NgsAdmixv2
This page contains information about the program called NGSadmix, which is a very nice tool for estimating individual admixture proportions from NGS data. It is based on genotype likelihoods and works well for medium and low coverage NGS data. It is a fancy multithreaded c/c++ program which makes it useful for large datasets.
The great thing about NGSadmix is that it is a new method that takes the uncertainty introduced in NGS sequencing data into account when inferring an individual's ancestry by using genotype likelihoods that considers the uncertainty caused by unobserved genotypes.
REMEMBER TO EDIT AND CITE: "NGSadmix is only sensitive to admixture recent enough to cause structures in the population in terms of differing allele frequencies. Historical admixture events after which many generations has passed in the population, leaves no signature in terms of systematic differences in allele frequencies between individuals and are not a concern in association studies. " ADD ADMIXTURE AND STRUCTURE AS
The method was published in 2013 and can be found here: [1]
Citation
http://www.genetics.org/content/early/2013/09/03/genetics.113.154138.full.pdf
Skotte, L., Korneliussen, T. S., & Albrechtsen, A. (2013). Estimating individual admixture proportions from next generation sequencing data. Genetics, 195(3), 693–702. doi:10.1534/genetics.113.154138
- Bibtex
- % 24026093
- @Article{pmid24026093,
- Author="Skotte, L. and Korneliussen, T. S. and Albrechtsen, A. ",
- Title="{{E}stimating {I}ndividual {A}dmixture {P}roportions from {N}ext {G}eneration {S}equencing {D}ata}",
- Journal="Genetics",
- Year="2013",
- Pages=" ",
- Month="Sep"
- }
Software Download
The latest version of NGSadmix is ngsadmix32 from June 25, 2013 and can be downloaded here: [2].
- Older Versions
- The previous version of NGSadmix, ngsadmix31 can be found here: [3].
- Version Log:
- v32 june 25-2013; modified code such that it now compiles on OSX
- v31 june 24-2013; First public version.
Installation
NGSadmix can be installed independently or as a part of ANGSD.
NGSadmix Independent Installation
1. Login to your server using ssh on your terminal window.
2. Create the directory where you will install your software and enter it, such as
mkdir ~/Softwarecd ~/Software
3. Download the source code:
4. Configure, Compile and Install:
g++ ngsadmix32.cpp -O3 -lpthread -lz -o NGSadmix
5. Delete source code to save space:
rm ~/Software/ngsadmix32.cpp
NGSadmix Installation from ANGSD
Run command example
Download the input file
wget popgen.dk/software/download/NGSadmix/data/input.gz
Execute NGSadmix
./NGSadmix -likes input.gz -K 3 -P 4 -o myoutfiles -minMaf 0.05
Detailed Examples and Tutorial
Please refer to the tutorial [4]
Parameters
./NGSadmix
*** see doc for options/possible ranges/ and further explanation Arguments: -likes .beagle format filename with genotype likelihoods -K Number of ancestral populations Optional: -fname Ancestral population frequencies -qname Admixture proportions -outfiles Prefix for output files -printInfo print ID and mean maf for the SNPs that were analysed Setup: -seed Seed for initial guess in EM -P Number of threads -method If 0 no acceleration of EM algorithm -misTol Tolerance for considering site as missing Stop criteria: -tolLike50 Loglikelihood difference in 50 iterations -tol Tolerance for convergence -dymBound Use dymamic boundaries (1: yes (default) 0: no) -maxiter Maximum number of EM iterations Filtering -minMaf Minimum minor allele frequency -minLrt Minimum likelihood ratio value for maf>0 -minInd Minumum number of informative individuals NB All parameters are set using '''-par value'''. So to get additional information you would write '''-printInfo 1'''.
Input File
Input files are contains genotype likelihoods in genotype likelihood beagle input file format [5]. We recommend ANGSD for easy transformation of Next-generation sequencing data to beagle format. See Creation of Beagle files with ANGSD
Example of a beagle genotype likelihood input file for 3 individuals.
marker allele1 allele2 Ind0 Ind0 Ind0 Ind1 Ind1 Ind1 Ind2 Ind2 Ind2 1_14000023 1 0 0.941 0.058 0.000 0.799 0.199 0.001 0.666 0.333 0.001 1_14000072 2 3 0.709 0.177 0.112 0.941 0.058 0.000 0.665 0.332 0.001 1_14000113 0 2 0.855 0.106 0.037 0.333 0.333 0.333 0.799 0.199 0.000 1_14000202 2 0 0.835 0.104 0.060 0.799 0.199 0.000 0.333 0.333 0.333 ...
