![Page 1: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/1.jpg)
RNA-seqanalysis:Fromreadstodifferen6alexpression
AliciaOshlackMurdochChildrensResearchIns6tute
@AliciaOshlack
![Page 2: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/2.jpg)
The current MCRI bioinformatics team • Dr Nadia Davidson • Dr Anthony Hawkins • Dr Jovana Maksimovic • Dr Katrina Bell • Dr Belinda Phipson • Dr Simon Sadedin • Harriet Dashnow • Luke Zappia • Rebecca Evans
PhDposi6onsavailable
![Page 3: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/3.jpg)
MCRIBioinforma6csCollabora6veanalysisandmethodsdevelopment
Transcriptomics Epigenomics Genomics ClinicalGenomics
• RNA-seq• miRNA-seq• Differen6al
expression• Cancer• Non-model
organisms• Alterna6ve
splicing• Singlecell
RNA-seq
• Methyla6onarrays
• Bisulfitesequencing
• Histonemodifica6ons
• ChIP-seq
• Exomeanalysis
• WGS• Targeted
capture• SNPs• CNV• Tandem
repeats
• Clinicalexomes
• TumourRNA-seq
![Page 4: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/4.jpg)
RNA-seqanalysis
![Page 5: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/5.jpg)
Genesandtranscripts
Gene
transcript
SlidefromAliciaOshlack
![Page 6: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/6.jpg)
RNA-seq
Pepkeetal,NatureMethods,2009
![Page 7: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/7.jpg)
Twowaystolookatsequencingdata
Sequenceof(mapped)read• genomesequencing• variantdetec6on• genomicrearrangements• Bisulfite-seq(methyla6on)• RNAedi6ngetc.
Posi6onofmappedread• RNA-seq• ChIP-seq• MeDIP-seqforDNAmethyla6onetc.
7
![Page 8: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/8.jpg)
TwowaystolookatRNA-seqdata
Sequenceof(mapped)read• Assembly• Determininggenes/transcripts
Posi6onofmappedread• Expressionlevels• Differen6alexpression
8
![Page 9: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/9.jpg)
Rawdata(fastqfiles)
• Shortsequencereads• Qualityscores
@HWI-ST1148:308:C694RACXX:5:1101:1768:1990 1:N:0:CGTACG NTAGGCCTTGGCAGTTTTGGAGAATCACTGCTGCCAAAGAGTCTACTTGG + #0<FFFFFFFFFFIIIIIIIIIIIIIIIIIIIIIIIIIIIIFFIIIIIII @HWI-ST1148:308:C694RACXX:5:1101:3409:1990 1:N:0:CGTACG NAGTTACCCTAGGGATAACAGCGCAATCCTATTCTAGAGTCCATATCAAC + #000BFBFFFFFFF<BFFFFBBBBBFBBFF<<FBFFIBFFFBFFFIIBFF
50bpsequence
![Page 10: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/10.jpg)
Differen6alexpression• Whichgenesarechangingexpressionlevelbetweensamples?– treatedvsuntreated,– diseasevsnondisease,– earlyvslate6mepoints,– cellsinoneenvironmentvsanotherenvironment,– etc,…
• Thousandsofgenesbutonlyafewsamples– Sophis6catedsta6s6calmethodsarerequiredforanalysis
![Page 11: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/11.jpg)
RNA-seqanalysisstepsRawsequencereads
Mapontogenome
Summarizereadstotranscripts
Sta6s6caltes6ng:Determinedifferen6allyexpressedgenes
Systemsbiology
DenovoassemblyAnnota6onbased Genomeguidedassembly
Whichtranscriptome?
![Page 12: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/12.jpg)
RNA-seqanalysisstepsRawsequencereads
Mapontogenome
Summarizereadstotranscripts
Sta6s6caltes6ng:Determinedifferen6allyexpressedgenes
Systemsbiology
DenovoassemblyAnnota6onbased Genomeguidedassembly
Whichtranscriptome?
![Page 13: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/13.jpg)
Mappingreadstothegenome• Wheredothemillionsofshortsequencescomefrominthegenome?
• Sequencingtranscripts,notthegenome
CDS CDS CDS CDS
CDS CDS CDS CDS
Gene
transcript
![Page 14: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/14.jpg)
Lotsofgoodalignershandlesplicejunc6onswell(e.g.TopHat,Star)
Exon1 Exon2
![Page 15: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/15.jpg)
RNA-seqdatainIGV
![Page 16: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/16.jpg)
Whichtranscriptometouse?
![Page 17: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/17.jpg)
Rawsequencereads
Mapontogenome
Summarizereadstotranscripts
Sta6s6caltes6ng:Determinedifferen6allyexpressedgenes
Systemsbiology
RNA-seqanalysissteps
DenovoassemblyAnnota6onbased GenomeguidedassemblyWhichtranscriptome?
