan Moore

— Day 12: Passage Pathing —

We have to find a way through this cave system.

How many paths through this cave system are there that visit small caves at most once?

library(tidyverse)
library(igraph)


Attaching package: 'igraph'

The following objects are masked from 'package:lubridate':

    %--%, union

The following objects are masked from 'package:dplyr':

    as_data_frame, groups, union

The following objects are masked from 'package:purrr':

    compose, simplify

The following object is masked from 'package:tidyr':

    crossing

The following object is masked from 'package:tibble':

    as_data_frame

The following objects are masked from 'package:stats':

    decompose, spectrum

The following object is masked from 'package:base':

    union

my_file <- here::here("2021", "data-2021-12.txt")
x <- readLines(my_file)

Let’s create a matrix and see what links up.

pairs = strsplit(x, "-")
caves = unique(unlist(pairs))

cave_mat = matrix(FALSE, 
                  nrow=length(caves), 
                  ncol=length(caves), 
                  dimnames=list(caves,caves))

for (c in 1:length(x)) { 
    cave_mat[pairs[[c]][1], pairs[[c]][2]] = TRUE
}

cave_mat

         rf    RL    wz    AV    mh   end    dm    gy    cg    VI start    qk
rf    FALSE  TRUE  TRUE  TRUE  TRUE FALSE FALSE  TRUE FALSE FALSE FALSE FALSE
RL    FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
wz    FALSE  TRUE FALSE FALSE  TRUE FALSE  TRUE  TRUE FALSE FALSE FALSE FALSE
AV    FALSE FALSE FALSE FALSE  TRUE FALSE FALSE  TRUE FALSE FALSE  TRUE FALSE
mh    FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
end   FALSE FALSE  TRUE FALSE  TRUE FALSE  TRUE FALSE FALSE FALSE FALSE FALSE
dm     TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
gy    FALSE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
cg    FALSE  TRUE FALSE  TRUE FALSE FALSE FALSE  TRUE FALSE FALSE FALSE FALSE
VI    FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE FALSE FALSE FALSE FALSE
start FALSE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE FALSE FALSE FALSE
qk    FALSE FALSE FALSE FALSE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE

But also we could try a proper graph packages

g = make_graph(edges=unlist(pairs), directed=FALSE)

plot(g)

all_simple_paths(g, "start", "end")

[[1]]
+ 6/12 vertices, named, from 714f468:
[1] start RL    rf    wz    mh    end  

[[2]]
+ 5/12 vertices, named, from 714f468:
[1] start RL    rf    wz    end  

[[3]]
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[1] start RL    rf    wz    dm    end  

[[4]]
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[1] start RL    rf    wz    gy    AV    mh    end  

[[5]]
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[1] start RL    rf    wz    gy    cg    AV    mh    end  

[[6]]
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[1] start RL    rf    AV    mh    wz    end  

[[7]]
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[1] start RL    rf    AV    mh    wz    dm    end  

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[1] start RL    rf    AV    mh    end  

[[9]]
+ 8/12 vertices, named, from 714f468:
[1] start RL    rf    AV    gy    wz    mh    end  

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+ 7/12 vertices, named, from 714f468:
[1] start RL    rf    AV    gy    wz    end  

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+ 8/12 vertices, named, from 714f468:
[1] start RL    rf    AV    gy    wz    dm    end  

[[12]]
+ 9/12 vertices, named, from 714f468:
[1] start RL    rf    AV    cg    gy    wz    mh    end  

[[13]]
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[1] start RL    rf    AV    cg    gy    wz    end  

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[1] start RL    rf    AV    cg    gy    wz    dm    end  

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[1] start RL    rf    mh    wz    end  

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[1] start RL    rf    mh    wz    dm    end  

[[17]]
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[1] start RL    rf    mh    AV    gy    wz    end  

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[1] start RL    rf    mh    AV    gy    wz    dm    end  

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[1] start RL    rf    mh    AV    cg    gy    wz    end  

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 [1] start RL    rf    mh    AV    cg    gy    wz    dm    end  

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[1] start RL    rf    mh    end  

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[1] start RL    rf    dm    wz    mh    end  

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[1] start RL    rf    dm    wz    end  

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+ 9/12 vertices, named, from 714f468:
[1] start RL    rf    dm    wz    gy    AV    mh    end  

