Equivalent Addresses

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Points:7
Time limit:2.0s
Memory limit:64M

Problem type

Recall that in real mode on the x86, the programmer have access to 1 MB of memory. However, being a 16-bit mode, 16-bit pointers only allows access to 64 KB (= 2^{16} bytes) of address space. This is of course no good for accessing the 1 MB of memory, so segments were introduced. A segment is another 16-bit of data to determine where the 16-bit pointer is relative to in memory. But we only have 20-bit of data (1 MB = 2^{20} bytes, requiring 20 bits to address all memory), and we have 32-bits of data in a segment:offset pair, so 12-bits are redundant. In other words, there are 2^{12} different segments, with different offsets, that gives the same memory address, hence there are 2^{12} = 4\,096 different ways to represent the same memory address. Any given address is accessible in 4\,096 different segments. Since switching segments is a very expensive operation, programmers are encouraged to choose a segment that have all their data visible.

The segment is multiplied by 16 before being added with the offset to yield the final address. For example, the address 06EF:1234: it has a segment of 0x06EF, which, multiplied by 16, gives the segment base address 0x06EF0, and adding the offset 0x1234 to the base gives the address 0x08124. Also recall that the lack of address lines A20 and beyond on the 8086 allows for addresses to wrap around. So segment 0xFFFF with the offset 0x0010 becomes 0xFFFF0 + 0x0010 = 0x100000, but wraps around to 0x00000. This was the primary reason for the existence of the A20 gate, since older programs before A20 relied on this trick.

To help other programmers in your company to choose a nice segment for some performance boost, you received your third assignment: given a pointer in segment:offset format, output all the equivalent segment:offset pairs that refers to the same memory address, with A20 pulled low.

Input Specification

The input consists one line, in the format SSSS:OOOO, where both S and O represent one hexadecimal digit. SSSS represents the segment and OOOO represents the offset of the address you are to use.

Output Specification

You are to output all the segment:offset pairs that resolves up to the same address as the one given to you, including the one given, in the SSSS:OOOO format. You may output them in any order.

