Forums > MaxMSP

### Max patching festival: quantized mapping

Feb 17 2007 | 6:34 pm

One of the things I did during the last Cycling ’74 Max beginner’s workshops was to share one of the recent "How might I make a patch that does X?" questions with several different solutions as a way to demonstrate the Max adage, "There’s always another way to do it." Some of the attendees found seeing all those answers together sufficiently constructive that they now ask me, "How *else* might I think about doing this?"

The recent list question falls so elegantly into that category that I almost wish the workshop was *next* week.

To that end, here’s an interesting question about non-linear mapping that strikes me as an interesting possible candidate for demonstrating your elegant patching skills:

The original question involved a patch that divides an output range into N units, and produces a "stepped" or "quantized" output across that range for any number you input [that is, if you specify a range of 0. – 1.0 and a quantization value of 4, then the step function will output only 0., .25, .5, or .75.

I suggested that perhaps it’d be smarter to have a patch that outputs .25 .5 .75 and 1.0 instead, but I’m being annoying.

Okay, Max heads. How many ways can you do this? Since our beginner’s workshop only uses vanilla Max objects (with the exception of fiddle~) until the very last day, you might wish to demonstrate your prowess by using vanilla objects only. And we’re not necessarily looking for the fewest objects – perhaps the most easily generalizable or graphically lovely?

Accentuating the positive,
gregory

Feb 17 2007 | 7:21 pm

bit tougher then I thought it would be.
heres what I have so far, though I feel like I did this much better in the past.. Ill have to sort through some old files and find it. 2 weird versions here.

#P window setfont "Sans Serif" 9.;
#P window linecount 1;
#P message 151 76 37 196617 \$1 20;
#P newex 151 97 40 196617 line;
#P flonum 176 185 35 9 0 0 0 3 0 0 0 221 221 221 222 222 222 0 0 0;
#P message 230 140 14 196617 4;
#P message 212 141 14 196617 3;
#P message 191 141 14 196617 2;
#P message 170 141 14 196617 1;
#P message 151 140 14 196617 0;
#P newex 152 118 112 196617 select 0 32 64 96 127;
#P number 35 141 35 9 0 0 0 3 0 0 0 221 221 221 222 222 222 0 0 0;
#P user hslider 33 52 18 128 128 1 0 0;
#P flonum 36 184 35 9 0 0 0 3 0 0 0 221 221 221 222 222 222 0 0 0;
#P newex 35 160 31 196617 / 31;
#P connect 2 0 3 0;
#P connect 3 0 0 0;
#P connect 0 0 1 0;
#P connect 2 0 12 0;
#P connect 12 0 11 0;
#P connect 4 0 5 0;
#P connect 11 0 4 0;
#P connect 4 1 6 0;
#P connect 9 0 10 0;
#P connect 8 0 10 0;
#P connect 7 0 10 0;
#P connect 6 0 10 0;
#P connect 5 0 10 0;
#P connect 4 2 7 0;
#P connect 4 3 8 0;
#P connect 4 4 9 0;
#P window clipboard copycount 13;

Feb 17 2007 | 8:12 pm

Feb 17 2007 | 8:29 pm

Feb 17 2007 | 9:02 pm

Feb 17 2007 | 9:05 pm

Feb 17 2007 | 10:26 pm

Feb 17 2007 | 11:53 pm

here’s my solution. it’s different than the others so far, probably because i was beginning to think
about how to something similar in a patch i’m working on… anyway, enjoy.