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+ 10/12 vertices, named, from 714f468:
 [1] start RL    rf    dm    wz    gy    cg    AV    mh    end  

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+ 5/12 vertices, named, from 714f468:
[1] start RL    rf    dm    end  

[[27]]
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[1] start RL    rf    gy    wz    mh    end  

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[1] start RL    rf    gy    wz    end  

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[1] start RL    rf    gy    wz    dm    end  

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[1] start RL    rf    gy    AV    mh    wz    end  

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[1] start RL    rf    gy    AV    mh    wz    dm    end  

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[1] start RL    rf    gy    AV    mh    end  

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+ 9/12 vertices, named, from 714f468:
[1] start RL    rf    gy    cg    AV    mh    wz    end  

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 [1] start RL    rf    gy    cg    AV    mh    wz    dm    end  

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[1] start RL    rf    gy    cg    AV    mh    end  

[[36]]
+ 7/12 vertices, named, from 714f468:
[1] start RL    wz    rf    AV    mh    end  

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[1] start RL    wz    rf    mh    end  

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[1] start RL    wz    rf    dm    end  

[[39]]
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[1] start RL    wz    rf    gy    AV    mh    end  

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+ 9/12 vertices, named, from 714f468:
[1] start RL    wz    rf    gy    cg    AV    mh    end  

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+ 7/12 vertices, named, from 714f468:
[1] start RL    wz    mh    rf    dm    end  

[[42]]
+ 8/12 vertices, named, from 714f468:
[1] start RL    wz    mh    AV    rf    dm    end  

[[43]]
+ 9/12 vertices, named, from 714f468:
[1] start RL    wz    mh    AV    gy    rf    dm    end  

[[44]]
+ 10/12 vertices, named, from 714f468:
 [1] start RL    wz    mh    AV    cg    gy    rf    dm    end  

[[45]]
+ 5/12 vertices, named, from 714f468:
[1] start RL    wz    mh    end  

[[46]]
+ 4/12 vertices, named, from 714f468:
[1] start RL    wz    end  

[[47]]
+ 8/12 vertices, named, from 714f468:
[1] start RL    wz    dm    rf    AV    mh    end  

[[48]]
+ 7/12 vertices, named, from 714f468:
[1] start RL    wz    dm    rf    mh    end  

[[49]]
+ 9/12 vertices, named, from 714f468:
[1] start RL    wz    dm    rf    gy    AV    mh    end  

[[50]]
+ 10/12 vertices, named, from 714f468:
 [1] start RL    wz    dm    rf    gy    cg    AV    mh    end  

[[51]]
+ 5/12 vertices, named, from 714f468:
[1] start RL    wz    dm    end  

[[52]]
+ 8/12 vertices, named, from 714f468:
[1] start RL    wz    gy    rf    AV    mh    end  

[[53]]
+ 7/12 vertices, named, from 714f468:
[1] start RL    wz    gy    rf    mh    end  

[[54]]
+ 7/12 vertices, named, from 714f468:
[1] start RL    wz    gy    rf    dm    end  

[[55]]
+ 8/12 vertices, named, from 714f468:
[1] start RL    wz    gy    AV    rf    mh    end  

[[56]]
+ 8/12 vertices, named, from 714f468:
[1] start RL    wz    gy    AV    rf    dm    end  

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+ 9/12 vertices, named, from 714f468:
[1] start RL    wz    gy    AV    mh    rf    dm    end  

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[1] start RL    wz    gy    AV    mh    end  

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+ 9/12 vertices, named, from 714f468:
[1] start RL    wz    gy    cg    AV    rf    mh    end  

[[60]]
+ 9/12 vertices, named, from 714f468:
[1] start RL    wz    gy    cg    AV    rf    dm    end  

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+ 10/12 vertices, named, from 714f468:
 [1] start RL    wz    gy    cg    AV    mh    rf    dm    end  

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[1] start RL    wz    gy    cg    AV    mh    end  

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[1] start RL    gy    rf    wz    mh    end  

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[1] start RL    gy    rf    wz    end  

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[1] start RL    gy    rf    wz    dm    end  

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[1] start RL    gy    rf    AV    mh    wz    end  

[[67]]
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[1] start RL    gy    rf    AV    mh    wz    dm    end  

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[1] start RL    gy    rf    AV    mh    end  

