# How much of me came from the Big Bang?

**URL:** <https://boards.straightdope.com/t/how-much-of-me-came-from-the-big-bang/677477>\
**Category:** Factual Questions\
**Created:** [December 30, 2013, 1:42pm UTC](https://boards.straightdope.com/t/how-much-of-me-came-from-the-big-bang/677477 "2013-12-30T13:42:59Z")\
**Posts on this page:** 20\
**Page:** 2

<div class="post-metadata">

**Author:** ![DrCube](https://avatars.discourse-cdn.com/v4/letter/d/a3d4f5/32.png) [@DrCube](https://boards.straightdope.com/u/DrCube)\
**Post date:** [December 30, 2013, 7:41pm UTC](https://boards.straightdope.com/t/how-much-of-me-came-from-the-big-bang/677477/21 "2013-12-30T19:41:05Z")

</div>

> [@Colibri](#):
>
> Considered over a time span of 16 billion years, particles that originated within the first few seconds of the Universe’s existence might as well be considered primordial.

XT’s cite says the first atoms didn’t exist for 300,000 years. The fact that iron and carbon took a few hundred thousand more years to be created in early supernovas doesn’t make it appreciably different to me. It was all caused by the Big Bang, not created ex nihilo after the fact, nor teleported over from alternate universes. You can say that some elements came before others, but none of them are “original” because the early universe was pure energy.

---

<div class="post-metadata">

**Author:** ![Colibri](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/colibri/32/1841_2.png) [@Colibri](https://boards.straightdope.com/u/Colibri)\
**Post date:** [December 30, 2013, 7:59pm UTC](https://boards.straightdope.com/t/how-much-of-me-came-from-the-big-bang/677477/22 "2013-12-30T19:59:11Z")

</div>

> [@DrCube](#):
>
> XT’s cite says the first atoms didn’t exist for 300,000 years.

The OP, however, talks about “matter” rather than atoms. Baryons and leptons, which certainly qualify as matter, formed within a few seconds after the Big Bang, and atomic nuclei soon after. The Universe ceased being “pure energy” very shortly after its creation.

---

<div class="post-metadata">

**Author:** ![DrCube](https://avatars.discourse-cdn.com/v4/letter/d/a3d4f5/32.png) [@DrCube](https://boards.straightdope.com/u/DrCube)\
**Post date:** [December 30, 2013, 8:19pm UTC](https://boards.straightdope.com/t/how-much-of-me-came-from-the-big-bang/677477/23 "2013-12-30T20:19:40Z")

</div>

> [@Colibri](#):
>
> The OP, however, talks about “matter” rather than atoms. Baryons and leptons, which certainly qualify as matter, formed within a few seconds after the Big Bang, and atomic nuclei soon after. The Universe ceased being “pure energy” very shortly after its creation.

Okay, but if we’re talking about baryons and leptons, that would include all the elements as well.

I’m trying to understand how anyone can interpret the question non-arbitrarily so that the answer is something other than “all” (all matter was created by the big bang), or “none” (all matter was created _after_ the big bang).

Are we saying hydrogen nuclei came early enough to count – and who cares when electrons joined the party – but iron is a relative newbie? Where is the cutoff? A few seconds after the big bang? Why is that or any other time period significant?

---

<div class="post-metadata">

**Author:** ![Exapno\_Mapcase](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/exapno_mapcase/32/1051_2.png) [@Exapno\_Mapcase](https://boards.straightdope.com/u/Exapno_Mapcase)\
**Post date:** [December 30, 2013, 8:50pm UTC](https://boards.straightdope.com/t/how-much-of-me-came-from-the-big-bang/677477/24 "2013-12-30T20:50:09Z")

</div>

> [@DrCube](#):
>
> I’m trying to understand how anyone can interpret the question non-arbitrarily so that the answer is something other than “all” (all matter was created by the big bang), or “none” (all matter was created _after_ the big bang).
> 
> Are we saying hydrogen nuclei came early enough to count – and who cares when electrons joined the party – but iron is a relative newbie? Where is the cutoff? A few seconds after the big bang? Why is that or any other time period significant?

