captivatingCA Posted April 2, 2019 Posted April 2, 2019 Past years: 2013, 2014, 2015, 2016, 2017, 2018 Here's the thread to submit your profile and results for stat and biostat programs for Fall 2019. You only have an hour after you post to edit, so it is best to post only when you have all of your results or have made a decision. Give as much detail as you feel comfortable with! Below is the template: Undergrad Institution: (School or type of school (such as Big state/Lib Arts/Ivy/Technical/Foreign (Country?))Major(s): Minor(s):GPA: Type of Student: (Domestic/International (Country?), Male/Female?, Minority?)GRE General Test: Q: xxx (xx%)V: xxx (xx%)W: x.x (xx%)GRE Subject Test in Mathematics: M: xxx (xx%)TOEFL Score: (xx = Rxx/Lxx/Sxx/Wxx) (if applicable)Grad Institution: (school or type of school?) (if applicable) Concentration: GPA: Programs Applying: (Statistics/Operation Research/Biostatistics/Financial Math/etc.) Research Experience: (At your school or elsewhere? What field? How much time? Any publications or conference talks etc...)Awards/Honors/Recognitions: (Within your school or outside?)Pertinent Activities or Jobs: (Such as tutor, TA, etc...) Letters of Recommendation: (what kinds of professors? "well-known" in field? etc.) Math/Statistics Grades: (calculus sequence, mathematical statistics, probability, real analysis etc.) Any Miscellaneous Points that Might Help: (Such as connections, grad classes, etc...)Applying to Where: (Color use here is welcome)School - Program / Admitted/Rejected/Waitlisted/Pending on (date) / Accepted/DeclinedSchool - Program / Admitted/Rejected/Waitlisted/Pending on (date) / Accepted/DeclinedSchool - Program / Admitted/Rejected/Waitlisted/Pending on (date) / Accepted/Declined Geococcyx and fireuponthedeep 2
blehperson Posted April 2, 2019 Posted April 2, 2019 (edited) Undergrad Institution: Ivy Major(s): Statistics and Mathematics Minor(s): Computer ScienceGPA: 3.88/ 4.00, major: 3.93 Type of Student: Domestic AsianGRE General Test: Q: 168V: 162W: 5.0GRE Subject Test in Mathematics: M: n/aTOEFL Score:n/a Programs Applying: Statistics PhD Research Experience: 1. 7 months research on spectral methods for estimating parameters of network models, culminated in senior thesis 2. physics REU Awards/Honors/Recognitions: 1. school level awards (magna cum laude, highest honors, etc.), award for being top 10% of the class Pertinent Activities or Jobs: 1. two internships - one in tech, one in finance 2. TA for 4 semesters: data science, linear algebra, machine learning, and grad level GLMs Letters of Recommendation: 2 from well known professors in the field (one from research), 1 from teaching faculty. All should be good. Math/Statistics Grades: Math: real analysis (A-), linear algebra (A), complex analysis (A), topology (A), dynamical systems (A), abstract algebra (A), combinatorics (A) Stat: probability (A), inference (A), machine learning (A), stochastic process (A), data science (A), nonparametric stat (A) grad level stuff: machine learning for NLP (A-), GLMs (A-), advanced probability (A-), advanced inference (A), market design (A) misc: E&M (A), Mechanics (A), quantum mechanics (A) Any Miscellaneous Points that Might Help: took 5 grad classes, TAd a grad class, good recs, good grades at a top school, low GRE (took it cold) Applying to Where: (Color use here is welcome) Harvard - Stat PhD/ admitted - DeclinedWharton - Stat PhD/admitted - Declined UWashington - Stat PhD/admitted - Declined UCLA - Stat PhD/admitted - Declined Wisconsin Madison - Stat PhD/admitted - Declined Columbia - Stat Phd/ waitlisted / admitted - Attending Duke - Stat Phd / admitted - Declined CMU - Stat Phd / rejected Stanford - Stat PhD / rejected (no math GRE...) Berkeley - Stat PhD / rejected Michigan - Stat PhD / pending / withdrew Chicago - Stat PhD / pending / withdrew Toronto - Stat PhD / pending / withdrew I decided to apply to PhD programs very late, and didn't have time to take the math GRE. Applied to Stanford anyways based on advice from my professors, but it didn't work. Overall, I'm pretty happy with the results though. Edited April 2, 2019 by blehperson fireuponthedeep and Geococcyx 2
