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Fundamental cycles in a 4x4 maze
# the output of this script has duplicates, and is unordered. it is meant to be
# piped to `sort -u`:
#
# $ perl6 01-cycles.p6 | sort -u > mazcyc
# 00 01 02
# 03 04 05
# 06 07 08
my @n =
[0, 3, 12, 13],
[1, 4, 13, 14],
[2, 5, 14, 15],
[3, 6, 16, 17],
[4, 7, 17, 18],
[5, 8, 18, 19],
[6, 9, 20, 21],
[7, 10, 21, 22],
[8, 11, 22, 23],
[0, 1, 2, 9, 10, 11, 12, 15, 16, 19, 20, 23],
;
# 00 01 02
# 12 13 14 15
# 03 04 05
# 16 17 18 19
# 06 07 08
# 20 21 22 23
# 09 10 11
my @w =
# vertical walls 4x3
[0, 9], [1, 9], [2, 9],
[0, 3], [1, 4], [2, 5],
[3, 6], [4, 7], [5, 8],
[6, 9], [7, 9], [8, 9],
# horizontal walls 3x4
[0, 9], [0, 1], [1, 2], [2, 9],
[3, 9], [3, 4], [4, 5], [5, 9],
[6, 9], [6, 7], [7, 8], [8, 9],
;
# 00 01 02 03
# 04 05 06 07
# 08 09 10 11
# 12 13 14 15
my @c =
{ 0 => 1, 12 => 4 }, { 0 => 0, 1 => 2, 13 => 5 }, { 1 => 1, 2 => 3, 14 => 6 }, { 2 => 2, 15 => 7 },
{ 3 => 5, 12 => 0, 16 => 8 }, { 3 => 4, 4 => 6, 13 => 1, 17 => 9 }, { 4 => 5, 5 => 7, 14 => 2, 18 => 10 }, { 5 => 6, 15 => 3, 19 => 11 },
{ 6 => 9, 16 => 4, 20 => 12 }, { 6 => 8, 7 => 10, 17 => 5, 21 => 13 }, { 7 => 9, 8 => 11, 18 => 6, 22 => 14 }, { 8 => 10, 19 => 7, 23 => 15 },
{ 9 => 13, 20 => 8 }, { 9 => 12, 10 => 14, 21 => 9 }, { 10 => 13, 11 => 15, 22 => 10 }, { 11 => 14, 23 => 11 },
;
sub area($s) {
my $area = 0;
my @queue = 0;
my %visited;
while @queue {
my $c = @queue.shift;
next if %visited{$c}++;
for @c[$c].kv -> $wall, $neighbor {
if $s.substr($wall, 1) eq "0" {
@queue.push($neighbor);
}
}
$area++;
}
# the grid gets split into two. we always return the smaller area.
return $area > 8 ?? 16 - $area !! $area;
}
sub find-cycles(@points, @walls) {
my $p1 = @points[*-1];
for @n[$p1].list -> $w {
next if $w ∈ @walls;
my @ww = @w[$w].list;
my $p2 = @ww[0] == $p1 ?? @ww[1] !! @ww[0];
if $p2 == @points[0] {
my $s = "000000000000000000000000";
my @cycle = @walls, $w;
for @cycle -> $i {
$s = $s.substr(0, $i) ~ "1" ~ $s.substr($i + 1);
}
my $vertical = @cycle ∩ (0, 1, 2, 9, 10, 11);
my $horizontal = @cycle ∩ (12, 15, 16, 19, 20, 23);
my $category =
($vertical && $horizontal) ?? "adjacent" !!
