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TLDR: I love mathematics but can't find a way to study/do research without becoming unhealthily obsessive. Any tips on how not to think about mathematics all the time, on how to manage intrusive thoughts?

Background: Three years ago I graduated with a Master's in pure maths & theoretical computer science from a top school in the UK. My grad thesis had applications in machine learning and led to 3-4 papers accepted to top conferences in that field. I loved every bit of it and could 'easily' have moved on to a phd, but decided to take a break.

My brain is somewhat obsessive by nature, and my last year at university was filled with thinking about problems regardless of my desire to do so. I generally seek to have a balanced lifestyle (friends family sports arts etc) and this is more important to me than excelling only at one thing (maths), but my brain would not let go of me. It became difficult not to think of problems in my free time, especially when trying to fall asleep (insomnia & waking up in the middle of the night to write solutions to problems). I still managed to keep a balanced lifestyle, but my life was sporadically permeated by obsessive thoughts about mathematical problems.

Post-math: At that point, I decided to stop maths for a bit. I worked for a year and then got a semi-random opportunity to go to a professional dance school for a couple years, which I recently finished. I'm still obsessive, but I've become somewhat less agitated in the brain and developed deeper connections to other people and to my own body/emotions. I'm 26 now. I could become a full-time dancer and might do that for a couple years, but it's not much of a long-term project. I'm still highly drawn to mathematics and could probably get back into it, whether phd or industry internships... But I'm afraid of my brain.

The question: Can I become a professional mathematician without becoming overly obsessive/compulsive/unable-to-control-my-thoughts? Do you have any tips on how to manage an obsessive/always-thinking mind? Would doing research in industry make for a better work-life separation than academia?

EDIT: Thank you so much for your thoughtful replies and good intentions. Their many flavours helped me get a sense of the many ways I could deal with my problem, and how there was hope in turning it from a curse to a blessing. I got in touch with a public mental health institution and hope to see a therapist in the coming months (long waiting list!).

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    I think this is a question only your therapist can answer. Oct 23 at 16:26
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    @AlexanderWoo Actually, only the OP themselves can ultimately answer this question, but it does seem very reasonable to me that a) advice from professional mathematicians familiar with the problem could be of tremendous help and b) that such advice could be found here (or over on mathoverflow).
    – Arno
    Oct 23 at 16:50
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    Well, the good news is the tendencies you are describing are an advantage for a mathematician.
    – Dan Romik
    Oct 23 at 17:22
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    Many or most mathematicians I know, including myself, are fairly obsessive about their work. Not necessarily excluding everything else, but certainly dominant in their thinking at all hours of the day, evenings, weekends, etc. In insomniac episodes, in my experience, it's maybe better to think about math than trying to solve the world's problems. One can do math lying in bed, eyes shut, relaxed. But/and what's the criterion for "overly" obsessed? Oct 23 at 21:51
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    “I graduated with a Master's […] from a top school in the UK” — In the UK, ‘school’ doesn't generally apply to Higher Education institutions. Eton and Harrow are schools; Oxford and Cambridge are not. (Mathematics isn't the only type of obsession :-)
    – gidds
    Oct 25 at 17:03

10 Answers 10

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Im going to go a slightly different route from the other answers.

In the one post, you describe your mind like this (in this area at least):

unhealthily obsessive

intrusive thoughts

somewhat obsessive by nature

filled with thinking about problems regardless of my desire to do so

I generally seek to have a balanced lifestyle ... but my brain would not let go of me

insomnia & waking up in the middle of the night my life was sporadically permeated by obsessive thoughts

I'm still obsessive

I'm afraid of my brain

 Can I become a professional mathematician without becoming overly obsessive/compulsive/unable-to-control-my-thoughts

My concern is that you're describing symptoms of a possible neurological/mental health condition. You emphasise over and over that you feel you lack control, and that this happens despite you, that its a case of you vs. your brain.(*)

If so, it may follow you in other areas, anyway. It may also unfairly impact your genuine enjoyment of mathematics by turning it from love of life to uncontrolled compulsive focus, overturning your need for a "balanced life" which you say you would like to prioritise (but cannot).

Without being a clinician or saying whether these are applicable, both OCD and ADHD can be described in the terms you use (lengthy personal experience confirms). OCD is the one that from your own language, you may have wondered. The latter strongly suggests itself as something to consider, because its a condition totally affecting focus and control over the brain, in which the brain can lock onto specific items of interest and not let go, or be easily distracted into focusing on them instead of (say) sleeping or other things. It also has genetic links to the body clock genes and strong links for insomnia and nighttime-too-awake-brain.