Geococcyx Posted April 5, 2019 Posted April 5, 2019 (edited) Undergrad Institution: Big State School, US News top 80 or so overallMajor(s): Statistics, Physics, Psychology (applied as a Math major too, decided not to take a non-statistics-related math class)Minor(s): MathGPA: 3.80 Type of Student: Domestic white male, very bland diversity-wiseGRE General Test: Q: 170 (96%)V: 167 (98%)W: 5.0 (98%) Programs Applying: Statistics/Biostatistics PhD programs Research Experience: Mostly some social science/psychology research, a little bit of stuff with epi/biostat this year.Awards/Honors/Recognitions: Phi Beta KappaPertinent Activities or Jobs: Some public speaking/science communication stuff Letters of Recommendation: Psychology research mentor (department head, did senior thesis with them), genetics professor from a class taught entirely off of journal article discussions, and a professor I had for 1 applied statistics class. Math/Statistics Grades: Calc I (AP Credit), Calc II (B+), Calc III (A-), Diff Eq (A), Linear Algebra (A), Proofs & Logic (A), Intro to Sequences [there were proofs in this, to be clear] (A-), Probability (A), Stat Inference (A*), Real Analysis (B*), a bunch of other applied stat classes that I got all A's in. * indicates that I was taking that class during the applications, hence only schools with late application deadlines (UNC biostat and Columbia stat) or that specifically requested transcripts (Wisconsin stat) got those grades.Any Miscellaneous Points that Might Help: Did SIBS at NC State, profs at my university might have had a few connections they used on my behalf but I don't really know. Any Miscellaneous Points that Might Hurt: Zero grad classes, lots of withdrawals, pretty lacking proofs background, strange choice of letter-writers (no professors from proofs-based classes), really weird personal statement.Applying to Where: Carnegie Mellon - Stat PhD / Rejected (2/18)Duke - Stat PhD / Admitted (2/7) / I might go here, not sayingColumbia - Stat PhD / Rejected (3/14) NC State - Stat PhD / Waitlisted (1/30) / Admitted (4/2) / I might go here, not saying Wisconsin - Stat PhD / Admitted (2/22) / Declined UCLA - Stat PhD / Admitted (2/09) / Declined Illinois (UIUC) - Stat PhD / Admitted (1/08) / Declined Ohio State - Stat PhD / Admitted (2/1) / Declined Harvard - Biostat PhD / Rejected (2/15)Johns Hopkins - Biostat PhD / Rejected (2/26)UNC - Biostat PhD / Admitted (1/22) / I might go here, not saying Minnesota - Biostat PhD / Waitlisted (2/27) / Withdrew in early April Brown - Biostat PhD / They said I was on a shortlist and asked how likely I would be to accept an offer, I'm interpreting that as a waitlist (2/27) / Withdrew in early March Pittsburgh - Biostat PhD / Waitlisted (4/2) / Withdrew in early April Based on my profile and my lackluster LoR choices, this seemed like a really top-heavy list of applications to send out (I had some safety school applications sitting on SOPHAS in case I hadn't heard anything by mid/late January). As such, I wonder whether lots of schools just liked me as a quirky applicant, in terms of majors, classes, and maybe personal statement (I know at least one professor did read it, they brought it up apropos of nothing at a visit). Given that I didn't take the Math GRE subject test, in retrospect I might apply to Washington biostat instead of Columbia stat, and I also might replace CMU or Minnesota with UPenn Perelman since I like neuroimaging and CMU just seems really dang tough to get admitted to. As you can imagine, I'm very happy with the results of my application cycle, and given that many of my best offers are from schools that I didn't expect would like me, it's important to remember than your impression of a good fit/likely admission is definitely not the same as the schools' impressions thereof. Edited April 5, 2019 by Geococcyx fireuponthedeep 1