Column 1:The marker name (the information is not atually used)
Column 2 and 3: the major and minor allele (these two columns are not used within the program and can contain whatever dummy value).
The rest of the colums are the genotypes likelihoods (not in log space). For each individual we have 3 columns. Note that the above values sum to one per sites for each individuals. This is just a normalization of the genotype likelihoods in order to avoid underflow problems in the beagle software it does not mean that they are genotype probabilities.
The input file is allowed to be compressed with gzip.
Output Files
Program outputs 3 files.
- PREFIX.log
- PREFIX.fopt.gz
- PREFIX.qopt
- The .log file contains log information of the run. Commandline used for running the program, what the likelihood is every 50 iterations, and finally how long it took to do the run.
- The .fopt.gz file is an compressed file, which contains an estimate of the frequency for each site for all populations.
- The .qopt file contains the admixture proportions for all individuals.
Examples of the output files are found below.
Log file (.log)
Contents of the file log file
-> Dumping file: tskSim/tsk6GL.beagle.s1.log -> Dumping file: tskSim/tsk6GL.beagle.s1.filter Input: lname=tskSim/tsk6GL.beagle nPop=3, fname=(null) qname=(null) outfiles=tskSim/tsk6GL.beagle.s1 Setup: seed=1 nThreads=10 method=1 Convergence: maxIter=2000 tol=0.000000 tolLike50=0.010000 dymBound=0 Filters: misTol=0.050000 minMaf=0.000000 minLrt=0.000000 minInd=0 Input file has dim: nsites=100000 nind=75 Input file has dim (AFTER filtering): nsites=100000 nind=75 iter[start] like is=9299805.984931 iter[50] like is=-6531138.892608 thres=0.002800 iter[100] like is=-6528710.773349 thres=0.001289 iter[150] like is=-6528405.896951 thres=0.001211 iter[200] like is=-6528306.803820 thres=0.000420 iter[250] like is=-6528277.160993 thres=0.000546 iter[300] like is=-6528271.925055 thres=0.000033 iter[350] like is=-6528271.177692 thres=0.000008 iter[400] like is=-6528270.876315 thres=0.000005 iter[450] like is=-6528270.772894 thres=0.000140 iter[500] like is=-6528270.747721 thres=0.000002 iter[550] like is=-6528270.740654 thres=0.000002 Convergence achived because log likelihooditer difference for 50 iteraction is less than 0.010000 best like=-6528270.740654 after 550 iterations -> Dumping file: tskSim/tsk6GL.beagle.s1.qopt -> Dumping file: tskSim/tsk6GL.beagle.s1.fopt.gz [ALL done] cpu-time used = 671.82 sec [ALL done] walltime used = 114.00 sec
Allele frequency ouput (.fopt)
Each column correponds to the estimated allele frequencies for each population and each line is a SNP
Example of a .fopt file for -K 3
... 0.75331646167520038837 0.51190946588401886608 0.50134051056701267601 0.99999999900000002828 0.80165850924934911603 0.97470665326916294813 0.99999999900000002828 0.89560828888972687789 0.88062641752218895341 0.99999999900000002828 0.99999999900000002828 0.86109994249930577048 0.70560445653074521655 0.78994686954000448154 0.93076614062025020413 0.99999999900000002828 0.88878537780630872955 0.92662857068149151463 0.05322676762098016434 0.22871739860812340117 0.17394852600322696645 0.00000000100000000000 0.27428885137150410545 0.19029599645013275944 0.57086006389212373691 0.42232596591112880891 0.74080063581586474974 0.77359733910003525281 0.47380864146016693494 0.72073560889718923939 0.49946404159405927148 0.21684946347150244050 0.15201985942558055021 0.41802171086717271331 0.55490556205954566504 0.85691127728452165524 0.77095213528720529794 0.60074618451005279418 0.70219544996184157792 0.26517850405564091787 0.48500265408436060710 0.85432254709914456914 0.80055081986260245852 0.74423201242010783574 0.87110476762969968334 0.30563054476851375663 0.05233529475348827620 0.25911912824038613179 0.51084997710733415222 0.62263692178557350498 0.50738250264097506381 0.64790272562679740442 0.91230541484222271720 0.73015721390331478347 0.07124629651164265942 0.37896482494356753534 0.29218012479334326548 0.00000000100000000000 0.26969100790961914038 0.28395781874856029781 0.97074775756045073027 0.79093498372643300520 0.64006920058897498471 0.64661948716978157048 0.84130009558421925409 0.76730057769159087933 