max v2;
#N vpatcher 144 153 690 655;
#P window setfont "Sans Serif" 9.;
#P number 461 62 35 9 0 0 0 3 0 0 0 221 221 221 222 222 222 0 0 0;
#P window linecount 1;
#P newex 86 99 53 196617 t b b b b;
#P newex 198 164 40 196617 t f f f;
#P newex 198 141 27 196617 f;
#P newex 341 141 27 196617 f;
#P newex 444 164 40 196617 t f f f;
#P newex 444 141 27 196617 f;
#P newex 86 454 32 196617 print;
#P newex 282 254 27 196617 / 1.;
#P newex 282 225 27 196617 – 0.;
#P comment 457 49 44 196617 # steps;
#P comment 362 49 24 196617 max;
#P flonum 358 62 35 9 0 0 0 3 0 0 0 221 221 221 222 222 222 0 0 0;
#P flonum 215 62 35 9 0 0 0 3 0 0 0 221 221 221 222 222 222 0 0 0;
#P message 40 305 14 196617 1;
#P newex 40 284 32 196617 sel 4;
#P newex 86 414 27 196617 + 0.;
#P button 86 62 15 0;
#P newex 86 226 40 196617 uzi 4;
#P newex 86 374 29 196617 * 0.;
#N counter 1 100;
#X flags 0 0;
#P newobj 86 331 74 196617 counter 1 100;
#P comment 219 49 24 196617 min;
#P comment 80 49 33 196617 do it!;
#P fasten 2 0 7 0 91 351 36 351 36 281 45 281;
#P connect 7 0 8 0;
#P fasten 17 1 7 1 464 276 67 276;
#P connect 5 0 21 0;
#P connect 21 0 4 0;
#P connect 4 0 2 0;
#P connect 2 0 3 0;
#P connect 3 0 6 0;
#P fasten 20 0 15 0 203 446 91 446;
#P connect 6 0 15 0;
#P fasten 20 1 6 1 218 411 108 411;
#P fasten 14 0 3 1 287 370 110 370;
#P fasten 17 0 4 1 449 193 121 193;
#P fasten 8 0 2 2 45 322 123 322;
#P fasten 21 2 19 0 119 131 203 131;
#P connect 19 0 20 0;
#P connect 9 0 19 1;
#P fasten 18 0 13 0 346 212 287 212;
#P connect 13 0 14 0;
#P fasten 20 2 13 1 233 218 304 218;
#P fasten 17 2 14 1 479 248 304 248;
#P fasten 21 1 18 0 105 128 346 128;
#P connect 10 0 18 1;
#P fasten 21 3 16 0 133 125 449 125;
#P connect 16 0 17 0;
#P connect 22 0 16 1;
#P pop;

david

———- Original Message ———————————-
From: Gregory Taylor
Date: Sat, 17 Feb 2007 11:34:11 -0700

>
>One of the things I did during the last Cycling ’74 Max beginner’s workshops was to share one of
the recent "How might I make a patch that does X?" questions with several different solutions as a
way to demonstrate the Max adage, "There’s always another way to do it." Some of the attendees
found seeing all those answers together sufficiently constructive that they now ask me, "How *else*
might I think about doing this?"
>
>The recent list question falls so elegantly into that category that I almost wish the workshop was
*next* week.
>
>To that end, here’s an interesting question about non-linear mapping that strikes me as an
interesting possible candidate for demonstrating your elegant patching skills:
>
>The original question involved a patch that divides an output range into N units, and produces a
"stepped" or "quantized" output across that range for any number you input [that is, if you specify a
range of 0. – 1.0 and a quantization value of 4, then the step function will output only 0., .25, .5, or .
75.
>
>I suggested that perhaps it’d be smarter to have a patch that outputs .25 .5 .75 and 1.0 instead,
but I’m being annoying.
>
>Okay, Max heads. How many ways can you do this? Since our beginner’s workshop only uses vanilla
Max objects (with the exception of fiddle~) until the very last day, you might wish to demonstrate
your prowess by using vanilla objects only. And we’re not necessarily looking for the fewest objects –
perhaps the most easily generalizable or graphically lovely?
>
>Accentuating the positive,
>gregory
>
>
>–
>knowledge is not enough/science is not enough/Love is dreaming this equation
>

Need personalized email and website? Look no further. It’s easy

Feb 18 2007 | 4:11 am

Part of the reason that this particular kind of question caught my attention was that I was curious to see whether or not anyone would think of the problem in other ways than using the expr object, opting for solutions that would be more akin to the "flow" of data than expressions….

Feb 18 2007 | 10:32 am

It’s always good to have an example of what not to do. Am I’m embarrasing myself by posting this?

