{"id":6124,"date":"2026-06-18T12:21:20","date_gmt":"2026-06-18T12:21:20","guid":{"rendered":"https:\/\/cloudsave.app\/knowledge-base\/calculate-rto-and-rpo-databases\/"},"modified":"2026-06-18T12:46:32","modified_gmt":"2026-06-18T12:46:32","slug":"rto-un-rpo-apr%c4%93%c4%b7in%c4%81%c5%a1ana-kritiski-svar%c4%abg%c4%81m-datub%c4%81z%c4%93m-dba-rokasgr%c4%81mata","status":"publish","type":"post","link":"https:\/\/cloudsave.app\/lv\/knowledge-base\/rto-un-rpo-apr%c4%93%c4%b7in%c4%81%c5%a1ana-kritiski-svar%c4%abg%c4%81m-datub%c4%81z%c4%93m-dba-rokasgr%c4%81mata\/","title":{"rendered":"RTO un RPO apr\u0113\u0137in\u0101\u0161ana kritiski svar\u012bg\u0101m datub\u0101z\u0113m: DBA rokasgr\u0101mata"},"content":{"rendered":"<p>DevOps in\u017eenieriem, datub\u0101\u017eu administratoriem (DBA) un IT sist\u0113mu arhitektiem atjauno\u0161anas laika m\u0113r\u0137is (RTO) un atjauno\u0161anas punkta m\u0113r\u0137is (RPO) ir kas vair\u0101k nek\u0101 tikai biznesa nep\u0101rtraukt\u012bbas \u017eargons \u2014 tie ir stingri in\u017eeniertehniskie ierobe\u017eojumi. P\u0101rvaldot kritiski svar\u012bgas datub\u0101zes, nesp\u0113ja prec\u012bzi apr\u0113\u0137in\u0101t, izstr\u0101d\u0101t arhitekt\u016bru un valid\u0113t \u0161os r\u0101d\u012bt\u0101jus var izrais\u012bt katastrof\u0101lu datu zudumu un ilgsto\u0161u d\u012bkst\u0101vi.<\/p>\n<p>M\u016bsdienu uz\u0146\u0113mumu vid\u0113s RTO un RPO apr\u0113\u0137in\u0101\u0161anai ir nepiecie\u0161ama padzi\u013cin\u0101ta izpratne par datub\u0101zes iek\u0161\u0113jo darb\u012bbu, kr\u0101tuves I\/O, t\u012bkla caurlaidsp\u0113ju un transakciju \u017eurn\u0101lu meh\u0101niku. \u0160aj\u0101 rokasgr\u0101mat\u0101 ir apl\u016bkotas tehnisk\u0101s metodolo\u0123ijas RTO un RPO apr\u0113\u0137in\u0101\u0161anai, test\u0113\u0161anai un optimiz\u0113\u0161anai ra\u017eo\u0161anas datub\u0101\u017eu sist\u0113m\u0101m.<\/p>\n<h2>RPO (atjauno\u0161anas punkta m\u0113r\u0137a) dekonstrukcija datub\u0101\u017eu sist\u0113m\u0101s<\/h2>\n<p>RPO nosaka maksim\u0101lo pie\u013caujamo datu zuduma apjomu, kas m\u0113r\u012bts laik\u0101. Ja j\u016bsu RPO ir 15 min\u016btes, katastrofa, kas notiek plkst. 12:00, noz\u012bm\u0113, ka jums ir j\u0101sp\u0113j atjaunot visas apstiprin\u0101t\u0101s transakcijas vismaz l\u012bdz plkst. 11:45.<\/p>\n<p>Datub\u0101z\u0113m RPO nosaka j\u016bsu transakciju \u017eurn\u0101lu p\u0101rvald\u012bbas strat\u0113\u0123ija (WAL PostgreSQL, Redo \u017eurn\u0101li Oracle, transakciju \u017eurn\u0101li SQL Server).<\/p>\n<h3>Datu zuduma un \u017eurn\u0101lu \u0123ener\u0113\u0161anas meh\u0101nika<\/h3>\n<p>Lai apr\u0113\u0137in\u0101tu sasniedzamo RPO, vispirms ir j\u0101saprot j\u016bsu datub\u0101zes transakciju \u017eurn\u0101lu \u0123ener\u0113\u0161anas \u0101trums. Ja j\u016bs s\u016bt\u0101t \u017eurn\u0101lus uz rezerves kopiju repozitoriju ik p\u0113c 15 min\u016bt\u0113m, bet j\u016bsu t\u012bkls nesp\u0113j p\u0101rs\u016bt\u012bt 15 min\u016b\u0161u \u017eurn\u0101lus \u0161aj\u0101 log\u0101, j\u016bsu faktiskais RPO past\u0101v\u012bgi pasliktin\u0101sies.