0.86990900887920663553 0.79410745692063922085 0.69416721874359499367 0.34956069940263900797 0.27773038429396151860 0.25923476721423144298 0.77739744690560164120 0.51272232330145017798 0.53888718200036844763 0.35431569298041332150 0.20022780744715171219 0.43176580786072032980 0.91858160919413811563 0.99999999900000002828 0.93584179237779097082 0.90339823126358831384 0.94729687041528465308 0.84358671720630329371 0.87068129661127857677 0.65267891763324525911 0.59315740612546075106 0.24102496839012735319 0.42777100607917967201 0.39594098602469629533 0.99999999900000002828 0.99999999900000002828 0.78549330115836857313 0.15386277372522660922 0.18035502891341426146 0.26583557049163752950 0.22456748943597096280 0.25110807159057474403 0.17244618960511531869 0.74816053649164548922 0.54769319158907958656 0.44532166240679449398 0.76350303696805599252 0.86547244122202959815 0.94111974586621383043 0.40940400475566068872 0.67767095908245833513 0.40793761498610620064 0.85389765162910868934 0.78901563183853873351 0.93614065916219291186 0.54108661985898742763 0.61895909938546000983 0.88522763262549941654 0.99051495581855464323 0.78855843624128341141 0.77646441702623147929 0.51133721761171413434 0.74521610846562824637 0.32689774480116673416 0.66618479413060949224 0.67891474309775079465 0.80762116232856140385 0.81793598261160704865 0.77752326447671193943 0.95349025244041396565 0.82120324647844433752 0.99999999900000002828 0.89800731971059466474 ...
Use the "-printInfo 1" option to get the position of the lines in the fopt file if some sites have been flltered from the analysis (-minMaf, minInd, minLRT etc)
Admixture proportion output file (.qopt)
Infered admixture proporsions. Each line is an individual and each column is a population.
Contents of the qopt file # cat tsk48GL.beagle.gz.s1.qopt
0.00254460532103031574 0.00108987228478324210 0.99636552239418640919 0.00000015905647541105 0.00000000100000000000 0.99999983994352459327 0.00034770382567266174 0.02639209238328452459 0.97326020379104283275 0.00000000100000000000 0.00000000100000000000 0.99999999800000005656 0.00000467398081877176 0.00000000100000000000 0.99999532501918120264 0.00000000907496942853 0.00585150933779484805 0.99414848158723567728 0.00515826525767644137 0.01138897436535154552 0.98345276037697204607 0.03914841746468285949 0.00000000100000000000 0.96085158153531713410 0.00000000100000000000 0.00629199375758324100 0.99370800524241675866 0.00771173022930659625 0.00000154720357311662 0.99228672256712036059 0.00000000100000000000 0.00075135345721917719 0.99924864554278081119 0.00000000100000000000 0.00000000100000000000 0.99999999799999994554 0.00000005468413042120 0.00087279924180633879 0.99912714607406327705 0.00000000100000000000 0.00000000100000000000 0.99999999800000005656 0.00712941313019542066 0.00118955677574110528 0.99168103009406338710 0.00000000100000000000 0.00000000100000000000 0.99999999799999994554 0.00000000100000000000 0.00165385222968000606 0.99834614677032007535 0.00000000100000000000 0.00006297763597355473 0.99993702136402651259 0.00519087111391381209 0.00000000100000000000 0.99480912788608621966 0.00000000100000000000 0.00000000100000000000 0.99999999800000005656 0.00202872783596746379 0.00000000100000000000 0.99797127116403261393 0.00876424336999809782 0.00949457841911990376 0.98174117821088191516 0.00000000100000000000 0.00000000100000000000 0.99999999799999994554 0.00000000100000000000 0.00000000100000000000 0.99999999799999994554 0.00000000100000000000 0.00000000100000000000 0.99999999799999994554 0.00000000100000000000 0.00000000100000000000 0.99999999799999994554 0.00000000100000000000 0.00000000100000000000 0.99999999800000005656 0.01820430093358888640 0.00000694033297829119 0.98178875873343274261 0.00351013812443964728 0.00000020340562512923 0.99648965846993520223 0.00771897550085272680 0.00605259705033356268 0.98622842744881378252 0.00600595292580561029 0.00000000100000000000 0.99399404607419439284 0.01454910070242997067 0.00543457657939076105 0.98001632271817917808 0.02567862615486414535 0.00160921436783232220 0.97271215947730349516 0.00000000100000000000 0.00000000100000000000 0.99999999800000005656 0.00000000100000000000 0.00001041560507852223 0.99998958339492149960 