if a = 1 and z = 26

  • Thread starter Thread starter Lius
  • Start date Start date
Lius said:
any software that can determine the words that add up to 100 besides
the word "attitude" ?
Click to expand...

Dunno, but if A=6, B=12, C=18, ... , then MARK OF BEAST adds up to 666,
as does BEASTLY CODE, WITCHCRAFT, SORCEROR, and some more. Also the same
formula makes JESUS add up to 444, as does CROSS, GOSPEL, PARABLES,
MESSIAH, HEAVENS, and some more. Co-incidence? I don't think so.
 
123 said:
Dunno, but if A=6, B=12, C=18, ... , then MARK OF BEAST adds up to 666,
as does BEASTLY CODE, WITCHCRAFT, SORCEROR, and some more. Also the same
formula makes JESUS add up to 444, as does CROSS, GOSPEL, PARABLES,
MESSIAH, HEAVENS, and some more. Co-incidence? I don't think so.
Click to expand...

why a=6,the logic? why not 9 or 7?
 
Lius said:
why a=6,the logic? why not 9 or 7?
Click to expand...

I used 6 so that MARK OF BEAST would add up to 666, which is logical.
I then discovered that this made JESUS etc add up to 444, which was
a bit of shock. I've run with it ever since.

If you want a more solid explanation, the Greeks said 6 is the first
"perfect number", and indeed PERFECTION adds up to 666 to support it,
but then that's probably at odds with what 666 is meant to represent.
 
123 said:
I used 6 so that MARK OF BEAST would add up to 666, which is logical.
Click to expand...

Besides, the base number is not really the issue... the issue is why
do these phrases all arrive at the same total? Did the writers of the
English language sit down one day and do the maths to make sure they
added up? Of course not... and I don't buy into co-incidence being
the reason.
 
Lius said:
any software that can determine the words that add up to 100 besides the
word "attitude" ?
Click to expand...

Would be a perfect job for a small Python script... and looks like a
wonderful exercise for beginners :-)

Just write a script that accepts a word list (text file) as input. The
script reads these words one at a time and calculates the sum of the
letters as you propose. If sum=100, write it to an output text file.

The only missing piece is an input file containing words. I'm sure you'll
find some dictionary files somewhere on the internet...

Regards,
Wald
 
I used 6 so that MARK OF BEAST would add up to 666, which is logical.
I then discovered that this made JESUS etc add up to 444, which was
a bit of shock. I've run with it ever since.

If you want a more solid explanation, the Greeks said 6 is the first
"perfect number", and indeed PERFECTION adds up to 666 to support it,
but then that's probably at odds with what 666 is meant to represent.
Click to expand...

Is this different to the Jewish thought of the number 7 being perfect.
(Sabbath day I guess). And the reason that Jesus changed the 6 jars of water
into wine at the wedding in Cana?

For a bit of a laugh you can try the Bible Hoax program by the late Jef
Raskin:
http://jef.raskincenter.org/published/bible_hoax_program.html

Anthony
 
Le Wed, 16 Mar 2005 12:46:18 +0000, Wald a écrit :
Would be a perfect job for a small Python script... and looks like a
wonderful exercise for beginners :-)
Click to expand...

Yes, or awk for beginners, too ! crosspost started this post,
(feel free to block if inconvenient !)

For instance, with this little exemple as starting help (oneliner) :

$ echo "MARKOFBEAST" | awk 'BEGIN{RS=FS="";ii=1; tot=0} {while($ii){
indi=index("ABCDEFGHIJKLMNOPQRSTUVWXYZ",$ii);tot+=6*indi ; ii++} };
END{print"TOTAL="tot}' RS=''

Go on for the multi list script you describe here :
Just write a script that accepts a word list (text file) as input. The
script reads these words one at a time and calculates the sum of the
letters as you propose. If sum=100, write it to an output text file.

The only missing piece is an input file containing words. I'm sure you'll
find some dictionary files somewhere on the internet...
Click to expand...

They're legion ;-)
 
Loki said:
Le Wed, 16 Mar 2005 12:46:18 +0000, Wald a écrit :




Yes, or awk for beginners, too ! crosspost started this post,
(feel free to block if inconvenient !)