[[69]]
+ 7/12 vertices, named, from 714f468:
[1] start RL    gy    rf    mh    wz    end  

[[70]]
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[1] start RL    gy    rf    mh    wz    dm    end  

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+ 6/12 vertices, named, from 714f468:
[1] start RL    gy    rf    mh    end  

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[1] start RL    gy    rf    dm    wz    mh    end  

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[1] start RL    gy    rf    dm    wz    end  

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[1] start RL    gy    rf    dm    end  

[[75]]
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[1] start RL    gy    wz    rf    AV    mh    end  

[[76]]
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[1] start RL    gy    wz    rf    mh    end  

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[1] start RL    gy    wz    rf    dm    end  

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[1] start RL    gy    wz    mh    rf    dm    end  

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[1] start RL    gy    wz    mh    AV    rf    dm    end  

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+ 6/12 vertices, named, from 714f468:
[1] start RL    gy    wz    mh    end  

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+ 5/12 vertices, named, from 714f468:
[1] start RL    gy    wz    end  

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+ 9/12 vertices, named, from 714f468:
[1] start RL    gy    wz    dm    rf    AV    mh    end  

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[1] start RL    gy    wz    dm    rf    mh    end  

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[1] start RL    gy    wz    dm    end  

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[1] start RL    gy    AV    rf    wz    mh    end  

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[1] start RL    gy    AV    rf    wz    end  

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[1] start RL    gy    AV    rf    wz    dm    end  

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[1] start RL    gy    AV    rf    mh    wz    end  

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[1] start RL    gy    AV    rf    mh    wz    dm    end  

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[1] start RL    gy    AV    rf    mh    end  

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+ 9/12 vertices, named, from 714f468:
[1] start RL    gy    AV    rf    dm    wz    mh    end  

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[1] start RL    gy    AV    rf    dm    wz    end  

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[1] start RL    gy    AV    rf    dm    end  

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[1] start RL    gy    AV    mh    rf    wz    end  

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[1] start RL    gy    AV    mh    rf    wz    dm    end  

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[1] start RL    gy    AV    mh    rf    dm    wz    end  

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[1] start RL    gy    AV    mh    rf    dm    end  

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[1] start RL    gy    AV    mh    wz    rf    dm    end  

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[1] start RL    gy    AV    mh    wz    end  

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[1] start RL    gy    AV    mh    wz    dm    end  

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[1] start RL    gy    AV    mh    end  

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+ 9/12 vertices, named, from 714f468:
[1] start RL    gy    cg    AV    rf    wz    mh    end  

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[1] start RL    gy    cg    AV    rf    wz    end  

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[1] start RL    gy    cg    AV    rf    wz    dm    end  

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[1] start RL    gy    cg    AV    rf    mh    wz    end  

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 [1] start RL    gy    cg    AV    rf    mh    wz    dm    end  

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+ 8/12 vertices, named, from 714f468:
[1] start RL    gy    cg    AV    rf    mh    end  

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+ 10/12 vertices, named, from 714f468:
 [1] start RL    gy    cg    AV    rf    dm    wz    mh    end  

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[1] start RL    gy    cg    AV    rf    dm    wz    end  

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[1] start RL    gy    cg    AV    rf    dm    end  

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+ 9/12 vertices, named, from 714f468:
[1] start RL    gy    cg    AV    mh    rf    wz    end  

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 [1] start RL    gy    cg    AV    mh    rf    wz    dm    end  

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 [1] start RL    gy    cg    AV    mh    rf    dm    wz    end  

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[1] start RL    gy    cg    AV    mh    rf    dm    end  

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 [1] start RL    gy    cg    AV    mh    wz    rf    dm    end  

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[1] start RL    gy    cg    AV    mh    wz    end  

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[1] start RL    gy    cg    AV    mh    wz    dm    end  

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[1] start RL    gy    cg    AV    mh    end  

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[1] start RL    cg    AV    rf    wz    mh    end  

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[1] start RL    cg    AV    rf    wz    end  

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[1] start RL    cg    AV    rf    wz    dm    end  

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[1] start RL    cg    AV    rf    mh    wz    end  

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[1] start RL    cg    AV    rf    mh    wz    dm    end  

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[1] start RL    cg    AV    rf    mh    end  

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[1] start RL    cg    AV    rf    dm    wz    mh    end  

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[1] start RL    cg    AV    rf    dm    wz    end  