fireuponthedeep Posted April 5, 2019 Posted April 5, 2019 (edited) Undergrad Institution: Top 60 Liberal Arts (according to super accurate USnews lol)Major(s): MathematicsMinor(s): Biology, PsychologyGPA: 3.76 Major GPA: 3.79 Type of Student: DMWGRE General Test: Q: 164 (86%)V: 168 (98%)W: 5.0 (92-94%, Can't remember exact percentage tbh)GRE Subject Test in Mathematics: M: N/A Programs Applying: (Biostatistics MS, Wisconsin Statistics MS - Biostats option) Research Experience: Lol literally noneAwards/Honors/Recognitions: Magna Cum Laude, Dean's List most semesters, few academic scholarshipsPertinent Activities or Jobs: Math TA for several semesters Letters of Recommendation: Letter of rec from Psychology professor, Biology professor, Classics professor, and my college swim coach. Psych professor is the most prolific researcher, but even they're not particularly well known. Undergrad was wayyyyyyyy more teaching focused than research intensive. Math/Statistics Grades: Calc I-II (A-/A-), Linear Algebra (A-), Abstract Algebra (A), Multivariable Calc (A), Combinatorics (A-), Euclidean/Non-euclidean Geometry (A), Numerical Analysis (A), Probability Models (B), Statistical Models (A). About half of my courses were primarily proof based, from spring semester sophomore year onwards, which I think was very beneficial to my application. Didn't take Real Analysis unfortunately, didn't like the professor. Any Miscellaneous Points that Might Help: None that I can think of relating to actual biostatistics/statistics. I'd like to think I was a unique applicant, I swam varsity collegiately for all 4 years in undergrad, served an AmeriCorp term after I graduated, really interested in Public Health and that shone through in my SOPs. But I have no clue if any of that made a difference lol. Also got a D in physics my first semester due to mental health issues + lack of readiness for college, so that tanked my GPA pretty hardcore, would've been 3.85 w/o it. Idk if it was beneficial to my applications that my GPA would've been drastically better w/o that one disaster, or if they were damaged by doing so spectacularly poorly. Or made no impact. At the very least, future applicants know that they can eff up in a non math stem course and get into someplace lmao.Applying to Where: School - University of Minnesota/ Admitted / AcceptedSchool - UNC Chapel Hill / Admitted / DeclinedSchool - Emory / Admitted / Declined School - JHU / Rejected School - Wisconsin / Rejected School - Colorado / Admitted / Declined School - IUPUI / Admitted / Declined School - Vanderbilt / Applied to PhD with assumption I'd get auto-rejected and hopefully be considered for MS lol. I was asked to Interview for one of 4 MS spots, but declined to do so due to Minnesota acceptance Overall I was pretty satisfied, UMN was my top choice. In retrospect, maybe getting letters of rec from my mathematics professors would've been smarter, but I was closer with the others and naively thought LOR were just intended to be like "Hey, this person is cool, let them into your school" rather than speaking on research suitability and whatnot. Although I'd like think my Psych/Bio/Classics professors actually wrote letters that were very complimentary of my research potential. Plus for just an MS I don't think LORs really matter too much lmao, as long as they're not damning. Seems like a numbers game, get the GRE/GPA/Course Prereqs, launch those apps into the abyss and you'll probs get in somewhere. I also feel like I lucked out as far as coursework and grades, I had zero inkling wtf biostats was in undergrad, and sorta stumbled into the math major path cuz I like being tortured by proofs and it turned out everything I took ended up being necessary or helpful. But yeah, best of luck to everyone at your respective programs! Edited April 5, 2019 by fireuponthedeep Geococcyx 1
Fred210 Posted April 5, 2019 Posted April 5, 2019 Undergrad Institution: International University at Western European country(3 year) Major(s): Mathematics and Physics double BSMinor(s): StatisticsGPA: 3.9 Type of Student: (Domestic, Male)GRE General Test: Q: 170 V: 160 W: 5GRE Subject Test in Mathematics: M: 800 (79%)TOEFL Score: US Born Programs Applying: Statistics masters and Mathematics masters(Didn't directly apply to any Ph.D's) Letters of Recommendation: Three strong letters from professors whose courses I did well in. Math/Statistics Grades: Grades were all equivalent to an A in US. In total, I have/will complete around 40 courses in mathematics/physics/statistics. Some relevant courses are as follows: Lin algebra and calculus sequences, real