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SHDTLOP1LOP2BLMTSHTI ITITzLOIIBYSOATIT BYSWEND TRTISHDTLOP1LOP2END TRTOSHDTLOP1LOP2END SHTI$reDR,(ZreVR,(ZSHTYTETETXITTEXTtdtx Search TreeswdfgUwdalwdesdwdxdwdy(nnm+wdpowdpfnnm-nnm+wdfowdffnnm-nnm+wdyowdyfnnm-nnm+wdzowdzfnnm-nnm+wdcowdcfnnm-nnl+wdlowdlfnnl-nndnnndnEND BYTXLOMI[END ITITLOIIBYSOATIT BYSWEND TRTISHDTLOP1LOP2END TRTOSHDTLOP1LOP2END SHMI*SHTIVreDRgreVRgSHTYTETE[TXITOTEXTCtdtxPart 3 Red/Black TreeswdfgUwdalwdesdwdxU}dwdyPnnpabypVwdpiwdpxwdpm@dwp1dwpldwprwdptwdpbdwdpwdwdphdwdpswdpnwdppwdpYwduMwdPfwdPz wdPlwdPc nnrtnnm+wdpowdpf@nnm-nnm+wdfowdffnnm-nnm+wdyowdyfnnm-nnm+wdzowdzfnnm-nnm+wdcowdcfnnm-nnl+wdlowdlfnnl-nndnnndnEND BYTXLOMI\END SNSS:SHIDSHMISHMO}SHTISHTO}BLRPBLBSLOVL@SHSIEND END SLSL%SHIDBYWTSHMISTNMSlide 1LOTMcBLSRCSCSSTNMGreenHACLffff3ff33ffffff33f3ff33fEND SHDTLOP1LOP2BLMTSHTI ITITLOIIBYSOATIT BYSWEND TRTISHDTLOP1LOP2END TRTOSHDTLOP1LOP2END SHTI$reDR,(ZreVR,(ZSHTYTETETXITTEXTtdtxModeling 2,3,4-TreeswdfgUwdalwdesdwdxdwdy(nnm+wdpowdpfnnm-nnm+wdfowdffnnm-nnm+wdyowdyfnnm-nnm+wdzowdzfnnm-nnm+wdcowdcfnnm-nnl+wdlowdlfnnl-nndnnndnEND BYTXLOMIYEND ITITLOIIBYSOATIT?BYFPCLFF BYLPCLLFLOWTLOLXLOLYBYSWEND pgIPSSUeUUUeUeU]U]UUUګ]UU]UeUreDRdUkreVRdUkSHTYEND ITITLOIIBYSOATIT?BYFPCLFF BYLPCLLF LOWTLOLXLOLYBYSWEND pgIPSSh8PUPUh82UUreDRT{$* reVRT{$* SHTYEND ITIThLOIIBYSOATIT BYSWEND reDRE!5reVRE!5SHTYTETE TXITTEXTtdtxORwdfgUwdalwdesdwdxdwdy`nncowdcidwcrnnrtnncowdcidwcrnnrtnncowdcidwcr33dwu1 nnrtnnm+wdpowdpfnnm-nnm+wdfowdffnnm-nnm+wdyowdyfnnm-nnm+wdzowdzfnnm-nnm+wdcowdcf@nnm-nnl+wdlowdlfnnl-nndnnndnEND BYTXEND ITITLOIIBYSOATIT\BYFPCLFF BYLPCLLF LOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDRoY s7reVRoY s7SHTYBYDREND ITIT[LOIIBYSOATITBYFPCLFF BYSWEND SLMGSHIDLOTM:ITITLOII BYSOATIT?BYFPCLFFfBYLPCLLFLOWTLOLXLOLYBYSWEND reDRò8reVRò8SHTYEND ITITLOII BYSOATIT\BYFPCLFF BYLPCLLFLOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDR.1reVR.1SHTYBYDREND ITITLOII BYSOATIT\BYFPCLFF BYLPCLLFLOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDRS/'UlxreVRS/'UlxSHTYEND ITITLOII BYSOATIT BYSWEND reDRreVRSHTYTETETXITTEXTwtdtx2wdfgUwdalwdesdwdxB/dwdyWnncowdcidwcrnnrtnncowdcidwcrnnrtnncowdcidwcrdwu1nnrtnnpabypVwdpiwdpxwdpmdwp1dwpldwprwdptwdpbdwdpwdwdphdwdpswdpnwdppwdpYwduMwdPfwdPz wdPlwdPc@nnrtnnm+wdpowdpf@nnm-nnm+wdfowdffnnm-nnm+wdyowdyfnnm-nnm+wdzowdzfnnm-nnm+wdcowdcfnnm-nnl+wdlowdlfnnl-nndnnndnEND BYTXEND END reDRU-UmUreVRU-UmUSHTY BYDREND ITITLOII BYSOATITBYFPCLFF BYSWEND SLMGLSHIDLOTM:ITITLOIIBYSOATIT?BYFPCLFFfBYLPCLLFffLOWTLOLXLOLYBYSWEND reDRsP"TreVRsP"TSHTYEND ITITLOIIBYSOATIT\BYFPCLFF BYLPCLLFffLOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDRA=zreVRA=zSHTYBYDREND ITITLOIIBYSOATIT\BYFPCLFF BYLPCLLFffLOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDRS4reVRS4SHTYEND ITITILOIIBYSOATIT BYSWEND reDRQƓreVRQƓSHTYTETETXITTEXTtdtx2wdfgUwdalwdesdwdxB/dwdyWnncowdcidwcrnnrtnncowdcidwcrnnrtnnm+wdpowdpfnnm-nnm+wdfowdffnnm-nnm+wdyowdyfnnm-nnm+wdzowdzfnnm-nnm+wdcowdcfnnm-nnl+wdlowdlfnnl-nndnnndnEND BYTXEND END reDRUB=UUreVRUB=UUSHTY BYDREND ITITLOIIBYSOATITBYFPCLFF