#P window setfont Helvetica 9.;
#P window linecount 1;
#P newex 153 401 18 1376265 t b;
#P newex 290 148 40 1376265 v quant;
#P comment 332 56 59 1376265 < - get some;
#P newex 22 72 35 1376265 r done;
#P newex 233 355 27 1376265 + 1;
#P newex 194 336 22 1376265 v lo;
#P message 194 424 143 1376265 0. 0.25 0.5 0.75 1.;
#P newex 194 401 58 1376265 prepend set;
#P button 260 27 68 0;
#P newex 260 103 176 1376265 t b b b b b b;
#P newex 233 332 39 1376265 v quant;
#P newex 194 375 49 1376265 zl group 4;
#P newex 260 195 35 1376265 t b b;
#P newex 425 296 37 1376265 v step;
#P flonum 425 275 35 9 0 0 0 21 0 0 0 221 221 221 222 222 222 0 0 0;
#P newex 425 248 27 1376265 / 1.;
#P newex 469 221 40 1376265 v quant;
#P newex 140 147 40 1376265 v quant;
#P flonum 425 223 35 9 0 0 0 21 0 0 0 221 221 221 222 222 222 0 0 0;
#P newex 449 172 22 1376265 v lo;
#P newex 425 199 34 1376265 – 0.;
#P newex 425 172 22 1376265 v hi;
#P newex 260 173 40 1376265 uzi 4;
#P newex 81 147 22 1376265 v hi;
#P newex 22 147 22 1376265 v lo;
#P window setfont Helvetica 12.;
#P flonum 140 110 46 12 0 0 0 21 0 0 0 221 221 221 222 222 222 0 0 0;
#P window setfont Helvetica 9.;
#P comment 140 95 59 1376265 quantization;
#P window setfont Helvetica 12.;
#P flonum 81 110 46 12 0 0 0 21 0 0 0 221 221 221 222 222 222 0 0 0;
#P flonum 22 110 46 12 0 0 0 21 0 0 0 221 221 221 222 222 222 0 0 0;
#P window setfont Helvetica 9.;
#P comment 32 95 87 1376265 low –range– high;
#P newex 153 424 37 1376265 s done;
#P newex 285 219 35 1376265 v step;
#P newex 260 219 22 1376265 v lo;
#P newex 260 303 22 1376265 v lo;
#P flonum 260 273 35 9 0 0 0 21 0 0 0 221 221 221 222 222 222 0 0 0;
#P newex 260 242 35 1376265 + 0.;
#P connect 32 0 7 0;
#P connect 7 0 11 0;
#P connect 8 0 12 0;
#P connect 10 0 18 0;
#P fasten 24 0 35 0 199 396 158 396;
#P connect 35 0 5 0;
#P fasten 26 1 30 0 298 128 199 128;
#P fasten 1 0 24 0 265 297 223 297 223 359 199 359;
#P connect 30 0 24 0;
#P connect 24 0 28 0;
#P connect 28 0 29 0;
#P fasten 26 5 25 0 430 126 408 126 408 326 238 326;
#P connect 25 0 31 0;
#P connect 31 0 24 1;
#P connect 27 0 26 0;
#P connect 26 0 13 0;
#P connect 13 0 23 0;
#P connect 23 0 3 0;
#P connect 3 0 0 0;
#P connect 0 0 1 0;
#P connect 1 0 2 0;
#P connect 23 1 4 0;
#P connect 4 0 0 1;
#P fasten 26 2 34 0 331 137 295 137;
#P connect 34 0 13 1;
#P fasten 26 3 14 0 364 154 430 154;
#P connect 14 0 15 0;
#P connect 15 0 17 0;
#P connect 17 0 20 0;
#P connect 20 0 21 0;
#P connect 21 0 22 0;
#P fasten 19 0 20 1 474 243 447 243;
#P fasten 26 4 16 0 397 140 454 140;
#P connect 16 0 15 1;
#P fasten 26 5 19 0 430 126 474 126;
#P window clipboard copycount 36;

Feb 18 2007 | 2:00 pm

Feb 18 2007 | 2:06 pm

Or this?

#P window setfont "Sans Serif" 9.;
#P window linecount 1;
#P message 746 233 20 196617 \$3;
#P message 690 173 46 196617 0. 1. 17;
#P message 673 149 46 196617 3. 7. 11;
#P message 729 274 83 196617 \$1 , bang , \$2 \$3;
#P newex 673 272 40 196617 uzi;
#P newex 673 196 27 196617 t b l;
#P newex 673 339 32 196617 print;
#P newex 673 310 111 196617 bline;
#P fasten 2 1 4 0 695 243 734 243;
#P fasten 2 1 7 0 695 223 751 223;
#P connect 4 0 0 0;
#P fasten 7 0 3 1 751 260 708 260;
#P connect 6 0 2 0;
#P connect 5 0 2 0;
#P connect 2 0 3 0;
#P connect 3 0 0 0;
#P connect 0 0 1 0;
#P window clipboard copycount 8;

