## [SA2B] Relationship between Chao Stats and Velocity (Ongoing)

- Quickhand413
- Newborn Chao
**Posts:**7**Joined:**Wed Mar 30, 2016 2:02 am**Motto:**Every question probably has an answer.

### [SA2B] Relationship between Chao Stats and Velocity (Ongoing)

Hello Chao Community,

I've been racing chao a lot in my SA2B game, and I thought I'd conduct some research on the relationship between the numerical value between the chao's stats and the speed at which the chao travels. It's in it's EXTREMELY early stages (only have 5 data points out of the 400 I've got planned), and it's going to attempt to track the velocity of a chao at different stat values, from it's inital value of 0 all the way to the "perfect" chao stat of 3266, the stat soft cap at 4000, and the stat hard cap at 65535 (highest value for a 16-bit integer.) If any of you guys are interested I'm going to post semi-regularly once I have some concrete evidence on their stats, and I do have a couple of loose ends that would make the study even more scientific if there are users who can help me out with this (such as making a definite measurement system like pixels/second or Chaolengths/second) (Also, I'm new to the Forums area, so if I should create a separate thread in the Chao Help section, please let me know!) If you want to provide some data points for the study yourself, the way I'm conducting the study is as follows:

I'm using SA2B on Steam, and using the Fusion Chao Editor to manipulate the stats.

1) The chao should have a stamina stat high enough to last them through a beginner race without boosting.

2) The stat being tested will be set at the value to be tested at, all other stats will be left at 0

3) the measurements will be taking place on the beginner course that tests that specific stat.

4) The time for the stat will be measured only when that stat is active, and not before the race

(The figures I have for this is for the Swim stat in the beginner race, one should subtract 2.75 seconds from their result, that's how long it takes to hop in. The Power course has about 3.8 seconds of running when the Run stat equals 0, The run course doesn't need this figure b/c all you're doing is running, and it takes about 8 seconds to jump off to the flying segment in the flying race, but it's variable depending on other chao's behavior.)

5) The timing ends when either the race ends, or the segment of the race that uses the stat ends (only in the flying race.)

Hopefully this study will produce some interesting mathematical relationship between stat and velocity, and benefit the Chao Community as a whole.

On a side note, I discovered through some of my early testing that when you use a Chao's stamina to cheer it and make it go faster, the chao's velocity increases by about 30% (I had 2 1.30's and 1 1.27, so it's a safe assumption that velocity goes from 1 to 1.3 when cheered)

-Quickhand413

I've been racing chao a lot in my SA2B game, and I thought I'd conduct some research on the relationship between the numerical value between the chao's stats and the speed at which the chao travels. It's in it's EXTREMELY early stages (only have 5 data points out of the 400 I've got planned), and it's going to attempt to track the velocity of a chao at different stat values, from it's inital value of 0 all the way to the "perfect" chao stat of 3266, the stat soft cap at 4000, and the stat hard cap at 65535 (highest value for a 16-bit integer.) If any of you guys are interested I'm going to post semi-regularly once I have some concrete evidence on their stats, and I do have a couple of loose ends that would make the study even more scientific if there are users who can help me out with this (such as making a definite measurement system like pixels/second or Chaolengths/second) (Also, I'm new to the Forums area, so if I should create a separate thread in the Chao Help section, please let me know!) If you want to provide some data points for the study yourself, the way I'm conducting the study is as follows:

I'm using SA2B on Steam, and using the Fusion Chao Editor to manipulate the stats.

1) The chao should have a stamina stat high enough to last them through a beginner race without boosting.

2) The stat being tested will be set at the value to be tested at, all other stats will be left at 0

3) the measurements will be taking place on the beginner course that tests that specific stat.

4) The time for the stat will be measured only when that stat is active, and not before the race

(The figures I have for this is for the Swim stat in the beginner race, one should subtract 2.75 seconds from their result, that's how long it takes to hop in. The Power course has about 3.8 seconds of running when the Run stat equals 0, The run course doesn't need this figure b/c all you're doing is running, and it takes about 8 seconds to jump off to the flying segment in the flying race, but it's variable depending on other chao's behavior.)

5) The timing ends when either the race ends, or the segment of the race that uses the stat ends (only in the flying race.)

