day 8

08-seven-segment-search/code.scm

@@ -0,0 +1,178 @@
+(import (srfi :43)) ; vector extensions
+(load "../common.scm")
+
+; convert wire's letter to corresponding bit of 7-segment display
+(define (signal->bit c)
+  (case c
+    [#\a #b0000001]
+    [#\b #b0000010]
+    [#\c #b0000100]
+    [#\d #b0001000]
+    [#\e #b0010000]
+    [#\f #b0100000]
+    [#\g #b1000000]))
+
+; read a set of wires and return corresponding bits
+(define (parse-wires file)
+  (let loop [(n 0)]
+    (let [(c (get-char file))]
+      (if (and (not (eof-object? c))
+	       (char-alphabetic? c))
+	[loop (bitwise-ior (signal->bit c) n)]
+	n))))
+
+; reads a set of 10 signals and 4 digits
+; returned as a two lists of bitfields
+(define (parse-line file)
+  (let loop [(signals '()) (digits '()) (n 0)]
+    (cond
+      [(< n 10)
+       (loop (cons (parse-wires file) signals) digits (+ n 1))]
+      [(= n 10)
+       (get-char file) ; consume |
+       (get-char file) ; consume space
+       (loop signals digits (+ n 1))]
+      [(< n 15)
+       (loop signals (cons (parse-wires file) digits) (+ n 1))]
+      [else
+	(list (reverse signals) (reverse digits))])))
+
+; read all the sets of signals/digits
+(define (parse-file file)
+  (let loop [(lines '())]
+    (if (eof-object? (peek-char file))
+      lines
+      (loop (cons (parse-line file) lines)))))
+
+; count digits that are easily recognized as 1, 4, 7 or 8
+; since they are the only combinations of 2, 4, 3 and 7 wires
+; it's as easy as counting the number of bits set in the bitfield
+(define (count-easy-digits lines)
+  (let [(count 0)]
+    (for-each
+      (lambda (line)
+	(for-each
+	  (lambda (digit)
+	    (let [(bit-count (bitwise-bit-count digit))]
+	      (when (or
+		      (= bit-count 2)  ; that's a 1
+		      (= bit-count 4)  ; that's a 4
+		      (= bit-count 3)  ; that's a 7
+		      (= bit-count 7)) ; that's an 8
+		(set! count (+ count 1)))))
+	  (cadr line)))
+      lines)
+    count))
+
+; returns a vector of 10 encodings for numbers 0 to 9 from the 10 signals received
+(define (build-decoder signals)
+  (let [(decoder (make-vector 10))
+	(encode-2-3-5 '())
+	(encode-0-6-9 '())]
+    (for-each 
+      (lambda (signal)
+	(case (bitwise-bit-count signal)
+	  (2 (vector-set! decoder 1 signal))
+	  (3 (vector-set! decoder 7 signal))
+	  (4 (vector-set! decoder 4 signal))
+	  (5 (set! encode-2-3-5 (cons signal encode-2-3-5)))
+	  (6 (set! encode-0-6-9 (cons signal encode-0-6-9)))
+	  (7 (vector-set! decoder 8 signal))))
+      signals)
+    ; between the 3 possible encodings of 3,
+    ; only the one with both the bits of 1 set can be correct
+    (let [(encode-1 (vector-ref decoder 1))]
+      (vector-set! decoder 3
+		   (fold-left
+		     (lambda (encoding signal)
+		       (if (= (bitwise-and signal encode-1) encode-1)
+			 signal
+			 encoding))
+		     0 encode-2-3-5)))
+    ; between the 3 possible encodings of 9,
+    ; only the one with all the bits of 4 set can be correct
+    (let [(encode-4 (vector-ref decoder 4))]
+      (vector-set! decoder 9
+		   (fold-left
+		     (lambda (encoding signal)