On 2/17/07 6:54 PM, "David Morneau" wrote:

> max v2;
> #N vpatcher 144 153 690 655;
> #P window setfont "Sans Serif" 9.;
> #P number 461 62 35 9 0 0 0 3 0 0 0 221 221 221 222 222 222 0 0 0;
> #P window linecount 1;
> #P newex 86 99 53 196617 t b b b b;
> #P newex 198 164 40 196617 t f f f;
> #P newex 198 141 27 196617 f;
> #P newex 341 141 27 196617 f;
> #P newex 444 164 40 196617 t f f f;
> #P newex 444 141 27 196617 f;
> #P newex 86 454 32 196617 print;
> #P newex 282 254 27 196617 / 1.;
> #P newex 282 225 27 196617 – 0.;
> #P comment 457 49 44 196617 # steps;
> #P comment 362 49 24 196617 max;
> #P flonum 358 62 35 9 0 0 0 3 0 0 0 221 221 221 222 222 222 0 0 0;
> #P flonum 215 62 35 9 0 0 0 3 0 0 0 221 221 221 222 222 222 0 0 0;
> #P message 40 305 14 196617 1;
> #P newex 40 284 32 196617 sel 4;
> #P newex 86 414 27 196617 + 0.;
> #P button 86 62 15 0;
> #P newex 86 226 40 196617 uzi 4;
> #P newex 86 374 29 196617 * 0.;
> #N counter 1 100;
> #X flags 0 0;
> #P newobj 86 331 74 196617 counter 1 100;
> #P comment 219 49 24 196617 min;
> #P comment 80 49 33 196617 do it!;
> #P fasten 2 0 7 0 91 351 36 351 36 281 45 281;
> #P connect 7 0 8 0;
> #P fasten 17 1 7 1 464 276 67 276;
> #P connect 5 0 21 0;
> #P connect 21 0 4 0;
> #P connect 4 0 2 0;
> #P connect 2 0 3 0;
> #P connect 3 0 6 0;
> #P fasten 20 0 15 0 203 446 91 446;
> #P connect 6 0 15 0;
> #P fasten 20 1 6 1 218 411 108 411;
> #P fasten 14 0 3 1 287 370 110 370;
> #P fasten 17 0 4 1 449 193 121 193;
> #P fasten 8 0 2 2 45 322 123 322;
> #P fasten 21 2 19 0 119 131 203 131;
> #P connect 19 0 20 0;
> #P connect 9 0 19 1;
> #P fasten 18 0 13 0 346 212 287 212;
> #P connect 13 0 14 0;
> #P fasten 20 2 13 1 233 218 304 218;
> #P fasten 17 2 14 1 479 248 304 248;
> #P fasten 21 1 18 0 105 128 346 128;
> #P connect 10 0 18 1;
> #P fasten 21 3 16 0 133 125 449 125;
> #P connect 16 0 17 0;
> #P connect 22 0 16 1;
> #P pop;

Cheers
Gary Lee Nelson
Oberlin College
http://www.timara.oberlin.edu/GaryLeeNelson

Feb 18 2007 | 2:13 pm

Oops. I saved way right in a large window. Here is is on the left.

#P window setfont "Sans Serif" 9.;
#P window linecount 1;
#P message 118 126 20 196617 \$3;
#P message 62 66 46 196617 0. 1. 17;
#P message 45 42 46 196617 3. 7. 11;
#P message 101 167 83 196617 \$1 , bang , \$2 \$3;
#P newex 45 165 40 196617 uzi;
#P newex 45 89 27 196617 t b l;
#P newex 45 232 32 196617 print;
#P newex 45 203 111 196617 bline;
#P fasten 2 1 4 0 67 136 106 136;
#P fasten 2 1 7 0 67 116 123 116;
#P connect 0 0 1 0;
#P connect 3 0 0 0;
#P connect 2 0 3 0;
#P connect 5 0 2 0;
#P connect 6 0 2 0;
#P fasten 7 0 3 1 123 153 80 153;
#P connect 4 0 0 0;
#P window clipboard copycount 8;