BYSWEND SLMGHSHIDLOTM:ITITLOIIBYSOATIT?BYFPCLFFfBYLPCLLFffLOWTLOLXLOLYBYSWEND reDR! ϑreVR! ϑSHTYEND ITITLOIIBYSOATIT\BYFPCLFF BYLPCLLFffLOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDRr$reVRr$SHTYBYDREND ITITLOIIBYSOATIT\BYFPCLFF BYLPCLLFffLOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDRoreVRoSHTYEND ITITLOIIBYSOATIT\BYFPCLFF BYLPCLLFffLOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDRdZǧZreVRdZǧZSHTYEND ITITILOIIBYSOATIT BYSWEND reDR0J{$=LreVR0J{$=LSHTYTETETXITTEXTtdtx3wdfgUwdalwdesdwdx-dwdyCJnncowdcidwcrnnrtnncowdcidwcrnnrtnnm+wdpowdpfnnm-nnm+wdfowdffnnm-nnm+wdyowdyfnnm-nnm+wdzowdzfnnm-nnm+wdcowdcfnnm-nnl+wdlowdlfnnl-nndnnndnEND BYTXEND ITITILOIIBYSOATIT BYSWEND reDR.~{#reVR.~{#SHTYTETETXITTEXTtdtx4wdfgUwdalwdesdwdx-dwdyLnncowdcidwcrnnrtnncowdcidwcrnnrtnnm+wdpowdpfnnm-nnm+wdfowdffnnm-nnm+wdyowdyfnnm-nnm+wdzowdzfnnm-nnm+wdcowdcfnnm-nnl+wdlowdlfnnl-nndnnndnEND BYTXEND END reDR  UreVR  USHTY BYDREND ITIT8LOIIBYSOATITBYFPCLFF BYSWEND SLMGSHIDLOTM:ITITLOIIBYSOATIT?BYFPCLFFfBYLPCLLFLOWTLOLXLOLYBYSWEND reDR`GcdgreVR`GcdgSHTYEND ITITLOIIBYSOATIT\BYFPCLFF BYLPCLLFLOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDRtcN"reVRtcN"SHTYBYDREND ITITLOIIBYSOATIT\BYFPCLFF BYLPCLLFLOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDRmf)reVRmf)SHTYEND ITITLOIIBYSOATIT BYSWEND reDR*"kdreVR*"kdSHTYTETETXITTEXTwtdtx3wdfgUwdalwdesdwdxB/dwdyWnncowdcidwcrnnrtnncowdcidwcrnnrtnncowdcidwcrdwu1nnrtnnpabypVwdpiwdpxwdpmdwp1dwpldwprwdptwdpbdwdpwdwdphdwdpswdpnwdppwdpYwduMwdPfwdPz wdPlwdPc@nnrtnnm+wdpowdpf@nnm-nnm+wdfowdffnnm-nnm+wdyowdyfnnm-nnm+wdzowdzfnnm-nnm+wdcowdcfnnm-nnl+wdlowdlfnnl-nndnnndnEND BYTXEND ITITLOIIBYSOATIT?BYFPCLFFfBYLPCLLFLOWTLOLXLOLYBYSWEND reDR) A-reVR) A-SHTYEND ITITLOIIBYSOATIT\BYFPCLFF BYLPCLLF 33LOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDR^f%٨reVR^f%٨SHTYBYDREND ITITLOII BYSOATIT\BYFPCLFF BYLPCLLFLOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDR5rreVR5rSHTYEND ITITLOII!BYSOATIT BYSWEND reDR&,reVR&,SHTYTETETXITTEXTwtdtx4wdfgUwdalwdesdwdxB/dwdyWnncowdcidwcrnnrtnncowdcidwcrnnrtnncowdcidwcrdwu1nnrtnnpabypVwdpiwdpxwdpmdwp1dwpldwprwdptwdpbdwdpwdwdphdwdpswdpnwdppwdpYwduMwdPfwdPz wdPlwdPc@nnrtnnm+wdpowdpf@nnm-nnm+wdfowdffnnm-nnm+wdyowdyfnnm-nnm+wdzowdzfnnm-nnm+wdcowdcfnnm-nnl+wdlowdlfnnl-nndnnndnEND BYTXEND END reDRUUUrreVRUUUrSHTY BYDREND ITIT8LOII"BYSOATITBYFPCLFF BYSWEND SLMGSHIDLOTM:ITITLOII#BYSOATIT?BYFPCLFFfBYLPCLLFLOWTLOLXLOLYBYSWEND reDR]\reVR]\SHTYEND ITITLOII$BYSOATIT\BYFPCLFF BYLPCLLFLOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDR0(rreVR0(rSHTYBYDREND ITITLOII%BYSOATIT\BYFPCLFF BYLPCLLF 33LOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDR%S'yreVR%S'ySHTYEND ITITLOII&BYSOATIT BYSWEND reDRm g:reVRm g:SHTYTETETXITTEXTwtdtx3wdfgUwdalwdesdwdxB/dwdyWnncowdcidwcrnnrtnncowdcidwcrnnrtnncowdcidwcrdwu1nnrtnnpabypVwdpiwdpxwdpmdwp1dwpldwprwdptwdpbdwdpwdwdphdwdpswdpnwdppwdpYwduMwdPfwdPz wdPlwdPc@nnrtnnm+wdpowdpf@nnm-nnm+wdfowdffnnm-nnm+wdyowdyfnnm-nnm+wdzowdzfnnm-nnm+wdcowdcfnnm-nnl+wdlowdlfnnl-nndnnndnEND BYTXEND ITITLOII'BYSOATIT?BYFPCLFFfBYLPCLLFLOWTLOLXLOLYBYSWEND