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a blog from Eli the Bearded
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Matched Pairs


In vi (and vim), there's a "motion" command, % that moves you to an enclosing symbol. In the previous sentence, with the cursor on the "v" of vim, using % will move the cursor to the "(", which is the start of the enclosed sequence. On that "(", the % motion moves to the matching ")".

Out of the box, vi knows the pairs "()", "[]", and "{}". You can change the pairs with the configuration variable matchpairs and people frequently do to add "<>" for XML or HTML work:

set matchpairs=(:),[:],{:},<,>

But there are a lot more, like quoting angles "«»" and smart quotes. And vim happily accepts UTF-8 characters for each half of a pair. So I could think up some Unicode pairs and stick them in there. Or I could look for all pairs that exist in Unicode.

Here's a stab at doing just that.

First off, we need the list of characters in Unicode. This is surprisingly easy to get. Unicode themselves provide an easy to parse list of characters in plain ASCII(!).

$ curl -sO http://www.unicode.org/Public/UNIDATA/UnicodeData.txt

The list is not fixed, new stuff gets added with each version of Unicode. Releases happen every 12 to 18 months. Refreshing that file is the major change needed to update my Unicode Toys for a new version.

So how about a quick script to find "LEFT" characters that have a matching "RIGHT" version?

#!/usr/bin/perl
# Read the UnicodeData.txt file to create a vim 
# matchpair list.
#
# May 2022 "Eli the Bearded"
use strict;
use warnings;

my $in = 'UnicodeData.txt';
my %found;
my %pool;
my %check;
my $id;
my $pid;
my $name;
my $count = 1; # first pair is the hardcoded one

# Tag characters are an obsolete invisible set of
# ASCII for hidden metadata. Modifiers and Combining
# should not be used on their own. Arabic are not
# left-to-right text, so I decided I don't need them.
# You may decide otherwise. The others, by inspection,
# don't have anything I'd want as a pair. (Some
# are part of of larger sets, like up/down/left/right
# quads, or parts of multicharacter pictures.) This
# still leaves some unlikely pairs including box drawing
# stuff. It's a quick list.
#
# These are checked with word boundaries, so CIRCLE
# will not skip CIRCLED.
my @skip = qw[ TAG MODIFIER COMBINING ARABIC IDEOGRAPH
	       ARROWHEAD ARROW
	       AFFIX CIRCLE HALF
	       UP UPWARDS
	       DOWN DOWNWARDS
	     ];
my $skip = join('|', @skip);
my $skip_re = qr/\b(?:$skip)\b/; # \b for boundary

# no boundary check, allow "leftfacing" and the like
my $keep_re = qr/(?:LEFT|RIGHT)/;

binmode(STDOUT, ':utf8');
open(STDIN, '<', $in) or die;

while(<>) {
  # keep code point and name only
  /^([^;]+);([^;]+);/ or next;
  $id = $1;
  $name = $2;

  # Stop checking if on skip list
  next if /$skip_re/;

  # if left or right, keep, but separately
  if (/$keep_re/) {
    if (/RIGHT/) {
      $check{$name} = $id;
    } else {
      $pool{$name} = $id;
    }
  }
}
close STDIN;

for $name (keys %check) {
  my $pair = $name;
  # %check has RIGHTs, see if there is a matching left
  $pair =~ s/RIGHT/LEFT/g;
  if (length( $pid = $pool{$pair} )) {
     $id = $check{$name};
     $found{$pid} = $id;

     # In .exrc or .vimrc " is used to begin a comment.
     # These three printf()s just document the pairs.
     printf(qq{" U+%s\t%c\t%s\n}, $pid, hex($pid), $pair);
     printf(qq{" U+%s\t%c\t%s\n}, $id, hex($id), $name);
     printf "\"\n";
     $count ++;
  }
}
print STDERR "Found $count pairs\n";

# Unfortunately < and > are not named with LEFT and RIGHT
# so hardcode that.
printf "set matchpairs=<:>";
for $id (sort { $a cmp $b } (keys %found)) {
  $pid = $found{$id};
  printf ",%c:%c", hex($id), hex($pid);
}
printf "\n";
__END__

Saved as matchmaker, with the Unicode data file in same directory, let's try it.