I did this in post #16. “Some” is probably the best answer to the question, IMO.

The cutoff is at iron because elements with higher atomic numbers require an external source of energy. That doesn’t have to be from a supernova - [other processes can contribute](http://www.researchgate.net/post/Are_Supernova_explosions_the_only_means_by_which_we_can_form_elements_heavier_than_Iron) - but that is the most likely source. And since our sun is a third generation star, it’s also most likely that these elements were formed much later than the very earliest days of the universe.

You can also nitpick and point out that the first stars took an appreciable amount of time to form after the Big Bang, and so any elements other than hydrogen, helium, and lithium are certainly a second and younger generation.

---

<div class="post-metadata">

**Author:** ![ZenBeam](https://avatars.discourse-cdn.com/v4/letter/z/3ab097/32.png) [@ZenBeam](https://boards.straightdope.com/u/ZenBeam)\
**Post date:** [December 30, 2013, 8:56pm UTC](https://boards.straightdope.com/t/how-much-of-me-came-from-the-big-bang/677477/25 "2013-12-30T20:56:05Z")

</div>

> [@bump](#):
>
> I don’t know if I’d say created so much as I’d say transmuted. If you take an atom of deuterium and an atom of tritium and fuse them, the resulting helium is “new” but it’s substance is that of the hydrogen isotopes that were fused, so I’d say that it was still created in the big bang.
> 
> It’s similar, albeit on a smaller scale to saying that isopropyl alcohol isn’t made from petroleum because it’s made from propene and water. However that propene is usually a byproduct of petroleum refining, so I think it’s fair to say that isopropyl alcohol is made from petroleum, at a step’s remove.

The constituent protons and neutrons were created in the Big Bang, but I’d say that the _Helium_ wasn’t created until the nuclei with two protons were made. In your analogy, you talk about isopropyl alcohol being “made”, not about it already existing when when the petroleum is pumped from a well.

> [@DrCube](#):
>
> I’m trying to understand how anyone can interpret the question non-arbitrarily so that the answer is something other than “all” (all matter was created by the big bang), or “none” (all matter was created after the big bang).
> 
> Are we saying hydrogen nuclei came early enough to count – and who cares when electrons joined the party – but iron is a relative newbie? Where is the cutoff? A few seconds after the big bang? Why is that or any other time period significant?

To me, it isn’t just the time, but also the mechanism. The [Big Bang nucleosynthesis](http://en.wikipedia.org/wiki/Big_Bang_nucleosynthesis) was over after the first 20 minutes. Until stars formed, and began fusing the primordial elements, new elements weren’t being created. That was some [500 million years later](http://en.wikipedia.org/wiki/Nucleosynthesis#Timeline), and a completely different process. It’s not just some arbitrary line someone drew.

As for what precisely the Big Bang includes, Note 1 on the [Wikipedia Big Bang page](http://en.wikipedia.org/wiki/Big_Bang#Timeline_of_the_Big_Bang) says:

> [@](#):
>
> There is no consensus about how long the Big Bang phase lasted. For some writers this denotes only the initial singularity, for others the whole history of the Universe. Usually, at least the first few minutes (during which helium is synthesized) are said to occur “during the Big Bang”.[20] (see also Big Bang nucleosynthesis)

At any rate, you’re free to answer in terms of protons and neutrons, rather than elements, and say it was all made shortly after the Big Bang, and I wouldn’t have a problem with that.

---

<div class="post-metadata">

**Author:** ![Colibri](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/colibri/32/1841_2.png) [@Colibri](https://boards.straightdope.com/u/Colibri)\
**Post date:** [December 30, 2013, 9:03pm UTC](https://boards.straightdope.com/t/how-much-of-me-came-from-the-big-bang/677477/26 "2013-12-30T21:03:28Z")

</div>

> [@DrCube](#):
>
> I’m trying to understand how anyone can interpret the question non-arbitrarily so that the answer is something other than “all” (all matter was created by the big bang), or “none” (all matter was created _after_ the big bang).

According to my own interpretation of the OP, I would say that essentially all “matter” (in the sense of baryons and leptons) was created by the Big Bang or immediately (within a few seconds) afterwards.

