{"id":"https://openalex.org/W3028385587","doi":"https://doi.org/10.1109/tkde.2020.2995195","title":"Enhanced Discrete Multi-Modal Hashing: More Constraints Yet Less Time to Learn","display_name":"Enhanced Discrete Multi-Modal Hashing: More Constraints Yet Less Time to Learn","publication_year":2020,"publication_date":"2020-05-18","ids":{"openalex":"https://openalex.org/W3028385587","doi":"https://doi.org/10.1109/tkde.2020.2995195","mag":"3028385587"},"language":"en","primary_location":{"id":"doi:10.1109/tkde.2020.2995195","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tkde.2020.2995195","pdf_url":null,"source":{"id":"https://openalex.org/S30698027","display_name":"IEEE Transactions on Knowledge and Data Engineering","issn_l":"1041-4347","issn":["1041-4347","1558-2191","2326-3865"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Knowledge and Data Engineering","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100630707","display_name":"Yong Chen","orcid":"https://orcid.org/0000-0002-1348-9218"},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yong Chen","raw_affiliation_strings":["Key Lab of Machine Perception, School of Electronics Engineering and Computer Science, Peking University, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0002-1348-9218","affiliations":[{"raw_affiliation_string":"Key Lab of Machine Perception, School of Electronics Engineering and Computer Science, Peking University, Beijing, China","institution_ids":["https://openalex.org/I20231570"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100323546","display_name":"Hui Zhang","orcid":"https://orcid.org/0000-0003-2569-1824"},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hui Zhang","raw_affiliation_strings":["Department of Computer Science and Engineering, Beihang University, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0003-2569-1824","affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, Beihang University, Beijing, China","institution_ids":["https://openalex.org/I82880672"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010035288","display_name":"Zhibao Tian","orcid":null},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhibao Tian","raw_affiliation_strings":["Department of Computer Science and Engineering, Beihang University, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, Beihang University, Beijing, China","institution_ids":["https://openalex.org/I82880672"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100384767","display_name":"Jun Wang","orcid":"https://orcid.org/0000-0002-5890-0365"},"institutions":[{"id":"https://openalex.org/I45129253","display_name":"University College London","ror":"https://ror.org/02jx3x895","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I45129253"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Jun Wang","raw_affiliation_strings":["University College London, London, U.K"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University College London, London, U.K","institution_ids":["https://openalex.org/I45129253"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015784640","display_name":"Dell Zhang","orcid":"https://orcid.org/0000-0002-8774-3725"},"institutions":[{"id":"https://openalex.org/I3163766975","display_name":"Blue Cross and Blue Shield of Kansas City","ror":"https://ror.org/05eatzc79","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I3163766975"]},{"id":"https://openalex.org/I98259816","display_name":"Birkbeck, University of London","ror":"https://ror.org/02mb95055","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I98259816"]}],"countries":["GB","US"],"is_corresponding":false,"raw_author_name":"Dell Zhang","raw_affiliation_strings":["Birkbeck, University of London, London, United Kingdom","Blue Prism AI Labs, London, U.K"],"raw_orcid":"https://orcid.org/0000-0002-8774-3725","affiliations":[{"raw_affiliation_string":"Birkbeck, University of London, London, United Kingdom","institution_ids":["https://openalex.org/I98259816"]},{"raw_affiliation_string":"Blue Prism AI Labs, London, U.K","institution_ids":["https://openalex.org/I3163766975"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5106943753","display_name":"Xuelong Li","orcid":"https://orcid.org/0000-0003-2924-946X"},"institutions":[{"id":"https://openalex.org/I17145004","display_name":"Northwestern Polytechnical