<\/p>\n<p>J\u016bs varat noteikt \u017eurn\u0101lu \u0123ener\u0113\u0161anas \u0101truma b\u0101zes l\u012bniju, izmantojot SQL komandas. Piem\u0113ram, PostgreSQL (versija 10+) varat izm\u0113r\u012bt Write-Ahead Log (WAL) \u0123ener\u0113\u0161anas \u0101trumu noteikt\u0101 interv\u0101l\u0101:<\/p>\n<pre><code class=\"language-sql\">-- Izpildiet \u0161o pie T=0\nSELECT pg_current_wal_lsn() AS start_lsn;\n\n-- Pagaidiet tie\u0161i 5 min\u016btes (300 sekundes), tad izpildiet:\nSELECT pg_current_wal_lsn() AS end_lsn,\n       pg_size_pretty(pg_wal_lsn_diff(pg_current_wal_lsn(), 'START_LSN_VALUE')) AS wal_generated_size,\n       pg_wal_lsn_diff(pg_current_wal_lsn(), 'START_LSN_VALUE') \/ 300 AS bytes_per_second;\n<\/code><\/pre>\n<p>Ja \u0161is vaic\u0101jums atkl\u0101j, ka maksim\u0101l\u0101s slodzes laik\u0101 j\u016bs \u0123ener\u0113jat 50 MB\/s WAL datu, 15 min\u016b\u0161u RPO prasa p\u0101rs\u016bt\u012bt 45 GB \u017eurn\u0101lu datu uz j\u016bsu rezerves kr\u0101tuvi. J\u016bsu t\u012bklam un kr\u0101tuves m\u0113r\u0137iem ir j\u0101atbalsta past\u0101v\u012bgs rakst\u012b\u0161anas \u0101trums, kas p\u0101rsniedz 50 MB\/s, lai saglab\u0101tu \u0161o RPO.<\/p>\n<h3>Sinhron\u0101s un asinhron\u0101s replik\u0101cijas ietekme<\/h3>\n<p>Daudzi DBA pa\u013caujas uz augstas pieejam\u012bbas (HA) replik\u0101ciju, lai izpild\u012btu RPO. Tom\u0113r replik\u0101cija nav rezerves kopija. Izdz\u0113sta tabula (<code>DROP TABLE users;<\/code>) tiek replic\u0113ta acumirkl\u012b.<\/p>\n<p>Izmantojot replik\u0101ciju katastrofu atkop\u0161anai (DR), replik\u0101cijas re\u017e\u012bms tie\u0161i ietekm\u0113 RPO:<br \/>\n*   <strong>Sinhron\u0101 replik\u0101cija:<\/strong> Garant\u0113 nulles RPO (RPO=0). Prim\u0101r\u0101 datub\u0101ze neapstiprin\u0101s transakciju, kam\u0113r gaidst\u0101ves (standby) datub\u0101ze neapstiprin\u0101s t\u0101s sa\u0146em\u0161anu. Kompromiss ir palielin\u0101ta latentuma pak\u0101pe prim\u0101raj\u0101s rakst\u012b\u0161anas oper\u0101cij\u0101s.<br \/>\n*   <strong>Asinhron\u0101 replik\u0101cija:<\/strong> Ievie\u0161 replik\u0101cijas aizkavi. J\u016bsu RPO faktiski ir vien\u0101ds ar j\u016bsu pa\u0161reiz\u0113jo replik\u0101cijas aizkavi.