The rest of it is just that matter becoming organized in different more complex structures, including nuclei and atoms of different elements.

---

<div class="post-metadata">

**Author:** ![MikeS](https://avatars.discourse-cdn.com/v4/letter/m/919ad9/32.png) [@MikeS](https://boards.straightdope.com/u/MikeS)\
**Post date:** [December 30, 2013, 9:08pm UTC](https://boards.straightdope.com/t/how-much-of-me-came-from-the-big-bang/677477/27 "2013-12-30T21:08:02Z")

</div>

> [@Half\_Man\_Half\_Wit](#):
>
> Of course, if you go down to that level, there’s really no meaning to speaking about the identity of elementary particles, i.e. saying _this_ one is primordial, while _that_ one is recent. In a reaction such as the one producing a proton p and an antiproton p’ due to a proton interacting with a nucleus A, i.e. p + A –\> p + A + p + p’, you can’t point to one of the reaction products and say ‘this was the original proton that interacted with the nucleus’, and ‘that is the proton produced in the reaction’; so there’s really no good way to identify either particle as primordial or recent.

Fair point. You could more easily say, though, that electrons (or neutrinos) resulting from a cosmic-ray shower with a proton or nuclide primary are non-primordial.

Also, it was pointed out to me by a fellow physicist that the number of nuclear decays in your body at any given time (several thousand per second, from carbon-14 and potassium-40 among others) guarantees that there will be quite a few non-primordial electrons in your body at any given moment.

> [@DrCube](#):
>
> I’m trying to understand how anyone can interpret the question non-arbitrarily so that the answer is something other than “all” (all matter was created by the big bang), or “none” (all matter was created _after_ the big bang).
> 
> Are we saying hydrogen nuclei came early enough to count – and who cares when electrons joined the party – but iron is a relative newbie? Where is the cutoff? A few seconds after the big bang? Why is that or any other time period significant?

I’m in agreement with you that the distinction between primordial atoms (H & He) vs. johnny-come-lately atoms (like Fe) is somewhat arbitrary. On a fundamental level, the synthesis of heavier nuclei in the later Universe is really just the rearrangement of a fixed number of nucleons and leptons (which were [created in great numbers shortly after the Big Bang](http://en.wikipedia.org/wiki/Chronology_of_the_universe#Hadron_epoch)) into different configurations.

However, there are also processes, such as pair production and nuclear decays, that occurred much later in the Universe as well, after the great majority of nucleons formed and after most of the primordial electron/anti-electron pairs had annihilated each other. There’s a useful distinction to be drawn between an electron that has existed since the Big Bang and one that has was created just now via a carbon-14 decay. The latter electron was created from nuclear energy, and couldn’t really have been said to “exist” before the decay occurred.

---

<div class="post-metadata">

**Author:** ![PlaceboTarget](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/placebotarget/32/1073_2.png) [@PlaceboTarget](https://boards.straightdope.com/u/PlaceboTarget)\
**Post date:** [December 30, 2013, 9:26pm UTC](https://boards.straightdope.com/t/how-much-of-me-came-from-the-big-bang/677477/28 "2013-12-30T21:26:39Z")

</div>

> [@Colibri](#):
>
> It’s fine if you wish to advance a different interpretation of the question. However, dismissive comments about other interpretations aren’t particularly helpful.

I understand I was sarcastic and that was wrong. I’ve promised I’ll refrain myself. I’m reiterating this promise and I express my genuine regret for not having been more respectful in the first place. It won’t happen again.

As for the matter under discussion, my knowledge does not entitle me to advance any novel interpretations. The few books I’ve read on the subject enumerate the stages following the birth of the universe and mention the time passed since the Big Bang. Rigorously speaking, Big Bang is the expanding singularity. If we regard the 300,000-400,000 years that were necessary for hydrogen, helium, lithium and beryllium to form as part of the Big Bang, I think the 12-14 billion year scale allows us to add the next 0.5 billion years to the Big Bang so that we can include the formation of stars and the rest of the elements as well. I for one wouldn’t go this far.