![Page 18: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/18.jpg)
Op6on1
• Useannota6on(knowngenes)– Workswellforwellstudiedorganisms(human,mouse,arabidopsis,drosophila,…)
– onlyasgoodasyourannota6on– Nonoveltranscriptsareanalysed
![Page 19: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/19.jpg)
Op6on2:Genomeguidedtranscriptassembly
• Usestheloca6onanddensityofreadsalongthegenometoassembletranscripts
• E.g.Cufflinks
• Can’tassembleacrossbreaksinthegenome– Cancer,poorgenomes
![Page 20: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/20.jpg)
Op6on3:Denovotranscriptomeassembly
• Assembletranscriptsfromthedatawithoutusingareferencegenome
• “Harder”thangenomeassembly– Ordersofmagnitudevaria6onincoverage– Con6gsareshort– Alterna6veisoforms/transcriptshaveoverlappingsequences– *Very*computa6onallyintensive
• Sokwareincludes – Trinity– Oases(velvet)– TransAbyss– …
![Page 21: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/21.jpg)
Example:Annota6ngthechickenWchromosome
ZZ ZW
Male Female
Twohypothesesformechanismsofaviansexdetermina6on:1. DominantovarydetermininggeneonW(cfmammals)2. DosageofZ-linkedgenes
![Page 22: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/22.jpg)
Thereisanannotatedchickengenome
• ChickenWchromosomeispoorlyassembled• AregenesonotherchromosomesreallyontheW,inpar6culartherandomchromosome?
Chromosome Assembled Size (Mb)
Size inc. random (Mb)
Estimated Size (Mb)
Estimated Genes
(Ensembl) Z 69 70 80 796
W 0.24 0.89 18-54 46
Un_random 56 - - 1287
![Page 23: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/23.jpg)
Experimentaldesign
PCRSexing
+12hourBlastoderms
HandplateforPCRSexing
RNA
Stage26pairedgonads(day4.5)
12Female
RNA
16Femalegonads
PooledSamples
12Female
16Femalegonads
12Male
12Male
16Malegonads
16Malegonads
RNA-seq• IlluminaHiSeq2000• Paired-end100bp• 4lanes• >80millionreads/sample
![Page 24: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/24.jpg)
Definingthetranscriptome
• Annota6on~20,000genes• Genomeguidedassembly(Cufflinks)~45,000genes
• Denovotranscriptomeassembly~2.5milliontranscripts(Abysswithfiltering)!
Acombinedapproach• Assemblecufflinkgenesusingtranscriptsfromourdenovoassembly
![Page 25: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/25.jpg)
Annota6onofthechickenWcombinedallthreeapproaches
W/W_random ChromsomeUn_random ChromosomeAutosomes
Blastoderm CoverageGonads Coverage
Abyss TranscriptsCufflinks TranscriptsEnsembl Transcripts
1000 1500 2000 2500 3000 3500
base position
039
1
Coverage
Genome
EnsemblCufflinks
AbyssRASA1−W
1400 1600 1800 2000 2200
base position
012
6
Coverage
Genome
EnsemblCufflinks
AbyssST8SIA3−W
2000 2200 2400 2600 2800
base position
069
9
Coverage
Genome
EnsemblCufflinks
AbyssGOLPH3−W
0 500 1000 1500 2000 2500
base position
019
4
Coverage
Genome
EnsemblCufflinks
AbyssZSWIM6−W
0 200 400 600 800 1000 1200 1400
base position
082
Coverage
Genome
EnsemblCufflinks
AbyssNEDD4−like−W
FulllistofWgenes/transcriptsfordifferen6alexpressionAyersetal,2013
![Page 26: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/26.jpg)
RNA-seqanalysisstepsRawsequencereads
Mapontogenome
Summarizereadstotranscripts
Sta6s6caltes6ng:Determinedifferen6allyexpressedgenes
Systemsbiology
DenovoassemblyAnnota6onbased Genomeguidedassembly
Whichtranscriptome?
![Page 27: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/27.jpg)
Summariza6on
Takeyour“transcriptome”andaddupthereads
![Page 28: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/28.jpg)
Coun6ngoverexonsvscoun6ngovergenes
Exon1 Exon2
Exon1=8readsExon2=10reads
Coun6ngoverwholegene(Exon1+Exon2)=15
![Page 29: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/29.jpg)
Non-modelorganismsDenovotranscriptomeassembly
1. Clusterassembledcon6gsinto“genes”(independentoftheassembler)
2. Performreadcoun6ngpercluster
Corset Ourmethod
Davidson&Oshlack,GenomeBiology,2014
![Page 30: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/30.jpg)
Summariza6onturnsmappedreadsintoatableofcounts
**veryhighdimensionaldata**
TagID A1 B1ENSG00000124208 478 4830
ENSG00000182463 27 48
ENSG00000125835 132 560ENSG00000125834 42 131ENSG00000197818 21 52ENSG00000125831 0 0ENSG00000215443 4 9ENSG00000222008 30 0ENSG00000101444 46 54ENSG00000101333 2256 2702
… …tensofthousandsmoretags…
![Page 31: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/31.jpg)
RNA-seqanalysisstepsRawsequencereads
Mapontogenome
Summarizereadstotranscripts
Sta6s6caltes6ng:Determinedifferen6allyexpressedgenes
Systemsbiology
DenovoassemblyAnnota6onbased Genomeguidedassembly
Whichtranscriptome?