<\/p>\n<p>Lai uzraudz\u012btu asinhron\u0101s replik\u0101cijas aizkavi PostgreSQL, izmantojiet:<\/p>\n<pre><code class=\"language-sql\">SELECT application_name,\n       client_addr,\n       state,\n       sync_state,\n       pg_wal_lsn_diff(pg_current_wal_lsn(), replay_lsn) AS replication_lag_bytes\nFROM pg_stat_replication;\n<\/code><\/pre>\n<h2>RTO (atjauno\u0161anas laika m\u0113r\u0137a) dekonstrukcija liela m\u0113roga datub\u0101z\u0113m<\/h2>\n<p>RTO ir maksim\u0101lais pie\u013caujamais d\u012bkst\u0101ves ilgums. Datub\u0101zes RTO apr\u0113\u0137in\u0101\u0161ana ir \u013coti sare\u017e\u0123\u012bta, jo tas nav tikai laiks, kas nepiecie\u0161ams failu kop\u0113\u0161anai atpaka\u013c uz serveri.<\/p>\n<h3>RTO apr\u0113\u0137in\u0101\u0161anas matem\u0101tiskais modelis<\/h3>\n<p>Re\u0101listisk\u0101 datub\u0101zes RTO apr\u0113\u0137in\u0101 ir j\u0101\u0146em v\u0113r\u0101 \u010detras at\u0161\u0137ir\u012bgas f\u0101zes:<\/p>\n<p><strong>RTO = T(infra) + T(transfer) + T(restore) + T(recovery)<\/strong><\/p>\n<ol>\n<li><strong>T(infra) \u2013 Infrastrukt\u016bras nodro\u0161in\u0101\u0161ana:<\/strong> Laiks, lai iedarbin\u0101tu aizst\u0101j\u0113jresursus un kr\u0101tuvi. (Var b\u016bt tuvu nullei ar iepriek\u0161 nodro\u0161in\u0101t\u0101m DR vietn\u0113m vai Infrastructure-as-Code cauru\u013cvadiem).<\/li>\n<li><strong>T(transfer) \u2013 Datu p\u0101rs\u016bt\u012b\u0161ana:<\/strong> Laiks, lai p\u0101rvietotu rezerves kopijas datus no repozitorija uz datub\u0101zes serveri.<\/li>\n<li><strong>T(restore) \u2013 Fizisk\u0101 atjauno\u0161ana:<\/strong> Laiks, lai ierakst\u012btu datu failus m\u0113r\u0137a disk\u0101.<\/li>\n<li><strong>T(recovery) \u2013 Datub\u0101zes av\u0101rijas atkop\u0161ana:<\/strong> Laiks, kas nepiecie\u0161ams datub\u0101zes dzin\u0113jam, lai atk\u0101rtoti atska\u0146otu transakciju \u017eurn\u0101lus, veiktu apstiprin\u0101to transakciju izpildi un atceltu neapstiprin\u0101t\u0101s.<\/li>\n<\/ol>\n<h3>P\u0101rs\u016bt\u012b\u0161anas un atjauno\u0161anas laiku apr\u0113\u0137in\u0101\u0161ana<\/h3>\n<p>Lai apr\u0113\u0137in\u0101tu <code>T(transfer)<\/code> un <code>T(restore)<\/code>, jums ir j\u0101nosaka sava t\u012bkla joslas platuma un diska IOPS\/caurlaidsp\u0113jas b\u0101zes l\u012bnija. Nepa\u013caujieties uz teor\u0113tiskajiem maksimumiem; p\u0101rbaudiet savu faktisko infrastrukt\u016bru.<\/p>\n<p>Izmantojiet <code>iperf3<\/code>, lai p\u0101rbaud\u012btu t\u012bkla caurlaidsp\u0113ju starp j\u016bsu rezerves kopiju repozitoriju un datub\u0101zes serveri:<\/p>\n<pre><code class=\"language-bash\"># Rezerves kopiju repozitorij\u0101 (server\u012b)\niperf3 -s\n\n# Datub\u0101zes server\u012b (klient\u0101)\niperf3 -c &lt;backup_repo_ip&gt; -t 60 -P 4\n<\/code><\/pre>\n<p>Izmantojiet <code>fio<\/code>, lai p\u0101rbaud\u012btu savu datub\u0101zes kr\u0101tuves s\u0113jumu sec\u012bg\u0101s rakst\u012b\u0161anas veiktsp\u0113ju, simul\u0113jot datub\u0101zes atjauno\u0161anas oper\u0101ciju:<\/p>\n<pre><code class=\"language-bash\">fio --name=restore_sim --ioengine=libaio --rw=write --bs=1M --size=10G --numjobs=4 --iodepth=32 --direct=1 --filename=\/var\/lib\/postgresql\/data\/testfile\n<\/code><\/pre>\n<p>Ja j\u016bsu datub\u0101ze ir 5 TB un j\u016bsu <code>fio<\/code> testi uzr\u0101da maksim\u0101lo past\u0101v\u012bgo rakst\u012b\u0161anas \u0101trumu 500 MB\/s, j\u016bsu absol\u016btais minim\u0101lais <code>T(restore)<\/code> ir aptuveni 2,8 stundas. Ja j\u016bsu biznesa SLA pieprasa 1 stundas RTO, tradicion\u0101l\u0101 straum\u0113\u0161anas atjauno\u0161ana neizdosies. Jums ir j\u0101maina sava arhitekt\u016bra uz kr\u0101tuves l\u012bme\u0146a momentuz\u0146\u0113mumiem vai bloku l\u012bme\u0146a replik\u0101ciju.<\/p>\n<h3>Sl\u0113ptais slazds: T(recovery)<\/h3>\n<p>Visbie\u017e\u0101k nepienov\u0113rt\u0113tais main\u012bgais ir <code>T(recovery)<\/code>. Ja atjaunojat ikned\u0113\u013cas pilno rezerves kopiju un jums ir j\u0101piem\u0113ro 6 dienu transakciju \u017eurn\u0101li, lai sasniegtu savu RPO, datub\u0101zes dzin\u0113jam ir sec\u012bgi j\u0101atska\u0146o katra transakcija.<\/p>\n<p>500 GB transakciju \u017eurn\u0101lu atska\u0146o\u0161ana var aiz\u0146emt stundas, ko b\u016btiski ierobe\u017eo vienas v\u012btnes CPU veiktsp\u0113ja un kr\u0101tuves IOPS. Lai samazin\u0101tu <code>T(recovery)<\/code>, palieliniet savu pilno vai diferenci\u0101lo rezerves kopiju bie\u017eumu.<\/p>\n<h2>At\u0161\u0137ir\u012bbu mazin\u0101\u0161ana: praktiski so\u013ci RTO un RPO valid\u0113\u0161anai<\/h2>\n<p>Teor\u0113tisk\u0101 RTO un RPO apr\u0113\u0137in\u0101\u0161ana ir tikai pirmais solis. Kritiski svar\u012bg\u0101m vid\u0113m ir nepiecie\u0161ama nep\u0101rtraukta valid\u0101cija.<\/p>\n<h3>1. solis: Ieviesiet nep\u0101rtrauktu arhiv\u0113\u0161anu<\/h3>\n<p>Lai sasniegtu zem min\u016btes RPO bez sinhron\u0101s replik\u0101cijas veiktsp\u0113jas samazin\u0101juma, ieviesiet nep\u0101rtrauktu \u017eurn\u0101lu arhiv\u0113\u0161anu. T\u0101 viet\u0101, lai gaid\u012btu, l\u012bdz \u017eurn\u0101la fails aizpild\u0101s (kas var aiz\u0146emt stundas zemas trafika periodos), piespiedu k\u0101rt\u0101 veiciet \u017eurn\u0101lu p\u0101rsl\u0113g\u0161anu regul\u0101ros interv\u0101los.<\/p>\n<p>SQL Server varat automatiz\u0113t bie\u017eas transakciju \u017eurn\u0101lu rezerves kopijas:<\/p>\n<pre><code class=\"language-sql\">BACKUP LOG [MissionCriticalDB] \nTO DISK = N'\\BackupRepoSQLMissionCriticalDB_Log.trn' \nWITH NOFORMAT, NOINIT, \nNAME = N'MissionCriticalDB-Transaction Log Backup', \nSKIP, NOREWIND, NOUNLOAD, COMPRESSION, STATS = 10;\n<\/code><\/pre>\n<p><em>Lab\u0101k\u0101 prakse:<\/em> Iepl\u0101nojiet \u0161o uzdevumu izpildei ik p\u0113c 1\u20135 min\u016bt\u0113m atkar\u012bb\u0101 no j\u016bsu RPO pras\u012bb\u0101m.