---

<div class="post-metadata">

**Author:** ![ZenBeam](https://avatars.discourse-cdn.com/v4/letter/z/3ab097/32.png) [@ZenBeam](https://boards.straightdope.com/u/ZenBeam)\
**Post date:** [December 30, 2013, 9:56pm UTC](https://boards.straightdope.com/t/how-much-of-me-came-from-the-big-bang/677477/29 "2013-12-30T21:56:28Z")

</div>

> [@PlaceboTarget](#):
>
> If we regard the 300,000-400,000 years that were necessary for hydrogen, helium, lithium and beryllium to form as part of the Big Bang,

As I already pointed out, Big Bang Nucleosynthesis occurred in the first 20 minutes. 300,000 to 400,000 years is the era when recombination occurred, i.e. the nuclei captured electrons to form neutral atoms.

---

<div class="post-metadata">

**Author:** ![PlaceboTarget](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/placebotarget/32/1073_2.png) [@PlaceboTarget](https://boards.straightdope.com/u/PlaceboTarget)\
**Post date:** [December 30, 2013, 10:31pm UTC](https://boards.straightdope.com/t/how-much-of-me-came-from-the-big-bang/677477/30 "2013-12-30T22:31:22Z")

</div>

> [@ZenBeam](#):
>
> As I already pointed out, Big Bang Nucleosynthesis occurred in the first 20 minutes. 300,000 to 400,000 years is the era when recombination occurred, i.e. the nuclei captured electrons to form neutral atoms.

But what matters here is that there are several stages, distinct from the actual Big Bang singularity. Time is not really an issue. If it is, then we’d better reconsider the length of the first day of creation again.

---

<div class="post-metadata">

**Author:** ![XT](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/xt/32/456_2.png) [@XT](https://boards.straightdope.com/u/XT)\
**Post date:** [December 30, 2013, 10:57pm UTC](https://boards.straightdope.com/t/how-much-of-me-came-from-the-big-bang/677477/31 "2013-12-30T22:57:52Z")

</div>

> [@Colibri](#):
>
> According to my own interpretation of the OP, I would say that essentially all “matter” (in the sense of baryons and leptons) was created by the Big Bang or immediately (within a few seconds) afterwards.
> 
> The rest of it is just that matter becoming organized in different more complex structures, including nuclei and atoms of different elements.

That’s pretty much how I interpret it too. I freely concede that you can look at it in a number of different ways and come to a number of different answers depending on exactly how you read it and how you define the terms. To me, all ‘matter’ was created in the Big Bang, it’s just a matter of how it eventually formed, fused and combined to get to where we are today.

---

<div class="post-metadata">

**Author:** ![johnpost](https://avatars.discourse-cdn.com/v4/letter/j/f17d59/32.png) [@johnpost](https://boards.straightdope.com/u/johnpost)\
**Post date:** [December 30, 2013, 11:03pm UTC](https://boards.straightdope.com/t/how-much-of-me-came-from-the-big-bang/677477/32 "2013-12-30T23:03:29Z")

</div>

the last cell you had containing any particles from then were lost the last time you brushed your teeth and it was spit down the drain.

---

<div class="post-metadata">

**Author:** ![XT](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/xt/32/456_2.png) [@XT](https://boards.straightdope.com/u/XT)\
**Post date:** [December 30, 2013, 11:04pm UTC](https://boards.straightdope.com/t/how-much-of-me-came-from-the-big-bang/677477/33 "2013-12-30T23:04:31Z")

</div>

Matter can neither be created nor destroyed, even by spitting it down the drain. 😛

---

<div class="post-metadata">

**Author:** ![Exapno\_Mapcase](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/exapno_mapcase/32/1051_2.png) [@Exapno\_Mapcase](https://boards.straightdope.com/u/Exapno_Mapcase)\
**Post date:** [December 30, 2013, 11:11pm UTC](https://boards.straightdope.com/t/how-much-of-me-came-from-the-big-bang/677477/34 "2013-12-30T23:11:30Z")

</div>

> [@XT](#):
>
> Matter can neither be created nor destroyed, even by spitting it down the drain. 😛

It can be lost, though, in the form of particles called “socks”.