($vertical || $horizontal) ?? "opposite" !! "internal";
my $area = area($s);
say "$s\t$category/{(+@cycle).fmt("%02d")}/$area";
}
next if $p2 ∈ @points;
find-cycles([@points, $p2], [@walls, $w]);
}
}
for 0..9 -> $p {
find-cycles([$p], []);
}
$ cut -f2 mazcyc | perl6 -ne '%h{$_}++; END { for %h.keys.sort { say "$_:"; say ""; shell "grep $_ mazcyc | perl6 draw-em" } }'
adjacent/02/1:
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | |
+ + + + + + + + + + + + + +--+ +--+ + + +
| | | | | | | |
+ + + + + + + + + + + + + + + + + + + +
| | | | | | | |
+ + + +--+ +--+ + + + + + + + + + + + + +
| | | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
adjacent/03/2:
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | | |
+ + + + + + + + + + + + + + + + + + + + + + + + +
| | | | | | | | | | |
+ + + + + + + + + + + + + +--+ +--+ + + + + + + +--+
| | | | | | | | | | | |
+ + +--+--+ +--+--+ + + + + + + + + + + + + + + + + +
| | | | | | | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | |
+ + +--+--+ +--+--+ + + + + + + +
| | | | | | |
+ + + + + + + + + + +--+ + + +
| | | | | |
+ + + + + + + + + + + + + + +
| | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+
adjacent/04/3:
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | |
+ + + + + + + + + + + + + + + + + + + + + + + +--+
| | | | | | | | | | |
+ + + + + + + + + + + + + +--+ +--+ + + + + + + + +
| | | | | | | | | | | | |
+--+--+--+ + + +--+--+--+ + + +--+ + + +--+ + + + + + + +
| | | | | | | | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | | | | | |
+--+ + + + +--+--+--+ + + + + + + + + +--+ + + +--+ + +
| | | | | | | | | | | | | |
+ + + + + + + + + + + + + + + + + + +--+ +--+ + + +
| | | | | | | | | | | |
+ + + + + + + + + + + + + +--+ + + + + + + + + + +
| | | | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
+--+--+--+--+ +--+--+--+--+
| | | | | |
+ +--+--+--+ + + + + +
| | | | |
+ + + + + + + + + +
| | | | |
+ + + + + +--+ + + +
| | | |
+--+--+--+--+ +--+--+--+--+
adjacent/04/4:
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | |
+ + + + + + + + + + + + + + + + + + + +
| | | | | | | | | |
+ + +--+--+ +--+--+ + + + + +--+--+ +--+--+ + +
| | | | | | | | | |
+ + + + + + + + + + + + + + + + + + + +
| | | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
adjacent/05/3:
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | | |
+ + + + + + + + + + + + + + + + + + + + + + +--+ +
| | | | | | | | | | |
+ + +--+--+ +--+--+ + + + + +--+ + + +--+ + + + + +--+--+
| | | | | | | | | | | | | | | |
+ + +--+ + + +--+ + + + + + +--+ +--+ + + + + + + + +
| | | | | | | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | |
+ + + +--+ +--+ + + + + +--+ + +
| | | | | | | | | | |
+ + +--+ + + +--+ + + +--+--+ + +
| | | | | |
+ + + + + + + + + + + + + + +
| | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+
adjacent/05/4:
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | | |
+ + + + + + + + + + + + + +--+ +--+ + + + + +--+--+ +
| | | | | | | | | | | | |
+ + + +--+ +--+ + + + + + + + + + + + + + +--+ + + +
| | | | | | | | | | | | | |
+ +--+--+ + + +--+--+ + + + +--+ + + +--+ + + + + + + +
| | | | | | | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | |
+ + +--+ + + +--+ + + + +--+--+ +
| | | | | | | | |
+ + + + + + + + + + + + + +--+
| | | | | | | |
+ + + +--+ +--+ + + + + + + + +
| | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+
adjacent/05/5:
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | | |
+ + + + + + + + + + + + + +--+ +--+ + + + + + +--+ +
| | | | | | | | | | | | |
+--+--+ + + + + +--+--+ + + +--+ + + +--+ + + +--+--+ + +
| | | | | | | | | | | | | |
+ + +--+ + + +--+ + + + + + + + + + + + + + + + + +
| | | | | | | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | |
+ + + + + + + + + + + +--+ + +
| | | | | | | | |
+ + +--+ + + +--+ + + + + +--+--+
| | | | | | | |
+ + + +--+ +--+ + + + + + + + +
| | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+
adjacent/05/6:
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | | |
+ + + + + + + + + + + + +--+--+ +--+--+ + + + + + + +