![Page 32: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/32.jpg)
Summariza6onturnsmappedreadsintoatableofcounts
**veryhighdimensionaldata**
TagID A1 B1ENSG00000124208 478 4830
ENSG00000182463 27 48
ENSG00000125835 132 560ENSG00000125834 320 131ENSG00000197818 21 52ENSG00000125831 0 0ENSG00000215443 4 9ENSG00000222008 30 0ENSG00000101444 46 54ENSG00000101333 2256 2702
… …tensofthousandsmoretags…
![Page 33: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/33.jpg)
Whichgenesaredifferen6allyexpressed?
• LikeanyotherexperimentRNA-seqneedstobereplicatedsowecangetameasureofvariance
![Page 34: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/34.jpg)
Replica6onisessen6al
TagID A1 A2 A3 B1 B2 B2ENSG00000124208 478 619 559 4830 7165 6651
ENSG00000182463 27 20 18 48 55 56
ENSG00000125835 132 290 450 560 408 266ENSG00000125834 320 462 355 131 99 91ENSG00000197818 21 29 23 52 44 65ENSG00000125831 0 0 0 0 0 0ENSG00000215443 4 4 4 9 7 3ENSG00000222008 30 23 23 0 0 0ENSG00000101444 46 63 55 54 53 52ENSG00000101333 2256 2793 2931 2702 2976 2226
… …tensofthousandsmoretags…
**veryhighdimensionaldata**
![Page 35: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/35.jpg)
Qualitycontrol–checkyourdata!
DatafromAndrewElefanty
Sortedcellpopula6ons
![Page 36: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/36.jpg)
Dataexplora6on
![Page 37: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/37.jpg)
Sta6s6caltestsfordifferen6alexpression
TagID A1 A2 A3 B1 B2 B2ENSG00000124208 478 619 559 4830 7165 6651
ENSG00000182463 27 20 18 48 55 56
ENSG00000125835 132 290 450 560 408 266ENSG00000125834 320 462 355 131 99 91ENSG00000197818 21 29 23 52 44 65ENSG00000125831 0 0 0 0 0 0ENSG00000215443 4 4 4 9 7 3ENSG00000222008 30 23 23 0 0 0ENSG00000101444 46 63 55 54 53 52ENSG00000101333 2256 2793 2931 2702 2976 2226
… …tensofthousandsmoretags…
**veryhighdimensionaldata**
![Page 38: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/38.jpg)
• Normalisa6on– Librarysize(sequencingdepth)
• IncludeasoffsetinGLM• Scalingnormalisa6on(sizefactors)
– Composi6onbias(TMM)– Batcheffects(RUVSeq)
Thingstothinkaboutbeforesta6s6caltes6ng
.
(a)
log2(Kidney1 NK1) − log2(Kidney2 NK2)
Den
sity
-6 -4 -2 0 2 4 6
0.0
0.4
0.8
log2(Liver NL) - log2(Kidney NK)
Den
sity
-6 -4 -2 0 2 4 6
0.0
0.2
0.4(b)
●
●
●
●
●
●
●
●
●
●
●●
●●
●●
●
●
●●
●
●●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●●●
●
●
●
●
●●
●
●
●●
●●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●● ●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
● ●●
● ●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●●
●●●
●
●
● ●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
● ●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●●
●●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●●
●●
●●●
●
●●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
● ●
●
●
●
●
●●
●
●
●
● ●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
● ●
●●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●●
●
●
● ●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
● ●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
● ●●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
● ●
●
●
●
●
●●
●
●
●
●
●●●
●
●
● ●
●
●
●
●
●
●
●
●
●●
●●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●●
●
●
●
●
●●
●
●
●
●●
●
●
● ●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●●●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●●
●●
●
●● ●
●
●
●
●
●
● ●
●
●●
●●
●
● ●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
● ●●
●●
●
●
●
●
●
●
●
●● ●
●
●●
●
●
●●●
●
●
●
● ●
●
●
●
●
●
●
●●
●
●
●●●
●●
●
●
●
●●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
● ●● ●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
● ●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
● ●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●● ●●
●●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●●
●●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●● ●●●
●
●
●
●
●
●
●
●
●
●●
●
● ●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
● ●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●●● ●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
● ●
●●
●
●
●
●
●
●
●
●
●
●
●
● ●
●●
●
●
●
●
●●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
● ●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●● ●
●
●
●
●
●
●
●
●
●●
●
●
●
● ●
●
●●
●
●
●
●
● ●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
● ● ●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
● ●●
●
● ● ●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●●
●
●
●
●
●
●●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
● ●●
●
●
●
●
●
●● ●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
● ●●
●●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
● ●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●●
●
●●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
● ●
●
● ●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●●●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●● ●●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●●●
●
●
●
●
● ●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
● ●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
● ●●
●●●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●● ●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●● ●
●●
●
●
●
●●●
●
●
●
●
●
●●
●●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●● ●●● ● ●
●
●●●
●●
●
●● ●
●
● ●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●●
●●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●● ●
●
●
●
●
●
●
●
●
●
●
● ●
●●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
● ●
●
●
●●
●
●
●●
●
● ●
●
●
● ●
●
●
●
●●
●
●
●● ● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●● ●