Sample Input

D313:BFED

Sample Output

DF11:000D
DF10:001D
DF0F:002D
DF0E:003D
DF0D:004D
DF0C:005D
DF0B:006D
DF0A:007D
DF09:008D
DF08:009D
DF07:00AD
DF06:00BD
DF05:00CD
DF04:00DD
DF03:00ED
DF02:00FD
DF01:010D
DF00:011D
DEFF:012D
DEFE:013D
DEFD:014D
DEFC:015D
DEFB:016D
DEFA:017D
DEF9:018D
DEF8:019D
DEF7:01AD
DEF6:01BD
DEF5:01CD
DEF4:01DD
DEF3:01ED
DEF2:01FD
DEF1:020D
DEF0:021D
DEEF:022D
DEEE:023D
DEED:024D
DEEC:025D
DEEB:026D
DEEA:027D
DEE9:028D
DEE8:029D
DEE7:02AD
DEE6:02BD
DEE5:02CD
DEE4:02DD
DEE3:02ED
DEE2:02FD
DEE1:030D
DEE0:031D
DEDF:032D
DEDE:033D
DEDD:034D
DEDC:035D
DEDB:036D
DEDA:037D
DED9:038D
DED8:039D
DED7:03AD
DED6:03BD
DED5:03CD
DED4:03DD
DED3:03ED
DED2:03FD
DED1:040D
DED0:041D
DECF:042D
DECE:043D
DECD:044D
DECC:045D
DECB:046D
DECA:047D
DEC9:048D
DEC8:049D
DEC7:04AD
DEC6:04BD
DEC5:04CD
DEC4:04DD
DEC3:04ED
DEC2:04FD
DEC1:050D
DEC0:051D
DEBF:052D
DEBE:053D
DEBD:054D
DEBC:055D
DEBB:056D
DEBA:057D
DEB9:058D
DEB8:059D
DEB7:05AD
DEB6:05BD
DEB5:05CD
DEB4:05DD
DEB3:05ED
DEB2:05FD
DEB1:060D
DEB0:061D
DEAF:062D
DEAE:063D
DEAD:064D
DEAC:065D
DEAB:066D
DEAA:067D
DEA9:068D
DEA8:069D
DEA7:06AD
DEA6:06BD
DEA5:06CD
DEA4:06DD
DEA3:06ED
DEA2:06FD
DEA1:070D
DEA0:071D
DE9F:072D
DE9E:073D
DE9D:074D
DE9C:075D
DE9B:076D
DE9A:077D
DE99:078D
DE98:079D
DE97:07AD
DE96:07BD
DE95:07CD
DE94:07DD
DE93:07ED
DE92:07FD
DE91:080D
DE90:081D
DE8F:082D
DE8E:083D
DE8D:084D
DE8C:085D
DE8B:086D
DE8A:087D
DE89:088D
DE88:089D
DE87:08AD
DE86:08BD
DE85:08CD
DE84:08DD
DE83:08ED
DE82:08FD
DE81:090D
DE80:091D
DE7F:092D
DE7E:093D
DE7D:094D
DE7C:095D
DE7B:096D
DE7A:097D
DE79:098D
DE78:099D
DE77:09AD
DE76:09BD
DE75:09CD
DE74:09DD
DE73:09ED
DE72:09FD
DE71:0A0D
DE70:0A1D
DE6F:0A2D
DE6E:0A3D
DE6D:0A4D
DE6C:0A5D
DE6B:0A6D
DE6A:0A7D
DE69:0A8D
DE68:0A9D
DE67:0AAD
DE66:0ABD
DE65:0ACD
DE64:0ADD
DE63:0AED
DE62:0AFD
DE61:0B0D
DE60:0B1D
DE5F:0B2D
DE5E:0B3D
DE5D:0B4D
DE5C:0B5D
DE5B:0B6D
DE5A:0B7D
DE59:0B8D
DE58:0B9D
DE57:0BAD
DE56:0BBD
DE55:0BCD
DE54:0BDD
DE53:0BED
DE52:0BFD
DE51:0C0D
DE50:0C1D
DE4F:0C2D
DE4E:0C3D
DE4D:0C4D
DE4C:0C5D
DE4B:0C6D
DE4A:0C7D
DE49:0C8D
DE48:0C9D
DE47:0CAD
DE46:0CBD
DE45:0CCD
DE44:0CDD
DE43:0CED
DE42:0CFD
DE41:0D0D
DE40:0D1D
DE3F:0D2D
DE3E:0D3D
DE3D:0D4D
DE3C:0D5D
DE3B:0D6D
DE3A:0D7D
DE39:0D8D
DE38:0D9D
DE37:0DAD
DE36:0DBD
DE35:0DCD
DE34:0DDD
DE33:0DED
DE32:0DFD
DE31:0E0D
DE30:0E1D
DE2F:0E2D
DE2E:0E3D
DE2D:0E4D
DE2C:0E5D
DE2B:0E6D
DE2A:0E7D
DE29:0E8D
DE28:0E9D