---

<div class="post-metadata">

**Author:** ![XT](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/xt/32/456_2.png) [@XT](https://boards.straightdope.com/u/XT)\
**Post date:** [December 30, 2013, 11:16pm UTC](https://boards.straightdope.com/t/how-much-of-me-came-from-the-big-bang/677477/35 "2013-12-30T23:16:48Z")

</div>

> [@Exapno\_Mapcase](#):
>
> It can be lost, though, in the form of particles called “socks”.

But only in the singularity of a ‘drier’ (or, possibly under a ‘bed’, though the uncertainty principle is definitely in effect there)…

---

<div class="post-metadata">

**Author:** ![ZenBeam](https://avatars.discourse-cdn.com/v4/letter/z/3ab097/32.png) [@ZenBeam](https://boards.straightdope.com/u/ZenBeam)\
**Post date:** [December 30, 2013, 11:56pm UTC](https://boards.straightdope.com/t/how-much-of-me-came-from-the-big-bang/677477/36 "2013-12-30T23:56:29Z")

</div>

> [@PlaceboTarget](#):
>
> But what matters here is that there are several stages, distinct from the actual Big Bang singularity. Time is not really an issue. If it is, then we’d better reconsider the length of the first day of creation again.

I really have no idea what you’re trying to say here.

---

<div class="post-metadata">

**Author:** ![Ranger\_Jeff](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/ranger_jeff/32/2065_2.png) [@Ranger\_Jeff](https://boards.straightdope.com/u/Ranger_Jeff)\
**Post date:** [December 31, 2013, 5:47am UTC](https://boards.straightdope.com/t/how-much-of-me-came-from-the-big-bang/677477/37 "2013-12-31T05:47:57Z")

</div>

I’m satisfied with this:

“_We are stardust  
We are golden  
We are billion year old carbon  
And we’ve got to get ourselves back to the Garden_”

---

<div class="post-metadata">

**Author:** ![PlaceboTarget](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/placebotarget/32/1073_2.png) [@PlaceboTarget](https://boards.straightdope.com/u/PlaceboTarget)\
**Post date:** [December 31, 2013, 6:51am UTC](https://boards.straightdope.com/t/how-much-of-me-came-from-the-big-bang/677477/38 "2013-12-31T06:51:05Z")

</div>

> [@ZenBeam](#):
>
> I really have no idea what you’re trying to say here.

I’ll rephrase it. I’m aware my knowledge is limited and I may be wrong.

Time is not the issue. The singularity whose expansion led to the existence of the universe (Big Bang) is one thing, and the chronology of the universe is another. In the aftermath of the initial release of energy, there were several distinct phases during which material structures appeared and evolved to the structures we know today. Some scientists say the universe had stars when it was still a ‘baby’, but I don’t think we should conclude the initial singularity is the same as the baby that enjoyed stars at an early (st)age.

Take the human embryo, for example. (It’s not the best analogy but the ‘baby’ metaphor above made think of it.) We know the adult comes from the embryo, but we don’t equate the two phases. And when abortion of the fetus is legal, it is allowed based on its stages of development, not on the time that has passed since its conception (although doctors express this in units of time).

---

<div class="post-metadata">

**Author:** ![Senegoid](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/senegoid/32/6606_2.png) [@Senegoid](https://boards.straightdope.com/u/Senegoid)\
**Post date:** [December 31, 2013, 8:13am UTC](https://boards.straightdope.com/t/how-much-of-me-came-from-the-big-bang/677477/39 "2013-12-31T08:13:25Z")

</div>

Couldn’t you distinguish “old” electrons from “new” electrons by cutting a cross-section of one and counting the rings?

Same for various baryons?