| | | | | | | | | | | | |
+--+--+--+ + + +--+--+--+ + + + + + + + + + + +--+--+--+ +
| | | | | | | | | | | | | |
+ + + + + + + + + + + + + + + + + + + + + + + + +
| | | | | | | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | |
+ + + + + + + + + + + + + + +
| | | | | | | | |
+ + + + + + + + + + + +--+--+--+
| | | | | | | |
+ + +--+--+ +--+--+ + + + + + + +
| | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+
adjacent/06/4:
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | |
+ + + + + + + + + + + + + + + + + + + + + + + +--+
| | | | | | | | | | |
+ + +--+ + + + +--+ + + +--+ + + + +--+ + + + + +--+ +
| | | | | | | | | | | | | | | | | | |
+--+--+ + + + +--+ +--+ +--+ +--+ + + + +--+--+ + + +--+ +
| | | | | | | | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | | | |
+ + +--+--+ +--+--+ + + +--+ + + + + + + + + + + +--+ +
| | | | | | | | | | | | | | |
+ + +--+ + + +--+ + + + +--+ + + + + +--+ + + + +--+ +
| | | | | | | | | | | | | | |
+ + + + + + + + + + + +--+ + + + + +--+--+ + + + +--+
| | | | | | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | | | | | | |
+--+--+ + + +--+ +--+ + + +--+ + + + +--+ +--+ + + + + +
| | | | | | | | | | | | | | | | | |
+ + +--+ + + +--+ + + + +--+ + + + + +--+ + + +--+ + +
| | | | | | | | | | | |
+ + + + + + + + + + +--+ + + + + + + + + +--+--+ + +
| | | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
+--+--+--+--+
| | |
+ + +--+--+
| | | |
+ +--+ + +
| |
+ + + + +
| |
+--+--+--+--+
adjacent/06/5:
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | |
+ + + + + + + + + + + + + + + + + + + + + + + +--+
| | | | | | | | | | |
+--+--+--+ + + +--+--+--+ + +--+--+ + + +--+--+ + + + + + +
| | | | | | | | | | | | | | | | |
+ + +--+ + + +--+ + + +--+ + + + + + + +--+ + +--+--+ +
| | | | | | | | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | |
+ + +--+--+ +--+--+ + + + + +--+ + +--+ + + + + +--+ + +
| | | | | | | | | | | | | | | | |
+ + + + + + + + + + + + + +--+ + + + + + +--+ + + +
| | | | | | | | | | | | | | |
+ + +--+ + + +--+ + + + + + + + + +--+--+ + + + + + +
| | | | | | | | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | | | | | | |
+ + +--+ + + +--+--+ + +--+ + + + + + +--+ + + + + + +
| | | | | | | | | | | | | | | |
+ + + + + + + + + + + +--+--+ + +--+--+--+ + + + + +--+
| | | | | | | | | | | | | |
+ + +--+--+ +--+ + + + + + + + + + + + + + + + +--+ +
| | | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | | | | | | |
+ + + + + + +--+ + + + +--+--+ + + +--+ + + + + + +--+
| | | | | | | | | | | | | | | |
+--+ + + + + +--+--+--+ + + + + + + + + + + + +--+--+ +
| | | | | | | | | | | | | |
+ +--+ + + + + + + + + + + +--+ +--+--+ + + + + + + +
| | | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
adjacent/06/6:
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | |
+ + + +--+ +--+ + + + + + +--+ + + +--+ + +
| | | | | | | | | | | |
+ + +--+ + + +--+ + + + +--+ + + + + +--+ +
| | | | | | | | | | | |
+ +--+ + + + + +--+ + +--+ + + + + + + +--+
| | | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
adjacent/06/7:
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | |
+--+--+--+ + + + + +--+ +--+--+ + + + + +--+--+ +--+ + + +
| | | | | | | | | | | | | | |
+ + + + + + +--+--+ + + + + + + + + + + + + +--+--+ +
| | | | | | | | | | | | | | |
+ + + + + + + + + + + + +--+ + + +--+ + + + + + + +
| | | | | | | | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | | | | | |
+ +--+--+--+ + + + + + + + + + + + + +--+ + + +--+ + +
| | | | | | | | | | | | | | |
+ + + + + + + + + + + +--+--+ + + + + + + + + + + +
| | | | | | | | | | | | | | |
+ + + + + +--+--+--+ + +--+ + + + +--+--+ + + + + +--+--+
| | | | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
+--+--+--+--+ +--+--+--+--+
| | | | | |
+ + + + + + + + + +
| | | | | |
+ +--+--+ + + + + + +
| | | | | |
+ + + +--+ + +--+--+--+
| | | |
+--+--+--+--+ +--+--+--+--+
adjacent/06/8:
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | |
+--+--+ + + + + +--+--+ + + + + + + + + + +
| | | | | | | | | | | |
+ + +--+ + + +--+ + + + + +--+ + + +--+ + +