I would suggest checking with a clinician, whether there is a clinical condition involved. That has a few benefits.

  • You clearly wonder if you do, and fear it as it stands. Asking may give peace of mind, help, or reassurance.
  • You are afraid to follow a subject you clearly love and have passion for
  • If there is a clinical issue, it may (visibly or invisibly) impact other areas, or follow into other things you do. It may be having effects you dont connect to this. Avoidance may be tricky.

(*) In fairness you use the word "somewhat" at one point. I discount this because its a common "Im not sure how severely to express this, so lets be cautious", and is contradicted by the rest of your descriptions. People also routinely minimise the impact of issues, when first asking, for fear of overstating them.

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    Based only on my very limited experience: please, please check with a clinician, even if it feels extravagant. I know it can be prohibitively expensive, and I'm afraid I don't know any ways to get financial assistance for it. If you can afford it, though, I would judge the expectation value of the benefit to be decisively greater than the cost.
    – Vectornaut
    Oct 24 at 10:50
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    Could also be a variant of bipolar, even. Or any of a hundred things. So let me re-emphasize having a professional diagnose you, rather than people on the internet who only limited information. Oct 24 at 17:41
  • What both these comments say. Very much so. We can suggest it has value and may apply. Only a trained clinician can add certainty and (if needed) proper assistance.
    – Stilez
    Oct 24 at 18:35
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    Thanks Stilez. This part: 'it may also unfairly impact your genuine enjoyment of mathematics by turning it from love of life to uncontrolled compulsive focus', is right on the mark. I have also seen this obsessive tendency affecting other parts of life (going shopping, making small decisions), so pointing out the possibility of a mental health condition is helpful. I've wondered about OCD, but it never felt quite serious enough (I felt like I would be a crybaby to go, compared to people with life-threatening conditions). Now I will definitely go see one, even if financially demanding.
    – smalldog
    Oct 25 at 17:08
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I generally seek to have a balanced lifestyle (friends family sports arts etc) and this is more important to me than excelling only at one thing (maths), but my brain would not let go of me.

My view may be unwelcome, but I'll provide it anyway.

It may be possible that some angst you might be experiencing comes from trying to be something you are not, because you feel you should be.

What makes you generally seek to have a balanced lifestyle? Is it because you genuinely enjoy and derive the same pleasure and satisfaction from "friends family sports arts etc" as you do from mathematics?

Or could it be because you feel you should enjoy and derive pleasure and satisfaction from them, perhaps by internalizing social/societal views?

If you are trying to be a "well-rounded" person because that's how people should be, or that's the kind of person you imagine you would like to be, I'm going to go out on a limb and say that those are the wrong reasons.

Trying to be different than what we are usually results in all kinds of mental stresses and that manifests itself in various ways, including physical health.

If you enjoy or at least don't actually mind the feeling of being passionate about math at almost every waking moment, and it doesn't interfere with the basics (food, water, shelter...) then consider trusting your brain more and letting it take you where it thinks you need to go.

Especially in the case of mathematicians, much of their best work is done early in life. It's quite okay to be passionate or consumed by mathematics.

Please reexamine why you feel you need to resist your passions, because trying to be anything besides who you are can be dangerous and destructive to the spirit, and often the damage shows up later in life.

It became difficult not to think of problems in my free time, especially when trying to fall asleep (insomnia & waking up in the middle of the night to write solutions to problems).

So what? That's called passion! As long as you can manage to get enough sleep overall, how is this an actual problem, and not a blessing?

I still managed to keep a balanced lifestyle, but my life was sporadically permeated by obsessive thoughts about mathematical problems.

Again, so what?

Passion for something is a blessing that many/most people never really experience much of. If you've got it, consider welcoming, cherishing and nurturing it!