University","ror":"https://ror.org/01y0j0j86","country_code":"CN","type":"education","lineage":["https://openalex.org/I17145004"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xuelong Li","raw_affiliation_strings":["School of Computer Science and Center for OPTical IMagery Analysis and Learning (OPTIMAL), Northwestern Polytechnical University, Xi&#x0027;an, China","School of Computer Science and Center for OPTical IMagery Analysis and Learning (OPTIMAL), Northwestern Polytechnical University, Xi&#x0027","an, China"],"raw_orcid":"https://orcid.org/0000-0003-2924-946X","affiliations":[{"raw_affiliation_string":"School of Computer Science and Center for OPTical IMagery Analysis and Learning (OPTIMAL), Northwestern Polytechnical University, Xi&#x0027;an, China","institution_ids":["https://openalex.org/I17145004"]},{"raw_affiliation_string":"School of Computer Science and Center for OPTical IMagery Analysis and Learning (OPTIMAL), Northwestern Polytechnical University, Xi&#x0027","institution_ids":["https://openalex.org/I17145004"]},{"raw_affiliation_string":"an, China","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2045,"currency":"USD","value_usd":2045},"apc_paid":null,"fwci":1.3998,"has_fulltext":false,"cited_by_count":50,"citation_normalized_percentile":{"value":0.81588922,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":100},"biblio":{"volume":"34","issue":"3","first_page":"1177","last_page":"1190"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10627","display_name":"Advanced Image and Video Retrieval Techniques","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10627","display_name":"Advanced Image and Video Retrieval Techniques","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11714","display_name":"Multimodal Machine Learning Applications","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10824","display_name":"Image Retrieval and Classification Techniques","score":0.9922999739646912,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7971464395523071},{"id":"https://openalex.org/keywords/hash-function","display_name":"Hash function","score":0.7275658249855042},{"id":"https://openalex.org/keywords/discrete-optimization","display_name":"Discrete optimization","score":0.6163970232009888},{"id":"https://openalex.org/keywords/dynamic-perfect-hashing","display_name":"Dynamic perfect hashing","score":0.5967340469360352},{"id":"https://openalex.org/keywords/k-independent-hashing","display_name":"K-independent hashing","score":0.5452103018760681},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.5372459888458252},{"id":"https://openalex.org/keywords/binary-code","display_name":"Binary code","score":0.5336970090866089},{"id":"https://openalex.org/keywords/modal","display_name":"Modal","score":0.5322465896606445},{"id":"https://openalex.org/keywords/universal-hashing","display_name":"Universal hashing","score":0.516704797744751},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4806865155696869},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4205717146396637},{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.4162999391555786},{"id":"https://openalex.org/keywords/hash-table","display_name":"Hash table","score":0.3974728584289551},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.3530772030353546},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.3441394567489624},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.3369382619857788},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3222932815551758},{"id":"https://openalex.org/keywords/double-hashing","display_name":"Double hashing","score":0.26458990573883057},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.1302613615989685},{"id":"https://openalex.org/keywords/database","display_name":"Database","score":0.08946889638900757}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7971464395523071},{"id":"https://openalex.org/C99138194","wikidata":"https://www.wikidata.org/wiki/Q183427","display_name":"Hash function","level":2,"score":0.7275658249855042},{"id":"https://openalex.org/C145671259","wikidata":"https://www.wikidata.org/wiki/Q1493786","display_name":"Discrete optimization","level":3,"score":0.6163970232009888},{"id":"https://openalex.org/C122907437","wikidata":"https://www.wikidata.org/wiki/Q5318999","display_name":"Dynamic perfect