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| The Case for using Decibel Measurements for Gurps 4th Edition, (G4dB) Posted by The DS Note: This article is intended to illustrate some of the benefits of using the decibel measurement system and not to be a set of rules. Rules using dB will be posted in a different article. If you have any comments about this article, post in this thread (http://forums.sjgames.com/showthread.php?p=53813#post53813) at the SJG forums. IntroductionYou have probably heard of decibels as they apply to the loudness of a sound, but you likely have no idea what a decibel really is. A decibel is a ratio, such that a change of 10 is a factor of 10 (by definition), so therefore a change of 20 is a factor of 100, and a change of 30 is a factor of 1000. A difference of 1 decibel (hereafter: dB) is a factor of about 1.25, and a difference of 3 dB is a factor of about 2. Zero dB is defined as some value. For measurement of electrical energy, 0 dBm = 1 milliWatt, which means that 30 dBm = 1 Watt. Yes, 0 dB has a non-zero value of whatever you're measuring with them, and you can have negative dB values. The progression from 0 dB to 10 dB is consistent, and progressing from 10 to 20 requires simply multiplying by 10. Here is a progression from 0 to 20 to show you this.
You will notice that if you add or subtract 3 dB, you multiply or divide your Multiplier by 2, and that if you add or subtract 10 dB, you multiply or divide by 10. The above numbers are only slightly rounded, but +10 per x10 is the definition of a dB, and is therefore exact. Another bonus of decibels is that you finally can use the LOG and 10^x buttons on your calculator, and you will better understand how a slide rule works! Now, how do we apply decibels to Gurps? There are a number of progressions which naturally lend themselves to this kind of consistent progression, and I'll go over most of them in a moment. They include range, speed, height (all basically subsumable into Distance), and character strength and weight. Range:There are quite a few Advantages and Modifiers that list range of effect as having some effect on cost, and range to target also affects the DMs to hit it. I think without exception, they all start at a given distance of effect (usually 1 yard) and then each change occurs at double the distance of the previous one. For instance, the Area Effect Enhancement costs +50% per doubling of Radius of Effect, or per 3 dB. So you buy your Advantage (say, Mind Reading for 30 pts), and it has a base range of effect of 1 yard. You want this to be 1000 yards, which is 30dBr. (Let us say that 0 dBr = 1 yard, so 30 dBr = 1000 yards.) Since the Enhancement is priced at +50% per doubling, this is the same as saying +50% per 3 dBr (decibels of Range), so 30 dBr is 10 doublings of range, which is +500%, or a total cost of 180 pts for Mind Reading at 1000 yards. This sounds a bit overcomplicated at first, but it allows you to permit smaller gradations of the enhancement. If the cost was rewritten to a cost per 1 dB instead of per 3 dB, +1 dBr costs +17% (or maybe would be rounded down to 15%), which means you could have a range of 1600 yards (very close to a mile) for +534% (or 530%). (In a totally separate argument, if Gurps used Metric instead of Imperial, instead of 1600 yards, that would be 1600 meters, which is almost exactly a mile!) On the Range table on page 550, we see the progression is roughly in multiples of 1.5, but rounding messes up this nice progression so that actual multiples are anywhere from 1.4 to 2.0, requiring you to look up whatever you're talking about. However, there is no clear point at which doubling is consistent, and so you don't have any way to use the range table here to help you figure out your radius of effect for really powerful multipliers - the table here doesn't correspond at all to the one for Area Effect. If we used decibels, however, it does remain consistent. Of course, the range table's DMs start at 2 yards whereas the Area Effect table starts at 1 yard. For reasons to be explained later, instead of creating a whole new dB definition, the simplest thing to do would be to go ahead and use dBr as our term of preference, but to redefine it so that 0 dBr = 2 yards. This means the Area Effect will instead of automatically being 0dBr for 0 points, it is now -3 dBr for 0 points. This will make more sense in a few minutes. Speed:Our DM versus a moving object is equal to its dB value / 3, dropping fractions. For instance, we (re)defined 0 dBr as 2 yards, so we can also say 0 dBv (for Velocity/Speed) = 2 yards per turn. That means something moving 4 yards per turn is moving at twice the speed and gets a -1 to be hit, because that's +3 dBv. Since we like the idea of doubling