reDRf:Cj>reVRf:Cj>SHTYEND ITITLOII(BYSOATIT\BYFPCLFF BYLPCLLFLOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDR&)Zw^lreVR&)Zw^lSHTYBYDREND ITITLOII)BYSOATIT\BYFPCLFF BYLPCLLFLOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDR!W+reVR!W+SHTYEND ITITLOII*BYSOATIT BYSWEND reDR3=reVR3=SHTYTETETXITTEXTwtdtx4wdfgUwdalwdesdwdxB/dwdyWnncowdcidwcrnnrtnncowdcidwcrnnrtnncowdcidwcrdwu1nnrtnnpabypVwdpiwdpxwdpmdwp1dwpldwprwdptwdpbdwdpwdwdphdwdpswdpnwdppwdpYwduMwdPfwdPz wdPlwdPc@nnrtnnm+wdpowdpf@nnm-nnm+wdfowdffnnm-nnm+wdyowdyfnnm-nnm+wdzowdzfnnm-nnm+wdcowdcfnnm-nnl+wdlowdlfnnl-nndnnndnEND BYTXEND END reDR]UU]U*reVR]UU]U*SHTY BYDREND SNSS:SHIDSHMISHMO}SHTISHTO}BLRPBLBSLOVL@SHSIEND END SLSLlSHIDBYWTSHMISTNMSlide 3LOTM@BLSRCSCSSTNMGreenHACLffff3ff33ffffff33f3ff33fEND SHDTLOP1LOP2BLMTSHTI ITIT~LOII+BYSOATIT BYSWEND TRTISHDTLOP1LOP2END TRTOSHDTLOP1LOP2END SHTI$reDR,(ZreVR,(ZSHTYTETETXITTEXTtdtxModeling 4-NodeswdfgUwdalwdesdwdxdwdy(nnm+wdpowdpfnnm-nnm+wdfowdffnnm-nnm+wdyowdyfnnm-nnm+wdzowdzfnnm-nnm+wdcowdcfnnm-nnl+wdlowdlfnnl-nndnnndnEND BYTXLOMIYEND ITITLOII,BYSOATIT?BYFPCLFF BYLPCLLFLOWTLOLXLOLYBYSWEND pgIPSSxUxxګ8ګ8UU88xreDRxZireVRxZiSHTYEND ITIT LOII-BYSOATITBYFPCLFF BYSWEND SLMG SHIDLOTM:ITITLOII.BYSOATIT?BYFPCLFFfBYLPCLLFLOWTLOLXLOLYBYSWEND reDR0VZreVR0VZSHTYEND ITITLOII/BYSOATIT\BYFPCLFF BYLPCLLF 33LOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDRt\0reVRt\0SHTYBYDREND ITITLOII0BYSOATIT\BYFPCLFF BYLPCLLF 33LOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDR HwreVR HwSHTYEND ITITLOII1BYSOATIT BYSWEND reDR@òreVR@òSHTYTETETXITTEXTwtdtx6wdfgUwdalwdesdwdxB/dwdyWnncowdcidwcrnnrtnncowdcidwcrnnrtnncowdcidwcrdwu1nnrtnnpabypVwdpiwdpxwdpmdwp1dwpldwprwdptwdpbdwdpwdwdphdwdpswdpnwdppwdpYwduMwdPfwdPz wdPlwdPc@nnrtnnm+wdpowdpf@nnm-nnm+wdfowdffnnm-nnm+wdyowdyfnnm-nnm+wdzowdzfnnm-nnm+wdcowdcfnnm-nnl+wdlowdlfnnl-nndnnndnEND BYTXEND ITITLOII2BYSOATIT?BYFPCLFFfBYLPCLLFLOWTLOLXLOLYBYSWEND reDRZ^reVRZ^SHTYEND ITITLOII3BYSOATIT\BYFPCLFF BYLPCLLFLOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDR5`*reVR5`*SHTYBYDREND ITITLOII4BYSOATIT\BYFPCLFF BYLPCLLFLOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDR{.qreVR{.qSHTYEND ITITLOII5BYSOATIT BYSWEND reDR3 breVR3 bSHTYTETETXITTEXTwtdtx5wdfgUwdalwdesdwdxB/dwdyWnncowdcidwcrnnrtnncowdcidwcrnnrtnncowdcidwcrdwu1nnrtnnpabypVwdpiwdpxwdpmdwp1dwpldwprwdptwdpbdwdpwdwdphdwdpswdpnwdppwdpYwduMwdPfwdPz wdPlwdPc@nnrtnnm+wdpowdpf@nnm-nnm+wdfowdffnnm-nnm+wdyowdyfnnm-nnm+wdzowdzfnnm-nnm+wdcowdcfnnm-nnl+wdlowdlfnnl-nndnnndnEND BYTXEND ITITLOII6BYSOATIT?BYFPCLFFfBYLPCLLFLOWTLOLXLOLYBYSWEND reDRAreVRASHTYEND ITITLOII7BYSOATIT\BYFPCLFF BYLPCLLFLOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDRO7reVRO7SHTYBYDREND ITITLOII8BYSOATIT\BYFPCLFF BYLPCLLFLOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDR~reVR~SHTYEND ITITLOII9BYSOATIT BYSWEND reDRe_reVRe_SHTYTETETXITTEXTwtdtx7wdfgUwdalwdesdwdxB/dwdyWnncowdcidwcrnnrtnncowdcidwcrnnrtnncowdcidwcrdwu1nnrtnnpabypVwdpiwdpxwdpmdwp1dwpldwprwdptwdpbdwdpwdwdphdwdpswdpnwdppwdpYwduMwdPfwdPz wdPlwdPc@nnrtnnm+wdpowdpf@nnm-nnm+wdfowdffnnm-nnm+wdyowdyfnnm-nnm+wdzowdzfnnm-nnm+wdcowdcfnnm-nnl+wdlowdlfnnl-nndnnndnEND BYTXEND END reDR0U5UreVR0U5USHTY BYDREND ITIT LOII:BYSOATITBYFPCLFF BYSWEND SLMG -SHIDLOTM:ITITLOII;BYSOATIT?BYFPCLFFfBYLPCLLFffLOWTLOLXLOLYBYSWEND reDRzL^0WreVRzL^0WSHTYEND ITITLOIIBYSOATIT\BYFPCLFF BYLPCLLFffLOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDR_%_reVR_%_SHTYEND ITITLOII?BYSOATIT\BYFPCLFF BYLPCLLFffLOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDR^S*!