0.00000000100000000000 0.01383432553657116572 0.98616567346342876021 0.00343840097404925389 0.00000000100000000000 0.99656159802595079000 0.00000000100000000000 0.00000000100000000000 0.99999999800000005656 0.00000000100000000000 0.00000000100000000000 0.99999999800000005656 0.00051244065751142103 0.00404846039501185508 0.99543909894747661937 0.02003953974792894652 0.00000004934009128878 0.97996041091197982897 0.00000000100000000000 0.00000000100000000000 0.99999999799999994554 0.00000000100000000000 0.00000000100000000000 0.99999999799999994554 0.00000000100000000000 0.00000000100000000000 0.99999999800000005656 0.00000000100000000000 0.00000000100000000000 0.99999999799999994554 0.02176809890633762956 0.00000000100000000000 0.97823190009366245423 0.00000000100000000000 0.00000000100000000000 0.99999999800000005656 0.01563096189267457192 0.00970868396771427770 0.97466035413961116252 0.00000000100000000000 0.00000000100000000000 0.99999999800000005656 0.00002540964943070735 0.00000000100000000000 0.99997458935056915408 0.99999999799999994554 0.00000000100000000000 0.00000000100000000000 0.99501476026684787524 0.00000000100000000000 0.00498523873315206718 0.99999999799999994554 0.00000000100000000000 0.00000000100000000000 0.99520671498720802983 0.00479241730266987201 0.00000086771012207898 0.95884374919730619435 0.00000000100000000000 0.04115624980269377842 0.99002104218586972628 0.00000000100000000000 0.00997895681413022567 0.99999999799999994554 0.00000000100000000000 0.00000000100000000000 0.99999999800000005656 0.00000000100000000000 0.00000000100000000000 0.99999999770925251941 0.00000000129074746013 0.00000000100000000000 0.99999999799999994554 0.00000000100000000000 0.00000000100000000000 0.99999999799999994554 0.00000000100000000000 0.00000000100000000000 0.99999999800000005656 0.00000000100000000000 0.00000000100000000000 0.99999999800000005656 0.00000000100000000000 0.00000000100000000000 0.98980053177767901573 0.00000005577971952226 0.01019941244260143612 0.99999999800000005656 0.00000000100000000000 0.00000000100000000000 0.99999785004878083416 0.00000000100000000000 0.00000214895121910354 0.99999999800000005656 0.00000000100000000000 0.00000000100000000000 0.99999999800000005656 0.00000000100000000000 0.00000000100000000000 0.99220030909132039820 0.00000000100000000000 0.00779968990867968733 0.99999996788621803301 0.00000000100000000000 0.00000003111378189772 0.99736783433174225344 0.00255940950853666971 0.00007275615972113173 0.99998096423035520708 0.00000000574461213317 0.00001903002503262207 0.99711097909957713270 0.00288887008493822353 0.00000015081548462101 0.99999999799999994554 0.00000000100000000000 0.00000000100000000000 0.99999999800000005656 0.00000000100000000000 0.00000000100000000000 0.99999999800000005656 0.00000000100000000000 0.00000000100000000000 0.99769262012085335734 0.00000000100000000000 0.00230737887914652393 0.99999820787375570674 0.00000000433914936351 0.00000178778709493472 0.98047422489554170166 0.00012980111977614777 0.01939597398468214523 0.99999999799999994554 0.00000000100000000000 0.00000000100000000000 0.98208006049140339488 0.00000000100000000000 0.01791993850859651197 0.97530298545159921364 0.00000000100000000000 0.02469701354840085974 0.99657542812406740840 0.00000000100000000000 0.00342457087593254226 0.99954556420189066834 0.00045443479810919004 0.00000000100000000000 0.99999999800000005656 0.00000000100000000000 0.00000000100000000000 0.99531584565237773976 0.00410740812985130408 0.00057674621777084644 0.99999999800000005656 0.00000000100000000000 0.00000000100000000000 0.99878572597704817770 0.00000000100000000000 0.00121427302295177490 0.98571687209123504125 0.00400077401169816448 0.01028235389706666329 0.99027397554762419674 0.00840892511494516215 0.00131709933743062008 0.99999993504923445631 0.00000000100000000000 0.00000006395076564386 0.95946639819101930957 0.00000000100000000000 0.04053360080898076034 0.99999999800000005656 0.00000000100000000000 0.00000000100000000000 0.98414939425022363029 0.01585059024074651421 0.00000001550902978739 0.99999999622245250297 0.00000000277754757396 0.00000000100000000000 0.99525652466242930938 0.00000001683386219288 0.00474345850370842034 