●
● ●●
●
●
●
● ●●
●
●
●
●● ●
●
●
●
●
●
●
● ●
●
●
●●
●
●●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
● ●
●
●●
●
● ●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●●
● ●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
● ●●
●
●
●
●
●
●●
●
●
●
●
●
●●
● ●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
● ●
●●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●●
●
●
●
●
●●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●● ●
●●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
● ●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●●●
●
●
●
●
●
●●
●
●
● ●
●
●
●
●●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
● ●
●● ●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●●
●
●
●●
●
●●
●
●
●
● ●
●
●●
● ●
●
●
●
●
●
●
●
●●
●
●
● ●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
● ●
●
●
●
●
●
●
●
●●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●● ●
●
●
●
●
●
●
●
●
●
●
●●●●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●●
●
●
●
●
●
● ●
●
●
●
●
●●
●●
●
● ●●
●
●
● ●
●
●
●
●
●
●● ●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
● ●
●
●
●
●
●
●
●
● ● ●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
● ●●
●
●
●
●
●
●
●●
●●● ●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●● ●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●●●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
● ●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●●
●
●
●
●
●
●
● ●
●
●
●
●
●
●● ●
●
●
●
●
●
● ●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
● ●
●●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●●
●
●●
●
●
●
●
● ●
●
●
●
●●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●●
●●
●
● ●●
●
●
●
●●
●●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●● ●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
● ●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●●
●
●
●●
●
●●
● ●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
● ●●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
● ●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●● ●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
● ● ●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
● ● ●●
●
●
●
●
●
●
●●
● ●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
● ●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●● ●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●●●●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●●
●
●●
●
●
●
●
●●
●
● ●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
● ●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
● ●
●
●
●
●●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●● ●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●● ●●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●●
●
● ●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
● ●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
● ●●
●
●
●
●
● ●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●● ●●
●
●●
●
●
●
●
●●
●
●
●
●● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●● ●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●● ●
●
●
●
●
●
●●
●
● ●●
●
●
●
●
●
●
●
●
●
● ●
●
●
●●
●
●
●
●●
●
● ● ●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●●
●●
●
●
●
● ●
●
●
●●
●
●●
●
●
● ● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●●
● ●
●
●
● ●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●●● ●● ●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
● ●
● ●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●●●
●
●
●
●
● ● ●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
● ●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●●
● ●●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
● ●●
●
●●●●●
●●●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●●●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
● ●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●● ●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●●
●
●
●
●●
●
●●
●
●
●
●●
●
●
●
●
●●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
● ●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
● ●●
●
● ●
●
●
● ●
●
●●●
●
●
●
●
●
●
● ●●
●
●
●
●
●
●
●
●
●
●
● ●
●●
●
●
● ●
●
●
●●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
● ●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
● ●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●●
●
● ●
●
●
● ●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●● ●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
● ●● ●
●
●
●
● ●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●●
● ●
●
●
●
●●
●
●
●●
●
●●
●
●
● ●
●
●
●
●
●
●●
●
●
●●
●
●
●
●●●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
● ●
●
●
●
●
●●
●
●
●
●
●●
●●
●
●●
●
●●
●
●
●
●
●
●
●
● ●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●● ●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●●●
●
●
●
●
●
● ●
●
● ● ●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●● ●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●●
●
●
● ●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
● ●●
●
●
●
●
●
● ●
●
●
●
●
●
● ●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
● ●●
●
●
●
●●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●●
●●
●
●
●●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●●●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●●●
●
●
●●
●
●
●
●
● ●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●●
●
●
●
● ●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●● ●●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●●
●
●
●●
●
●
●
●
●
●●
●
●
● ●●
●
●●● ●
●
●
●
● ●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
● ●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
● ●
●●
●●
●
●
●
●
●
●
●
●
●●
●● ●●●
●●
●
●●
●●
●
●
●