analysis, Complex Analysis, group theory, ODE, PDE, Systems Theory, Dynamical Systems, metric spaces/topology, differential geometry, measure theory, manifold analysis, functional analysis, numerical mathematics, probability theory, statistical inference, asymptotic statistics, generalized linear models. Some physics courses: Mechanics, EM, StatPhys/Thermo, Quantum Physics, Lagrangian/Hamiltonian Mechanics, QFT, Representation TheoryApplying to Where: Statistics Masters:School - UC Berkeley / AdmittedSchool - University of Washington Seattle / Admitted School -Columbia / Admitted School - John Hopkins / Admitted School - UCLA / Admitted School - NCSU / Admitted School - Stanford(Data Science Track) / Rejected Mathematics Ph.D: (Both programs I had applied to the masters and was instead considered for Ph.D.) School - UC Davis / Admitted School - University of Washington Seattle / Waitlisted Mathematics Masters: School - University of Pennsylvania / Admitted
causalinf Posted April 6, 2019 Posted April 6, 2019 (edited) Undergrad Institution: One of top 10 U.S. private universities Major(s): StatisticsMinor(s): Computer ScienceGPA: Major GPA 3.81/4.00, Overall GPA 3.78/4.00 Type of Student: International Asian MaleGRE General Test: Q: 170 V: 160 W: 4.0 GRE Subject Test in Mathematics: M: Did not take it due to lack of time to prepareTOEFL Score: NA Programs Applying: Statistics/Biostatistics PhD Research Experience: I worked on missing data research with a senior faculty for my senior thesis. I also worked on causal inference + ML research with two junior faculties. One paper submission to statistical computing journal. Awards/Honors/Recognitions: Graduation with distinction in stats and a bunch of award in musicPertinent Activities or Jobs: I worked as a TA for undergrad-level class in mathematical statistics and grad-level class in Bayesian statistics Letters of Recommendation: Two senior faculties in stats and one junior faculty in CS (I had good working relationship with all of them. They promised they would write good letters for me, so I assumed all letters are strong.) Math/Statistics Grades: Statistics: Bayesian Stats (A+), Machine Learning (A), Mathematical Stats (A), Regression Analysis (A-), Statistical Consulting (A), Decision Analysis (A-), Causal Inference (A+) Mathematics: Linear Algebra & Differential Equations (A), Multivariable Calculus (A-), Probability (A), Real Analysis (A-) Any Miscellaneous Points that Might Help: I only took the required math courses for statistics major, and was quite concerned with my lack of math background. As a result, I applied to 20+ schools. The total application fee was outrageous. I was extremely frustrated with SOPHAS application portal. It was the most expensive one and it took a month for them to process my transcript. Applying to Where: Harvard - Biostat PhD / AdmittedJohns Hopkins - Biostat PhD / Rejected UW- Biostat PhD / Rejected for PhD Admitted to MasterUNC - Biostat PhD / Admitted U Michigan - Biostat PhD / Admitted U of Wisconsin - Biomedical Data Science PhD / Admitted Stanford - Management Science & Engineering PhD (Computational Social Science Track) / Rejected NYU - Data Science PhD / Rejected CMU - Stat PhD / Rejected Harvard - Stat PhD / Rejected UC Berkeley - Stat PhD / Rejected U Michigan - Stat PhD / Rejected U Penn - Stat PhD / Rejected U of Washington - Stat PhD / Rejected Duke - Stat PhD / Rejected UC Davis - Stat PhD / Rejected Columbia - Stat PhD / Rejected Texas A&M - Stat PhD / Haven't heard back yet (assume rejection at this point) Wisconsin - Stat PhD / Haven't heard back yet (assume rejection at this point) Johns Hopkins - Applied Math and Stat PhD / Admitted UCLA - Stat PhD / Admitted Edited April 6, 2019 by causalinf Geococcyx 1