$ perl matchmaker >> .vimrc
Found 186 pairs
$ tail -1 .vimrc
set matchpairs=<:>,(:),[:],{:},«:»,֎:֍,܆:܇,࿖:࿕,࿘:࿗,𐡷:𐡸,𝄆:𝄇,𝅊:𝅌,𝅋:𝅍,👈:👉,🔍:🔎,🕃:🕄,🕻:🕽,🖉:✎,🖘:🖙,🖚:🖛,🖜:🖝,🗦:🗧,🗨:🗩,🗬:🗭,🗮:🗯,🙬:🙮,🤛:🤜,🫲:🫱,🭪:🭨,🭬:🭮,🭼:🭿,🭽:🭾,🮜:🮝,🮟:🮞,🮠:🮡,🮢:🮣,🮤:🮥,🯇:🯈,‘:’,“:”,‹:›,⁅:⁆,⁌:⁍,⁽:⁾,₍:₎,⇇:⇉,⊣:⊢,⋉:⋊,⋋:⋌,⌈:⌉,⌊:⌋,⌍:⌌,⌏:⌎,⌜:⌝,⌞:⌟,〈:〉,⌫:⌦,⍅:⍆,⎛:⎞,⎜:⎟,⎝:⎠,⎡:⎤,⎢:⎥,⎣:⎦,⎧:⎫,⎨:⎬,⎩:⎭,⎸:⎹,⏋:⎾,⏌:⎿,⏪:⏩,⏮:⏭,⏴:⏵,┤:├,┥:┝,┨:┠,┫:┣,╡:╞,╢:╟,╣:╠,╴:╶,╸:╺,▉:🮋,▊:🮊,▋:🮉,▍:🮈,▎:🮇,▏:▕,▖:▗,▘:▝,◀:▶,◁:▷,◂:▸,◃:▹,◄:►,◅:▻,◜:◝,◟:◞,◣:◢,◤:◥,◰:◳,◱:◲,◸:◹,◺:◿,☚:☛,☜:☞,⚟:⚞,⛦:⛥,❨:❩,❪:❫,❬:❭,❮:❯,❰:❱,❲:❳,❴:❵,⟅:⟆,⟕:⟖,⟞:⟝,⟢
 :⟣,⟤:⟥,⟦:⟧,⟨:⟩,⟪:⟫,⟬:⟭,⟮:⟯,⥼:⥽,⦃:⦄,⦅:⦆,⦇:⦈,⦉:⦊,⦋:⦌,⦍:⦐,⦏:⦎,⦑:⦒,⦗:⦘,⧘:⧙,⧚:⧛,⧼:⧽,⫍:⫎,⫥:⊫,⬱:⇶,⮄:⮆,⮐:⮑,⮒:⮓,⯇:⯈,⸂:⸃,⸄:⸅,⸉:⸊,⸌:⸍,⸜:⸝,⸠:⸡,⸦:⸧,⸨:⸩,⸶:⸷,⹑:⹐,⹕:⹖,⹗:⹘,⿸:⿹,〈:〉,《:》,「:」,『:』,【:】,〔:〕,〖:〗,〘:〙,〚:〛,꧁:꧂,﴾:﴿,︵:︶,︷:︸,︹:︺,︻:︼,︽:︾,︿:﹀,﹁:﹂,﹃:﹄,﹇:﹈,﹙:﹚,﹛:﹜,﹝:﹞,(:),[:],{:},⦅:⦆,「:」
$

There are a lot of good pairs in that. But some pairs might need to be switched for taste. (Looking at those hands.)

Unicode Sponsorship


Inspired by someone else's tale of "adopting" a Unicode character, I looked at the "adoption" form yesterday and decided that I could easily afford the low-end "bronze" level for U+2417 SYMBOL FOR END OF TRANSMISSION BLOCK, the icon for ASCII character 0x17 END OF TRANSMISSION BLOCK, commonly called ETB. The shared initials with "Eli the Bearded" attracted me to those pair of characters, one of which has a symbol that shows those initials.

I've had a fondness for Unicode in general for years which is how I ended up writing my Unicode Toys, first the grep tool to explore the characters and see them, then show tool to identify characters found in the wild, and after that the rest of them. The convert tool is the one that has attracted the most attention. It does real and toy shifts of characters to other parts of Unicode.

I have mixed feelings about that one. The converter is a fun toy, but also sadly somewhat overused. Because the characters have meanings besides their appearance, using them for for their appearance alone ends up being a huge accessibility barrier. The only conversions I use on a regular basis are the the fraction maker to access the super and subscripts and vulgar fractions plus the Braille converter.

I see Braille on-screen as quite ironic: non-raised dots that are only accessible to the sighted, but are quite unreadable to the sighted. The doubly unaccessible nature of that quite tickles me.