● ●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●● ●
●
●
● ●●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●● ●
●
●
●
●●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
● ●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●●
●
●
●●
●●
●
●
●
●
●
●
●
●●●
●
●
●
● ●
●
●
●
●
●
●
●●
●● ●
●
●
● ●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
● ●
●
●
●
●●
●
●
●●
●
●
●
●●
●
●
●
●
●
●●
●●
●
●
●
●
●
● ●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●● ●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●●
●
●●
●
● ●
●
●
●
●
●
●
●
●● ●●
●
●●
●
● ●
●
●
● ●
●
●
●
●
●
● ●
●
●
●●●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●● ●
●
●
●
● ●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●● ● ●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
● ●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●●
●
●
●●●
●
●
●
●
●●
●
●
●●
●
●
●
●
●●● ● ●●●
●
●
●
●
●
●
●
●
●
●●
●
●
● ●●
●
●
●
●
●●●
●
●
●
●
● ● ●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●●●
●
●
●
●●
●
●● ●
●●
●
●
●
●●
●
● ●●
●
●
●
●
●
●
●●
●
●
●
●
●
●●●●
●
●
●
●
●
●
●
● ●●●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●● ●
●
●
●
●
●
●
●
●
● ●●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●●
●
●
●
●
●
● ● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●●
●
●
● ●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
● ●
●
●●●
●
●●
● ●
●
●
●
●
●●
●
●
●
●
●●
●
●
● ●
●
●
●
●
●●
●
●●
●
●●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●●
●
●
●
●
● ●
●
●
●
●
●●
●
●
●
●● ●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●●
●
●
●
●
●
● ●
●
●
●●
●● ●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●●
●
●
●
●
●
●
●
●●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
● ●
●
●
●
●
● ●
●
●
●
●
● ●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●●
●
●
●
●
●
●●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●● ●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●● ●
● ●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●● ●●● ●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●●●
●
● ●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
● ●●●
●
●
●
●
●●●●
●
●● ●
● ● ●
●● ●
●
●
●
●
●
●
●●
●
●● ●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●●●
●
●
● ●
● ●●
●
●
● ●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●●
●
●
●● ●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ● ●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●●
●
●
●
●
●
●● ●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●●
●●
●
●
●
●
●
●●
●
●●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●●
●
●●
●
●
● ●●
●
●
●
●
●
●●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
● ●
●
●
●
●
●
●
●●
●
●
●
● ●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●● ●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
● ●
●●
●
●
●
●
●
●
●●
●
●●
●
●
●● ●
●
●
●
●● ●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
● ●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●●
●●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●●
● ●
●
● ●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●●
●●
●
●
●
●
● ●
●
●
●
●
●
●●●
●
●
●●
●
●
●●
●
●●
●●
● ●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
● ●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●●
●
●
● ●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●●
●
●
● ●
●
●
● ●
●
●
●
●
●● ●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●●
●
●
●
●
● ●
●
●
●●
● ●
●
●
● ●
●
●●●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
● ●
●
●●
●
●
●
●●
●●
●
●
●
●●
●
●
●●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●●
●
●●
●●
●
●
● ●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●●
●
●●
●●
●
●
●
●
●
●●
● ●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
● ●
●
●
●
●
●
●●
●●●
●●
●●●
●
●
●
● ●
●●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
● ●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
● ●
●
●
● ●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●●
●
●
●
●
●
●
●
●
●
● ●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●●
●
●
●
●
●
●
●
●●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●●
●●
●
●
● ●●●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
● ●
●
●●
●
●
●
●●
●●
●●
●●
●●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
● ●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●● ●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
● ●
●
●
●
●
● ●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
● ●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●●●
●●
●
●
●
●●
●●
●
●
●●
●
●● ●
●
●●
● ●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
● ●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
● ●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
● ●●
●
●
●
● ●
●
●
●
●●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
● ●
●
● ●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●● ●
●●
●
●
●
●
●
●●
●
● ●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●● ●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●●
●●
●
●
●
●
●
●
●● ●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●●
●
●
●
●●
●
●●
●
●●
●
● ●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
● ●
●
● ●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●●●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●●
●
●● ●
●
● ●
●
●
●
●
●
●●
●
●
●
●
●
●
●● ●
●●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
● ●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
● ●
●
●
●
●
●
●●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●●
● ●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●●
●
● ●
●
●
●
●●
●
●●
●●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●●
●
●
●●
●● ●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●●
●
●● ●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