BL250604 Posted April 13, 2019 Posted April 13, 2019 Undergrad Institution: Small Liberal Arts College, top 60 in US, top 10 in region Major(s): Double: Mathematics and Finance ; BS, BAMinor(s): Double: Computer Science & AnalyticsGPA: 3.5 Type of Student: Domestic, MaleGRE General Test: Q: 159V: 152W: 5.5GRE Subject Test in Mathematics: 64%ile (Not submitted)TOEFL Score: N/A Programs Applying: Ph.D. in Statistics, M.S. in Statistics Letters of Recommendation: Four strong letters from professors. All of whom I did research with for over 2 years (one ran the REU, one is the dept chair and the others are my advisors) Math/Statistics Grades: Math Stat I, II: B, B; Linear Algebra: C+, Calc I-III: A-, A-, B-; Real Analysis: B; Abstract Algebra: A; Computer Science I, II: A+, A+ ; Bayesian Statistics: A ; Applied Mathematics: A; Combinatorics: B+ ** Important Notes: Very strong Letters of rec from professors who I know incredibly well. I have submitted 2 statistics projects for publication and both are pending. I have presented my research at over 8 conferences (2 JMM's, many MAA's, etc.) and given 7 poster presentations.Applying to Where: Statistics Masters School - John Hopkins / Rejected School - Columbia / Admitted School - NYU / Admitted School - Georgetown / Admitted Statistics Ph.D: Withdrawn: UMD, UNC (STOR), Temple Accepted: South Carolina (ATTENDING!), Florida State, Virginia Waitlisted: Michigan, Virginia (then admitted) Rejected: NCSU, George Mason, UConn, PSU, OSU, GW, Virginia Tech Geococcyx 1
sicdrag Posted April 13, 2019 Posted April 13, 2019 (edited) Undergrad Institution: Large public school (top 150).Major(s): Math with concentration in stats Minor(s):GPA: 4.0/4.0 Type of Student: Domestic White MaleGRE General Test: Q: 168 (94%)V: 167 (98%)W: 5.0 (92%)GRE Subject Test in Mathematics: Did not take Programs Applying: Stats PhD and a few Biostats PhD Research Experience: Senior capstone project in statistics adjacent part of game theory. No publicationsAwards/Honors/Recognitions: Honors college, national merit scholar, grade related awardsPertinent Activities or Jobs: Internship doing data science type work at insurance company Letters of Recommendation: One from real analysis/diffeq professor, one from numerical analysis professor, one from stochastic processes professor. I think they were all fairly strong. Math/Statistics Grades: Calc I/II/III(A+), Linear Algebra (A+), DiffEq (A) , Real Analysis I/II (A+/A), Abstract Algebra I (A+), Numerical Analysis (A+), Data Analysis (A), Probability (A+), Mathematical Stats (A), Stochastic Processes (A+) , Topology (A+), Complex Variables (A+), various CS/Econ classes Applying to Where: NC State- Stats PhD/ Waitlisted on 1/29/ Admitted on 4/6 /DeclinedWisconsin- Stats PhD/ Admitted on 2/22 / DeclinedTexas A&M- Stats PhD/ Admitted on 1/23 / AttendingMinnesota - Stats PhD / Admitted on 2/11 / DeclinedIowa State - Stats PhD / Admitted on 3/6 / DeclinedFlorida - Stats PhD / Admitted on 1/24 / DeclinedEmory - Biostats PhD / Rejected (possibly because one of my letters never got submitted here -- not sure)UC Santa Cruz - Stats PhD / Admitted / DeclinedMedical College of Wisconsin - Biostats PhD / Interview / Admitted / Declined I was pretty surprised to get in everywhere to be honest, but obviously very happy. In hindsight, I would have added a few reaches and done a few less safeties. But going in, it's hard to know exactly where you stand especially with some variance involved with letters. Edited April 13, 2019 by sicdrag Geococcyx and SomeNerd 2
galois Posted April 24, 2019 Posted April 24, 2019 (edited) Undergrad Institution: Top 30 Liberal Arts CollegeMajor: Mathematics Concentration: Scientific ComputingGPA: 3.91 Type of Student: Domestic Mixed-Race MaleGRE General Test: Q: 167 (98%)V: 168 (94%)W: 4.0 (59%)GRE Subject Test in Mathematics: N/A Programs Applying: Statistics/Applied Math Research Experience: - REU in combinatorial mathematics: presented at JMM, won a poster presentation award, resulted in publication - REU in gravitational physics: worked in a lab in Paris doing some experiments and analysis on a table top simulator for LISA mission. Awards/Honors/Recognitions: A fair number of awards and scholarships in undergrad.Pertinent Activities or Jobs: Lead tutor for Calculus I-III for a few years. Software engineer for a number of years now. Letters of Recommendation: All three from the math department, and very likely strong letters. Math/Statistics Grades: Calculus I-III (A), Intro Statistics (A), Linear Algebra I-II (A), Abstract Algebra I-II (A), Number Theory Seminar (A), Mathematical Logic Seminar (A), Complex Functions (A), Real Analysis I (A).Any Miscellaneous Points that Might Help: Software dev job experience; no stats background. Applying to Where: Caltech - Computing & Mathematical Sciences PhD / RejectedU Washington - Applied Math PhD / Rejected (accepted to masters unfunded) U Washington - Math MS / Admitted Carnegie Mellon - Stat PhD / RejectedDuke - Stat PhD / Rejected UNC Chapel Hill - Stat PhD / RejectedUT Austin - Stat PhD / Rejected U Washington - Stat PhD / Admitted NC State - Stat PhD / Admitted UCLA - Stat PhD / Admitted UC Irvine - Stat PhD / Admitted U Florida - Stat PhD / Admitted I really had no clue what to target when I started the process of finding programs. This forum was incredibly helpful in finding a good spread of safety-target-reach schools. I was rejected/accepted by exactly half/half of the programs I applied to, which seems like a good result. Edited April 24, 2019 by galois Geococcyx 1
danny1997 Posted April 25, 2019 Posted April 25, 2019 Undergrad Institution: Large State University, R1 Research InstitutionMajor(s): Mathematics and Biology Minor(s): StatisticsGPA: 3.37 Type of Student: Domestic MaleGRE General Test: Q: 166 (90%)V: 160 (86%)W: 4 (59%) Programs Applying: Statistics PhD/ Masters Research Experience: Four years of plant biology research through my undergraduate institutionAwards/Honors/Recognitions: Summer Research Funding through my university, National Conference poster presentationPertinent Activities or Jobs: Calculus II SI leader one year, mathematics and statistics tutoring for one year Letters of Recommendation: PI in biology research, head of universities undergraduate research office, and accomplished statistics professor Math/Statistics Grades: Numerical Methods for Mathematics and Statistics (A), Linear Algebra (A), Biometry (A), Theory of Probability (A), Theory of Statistics (B), Data Analysis (B), Complex Variables (A), Real Analysis (B), Deterministic Mathematical Modeling (A), Numerical Analysis (A), Introductory Design and Analysis (A) Any Miscellaneous Points that Might Help: (Such as connections, grad classes, etc...)Applying to Where: School - Wisconsin PhD, MS RejectedSchool - Rutgers PhD, RejectedSchool - The Ohio State University PhD, Rejected School - UVA PhD, Rejected from WaitlistSchool - UMBC PhD, Rejected but accepted for MS. Turned down due to lack of funding, program does not accept students into PhD program without MastersSchool - UMass PhD, MS, rejected but accepted to satellite campus, turned down due to lack of funding School - Stevens Institute MS (mathematics), accepted with partial funding, declined offerSchool - Bowling Green State University, MS (Applied Statistics), generous financial offer, turned down. School - Wake Forest, MA, partial scholarship and opportunity to tutor, attending!! Geococcyx 1
tma523 Posted April 25, 2019 Posted April 25, 2019 Undergrad Institution: Private liberal arts Major(s): Mathematics, Philosophy Minor(s): Actuarial ScienceGPA: 3.9 Type of Student: Domestic femaleGRE General Test: Q: 161 V: 166W: 4.5 GRE Subject Test in Mathematics: Didn't takeTOEFL Score: n/a Programs Applying: Statistics Ph.D. Research Experience: nothing reallyAwards/Honors/Recognitions: Phi Beta Kappa, math departmental award, national honor society scholarship, university scholarshipPertinent Activities or Jobs: Math tutor/volunteer, interned as statistician at government agency Letters of Recommendation: Chair of the math department, two other math professors. None are very well known but they all knew me very well because we have a small department. Math/Statistics Grades: Calc I, II, II (A), Real Analysis (A), Linear Algebra (A), Probability and Statistics (A), Statistics for Engineers (A), Abstract Algebra I, II (A-), Statistical Inference (graduate level) (A), Econometrics (A-), Differential Equations (A), Intro Proofs Class (A), Complex Analysis (in progress), Financial Mathematics (in progress)Applying to Where: (Color use here is welcome)NCSU- Ph.D. Statistics/Admitted UNC Chapel Hill - Ph.D. Statistics/AdmittedDuke - Ph.D. Statistics/Rejected Texas A&M- Ph.D. Statistics/ Haven't heard back, assuming rejection Geococcyx 1
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