+		       (if (= (bitwise-and signal encode-4) encode-4)
+			 signal
+			 encoding))
+		     0 encode-0-6-9)))
+    ; (xor (encode 4) (encode 1) yields the bits corresponding to
+    ; the top left and middle segments
+    (let [(tl+m (bitwise-xor (vector-ref decoder 1)
+			     (vector-ref decoder 4)))]
+      ; between the 3 possible encodings of 5,
+      ; only the one with both of those bits set can be correct
+      (vector-set! decoder 5
+		   (fold-left
+		     (lambda (encoding signal)
+		       (if (= (bitwise-and signal tl+m) tl+m)
+			 signal
+			 encoding))
+		     0 encode-2-3-5))
+      ; between the 3 possible encodings of 6,
+      ; only the one that is not nine and has top-left and mid segment set can be correct
+      (let [(encode-9 (vector-ref decoder 9))]
+	(vector-set! decoder 6
+		     (fold-left
+		       (lambda (encoding signal)
+			 (if (and (= (bitwise-and signal tl+m) tl+m)
+				  (not (= signal encode-9)))
+			   signal
+			   encoding))
+		       0 encode-0-6-9))))
+    ; encoding for two is the last possible encoding
+    (let [(encode-3 (vector-ref decoder 3))
+	  (encode-5 (vector-ref decoder 5))]
+      (vector-set! decoder 2
+		   (fold-left
+		     (lambda (encoding signal)
+		       (if (not (or (= signal encode-3)
+				    (= signal encode-5)))
+			 signal
+			 encoding))
+		     0 encode-2-3-5)))
+    ; encoding for zero is the last possible encoding
+    (let [(encode-6 (vector-ref decoder 6))
+	  (encode-9 (vector-ref decoder 9))]
+      (vector-set! decoder 0
+		   (fold-left
+		     (lambda (encoding signal)
+		       (if (not (or (= signal encode-6)
+				    (= signal encode-9)))
+			 signal
+			 encoding))
+		     0 encode-0-6-9)))
+    decoder)) 
+
+; with given decoder vector, decode input digit
+(define (decode decoder input)
+  (vector-index (lambda (encoding) (= encoding input))
+		decoder))
+
+; returns the number read on the 4x 7-segment display
+; by decoding the encoding of digits with the signals
+; and applying the decoded bitfields to the digits received
+(define (decode-digits line)
+  (let [(signals (car line))
+	(digits (cadr line))]
+    (let [(decoder (build-decoder signals))]
+      (fold-left
+	(lambda (result digit)
+	  (+ 
+	    (* 10 result)
+	    (decode decoder digit)))
+	0
+	digits))))
+
+(call-with-input-file
+  "input"
+  (lambda (file)
+    (let [(lines (parse-file file))]
+      (printf "part 1:~% Number of easy digits (1, 4, 7 or 8): ~a~%"
+	      (count-easy-digits lines))
+      (printf "part 2:~% Sum of all decoded digits: ~a~%"
+	      (apply + (map decode-digits lines))))))
+

08-seven-segment-search/input

@@ -0,0 +1,200 @@
+dbc gfecab afcdg dfebcag bd dgbe bcaeg dcefab ecgadb agcbd | acdgb gbcda gdecfba bacge
+bacdegf aefbdc ebf fdbcag edbfa gdaeb acfdb cdegbf face fe | ebf ecdabf fcbad afcdbg
+cabgde gd becgfd dgfe cebgf gfdeacb fdbac bcgaef bgdfc gdc | cbfad dg dgef ecfbdg
+adecgf egfdc cgeadb adbfce dafg bcfeg dge dg fadec dcbegaf | dg dcegf cdgafe gbacfed
+badeg gdbfcea acgef fgdc bgcaef cd ebcfda gadce edcgaf edc | dce efcga dbgea dc