Hopefully this study will produce some interesting mathematical relationship between stat and velocity, and benefit the Chao Community as a whole.

On a side note, I discovered through some of my early testing that when you use a Chao's stamina to cheer it and make it go faster, the chao's velocity increases by about 30% (I had 2 1.30's and 1 1.27, so it's a safe assumption that velocity goes from 1 to 1.3 when cheered)

-Quickhand413

Until next time!

Quickhand413

Quickhand413

- Quickhand413
- Newborn Chao
**Posts:**7**Joined:**Wed Mar 30, 2016 2:02 am**Motto:**Every question probably has an answer.

### Re: [SA2B] Relationship between Chao Stats and Velocity (Ongoing)

Sorry this study is taking so long, life ramped up on me a little bit.

Anyways, the data for the experiment is about 5% complete, and I made an interesting discovery that could give an insight on the formula the game is using.

The formula the game is using is almost certainly non-linear.

I decided to test this formula at it's extremes (0 and 65535), as well as 50 away from them (50 and 65485) on the power course. When the chao was at power = 0, the chao completed the climbing section in 13.05 seconds, and when power = 50, the chao completed the same portion in 12.80 seconds, which is a .25 second improvement. The improvement for the chao from 65485 to 65535 was only .02 seconds. So, the function (on a graph of stats on the x axis and time on the y axis), the formula is likely hyperbolic. I know the examples are a bit extreme, but that still means that as the stat grows higher in a chao, even from 0 to 3266, the amount of time it takes to finish the race doesn't always go up the same amount. I'll be working on the study a bit more diligently more often, and i'll let you guys know if any new developments come up.

tl;dr: a jump from 0 to 100 is more noticable than a jump from 3000 to 3100.

-Quickhand413

Anyways, the data for the experiment is about 5% complete, and I made an interesting discovery that could give an insight on the formula the game is using.

The formula the game is using is almost certainly non-linear.

I decided to test this formula at it's extremes (0 and 65535), as well as 50 away from them (50 and 65485) on the power course. When the chao was at power = 0, the chao completed the climbing section in 13.05 seconds, and when power = 50, the chao completed the same portion in 12.80 seconds, which is a .25 second improvement. The improvement for the chao from 65485 to 65535 was only .02 seconds. So, the function (on a graph of stats on the x axis and time on the y axis), the formula is likely hyperbolic. I know the examples are a bit extreme, but that still means that as the stat grows higher in a chao, even from 0 to 3266, the amount of time it takes to finish the race doesn't always go up the same amount. I'll be working on the study a bit more diligently more often, and i'll let you guys know if any new developments come up.

tl;dr: a jump from 0 to 100 is more noticable than a jump from 3000 to 3100.

-Quickhand413

Until next time!

Quickhand413

Quickhand413

- Mooncow
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### Re: [SA2B] Relationship between Chao Stats and Velocity (Ongoing)

So what you're saying it, you are testing to see if the actual speed of a Chao changes in batches rather than a smooth curve?

So for example instead of the run stat increasing by a percentage with every stat, it may increase in every bunch of 10 or 20 ? Or it may increase per stat or be unnoticeable?

I hope I got that right, if not please feel free to explain in more detail!

So for example instead of the run stat increasing by a percentage with every stat, it may increase in every bunch of 10 or 20 ? Or it may increase per stat or be unnoticeable?

I hope I got that right, if not please feel free to explain in more detail!

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### Re: [SA2B] Relationship between Chao Stats and Velocity (Ongoing)

I don't know how I never saw this thread until today. I would have commented on it much sooner. This is an interesting topic, although with a lot of potential testing required.

Mooncow, I think the main goal is to be able to get equations for speed, as a function of stat values, just using the increments as data points. Full on functions may be a bit extreme (and could even be not possible) but something along those lines. (And, at least I assume, under the assumption that even a stat change of +1 would increase the speed.)

Not to put words in Quickhand's mouth.

A few thoughts:

On the topic of hyperbolic, nonlinear increases in speed, I would think testing around the soft cap value, instead of the insanely high 65535 values, should give a more meaningful scale on just how nonlinear speed is (like where the asymptote may lie, past where people can reach normally or not.)