for effects, we say each 3 dBv yields a + or -"" 1 DM. It's a fairly simple matter to divide by 2 a number of times, and count how many times you do it, but the dB progression looks so much nicer than the chart in the book. Height:Now we're getting into how this all applies to characters, and height is the primary determination of the Size Modifier (SM). By using our dBr scale, SM = dBr. That is, a Size Mod of 0 = 0 dBr = 2 yards tall. SM 3 = 3 dBr = 4 yards tall. SM 6 = 6 dBr = 8 yards tall. And so on. The scale goes in the opposite direction too. SM-3 = -3 dBr = 1 yard tall. SM-10 = -10 dBr = 0.2 yards tall. And so on. Now you should be starting to see the benefits, but there are much bigger ones coming right up. Character Strength and Weight:Assume for a moment we have a human character able to alter his height up or down, but he retains his proportions. When you double the height of this person, or increase his SM from 0 to +3, his weight increases by 8-fold, and his strength increases by 4-fold. If you don't believe me, check out GURPS GULLIVER; the explanation of why this is so is a bit outside the scope of this article. Well, 4 and 8 can be represented with 6 dB and 9 dB respectively. Keeping this in mind, we could say that for every SM our character grows, his height goes up 1 dB, his strength goes up 2 dB, and his mass goes up 3 dB. Since Gurps defines a normal human to have a strength of 10, we must add 10 to the above dB ratio. A strength of 10 allows a person to carry 20 pounds of stuff, so we will have to define 0 dBst as the ability to lift 2 pounds. Therefore, at 10 dBst, the character can lift 20 pounds. When our character grows 3 dB from SM 0 to SM +3, his ST needs to go up 6 dB, so ST goes from 10 to 16. Next, if we take a look at the Build Table, we see that for a ST 10 person with average build, their average weight is 145 pounds. Looking at the definitions of Skinny, Overweight, Fat, and Very Fat, we see that these impose weight modifiers of 2/3, 1.3, 1.5, and 2.0 respectively. With just a touch of rounding, this comes out to -2 dB for Skinny, +1 dB for Overweight, +2 dB for Fat, and +3 dB for Very Fat, a fairly natural progression. We COULD define dBwt (for weight) to be 145 pounds, but characters with less than ST 10 would tend to have negative weights, and although this doesn't hurt our decibel scale one iota, it does seem a bit strange, especially since ST starts out at 10, so let us simply reuse the dBst scale, in which 2 pounds = 0 dBst, but to keep from getting confused, we'll use dBwt to tell the difference between weight and strength. One side note: There exist plenty of people who are extremely fat and break this mold quite easily. If you wanted to, you could create further Builds, such as Extremely Fat at +6 dBwt, or go even further. The record would probably be around +10 to +12 dBwt, but I haven't done the calculations and leave them to those who feel it's important to do so. This in no way should be construed as thinking that there is a problem with the variance limit of +/- 2 that I and the book suggest; variance is variance of established values, and just because the book didn't mention that the largest man in the world weighed well over 1000 pounds and didn't create a rule specifically for him doesn't mean the authors didn't know he existed. The wonderful thing about having dBst = dBwt is that you know immediately whether or not you can pick something up. If its dBwt =< (is equal to or less than) the character's ST, you can carry it unencumbered (assuming you're not carrying much else). Since a character can Shift Slightly up to 50 times his Lift rating, that's a simple 17 dB, so if your ST 15 character comes up to a boulder, and it weighs no more than 34 dBwt (5000 pounds), he can Slightly Shift it without having to use Extra Effort. (Side note: when using Extra Effort to increase ST, the 1FP per 5% increase refers to the number of pounds, not to the strength value of the character.) Some commonly encountered figures:No Encumbrance = ST, Light Encumbrance = ST +3, Medium = ST +4, Heavy = ST +7, and Extra-Heavy = ST +10. Basic Lift = ST, One Handed Lift = ST +3, Two Handed Lift = ST +9, Shove and Knock Over = ST +11, Carry on Back or Drag = ST +12, Shift Slightly = ST +17. (See pages 17 and 353.) An average character with average build should weigh about 18.5 dBwt (140 lb). If it wouldn't cause a firestorm to do so, I would say that female average is 18 dBwt (125 lbs) and male average is 19 dBwt (160 lbs), assuming the average is SM 0 and ST 10, as these are fairly close to the actual average weights of women and men, but since no one wants to hear that men and women are not physically identical, please ignore this whole sentence. For every point of ST above