+bgfec dbfgec ebgafc afegcdb fca af cgdabf aegf badce cfabe | caf ebacf bafgec cbfeag
+begacd bd cfadbeg fbecg begfd bgd cdfeag gbaedf fdba agefd | cbgfe fdab efbdg bd
+bg gfdebc beg gabd fcbae fgaeb afegd gafdce dacbfge efgbda | gdba dfgae dgba gb
+cfd edcfbg abfcg gfdcb gbcefda dgcbe defg df acebfd caedbg | agedcbf dgbfaec gbfecd cdf
+bdcag acgebfd eac ae bade abcdgf bdacge bcgea aedgcf efcbg | cfdagb degacb eac edab
+ga ebcadgf gdaf bga fgecb dfabcg adcfb gadecb fecdab gbacf | fgda gdaf agb gfda
+gbcdaf fabdceg gbe ebfgad bfdga eg cefabg fdge adegb cedba | ge fcaedbg ebg aecbdfg
+ab bdeag gbdefc cgafdb fgedb agb befa bagfdec ecgda agfedb | ab aefb abg ab
+fgceab fcgdb fdcebg cbf gafbd cegfd bced cb cadfge cbdgafe | ecbagf cbfdeg cb bc
+fgb eafdgcb cefg ebdgac fcbged fbade fg gbfed gbecd fcabdg | fg eadfcgb fgcbda gedcb
+ecgfda faebc cb fadeb adecbg edfgabc bfgc cab gecaf ecbfag | fcgb bca gbcf cgbf
+gfaed cg cgab abdcf fabcgd gcfda fgc fdgacbe cbdaef fcebdg | fgc cfdageb cbfgad degfa
+fbacd gedfac fadegbc gbf degb ecgdf gb bdecfg gcdbf efbcag | cgedfb gb bcdfa cfdagbe
+dceg deacbg acfbeg egdafbc ebfda dc bcd cgabe gbdafc dbace | cged fabegc febad ebgcfa
+gbdcae cfgade dc dgbface fdage cbgfa adc gdafc dcfe gbdaef | fedc adgcf fcde dgacbfe
+afdgbe cgfabe dcgeab aef feacb fbgcade bgace cgef bcafd fe | ebacf abfdegc dbfac facgeb
+fbeg dgfecba cfgabd eafcb gb edacg gecfab aebcdf ebcag gcb | cfadeb gecda bg gb
+bfcaeg gd fbagc fgad fgcaedb fdgbac cdaeb dgfecb cagdb bdg | cbfgda dg afcedgb egfacb
+gd dcafgb dacfbe edbgacf gfbdc fbceg dbg dfag bdfca begdac | aecfdb eagdcfb fdcbgea fgdbc
+gf dfgc ebfgac bfdace gabfd adgfbc acbfd ecfagbd bgf aedgb | dfgc fdcg gfb gbf
+gbdae ebadf dbcfag acfdb dfec feacdbg geafcb dcbafe fe fae | efa bdcfa eaf debacgf
+deafgc fbgedca gfd dcga dcgbef aecfg dg agfebc adgfe dfabe | dgf badgcef fgace cabefgd
+badcg bagdce bdafgce efgbc df cbgfda cfdbg edgfac fgd adbf | dfcbg df cgbdae bdfgc
+dgabe beagc gbd gfcbdae gd bdegfa bgfedc fbcdae bafde fagd | bcdfge bgd bcage dfga
+adgf adgfce aecfg cdega dbgaecf abcgfe egd egcdfb dg deabc | cdgae dafg dfag afdg
+fbadec afcbg begac be ebcgda dceag edgb efdcga ebdacgf cbe | adfcebg ecafbd debgac edcafg
+cbd dcga cagbf dcafb cd cdebfg dgafcb baefd cbfaeg cfdgeab | fcdab geacbf gfbdce dgcafb
+becd abfdc cgbaf efcda bd ebdcaf gdfaceb bdf bdgeaf cedfga | ebdc fbd bdf fbgdae
+gefacd adcg fedbc cdgfe egd dg dbfega cgbfeda aecfg bcefga | defbcga efcga afgced gdecf
+gfacbd fbcgde cefba efdcga bfgcead egcdf gfb gcfbe bg edgb | gb fdegc gfb fgb
+ag agfdcb egfad fag adefb fdgec bdfgcae acfegd gebfdc aecg | fga ag egafd fcgebd
+cadgbf cd gefbac cdfba fbead cedagb gdcf adc gacbf fgebcda | gcbafd bdcaf gfcd abdfe
+fgebda fd afceb fcdeb fcad cgbed gabfcde dcabfe def befagc | eacfb efd efagcb def
+beaf gfcaebd fdeag dae acdgeb gcdfa dgabef gbedf ea dcbgef | ae aed ae ade
+gb dgeca gecab gcdfaeb ceafb bgc fagb adfceb baegcf gebfdc | fgba bg fecgab bg
+daf gbfda afcedg geadfb fbcdg fgaebc ad dbagefc dbae aebgf | aebd eadcbgf dfa beda
+dcbaef cabfd efgcba cbdgfa aedfg abecfdg ace cbde dfcae ce | cbefag ebcd cdabgf cbfda