ASCII art and "ASCII" art


I first had email, and first saw a :-) smiley face in 1990. It was about that time, also, that I was exposed to concrete poetry. Both the smiley and the pictures of words poetry were influential on my mind.

I've had a long lasting love of ASCII art and things near to it since. The first program I saw that could create ASCII art from another image was pbmtoascii from the netpnm package. It worked, but it was kinda disappointing. I had seen, and even made myself, hand drawn ASCII art that was much better than the output of that tool.

$ pnmscale -w 60 < fine.pgm |pgmtopbm |pnminvert |pbmtoascii
 ooo" M o"o" oMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMo"
M oo"o" M o" MMMMM"MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM "
o"o M "o M "oMMMMM"oM "MoM oMMMMMoo""MMM"ooM"o""" oMMMMMMM "
o" " M o"o"  MMMMMMMoMoMoMMoMMMMMoMMoMMMMoMMMoMMoM"MMMMMMM "
o""oo o o o"o""MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM o"
o"M M M"oM M "o""MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM"o"o"
"o"" "" o"" ""o"ooo""""M"M"MMMMMMMMMMMMMMMMMMMMMMM""" o"o"oM
MM"MMMMMoo"M"oo ooo"oooMoMoooooo MMM M"o"oo" ooooo"o"M o ooo
MMMM"MM oM"oM"oMoM""MMMMM"MMM"MM MM MMMMMMMMMooooooooooMMM o
""MMMMM Mo"" "   o"M MoMMMMMMMMo"MM MMMoMMM"MM"MM"MM"MMMo"oM
 MM"MM" o     o MoM"o"M"MMoMMMM MM"MMM"MMoMMMMMMMMMMM"MM"o"M
 MMM o"Mo"Mo"o"M Mo" M""MMMMMoM M"oMMMMM"MMMo"MoMMoMMM"o"M"M
 M"o"o"oM" """" "ooM"oMo"MoMMMM"oMMMMM"MMMMM"o"M"MMM""oMMM"M
o"oM"oMo "M"M"M"Mo"oM"o"ooM""MooMMMoMMMMMoM"oM MMM"o"Mo"o"Mo
M Mo"M" "M"oM oMoo""o"oMM  " "MMMM"MMM"MMM"oMM MM MM"Mo"M"oM
"MoM"   o"M MMM"""MM MM"     "M"MMMMM""""M"M"Mo"oM"M"oMoM"Mo
"Mo"     "oMMM     "oMMo    o MM"""       "M MoM"M"oMMooMM"M
"M    o  M MMM      "oMo "   o"oM     "    MM MM"oMMo"MoMM"M
M        "o"MMo    o M M""" M"Mo     o    M"MoM"oMMoMMMoM"M"
o   "    ""o""Mo"o o"M"oMM"M"oMoo o     o MMMoM MMo"MoMM"M"M
         M"M"oooMo"M M"oM M"oMo"ooo oo"M MMoMM"MMoMM"MoM"MoM
o "  "   M"o"M M M "oo" M"oMo"oMo"oM"o"o"MoM"M"MoMMMMMoM"MoM
M       M"M M"oMoo" M "oo " ""o M oooMM"MMo"MMM"MoMoMM"M"MoM
o Moo"o"M M"o"oM M"o" o   "o"MMM"oMoMoMMMo"MMoMM"o"" """"o""
 "oo" M"o"M M"o"oM Mo"oo oo"o"Mo"MooMMoM"M"MoM"Moo""""" " M
o"Mo "o" M "o"o"o"o"oM M oo"Mo" MM MoMM"M"Mo"M"Mo"MMoMoMMMM
 MM "M M M M M M M"o"o"oM M "oMo"Mo"MoMM"M"oMM"Mo"M"M"MoMMM
"oMo""M "o M M M M M M"o"o"o"oM"Mo"MMo"MM"M"oMMMo""MMM"MoMM
"oM "M M Mo M Mo"oM M M M Mo "Mo"oMMoM"MoMM"M "oo"""o"""o"o"
"o"o"oMo M M M"oM M"o"oM Mo" MM"M"oM"M"Mo" oo"M M""Mo"M"oM M

Eventually I learned there is a higher quality option to the program.