DE27:0EAD
DE26:0EBD
DE25:0ECD
DE24:0EDD
DE23:0EED
DE22:0EFD
DE21:0F0D
DE20:0F1D
DE1F:0F2D
DE1E:0F3D
DE1D:0F4D
DE1C:0F5D
DE1B:0F6D
DE1A:0F7D
DE19:0F8D
DE18:0F9D
DE17:0FAD
DE16:0FBD
DE15:0FCD
DE14:0FDD
DE13:0FED
DE12:0FFD
DE11:100D
DE10:101D
DE0F:102D
DE0E:103D
DE0D:104D
DE0C:105D
DE0B:106D
DE0A:107D
DE09:108D
DE08:109D
DE07:10AD
DE06:10BD
DE05:10CD
DE04:10DD
DE03:10ED
DE02:10FD
DE01:110D
DE00:111D
DDFF:112D
DDFE:113D
DDFD:114D
DDFC:115D
DDFB:116D
DDFA:117D
DDF9:118D
DDF8:119D
DDF7:11AD
DDF6:11BD
DDF5:11CD
DDF4:11DD
DDF3:11ED
DDF2:11FD
DDF1:120D
DDF0:121D
DDEF:122D
DDEE:123D
DDED:124D
DDEC:125D
DDEB:126D
DDEA:127D
DDE9:128D
DDE8:129D
DDE7:12AD
DDE6:12BD
DDE5:12CD
DDE4:12DD
DDE3:12ED
DDE2:12FD
DDE1:130D
DDE0:131D
DDDF:132D
DDDE:133D
DDDD:134D
DDDC:135D
DDDB:136D
DDDA:137D
DDD9:138D
DDD8:139D
DDD7:13AD
DDD6:13BD
DDD5:13CD
DDD4:13DD
DDD3:13ED
DDD2:13FD
DDD1:140D
DDD0:141D
DDCF:142D
DDCE:143D
DDCD:144D
DDCC:145D
DDCB:146D
DDCA:147D
DDC9:148D
DDC8:149D
DDC7:14AD
DDC6:14BD
DDC5:14CD
DDC4:14DD
DDC3:14ED
DDC2:14FD
DDC1:150D
DDC0:151D
DDBF:152D
DDBE:153D
DDBD:154D
DDBC:155D
DDBB:156D
DDBA:157D
DDB9:158D
DDB8:159D
DDB7:15AD
DDB6:15BD
DDB5:15CD
DDB4:15DD
DDB3:15ED
DDB2:15FD
DDB1:160D
DDB0:161D
DDAF:162D
DDAE:163D
DDAD:164D
DDAC:165D
DDAB:166D
DDAA:167D
DDA9:168D
DDA8:169D
DDA7:16AD
DDA6:16BD
DDA5:16CD
DDA4:16DD
DDA3:16ED
DDA2:16FD
DDA1:170D
DDA0:171D
DD9F:172D
DD9E:173D
DD9D:174D
DD9C:175D
DD9B:176D
DD9A:177D
DD99:178D
DD98:179D
DD97:17AD
DD96:17BD
DD95:17CD
DD94:17DD
DD93:17ED
DD92:17FD
DD91:180D
DD90:181D
DD8F:182D
DD8E:183D
DD8D:184D
DD8C:185D
DD8B:186D
DD8A:187D
DD89:188D
DD88:189D
DD87:18AD
DD86:18BD
DD85:18CD
DD84:18DD
DD83:18ED
DD82:18FD
DD81:190D
DD80:191D
DD7F:192D
DD7E:193D
DD7D:194D
DD7C:195D
DD7B:196D
DD7A:197D
DD79:198D
DD78:199D
DD77:19AD
DD76:19BD
DD75:19CD
DD74:19DD
DD73:19ED
DD72:19FD
DD71:1A0D
DD70:1A1D
DD6F:1A2D
DD6E:1A3D
DD6D:1A4D
DD6C:1A5D
DD6B:1A6D
DD6A:1A7D
DD69:1A8D
DD68:1A9D
DD67:1AAD
DD66:1ABD
DD65:1ACD
DD64:1ADD
DD63:1AED
DD62:1AFD
DD61:1B0D
DD60:1B1D
DD5F:1B2D
DD5E:1B3D
DD5D:1B4D
DD5C:1B5D
DD5B:1B6D
DD5A:1B7D
DD59:1B8D
DD58:1B9D
DD57:1BAD
DD56:1BBD
DD55:1BCD
DD54:1BDD
DD53:1BED
DD52:1BFD
DD51:1C0D
DD50:1C1D
DD4F:1C2D
DD4E:1C3D
DD4D:1C4D
DD4C:1C5D
DD4B:1C6D
DD4A:1C7D
DD49:1C8D
DD48:1C9D
DD47:1CAD
DD46:1CBD
DD45:1CCD
DD44:1CDD
DD43:1CED
DD42:1CFD
DD41:1D0D
DD40:1D1D
DD3F:1D2D
DD3E:1D3D
DD3D:1D4D
DD3C:1D5D
DD3B:1D6D
DD3A:1D7D
DD39:1D8D