+bcgefa bgfcead cd fcbadg bdcga dac gbaed gafdce cfbd bcagf | cbfag acd cfbd bdfc
+dgfcb aebgd gadefc bgfdec cbafgd cgbad egbdafc ac acbf cga | ca ac cabf abcf
+cgaed gafbdec fgaedc ba baegcd edfbg agcb bcdeaf ebdag bea | gfceda ecabfgd defgacb aeb
+cbfag cgdaf dcefab bac ba bdfceg cfgeb eagb cbfgea abcfdge | ba bac gabe cfbeda
+efcgd ecbafdg fgabed edb ebcg adcfb be efcdgb dfcgae dbefc | dcgef ebd becg gdfaebc
+fgedabc dafeb eg ged aegfbd afbecd fbgdc edfgb egaf dacegb | gaecdb cbegad fega fega
+bgfcdae fbcda df eafd gbcaed bdeca gfbac gfdbce bfadce bdf | afcbdeg gabfcde deaf cbeda
+fcgebda fcga bgfcd ebdfcg degba baf bafgd dfagbc bfcade af | afb agfc af cfegabd
+cbfg bfd eabfdg facbdg edfcgab bf fcabd aedcf ebgdac badcg | eafdc bdf bf fbcg
+fbdgce eagbfd dbacfeg dagb geabf cdeaf ebd bd fgbcae afebd | defac bed edb db
+aegcd bad gdaebcf cabfg db ecbd gafdce gcabd gbcade faebdg | dab dba dba cgfba
+ecdba bedacfg cdgeba dagcb bdge gdbfac fcadeg ced de acfeb | ed badfgc beacf bcgdafe
+fg abdeg fgebdca agdceb gfbd gdfae fga cdefa efagbc febgad | fg bgaefc gf bgafcde
+beadc gcbfed fdc bacf fc cbadefg feadc dgfea dcbefa dcgeba | cdf gefda dfc fbca
+bd bgcedf decafg gafcdb acgdf agbce bafd gaefbcd cdb acbdg | fcdga afbd cbfdeg cafdgb
+dabe bgcda egcdb fcdage dcebga bcfge dafgebc gdafcb ed ecd | ebad deba de gcbde
+ga gadcb ebcfdg egbcd agebdc eagb afcedg dbfca dfceagb dga | dabgc ga agd adbcg
+cbfagde ecdgf eabgfc fbd egbdf fageb edba dacbgf bdaegf bd | beda deab abgfe cegfd
+gcdfa gfea ef bdacfeg aedbc efc gfebdc adgbcf fecad aefcdg | feadc fe efc fgcad
+gdcae fga af acegfb fbda gfead edfgbc agdfecb dbgafe fdbge | fabd gfaed efgbd dagce
+afdebg febc cdbae abe eb dbfcea dabcfeg aecgdf dabgc dafce | cefb cedgaf eab acefd
+fgc dcabg gbdefac dfeg ecfdgb bfgcd gebcaf beafdc fg edbfc | cdfeb fcagbe fgbdace febdc
+aegfbd gacdeb fdeacgb dea dgcefb faeg bdfac dgefb ae debaf | debfg dea ea ead
+acgedb cfgae egfcbda fdeac eacbfd fd bdagfe dabec def fdcb | fed fd fcbd fde
+dba bgcfde da cdaf acfbgde fbgdc fgadeb dcbag agbec acgfdb | gacbdef adfgbe bgcad fcdabge
+acdfe cfgdab cdgea afgcebd dcgbae daf gfea fa egdfac bedfc | fa fad fa cedga
+caedg bafgde egcba dabegc agd fecdbga bcfeag fecdg ad abdc | gad cbeag dag cabd
+adfebg fedcagb fagdc gda eadc degcf gdafec ad cdbfge facbg | da aedc cbfgdea ad
+ecfdba dg dgafec gcabdfe fbadg fadcb gbdfca gfd bgefa dgbc | cgbd dbcaf cgdb dbgcfa
+ebacg eb begd dcebaf cdgea gafdce ecb cagfb bfadcge egcdba | bgdaecf bedacg dbeg cbdgae
+ebdagcf cgbea fe agefbc abgdf agfeb egafdc bcef feg deabcg | cegabd ecgafbd ef fe
+cd cgebdfa fgeabd cbd cabed gfbdec adcf abgce eafbd fcebad | efabcdg bcefgd baedc abfde
+acfg gbacfd edgfabc bdcaf dca caebdg dafbe gbcdf ac dfbgec | bgcfed cda dbgfc acd
+agdbefc abdc ecd gfcae aedbf gbcdef ebafdg ecadbf efadc cd | afdeb cde dbafce bfadge
+begad de fged gfbea dbe gbdac ebfgdac efgabd cadfbe fegabc | de dgfe cgfaeb gadbc
+gefdc gdfb gdbcaef deb ebfcd gcebad bd dacefg gdcbef fabce | gfedabc deb gcfade fdgb
+bdec dagcf cefbg bfgace bgedfc edacfbg fgdec fde adgefb de | dbfaegc cedb edfabcg fcdeg