0.99999999799999994554 0.00000000100000000000 0.00000000100000000000 0.99999999799999994554 0.00000000100000000000 0.00000000100000000000 0.99999965447943561792 0.00000000100000000000 0.00000034452056438734 0.99864814059528783652 0.00135185840471215468 0.00000000100000000000 0.00000000100000000000 0.99999999799999994554 0.00000000100000000000 0.00000000100000000000 0.99999999800000005656 0.00000000100000000000 0.00000001076370464123 0.99999998823629543399 0.00000000100000000000 0.00000000100000000000 0.99999999799999994554 0.00000000100000000000 0.00000000100000000000 0.99999999799999994554 0.00000000100000000000 0.00000000099999999999 0.99999999799999994554 0.00000000099999999999 0.00000000099999999999 0.99999999799999994554 0.00000000099999999999 0.00000000100000000000 0.99999999800000005656 0.00000000100000000000 0.00000000100000000000 0.99999999800000005656 0.00000000100000000000 0.00000000100000000000 0.99999999799999994554 0.00000000100000000000 0.00000000099999999999 0.99999999799999994554 0.00000000099999999999 0.00000000099999999999 0.99999999800000005656 0.00000000099999999999 0.00000000100000000000 0.99999999799999994554 0.00000000100000000000 0.00000000100000000000 0.99999999799999994554 0.00000000100000000000 0.00000000099999999999 0.99999999800000005656 0.00000000099999999999 0.00000000100000000000 0.99999999799999994554 0.00000000100000000000 0.00000000099999999999 0.99999999800000005656 0.00000000099999999999 0.00000000100000000000 0.99999999800000005656 0.00000000100000000000 0.00000000100000000000 0.99999999799999994554 0.00000000100000000000 0.00000000100000000000 0.99999999800000005656 0.00000000100000000000 0.00000000100000000000 0.99999999799999994554 0.00000000100000000000 0.00000000100000000000 0.99999999799999994554 0.00000000100000000000 0.00000000099999999999 0.99999999800000005656 0.00000000099999999999 0.00000000099999999999 0.99999999800000005656 0.00000000099999999999 0.00000000099999999999 0.99999999799999994554 0.00000000099999999999 0.00000000099999999999 0.99999999799999994554 0.00000000099999999999 0.00000000099999999999 0.99999999800000005656 0.00000000099999999999 0.00000000100000000000 0.99999999799999994554 0.00000000100000000000 0.00000000100000000000 0.99999999800000005656 0.00000000100000000000 0.00000000099999999999 0.99999999799999994554 0.00000000099999999999 0.00000000099999999999 0.99999999799999994554 0.00000000099999999999 0.00000000099999999999 0.99999999799999994554 0.00000000099999999999 0.00000000100000000000 0.99999999800000005656 0.00000000100000000000 0.00000000100000000000 0.99999999799999994554 0.00000000100000000000 0.00000000100000000000 0.99999999799999994554 0.00000000100000000000 0.00000000100000000000 0.99999999800000005656 0.00000000100000000000 0.00000000100000000000 0.99999999799999994554 0.00000000100000000000 0.00000000100000000000 0.99999999800000005656 0.00000000100000000000 0.00000000100000000000 0.99999999799999994554 0.00000000100000000000 0.00000000100000000000 0.99999999800000005656 0.00000000100000000000 0.00000000100000000000 0.99999999800000005656 0.00000000100000000000 0.00000000099999999999 0.99999999799999994554 0.00000000099999999999 0.00000000100000000000 0.99999999799999994554 0.00000000100000000000 0.00000000100000000000 0.99999999800000005656 0.00000000100000000000 0.00000000100000000000 0.99999986659623718577 0.00000013240376283687 0.00000000099999999999 0.99999999799999994554 0.00000000099999999999 0.00000000099999999999 0.99999999799999994554 0.00000000099999999999 0.00000000100000000000 0.99632783404679736705 0.00367216495320256799 0.00000000100000000000 0.99999999799999994554 0.00000000100000000000 0.00000000099999999999 0.99999999800000005656 0.00000000099999999999 0.35919621347731411909 0.32381633362411937904 0.31698745289856661289 0.31048363757756514136 0.30902410742704566893 0.38049225499538924522 0.36341140678787386964 0.33678307361394943520 0.29980551959817652863 0.34550713774447228133 0.34037087985425079628 0.31412198240127681137 0.34705579219215104692 0.35218792485566730033 0.30075628295218165276 0.33646039412306782967 0.32632754139618752598 0.33721206448074481088 0.31881401220765009930 0.34885621407165418040 0.33232977372069577582 