DD38:1D9D
DD37:1DAD
DD36:1DBD
DD35:1DCD
DD34:1DDD
DD33:1DED
DD32:1DFD
DD31:1E0D
DD30:1E1D
DD2F:1E2D
DD2E:1E3D
DD2D:1E4D
DD2C:1E5D
DD2B:1E6D
DD2A:1E7D
DD29:1E8D
DD28:1E9D
DD27:1EAD
DD26:1EBD
DD25:1ECD
DD24:1EDD
DD23:1EED
DD22:1EFD
DD21:1F0D
DD20:1F1D
DD1F:1F2D
DD1E:1F3D
DD1D:1F4D
DD1C:1F5D
DD1B:1F6D
DD1A:1F7D
DD19:1F8D
DD18:1F9D
DD17:1FAD
DD16:1FBD
DD15:1FCD
DD14:1FDD
DD13:1FED
DD12:1FFD
DD11:200D
DD10:201D
DD0F:202D
DD0E:203D
DD0D:204D
DD0C:205D
DD0B:206D
DD0A:207D
DD09:208D
DD08:209D
DD07:20AD
DD06:20BD
DD05:20CD
DD04:20DD
DD03:20ED
DD02:20FD
DD01:210D
DD00:211D
DCFF:212D
DCFE:213D
DCFD:214D
DCFC:215D
DCFB:216D
DCFA:217D
DCF9:218D
DCF8:219D
DCF7:21AD
DCF6:21BD
DCF5:21CD
DCF4:21DD
DCF3:21ED
DCF2:21FD
DCF1:220D
DCF0:221D
DCEF:222D
DCEE:223D
DCED:224D
DCEC:225D
DCEB:226D
DCEA:227D
DCE9:228D
DCE8:229D
DCE7:22AD
DCE6:22BD
DCE5:22CD
DCE4:22DD
DCE3:22ED
DCE2:22FD
DCE1:230D
DCE0:231D
DCDF:232D
DCDE:233D
DCDD:234D
DCDC:235D
DCDB:236D
DCDA:237D
DCD9:238D
DCD8:239D
DCD7:23AD
DCD6:23BD
DCD5:23CD
DCD4:23DD
DCD3:23ED
DCD2:23FD
DCD1:240D
DCD0:241D
DCCF:242D
DCCE:243D
DCCD:244D
DCCC:245D
DCCB:246D
DCCA:247D
DCC9:248D
DCC8:249D
DCC7:24AD
DCC6:24BD
DCC5:24CD
DCC4:24DD
DCC3:24ED
DCC2:24FD
DCC1:250D
DCC0:251D
DCBF:252D
DCBE:253D
DCBD:254D
DCBC:255D
DCBB:256D
DCBA:257D
DCB9:258D
DCB8:259D
DCB7:25AD
DCB6:25BD
DCB5:25CD
DCB4:25DD
DCB3:25ED
DCB2:25FD
DCB1:260D
DCB0:261D
DCAF:262D
DCAE:263D
DCAD:264D
DCAC:265D
DCAB:266D
DCAA:267D
DCA9:268D
DCA8:269D
DCA7:26AD
DCA6:26BD
DCA5:26CD
DCA4:26DD
DCA3:26ED
DCA2:26FD
DCA1:270D
DCA0:271D
DC9F:272D
DC9E:273D
DC9D:274D
DC9C:275D
DC9B:276D
DC9A:277D
DC99:278D
DC98:279D
DC97:27AD
DC96:27BD
DC95:27CD
DC94:27DD
DC93:27ED
DC92:27FD
DC91:280D
DC90:281D
DC8F:282D
DC8E:283D
DC8D:284D
DC8C:285D
DC8B:286D
DC8A:287D
DC89:288D
DC88:289D
DC87:28AD
DC86:28BD
DC85:28CD
DC84:28DD
DC83:28ED
DC82:28FD
DC81:290D
DC80:291D
DC7F:292D
DC7E:293D
DC7D:294D
DC7C:295D
DC7B:296D
DC7A:297D
DC79:298D
DC78:299D
DC77:29AD
DC76:29BD
DC75:29CD
DC74:29DD
DC73:29ED
DC72:29FD
DC71:2A0D
DC70:2A1D
DC6F:2A2D
DC6E:2A3D
DC6D:2A4D
DC6C:2A5D
DC6B:2A6D
DC6A:2A7D
DC69:2A8D
DC68:2A9D
DC67:2AAD
DC66:2ABD
DC65:2ACD
DC64:2ADD
DC63:2AED
DC62:2AFD
DC61:2B0D
DC60:2B1D
DC5F:2B2D
DC5E:2B3D
DC5D:2B4D
DC5C:2B5D
DC5B:2B6D
DC5A:2B7D
DC59:2B8D
DC58:2B9D
DC57:2BAD
DC56:2BBD
DC55:2BCD
DC54:2BDD
DC53:2BED
DC52:2BFD
DC51:2C0D
DC50:2C1D
DC4F:2C2D
DC4E:2C3D
DC4D:2C4D
DC4C:2C5D
DC4B:2C6D