● ●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●●
●
●
●
●
●●
●
●●
●
●●
●
●
●
●
●●
●
●
●
●●
●
●
●●
●●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
● ●
●
●
●
●●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
● ●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ● ●
●
●● ●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
● ●● ●
●●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●●
●
● ●
●
●
●
●
●●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
● ●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
● ●
●
●
●●●
●
●●
●
●
● ●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
● ●
●
●
●●
● ●
●
●
●
●●●
●
●
●
●
●
●● ●
●
●
●
●
●
●
●
●
●
●
●
● ●●
●
●●
●●
●
●
●
●
●
●
●
●●
●
●
● ●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●●
●●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●●
● ●
●
●
●
●
●●
●
● ●●
●
● ●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●●
●
●●
●
●●
●
●●●
●
●●
●
●
●
●
●
● ●
●
●●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
● ●
●●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●● ●
●
●●●● ●
●
●
●
●
●
●●
● ●
●
●
●
●
●●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●● ●
●
● ●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●● ●●
●
●●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●●
● ●
●●
●●
●
●
●●
●●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●●
●
●
●●●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●●●
● ●● ●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
● ●
●
●
●
●
●
● ●
●
●
●●
●
●●●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
● ●●
●
● ●
●
● ●●●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●●
●●●
●●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●●
●
●
●
●
●●
●
●
● ●
●
●
●●●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
● ●●●
●
●
●●
●
●
●
●
●
●
● ●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
● ●●
●
●
●
●
●
●●
●
●●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●● ●● ●
●
●
●
● ●●
●
●
●
●
●
●
●
●●
●● ●● ●●
● ●
●
●●
●
● ●
●●
●
●
●
●●
●
●
●●
●
●
●
●
●●
●●
●
●
● ●
● ●
●
●
●●●
●
●
●
●
●● ●
●
●●
●
● ●
●●
●
● ●
●
●
●
●
● ●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●● ●
●
●●
●
●●
●
●
●
●
● ●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●● ●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ● ●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
● ●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
● ●●
●
●
●
●
●
●
●
●
●
●●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
● ●●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
● ●●
●●
●
● ●
●
●
●
● ●
●
●●
●●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●● ●
●
●
●
●
●
●●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●●
● ●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●●
●
● ●
●
●
●●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
● ●
●
●
●
●●● ●
● ●
● ●
●●
●●
●
●
●
●
●●
●
●
●
●●
●●●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
● ●●●● ●●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●● ● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●●●
●
●
●
●
●
●●
● ●
●
●● ●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●●
●
●
●
●●
●
●
●
●
● ●
●
●
●
●●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●●
●●
● ●
●
●
●
●●●
●
●●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●●●
●●
●
●●
●
●
●●
●
●
●
●
●
● ● ●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●● ●
●
●
● ●
● ●
●●
●
●
●
●
●
●
●
●
●
●
● ●
●●
●
●
●
●
●
●
●
●
●
●●
● ●●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●●●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●●
●
●
● ●
●
●
●
●
● ●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
● ●
●● ●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
● ●
●
●
●
●
●●●●
●●●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
● ●
●
●
●●
●
●
●
●
●●
●
●
●
●
●●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
● ●●
●●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
● ●
● ●
●
●
●
●
●●
●
●
●
● ●
●
● ●
●
●●●
●
●
●
●
●●
●
●
●
●
●
●●
●
●●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●●
●
●
●●
●
●●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
● ●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●●
●
●●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
● ●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
● ●
●●
●
●
●
●●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
● ●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
● ●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●●
●
●
●
●
●
●●
● ●●●●
●
●
●
●
●
●
●
●●●
●
●
●●
●
●
●
●● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
● ● ●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●● ●
●
●●
●
●
●
●●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●●●
●
●
●
●
●
●●
● ●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●●
●
●
● ●
●
●
●
●●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●●
●
●●
●
●●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
● ●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
● ●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●●
●
●
●●●●
●●●
● ●●
●
● ●
●
●●
●
●
●● ●●
●
●
●
●
●●
●
●
●
●
●
●
●
● ●●
●● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●●
●●●
●
● ●
●
●
● ●
●●
●
●
●
● ●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
● ●
●
●
●
●●
●
●●
●
●
●
●●
●
● ●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
● ●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
● ●
●
●
● ●●
●
●●
● ●●
●●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●●
● ●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●● ●
●
●
●●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●●● ●
●
●●
●
●
●
●●
●●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