For instance, with this little exemple as starting help (oneliner) :

$ echo "MARKOFBEAST" | awk 'BEGIN{RS=FS="";ii=1; tot=0} {while($ii){
indi=index("ABCDEFGHIJKLMNOPQRSTUVWXYZ",$ii);tot+=6*indi ; ii++} };
END{print"TOTAL="tot}' RS=''

Go on for the multi list script you describe here :



They're legion ;-)
Click to expand...

Assuming you only care about upper and lower case letters (not digits,
punctuation, etc.):

awk -vRS="" '{t=$0}gsub("[[:alpha:]]","",t)==100' file

Regards,

Ed.
 
Ed said:
Loki said:
Le Wed, 16 Mar 2005 12:46:18 +0000, Wald a écrit :





Yes, or awk for beginners, too ! crosspost started this post,
(feel free to block if inconvenient !)

For instance, with this little exemple as starting help (oneliner) :

$ echo "MARKOFBEAST" | awk 'BEGIN{RS=FS="";ii=1; tot=0} {while($ii){
indi=index("ABCDEFGHIJKLMNOPQRSTUVWXYZ",$ii);tot+=6*indi ; ii++} };
END{print"TOTAL="tot}' RS=''

Go on for the multi list script you describe here :




They're legion ;-)
Click to expand...


Assuming you only care about upper and lower case letters (not digits,
punctuation, etc.):

awk -vRS="" '{t=$0}gsub("[[:alpha:]]","",t)==100' file
Click to expand...

Hmm, the text seems to want the input file to be output if the sum is
100, but the posted example shows the sum being output. The above prints
the file, this would print the sum:

awk -vRS="" '{print "TOTAL="gsub("[[:alpha:]]","")}' file

whichever it is you're really looking for....

Ed.
 
Le Tue, 22 Mar 2005 07:25:45 -0600, Ed Morton a écrit :
Yes, or awk for beginners, too ! crosspost started this post,
(feel free to block if inconvenient !)

For instance, with this little exemple as starting help (oneliner) :

$ echo "MARKOFBEAST" | awk 'BEGIN{RS=FS="";ii=1; tot=0} {while($ii){
indi=index("ABCDEFGHIJKLMNOPQRSTUVWXYZ",$ii);tot+=6*indi ; ii++} };
END{print"TOTAL="tot}' RS=''

Go on for the multi list script you describe here :



They're legion ;-)
Click to expand...

Assuming you only care about upper and lower case letters (not digits,
punctuation, etc.):

awk -vRS="" '{t=$0}gsub("[[:alpha:]]","",t)==100' file
Click to expand...


Mmm, nice try but I guess either you didn't read carefully enough
my post or my post was a bit shady !

I reformulate this :

1. being an arithmetic progression of 6
2. project this ari progression on the alphabet
thus giving
A=6
B=12
C=18, etc.

pick words or sentences, sum up the values according to
the defined ari progression.

for instance, like in my sample,
MARKOFBEAST gives 666 (as do PERFECTION or WITCHCRAFT :-)
or giving 444 are JESUS, GOSPEL, MESSIAH, etc.

The script to write for fun (not for me ;-) is :
===>>
Have dictionnaries
Pick a value, for instance 666 or 100
List all words giving the picked value ...
<<===

Were I a bit clearer this time ?-D)
 
Loki said:
Le Tue, 22 Mar 2005 07:25:45 -0600, Ed Morton a écrit :

Yes, or awk for beginners, too ! crosspost started this post,
(feel free to block if inconvenient !)

For instance, with this little exemple as starting help (oneliner) :

$ echo "MARKOFBEAST" | awk 'BEGIN{RS=FS="";ii=1; tot=0} {while($ii){
indi=index("ABCDEFGHIJKLMNOPQRSTUVWXYZ",$ii);tot+=6*indi ; ii++} };
END{print"TOTAL="tot}' RS=''

Go on for the multi list script you describe here :


Just write a script that accepts a word list (text file) as input. The
script reads these words one at a time and calculates the sum of the
letters as you propose. If sum=100, write it to an output text file.

The only missing piece is an input file containing words. I'm sure you'll
find some dictionary files somewhere on the internet...


They're legion ;-)
Click to expand...

Assuming you only care about upper and lower case letters (not digits,
punctuation, etc.):

awk -vRS="" '{t=$0}gsub("[[:alpha:]]","",t)==100' file
Click to expand...