Also, you tested how much a stamina boost increases the speed, which is good to know. I think a good follow up on thought is how speed decreases when the chao runs out of stamina.

On units of speed, what have you been using so far? You gave some numbers when referring to cheer speed increase, but I am not sure on the units.

I think this is a really good project, although as usual, I can not engage in it directly, due to not having PC SA2B. I will definitely like to look at this thought. And I definitely think run is the go to first thing to test for, although slopes are possibly something to take into account as a source of variable speeds.

Mooncow, I think the main goal is to be able to get equations for speed, as a function of stat values, just using the increments as data points. Full on functions may be a bit extreme (and could even be not possible) but something along those lines. (And, at least I assume, under the assumption that even a stat change of +1 would increase the speed.)

Not to put words in Quickhand's mouth.

A few thoughts:

On the topic of hyperbolic, nonlinear increases in speed, I would think testing around the soft cap value, instead of the insanely high 65535 values, should give a more meaningful scale on just how nonlinear speed is (like where the asymptote may lie, past where people can reach normally or not.)

Also, you tested how much a stamina boost increases the speed, which is good to know. I think a good follow up on thought is how speed decreases when the chao runs out of stamina.

On units of speed, what have you been using so far? You gave some numbers when referring to cheer speed increase, but I am not sure on the units.

I think this is a really good project, although as usual, I can not engage in it directly, due to not having PC SA2B. I will definitely like to look at this thought. And I definitely think run is the go to first thing to test for, although slopes are possibly something to take into account as a source of variable speeds.

- Quickhand413
- Newborn Chao
**Posts:**7**Joined:**Wed Mar 30, 2016 2:02 am**Motto:**Every question probably has an answer.

### Re: [SA2B] Relationship between Chao Stats and Velocity (Ongoing)

First off, thanks for your guys' interest, I'm honored to see that you're interested

Looking back on some of my posts, as well as my notes from when I took physics, I may have misstated a few things.

First off, I am using the increments as data points for an overall function, just as Mamkute said.

I've been mostly basing the study on timing, which to the average player is what they would look to for seeing how "fast" their chao is. The function of everything according to time appears to some extent to be hyperbolic. That being said, it's completely normal for a time function to be this way, since v = d/t. So, I can't exactly rule out a linear velocity anymore. But, if you're racing chao with the objective of getting better and better times, the amount of time shaven off with each increase gets lower and lower.

I've also come up with a bit of a hypothesis on how these functions could be built. If you go time-sided, the function will (hopefully) be something like K(m/(x-b^-1), where K is a constant based on the stat measured (power, swim, run, or fly), m being some sort of unifying constant in the base function, x being the stat value, and b being the time it takes to finish the race at x=0. If velocity were to follow the trend this time function, I wouldn't be surprised if it's just k(mx+b), with the variables following the same definitions.

As for testing around 65535, I just did that to make sure I was on the right track graph-wise, I wanted the most extreme distance in stats to help me prove my point.

I haven't got any solid units for distance, mainly because I don't know of any methods to access them. The simplest way I can see going about this is by counting pixels on a minimap and just putting it in terms of map pixels, which might be a bit sketchy (human error and all). There's probably a memory address for where the position of a chao is stored, but I don't have any idea how to properly memory hack.

Measuring a decrease in stats when there's no stamina left is an interesting topic, but it'll be a little harder to do because chao always have stamina at the beginning of a race, and I doubt stat values can go negative. I have a few ideas, such as running a longer race until you get to a previously measured segment (viable), or memory hacking the value of the stamina to 0 at the beginning of the race (probably a little complex).

Now, I know you're probably thinking it'd be hard to measure the boost in in velocity without distance. Well, since I tested all instances of "boosting" through a course on the same course, the distance over which the boosting takes place is equal, meaning that v(cheer)t(cheer)=v(reg.)t(reg.). After putting in the times, I got v(boost)=1.3v(reg.) (I was quite happy to see the numbers were really clean for an experiment this exact ). Seeing as formulas tend to be methodical to save space on games, I wouldn't be too surprised to see that running out of stamina decreases velocity by 30%

So, hopefully that clears things up, and if anyone out there can help me find the distance of courses through memory hacking or some other idea, it would be awesome if you posted something on here.

I'll try and be more active in the near future, preferably after I've taken my AP exams. Sorry if I seem like I'm sleeping on the job over here.