0.34999374672052624424 0.33030931848049555066 0.31969693479897826061 0.33152251818028721786 0.32339147992992234304 0.34508600188979043910 0.31959998197389311025 0.33152491237148390413 0.34887510565462298562 0.34724548642936803322 0.31809475756470984020 0.33465975600592196004 0.33378069767858009609 0.33223636639277298599 0.33398293592864686241 0.32023090400419051971 0.33179989332826043125 0.34796920266754916007 0.35205158009776410521 0.33547091017851976558 0.31247750972371612921 0.34291063455495451873 0.31853488093100223999 0.33855448451404313026 0.31929132670383747472 0.32755905579808902717 0.35314961749807355362 0.34114474726121107873 0.34607065583774476725 0.31278459690104404300 0.33725705347681012025 0.32910919226619778089 0.33363375425699209886 0.33918213722968154622 0.32278745806952213737 0.33803040470079642743 0.33788659799509024317 0.34692305448657090317 0.31519034751833896468 0.35876135180876589370 0.33843260979944000955 0.30280603839179404124 0.34721570614318736370 0.34395335873604998556 0.30883093512076259524 0.34165097731337079612 0.32814110943000784903 0.33020791325662146587 0.33922542743931027864 0.32639619830977489867 0.33437837425091476717 0.34461619391735059947 0.33133174331942943924 0.32405206276321996128 0.34277551565686120716 0.32746953398981676342 0.32975495035332202942 0.33842982221926010133 0.31224638933762871584 0.34932378844311123833 0.34443810815667752490 0.32640113997211872565 0.32916075187120380496 0.31723258569943768581 0.34955203711397470068 0.33321537718658750249 0.35394053250677920408 0.33291498389624818444 0.31314448359697255597 0.33504517457864940733 0.34188143503173562543 0.32307339038961496724 0.33240938202788244960 0.34671459781042585080 0.32087602016169164409 0.31745792352948248860 0.33722730677636020280 0.34531476969415725309 0.33098224522913716195 0.33312298285105168549 0.33589477191981131909 0.34090909280056919117 0.32423671881295645925 0.33485418838647434958 0.32985465610121944557 0.32124851771265583444 0.34889682618612483100 0.33525528582568764335 0.31967441393853385234 0.34507030023577844879 0.33823045943274382408 0.33932114218381809190 0.32244839838343819505 0.34374166546335593875 0.33527470302709477812 0.32098363150954922762 0.32177399566214615056 0.34277626859597382092 0.33544973574188002852 0.34915111840878915173 0.33072079898488659921 0.32012808260632419355 0.31132788816691708833 0.32844185942225745389 0.36023025241082540227 0.33067206673512555826 0.34601992411426535368 0.32330800915060908807 0.31337643746173032833 0.33835721859074846529 0.34826634394752131740 0.32762993090356395953 0.34856645453438306337 0.32380361456205303261 0.33558678075595765877 0.34449062515269568419 0.31992259409134682357 0.33433652456352996873 0.32868556951924504661 0.33697790591722515119 0.32115036446030281736 0.35050069566489522321 0.32834893987480190392 0.32524569843140932468 0.33953480032298033464 0.33521950124561045170 0.33520046917246110185 0.31124301814705779279 0.35355651268048110536 0.51565151014669796670 0.00027180960956305278 0.48407668024373901039 0.51978922685130035664 0.01333903580405943964 0.46687173734464021413 0.48123878312258933088 0.00648941795451128591 0.51227179892289931296 0.48941833241028537271 0.00512373007237581363 0.50545793751733880672 0.48421136927686320162 0.00600153379448644612 0.50978709692865020742 0.53246468447754891073 0.00000000100000000000 0.46753531452245111755 0.50637710620505416159 0.01564455874020675985 0.47797833505473913407 0.49416813414210103428 0.00000000100000000000 0.50583186485789899400 0.51328206693115174808 0.00000000100000000000 0.48671793206884833571 0.50420356848059588728 0.00779539942445491366 0.48800103209494921641 0.51589943710654184716 0.00000000100000000000 0.48410056189345807010 0.46643393286795947761 0.00024627960390510270 0.53331978752813535838 0.50134326603627110686 0.00000000100000000000 0.49865673296372897694 0.52516062216154979492 0.00887494007947397384 0.46596443775897622430 0.50553300231497877437 0.00610541400596737328 0.48836158367905380118 0.48505848053244243756 0.00412236953776635561 0.51081914992979127188 0.50419106430093152404 0.00671707921410998055 0.48909185648495850929 0.51266037905765671212 0.00565931340437971983 0.48168030753796364785 