DC4A:2C7D
DC49:2C8D
DC48:2C9D
DC47:2CAD
DC46:2CBD
DC45:2CCD
DC44:2CDD
DC43:2CED
DC42:2CFD
DC41:2D0D
DC40:2D1D
DC3F:2D2D
DC3E:2D3D
DC3D:2D4D
DC3C:2D5D
DC3B:2D6D
DC3A:2D7D
DC39:2D8D
DC38:2D9D
DC37:2DAD
DC36:2DBD
DC35:2DCD
DC34:2DDD
DC33:2DED
DC32:2DFD
DC31:2E0D
DC30:2E1D
DC2F:2E2D
DC2E:2E3D
DC2D:2E4D
DC2C:2E5D
DC2B:2E6D
DC2A:2E7D
DC29:2E8D
DC28:2E9D
DC27:2EAD
DC26:2EBD
DC25:2ECD
DC24:2EDD
DC23:2EED
DC22:2EFD
DC21:2F0D
DC20:2F1D
DC1F:2F2D
DC1E:2F3D
DC1D:2F4D
DC1C:2F5D
DC1B:2F6D
DC1A:2F7D
DC19:2F8D
DC18:2F9D
DC17:2FAD
DC16:2FBD
DC15:2FCD
DC14:2FDD
DC13:2FED
DC12:2FFD
DC11:300D
DC10:301D
DC0F:302D
DC0E:303D
DC0D:304D
DC0C:305D
DC0B:306D
DC0A:307D
DC09:308D
DC08:309D
DC07:30AD
DC06:30BD
DC05:30CD
DC04:30DD
DC03:30ED
DC02:30FD
DC01:310D
DC00:311D
DBFF:312D
DBFE:313D
DBFD:314D
DBFC:315D
DBFB:316D
DBFA:317D
DBF9:318D
DBF8:319D
DBF7:31AD
DBF6:31BD
DBF5:31CD
DBF4:31DD
DBF3:31ED
DBF2:31FD
DBF1:320D
DBF0:321D
DBEF:322D
DBEE:323D
DBED:324D
DBEC:325D
DBEB:326D
DBEA:327D
DBE9:328D
DBE8:329D
DBE7:32AD
DBE6:32BD
DBE5:32CD
DBE4:32DD
DBE3:32ED
DBE2:32FD
DBE1:330D
DBE0:331D
DBDF:332D
DBDE:333D
DBDD:334D
DBDC:335D
DBDB:336D
DBDA:337D
DBD9:338D
DBD8:339D
DBD7:33AD
DBD6:33BD
DBD5:33CD
DBD4:33DD
DBD3:33ED
DBD2:33FD
DBD1:340D
DBD0:341D
DBCF:342D
DBCE:343D
DBCD:344D
DBCC:345D
DBCB:346D
DBCA:347D
DBC9:348D
DBC8:349D
DBC7:34AD
DBC6:34BD
DBC5:34CD
DBC4:34DD
DBC3:34ED
DBC2:34FD
DBC1:350D
DBC0:351D
DBBF:352D
DBBE:353D
DBBD:354D
DBBC:355D
DBBB:356D
DBBA:357D
DBB9:358D
DBB8:359D
DBB7:35AD
DBB6:35BD
DBB5:35CD
DBB4:35DD
DBB3:35ED
DBB2:35FD
DBB1:360D
DBB0:361D
DBAF:362D
DBAE:363D
DBAD:364D
DBAC:365D
DBAB:366D
DBAA:367D
DBA9:368D
DBA8:369D
DBA7:36AD
DBA6:36BD
DBA5:36CD
DBA4:36DD
DBA3:36ED
DBA2:36FD
DBA1:370D
DBA0:371D
DB9F:372D
DB9E:373D
DB9D:374D
DB9C:375D
DB9B:376D
DB9A:377D
DB99:378D
DB98:379D
DB97:37AD
DB96:37BD
DB95:37CD
DB94:37DD
DB93:37ED
DB92:37FD
DB91:380D
DB90:381D
DB8F:382D
DB8E:383D
DB8D:384D
DB8C:385D
DB8B:386D
DB8A:387D
DB89:388D
DB88:389D
DB87:38AD
DB86:38BD
DB85:38CD
DB84:38DD
DB83:38ED
DB82:38FD
DB81:390D
DB80:391D
DB7F:392D
DB7E:393D
DB7D:394D
DB7C:395D
DB7B:396D
DB7A:397D
DB79:398D
DB78:399D
DB77:39AD
DB76:39BD
DB75:39CD
DB74:39DD
DB73:39ED
DB72:39FD
DB71:3A0D
DB70:3A1D
DB6F:3A2D
DB6E:3A3D
DB6D:3A4D
DB6C:3A5D
DB6B:3A6D
DB6A:3A7D
DB69:3A8D
DB68:3A9D
DB67:3AAD
DB66:3ABD
DB65:3ACD
DB64:3ADD
DB63:3AED
DB62:3AFD
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