| | | | | | | | | | | |
+ + + + + + + + + + +--+--+ + + + + +--+--+
| | | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
adjacent/07/4:
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | |
+ + + + + + + + + + + + + + + + + + + + + + +--+ +
| | | | | | | | | | | |
+--+--+--+ + + +--+--+--+ + +--+--+ + + +--+--+ + + + + +--+
| | | | | | | | | | | | | | | | |
+ +--+--+ + + +--+--+ + + +--+ +--+ +--+ +--+ + + + +--+ +
| | | | | | | | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | | | |
+ + +--+ + + +--+ + + + +--+ + + + + +--+ + + +--+--+ +
| | | | | | | | | | | | | | | | | |
+ + + + + +--+ + + + + + + + + + + + +--+ + +--+--+--+
| | | | | | | | | | | | | | | | |
+ + + +--+ + +--+ + + +--+ + + + + + +--+ + + + + + +
| | | | | | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | | | | | | |
+ + + +--+ + +--+ +--+ +--+ +--+ + +--+ + + + + +--+--+ +
| | | | | | | | | | | | | | | | | | |
+ + + + + + +--+--+ + + +--+--+ + + + + + + +--+--+--+ +
| | | | | | | | | | | | | |
+ + +--+ + + + + + + + + + + + + +--+ + + + + + + +
| | | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
+--+--+--+--+
| | |
+ +--+ + +
| | |
+--+ + + +
| | | |
+ +--+ + +
| |
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| | | |
+ +--+ + +
| |
+--+--+--+--+
adjacent/09/7:
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | | |
+ +--+--+ + + +--+--+ + +--+ +--+ + + +--+ +--+ + + +--+ +
| | | | | | | | | | | | | | | | | | | | |
+--+ +--+ + + +--+ +--+ + +--+ + + + + +--+ + +--+ +--+ +
| | | | | | | | | | | | | | | |
+ + +--+ + + +--+ + + + + +--+ + + +--+ + + + +--+--+ +
| | | | | | | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | |
+ + +--+ + + +--+ + + + +--+ + +
| | | | | | | | |
+ +--+ + + + + +--+ + + +--+ +--+
| | | | | | | | | | | | | |
+--+ +--+ + + +--+ +--+ + +--+--+ +
| | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+
adjacent/10/6:
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | |
+--+--+--+ + + +--+--+--+ + +--+--+ + + +--+--+ + + +--+--+ +
| | | | | | | | | | | | | | | | | |
+ +--+ + + + + +--+ + + +--+ + + + +--+ + + + + +--+ +
| | | | | | | | | | | | | | | | | | | | | |
+ + +--+ + + +--+ + + +--+--+ + + + +--+ +--+ +--+ +--+ +
| | | | | | | | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | | | |
+ +--+--+ + +--+ +--+ + + +--+ +--+ +--+--+ + + + +--+--+ +
| | | | | | | | | | | | | | | | | | | | |
+ + +--+ + + +--+ + + + + +--+ + + +--+ + + + + +--+ +
| | | | | | | | | | | | | | | | | | |
+ + +--+--+ + +--+--+ + + +--+--+ + + +--+--+ + + +--+ +--+
| | | | | | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | | | | | | |
+--+ +--+ + + +--+ + + + +--+--+ + + +--+ +--+ + + +--+--+
| | | | | | | | | | | | | | | | | | | |
+ + +--+ + + + +--+ + + +--+ + + + +--+ + + + + +--+ +
| | | | | | | | | | | | | | | | | | | |
+ +--+--+ + + +--+--+--+ +--+ +--+ + + +--+--+ + + +--+--+ +
| | | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
+--+--+--+--+
| | |
+ + +--+ +
| | | | |
+ +--+ + +
| | |
+--+--+--+ +
| |
+--+--+--+--+
adjacent/10/7:
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | | |
+--+--+--+ + + +--+--+--+ +--+ +--+ + + +--+ +--+ + +--+--+ +
| | | | | | | | | | | | | | | | | | |
+ +--+--+ + + +--+--+ + + + + + + + + + + + + +--+--+ +
| | | | | | | | | | | | | | | | | | |
+ +--+--+ + + +--+--+ + + +--+ + + + + +--+ + +--+--+--+ +
| | | | | | | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | |
+ +--+ + + + +--+--+ + + + +--+ +
| | | | | | | | | | | | |
+ + + + + + +--+--+ + + + + + +
| | | | | | | | | | | | |
+--+ +--+ + + +--+--+--+ + +--+ +--+
| | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+
internal/04/1:
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | |
+ + + + + + + + + + + + +--+ + + +--+ + +
| | | | | | | | | | | |
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| | | | | | | | | | | |
+ + +--+ + + +--+ + + + + + + + + + + + +
| | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
internal/06/2:
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | |
+ + + + + + + +--+ + + +--+--+ + + +--+ + +
| | | | | | | | | | | | | |
+ +--+--+ + + + + + + + +--+--+ + + + + + +
| | | | | | | | | | | | | |
+ +--+--+ + + + +--+ + + + + + + + +--+ + +
| | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
internal/08/3:
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | |
+ + +--+ + + +--+--+ + + +--+--+ + + +--+ + +
| | | | | | | | | | | | | | | |
+ +--+ + + + +--+ + + + + +--+ + + + +--+ +
| | | | | | | | | | | | | | | |
+ +--+--+ + + + +--+ + + +--+ + + + +--+--+ +
| | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
internal/08/4:
+--+--+--+--+
| |
+ +--+--+ +
| | | |
+ + + + +
| | | |
+ +--+--+ +
| |
+--+--+--+--+
opposite/03/1:
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | |
+ + + + + + + + + + + + + + + + + + + + + + + +--+
| | | | | | | | | | |
+ + + + + + + + + + + + + +--+ +--+ + + + + + + +--+
| | | | | | | | | | | |
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| | | | | | | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | |
+--+ + + + + + +--+ + + +--+ + +
| | | | | | |
+--+ + + + + + + + + + + + + +
| | | | | |
+ + + + + + + + + + + + + + +
| | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+
opposite/04/2:
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | |
+ + + + + + + + +--+ +--+ + + + + +--+--+ +
| | | | | | | | | |
+ + + + + + + + + + + + + + + + + + + +
| | | | | | | | | |
+ +--+--+ + + + + +--+ +--+ + + + + + + + +
| | | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
opposite/04/4:
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | |
+ + + + + +--+--+--+--+ + + + + + + + + + +
| | | | | | | | | |
+ + + + + + + + + + + + + + + + + + + +
| | | | | | | | | |
+--+--+--+--+ + + + + + + + + + + + + + + +
| | | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
opposite/04/8:
+--+--+--+--+ +--+--+--+--+
| | | | |
+ + + + + + + + + +
| | | | |
+--+--+--+--+ + + + + +
| | | | |
+ + + + + + + + + +
| | | | |
+--+--+--+--+ +--+--+--+--+
opposite/05/2:
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | |
+ + + + + + + + + + + + + + + + + + + + + + +--+--+
| | | | | | | | | | |
+ + +--+--+ +--+--+ + + + + +--+ + + +--+ + + + + +--+--+
| | | | | | | | | | | | | | | |
+ + +--+--+ +--+--+ + + + + + + + + + + + + + + + + +
| | | | | | | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | |
+--+--+ + + + + + + + + + + + +
| | | | | | | | | | |
+--+--+ + + + + +--+ + + +--+ + +
| | | | | |
+ + + + + + + + + + + + + + +
| | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+
opposite/05/5:
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | | |
+ + + + + + + + + + +--+--+--+ + + +--+--+--+ + + + + +
| | | | | | | | | | | | |
+ + + +--+ +--+ + + + + + + +--+ +--+ + + + + + + + +
| | | | | | | | | | | | |
+--+--+--+ + + +--+--+--+ + + + + + + + + + + + + +--+ +
| | | | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | |
+ + +--+ + + +--+ + + + + + + +
| | | | | | | | |
+ + + + + + + + + + + + + + +
| | | | | | | | |
+ + + + + + + + + + + +--+ + +
| | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+
opposite/05/6:
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | | |
+ + + + + + + + + + + + +--+--+ +--+--+ + + + + + + +
| | | | | | | | | | | | |
+ + +--+--+ +--+--+ + + +--+--+ + + + + +--+--+ + + +--+ +
| | | | | | | | | | | | |
+--+--+ + + + + +--+--+ + + + + + + + + + + + + + + +
| | | | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | |
+ + + + + + + + + + + + + + +
| | | | | | | | |
+ + +--+ + + +--+ + + + +--+ + +
| | | | | | | | |
+ + + + + + + + + + + + + + +
| | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+
opposite/05/7:
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | | |
+ + + + + + + + + + + + + +--+ +--+ + + + + + +--+ +
| | | | | | | | | | | | |
+--+--+--+ + + +--+--+--+ +--+--+--+ + + +--+--+--+ + + + + +
| | | | | | | | | | | | |
+ + + +--+ +--+ + + + + + + + + + + + + + + + + + +
| | | | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | |
+ + + + + + + + + + + +--+ + +
| | | | | | | | |
+ + + + + + + + + + + + + + +
| | | | | | | | |