● ●●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
● ●
●
●
●
●●
●
●
●●●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●●
●
●●
●
●
●
●
●
●
●●
●●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
● ●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●●
●
●
●●
●
●●
●
●
●
●
●● ●
●
●
●
●
●
●
●
●
●●●●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●●
●
●
●
●●●
●
● ●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
● ●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
● ●
●
●
●
●
●●
●
●●
●
● ●●
●
●
●
●
●
●
●
●●
●
●
●
● ●●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●●
●
●
● ●
●●
●
●
●
●
●
●
●
●
●
●
●
● ●
● ●
●●
●
●●
●
●
●
●
●
●
●
●●
●
●●
●
●
● ●
●
●
●
●
●
●
●●
●
●●
●●
●
●
●
●
●
●●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●●
●●
●●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●●
●●
●
●
●
●
●●
●
●
● ●
●
●
●
●
●
●
●
●●●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●●
●● ●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●●
● ●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
● ●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
● ●
● ●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●● ●
●
●
●
●
●
●
●
●●
● ●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
● ●
●
●
●
●
●
●●
●●
●
●
●
●●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●●
●
●●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
● ●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
● ●
●
●
●
●
●
● ●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●● ● ●
●
●
●
●
●
●
●
●●
●●●
●
●●
●
●
● ●●
●
●●
●
●
●●
●
●
●●
●
●
● ●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
● ●●
●
●
● ●
●
●
●
●
●
●●
●
●
● ●
●
●
●
●
● ●
●●
●
●
●●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●●
●
●
●●
●
●
● ●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●●
●
●
●
●
●
●
●
●●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●●
●
●● ● ●
●
● ●●
●
●
●
● ●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
● ●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●●
●●
●
●
●
●
●
●
●
●●
●
●
●●
●
●●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
● ●
●
●●●
●
●
●
●
●●
●
●
●● ●
●
●
●
●
●
● ●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
● ●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●●●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●●
●
●
●
●
●●
●
●●
●
●
● ●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
● ●
●
●
●●●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●●
●
●
●
●
●
●
●
●●
●
●●●
●
●● ●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●● ●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
● ●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●●
●
●
● ●
●
●
●
●●
●
●
●
●
●
●
●
●
●●●
●●
●
●
●
●
●
●●●
●
● ●
●
●●
●●
●
●
●●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●●●● ●●
●
●
●
●
●
●
●
●
●●
● ●
●
●
●
●
●
●
●
●
●
● ●● ● ●●
●
●
●
●
● ●
●
●
●●
●
●
●
●●
●
●
●
●●
●
●
●●●●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●● ●
●
●
●
●
●
●
●
●
● ●●
●
●
●●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●●●
●
●
●●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●● ●●
●
●
● ●
●
●
●
●
●● ●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●●
●
●● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ● ●
●●
●
●
●
●
●
●
●
●
●
●
● ●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
● ● ●●
●●
●
●
●
●
●●●
●●
● ●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
● ● ●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
● ●●
●
●
●
●
●
●
●●
●
●● ●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●●
●
●
●
●
●
●
● ●● ●
●
●
●●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
● ●●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●●
●
●
●●
●
● ●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
● ●● ● ●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
● ●
●
●
●
●●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
● ●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
● ●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●● ●
●
●
●
●
●
●
●● ●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●● ●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●● ●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●●
●
●
●●
●
●
●
●
●
●●
●
●
●●
●
●
●●●
●●●
●
●
●●
●●●
●
●●
● ●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
● ●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●●
●
●
●
●
●
●●
● ●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●●
●●
●●
●● ●
●
●
● ●
●●
●●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●●
●
●●
●
●
●
●
●
● ●
●
● ●
●
●
● ●
●
●●
●
●●
●
●●
●
●
●
●
●
●
●
●●
●
●●
●
●
●●
●
●
●
●
●
●●
●●
●●
●
●
● ●
●
●
●
●
●
●●
●
● ●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●● ●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
● ● ●
●●
●
●
●
●
●
●
●
●
●
●
●
●
-20 -15 -10
-50
5
A = log2( Liver NL Kidney NK)
M=
log 2
(Liv
erN
L)-
log 2
(Kid
ney
NK)
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●●
● ●
●
●●
●
●
●
●
●●
●
●●●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●●●
●● ●
●
●
●
●
●
●
●
●●
●●
●
●
● ●
●
●
●
●
●
●
●●●
●
●
●
●
●●
●
●
●
●
●●
●●
●
●
●
●●
● ●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●●
●
●
●
● ●
●●
● ●
●
●
●
●
●
●●
●
●
●
●●
●●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
● ●●
●
●
●
●
●●
●
●●
●
●●
●●
●
●
●
●
●
● ●
●
●
●●
●
●●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
● ●
●
●
●
●
●
●
●●
●
●
●●
●
●
●●
●
●
●
●
●
●
Housekeeping genesUnique to a sample
(c)
![Page 39: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/39.jpg)
Sta6s6caltes6ngforDE
• ForEACHGENE,isthemeanexpressionlevelforthegeneunderonecondi6onsignificantlydifferentfromthemeanexpressionlevelunderadifferentcondi6on?