$ pnmscale -w 120 < fine.pgm |pgmtopbm |pnminvert |pbmtoascii -2x4
//,|>|i:(<>/|,HMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM?`S
SSS?!:?</:?? MMMMH##MMMMMMMHMMMMMHMHMMMMMMMMMMMMMMMMMMMMMH`S
??|!|::?://S!MMMMM}{&|'RTk:=MMMMM|?>dMMMk|qHT|9:?/:MMMMMMM S
::\\>\\\:i|>`HMMMM6HHJbM|Md?MMMMHJ6$dMMMkdMRJLHd?P&M]MMMM}i:
SSS>\:\,,:<??:HMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMH,\:
SS|$?S4?(L||/S>/*MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM",}$\
\\</|+`:?:`^`<??>,??"*##HHHHMMMMMMMMMMMMMMMMMMMMHH*"?:,/($([
RH&HHHH6'<&ST&v:$???$vd&pbqdoooo.MMP$$$?$$??::<v>\\\%%>/.vv,
M9MHH6R|S}&\S1%$?H*/H9H9RM9MH6M&:MM:HHH6H6H6H#\b????vo#H&M!?
<9&6M9M:F1>?^'''.<$[\9R6MHHHDM&}|MH:MRHRM6RMH9R6H6MHH&H9H/?k
|HHHHH/\:.    ./$S1S|JRHMHH6M9M!HM\M&RMHHHH&H6MHHHHHRMH&P|&H
:&M$?\$$$Z$}1?$S$>$?v??#RMMHHMH.H\HRMHH&RM9M9T&RM9M&M&F?/Z&&
:H?&|;4S%\??<^????>$&$S+:#HMHHP|?MH6M9RM96M&P??&6HHM>?d&1&$k
|&iD?D#d:&)&ZZ$\?F1%F$$$$?Z?HModH6MH9MHR6M&R|H/H6M$?S&H$|19|
&:/S&]>-?$S$>???$?<$Z+dM*"`"\?MHHHHHHHHHMH$d9&|9*>&$H&?${&$9
HFS$/-  :$S\MMM*"*Hb`HMT .- -`MM9M9RM**+#bR&$&L\{S6H>b$L$&kR
$Fk? .` :Z|MMR- .  ?|&M: .. -:Md#>*'  . .``H?&d1H&>b&kH+RH$&
DZ' . .  &:MM|.- ` .??Mc: ., $v$/-  `. .. .&9)DH$?HH&1&FkM&&
R  - . . |\?MM\ : -.\<?$PP??{47Z- . - .  .d&1c>$$9HH&1&FkkHZ
: .- -   |S}?*&qv\`,&Z/S$$$Z$k&S:   .   >,H&1&k?6&9H&H&S&$9{
 -. `.`  %&4%F>><1Z/|%$$$?FS$$Z/S\;_\v\&\/RH&H$HH&&DR66&&9S&
:- - . `.9%&4SFS$?!?o:<?$$\%Tk$S1%Z$$>::&6kM&FHH&RH&RH19&$9&
b.- -  /7/Z|$7/$?://?$-\b:?/'!???:?v/&M&&kH\6&HH&19H1&&19&19
//?+>|\$$%}S1?$S|k%|//:   '|?HRMP/FPd9&RH17H&&&FR/+^$???$$?\
:S$|S:%Z>}S$?($??|}Z\\\/,v$>??HT/&ZS&&9&1H?M%HH&|???"":`""?:
!ZF$ /||:S:(|||\\\4|?%|$S;v?&1;:H&>&FDFRH$1}&FkR|&9&H&#9&RM:
i$&||)S/?(|))))))?S??S4|%Z/|Z}&/&7/FRHFDF&k$RH&&|:M&DHHH&RH-
i&$||S}!%&:?SS?((((((((|$$?<:$$FR%FFk&9&S$&H$$R6k|9HFRH9&&M.
|&?||SF>|%Z:$S?SSSS?\\\??\\\`&$$|&&&&ZH&19?&&<???:?+?\<+*++|
|Z$\:S$$ $Z:\(}S4%$?L$$)?Z%||&ZH&&&&Z&&&1^`v>T/Z\\$&)F$$$14|

But that still seemed lack luster to me. About 21 years ago, the date I have in the file is 27 Dec 1999, I wrote my own tool that turns gray scale ("pgm") images instead of bitmap ("pbm") images into ASCII art.