Mmm, nice try but I guess either you didn't read carefully enough
my post or my post was a bit shady !

I reformulate this :

1. being an arithmetic progression of 6
2. project this ari progression on the alphabet
thus giving
A=6
B=12
C=18, etc.

pick words or sentences, sum up the values according to
the defined ari progression.

for instance, like in my sample,
MARKOFBEAST gives 666 (as do PERFECTION or WITCHCRAFT :-)
or giving 444 are JESUS, GOSPEL, MESSIAH, etc.

The script to write for fun (not for me ;-) is :
===>>
Have dictionnaries
Pick a value, for instance 666 or 100
List all words giving the picked value ...
<<===

Were I a bit clearer this time ?-D)
Click to expand...

Yes, now I see why your posted example didn't seem to fit the text - I
just thought you had no idea what you were doing. Sorry 'bout that! This
should do what you actually want (keeping as much of your example as
possible for easy comparison):

awk -vari=6 -vtgt=666 '{
for (i=1; i<=NF; i++) {
tot = 0;
c = split($i,x,"")
for (j=1; j<=c; j++) {
indi=index("ABCDEFGHIJKLMNOPQRSTUVWXYZ",x[j])
tot += ari*indi
}
if (tot == tgt) {
print $i
}
}
}' file

Like your original, it treats all non-blank characters that aren't
upper-case alphabetical as having zero value but still part of each "word".

For efficiency, it'd be much better to build an associative array in a
BEGIN section that maps each letter to it's ari progression value, then
just index that by x[j] in the body rather than computing the index()
and the multiplication for ever single letter in the file, e.g.:

awk -vari=6 -vtgt=666 'BEGIN {
c = split("ABCDEFGHIJKLMNOPQRSTUVWXYZ",tmp,"")
for (i=1; i<=c; i++)
map[tmp] = i * ari
}
{
for (i=1; i<=NF; i++) {
tot = 0;
c = split($i,x,"")
for (j=1; j<=c; j++)
tot += map[x[j]]
if (tot == tgt)
print $i
}
}' file

Regards,

Ed.
 
Le Tue, 22 Mar 2005 22:20:24 -0600, Ed Morton a écrit :
Loki said:
Le Tue, 22 Mar 2005 07:25:45 -0600, Ed Morton a écrit :
Yes, or awk for beginners, too ! crosspost started this post,

For instance, with this little exemple as starting help (oneliner) :

$ echo "MARKOFBEAST" | awk 'BEGIN{RS=FS="";ii=1; tot=0} {while($ii){
indi=index("ABCDEFGHIJKLMNOPQRSTUVWXYZ",$ii);tot+=6*indi ; ii++} };
END{print"TOTAL="tot}' RS=''

Go on for the multi list script you describe here :


Just write a script that accepts a word list (text file) as input. The
script reads these words one at a time and calculates the sum of the
letters as you propose. If sum=100, write it to an output text file.

The only missing piece is an input file containing words. I'm sure you'll
find some dictionary files somewhere on the internet...

They're legion ;-)

Assuming you only care about upper and lower case letters (not digits,
punctuation, etc.):

awk -vRS="" '{t=$0}gsub("[[:alpha:]]","",t)==100' file
Click to expand...

Mmm, nice try but I guess either you didn't read carefully enough
my post or my post was a bit shady !

I reformulate this :

1. being an arithmetic progression of 6
2. project this ari progression on the alphabet
thus giving
A=6
B=12
C=18, etc.

pick words or sentences, sum up the values according to
the defined ari progression.

for instance, like in my sample,
MARKOFBEAST gives 666 (as do PERFECTION or WITCHCRAFT :-)
or giving 444 are JESUS, GOSPEL, MESSIAH, etc.

The script to write for fun (not for me ;-) is :
===>>
Have dictionnaries
Pick a value, for instance 666 or 100
List all words giving the picked value ...
<<===

Were I a bit clearer this time ?-D)
Click to expand...

Yes, now I see why your posted example didn't seem to fit the text - I
just thought you had no idea what you were doing. Sorry 'bout that!
Click to expand...

Never mind :-) I should've been clearer first time, especially as
it was supposed to start a game for beginners :D)
Well, I hope I'll get better success with my trainees ;-)
This
should do what you actually want (keeping as much of your example as
possible for easy comparison):
Click to expand...