-Quickhand413

Looking back on some of my posts, as well as my notes from when I took physics, I may have misstated a few things.

First off, I am using the increments as data points for an overall function, just as Mamkute said.

I've been mostly basing the study on timing, which to the average player is what they would look to for seeing how "fast" their chao is. The function of everything according to time appears to some extent to be hyperbolic. That being said, it's completely normal for a time function to be this way, since v = d/t. So, I can't exactly rule out a linear velocity anymore. But, if you're racing chao with the objective of getting better and better times, the amount of time shaven off with each increase gets lower and lower.

I've also come up with a bit of a hypothesis on how these functions could be built. If you go time-sided, the function will (hopefully) be something like K(m/(x-b^-1), where K is a constant based on the stat measured (power, swim, run, or fly), m being some sort of unifying constant in the base function, x being the stat value, and b being the time it takes to finish the race at x=0. If velocity were to follow the trend this time function, I wouldn't be surprised if it's just k(mx+b), with the variables following the same definitions.

As for testing around 65535, I just did that to make sure I was on the right track graph-wise, I wanted the most extreme distance in stats to help me prove my point.

I haven't got any solid units for distance, mainly because I don't know of any methods to access them. The simplest way I can see going about this is by counting pixels on a minimap and just putting it in terms of map pixels, which might be a bit sketchy (human error and all). There's probably a memory address for where the position of a chao is stored, but I don't have any idea how to properly memory hack.

Measuring a decrease in stats when there's no stamina left is an interesting topic, but it'll be a little harder to do because chao always have stamina at the beginning of a race, and I doubt stat values can go negative. I have a few ideas, such as running a longer race until you get to a previously measured segment (viable), or memory hacking the value of the stamina to 0 at the beginning of the race (probably a little complex).

Now, I know you're probably thinking it'd be hard to measure the boost in in velocity without distance. Well, since I tested all instances of "boosting" through a course on the same course, the distance over which the boosting takes place is equal, meaning that v(cheer)t(cheer)=v(reg.)t(reg.). After putting in the times, I got v(boost)=1.3v(reg.) (I was quite happy to see the numbers were really clean for an experiment this exact ). Seeing as formulas tend to be methodical to save space on games, I wouldn't be too surprised to see that running out of stamina decreases velocity by 30%

So, hopefully that clears things up, and if anyone out there can help me find the distance of courses through memory hacking or some other idea, it would be awesome if you posted something on here.

I'll try and be more active in the near future, preferably after I've taken my AP exams. Sorry if I seem like I'm sleeping on the job over here.

-Quickhand413

Until next time!

Quickhand413

Quickhand413

- DarkyBenji
- Chao Expert
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### Re: [SA2B] Relationship between Chao Stats and Velocity (Ongoing)

Quickhand413 wrote:Seeing as formulas tend to be methodical to save space on games, I wouldn't be too surprised to see that running out of stamina decreases velocity by 30%

**30% ?!**

i though it was 80%~85%, i mean if my chao with 3200 on run, run out of stamina, he have the same speed of a chao with 640 run.

maybe it just run

### Re: [SA2B] Relationship between Chao Stats and Velocity (Ongoing)

Those are all very good observations, and I see you are a highly mathematical person. Good luck on AP tests Quickhand, I understand your pain (not currently, more like three years ago.) What are they, if I may ask?

More on topic. I suppose race time can only get you so far (compared to physical distance unit) since chao often take weird paths or get shoved out of the way by other chao, whch would make "race length" an inconsistent unit, although I suppose many runs could yield a reliable average.

Also, I asked earlier but this was not addressed, do you know if slopes are any factor in running speed? Those could make measurements more awkward.

Finally, and I know this is a large project, but what do you think of also testing for intelligence as it relates to speed of opening the boxes or getting the fruits (whether or not the chao gets the correct fruit is more a probability based on intelligence though.) And luck is thoroughly not a speed related stat, I suppose.

More on topic. I suppose race time can only get you so far (compared to physical distance unit) since chao often take weird paths or get shoved out of the way by other chao, whch would make "race length" an inconsistent unit, although I suppose many runs could yield a reliable average.