On 2/18/07 9:06 AM, "Gary Lee Nelson" wrote:

> #P window setfont "Sans Serif" 9.;
> #P window linecount 1;
> #P message 746 233 20 196617 \$3;
> #P message 690 173 46 196617 0. 1. 17;
> #P message 673 149 46 196617 3. 7. 11;
> #P message 729 274 83 196617 \$1 , bang , \$2 \$3;
> #P newex 673 272 40 196617 uzi;
> #P newex 673 196 27 196617 t b l;
> #P newex 673 339 32 196617 print;
> #P newex 673 310 111 196617 bline;
> #P fasten 2 1 4 0 695 243 734 243;
> #P fasten 2 1 7 0 695 223 751 223;
> #P connect 4 0 0 0;
> #P fasten 7 0 3 1 751 260 708 260;
> #P connect 6 0 2 0;
> #P connect 5 0 2 0;
> #P connect 2 0 3 0;
> #P connect 3 0 0 0;
> #P connect 0 0 1 0;
> #P window clipboard copycount 8;

Cheers
Gary Lee Nelson
Oberlin College
http://www.timara.oberlin.edu/GaryLeeNelson

Feb 18 2007 | 3:39 pm

———- Original Message ———————————-
From: Gary Lee Nelson
Date: Sun, 18 Feb 2007 09:13:15 -0500

>Oops. I saved way right in a large window. Here is is on the left.
>
>#P window setfont "Sans Serif" 9.;
>#P window linecount 1;
>#P message 118 126 20 196617 \$3;
>#P message 62 66 46 196617 0. 1. 17;
>#P message 45 42 46 196617 3. 7. 11;
>#P message 101 167 83 196617 \$1 , bang , \$2 \$3;
>#P newex 45 165 40 196617 uzi;
>#P newex 45 89 27 196617 t b l;
>#P newex 45 232 32 196617 print;
>#P newex 45 203 111 196617 bline;
>#P fasten 2 1 4 0 67 136 106 136;
>#P fasten 2 1 7 0 67 116 123 116;
>#P connect 0 0 1 0;
>#P connect 3 0 0 0;
>#P connect 2 0 3 0;
>#P connect 5 0 2 0;
>#P connect 6 0 2 0;
>#P fasten 7 0 3 1 123 153 80 153;
>#P connect 4 0 0 0;
>#P window clipboard copycount 8;
>
>
>
>On 2/18/07 9:06 AM, "Gary Lee Nelson" wrote:
>
>> #P window setfont "Sans Serif" 9.;
>> #P window linecount 1;
>> #P message 746 233 20 196617 \$3;
>> #P message 690 173 46 196617 0. 1. 17;
>> #P message 673 149 46 196617 3. 7. 11;
>> #P message 729 274 83 196617 \$1 , bang , \$2 \$3;
>> #P newex 673 272 40 196617 uzi;
>> #P newex 673 196 27 196617 t b l;
>> #P newex 673 339 32 196617 print;
>> #P newex 673 310 111 196617 bline;
>> #P fasten 2 1 4 0 695 243 734 243;
>> #P fasten 2 1 7 0 695 223 751 223;
>> #P connect 4 0 0 0;
>> #P fasten 7 0 3 1 751 260 708 260;
>> #P connect 6 0 2 0;
>> #P connect 5 0 2 0;
>> #P connect 2 0 3 0;
>> #P connect 3 0 0 0;
>> #P connect 0 0 1 0;
>> #P window clipboard copycount 8;
>
>
>Cheers
>Gary Lee Nelson
>Oberlin College
>http://www.timara.oberlin.edu/GaryLeeNelson
>
>
>

Need personalized email and website? Look no further. It’s easy

Feb 18 2007 | 4:24 pm

remembers something I’ve forgotten. This little programming match reminded
me that an integer in the left inlet of uzi fires that many bangs and defer
can be used for recursive programming without overflowing the stack.

On 2/18/07 10:40 AM, "David Morneau" wrote:

Cheers
Gary Lee Nelson
Oberlin College
http://www.timara.oberlin.edu/GaryLeeNelson

Feb 18 2007 | 4:33 pm

And singing the generalization song again…

Linterp by Peter Elsea. No example just look at the help file.