or below the norm for your size, the average dBwt for that character changes by 0.5 dB. So the average weight of a character is 18.5 dBwt at SM 0 and ST 10 with no Build modifiers (Skinny, fat, etc). If the character's SM is not 0, add 3 for each +SM or subtract 3 for each -SM. If its ST is different from this value, every additional 1 point of ST adds 0.5 dBwt, and every lack of 1 ST subtracts 0.5. And finally, if the character has a build besides Average, add -2, +1, +2, or +3 for the appropriate build. This is your character's average dBwt. You can vary it by up to 1 dB without stretching believability and 2 dB without stretching reality. Other useful tidbits:Because there is no way for dB to equal 0 of some unit, this means that it can scale endlessly in either direction, and that negative numbers have meaning. For instance, say we wanted our character to shrink down to SM -15. In Gurps the way it is, you wouldn't be able to realistically represent this. ST 1 is way too much, and ST 0 means it has no strength at all. But if we use the decibel scale, we know that a person at SM -15 should have a strength of -20 and a weight of -26.5 (assuming it has the ST I just mentioned and no alteration in Build). Why? Because Average SM = 0, average ST = 10, and average Wt = 18.5. When I subtracted 15 from SM, I had to subtract 30 from ST (giving -20) and 45 from weight (giving -26.5). If this character was Fat, and had a ST of -19, he'd weigh -24 dBwt. But these values don't mean the character has some weird, negative-kinetic-energy strength or weight, just that his ratio of strength and weight are negative. If you can accept a negative Size Mod, you can accept a negative ST and Wt. Converting:All this is great, but it doesn't mean anything if we can't quickly figure out what it means in real units. Within the normal human bounds, it's not that hard to remember a few key numbers, but games wouldn't be that interesting if we were forced to stick with normal human ranges. The book has a number of charts for these things, and you can create charts of your own. The difference is that once you have computed and listed values from 0 to 10, every other value can be had by adding/subtracting 10 or by multiplying/dividing by 10. To do this, a calculator is handy, but not required if you remember a little basic math. To build a chart without a calculator, remember that every change of 1 is a factor of 1.25, every change of 3 is a factor of 2, and every change of 10 is a factor of 10. Next, remember what you defined your 0 dB as for each scale, and the rest is as simply as filling in blanks by multiplying or dividing by 2. The chart I gave at the beginning of the article will help you out if you need it. So, for weight, we said 0 dBwt = 2 pounds (or 1 kg for you metric people). So write a column going from 0 to 10, and next to 0 write 2 lb. 10 is 10 more than 0, so at 10, write 20 lb, since that's 10 times 2. At 3, that's where you'd write 4 lb, and at 7 you'd write 10, and so on, filling in the blanks by simply multiplying or dividing by 2 at every 3 slots. You now have a few slots remaining, and you can get the value for 8 dB by multiplying the value at 7 by 1.25. Thus you'd multiply 10 by 1.25 and get 12.5, and this you'd write next to 8. Figuring out 5 is the same thing, but you'd use the value next to 4. If you take a look at the chart you just made, it should look very similar to the chart I made above, except the numbers are shifted by 3 positions. This is because my chart uses 1 as its 0 dB value, and yours uses 2, and since a factor of 2 = 3 dB, that's why your chart is so similar. You can use my chart to correct the errors you may have made in yours. Some slight errors are expected, since these values are slightly rounded; my table possesses the best values to round to. You can use the same dBwt chart for dBst, since they both define 0 dB as 2 pounds. Incidentally, you can also use it for your measurements of height, distance, and speed, since these used 2 yards as their definition of 0 dB. Now you know why I wanted to change dBr from 1 to 2. If you want to write out the DMs for to-hit as they apply to height, range, and distance, go ahead and add appropriate columns for those. And if you want to add a column to be used as a multiplier for Area of Effect and other similar Advantages and Modifiers, go ahead and add those in too. You will find that instead of a dozen charts scattered all over the book, you now have just ONE chart, and it's pretty small. (For convenience, you may want to extend the values up to 20 dB or more, especially if you are adding in DMs and stuff that shouldn't be multiplied by 10.) Now you're wondering how in the world I figured out that 18.5 dBwt = 140 pounds, since that number isn't on your chart anywhere. Simple: I used a calculator, and here's how. Decibels are actually 1/10th of a Bel, and now you know why I've been using "dB" instead of "DB"; because the prefix "deci" is not supposed to be capitalized to differentiate it from the prefix "Deca", which is supposed to be capitalized. (Deca- means x10, by the way, while deci- means /10.) A Bel (yes, it's named for the inventor of the telephone, even though his name has 2 "L"s) is a ratio of multiples of 10. 