hashing","level":5,"score":0.5967340469360352},{"id":"https://openalex.org/C187062812","wikidata":"https://www.wikidata.org/wiki/Q6322840","display_name":"K-independent hashing","level":5,"score":0.5452103018760681},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.5372459888458252},{"id":"https://openalex.org/C63435697","wikidata":"https://www.wikidata.org/wiki/Q864135","display_name":"Binary code","level":3,"score":0.5336970090866089},{"id":"https://openalex.org/C71139939","wikidata":"https://www.wikidata.org/wiki/Q910194","display_name":"Modal","level":2,"score":0.5322465896606445},{"id":"https://openalex.org/C116058348","wikidata":"https://www.wikidata.org/wiki/Q846912","display_name":"Universal hashing","level":5,"score":0.516704797744751},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4806865155696869},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4205717146396637},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.4162999391555786},{"id":"https://openalex.org/C67388219","wikidata":"https://www.wikidata.org/wiki/Q207440","display_name":"Hash table","level":3,"score":0.3974728584289551},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.3530772030353546},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.3441394567489624},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.3369382619857788},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3222932815551758},{"id":"https://openalex.org/C138111711","wikidata":"https://www.wikidata.org/wiki/Q478351","display_name":"Double hashing","level":4,"score":0.26458990573883057},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.1302613615989685},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.08946889638900757},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C188027245","wikidata":"https://www.wikidata.org/wiki/Q750446","display_name":"Polymer chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tkde.2020.2995195","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tkde.2020.2995195","pdf_url":null,"source":{"id":"https://openalex.org/S30698027","display_name":"IEEE Transactions on Knowledge and Data Engineering","issn_l":"1041-4347","issn":["1041-4347","1558-2191","2326-3865"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Knowledge and Data Engineering","raw_type":"journal-article"},{"id":"pmh:oai:eprints.bbk.ac.uk.oai2:31815","is_oa":false,"landing_page_url":"https://eprints.bbk.ac.uk/id/eprint/31815/1/tkde_edmh.pdf","pdf_url":"https://eprints.bbk.ac.uk/id/eprint/31815/1/tkde_edmh.pdf","source":{"id":"https://openalex.org/S4306400465","display_name":"BIROn (Birkbeck, University of London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I98259816","host_organization_name":"Birkbeck, University of London","host_organization_lineage":["https://openalex.org/I98259816"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G249233655","display_name":null,"funder_award_id":"2017YFB1400200","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G5911077673","display_name":null,"funder_award_id":"8206300295","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320321543","display_name":"China Postdoctoral Science Foundation","ror":"https://ror.org/0426zh255"},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":65,"referenced_works":["https://openalex.org/W1835419070","https://openalex.org/W1910300841","https://openalex.org/W1922199343","https://openalex.org/W1934863104","https://openalex.org/W1970055505","https://openalex.org/W1976258951","https://openalex.org/W2007972815","https://openalex.org/W2015175493","https://openalex.org/W2022398331","https://openalex.org/W2049993534","https://openalex.org/W2063049279","https://openalex.org/W2067766814","https://openalex.org/W2070753207","https://openalex.org/W2071207147","https://openalex.org/W2079666190","https://openalex.org/W2086958058","https://openalex.org/W2090836891","https://openalex.org/W2106277773","https://openalex.org/W2149414429","https://openalex.org/W2155803963","https://openalex.org/W2164530430","https://openalex.org/W2203543769","https://openalex.org/W2240204456","https://openalex.org/W2266728343","https://openalex.org/W2388114291","https://openalex.org/W2510911086","https://openalex.org/W2512032049","https://openalex.org/W2522148122","https://openalex.org/W2591669147","https://openalex.org/W2593190442","https://openalex.org/W2594227027","https://openalex.org/W2604880013","https://openalex.org/W2740755807","https://openalex.org/W2747853580","https://openalex.org/W2748725735","https://openalex.org/W2749145308","https://openalex.org/W2756077905","https://openalex.org/W2765440071","https://openalex.org/W2781821509","https://openalex.org/W2788843501","https://openalex.org/W2795832645","https://openalex.org/W2808301810","https://openalex.org/W2808341985","https://openalex.org/W2809191921","https://openalex.org/W2891193211","https://openalex.org/W2896038883","https://openalex.org/W2897841402","https://openalex.org/W2907166662","https://openalex.org/W2956335072","https://openalex.org/W2962933664","https://openalex.org/W2962955826","https://openalex.org/W2963187862","https://openalex.org/W2967957126","https://openalex.org/W2999412666","https://openalex.org/W3003735286","https://openalex.org/W3103717910","https://openalex.org/W4231510805","https://openalex.org/W4292363360","https://openalex.org/W6608183366","https://openalex.org/W6629956336","https://openalex.org/W6681077227","https://openalex.org/W6683120131","https://openalex.org/W6688759320","https://openalex.org/W6693399182","https://openalex.org/W6697214482"],"related_works":["https://openalex.org/W4385382899","https://openalex.org/W1481411695","https://openalex.org/W4386271002","https://openalex.org/W2480775723","https://openalex.org/W2292992741","https://openalex.org/W2142881874","https://openalex.org/W2207555655","https://openalex.org/W4212830455","https://openalex.org/W1992777851","https://openalex.org/W3006955796"],"abstract_inverted_index":{"Due":[0],"to":[1,14,56,68,150,206],"the":[2,28,35,45,84,118,125,130,140,160,185],"exponential":[3],"growth":[4],"of":[5,27,88,122,132,162,173,187,217],"multimedia":[6],"data,":[7,123],"multi-modal":[8,30,63,144],"hashing":[9,31,64,114],"as":[10,50,83],"a":[11,51,60,100,135,152,171],"promising":[12],"technique":[13],"make":[15],"cross-view":[16],"retrieval":[17,208],"scalable":[18],"is":[19],"attracting":[20],"more":[21,23,137],"and":[22,86,113,193],"attention.":[24],"However,":[25],"most":[26,216],"existing":[29],"methods":[32,65],"either":[33],"divide":[34],"learning":[36,155],"process":[37],"unnaturally":[38],"into":[39],"two":[40],"separate":[41],"stages":[42],"or":[43],"treat":[44],"discrete":[46,62,80,127,191],"optimization":[47,164],"problem":[48],"simplistically":[49],"continuous":[52],"one,":[53],"which":[54,109],"leads":[55],"suboptimal":[57],"results.":[58],"Recently,":[59],"few":[61],"that":[66,195],"try":[67],"address":[69],"such":[70],"issues":[71],"have":[72,166,183],"emerged,":[73],"but":[74,210],"they":[75],"still":[76],"ignore":[77],"several":[78,207],"important":[79],"constraints":[81,192],"(such":[82],"balance":[85],"decorrelation":[87],"hash":[89],"bits).":[90],"In":[91],"this":[92],"paper,":[93],"we":[94,146],"overcome":[95],"those":[96,188],"limitations":[97],"by":[98],"proposing":[99],"novel":[101],"method":[102],"named":[103],"\u201cEnhanced":[104],"Discrete":[105],"Multi-modal":[106],"Hashing":[107],"(EDMH)\u201d":[108],"learns":[110],"binary":[111],"codes":[112],"functions":[115],"simultaneously":[116],"from":[117],"pairwise":[119],"similarity":[120],"matrix":[121],"under":[124],"aforementioned":[126],"constraints.":[128],"Although":[129],"model":[131],"EDMH":[133,196],"looks":[134],"lot":[136],"complex":[138],"than":[139,202,215],"other":[141],"models":[142],"for":[143,157],"hashing,":[145],"are":[147],"actually":[148],"able":[149],"develop":[151],"fast":[153],"iterative":[154],"algorithm":[156],"it,":[158],"since":[159],"subproblems":[161],"its":[163],"all":[165],"closed-form":[167],"solutions":[168],"after":[169],"introducing":[170],"couple":[172],"auxiliary":[174],"variables.":[175],"Our":[176],"experimental":[177],"results":[178],"on":[179],"three":[180],"real-world":[181],"datasets":[182],"revealed":[184],"usefulness":[186],"previously":[189],"ignored":[190],"demonstrated":[194],"not":[197],"only":[198],"performs":[199],"much":[200,213],"better":[201],"state-of-the-art":[203],"competitors":[204],"according":[205],"metrics":[209],"also":[211],"runs":[212],"faster":[214],"them.":[218]},"counts_by_year":[{"year":2026,"cited_by_count":8},{"year":2025,"cited_by_count":14},{"year":2024,"cited_by_count":14},{"year":2023,"cited_by_count":9},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-08-28T12:50:07.497085","created_date":"2025-10-10T00:00:00"}