ϓreVR^S*!ϓSHTYEND ITITLOII@BYSOATIT BYSWEND reDRZ+KXNreVRZ+KXNSHTYTETETXITTEXTwtdtx5wdfgUwdalwdesdwdx-dwdyNnncowdcidwcrnnrtnncowdcidwcrnnrtnncowdcidwcrdwu1nnrtnnpabypVwdpiwdpxwdpmdwp1dwpldwprwdptwdpbdwdpwdwdphdwdpswdpnwdppwdpYwduMwdPfwdPz wdPlwdPc@nnrtnnm+wdpowdpf@nnm-nnm+wdfowdffnnm-nnm+wdyowdyfnnm-nnm+wdzowdzfnnm-nnm+wdcowdcfnnm-nnl+wdlowdlfnnl-nndnnndnEND BYTXEND ITITLOIIABYSOATIT BYSWEND reDRZ]reVRZ]SHTYTETETXITTEXTwtdtx6wdfgUwdalwdesdwdx$dwdyQnncowdcidwcrnnrtnncowdcidwcrnnrtnncowdcidwcrdwu1nnrtnnpabypVwdpiwdpxwdpmdwp1dwpldwprwdptwdpbdwdpwdwdphdwdpswdpnwdppwdpYwduMwdPfwdPz wdPlwdPc@nnrtnnm+wdpowdpf@nnm-nnm+wdfowdffnnm-nnm+wdyowdyfnnm-nnm+wdzowdzfnnm-nnm+wdcowdcfnnm-nnl+wdlowdlfnnl-nndnnndnEND BYTXEND ITITLOIIBBYSOATIT BYSWEND reDR[WreVR[WSHTYTETETXITTEXTwtdtx7wdfgUwdalwdesdwdx3dwdyLnncowdcidwcrnnrtnncowdcidwcrnnrtnncowdcidwcrdwu1nnrtnnpabypVwdpiwdpxwdpmdwp1dwpldwprwdptwdpbdwdpwdwdphdwdpswdpnwdppwdpYwduMwdPfwdPz wdPlwdPc@nnrtnnm+wdpowdpf@nnm-nnm+wdfowdffnnm-nnm+wdyowdyfnnm-nnm+wdzowdzfnnm-nnm+wdcowdcfnnm-nnl+wdlowdlfnnl-nndnnndnEND BYTXEND END reDRz«*reVRz«*SHTY BYDREND SNSS:SHIDSHMISHMO}SHTISHTO}BLRPBLBSLOVL@SHSIEND END SLSLSHIDBYWTSHMISTNMSlide 4LOTM:BLSRCSCSSTNMGreenHACLffff3ff33ffffff33f3ff33fEND SHDTLOP1LOP2BLMTSHTI ITIT~LOIICBYSOATIT BYSWEND TRTISHDTLOP1LOP2END TRTOSHDTLOP1LOP2END SHTIreDR,(ZreVR,(ZSHTYTETETXITTEXTtdtxModel PropertieswdfgUwdalwdesdwdxdwdy(nnm+wdpowdpfnnm-nnm+wdfowdffnnm-nnm+wdyowdyfnnm-nnm+wdzowdzfnnm-nnm+wdcowdcfnnm-nnl+wdlowdlfnnl-nndnnndnEND BYTXLOMI[END ITITNLOIIDBYSOATIT BYSWEND TRTISHDTLOP1LOP2END TRTOSHDTLOP1LOP2END SHMISHTIlUreDRQ(jreVRQ(jSHTYTETETXITTEXTxtdtxModel is a Legal Binary Tree Black Edges Represent 2,3,4-Tree Edges Red Edges Represent 3 & 4-Node Internal Edges Searching is Identical to Binary TreeswdfgUwdalwdesdwdx dwdyvnncowdcidwcr33dwu1 nnrtnnm+wdpowdpfnnm-nnm+wdfowdffnnm-nnm+wdyowdyfnnm-nnm+wdzowdzfnnm-nnm+wdcowdcfwdcoGwdcf@wdcoPwdcfnnm-nnl+wdlowdlfnnl-nndnnndnEND BYTXLOMI\STINTextEND SNSS:SHIDSHMISHMO}SHTISHTO}BLRPBLBSLOVL@SHSIEND END SLSLSHIDBYWTSHMISTNMSlide 5LOTMcBLSRCSCSSTNMGreenHACLffff3ff33ffffff33f3ff33fEND SHDTLOP1LOP2BLMTSHTI ITIT}LOIIEBYSOATIT BYSWEND TRTISHDTLOP1LOP2END TRTOSHDTLOP1LOP2END SHTI$reDR,(ZreVR,(ZSHTYTETETXITTEXTtdtxAdding ElementswdfgUwdalwdesdwdxdwdy(nnm+wdpowdpfnnm-nnm+wdfowdffnnm-nnm+wdyowdyfnnm-nnm+wdzowdzfnnm-nnm+wdcowdcfnnm-nnl+wdlowdlfnnl-nndnnndnEND BYTXLOMI[END ITITKLOIIFBYSOATIT BYSWEND TRTISHDTLOP1LOP2END TRTOSHDTLOP1LOP2END SHMI*SHTIVreDRreVRSHTYTETETXITTEXT~tdtxAdding is Identical to Binary Trees Except! Encountered 4-Nodes Must Be Broken New Edges are Always Red Illegal 3-Nodes Must Be