0 = 1, 1 = 10, 2 = 100, 3 = 1000, and so on. You may notice this means you can take 10 and raise it to the power of Bel to get the multiplier, and you may notice that the base-10 logarithm works in the same way. Antilog - or on your calculator you may have to use INV and then LOG - is simply 10^X; 10 raised to the power of X. So, when you have been given a value in dB, divide it by 10, and take the Antilog of it, then multiply by your 0 dB value, and you have the value in real units. So to illustrate, we defined 0 dBwt as 2 pounds, and we said that the weight we wanted to know was 18.5 dBwt. We'll need to divide 18.5 by 10, giving us 1.85. Now we hit our Antilog key on the calculator, and it should give us about 70.794. Now we must multiply by 2 lb (our definition of 0 dBwt) and we get about 141.589. This is then rounded to the convenient 140 lbs, and we're not far at all from the 145 the game says is average (and you know they rounded too) so we say this is pretty good. If you want, you can calculate these half-dB values and put them into your chart, since we are putting them to some use when it comes to computing average character weights, but to keep you from wondering which way to round, here are the correct half-decibel values which can be slipped into the decibel table above.
And for 10.5 to 19.5, just add 10 to the dB and multiply the multiplier by 10. What if you're given a range of (pull this out of the air) 876 yards and you want to know how many dBr that is? First, remember that 0 dBr = 2 yards, and then do the calculation in reverse. So divide 876 by 2 and you get 438, because 2 yards is our definition of 0 dB. Next, press the LOG key, giving you about 2.641, but remember, this is Bels, so we have to multiply by 10 to get 26.41 decibels. Since range is supposed to be a "this value or less for this DM", we round up to 27 dBr, and that's the range. To find out the DM for this, simply divide by 3 and drop fractions. If this is a range + a speed, it's a -9 DM to hit; if it's the SM of something we're shooting at, it's a +9 DM to hit; and if it's for the Area Effect Enhancement, we must remember that with no bonus, AE is -3, so we subtract that from the 27 dBr we got, giving us 30 dBr (not 24), which is 10 doublings of range (30/3), for a +500% cost multiplier. (Remember that DMs versus range and speed must add both together before looking up the sum of the table to find the DM.) Potential problems:You've seen many of the advantages that going to decibels would provide, and probably noticed that many facets of the game are already designed to take advantage of them with hardly any modification at all, but you might also have noticed that there could be a problem inherent with relation to character strength. I'll enumerate the possible problems as Lift, Damage, and Cost. (There may be others, but I haven't figured them out yet.) In game systems which don't have a CP cost for strength, these problems are mostly irrelevant, but in Gurps, they require addressing. Basic Lift:Under Gurps 3rd edition (G3 hereafter), Basic Lift was measured linearly in regard to ST, but ST had a varied scale for cost. Lift = ST x 2, and for ST 10 that's 20 lbs. You needed insane levels of strength in order to get a noticeable change between one high level and another. Under Gurps 4th Edition (G4), Basic Lift is measured as the square of ST, such that you square ST and divide by 5 to get 20 lbs, the normal value for a human. At the same time, the amount of damage done hardly changed at all. The lower values were shifted away from negative damage (1d-9?) and a few other values were apparently tweaked from rounding, but 95% of the damage chart remains the same. In order to lift great amounts of weight, you don't need nearly as much ST, you need roughly the square root of what you needed before. But still, at the higher levels, you will need larger and larger increases in strength to get noticeable changes. Using the decibel scale, with the terms we've so far been using, ST 10 allows the lifting of 20 lbs by definition; no math to do. Plus, no matter where we are on the scale, from super high strength to super low strength, a given change of ST always produces a noticeable and consistent change in the amount of lift. Let's see a chart.