Also, I asked earlier but this was not addressed, do you know if slopes are any factor in running speed? Those could make measurements more awkward.

Finally, and I know this is a large project, but what do you think of also testing for intelligence as it relates to speed of opening the boxes or getting the fruits (whether or not the chao gets the correct fruit is more a probability based on intelligence though.) And luck is thoroughly not a speed related stat, I suppose.

- Quickhand413
- Newborn Chao
**Posts:**7**Joined:**Wed Mar 30, 2016 2:02 am**Motto:**Every question probably has an answer.

### Re: [SA2B] Relationship between Chao Stats and Velocity (Ongoing)

Well, I was able to do some more testing, and I may have at least a partial answer as to how running out of stamina affects the chao's speed, and Darky may be on to something.

The only stats I felt I could feasibly test were swim and power, because the beginner's areas were far enough into a Jewel race so I could reach them without having any stamina. I couldn't do the run stat because the pedriot course is the only one with mushroom forest's track in it, and it's right at the start, so my chao would always have some form of stamina, and the fly stat is a beast in and of itself (haven't found any good, drawn out flight spots, and you'd have to take in vertical AND horizontal velocities into account.)

Anyway, the strange thing I found is that the swim stat and the power stat had different effects to their velocity when there was no stamina. When I ran the aquamarine course and got to the crab pool, i noticed that the velocity dropped to .666 of its original value (or 2/3 if you prefer). When I did climb, the numbers were a wider range, but they all seemed to hover around 3/4 of the original velocity. I'm probably going to go back and re-measure the boost in speed when I have more time, but this rabbit hole may go a little deeper than originally thought.

As for the question on slopes, until some sort of accurate distance measurement is discovered, I can't answer that question with any degree of certainty.

As for the AP's I'm taking, they're Chemistry, Calculus AB, English literature, and Macroeconomics. I'm on the "college path" that's at my school.

Until next time!

-Quickhand413

The only stats I felt I could feasibly test were swim and power, because the beginner's areas were far enough into a Jewel race so I could reach them without having any stamina. I couldn't do the run stat because the pedriot course is the only one with mushroom forest's track in it, and it's right at the start, so my chao would always have some form of stamina, and the fly stat is a beast in and of itself (haven't found any good, drawn out flight spots, and you'd have to take in vertical AND horizontal velocities into account.)

Anyway, the strange thing I found is that the swim stat and the power stat had different effects to their velocity when there was no stamina. When I ran the aquamarine course and got to the crab pool, i noticed that the velocity dropped to .666 of its original value (or 2/3 if you prefer). When I did climb, the numbers were a wider range, but they all seemed to hover around 3/4 of the original velocity. I'm probably going to go back and re-measure the boost in speed when I have more time, but this rabbit hole may go a little deeper than originally thought.

As for the question on slopes, until some sort of accurate distance measurement is discovered, I can't answer that question with any degree of certainty.

As for the AP's I'm taking, they're Chemistry, Calculus AB, English literature, and Macroeconomics. I'm on the "college path" that's at my school.

Until next time!

-Quickhand413

Until next time!

Quickhand413

Quickhand413

- Jeffery Mewtamer
- Ultimate Chaos Chao
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### Re: [SA2B] Relationship between Chao Stats and Velocity (Ongoing)

Wait, do Chao start with a non-empty stamina meter even if their stamina is 0?

I also find myself wondering if there's a way to narrow down the section of executable that runs during Chao races and disassemble that portion of the game's machine code to get the actual formulas the game is using. Making sense of the entire disassembly would drive even the most dedicated hackers insane, but if we could isolate the Chao Race code(or the Chao Karate code for that matter), it might be manageable.

I also find myself wondering if there's a way to narrow down the section of executable that runs during Chao races and disassemble that portion of the game's machine code to get the actual formulas the game is using. Making sense of the entire disassembly would drive even the most dedicated hackers insane, but if we could isolate the Chao Race code(or the Chao Karate code for that matter), it might be manageable.

Just so you know, I am blind.

Those who approach life like a child playing a game, moving and pushing pieces, possess the power of kings.

Those who approach life like a child playing a game, moving and pushing pieces, possess the power of kings.

- Quickhand413
- Newborn Chao
**Posts:**7**Joined:**Wed Mar 30, 2016 2:02 am**Motto:**Every question probably has an answer.