0.50479638826213368841 0.00082364200405335279 0.49437996973381287402 0.48963785250324892706 0.00000000100000000000 0.51036214649675115673 0.49861342640726780129 0.00000000100000000000 0.50138657259273211597 0.49321745088202589846 0.00000000100000000000 0.50678254811797418533 0.52297921048641760056 0.00000000100000000000 0.47702078851358242773 0.51351947193443381323 0.00000000100000000000 0.48648052706556610403 0.49861600587139209839 0.01143470350387426789 0.48994929062473369097 0.47497824395255133778 0.00413641430709298184 0.52088534174035572288 0.50602874958787047444 0.00000013752429825494 0.49397111288783129845 0.51347175918678078510 0.00477133273041653854 0.48175690808280269284 0.50359809216181616875 0.00000002299679746021 0.49640188484138642044 0.52201190781479689385 0.00000000100000000000 0.47798809118520296790 0.52427554763933403859 0.01637369304678280152 0.45935075931388308357 0.50464335890649447691 0.01062810063722730188 0.48472854045627822295 0.48795095623978190780 0.00032508303858300066 0.51172396072163517378 0.49273360783177866384 0.03185613233234574349 0.47541025983587564818 0.49075081269029041664 0.00043182816413278401 0.50881735914557668643 0.51236233643387329995 0.01050799870797843559 0.47712966485814828355 0.51939186110717183720 0.00638063180499700081 0.47422750708783106832 0.49685157861691658931 0.00000000100000000000 0.50314842038308338346 0.50376251978896124939 0.00609062514993390959 0.49014685506110500235 0.50469879197514677660 0.00000000100000000000 0.49530120702485330719 0.48806858812981018803 0.00000000100000000000 0.51193141087018978475 0.49345173654735252633 0.00767168036095551131 0.49887658309169191639 0.51926063211476558568 0.00000000100000000000 0.48073936688523438709 0.49182360714466144547 0.00000000100000000000 0.50817639185533869384 0.50012065040991493525 0.00101172020552988784 0.49886762938455525562 0.49490771372946151807 0.00000000100000000000 0.50509228527053839919 0.50981594186492362741 0.01168450085559137597 0.47849955727948501050 0.48459184220397827358 0.00000007440008454733 0.51540808339593724430 0.51153925961371649045 0.00045999176804108893 0.48800074861824249695 0.49380129779182529992 0.00214174101547949525 0.50405696119269527422 0.10504303642339951619 0.45848347542219436423 0.43647348815440606407 0.09383999674587484296 0.44580529318052469767 0.46035471007360045936 0.11801124345951279071 0.44619343422410290279 0.43579532231638429263 0.10150817897299509174 0.44474184109029252232 0.45374997993671234431 0.14144944553914898244 0.47426718065022838156 0.38428337381062249722 0.08656596263718574491 0.47201374694852676894 0.44142029041428754166 0.10422682420288104099 0.45665008652196642513 0.43912308927515242285 0.07422281507005458467 0.46668026430253822801 0.45909692062740725671 0.11152984148911383733 0.44326164444242566187 0.44520851406846068121 0.12101900721666984662 0.45534926548479054409 0.42363172729853953991 0.19287147372937366030 0.40220634979635128126 0.40492217647427497518 0.19868166550667537562 0.39952077624337684059 0.40179755824994778379 0.20144056442189406386 0.40552701281654912613 0.39303242276155692103 0.17400131741109717276 0.41572345587205422612 0.41027522671684846234 0.19363830614785534912 0.39941552029693161430 0.40694617355521295332 0.20932370419936904837 0.41063785306931777086 0.38003844273131326403 0.21496306930156286463 0.41077627378883840858 0.37426065690959875454 0.20887311245081657818 0.39219787302656328176 0.39892901452262014006 0.18789467459437667052 0.42880445734573224836 0.38330086805989094234 0.21467435158258502126 0.41396326091136687042 0.37136238750604805281 0.30215275924600598634 0.35114326369103593395 0.34670397706295807971 0.27985580964526363124 0.36766711333486662427 0.35247707701986974449 0.29214764907998119758 0.34353124024041165052 0.36432111067960715189 0.28098186396660507214 0.35436535705487937076 0.36465277897851555711 0.29909659519210785028 0.34708664349540557792 0.35381676131248662731 0.29960230758566036569 0.34764467237891033546 0.35275302003542929885 0.28690707484319816212 0.36958476358894237768 0.34350816156785934918 0.31218824558522878521 0.35988855578362860532 0.32792319863114272049 0.29371283648699086921 0.34536893102077848017 0.36091823249223065062 