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    Thanks for your thoughtful and detailed answer. You may be partly right that I think having a balanced lifestyle is desirable whereas I actually enjoy mathematics more than anything: I should keep this in mind and not resist so much. However I genuinely DON'T enjoy being consumed by thoughts about mathematics when I am doing other things than mathematics: these thoughts are intrusive, obsessive, and make me feel weighed down and unable to enjoy other things. I should definitely cherish my passion, as you say, but am trying to find ways to enjoy it while not being consumed by it. Thanks!
    – smalldog
    Oct 24 at 16:59
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    Hmm, nice frame challenge. Then again, OP "developed "deeper connections to other people and to [their] own body/emotions", while taking a break from maths. A "balanced lifestyle" is "more important" to them than "excelling at one thing". And OP was thinking of maths "regardless of [their] desire to do so". Sounds like there is a real issue here, i.e. more of a compulsion than just a passion.
    – henning
    Oct 24 at 17:48
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    @smalldog yes my post may seem like an "opposing view" to some of the other's. As you say clearly and unambiguously "don't enjoy being consumed" and "intrusive, obsessive, and make me feel weighed down" then my characterization as "a blessing" now seems less appropriate. Thought there is a lot of social bias and not all professionals are of equal quality and there are issues of expense, "intrusive thoughts" are something that a mental health professional might be able to help with. There might even be an underlying organic cause, something physical that can be addressed.
    – uhoh
    Oct 24 at 22:11
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    @smalldog meaning that consulting a professional (if possible) sooner rather than later might be a good idea. "Tips" or "tricks" to stop intrusive thoughts doesn't sound like the right approach to me, if they don't seem effective then consider the possibility of a professional, but one that you are comfortable with.
    – uhoh
    Oct 24 at 22:18
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    xkcd.com/602 Oct 25 at 13:31
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Since you are at the point where you describe your own desires being in conflict with your brain, and that you are afraid of your own brain (as if you are two distinct entities), you need to speak directly to a psychologist. Having said that, I think most mathematicians find themselves thinking about mathematics during their leisure hours and often when going to sleep (often to the chagrin of spouses). Indeed, many mathematicians have solved problems they were working on via subconscious thinking while asleep. There is nothing inherently unhealthy about that; mathematics is sufficiently interesting that it is a pleasant thought during leisure hours and going to sleep. So long as this is balanced with other interests and hobbies it is quite enjoyable.

Whether thoughts about mathematics get to the point of becoming "obsession" is a matter of degree, but since you self-describe as obsessive, I'll take your word for it. We are not really in a position to assist you in understanding whether or not you can be a professional mathematician, or whether you can do so without obsessive thoughts. (There is at least one well-known case of a successful mathematicians who was obsessive to the point of eschewing all other concerns in life, so obsession certainly does not preclude mathematical success.) I recommend making an appointment with a psychologist to get to the root of your feeling of lack-of-control over your own thoughts and brain. It is probably also good that you are pursuing other hobbies and interests that can serve as fodder for a more diversified range of thoughts.

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    Op isn’t interested in only mathematical success… they are interested in a balanced, healthy life.
    – Dawn
    Oct 23 at 21:02
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    Hence the advice to pursue other hobbies and seek psychological help with his obsession.
    – Ben
    Oct 23 at 22:48
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    Thanks Ben. The only thing I would disagree with is that 'mathematics is sufficiently interesting that it is a pleasant thought during leisure hours and going to sleep'. That may be true for some people, and I do find it pleasurable at times (alone in the bus), but it becomes highly unpleasant when it arises unwanted, when I would simply like to rest my mind or go to sleep and find myself unable to do so. :(
    – smalldog
    Oct 25 at 17:01
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I am quite sure that by the moment you will start a PhD, and maths will be your daylong "thing", you will be able to have a balanced lifestyle because now you are trying to do three things:

  1. have a job
  2. have a balanced life
  3. not think about mathematics

and you fare quite well. If you merge point 1 and 3, you will end up with

  1. have a job as mathematician
  2. have a balanced life

so problem solved, go for a PhD.

If you had the same "obsession", but instead of maths about dance, would you find the idea of becoming a dancer and a dance teacher strange?

No? So, why should it be a problem becoming a mathematician? Go for it!

Yes? You really need a good psychologist!

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    Dance doesn't lead me to the same kind of compulsive/intrusive thinking and suffering than mathematics, so there is something significantly different between the two.
    – smalldog
    Oct 25 at 14:58
  • @smalldog I am not comparing your current enjoyment of dancing with your current heavy mental involvment in Maths. I am wondering what if dance was for you similarly mentally involving? I still stand by my own opinion: try to work as a mathematician, you will stop using your free-time for maths (I am also sure you will be able to balance with sports/arts/family/friends, since you are already doing so). Do you feel any (social) pressure to not pursue a professional life as mathematician? Oct 25 at 20:33
  • I think I explained my situation poorly... I am no longer doing mathematics on the side, so no longer suffering from thought intrusion (at least not on the same scale). I am dancing full-time. Compulsive thinking was happening mostly while I was doing maths full-time, so that is why I am doubting whether to go back to mathematics. I feel no social pressure to pursue or not pursue either career (maths or dance).
    – smalldog
    Oct 27 at 6:47
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Allow me to speak as someone with some firsthand experience of this (albeit in a different field)...