---

<div class="post-metadata">

**Author:** ![Half\_Man\_Half\_Wit](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/half_man_half_wit/32/21766_2.png) [@Half\_Man\_Half\_Wit](https://boards.straightdope.com/u/Half_Man_Half_Wit)\
**Post date:** [December 31, 2013, 9:40am UTC](https://boards.straightdope.com/t/how-much-of-me-came-from-the-big-bang/677477/40 "2013-12-31T09:40:22Z")

</div>

> [@XT](#):
>
> From [here](http://staff.fcps.net/jswango/unit3/birth%20of%20elements%20article.pdf) Warning PDF):

The cite is a bit outdated, and some things are simplified in a way such as to be quite easily misunderstood. First, the accepted age of the universe, taking into account the recent data from the Planck satellite, is around 13.8 billion years, not 16 as claimed; but that’s a minor quibble. A little more serious in my eyes is the common, but misleading, gloss that “the matter of the entire universe was contained within a tiny but incredibly dense sphere”. While the early stages of the universe were certainly extremely dense, they needn’t have been ‘tiny’ at all; in fact, if the universe today is infinite, which is the simplest fit to the data, then it was infinite from the beginning.

But the big change in early universe cosmology has really been due to the theory of inflation, which denotes a phase of exponential expansion of the universe that is most legitimately considered to be something that has occurred _before_ the Big Bang, which was due to the decay of the field driving inflation, the inflaton. The end of inflation leaves the universe in an empty, and cold (in fact, supercooled) state. Then, a phase transition occurs, associated with the decay of the inflaton field, which couples to the standard model particles and thus, can decay into them. This is associated with a phenomenon known as reheating: similar to how a supercooled liquid becomes hot when it suddenly crystallizes (you know these hand warmer packs, where you have to trigger a kinetic impulse, by clicking this little sort of coin-like thing in them, which then spontaneously solidify and heat up—same kind of thing). That’s when, really, ‘Hot Big Bang’-type cosmology takes over.

This in particular means that we don’t necessarily have a singularity—there might be, but we don’t know. But one of the simplest models for the universe written down within this paradigm is that of Eternal Inflation, in which the inflaton field only decays locally, leading to ‘bubble universes’, our own being such a bubble, but on the whole inflates much faster than the bubbles expand, and thus, keeps going forever. There is no real ‘Big Bang singularity’ in this case, and it also makes it obvious why one ought to consider inflation pre-Big Bang, as it might have been going on a long time before our own universe was nucleated.

> [@Exapno\_Mapcase](#):
>
> Although matter and energy are often taught as if they were the same, because that’s quite close enough for everyday explanations, the professional physicists here have shown us in many threads that there are differences that are meaningful in advanced physics. Hydrogen is composed of a proton and an electron. The electron is not composed of other particles; the proton is. But you can’t really say that the quarks that make up a proton are made up of pure energy.
> 
> […]
> 
> But the universe was in a super energetic state at that time, with none of the particles that we think of as matter existing, so you can equally well say that none of ours dates back that far.

I think, especially since these two bits seem to be in contradiction otherwise, that in the first paragraph you meant to talk about _mass_ where you said _matter_. Because matter obviously can be converted into energy and be created from it; the annihilation of an electron and a positron to a photon has a particle that we would think of as constituting ‘matter’, the electron, going in, and none coming out. Likewise, in the proton+nucleus interaction I wrote down above, you’ve got more matter coming out than going in. It’s the invariant mass that’s separately conserved, following from energy conservation and mass-energy equivalence (energy can’t be destroyed and always retains its equivalent mass).

> [@PlaceboTarget](#):
>
> Take the human embryo, for example. (It’s not the best analogy but the ‘baby’ metaphor above made think of it.) We know the adult comes from the embryo, but we don’t equate the two phases. And when abortion of the fetus is legal, it is allowed based on its stages of development, not on the time that has passed since its conception (although doctors express this in units of time).

But in this analogy, one makes a useful, though conventional, distinction between the developmental stages in which abortion is legal, and the later stages in which it isn’t. You could equally well have those early stages equate to the Big Bang, before the universe was ‘fully formed’ so to speak, and thus, all nucleogenesis or -synthesis associated with that time period takes place ‘during the Big Bang’. But as has been stressed, it’s really a matter of convention.

[Previous page](https://boards.straightdope.com/t/how-much-of-me-came-from-the-big-bang/677477.md?page=1)

[Next page](https://boards.straightdope.com/t/how-much-of-me-came-from-the-big-bang/677477.md?page=3)