39
TagID A1 A2 A3 B1 B2 B2ENSG00000124208 478 619 559 4830 7165 6651
ENSG00000182463 27 20 18 48 55 56
ENSG00000125835 132 290 450 560 408 266ENSG00000125834 320 462 355 131 99 91ENSG00000197818 21 29 23 52 44 65
… …tensofthousandsmoretags…
![Page 40: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/40.jpg)
Samplingreadsfrompopula6onofDNAfragmentis(approx.)mul2nomial
• Take sample • Sequence DNA
Library 1
Feature 1 λ1 Feature 2 λ2 Feature 3 λ3 Feature 4 λ4 Feature 5 λ5 Feature 6 λ6 …
DNA population
![Page 41: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/41.jpg)
For a single gene, it’s a coin toss, i.e. Binomial
Library 1
… feature i λi …
Yi ~ Binomial( M, λi ) Yi - observed number of reads for feature i M - total number of sequences λi - proportion Large M, small λi à approximated well by Poisson( μi = M�λi )
![Page 42: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/42.jpg)
42
ASmallRNA-SeqExperiment(TechReps)
Condi6onA Condi6onB
λg1 λg2 λg3 λg4
yg1 yg2 yg3 yg4
Genesg=1,…,30k
M1
M2M3 M4
E(ygi)=MiλgiReadsMi≈20million
![Page 43: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/43.jpg)
TrueTechnicalRepsShowPoissonVaria6onforEachGene
Data:Marionietal.,GenomeRes,2008 43
DavisMcCarthy
![Page 44: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/44.jpg)
44
ASmallRNA-SeqExperiment(BiologicalReps)
Condi6onA Condi6onB
λg1 λg2 λg3 λg4
yg1 yg2 yg3 yg4
Genesg=1,…,30k
M1
M2M3 M4
E(ygi)=MiλgiReadsMi≈20million
DavisMcCarthy
![Page 45: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/45.jpg)
BiologicalReplicateDatashowsQuadra6cMean-VarianceRela6onship
(developmentcycleofslimemould,2samplesathr00,&2athr04)
binnedvariance,samplevariance
Data:Parikhetal,GenomeBiology,2010
45DavisMcCarthy
![Page 46: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/46.jpg)
Manydifferentsta6s6calmethods• Modelthecountsdirectly
– Nega6vebinomialmodellingisbestbecauseitcapturesbiologicalaswellastechnicalvariability
– MostpopularpackagesinR• edgeR• DESeq/DESeq2• Lotsofothersexist(baySeq,NBPSeq,…)
• Transformthecountsandusednormalbasedmethods– Voom+limma
![Page 47: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/47.jpg)
Sta6s6caltes6nggiveseachgeneap-valueforevidenceofDE
TagID P-valueENSG00000124208 0.0002
ENSG00000182463 0.12
ENSG00000125835 0.34
ENSG00000125834 0.08
ENSG00000197818 0.64
ENSG00000125831 1
ENSG00000215443 1
ENSG00000222008 0.06
ENSG00000101444 0.73
ENSG00000101333 0.22
… …tensofthousandsmoretags…
TagID A1 A2 A3 B1 B2 B2ENSG00000124208 478 619 559 4830 7165 6651ENSG00000182463 27 20 18 48 55 36ENSG00000125835 132 290 450 560 408 266ENSG00000125834 320 462 355 131 99 91ENSG00000197818 21 29 23 52 44 65ENSG00000125831 0 0 0 0 0 0ENSG00000215443 4 4 4 9 7 3ENSG00000222008 30 23 23 0 0 0ENSG00000101444 46 63 55 54 53 52ENSG00000101333 2256 2793 2931 2702 2976 2226
… …tensofthousandsmoretags…
![Page 48: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/48.jpg)
RNA-seqanalysisstepsRawsequencereads
Mapontogenome
Summarizereadstotranscripts
Sta6s6caltes6ng:Determinedifferen6allyexpressedgenes
Systemsbiology
DenovoassemblyAnnota6onbased Genomeguidedassembly
Whichtranscriptome?
![Page 49: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/49.jpg)
RNA-seqanalysisstepsRawsequencereads
Mapontogenome
Summarizereadstotranscripts
Sta6s6caltes6ng:Determinedifferen6allyexpressedgenes
Systemsbiology
DenovoassemblyAnnota6onbased Genomeguidedassembly
Whichtranscriptome?
Learnsomething!
![Page 50: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/50.jpg)
MovingbeyondDifferen6alExpression
![Page 51: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/51.jpg)
Findingfusiongenesincancer
• Genomicsbreaksandrearrangementscanleadtogenefusions• Somefusionsareoncogenic,otherarejustbystanders.• Iden6fyingoncogenicgenefusionsisbeneficialfor
• ClinicalTreatmentse.g.• BCR-ABLfusionin95%ofCMLsImaAnib
![Page 52: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/52.jpg)
• Transcriptomesofanyorganismscanbesequencedandanalysed
Non-modelorganisms
Blackwidowvenomtranscriptome
Desertpoplartranscriptomeinsalinecondi6ons
![Page 53: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/53.jpg)
Exploringthehumantranscriptome
Mostgeneshavemorethanoneexpressedisoform Mostgenehaveonemajorisoform
![Page 54: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/54.jpg)
Unknownandrareeventsinthehumantranscriptome
• ENCODEsays–75%ofthegenomeistranscribed
![Page 55: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/55.jpg)
Non-canonicalRNAstructuresCircularRNAs
Intronreten6on
Memczaketal.Nature,2013
Wongetal.Cell,2013
![Page 56: RNA-seq analysis - Bioinformaticsbioinformatics.org.au/ws/wp-content/uploads/sites/... · Collaborave analysis and methods development Transcriptomics Epigenomics Genomics Clinical](https://reader034.vdocuments.pub/reader034/viewer/2022042606/5f85c58880bfba6a2001452d/html5/thumbnails/56.jpg)
Thefuture
• Analysismethodologyiscri6calands6lldevelopingforspecificpurposes
• Effec6velydealingwithnogenomeorpoorqualitygenomesorcancer
• Integra6ngRNA-seqdatawithothergenomicsdata
• Opportuni6estousethisdatainnewandimagina6veways–requiresnewanalysismethodology