ConvertedwdfgUwdalwdesdwdx}dwdynncowdcidwcr33dwu1 nnrtnncowdcidwcr nnrtnnm+wdpowdpfwdpo.wdpfnnm-nnm+wdfowdffnnm-nnm+wdyowdyfnnm-nnm+wdzowdzfnnm-nnm+wdcowdcfwdco/wdcf@nnm-nnl+wdlowdlfnnl-nndnnndnEND BYTXLOMI\END SNSS:SHIDSHMISHMO}SHTISHTO}BLRPBLBSLOVL@SHSIEND END SLSL>SHIDBYWTSHMISTNMSlide 6LOTMXBLSRCSCSSTNMGreenHACLffff3ff33ffffff33f3ff33fEND SHDTLOP1LOP2BLMTSHTI ITIT~LOIIGBYSOATIT BYSWEND TRTISHDTLOP1LOP2END TRTOSHDTLOP1LOP2END SHTI*reDR,(ZreVR,(ZSHTYTETETXITTEXTtdtxBreaking 4-NodeswdfgUwdalwdesdwdxdwdy(nnm+wdpowdpfnnm-nnm+wdfowdffnnm-nnm+wdyowdyfnnm-nnm+wdzowdzfnnm-nnm+wdcowdcfnnm-nnl+wdlowdlfnnl-nndnnndnEND BYTXLOMIYEND ITITLOIIHBYSOATIT?BYFPCLFF BYLPCLLF LOWTLOLXLOLYBYSWEND pgIPSSjUU5UUUppU5UpjpUreDRj5reVRj5SHTYEND ITIT LOIIIBYSOATITBYFPCLFF BYSWEND SLMG TSHIDLOTM:ITITLOIIJBYSOATIT?BYFPCLFFfBYLPCLLFLOWTLOLXLOLYBYSWEND reDRoY]reVRoY]SHTYEND ITITLOIIKBYSOATIT\BYFPCLFF BYLPCLLF 33LOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDR\_reVR\_SHTYBYDREND ITITLOIILBYSOATIT\BYFPCLFF BYLPCLLF 33LOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDRœ0WreVRœ0WSHTYEND ITITLOIIMBYSOATIT BYSWEND reDRreVRSHTYTETETXITTEXTwtdtx6wdfgUwdalwdesdwdxB/dwdyWnncowdcidwcrnnrtnncowdcidwcrnnrtnncowdcidwcrdwu1nnrtnnpabypVwdpiwdpxwdpmdwp1dwpldwprwdptwdpbdwdpwdwdphdwdpswdpnwdppwdpYwduMwdPfwdPz wdPlwdPc@nnrtnnm+wdpowdpf@nnm-nnm+wdfowdffnnm-nnm+wdyowdyfnnm-nnm+wdzowdzfnnm-nnm+wdcowdcfnnm-nnl+wdlowdlfnnl-nndnnndnEND BYTXEND ITITLOIINBYSOATIT?BYFPCLFFfBYLPCLLFLOWTLOLXLOLYBYSWEND reDR]YalreVR]YalSHTYEND ITITLOIIOBYSOATIT\BYFPCLFF BYLPCLLFLOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDR< tc reVR< tc SHTYBYDREND ITITLOIIPBYSOATIT\BYFPCLFF BYLPCLLFLOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDR7cmQreVR7cmQSHTYEND ITITLOIIQBYSOATIT BYSWEND reDRKJreVRKJSHTYTETETXITTEXTwtdtx5wdfgUwdalwdesdwdxB/dwdyWnncowdcidwcrnnrtnncowdcidwcrnnrtnncowdcidwcrdwu1nnrtnnpabypVwdpiwdpxwdpmdwp1dwpldwprwdptwdpbdwdpwdwdphdwdpswdpnwdppwdpYwduMwdPfwdPz wdPlwdPc@nnrtnnm+wdpowdpf@nnm-nnm+wdfowdffnnm-nnm+wdyowdyfnnm-nnm+wdzowdzfnnm-nnm+wdcowdcfnnm-nnl+wdlowdlfnnl-nndnnndnEND BYTXEND ITITLOIIRBYSOATIT?BYFPCLFFfBYLPCLLFLOWTLOLXLOLYBYSWEND reDR)BreVR)BSHTYEND ITITLOIISBYSOATIT\BYFPCLFF BYLPCLLFLOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDR%]7reVR%]7SHTYBYDREND ITITLOIITBYSOATIT\BYFPCLFF BYLPCLLFLOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDR! W"^reVR! W"^SHTYEND ITITLOIIUBYSOATIT BYSWEND reDRݟM5b|reVRݟM5b|SHTYTETETXITTEXTwtdtx7wdfgUwdalwdesdwdxB/dwdyWnncowdcidwcrnnrtnncowdcidwcrnnrtnncowdcidwcrdwu1nnrtnnpabypVwdpiwdpxwdpmdwp1dwpldwprwdptwdpbdwdpwdwdphdwdpswdpnwdppwdpYwduMwdPfwdPz wdPlwdPc@nnrtnnm+wdpowdpf@nnm-nnm+wdfowdffnnm-nnm+wdyowdyfnnm-nnm+wdzowdzfnnm-nnm+wdcowdcfnnm-nnl+wdlowdlfnnl-nndnnndnEND BYTXEND ITITLOIIVBYSOATIT\BYFPCLFF BYLPCLLFLOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDRVQqreVRVQqSHTYEND END reDRUUuUҫreVRUUuUҫSHTY BYDREND ITIT LOIIWBYSOATITBYFPCLFF BYSWEND SLMG TSHIDLOTM:ITITLOIIXBYSOATIT?BYFPCLFFfBYLPCLLFLOWTLOLXLOLYBYSWEND reDRXqureVRXquSHTYEND ITITLOIIYBYSOATIT\BYFPCLFF BYLPCLLFLOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDR{reVR{SHTYBYDREND ITITLOIIZBYSOATIT\BYFPCLFF BYLPCLLFLOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDRtO7reVRtO7SHTYEND ITITLOII[BYSOATIT BYSWEND reDRhr]reVRhr]SHTYTETETXITTEXTwtdtx6wdfgUwdalwdesdwdxB/dwdyWnncowdcidwcrnnrtnncowdcidwcrnnrtnncowdcidwcrdwu1nnrtnnpabypVwdpiwdpxwdpmdwp1dwpldwprwdptwdpbdwdpwdwdphdwdpswdpnwdppwdpYwduMwdPfwdPz wdPlwdPc@nnrtnnm+wdpowdpf@nnm-nnm+wdfowdffnnm-nnm+wdyowdyfnnm-nnm+wdzowdzfnnm-nnm+wdcowdcfnnm-nnl+wdlowdlfnnl-nndnnndnEND BYTXEND ITITLOII\BYSOATIT?BYFPCLFFfBYLPCLLFLOWTLOLXLOLYBYSWEND reDRkBoreVRkBoSHTYEND ITITLOII]BYSOATIT\BYFPCLFF BYLPCLLFLOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDR%]#reVR%]#SHTYBYDREND ITITLOII^BYSOATIT\BYFPCLFF BYLPCLLFLOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDR!nW!1reVR!nW!1SHTYEND ITITLOII_BYSOATIT BYSWEND reDRݞ:l5aireVRݞ:l5aiSHTYTETETXITTEXTwtdtx5wdfgUwdalwdesdwdxB/dwdyWnncowdcidwcrnnrtnncowdcidwcrnnrtnncowdcidwcrdwu1nnrtnnpabypVwdpiwdpxwdpmdwp1dwpldwprwdptwdpbdwdpwdwdphdwdpswdpnwdppwdpYwduMwdPfwdPz wdPlwdPc@nnrtnnm+wdpowdpf@nnm-nnm+wdfowdffnnm-nnm+wdyowdyfnnm-nnm+wdzowdzfnnm-nnm+wdcowdcfnnm-nnl+wdlowdlfnnl-nndnnndnEND BYTXEND ITITLOII`BYSOATIT?BYFPCLFFfBYLPCLLFLOWTLOLXLOLYBYSWEND reDR\Hx,`|reVR\Hx,`|SHTYEND ITITLOIIaBYSOATIT\BYFPCLFF BYLPCLLFLOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDRGbUreVRGbUSHTYBYDREND ITITLOIIbBYSOATIT\BYFPCLFF BYLPCLLFLOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDR {@>reVR {@>SHTYEND ITITLOIIcBYSOATIT BYSWEND reDRlyreVRlySHTYTETETXITTEXTwtdtx7wdfgUwdalwdesdwdxB/dwdyWnncowdcidwcrnnrtnncowdcidwcrnnrtnncowdcidwcrdwu1nnrtnnpabypVwdpiwdpxwdpmdwp1dwpldwprwdptwdpbdwdpwdwdphdwdpswdpnwdppwdpYwduMwdPfwdPz wdPlwdPc@nnrtnnm+wdpowdpf@nnm-nnm+wdfowdffnnm-nnm+wdyowdyfnnm-nnm+wdzowdzfnnm-nnm+wdcowdcfnnm-nnl+wdlowdlfnnl-nndnnndnEND BYTXEND ITITLOIIdBYSOATIT\BYFPCLFF BYLPCLLF 33LOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDR Tq_޲reVR Tq_޲SHTYEND END reDR U]UreVR U]USHTY BYDREND SNSS:SHIDSHMISHMO}SHTISHTO}BLRPBLBSLOVL@SHSIEND END SLSLSHIDBYWTSHMISTNMSlide 7LOTMXBLSRCSCSSTNMGreenHACLffff3ff33ffffff33f3ff33fEND SHDTLOP1LOP2BLMTSHTI ITIT}LOIIeBYSOATIT BYSWEND TRTISHDTLOP1LOP2END TRTOSHDTLOP1LOP2END SHTI*reDR,(ZreVR,(ZSHTYTETETXITTEXTtdtxIllegal 4-NodeswdfgUwdalwdesdwdxdwdy(nnm+wdpowdpfnnm-nnm+wdfowdffnnm-nnm+wdyowdyfnnm-nnm+wdzowdzfnnm-nnm+wdcowdcfnnm-nnl+wdlowdlfnnl-nndnnndnEND BYTXLOMIYEND ITIT LOIIfBYSOATITBYFPCLFF BYSWEND SLMG TSHIDLOTM:ITITLOIIgBYSOATIT?BYFPCLFFfBYLPCLLFLOWTLOLXLOLYBYSWEND reDRFreVRFSHTYEND ITITLOIIhBYSOATIT\BYFPCLFF BYLPCLLF 33LOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDR RreVR RSHTYBYDREND ITITLOIIiBYSOATIT\BYFPCLFF BYLPCLLFLOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDR]=_zreVR]=_zSHTYEND ITITLOIIjBYSOATIT BYSWEND reDR%reVR%SHTYTETETXITTEXTwtdtx6wdfgUwdalwdesdwdxB/dwdyWnncowdcidwcrnnrtnncowdcidwcrnnrtnncowdcidwcrdwu1nnrtnnpabypVwdpiwdpxwdpmdwp1dwpldwprwdptwdpbdwdpwdwdphdwdpswdpnwdppwdpYwduMwdPfwdPz wdPlwdPc@nnrtnnm+wdpowdpf@nnm-nnm+wdfowdffnnm-nnm+wdyowdyfnnm-nnm+wdzowdzfnnm-nnm+wdcowdcfnnm-nnl+wdlowdlfnnl-nndnnndnEND BYTXEND ITITLOIIkBYSOATIT?BYFPCLFFfBYLPCLLFLOWTLOLXLOLYBYSWEND reDRJxreVRJxSHTYEND ITITLOIIlBYSOATIT\BYFPCLFF BYLPCLLFLOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDR[ XLreVR[ XLSHTYBYDREND ITITLOIImBYSOATIT\BYFPCLFF BYLPCLLFLOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDRW!#reVRW!#SHTYEND ITITLOIInBYSOATIT BYSWEND reDRnkcreVRnkcSHTYTETETXITTEXTwtdtx5wdfgUwdalwdesdwdxB/dwdyWnncowdcidwcrnnrtnncowdcidwcrnnrtnncowdcidwcrdwu1nnrtnnpabypVwdpiwdpxwdpmdwp1dwpldwprwdptwdpbdwdpwdwdphdwdpswdpnwdppwdpYwduMwdPfwdPz wdPlwdPc@nnrtnnm+wdpowdpf@nnm-nnm+wdfowdffnnm-nnm+wdyowdyfnnm-nnm+wdzowdzfnnm-nnm+wdcowdcfnnm-nnl+wdlowdlfnnl-nndnnndnEND BYTXEND ITITLOIIoBYSOATIT?BYFPCLFFfBYLPCLLFLOWTLOLXLOLYBYSWEND reDR XreVR XSHTYEND ITITLOIIpBYSOATIT\BYFPCLFF BYLPCLLF 33LOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDRa.fXreVRa.fXSHTYBYDREND ITITLOIIqBYSOATIT\BYFPCLFF BYLPCLLFLOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDR]WYreVR]WYSHTYEND ITITLOIIrBYSOATIT BYSWEND reDR|qreVR|qSHTYTETETXITTEXTwtdtx7wdfgUwdalwdesdwdxB/dwdyWnncowdcidwcrnnrtnncowdcidwcrnnrtnncowdcidwcrdwu1nnrtnnpabypVwdpiwdpxwdpmdwp1dwpldwprwdptwdpbdwdpwdwdphdwdpswdpnwdppwdpYwduMwdPfwdPz wdPlwdPc@nnrtnnm+wdpowdpf@nnm-nnm+wdfowdffnnm-nnm+wdyowdyfnnm-nnm+wdzowdzfnnm-nnm+wdcowdcfnnm-nnl+wdlowdlfnnl-nndnnndnEND BYTXEND ITITLOIIsBYSOATIT\BYFPCLFF BYLPCLLFLOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDRQ[reVRQ[SHTYEND END reDR reVR SHTY BYDREND ITIT LOIItBYSOATITBYFPCLFF BYSWEND SLMG TSHIDLOTM:ITITLOIIuBYSOATIT?BYFPCLFFfBYLPCLLFLOWTLOLXLOLYBYSWEND reDR^̲}bAreVR^̲}bASHTYEND ITITLOIIvBYSOATIT\BYFPCLFF BYLPCLLFLOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDR`!d1reVR`!d1SHTYBYDREND ITITLOIIwBYSOATIT\BYFPCLFF BYLPCLLFLOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDR[8uxreVR[8uxSHTYEND ITITLOIIxBYSOATIT BYSWEND reDR oreVR oSHTYTETETXITTEXTwtdtx6wdfgUwdalwdesdwdxB/dwdyWnncowdcidwcrnnrtnncowdcidwcrnnrtnncowdcidwcrdwu1nnrtnnpabypVwdpiwdpxwdpmdwp1dwpldwprwdptwdpbdwdpwdwdphdwdpswdpnwdppwdpYwduMwdPfwdPz wdPlwdPc@nnrtnnm+wdpowdpf@nnm-nnm+wdfowdffnnm-nnm+wdyowdyfnnm-nnm+wdzowdzfnnm-nnm+wdcowdcfnnm-nnl+wdlowdlfnnl-nndnnndnEND BYTXEND ITITLOIIyBYSOATIT?BYFPCLFFfBYLPCLLFLOWTLOLXLOLYBYSWEND reDR3reVR3SHTYEND ITITLOIIzBYSOATIT\BYFPCLFF BYLPCLLFLOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDR*A+reVR*A+SHTYBYDREND ITITLOII{BYSOATIT\BYFPCLFF BYLPCLLF 33LOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDR\#^rreVR\#^rSHTYEND ITITLOII|BYSOATIT BYSWEND reDRWreVRWSHTYTETETXITTEXTwtdtx5wdfgUwdalwdesdwdxB/dwdyWnncowdcidwcrnnrtnncowdcidwcrnnrtnncowdcidwcrdwu1nnrtnnpabypVwdpiwdpxwdpmdwp1dwpldwprwdptwdpbdwdpwdwdphdwdpswdpnwdppwdpYwduMwdPfwdPz wdPlwdPc@nnrtnnm+wdpowdpf@nnm-nnm+wdfowdffnnm-nnm+wdyowdyfnnm-nnm+wdzowdzfnnm-nnm+wdcowdcfnnm-nnl+wdlowdlfnnl-nndnnndnEND BYTXEND ITITLOII}BYSOATIT?BYFPCLFFfBYLPCLLFLOWTLOLXLOLYBYSWEND reDRr-vreVRr-vSHTYEND ITITLOII~BYSOATIT\BYFPCLFF BYLPCLLF 33LOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDRsreVRsSHTYBYDREND ITITLOIIBYSOATIT\BYFPCLFF BYLPCLLFLOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDRoW$uYa8reVRoW$uYa8SHTYEND