0.32028624797598659324 0.35059182523172049972 0.32912192679229296255 0.39315538655109805166 0.30778919233772789044 0.29905542111117405790 0.39625700997625840083 0.29350948690034872612 0.31023350312339292856 0.40087160410050781678 0.31851581382017457589 0.28061258207931755182 0.40117357253398744366 0.30569836130272198815 0.29312806616329067921 0.40013703551439627759 0.28691859513594913933 0.31294436934965452757 0.39131222513930874474 0.30759794867682349606 0.30108982618386764818 0.40826221599444090238 0.30658973748486684219 0.28514804652069231095 0.41420080477834714250 0.28227625784283560950 0.30352293737881719249 0.39119930707342420728 0.32102763805993583812 0.28777305486664006562 0.37635520411942069430 0.29805329179310008358 0.32559150408747933314 0.51400585200303006150 0.26100245041580294458 0.22499169758116702167 0.50336119658518030384 0.25110166586697690860 0.24553713754784287082 0.47299237773462793344 0.26084178003823194070 0.26616584222714018138 0.49359314224598493936 0.26013978211456978418 0.24626707563944530421 0.52795469779405246324 0.26499345968140075591 0.20705184252454675309 0.48219467330650939152 0.25987283477635270135 0.25793249191713785162 0.47626160019217189667 0.25351817092177358903 0.27022022888605456981 0.51617477226059282902 0.23162353057460718930 0.25220169716479995392 0.49698887507445854705 0.24557159475841641716 0.25743953016712495252 0.52733914260860248469 0.25309832534801629533 0.21956253204338116447 0.56749881833694781896 0.19172441472755546998 0.24077676693549673881 0.59339160859286765870 0.19241414198845174788 0.21419424941868048240 0.62308540846251914136 0.18054125203843729430 0.19637333949904353658 0.59485531592769125275 0.20909554531024135415 0.19604913876206744860 0.61310545246842529377 0.20645329445333451823 0.18044125307824007698 0.60102956519838679483 0.21237444166376903687 0.18659599313784405727 0.59278179178128642679 0.20826418834431797977 0.19895401987439562119 0.60456224253100432353 0.20686687908046738626 0.18857087838852840123 0.59417710257213784963 0.21264514488765640099 0.19317775254020574938 0.59059286756608764257 0.21451811369415349495 0.19488901873975889023 0.69484036887292865980 0.14634823390637874407 0.15881139722069256837 0.69945423984127830241 0.16333221995631252987 0.13721354020240922322 0.69115689116107958956 0.14927316115273414621 0.15956994768618620872 0.68851717088680941536 0.14201541767923545057 0.16946741143395496754 0.69288781352263861812 0.14270021794166909412 0.16441196853569234326 0.68819873910998985433 0.16242980538224471854 0.14937145550776548264 0.68619763716276405141 0.14370194479775053042 0.17010041803948539041 0.68596343194490616568 0.16051691534743553480 0.15351965270765843830 0.70684340251150390433 0.16654037983665334610 0.12661621765184280508 0.70657158115262697073 0.14984891346689468983 0.14357950538047842270 0.79161214498168253062 0.10430887542937690438 0.10407897958894059276 0.79477141808375573184 0.10274451187208989700 0.10248407004415439892 0.80425538032447896342 0.10720945367236509038 0.08853516600315590457 0.79445836435866723502 0.11481368508653701233 0.09072795055479568327 0.80626524450581027459 0.08599284906042292675 0.10774190643376663212 0.77991736902186048486 0.08777798585427237787 0.13230464512386716502 0.77897241390666871474 0.11419808069913564563 0.10682950539419577840 0.80225596727756287585 0.10739115862914316857 0.09035287409329402497 0.81035643868218754093 0.11405964018980654928 0.07558392112800596530 0.80474324803558927588 0.09992219310105134034 0.09533455886335934215 0.89147290804053958002 0.05818869713285088757 0.05033839482660958098 0.87135519951168793895 0.04885203404408157424 0.07979276644423052844 0.90273220877706750187 0.05642671780738096193 0.04084107341555152232 0.90299890240805003039 0.05982401615206547896 0.03717708143988454617 0.88622329583732417646 0.03227381365259313073 0.08150289051008267893 0.89149278212958615875 0.03556871666107842139 0.07293850120933542680 0.90540444756330573650 0.06637446770308205735 0.02822108473361228942 0.89581315874618450135 0.06675457610008654619 0.03743226515372900798 0.86941364504212315101 0.03330392614486758773 0.09728242881300920575 0.88098981477392690476 0.04673780362475228600 0.07227238160132080924