There's a fine distinction to be made — and one that only you can make, truth be told — between the ecstatic and the neurotic. I mean, honestly... Anything we do well, with commitment, dedication, and conscious attention, can produce ecstatic states. For me and for you (apparently) the deep dive into an intellectual problem opens something clear and bright (divorced from rational assessment) within us. Call it an endorphin rush if you want to be agnostic about it, but there's a euphoria in working with a problem that most people neither feel nor understand. They get 'satisfaction' from figuring something out; you and I get 'bliss' from seeing it in all its dimensions. It's a beautiful thing one shouldn't deny.

On the other hand, academia does tend to breed neuroses. The drive to be better than others, to jump through senseless and convoluted hoops, to gain acclaim and reward, to do something 'significant' and 'meaningful'... All of these can warp us, and can toss a dose of bitter herbs into something we would otherwise find sweet. It's a problem that some people handle better and some people handle worse (and that I handle worse than most). We should all be aware of it. Academia is geared towards the pedantic, not the ecstatic, perhaps to its own sorrow.

So really, this is a judgement call. Say you find yourself lost in a problem, waking up in the middle of the night to jot down insights, forgetting to eat, neglecting friends and family, etc.: yeah, I've been there. Now ask yourself a simple question: Am I lost in the joy of this, or am I driving myself like a mule to squeeze out every last drop of my ability? The first is ecstatic, the second neurotic, and you definitely want to prefer the first. The other just leads to burnout.

Of course, one can be neurotic about balance just as easily as being neurotically extreme. If you push yourself away from something that gives you deep joy in order to be more 'social', 'friendly', 'normal', or however you want to cast it, you are doing yourself a disservice. If you do what you love, you will be a beloved figure. People might think you are eccentric, but it's impossible not to be drawn to someone who does what they love with their whole heart. Do what you love with your whole heart and you become iconic; there's no other way to put it.

Don't be afraid of your own mind's capacity for ecstasy; learn to embrace it, and to live it. Meditation would help if you're inclined that way; it clears away the thoughts that act as bitter pills, lets your mind run more freely, and helps you distinguish the ecstatic from the neurotic. Ignore the religiosity of it — I do — and look to the philosophy and the practice. You're 26, your (physical) brain has just reached its maturity with plenty of room for (mental/intellectual) growth. Don't label ecstasy (if that's what it is) as obsession; you'll merely teach yourself to fear it. There is no harm in pursuing what you love.

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  • Thanks Ted. You are right that I should learn to distinguish between patterns that are truly neurotic, and need to be remediated through therapy or otherwise, and those that are ecstatic - and learn not to fear the latter.
    – smalldog
    Oct 25 at 16:54
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I think that you should just follow your passion. If you're trying not to be too addicted, then take constant breaks. Maybe even discuss with other people who pursue similar interests. Since you have such a deep love in math, why not continue excelling at it. When you feel like you need a break, or maybe create your own breaks and schedules, do it! Pursue your lives interests and at any point it feels like too much, find something else and maybe come back to it later. This is my advice, but I feel like maybe you should seek help with a therapist or someone else with the answer to your question. I hope this helped. :)

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Disclaimer: This advice comes from a layman. I am not a professional within psychotherapy, and this answer provides only a discussion, based on the OP's challenges, about which family of psychotherapy (PT) that could be a good starting point, if deciding to seek professional help. Better advice as to what family of PT could be viable is best left to a real professional, whilst noting, however, that the PT industry can be very biased between different families of PT, and a professional practitioner of e.g. psychodynamic psychotherapy may not recommend cognitive behavior therapy, and vice versa.


[…] But I'm afraid of my brain.

  1. Can I become a professional mathematician without becoming overly obsessive/compulsive/unable-to-control-my-thoughts?

  2. Do you have any tips on how to manage an obsessive/always-thinking mind?

  3. Would doing research in industry make for a better work-life separation than academia?

Your fear of "unable-to-control-my-thoughts" (2) is not an uncommon false metacognition belief, and I would argue that attempting to change the contexts of your life (1, 3) as a way to face this metacognition would be letting a false belief inhibit your passions in and ultimately your overall quality of life.