You'll notice I threw in a couple extra values, to illustrate that values of 0 or less are pretty much illegal under G3 and G4, but completely valid and meaningful when using decibels. Under G3, a change of 10 is a consistent linear progression, but if we want a 60 foot tall giant, we're going to need ST measured in hundreds if not thousands. Under G4, the change is less obvious unless you know what you're looking at. On the good side, you don't need as much ST to power your giant, but according to the information about the Growth Advantage (p 58), you should have 5 ST per yard of height, you need ST 100, giving a Lift of 2000 lbs and costing 1000 points. And under the dB system, you see the progression is completely consistent and natural, that each change is a consistent gain over the previous value, meaning you need even less ST for your 60 foot giant. Since 60 is 10 times SM 0, this makes our giant SM +10 in the DB system, meaning he needs 20 more ST than a human, or ST 30, giving a lift of 2000 lbs, exactly what G4 says he needs. (I didn't plan that, I expected 5 x yards on page 58 to be wrong.) Under G3, it was obvious that the supposed Human max of 20 was not nearly correct, that humans can lift more than that. G4's squaring rule comes closer, but still, 20 just isn't enough for all humans, and the book even says so on page 15. However, under dB, ST 20 is a considerable amount of strength, and I am not aware of any human being quite up to that level, finally making the "upper limit of 20" meaningful. Damage:I sort of touched on this earlier when I mentioned that between G3 and G4 there has been effectively no change in the amount of damage a given amount of strength will inflict, but let me point out something that could use some clearing up about the damage table. With only a few exceptions, particularly below ST 10, the damage table is arranged in increments of quarter-dice; that is, 1/4 of a die. Some of you may be familiar with a half-die; it is basically a D6 numbered from 1 to 3, twice. Effectively it is a D3. In practice, a half-die is represented as +2, because that's the average value you will roll with it, so those who don't like rolling D3s simply convert them into +2. Gurps also makes use of +1 and -1 with a lot of regularity in the table; a typical progression seems to go:
and so on. Four steps between full dice. +1 is obviously half of +2, and is therefore a quarter of a die, and that means 1d-1 is 3/4 of a die. All this taken together yields quarter-dice increments. At ST 10 and below, the quarter-die method breaks down for lack of granularity, but above that, you can see it is in full force. It appears that at ST 10, the desire was to have Thrust do 1/2 die and Swing to do 1 die. If you compare the values up to about ST 26 on page 16, you'll see that they maintain the 1:2 ratio of Thrust to Swing pretty consistently, but after that, the 2.5 die difference slowly degrades down to a 2 die difference at ST 70, at which point it stays there. Additionally, increases in ST yield lesser increases in damage, to the point that getting another die of damage requires another 10 ST instead of 4. While the existing damage chart is probably usable as it is with no modification, I can't help but wonder if there's a better way. The amount of damage you do is a function of how strong you are and also how much you weigh. If I were to muck with it in a quick, barely-thought-out manner to make it more compatible with the decibel ST system, I would say that at ST 10, you do 1 full die of swing damage, and every ST point above that gives an additional half die of damage, and that thrust damage is always equal to half of Swing damage. Below ST 10, we still have the odd problem of granularity since I am not going to suggest using decibels for hit points and damage, so for now, let us say the existing values are good enough. But, this is really something requiring a lot more thought, so I won't mention it at all right now. Point Cost:Let's see what ST is giving us. Lift scales up a lot quicker Damage would probably scale up quicker if I thought about "fixing it" 1 Hit Point per ST Hmmm, it's mostly the same stat as it's always been, the biggest difference is the Lift amount. At lower values, close to ST 10, G4 strength changes make a big change in Lift. To illustrate, the book mentions that ST 14 is about twice as strong as ST 10, and that ST 20 is 4 times as strong. That's a difference of 4, then 6, and to get to 8 times as strong you need to be ST 28, a difference of 8. As your ST goes up, the benefit goes up more slowly, requiring you to spend more points if