+ + +--+ + + +--+ + + + + + + +
| | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+
opposite/06/3:
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | |
+ + + + + + + + + + + + + +--+ + + +--+--+ +--+--+ + +
| | | | | | | | | | | | |
+ + +--+ + + +--+ + + + + +--+ + + + +--+ + + +--+ + +
| | | | | | | | | | | | | | | | |
+ +--+ + + + + +--+ + + + +--+--+ + + + +--+ +--+ + + +
| | | | | | | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | |
+--+ + + + + +--+ + + + + +--+ +
| | | | | | | | | | |
+ +--+ + + + + +--+ + + +--+ + +
| | | | | | |
+--+--+ + + + + + + + + + + + +
| | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+
opposite/06/4:
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | |
+ + + + + + + +--+--+ +--+--+ + + + + + + +
| | | | | | | | | | | |
+ +--+--+ + + + + + + + + + + + + +--+--+ +
| | | | | | | | | | | |
+ + + + + + + +--+--+ +--+--+ + + + + + + +
| | | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
opposite/06/5:
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | | |
+ + + + + + + + + + +--+--+ +--+ +--+ +--+--+ + + + + +
| | | | | | | | | | | | | | |
+ + +--+ + + +--+ + + + + +--+ + + +--+ + + + + +--+ +
| | | | | | | | | | | | | | |
+--+--+ +--+ +--+ +--+--+ + + + + + + + + + + + + +--+ +
| | | | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | |
+ + +--+ + + +--+ + + + + + + +
| | | | | | | | |
+ + +--+ + + +--+ + + + +--+ + +
| | | | | | | | |
+ + + + + + + + + + + +--+ + +
| | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+
opposite/06/6:
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | |
+ + + + + + + + + + + + + +--+ +--+--+--+ + + +--+--+--+
| | | | | | | | | | | | |
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| | | | | | | | | | | | | | | | |
+--+ + +--+ + +--+--+ + +--+--+--+ + + + + +--+ +--+ + + +
| | | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | | | |
+--+ + + + + +--+--+ + +--+ + +--+ + + + + + + + +--+ +
| | | | | | | | | | | | | | | | |
+ + + + + +--+ + +--+ + +--+--+ + + + + + + + + + + +
| | | | | | | | | | | | |
+ +--+--+--+ + + + + + + + + + + + +--+--+ + + + +--+ +
| | | | | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | | | | | | |
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| | | | | | | | | | | | | | |
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| | | | | | | | | | | | | | |
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| | | | | | | | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
+--+--+--+--+
| | |
+ + + + +
| | |
+ + + + +
| | |
+ +--+--+ +
| | |
+--+--+--+--+
opposite/06/7:
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | |
+ + + + + + + + + + + + + +--+ +--+--+ + + + + +--+--+
| | | | | | | | | | | | |
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| | | | | | | | | | | | | | | | |
+ + +--+ + + +--+ + + +--+--+ + + + + + +--+ +--+ + + +
| | | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | | | |
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| | | | | | | | | | | | | | | | |
+--+--+ +--+ + +--+ + + +--+ +--+--+ + + +--+ + + +--+ + +
| | | | | | | | | | | | |
+ + + + + + + +--+--+ + + + + + + +--+ + + + + + + +
| | | | | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | | | | | | |
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| | | | | | | | | | | | | | |
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| | | | | | | | | | | | | | |
+ + + + + + + +--+ + + +--+ + + + + + + + + + + + +
| | | | | | | | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
+--+--+--+--+
| | |
+ + + + +
| | |
+ +--+ + +
| | |
+ + +--+ +
| | |
+--+--+--+--+
opposite/06/8:
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | | |
+ + + +--+ + + +--+--+ +--+--+ + + +--+ + + + + + + + +
| | | | | | | | | | | | | | |
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| | | | | | | | | | | | | | |
+--+ + + + +--+--+ + + + + +--+--+ + + + +--+ + + + + +
| | | | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | |
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| | | | | | | | |