pnmscale -w 60 -h 30 < /tmp/fine.pgm | pgmtoascii
zzxxxzmmzzmzzxOWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWmxz
mmmmmzzzzzzz;WWWWMOOWWWWWWMMWWWWWWWMWWWWWWWWWWWWWWWWWWWWWM,z
mmmmzzzzzzzzxWWWWWYYUmxOYCxXWWWWMXXzUWWWUzUOUXUmYzzWWWWWWM,z
zxzzzzzzzzxz,MWWWWOMOUYMYWUXWWWWOYOUUWWWCUWOUUOUXYUWOWWWWY+z
mmmzx++;++xzmxOWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWO+z+
XXXYYYYYYXmmzmxzUWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWMYzUXm
mmmmmzzzmxmzxzXXmzmXYUCOMMMWWWWWWWWWWWWWWWWWWWWWWOUYXzxmXYYY
OOCCCMMOzmYUYXz+XmmmXmXUUYYYXXXm;WWUYYYYYYYmxmXmzmXXXXmx,xzz
MMMMMMMxYUUUUUUUmOUUOMMMMMMMMMMO+WWxMMMMMMMMMUXXXmmzzXUCOMmm
UCMMMMM+UUYmx;,.,zUYzCMMMMMMMMMUXWMzMMMMMMMMMMMMMMMMMMMMMUmC
+CMMMMUz+,    ,zUUUUmYMMMMMMMMMzCWzOMMMMMMMMMMMMMMMMMMMMUmCC
+OMUmzYUUUYXmXUUUUYmmXXCWMWWWMWxMmOMMMMMMMMMMYOMMMMMMMCmYCCU
+OYUmxUYXmmmmmmmmzXUUUUmzCWWWWUmXMMMMMMMMMMMCmmMMMMMCXXCCCCC
xUmCXCUY+UUUUUUUUUUUUUYYUmUUOWXCMWMMMMMMMMMCmCzOMMUXYCOYXCCY
U+UYUUU;mUUUXXXXXXmYUXCWUx;++UMMWMMMMMMMMMUYCOmCUXUCCCYYUCUC
OCUUX;. +UUXMWWUXYOYzOWX.....;MMMMWMMUUUUCOCUOYxYCOOUYUXUCCC
CUCz... ,UmMWM;....XYUW;.....+MOUUX;......zCXCUUOOUYCCCUCCCC
UU;.... .YzWWU......mXWU,..,,zXXX;  .......CCXOOUYCOCCCCCCCC
U,.....  mXYWW+....,+XmYYXmzYUUU,   ...  .YOOUUUUOOCCOOOCCCU
+......  zUXmUCXx;;zYUUUUUUUUUUU,      .x+OOOOUXOOOOOOOCCCCU
.......  XUUUUXXXXYYYYUUUYUUUUUUYz+;+xmUzUOOOOCOOOOOOOCCCCUC
+.....  ;UUYUUUYYXzmmxmXYYYUUUUUUUUUYXmmUOCOOOOOOOOOOOOCCCCC
U,.... ;YYYXYYYYXmxzXY,Xm+zxzzzmmxmmmUOOOCOUOOOOOOOOOCOOCCCC
xzXzz;XYYYYYYYYYYYYzxz,...,mXMMWUYOUUOOOOOCUCOOOUYXXXXXXYYYY
+XXXm+YYXYXYYYXYYYYYYmz+;xXXXXOUXCUYOOOOCOUOUOOOmXmx+++++xm+
xUUY;XXmzmxmXXXXXXXYYYYXmzzmCUzxCCXCOOOOOUCUCOOOXUMOCUUCOOO+
mUUmxYYzmX+zXXXXXXXXYYYYYYYxYUUYCUYCCCCOCCUUCCOOXXOOMOOOOOO+
mUUzmUUxmYzzXXXXXXXXXXXXXXXX+UUCCYCCCCCCCCUCCOOOUzOOOOOOOOO;
mUUxzUUzzYX+YYXXXXXXmXXXXXXX,CCUXUCCCCCCCCUCUXXXXxXXYYYYYYmm
mUUm+UUY;YU+YYYYYYYYYYYYXXYmxCCCCCCCCUCCCz+xmYYYUUUUUUYYYYYY

Later I did things like convert ASCII art back into images in various ways. asciiversion2color is not a great program (and didn't even work for me today, because pamarith has been is named pnmarith on this system, a hazard of the netpbm tools being old and reaching different places from different paths, but when I did git it working:

$ pnmscale -w 120 fine300.ppm > fine.ppm
$ asciiversion2color fine.ppm textfine.ppm
pnmarith: promoting second file to PPM
pnmarith: promoting second file to PPM
pnmarith: promoting second file to PPM
HTML version in textfine.ppm.html
$  cjpeg textfine.ppm > textfine.jpg
This is fine, in three color ASCII art

asciiversion2color creates three pbmascii images, one for each RGB channel (in the "ppm" pixmap), converts the ASCII to text-in-image form, then combines the three with a slight offset.