ITITLOIIBYSOATIT BYSWEND reDR+s reVR+s SHTYTETETXITTEXTwtdtx7wdfgUwdalwdesdwdxB/dwdyWnncowdcidwcrnnrtnncowdcidwcrnnrtnncowdcidwcrdwu1nnrtnnpabypVwdpiwdpxwdpmdwp1dwpldwprwdptwdpbdwdpwdwdphdwdpswdpnwdppwdpYwduMwdPfwdPz wdPlwdPc@nnrtnnm+wdpowdpf@nnm-nnm+wdfowdffnnm-nnm+wdyowdyfnnm-nnm+wdzowdzfnnm-nnm+wdcowdcfnnm-nnl+wdlowdlfnnl-nndnnndnEND BYTXEND ITITLOIIBYSOATIT\BYFPCLFF BYLPCLLFLOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDRQ 5reVRQ 5SHTYEND END reDRi @vreVRi @vSHTY BYDREND ITITyLOIIBYSOATIT BYSWEND reDR(!reVR(!SHTYTETETXITTEXTtdtx(And Mirror Images)wdfgUwdalwdesdwdxjdwdyUnncowdcidwcrnnrtnncowdcidwcrnnrtnncowdcidwcr33dwu1 nnrtnnm+wdpowdpfnnm-nnm+wdfowdffnnm-nnm+wdyowdyfnnm-nnm+wdzowdzfnnm-nnm+wdcowdcf@nnm-nnl+wdlowdlfnnl-nndnnndnEND BYTXEND SNSS:SHIDSHMISHMO}SHTISHTO}BLRPBLBSLOVL@SHSIEND END SLSL5eSHIDBYWTSHMISTNMSlide 8LOTMXBLSRCSCSSTNMGreenHACLffff3ff33ffffff33f3ff33fEND SHDTLOP1LOP2BLMTSHTI ITITLOIIBYSOATIT BYSWEND TRTISHDTLOP1LOP2END TRTOSHDTLOP1LOP2END SHTI*reDR,(ZreVR,(ZSHTYTETETXITTEXTtdtxFixing Linear 4-NodeswdfgUwdalwdesdwdxdwdy(nnm+wdpowdpfnnm-nnm+wdfowdffnnm-nnm+wdyowdyfnnm-nnm+wdzowdzfnnm-nnm+wdcowdcfnnm-nnl+wdlowdlfnnl-nndnnndnEND BYTXLOMIYEND ITIT LOIIBYSOATITBYFPCLFF BYSWEND SLMG TSHIDLOTM:ITITLOIIBYSOATIT?BYFPCLFFfBYLPCLLFLOWTLOLXLOLYBYSWEND reDRd4reVRd4SHTYEND ITITLOIIBYSOATIT\BYFPCLFF BYLPCLLF 33LOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDRGaRreVRGaRSHTYBYDREND ITITLOIIBYSOATIT\BYFPCLFF BYLPCLLFLOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND reDRB+xhreVRB+xhSHTYEND ITITLOIIBYSOATIT BYSWEND reDR`W#reVR`W#SHTYTETETXITTEXTwtdtx6wdfgUwdalwdesdwdxB/dwdyWnncowdcidwcrnnrtnncowdcidwcrnnrtnncowdcidwcrdwu1nnrtnnpabypVwdpiwdpxwdpmdwp1dwpldwprwdptwdpbdwdpwdwdphdwdpswdpnwdppwdpYwduMwdPfwdPz wdPlwdPc@nnrtnnm+wdpowdpf@nnm-nnm+wdfowdffnnm-nnm+wdyowdyfnnm-nnm+wdzowdzfnnm-nnm+wdcowdcfnnm-nnl+wdlowdlfnnl-nndnnndnEND BYTXEND ITITLOIIBYSOATIT?BYFPCLFFfBYLPCLLFLOWTLOLXLOLYBYSWEND reDRkb8freVRkb8fSHTYEND 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ITIT&LOIIBYSOATITBYFPCLFFBYSWEND SLMGSHIDLOTM:ITITLOIIBYSOATIT?BYFPCLFFfBYLPCLLFLOWTLOLXLOLYBYSWEND SHMI>SHTI>reDRe+reVRe+SHTYEND ITITLOIIBYSOATIT BYSWEND SHMI>SHTI>reDR/m/{reVR/m/{SHTYTETETXITTEXTytdtx6.5wdfgUwdalwdesdwdxbdwdyHnncowdcidwcrnnrtnncowdcidwcrnnrtnncowdcidwcrdwu1nnrtnnpabypVwdpiwdpxwdpmdwp1dwpldwprwdptwdpbdwdpwdwdphdwdpswdpnwdppwdpYwduMwdPfwdPz wdPlwdPc@nnrtnnm+wdpowdpf@nnm-nnm+wdfowdffnnm-nnm+wdyowdyfnnm-nnm+wdzowdzfnnm-nnm+wdcowdcfnnm-nnl+wdlowdlfnnl-nndnnndnEND BYTXEND END SHMI>SHTI>reDRe+reVRe+SHTY BYDREND ITITLOIIBYSOATITBYFPCLFFBYSWEND SLMGSHIDLOTM:ITITLOIIBYSOATIT\BYFPCLFF BYLPCLLFLOWTLOLXLOLYBYARLOAL5ULOAS5ULOAI UBYSWEND SHMISHMO2SHTI+SHTO%reDR-U«reVRU-USHTYEND ITITLOIIBYSOATIT?BYFPCLFFffBYLPCLLFLOWTLOLXLOLYBYSWEND SHMISHMO2SHTI+SHTO%reDRuUreVRuUSHTYEND ITIT|LOIIBYSOATIT BYSWEND SHMISHMO2SHTI+SHTO%reDRʫUreVRʫUSHTYTETETXITTEXTtdtx8wdfgUwdalwdesdwdx:dwdyHnncowdcidwcrnnrtnncowdcidwcrnnrtnncowdcidwcrfdwu1nnrtnncowdcidwcrfdwu1nnrtnncowdcidwcr33dwu1 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