<\/p>\n<h3>2. solis: Automatiz\u0113jiet atjauno\u0161anas test\u0113\u0161anu<\/h3>\n<p>Nep\u0101rbaud\u012bta rezerves kopija ir tikai teor\u0113tisks j\u0113dziens. Lai garant\u0113tu savu apr\u0113\u0137in\u0101to RTO, jums ir j\u0101veic automatiz\u0113ta atjauno\u0161anas test\u0113\u0161ana.<\/p>\n<p>Uz\u0146\u0113mumu rezerves kopiju platformas, piem\u0113ram, CloudSave, to vienk\u0101r\u0161o, nodro\u0161inot automatiz\u0113tu, izol\u0113tu atkop\u0161anas test\u0113\u0161anu. CloudSave var autom\u0101tiski iedarbin\u0101t smil\u0161kastes vidi, uzst\u0101d\u012bt jaun\u0101ko rezerves kopiju, veikt pilnu datub\u0101zes atkop\u0161anu un izpild\u012bt piel\u0101gotus valid\u0101cijas skriptus (piem\u0113ram, <code>DBCC CHECKDB<\/code> SQL Server), lai izm\u0113r\u012btu prec\u012bzu RTO un nodro\u0161in\u0101tu datu integrit\u0101ti. Tas p\u0101rv\u0113r\u0161 RTO no apr\u0113\u0137in\u0101ta min\u0113juma par pier\u0101d\u012btu, atskait\u0101mu r\u0101d\u012bt\u0101ju.<\/p>\n<h3>3. solis: Uzraugiet un br\u012bdiniet par SLA p\u0101rk\u0101pumiem<\/h3>\n<p>J\u016bsu uzraudz\u012bbas stakam (Prometheus, Datadog, Zabbix) ir akt\u012bvi j\u0101seko r\u0101d\u012bt\u0101jiem, kas apdraud j\u016bsu RTO\/RPO SLA. Br\u012bdin\u0101jumu noteikumi j\u0101konfigur\u0113 \u0161\u0101diem gad\u012bjumiem:<br \/>\n*   <strong>Rezerves kopiju uzdevumu k\u013c\u016bmes:<\/strong> T\u016bl\u012bt\u0113ji draudi RPO.<br \/>\n*   <strong>\u017durn\u0101lu s\u016bt\u012b\u0161anas latentums:<\/strong> Ja \u017eurn\u0101lu p\u0101rs\u016bt\u012b\u0161ana aiz\u0146em ilg\u0101ku laiku nek\u0101 \u0123ener\u0113\u0161anas interv\u0101ls.<br \/>\n*   <strong>Kr\u0101tuves IOPS ierobe\u017eo\u0161ana:<\/strong> M\u0101ko\u0146pakalpojumu sniedz\u0113ji (piem\u0113ram, AWS EBS) ierobe\u017eo IOPS, ja p\u0101rsniegti &#8220;burst&#8221; kred\u012bti, kas \u0101rk\u0101rtas situ\u0101cij\u0101 klusi izn\u012bcin\u0101s j\u016bsu RTO.<\/p>\n<h2>Datub\u0101zes rezerves kopiju arhitekt\u016bras optimiz\u0113\u0161ana, lai izpild\u012btu stingrus SLA<\/h2>\n<p>Kad matem\u0101tiskie apr\u0113\u0137ini atkl\u0101j, ka j\u016bsu pa\u0161reiz\u0113j\u0101 arhitekt\u016bra nesp\u0113j izpild\u012bt biznesa SLA, jums ir j\u0101optimiz\u0113 sava rezerves kopiju strat\u0113\u0123ija.<\/p>\n<h3>1. Izmantojiet bloku l\u012bme\u0146a inkrement\u0101l\u0101s rezerves kopijas<\/h3>\n<p>Tradicion\u0101l\u0101s datub\u0101\u017eu izg\u0101ztuves (lo\u0123isk\u0101s rezerves kopijas, piem\u0113ram, <code>pg_dump<\/code> vai <code>mysqldump<\/code>) ir p\u0101r\u0101k l\u0113nas kritiski svar\u012bgiem RTO. Izmantojiet fizisk\u0101s, bloku l\u012bme\u0146a rezerves kopijas. Bloku l\u012bme\u0146a inkrement\u0101l\u0101s rezerves kopijas kop\u0113 tikai tos diska blokus, kas ir main\u012bju\u0161ies kop\u0161 p\u0113d\u0113j\u0101s rezerves kopijas, b\u016btiski samazinot <code>T(transfer)<\/code> un t\u012bkla noslodzi.