And texttopnm lets you specify an arbitrary tile for each character, as a way of introducing fonts. It has some code for UTF-8 fonts, but I've mostly used it with historic fonts.

$ (echo scale=5; echo 9/14 ) | bc
.64285
$ pnmscale -w 60 fine300.pgm | pnmscale -yscale .64285 > fine60.pgm
$ pgmtoascii fine60.pgm > fine60.txt
$ texttopnm -s .ppm -d font/9x14 fine60.txt 9x14.pgm
$ pnminvert 9x14.pgm |pnmtopng > 9x14.png
This is fine, IBM circa 1981 style

The 9x14 font is the IBM Monochrome Display Adapter hardware font from circa 1981. Quoting Wikipedia:

Each character is rendered in a box of 9×14 pixels, of which 7×11 depicts the character itself and the other pixels provide space between character columns and lines. [...] Each character cell can be set to one of 256 bitmap characters stored in ROM on the card, and this character set cannot be altered from the built-in hardware code page 437. The only way to simulate "graphics" is through ASCII art.

Most recently, I found someone else's code that was created for emulating monochrome bitmap graphics using Braille characters in Unicode in terminal windows. I loved it immediately, and forked it to add a pbmtodots still image converter.

⢅⢌⢔⠔⡔⡪⢊⢆⢣⢒⢕⢱⢑⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠑⡪
⠕⡕⢕⠕⡱⡡⡃⡇⢕⠜⡰⡱⢀⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⡪
⡣⡣⡣⢃⡣⡊⡢⢃⢕⢡⠪⡰⢨⣿⣿⣿⣿⣿⡗⢼⣞⠸⠃⣟⢹⣯⡐⠶⣿⣿⣿⣿⣿⢸⣅⡒⠿⣿⣿⣿⣗⠰⢶⣾⢹⡇⢻⠩⠏⠔⣂⣿⣿⣿⣿⣿⣿⣿ ⡪
⢌⢌⠪⠪⡰⢑⢅⠇⡆⡣⠱⠱ ⣿⣿⣿⣿⣿⣯⣽⣷⣸⣥⣿⢸⣿⣍⣥⣿⣿⣿⣿⣷⣸⣯⣩⣵⣿⣿⣿⣗⣼⣿⣟⣸⣇⣷⣼⣌⡛⣛⣿⣹⣿⣿⣿⣿⡗⠠⡣
⢕⢜⢜⢔⠔⡰⡠⡀⡄⡔⢔⢔⢕⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠠⡅⣁
⡪⡪⡪⡎⡏⡮⡺⡱⡝⣜⡜⡔⡅⡣⡢⡉⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡰⡽⢜⠔
⠕⠏⠞⠎⠇⠗⠙⣁⣍⡈⠚⠓⠑⠣⡣⣣⣒⢆⢍⣉⠛⠟⠿⠿⢿⢿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠟⠛⢋⢡⢄⠞⠝⡵⣱⢫
⡿⣾⣳⣷⣯⣿⡿⣯⠃⣔⢏⣏⡯⣒⢆⡡⢬⣡⣡⣡⣩⣤⢦⣾⣴⡶⣴⣴⣤⣤⣤⣤⠠⣿⣿⡟⣩⣩⣩⣉⣍⣩⣉⣉⠡⠥⣥⢤⡢⡆⡧⡫⡣⡳⡱⠑⠂⡤⣄⣅
⣿⢿⣽⡷⣿⢾⣟⠇⢼⢕⡯⣪⣺⢕⡯⣲⡩⢷⠟⠞⢿⡾⣿⢷⣯⣿⣻⣾⣻⣯⣿⡽⢐⣿⣿⡂⣽⡿⣽⣯⡿⣯⣿⣻⢿⣶⢦⣥⣡⣉⣌⣨⢤⣤⣴⡿⣽⣻⠇⡙
⡟⢻⣯⣿⣻⣿⣿⡈⢧⡳⡫⠚⠘⠈⢀ ⢀⢴⢝⡵⣊⢽⣟⣿⡷⣿⣻⣯⣿⡾⣷⡏⢸⣿⡿⢐⣿⣟⡿⣾⣟⡿⣾⣻⢿⣽⢿⣽⡿⣯⡿⣯⣟⣿⣯⡿⣯⡟⣨⢷
⡂⣽⡷⣿⣻⣾⠻⡃⡁⡁  ⠐ ⢀⡴⡹⣕⢯⢎⡇⣸⣿⣽⣿⢿⣯⡿⣾⣟⣿⡃⣽⣿⢃⣿⣻⣽⣿⢿⣽⡿⣯⣿⢿⣽⡿⣷⢿⣯⡿⣯⣿⢾⡷⣟⡟⣠⣟⣽
⡐⣽⣿⢏⠴⢡⢺⣪⢗⡽⣱⣣⢖⡞⣕⣏⢯⢎⡗⠝⣠⢕⡙⠷⣿⣟⣿⡿⣿⣽⣿⠠⡿⢃⣾⣿⣽⡷⣿⣻⣷⣿⢿⣽⣿⡋⢿⣻⡿⣯⣿⢿⣽⣻⡻⢃⢼⣺⣺⣺
⠠⡷⡏⣼⢨⡘⢵⢕⣕⢩⢚⠸⠑⠫⢚⢘⣡⢥⢴⢝⡵⣝⢼⢢⡑⢻⣿⣻⣟⣿⡝⡜⢥⣿⡷⣿⣽⢿⣯⡿⣾⣻⡿⣷⢟⢰⡩⣟⣿⢿⣽⣿⠯⢓⡼⣽⢽⣺⡺⣞
⡆⢟⢨⣗⡇⣟⣶⣥⢁⢞⡵⣫⢏⢯⡺⡕⡧⣳⣫⢞⡞⡮⡫⣃⣏⣤⣋⡛⢿⢿⣤⣾⡿⣷⣿⣯⡿⣿⣽⢿⣯⣿⢿⡽⡢⣟⡆⣟⣿⣟⢗⢣⢮⣳⣯⢓⢱⣻⣽⢱