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| | | | | | | | |
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opposite/07/3:
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| | | |
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| | |
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| | |
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| | | | | | | |
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opposite/08/5:
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | |
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opposite/08/6:
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opposite/08/8:
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opposite/09/4:
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opposite/09/5:
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | |
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opposite/09/7:
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| | | | | | | | | | |
+ + +--+ + + +--+ + + + +--+ +--+ +--+ +--+ + + +--+--+ +
| | | | | | | | | | | | | | | | | | | | |
+--+ + + + + + + +--+ +--+ + + + + + + +--+ + +--+--+ +
| | | | | | | | | | | | | | | | | | | | |
+ +--+ +--+ +--+ +--+ + + + +--+ + + +--+ + + + + +--+ +
| | | | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | |
+ + +--+ + + +--+ + + + +--+--+ +
| | | | | | | | |
+ +--+--+ + + +--+--+ + + +--+--+ +
| | | | | | | | |
+ +--+--+ + + +--+--+ + + +--+ + +
| | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+
opposite/09/8:
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | | |
+ + +--+--+ +--+--+ + + + +--+--+ + + +--+--+ + + +--+ + +
| | | | | | | | | | | | | | | | | | |
+--+ +--+ + + +--+ +--+ + +--+ +--+ +--+ +--+ + + + +--+ +
| | | | | | | | | | | | | | | | |
+ +--+--+ + + +--+--+ + +--+--+ + + + + +--+--+ + +--+ + +
| | | | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | |
+ + +--+ + + +--+ + + + + +--+ +
| | | | | | | | | | |
+ +--+ + + + + +--+ + + +--+ + +
| | | | | | | | | | | | |
+ + +--+ + + +--+ + + + + +--+ +
| | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+
opposite/10/5:
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | |
+--+--+--+ + + +--+--+--+ + +--+--+ + + +--+--+ + +--+ +--+ +
| | | | | | | | | | | | | | | | | | |
+ +--+ + + + + +--+ + + +--+ + + + + +--+ + + +--+ + +
| | | | | | | | | | | | | | | | | | | | |
+--+ +--+ + + +--+ +--+ + +--+ + + + + +--+ + +--+--+--+ +
| | | | | | | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | |
+ +--+ +--+ + +--+ + + + + +--+ +
| | | | | | | | | | | | |
+ + +--+ + + +--+ + + + + +--+ +
| | | | | | | | | | |
+ +--+--+--+ + +--+--+ + + +--+--+ +
| | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+
opposite/10/7:
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | | |
+--+--+ +--+ + +--+--+ + + +--+--+ + +--+ +--+--+ + +--+--+ +
| | | | | | | | | | | | | | | | | | |
+ +--+ + + + +--+ + + + + +--+ + + + +--+ + + + +--+ +
| | | | | | | | | | | | | | | | | | | | |
+ +--+--+ + +--+--+ +--+ +--+ +--+--+ + +--+--+ + + +--+ + +
| | | | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | |
+ +--+ + + + +--+--+ + + + +--+ +
| | | | | | | | | | | | |
+ + +--+ + + +--+ + + + +--+ + +
| | | | | | | | | | |
+ +--+--+ + + + +--+ + + +--+--+ +
| | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+
opposite/10/8:
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | | | |
+--+--+--+ + + +--+--+--+ + +--+ +--+ +--+ +--+ + + +--+--+ +
| | | | | | | | | | | | | | | | | | |
+ +--+--+ + + +--+--+ + + + + + + + + + + + + +--+--+ +
| | | | | | | | | | | | | | | | | | |
+ +--+--+--+ +--+--+--+ + +--+ +--+ + + +--+ +--+ + +--+--+ +
| | | | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ +--+--+--+--+
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+
| | | | | | | | |
+ +--+ + + + +--+--+ + + + +--+ +
| | | | | | | | | | | | |
+ + + + + + +--+--+ + + + + + +
| | | | | | | | | | | | |
+ + +--+ + + +--+--+ + + +--+ + +
| | | | | | | | |
+--+--+--+--+ +--+--+--+--+ +--+--+--+--+
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