### Re: [SA2B] Relationship between Chao Stats and Velocity (Ongoing)

Yeah, chao start with some stamina meter. It's also governed by a function that probably looks like y=mx+b, where the b is the amount of stamina the chao has at stamina=0.

As for the hacking of the formulas directly from the game, I have no knowledge on how to do that myself, but it would definitely speed up the process if we got some concrete formulas. I've been thinking if we can solidify what the velocity equations are from either testing or the program, it would only take some algebra to make a time formula where you could just plug in chao stats and find out how fast your chao would finish a given race. It might take longer than the actual race, but it helps if you're the type of guy that doesn't take chances.

Also, I've been doing more testing on the fly stat, and I believe I'm gonna have to throw out some data points due to them being over different distances. I did a little bit of fiddling around with the stats and I'm going to start collecting data points at fly≥350, because at that stat, (or a stat very close to that), it can bridge the gap in stump valley without falling into the water. 0-349 may be more useful for finding out the descent rate of the chao.

Until next time!

Quickhand413

As for the hacking of the formulas directly from the game, I have no knowledge on how to do that myself, but it would definitely speed up the process if we got some concrete formulas. I've been thinking if we can solidify what the velocity equations are from either testing or the program, it would only take some algebra to make a time formula where you could just plug in chao stats and find out how fast your chao would finish a given race. It might take longer than the actual race, but it helps if you're the type of guy that doesn't take chances.

Also, I've been doing more testing on the fly stat, and I believe I'm gonna have to throw out some data points due to them being over different distances. I did a little bit of fiddling around with the stats and I'm going to start collecting data points at fly≥350, because at that stat, (or a stat very close to that), it can bridge the gap in stump valley without falling into the water. 0-349 may be more useful for finding out the descent rate of the chao.

Until next time!

Quickhand413

Until next time!

Quickhand413

Quickhand413

- Quickhand413
- Newborn Chao
**Posts:**7**Joined:**Wed Mar 30, 2016 2:02 am**Motto:**Every question probably has an answer.

### Re: [SA2B] Relationship between Chao Stats and Velocity (Ongoing)

So, I decided to do some testing on stamina today, because it seemed like a topic that should be covered, especially for those who want to get the most out of their stamina and cheers. I finally have some concrete mathematical relationships to share on this topic, so a) something actually came out of the experiment, and b) there's something you guys can use to start optimizing your chao (I caught wind of something called the Chao Races). I arranged everything under spoiler bars so you don't have to scroll through some huge chunks of text to find what you want (You're welcome ).

Anyway, down to the math of it all. First off, I'm going to be using units of millibars in the equations (abbreviated mB). In case you couldn't infer, 1000mB = 1 full bar of stamina.

Hopefully you guys like this discovery, and use it well!

Until next time!

Quickhand413

Anyway, down to the math of it all. First off, I'm going to be using units of millibars in the equations (abbreviated mB). In case you couldn't infer, 1000mB = 1 full bar of stamina.

**The Actual Stamina Stat, and it's correlation with Millibars****Spoiler:**

**Stamina Decay****Spoiler:**

**mB of Stamina at Stamina = 0****Spoiler:**

**Cheering Decay****Spoiler:**

**To sum it all up, plus equations****Spoiler:**

Until next time!

Quickhand413

Until next time!

Quickhand413

Quickhand413

- Quickhand413
- Newborn Chao
**Posts:**7**Joined:**Wed Mar 30, 2016 2:02 am**Motto:**Every question probably has an answer.

### Re: [SA2B] Relationship between Chao Stats and Velocity (Ongoing)

Hey guys,

I'm going to be on hiatus for the next couple of weeks due to my APs. I might lurk the forums a little bit now and again, but don't expect any data or breakthroughs for a little while.

When I get back I'm pretty sure this study will be going better than ever thanks to some extended free time for me, so enjoy the stamina post until I get back

I'm going to be on hiatus for the next couple of weeks due to my APs. I might lurk the forums a little bit now and again, but don't expect any data or breakthroughs for a little while.

When I get back I'm pretty sure this study will be going better than ever thanks to some extended free time for me, so enjoy the stamina post until I get back

Until next time!

Quickhand413

Quickhand413