⢷⡈⣼⢪⢗⡵⡛⠂⠸⡕⡯⣺⠹⣘⣨⣌⣍⣌⡚⠵⣫⢚⣼⣿⠟⠉⠈⠉⢂⠻⣿⡾⣿⡿⣾⣻⣿⣯⣿⣻⣿⣽⢛⡴⡯⣗⡇⢽⡞⢥⢾⢽⢽⣺⡪⣎⢮⡗⡧⣟
⢯⣟⢵⣫⡞⠈  ⠩⣫⢮⢣⣾⣿⣿⠛⠛⠛⢿⣦⠑⣽⣿⠇⠂⠈ ⠂ ⠈⣿⢿⣯⣿⣻⡿⣾⠻⠫⠟⠽⢷⣻⣟⠽⡽⣕⠁⣮⢿⢽⢯⠟⣴⢽⢆⢯⡺⣯⢷
⢟⣺⣽⠊ ⢀⠈ ⠈⢮⡃⣿⣿⡿⠁⢀ ⠂ ⠹⣇⢽⣿⡁⠠ ⠂⠈⡀⠨⣿⡻⠿⠝⠟⠁⠠ ⠄ ⢀ ⠱⣳⡏⣽⢵⣫⢷⣻⡛⣥⡯⣗⣿⢵⣫⡯⣗⣟
⡧⣗⠁ ⠄ ⠄ ⠈⠧⡃⣿⣿⣗ ⡀⠠⠈⢀ ⠗⠸⣿⣧⡀⠄⠐⢀⢄⢨⡢⣖⣕⠃  ⠠ ⡀⠐ ⡀ ⡷⡷⡱⣯⢿⡝⣢⣯⡷⡯⣗⣿⢽⣺⢯⢗⣟
⣟  ⠂ ⠂ ⠄ ⢭⢇⡹⣿⣷⣄ ⠠ ⢀⠠⠡⡧⣩⣉⡛⡓⢛⡡⣜⢮⡫⣞   ⠂ ⢀ ⠄  ⡮⣟⣯⣧⠫⡟⢬⣷⣯⢯⡯⣗⣿⢽⣺⣻⢽⡺
⠅ ⠐ ⠁ ⠂  ⢸⢕⣖⢍⠻⠷⡮⡤⠤⠐⣨⣺⢕⢗⣕⢗⡽⣕⢽⡪⡗⣝⡮⡂⠠ ⠠   ⢀⢤⢨⢯⣗⡷⣯⢷⣡⢿⣺⣞⣟⣾⣳⣻⢽⡺⣺⣻⢼
 ⠈ ⡈ ⠐ ⠂ ⢕⢗⡵⡫⣳⢕⡖⣖⢵⢻⢜⢜⢝⢵⢕⢯⢪⣺⡱⣫⢏⡮⣺⢕⡦⣄⢄⢄⣔⢼⣪⠃⣾⢽⣺⣻⡯⣟⣽⣽⣺⢾⣻⡾⣽⣺⡯⡯⣗⡧⣟
⡌ ⠄ ⠈ ⠄ ⠨⣫⢧⢫⡫⣺⢕⢽⢜⡕⢙⢬⣤⡑⠫⠺⡕⣗⢵⡹⣜⢵⢝⡼⣱⡣⡗⡯⡧⠓⡋⡤⣞⣿⢽⣺⣯⢯⣗⣷⢿⡽⣯⢷⣻⣷⢽⣺⡯⣗⣯⢷
⠷⠂ ⠈ ⠂ ⢤⢝⢎⢞⢕⡝⣜⢕⡯⣪⢔⠡⡒⡍⣋⠂⢶⢦⠌⣈⠊⢃⢋⢃⢋⣘⡈⡥⡤⡆⣷⣻⣽⣳⡯⣯⢺⣺⣻⢾⡽⣽⡽⣽⡽⣞⣞⣟⢾⣫⣗⣿⢽
⡒⢬⢺⠴⡤⡂⢕⡧⡫⡮⣣⡳⣹⢜⢵⢕⢧⢫⡣⡆⡡⠣⠂  ⡀⠁⢜⢪⡿⣿⢿⡏⢼⡽⡏⣾⣳⣟⣞⢷⣻⣝⢾⣫⣯⣯⡯⣗⢛⠳⡙⢓⢋⢋⣋⣚⣊⣚⢹
⠐⡵⡱⣹⠜⢐⢇⢏⠞⡎⡞⡜⣎⢞⢕⢕⢏⢎⡞⡵⢕⡕⡦⡡⡠⡠⣪⠏⢦⡙⢿⡏⢼⢽⡺⣱⣽⣺⡷⡯⣟⣾⢣⣟⢞⣾⡺⣯⢇⢢⣍⡈⡉⠉⠉⢈⠁⢉⣨⠐
⠸⣕⢽⡸⢀⢇⢇⡇⠕⡕⡅⢪⢪⢪⢪⢣⢫⢪⡪⡺⡱⣹⢜⢍⣊⢥⢔⠸⡯⣗⢍⠢⡯⣟⢕⣽⣺⣳⢯⣟⡷⣏⣾⡳⢽⣺⣽⢯⡇⢝⣷⡿⡾⡾⣞⣾⡾⣿⢽⡂
⠸⡵⣻⡊⠤⡫⡮⡊⢪⢪⡂⢕⢕⢕⢕⢕⢵⢱⢕⢝⡜⡎⡮⡣⣣⢇⡗⡅⢫⡳⣳⣪⡿⡽⣸⢮⣗⢿⡽⡾⣝⣞⣞⢼⣻⡺⣞⣿⢎⠸⣷⣻⣟⣿⣻⣾⡽⣯⢿⡀
⢸⡽⣺⡂⢹⡹⣪⡃⢹⢜⡆⠜⣜⢜⢜⢕⢕⢕⢕⢇⢇⢏⢎⢞⢜⡜⣜⢕⠨⣞⡕⣟⣞⡣⣟⣽⣺⡯⡯⡯⣗⡯⡮⣟⣼⢯⢷⢯⣗⠸⣻⣞⣷⣻⣞⣷⣻⣯⢿⠠
⠸⣺⢕⡇⠸⣪⢧⡃⠥⣳⢣⠘⡮⡺⣸⢜⢜⢜⢜⢜⢜⢜⢜⡜⡜⡜⡜⣜ ⡷⣝⣎⢖⡽⣕⣗⣷⢽⣫⡯⣗⣯⡫⣞⠷⠛⢋⣋⢬⣈⢙⠚⠞⠳⠝⠞⠗⠯⠓⢸
⡸⣕⢗⢇⠘⡵⡕⣗⠈⡞⣕⡂⢏⢞⢮⢺⡱⡫⣺⢱⡣⣳⢕⢵⢱⢕⢵⡑⢨⣽⢮⢗⣟⡮⣗⣗⣗⢟⡾⣽⢵⠓⠡⠤⡪⡝⡵⡱⣫⢺⡹⡝⣝⢞⡵⡳⡕⣗⢽⢱

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