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[1] start RL    cg    AV    rf    dm    end  

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+ 9/12 vertices, named, from 714f468:
[1] start RL    cg    AV    rf    gy    wz    mh    end  

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[1] start RL    cg    AV    rf    gy    wz    end  

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[1] start RL    cg    AV    rf    gy    wz    dm    end  

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[1] start RL    cg    AV    mh    rf    wz    end  

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[1] start RL    cg    AV    mh    rf    wz    dm    end  

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[1] start RL    cg    AV    mh    rf    dm    wz    end  

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[1] start RL    cg    AV    mh    rf    dm    end  

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[1] start RL    cg    AV    mh    rf    gy    wz    end  

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 [1] start RL    cg    AV    mh    rf    gy    wz    dm    end  

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[1] start RL    cg    AV    mh    wz    rf    dm    end  

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[1] start RL    cg    AV    mh    wz    end  

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[1] start RL    cg    AV    mh    wz    dm    end  

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 [1] start RL    cg    AV    mh    wz    gy    rf    dm    end  

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+ 6/12 vertices, named, from 714f468:
[1] start RL    cg    AV    mh    end  

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+ 9/12 vertices, named, from 714f468:
[1] start RL    cg    AV    gy    rf    wz    mh    end  

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+ 8/12 vertices, named, from 714f468:
[1] start RL    cg    AV    gy    rf    wz    end  

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+ 9/12 vertices, named, from 714f468:
[1] start RL    cg    AV    gy    rf    wz    dm    end  

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+ 9/12 vertices, named, from 714f468:
[1] start RL    cg    AV    gy    rf    mh    wz    end  

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 [1] start RL    cg    AV    gy    rf    mh    wz    dm    end  

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[1] start RL    cg    AV    gy    rf    mh    end  

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 [1] start RL    cg    AV    gy    rf    dm    wz    mh    end  

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[1] start RL    cg    AV    gy    rf    dm    wz    end  

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[1] start RL    cg    AV    gy    rf    dm    end  

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[1] start RL    cg    AV    gy    wz    rf    mh    end  

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[1] start RL    cg    AV    gy    wz    rf    dm    end  

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 [1] start RL    cg    AV    gy    wz    mh    rf    dm    end  

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[1] start RL    cg    AV    gy    wz    mh    end  

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[1] start RL    cg    AV    gy    wz    end  

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+ 10/12 vertices, named, from 714f468:
 [1] start RL    cg    AV    gy    wz    dm    rf    mh    end  

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[1] start RL    cg    AV    gy    wz    dm    end  

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[1] start RL    cg    gy    rf    wz    mh    end  

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[1] start RL    cg    gy    rf    wz    end  

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[1] start RL    cg    gy    rf    wz    dm    end  

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[1] start RL    cg    gy    rf    AV    mh    wz    end  

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 [1] start RL    cg    gy    rf    AV    mh    wz    dm    end  

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[1] start RL    cg    gy    rf    AV    mh    end  

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[1] start RL    cg    gy    rf    mh    wz    end  

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[1] start RL    cg    gy    rf    mh    wz    dm    end  

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[1] start RL    cg    gy    rf    mh    end  

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[1] start RL    cg    gy    rf    dm    wz    mh    end  

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[1] start RL    cg    gy    rf    dm    wz    end  

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[1] start RL    cg    gy    rf    dm    end  

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[1] start RL    cg    gy    wz    rf    AV    mh    end  

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[1] start RL    cg    gy    wz    rf    mh    end  

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[1] start RL    cg    gy    wz    rf    dm    end  

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[1] start RL    cg    gy    wz    mh    rf    dm    end  

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 [1] start RL    cg    gy    wz    mh    AV    rf    dm    end  

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[1] start RL    cg    gy    wz    mh    end  

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[1] start RL    cg    gy    wz    end  

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 [1] start RL    cg    gy    wz    dm    rf    AV    mh    end  

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[1] start RL    cg    gy    wz    dm    rf    mh    end  

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[1] start RL    cg    gy    wz    dm    end  

[[180]]
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[1] start cg    gy    RL    rf    dm    wz    mh    end  

[[564]]
+ 8/12 vertices, named, from 714f468:
[1] start cg    gy    RL    rf    dm    wz    end  

[[565]]
+ 7/12 vertices, named, from 714f468:
[1] start cg    gy    RL    rf    dm    end  