Cheers
Gary Lee Nelson
Oberlin College
http://www.timara.oberlin.edu/GaryLeeNelson

Feb 18 2007 | 4:46 pm

Sorry…forgot we are quantizing

#P window setfont "Sans Serif" 9.;
#P window linecount 1;
#P newex 70 334 32 196617 print;
#P flonum 166 144 40 9 0 0 0 3 0 0 0 221 221 221 222 222 222 0 0 0;
#P message 40 52 124 196617 0 0 1 0 3 0 7;
#P newex 40 83 189 196617 t b l l;
#P newex 70 271 41 196617 * 0.25;
#P newex 70 251 27 196617 – 1;
#P newex 40 227 40 196617 uzi;
#P newex 129 200 27 196617 + 1;
#P newex 129 144 27 196617 – 1;
#P newex 129 169 34 196617 / 0.25;
#P newex 129 120 42 196617 Llength;
#P newex 70 304 42 196617 Linterp;
#P comment 229 145 100 196617 step interval;
#P connect 11 0 8 1;
#P connect 11 0 3 1;
#P fasten 5 0 6 1 134 222 75 222;
#P connect 3 0 5 0;
#P connect 1 0 12 0;
#P connect 8 0 1 0;
#P connect 9 0 6 0;
#P connect 9 1 2 0;
#P fasten 9 2 1 1 223 299 107 299;
#P connect 10 0 9 0;
#P connect 7 0 8 0;
#P connect 6 2 7 0;
#P connect 4 0 3 0;
#P connect 2 0 4 0;
#P window clipboard copycount 13;

On 2/18/07 11:33 AM, "Gary Lee Nelson" wrote:

> And singing the generalization song again…
>
> Linterp by Peter Elsea. No example just look at the help file.
>
> Cheers
> Gary Lee Nelson
> Oberlin College
> http://www.timara.oberlin.edu/GaryLeeNelson
>
>

Cheers
Gary Lee Nelson
Oberlin College
http://www.timara.oberlin.edu/GaryLeeNelson

Feb 19 2007 | 7:26 pm

Gregory Taylor wrote:
> solutions that would be more akin to the "flow" of data than
> expressions….

Two objects which seemed obvious for me didn’t show up yet:
scale and modulo…
(won’t work on Max 2.2, but scale is easy to haX… ;-)

#P window setfont "Sans Serif" 9.;
#P window linecount 1;
#P newex 210 270 85 196617 scale 0. 1. 0. 1.;
#P flonum 290 201 35 9 0 0 0 3 0 0 0 221 221 221 222 222 222 0 0 0;
#P comment 329 68 34 196617 steps;
#P comment 291 68 28 196617 high;
#P newex 210 247 29 196617 – 0.;
#P flonum 288 90 35 9 0 0 0 3 0 0 0 221 221 221 222 222 222 0 0 0;
#P flonum 249 90 35 9 0 0 0 3 0 0 0 221 221 221 222 222 222 0 0 0;
#P newex 297 174 28 196617 / 2.;
#P number 327 90 35 9 1 0 1 3 0 0 0 221 221 221 222 222 222 0 0 0;
#P newex 210 200 35 196617 + 0.5;
#P newex 327 129 33 196617 !/ 1.;
#P flonum 210 90 35 9 0 0 0 3 0 0 0 221 221 221 222 222 222 0 0 0;
#P newex 210 174 85 196617 scale 0. 1. 0. 1.;
#P newex 229 224 108 196617 % 1.;
#P comment 251 68 28 196617 low;
#P window linecount 3;
#P comment 101 201 102 196617 just get rid of this -> if you don’t want
rounding….;
#P flonum 210 294 35 9 0 0 0 3 0 0 0 221 221 221 222 222 222 0 0 0;
#P connect 16 0 0 0;
#P connect 11 0 4 2;
#P connect 11 0 16 4;
#P connect 10 0 4 1;
#P connect 10 0 16 3;
#P connect 12 0 16 0;
#P fasten 9 0 7 1 302 195 240 195;
#P connect 9 0 15 0;
#P connect 7 0 12 0;
#P connect 7 0 3 0;
#P connect 6 0 9 0;
#P connect 6 0 3 1;
#P connect 3 0 12 1;
#P connect 8 0 6 0;
#P connect 4 0 7 0;
#P connect 5 0 4 0;
#P window clipboard copycount 17;

Stefan Tiedje————x——-
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