Yes, but I am not much surprised, I know you as a good poster and coder !
Anyway, as it seems nobody but you bit the bait for this fun I guess
we'll stop the game here, maybe a sweepstake next time ?-)
Like your original, it treats all non-blank characters that aren't
upper-case alphabetical as having zero value but still part of each
"word".
Click to expand...

Righteous !
For efficiency, it'd be much better to build an associative array in a
BEGIN section that maps each letter to it's ari progression value, then
Click to expand...

I do agree; it was intented to be mentioned later as a complement
for the trainees still alive and eyes opened at the end of the day ...
just index that by x[j] in the body rather than computing the index()
and the multiplication for ever single letter in the file, e.g.:
Click to expand...

Ok, now a possible final script here, it's Ed's script with just a
line to eliminate the need to uppercase the wordlists given :

$ cat << _EOF_ >> AlittleWordGameInAwk
#!/bin/awk -f
BEGIN {
c = split("abcdefghijklmnopqrstuvwxyz",tmp,"")
split("ABCDEFGHIJKLMNOPQRSTUVWXYZ",TMP,"")
for (i=1; i<=c; i++)
{
map[tmp] = map[TMP] = i * ari
}
}
{
for (i=1; i<=NF; i++) {
tot = 0;
c = split($i,x,"")
for (j=1; j<=c; j++)
tot += map[x[j]]
if (tot == tgt)
print $i
}
}
_EOF_

Now, to definitely cool down the easy preys for witcheries
on curious mysteries snake oiling simple big numbers correlations
just running the script on a wordlist like the freja.diku
(english, 51899 words) give numerous hits for 666, 444 and 222 (666-444)
so much for black magic, you can see 'Jesus' and 'Lucifer' hit the 444 :-)


$ awk -vari=6 -vtgt=444 -f AlittleWordGameInAwk /usr/dict/freja.diku.dk |
wc -l
583

$ awk -vari=6 -vtgt=666 -f AlittleWordGameInAwk /usr/dict/freja.diku.dk | wc -l
465

$ awk -vari=6 -vtgt=222 -f AlittleWordGameInAwk /usr/dict/freja.diku.dk | wc -l
161


Now, let's see this collision cloud, (*Annex) and thank you all for
reading.
Thank you very much Ed for playing the game (and winning it).

Sorry for the ones who were accidentally harmed or bored to death during
the process ;-)

Good bye.


*Annex:

Testing again on the same wordlist with :
$ for ll in $(seq 1 700); do echo "For: "$ll" we get "$(awk -vari=1
-vtgt=${ll} -f AlittleWordGameInAwk /usr/dict/freja.diku.dk | wc -l)"
hits" ;done


Note: Yes, I put ari to value 1 (one), enough with this smokescreen :
the hypnotized who started to check how many sums of multiples of 6 were
giving 100 were not on the verge of going home ;-)

We get a gauss distribution (surprise, surprise)
with small holes (just listing the non null) :