<\/p>\n<h3>2. Izmantojiet kr\u0101tuves momentuz\u0146\u0113mumus<\/h3>\n<p>Datub\u0101z\u0113m ar vair\u0101kiem terabaitiem, kur\u0101m nepiecie\u0161ams RTO, kas maz\u0101ks par 15 min\u016bt\u0113m, tradicion\u0101l\u0101 failu kop\u0113\u0161ana pa standarta t\u012bkliem ir fiziski neiesp\u0113jama. Integr\u0101cija ar SAN vai m\u0101ko\u0146a viet\u0113jiem kr\u0101tuves momentuz\u0146\u0113mumiem (piem\u0113ram, AWS EBS Snapshots, Pure Storage) \u013cauj pan\u0101kt gandr\u012bz t\u016bl\u012bt\u0113ju <code>T(restore)<\/code>. P\u0113c tam datub\u0101zes dzin\u0113jam ir j\u0101veic tikai av\u0101rijas atkop\u0161ana no momentuz\u0146\u0113muma.<\/p>\n<h3>3. Ieviesiet paral\u0113lismu<\/h3>\n<p>P\u0101rliecinieties, ka j\u016bsu rezerves kopiju un atjauno\u0161anas r\u012bki izmanto vair\u0101kv\u012bt\u0146u apstr\u0101di. Atjaunojot PostgreSQL datub\u0101zi, izmantojot <code>pgbackrest<\/code>, vai SQL Server datub\u0101zi, skaidri defin\u0113jiet paral\u0113los darba pavedienus, lai pies\u0101tin\u0101tu pieejamo t\u012bkla un diska joslas platumu.<\/p>\n<pre><code class=\"language-bash\"># Paral\u0113l\u0101s atjauno\u0161anas piem\u0113rs ar pgBackRest\npgbackrest --stanza=prod_db --process-max=8 restore\n<\/code><\/pre>\n<h2>Secin\u0101jums<\/h2>\n<p>RTO un RPO apr\u0113\u0137in\u0101\u0161ana kritiski svar\u012bg\u0101m datub\u0101z\u0113m ir r\u016bp\u012bgs sist\u0113mu in\u017eenierijas vingrin\u0101jums. Tas prasa, lai DBA p\u0101rsniegtu noklus\u0113juma rezerves kopiju konfigur\u0101cijas un matem\u0101tiski model\u0113tu savu kr\u0101tuves I\/O, t\u012bkla jaudu un datub\u0101zes atkop\u0161anas meh\u0101niku.<\/p>\n<p>Nosakot \u017eurn\u0101lu \u0123ener\u0113\u0161anas \u0101truma b\u0101zes l\u012bniju, izprotot at\u0161\u0137ir\u012bg\u0101s datub\u0101zes atkop\u0161anas f\u0101zes un ievie\u0161ot automatiz\u0113tu test\u0113\u0161anu, izmantojot stabilas platformas, piem\u0113ram, CloudSave, IT komandas var p\u0101rliecino\u0161i garant\u0113t savus katastrofu atkop\u0161anas SLA. Atcerieties: datub\u0101\u017eu administr\u0113\u0161anas jom\u0101 cer\u012bba nav strat\u0113\u0123ija, un nep\u0101rbaud\u012btas rezerves kopijas ir risks.<\/p>\n<blockquote>\n<p>Uzziniet, k\u0101 DevOps in\u017eenieri un DBA var prec\u012bzi apr\u0113\u0137in\u0101t, test\u0113t un optimiz\u0113t RTO un RPO kritiski svar\u012bg\u0101m datub\u0101z\u0113m, izmantojot uzlabotu atkop\u0161anas meh\u0101niku, CLI r\u012bkus un automatiz\u0113tu test\u0113\u0161anu.<\/p>\n<\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>**<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"rank_math_title":"Calculate RTO & RPO for Mission-Critical Databases","rank_math_description":"**","rank_math_focus_keyword":"calculate RTO and 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