you want it to increase at a given rate. Because of this, and because dBst gives a much faster increase in capability once you've gotten above a couple nominal ST increases, I feel that it is easily worth 15 points apiece. Now you might think this is overpriced, but if you do, I heartily recommend you buy up your striking strength and hit points at a much more efficient cost. (I'm inclined to say Lifting ST should also be increased in cost by 5 points or more per level.) Of importance: There is no point break for large characters buying ST . I am not sure I can say the same for small characters; this is a matter requiring more study. What's the best way to make a believable character?: I believe that what you should do is choose the Size Mod that is normal for the race you want. Next, buy the appropriate average ST for that SM and adjust your weight this way as well. If Aging rolls matter to you, take note of the average ST for your SM (not necessarily for your race). By subtracting 10 from this, you have the value at which you will die if your strength reaches this value due to aging rolls. It is also the point at which you are considered powerless if you are under the effects of some kind of spell that saps strength. Next, choose whether or not to be a genetic Dwarf or Giant. This will be +/- 1 or 2 to your SM, and if you take 2 levels, it costs/gives twice as much as the listed value. Genetic giants and dwarfs have their average ST modified by only 1 per each of these Size Mods, rather than the normal change of 2, and weight is modified by 2 for each of these Size Mods rather than the normal change of 3. Now, choose the ST you want. The range of typical values is +/- 6 dB from the average you have so far (including the modifiers for Gigantism/Dwarfism), and the maximum "possible" amount is +/- 10. While you can go higher than this, doing so should be reserved for superhumans or races that are superhuman. If you wish a Build besides Average, you can choose among the four alternatives available, and adjust your weight accordingly, as explained several paragraphs above. Finally, your actual weight is adjustable by up to +/- 1 dB for a typical adjustment, or up to +/- 2 dB for something unusual but still within the realm of not-unheard-of, in .5 dB increments. From this point on out, you should be able to resume the normal generation process. Some example characters:Typical HumanSM 0 (1.6-2yd), ST 10, BL 10 (20 lbs), Wt 18.5 (140 lbs), Dead/Helpless ST 0 Cost = 0 pts Strong Human, maybe a football playerSM 0 (1.6-2yd), ST 15, BL 15 (64 lbs), Wt 21 (250 lbs), Dead/Helpless ST 0 Cost = 75 pts Very Fat Human, weight variance +1.5, lower STSM 0 (1.6-2yd), ST 8, BL 8 (12.5 lbs), Wt 22 (320 lbs), Dead/Helpless ST 0 Cost = -35 pts Typical Genetic Giant +2 (2 levels)SM 2 (2.5-3.2yd), ST 12, BL 12 (32 lbs), Wt 22.5 (360 lbs), Dead/Helpless ST 0 Cost = 30 pts Typical sub-Giant (racial sub-Giant, SM 2, proportionate to human)SM 2 (2.5-3.2yd), ST 14, BL 14 (50 lbs), Wt 24.5 (360 lbs), Dead/Helpless ST 4 Cost = 60 pts Typical sub-Giant Genetic Dwarf -2 (racial sub-Giant, SM 2), weight variance -0.5SM 0 (1.6-2yd), ST 12, BL 12 (32 lbs), Wt 20 (200 lbs), Dead/Helpless ST 4 Cost = 30 pts Typical Big-Giant (racial Big-Giant, SM 9, proportionate to human)SM 9 (12.5-16yd), ST 28, BL 28 (1250 lbs), Wt 45.5 (64,000 lbs), Dead/Helpless ST 18 Cost = 270 pts Typical Fairy (racial Fairy, SM -6, proportionate to human)SM -6 (0.4-0.5yd), ST -2, BL -2 (1.25 lbs), Wt 0.5 (2.25 lbs), Dead/Helpless ST -12 Cost = -180 pts Final notes:You should notice, especially comparing the Fairy with a human, that smaller creatures have a substantially larger Basic Lift to Weight ratio. This is because of the Square-Cube Law, not by any deficiency in Gurps or the decibel system presented. What this means in real life is that larger creatures must devote more strength to keeping themselves upright than smaller ones, and so they are going to move proportionately slower and be able to carry proportionately less. A Big-Giant, at 8x normal human height, may have a stride 8x as far (actually, this is unlikely, but for a separate reason), but he will not actually walk 8x as far in a given amount of time. The Square-Cube Law will prevent realistic characters from being too big or too small without using some of the adaptations that real life creatures of those sizes use. Things like this are discussed in much more depth in GURPS GULLIVER, so I recommend you stop by T-Bone's Diner (http://www.io.com/~tbone/gurps/) and check it out. Thanks for reading; The End. |
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