For: 4 we get 3 hits
For: 5 we get 2 hits
For: 6 we get 4 hits
For: 7 we get 6 hits
For: 8 we get 3 hits
For: 9 we get 8 hits
For: 10 we get 6 hits
For: 11 we get 6 hits
For: 12 we get 10 hits
For: 13 we get 11 hits
For: 14 we get 12 hits
For: 15 we get 13 hits
For: 16 we get 14 hits
For: 17 we get 24 hits
For: 18 we get 24 hits
For: 19 we get 28 hits
For: 20 we get 32 hits
For: 21 we get 32 hits
For: 22 we get 44 hits
For: 23 we get 50 hits
For: 24 we get 50 hits
For: 25 we get 52 hits
For: 26 we get 61 hits
For: 27 we get 71 hits
For: 28 we get 79 hits
For: 29 we get 78 hits
For: 30 we get 94 hits
For: 31 we get 92 hits
For: 32 we get 124 hits
For: 33 we get 116 hits
For: 34 we get 118 hits
For: 35 we get 131 hits
For: 36 we get 124 hits
For: 37 we get 161 hits
For: 38 we get 180 hits
For: 39 we get 185 hits
For: 40 we get 206 hits
For: 41 we get 223 hits
For: 42 we get 221 hits
For: 43 we get 226 hits
For: 44 we get 216 hits
For: 45 we get 252 hits
For: 46 we get 274 hits
For: 47 we get 297 hits
For: 48 we get 291 hits
For: 49 we get 295 hits
For: 50 we get 332 hits
For: 51 we get 344 hits
For: 52 we get 337 hits
For: 53 we get 367 hits
For: 54 we get 408 hits
For: 55 we get 403 hits
For: 56 we get 420 hits
For: 57 we get 408 hits
For: 58 we get 428 hits
For: 59 we get 462 hits
For: 60 we get 472 hits
For: 61 we get 476 hits
For: 62 we get 481 hits
For: 63 we get 499 hits
For: 64 we get 463 hits
For: 65 we get 522 hits
For: 66 we get 508 hits
For: 67 we get 509 hits
For: 68 we get 515 hits
For: 69 we get 543 hits
For: 70 we get 571 hits
For: 71 we get 605 hits
For: 72 we get 584 hits
For: 73 we get 620 hits
For: 74 we get 583 hits
For: 75 we get 610 hits
For: 76 we get 575 hits
For: 77 we get 596 hits
For: 78 we get 584 hits
For: 79 we get 658 hits
For: 80 we get 564 hits
For: 81 we get 636 hits
For: 82 we get 607 hits
For: 83 we get 617 hits
For: 84 we get 602 hits
For: 85 we get 632 hits
For: 86 we get 581 hits
For: 87 we get 584 hits
For: 88 we get 625 hits
For: 89 we get 568 hits
For: 90 we get 594 hits
For: 91 we get 602 hits
For: 92 we get 649 hits
For: 93 we get 609 hits
For: 94 we get 521 hits
For: 95 we get 581 hits
For: 96 we get 550 hits
For: 97 we get 535 hits
For: 98 we get 585 hits
For: 99 we get 549 hits
For: 100 we get 564 hits
For: 101 we get 501 hits
For: 102 we get 552 hits
For: 103 we get 547 hits
For: 104 we get 510 hits
For: 105 we get 492 hits
For: 106 we get 514 hits
For: 107 we get 445 hits
For: 108 we get 488 hits
For: 109 we get 479 hits
For: 110 we get 478 hits
For: 111 we get 465 hits
For: 112 we get 424 hits
For: 113 we get 446 hits
For: 114 we get 407 hits
For: 115 we get 418 hits
For: 116 we get 427 hits
For: 117 we get 422 hits
For: 118 we get 389 hits
For: 119 we get 372 hits
For: 120 we get 392 hits
For: 121 we get 395 hits
For: 122 we get 358 hits
For: 123 we get 356 hits
For: 124 we get 335 hits
For: 125 we get 323 hits
For: 126 we get 295 hits
For: 127 we get 349 hits
For: 128 we get 294 hits
For: 129 we get 356 hits
For: 130 we get 265 hits
For: 131 we get 281 hits
For: 132 we get 279 hits
For: 133 we get 286 hits
For: 134 we get 253 hits
For: 135 we get 266 hits
For: 136 we get 243 hits
For: 137 we get 214 hits
For: 138 we get 224 hits
For: 139 we get 221 hits
For: 140 we get 201 hits
For: 141 we get 207 hits
For: 142 we get 177 hits
For: 143 we get 205 hits
For: 144 we get 195 hits
For: 145 we get 167 hits
For: 146 we get 185 hits
For: 147 we get 164 hits
For: 148 we get 190 hits
For: 149 we get 149 hits
For: 150 we get 157 hits
For: 151 we get 144 hits
For: 152 we get 151 hits
For: 153 we get 114 hits
For: 154 we get 152 hits
For: 155 we get 111 hits
For: 156 we get 129 hits
For: 157 we get 114 hits
For: 158 we get 122 hits
For: 159 we get 115 hits
For: 160 we get 104 hits
For: 161 we get 86 hits
For: 162 we get 95 hits
For: 163 we get 90 hits
For: 164 we get 87 hits
For: 165 we get 87 hits
For: 166 we get 78 hits
For: 167 we get 74 hits
For: 168 we get 68 hits
For: 169 we get 82 hits
For: 170 we get 69 hits
For: 171 we get 55 hits
For: 172 we get 53 hits
For: 173 we get 47 hits
For: 174 we get 66 hits
For: 175 we get 86 hits
For: 176 we get 40 hits
For: 177 we get 56 hits
For: 178 we get 49 hits
For: 179 we get 56 hits
For: 180 we get 28 hits
For: 181 we get 49 hits
For: 182 we get 30 hits
For: 183 we get 32 hits
For: 184 we get 44 hits
For: 185 we get 41 hits
For: 186 we get 31 hits
For: 187 we get 39 hits
For: 188 we get 26 hits
For: 189 we get 23 hits
For: 190 we get 20 hits
For: 191 we get 29 hits
For: 192 we get 23 hits
For: 193 we get 17 hits
For: 194 we get 25 hits
For: 195 we get 19 hits
For: 196 we get 22 hits
For: 197 we get 16 hits
For: 198 we get 21 hits
For: 199 we get 14 hits
For: 200 we get 16 hits
For: 201 we get 8 hits
For: 202 we get 8 hits
For: 203 we get 15 hits
For: 204 we get 11 hits
For: 205 we get 16 hits
For: 206 we get 9 hits
For: 207 we get 8 hits
For: 208 we get 15 hits
For: 209 we get 6 hits
For: 210 we get 11 hits
For: 211 we get 7 hits
For: 212 we get 8 hits
For: 213 we get 2 hits
For: 214 we get 6 hits
For: 215 we get 2 hits
For: 216 we get 5 hits
For: 217 we get 3 hits
For: 218 we get 2 hits
For: 219 we get 6 hits
For: 220 we get 3 hits
For: 221 we get 2 hits
For: 222 we get 8 hits
For: 223 we get 3 hits
For: 224 we get 3 hits
For: 225 we get 3 hits
For: 226 we get 3 hits
For: 227 we get 1 hits
For: 229 we get 4 hits
For: 231 we get 3 hits
For: 232 we get 3 hits
For: 233 we get 3 hits
For: 234 we get 2 hits
For: 237 we get 2 hits
For: 238 we get 1 hits
For: 239 we get 5 hits
For: 241 we get 2 hits
For: 242 we get 1 hits
For: 244 we get 1 hits
For: 246 we get 1 hits
For: 247 we get 1 hits
For: 248 we get 2 hits
For: 251 we get 1 hits
For: 261 we get 1 hits
For: 272 we get 1 hits
For: 307 we get 1 hits
 