If applicable (finance, culture, ...), therapy is one common path to use to learn how to control/face these traits of the hyperactive mind, so that they may be used as tools for your passion for math to leverage whilst not inhibiting other parts of your life. If applicable for you, you may want to look into whether there’s any local professional therapist working with metacognitive therapy (MCT). Whilst cognitive behavioral therapy (CBT) is typically used as a tool to address worries and ruminations related to thought patterns, MCT is particularly suited for challenging thought patterns about thought patterns (hence the meta; "my thoughts on maths control me; I cannot control my thoughts on math, they are obsessive").

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  • Thanks for the reference to metacognitive therapy, which seems quite appropriate here. I hope to speak to a therapist soon and see which kind of therapy they recommend.
    – smalldog
    Oct 25 at 14:55
  • @smalldog Happy to help, I hope you can find your way. I’m living with similar struggles myself (hyperactive mind, overly ruminating) and have been through years of Psychodynamic Psychotherapy, CBT before finally landing at MCT. Its exercises are moreover interestingly overlapping with meditative techniques, particularly stable attention training and mindfulness, both also essential tools for those of us with an overly active mind (when spent ruminating and/or worrying). For self-studies into these meditation techniques, refer to e.g. The Mind Illuminated by Culadasa.
    – dfrib
    Oct 25 at 15:02
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    Thank you for these further details. I've been meditating (mostly mindfulness) every day for the past year and it has helped to some extent, so MCT seems interestingly complementary. Much appreciated.
    – smalldog
    Oct 25 at 16:51
  • Do you have any reading recommendations to get started with MCT? I can't find a therapist who does MCT in my area for the moment, so I will begin with a general therapist in the meantime. P.S: I've accepted another answer but this one had the most specific advice about types of therapy to look into - thanks again.
    – smalldog
    Nov 1 at 7:57
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    Thank you for taking the time to write all this. Really helpful, I will look into it without forgetting the centrality of actually seeing a professional.
    – smalldog
    Nov 1 at 12:34
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You listed you have passion and achievements in mathematics, many people would wish that.

Now, you have some concerns on the psychological side, intrusive thoughts etc, right? Then go and talk to a person who is qualified (psychologist) in that to give you advice how to manage that. And don't substitute instead your interests for dance classes!

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If you're enjoying mathematics, please do not stop unless you feel overwhelmed in which case you can take a break and then continue with it again. Being consumed by an subject is rare and only that will give you success. If thinking about mathematics is affecting you and making you feel worse and thereby making it harder for you to improve, then you should take a break. And then get consumed by it again. It's a good thing to be immersed in a field of study so please dont stop because of frivolous reasons.

However, if you don't enjoy it, consider a different path and pursue something else.

If you dont know how to take a break, I would suggest video games and drinking cool water.

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Have you considered transcendental meditation or NLP, both of which should help?

Failing either, when that last year was filled with thinking about problems, regardless… what else was different from your earlier years?

Do you see no difference between your brain not letting go of "you" and of "(your) maths problems"?

Do you see no difference between merely worrying, and (very) usefully waking up… to write solutions?

Can you specify how your life was "sporadically" permeated?

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    Again, how dreary it is for any of us to vote things down without explanation. I try never to do that and I beg everyone else to avoid it, too. For all I know, all four of my detractors here had valid arguments… or not! Oct 27 at 20:15
  • I suspect the downvotes are because your two suggestions are 1) a religious practice lacking scientific evidence, and 2) a psychological approach lacking scientific evidence.
    – Bryan Krause
    Oct 27 at 21:28
  • @BryanKrause Thanks and what are you talking about? Nothing I said had to do with religion. This clearly isn't the place for it - we'd be shut down for debating - yet if you have a reason to doubt either TM or NLP, are you citing mere prejudice or useful experience? Oct 27 at 21:41
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    Transcendental meditation is a spiritual/religious practice. There are other forms of meditation like mindfulness meditation that have empirical support. NLP, in general, is not scientifically supported. I don't wish to argue with you about either, only to provide a possible answer for the downvotes since you seemed frustrated at not having one.
    – Bryan Krause
    Oct 27 at 21:52
  • @BryanKrause Sorry, and TM is not a religious practice nor, in the way you seem to mean, spiritual. That's about your experience. NLP, in general, needs no particular "scientific" support. Try it, and see what you get. If you did that, and didn't then call for scientific study, you would be denying the basic principles of science. Again, that's about your experience. I don't wish to argue axioms with you and I do note that your suggestions are quite possible, and so what? Everyone should be allowed to vote stuff down with reason; neither you nor I nor anyone else, without. Oct 27 at 22:00

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