[[566]]
+ 9/12 vertices, named, from 714f468:
[1] start cg    gy    RL    wz    rf    AV    mh    end  

[[567]]
+ 8/12 vertices, named, from 714f468:
[1] start cg    gy    RL    wz    rf    mh    end  

[[568]]
+ 8/12 vertices, named, from 714f468:
[1] start cg    gy    RL    wz    rf    dm    end  

[[569]]
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[1] start cg    gy    RL    wz    mh    rf    dm    end  

[[570]]
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 [1] start cg    gy    RL    wz    mh    AV    rf    dm    end  

[[571]]
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[1] start cg    gy    RL    wz    mh    end  

[[572]]
+ 6/12 vertices, named, from 714f468:
[1] start cg    gy    RL    wz    end  

[[573]]
+ 10/12 vertices, named, from 714f468:
 [1] start cg    gy    RL    wz    dm    rf    AV    mh    end  

[[574]]
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[1] start cg    gy    RL    wz    dm    rf    mh    end  

[[575]]
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[1] start cg    gy    RL    wz    dm    end  

[[576]]
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[1] start cg    gy    wz    rf    AV    mh    end  

[[577]]
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[1] start cg    gy    wz    rf    mh    end  

[[578]]
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[1] start cg    gy    wz    rf    dm    end  

[[579]]
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[1] start cg    gy    wz    RL    rf    AV    mh    end  

[[580]]
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[1] start cg    gy    wz    RL    rf    mh    end  

[[581]]
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[1] start cg    gy    wz    RL    rf    dm    end  

[[582]]
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[1] start cg    gy    wz    mh    rf    dm    end  

[[583]]
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[1] start cg    gy    wz    mh    AV    rf    dm    end  

[[584]]
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[1] start cg    gy    wz    mh    end  

[[585]]
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[1] start cg    gy    wz    end  

[[586]]
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[1] start cg    gy    wz    dm    rf    AV    mh    end  

[[587]]
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[1] start cg    gy    wz    dm    rf    mh    end  

[[588]]
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[1] start cg    gy    wz    dm    end  

[[589]]
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[1] start cg    gy    AV    rf    RL    wz    mh    end  

[[590]]
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[1] start cg    gy    AV    rf    RL    wz    end  

[[591]]
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[1] start cg    gy    AV    rf    RL    wz    dm    end  

[[592]]
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[1] start cg    gy    AV    rf    wz    mh    end  

[[593]]
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[1] start cg    gy    AV    rf    wz    end  

[[594]]
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[1] start cg    gy    AV    rf    wz    dm    end  

[[595]]
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[1] start cg    gy    AV    rf    mh    wz    end  

[[596]]
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[1] start cg    gy    AV    rf    mh    wz    dm    end  

[[597]]
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[1] start cg    gy    AV    rf    mh    end  

[[598]]
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[1] start cg    gy    AV    rf    dm    wz    mh    end  

[[599]]
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[1] start cg    gy    AV    rf    dm    wz    end  

[[600]]
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[1] start cg    gy    AV    rf    dm    end  

[[601]]
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[1] start cg    gy    AV    mh    rf    RL    wz    end  

[[602]]
+ 10/12 vertices, named, from 714f468:
 [1] start cg    gy    AV    mh    rf    RL    wz    dm    end  

[[603]]
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[1] start cg    gy    AV    mh    rf    wz    end  

[[604]]
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[1] start cg    gy    AV    mh    rf    wz    dm    end  

[[605]]
+ 9/12 vertices, named, from 714f468:
[1] start cg    gy    AV    mh    rf    dm    wz    end  

[[606]]
+ 8/12 vertices, named, from 714f468:
[1] start cg    gy    AV    mh    rf    dm    end  

[[607]]
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[1] start cg    gy    AV    mh    wz    rf    dm    end  

[[608]]
+ 10/12 vertices, named, from 714f468:
 [1] start cg    gy    AV    mh    wz    RL    rf    dm    end  

[[609]]
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[1] start cg    gy    AV    mh    wz    end  

[[610]]
+ 8/12 vertices, named, from 714f468:
[1] start cg    gy    AV    mh    wz    dm    end  

[[611]]
+ 6/12 vertices, named, from 714f468:
[1] start cg    gy    AV    mh    end

# 611 low