Loki Harfagr wrote:
Ok, now a possible final script here, it's Ed's script with just a
line to eliminate the need to uppercase the wordlists given :

$ cat << _EOF_ >> AlittleWordGameInAwk
#!/bin/awk -f
BEGIN {
c = split("abcdefghijklmnopqrstuvwxyz",tmp,"")
split("ABCDEFGHIJKLMNOPQRSTUVWXYZ",TMP,"")
for (i=1; i<=c; i++)
{
map[tmp] = map[TMP] = i * ari
}
}
Click to expand...

<snip>
Not a big deal, but rather than list all the characters twice, you could
use toupper():

BEGIN {
c = split("abcdefghijklmnopqrstuvwxyz",tmp,"")
for (i=1; i<=c; i++)
{
map[tmp] = map[toupper(tmp)] = i * ari
}
}

Regards,

Ed.
 
Loki said:
for instance, like in my sample,
MARKOFBEAST gives 666 (as do PERFECTION or WITCHCRAFT :-)
or giving 444 are JESUS, GOSPEL, MESSIAH, etc.
Click to expand...

I think you mean *MY* sample, dude -- they were *MY* quotes.
 
Le Fri, 25 Mar 2005 15:39:44 +1100, 123 a écrit :
I think you mean *MY* sample, dude -- they were *MY* quotes.
Click to expand...

Hello, *dude*,

If you want to read, learn to read,
if you want to trim, learn to trim.

In the context of the text I wrote as an answer/complement
for Ed questioning, it was right to say "my sample".
Meaning that in this special answer I was quoting the
sample I had given for the little game of making a script
to give you answers on the samples *you* quoted.

I reckon the sample I used was using your quotes, it was as
a start for the searching.
Of course I could have used other words, many other words
as you may see if you end up reading the other posts (including
the one I made, not crossposted here to a.r.c) giving fields of
answers to your original question on words coincidences.

Here you're breaking the context to be able to call me names maybe,
are you trying to troll or is it just that you couldn't read the
rest ?-)

Cheers.
 
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