+eaf gabed cabegdf fe ecbgaf fadeg gadfc fcdega cfde cbgafd | adgef fced cgdbafe fae
+fcbaedg gadce abcg ceb bgedf adfbec decagf bc dbceg eabdcg | ceb bgafecd cabg acefbd
+dagb cfgde acgfeb fbgac fcgdb bd dbf cbfagd fcbeda bcefgad | db fegdbca dbceafg aedbfc
+edagb da dab fbdge cgdfbe acegb adfe abdgfce dfgeab bfgcad | abd dab gfbead eagbc
+bdfega dcbgf efcgabd ce fec fcegd agce fegad daebfc efdcga | ec ecf dgacef bfecad
+cdabgef bgdfe aecgb gcfa fc acgebf dcaebf dcbgae cfgeb efc | fc fcga bfecga faecbdg
+dfeac gdfcea fcg acdebf cdge cgefa bdcgaf cg fegbdac bfage | cfg cfg gfeca fegac
+bfad bcf bedcga cadeb bf bceafd bcegfd dbaegfc ecfga cfbae | efacdb afbd bcf fb
+aegfcd bcdeg abcefg gcfea bcgafed bga afbe bagec ab fbdgac | gceba gacbe gbacef gab
+dca ebda bdfaceg acgdb gbcdea begcd efbdcg efacgd bfagc ad | adcbeg ad cbfga cfbgeda
+fadebc gcfbea becgf gf fgc abfg ecgbd dfecabg fcedag eafcb | ebfgc gaedfc bgcef gedabfc
+fadg eafgb gbead bdaec ecagbf dg gdb agfebd aedcgfb cfgbde | bfecdag bgd badce gd
+egcd efadb gacbfd bcaeg ecadgb adc bacegf adecb dc agedcfb | fcgabe degc acd cd
+bedfcag gc fagdec gfabce bfgec acgb befac gfc bgdef aecfbd | cg ebfdg cfg gc
+aegbdf gfabced fadebc gfde ed bcaeg fbgda eadbg fgbacd bde | dbcefag bed afcbged aegdb
+agd fagec cfbgda bfceagd fgeacb cdae gdbef dagef da efcdga | edbgf gda gedaf cdgfaeb
+fgaec eb fcgbd agfdeb cedb fabcdeg egb febcg dfbgec cdfgab | fgbcde dbeafg egcfdba gcbfd
+gfe fdbae ge bfgdc dgfaec cgeb dcfgbe dabfgc fdegb eabgcdf | gebc gceb defbcag afbcedg
+dfce cgbed fbcagd bcdgf ged bdfgae ed bdfceg agebc fabdegc | fcde gde gecdbf de
+dba dcafbg gcdefb fbged dgeab bfegad gaecd ba aebf egafdcb | beadg cfdbage bgafde acdge
+bcgdef cbdgeaf ae fbdace afbde gcdabe gdbfa edbcf fcea bea | dgafb adbfce ea fbdecga
+afdg fgebc fdeacbg fd gadcb fdcgb gfacbd gbeacd acdfeb dfc | fd bdcafeg caefbd dafg
+dfebag defa bdgfa beafg agbcfd eab cbagefd cfgbe ea acbgde | abdcge abe ae fecbg
+ef bgfdeac bdcefg cfdba ecf dgecba gfae abgefc ecbga acefb | debcag afge efag fe
+cg gbfc gabcd bgade dgc gbecafd egdfac dfbac abdcfe gabfdc | gcbad degfabc cgafbd adbgcf
+edbcgf acgbf fbaedc cbfae gfc agcdb dagecfb fg fcgbea eagf | fg adcbef fbeac fadcgeb
+deacg daeb dagbce ecdbgf edc ed bgaefc gecba dagcf abdgecf | cdaeg abcge dec ecd
+fcgadb caged bedc cdabeg dfaecbg befag db dgb eagbd gacdef | fecagdb begad dgb db
+fbcdga fgcad fecdg gcedab bfca adc ac bfdga dbfega eafbcdg | adc cbgade fgcadb ceabgd
+cefdbg gde bgfeac ed begcd cbefg bfde aedcgf cbafegd gacbd | fegbdac gcbefd cbgef bgedc
+bfdagc afdc bagcf gbfdc begcd begdaf beafgc dbefgac gfd fd | fcda df dfac dcbfg
+gcbfe bfeacg cedbf ge bfcga gfe gfecda ecbgdfa bgfadc bage | feg eagb gef abfgc
+bgfec bac abecdfg ab gdcea ebgcfa fagb aebcg caebfd gfcbed | ab ab cba acgbe
+gdbcf cbedg ce ceg abcgde adbeg efgcab bdfegac adec adfbeg | gaecdfb bedga cge cead
+eafcb cfdbe aeb acfeg ab dcgbfe adfb fgacedb ecabgd fdbcae | fbcde aedfcbg bea edcbf
+ebdca egc cgabe fbge cgbfda ge bacfg geacbf afdgec gebacfd | badce cge bgfcea ge
+gdfecb bdge gdf dgbcaf aefbgc bfecg fgdec dg ecdbfga deacf | dgf fedcagb gd gcedf
+agdeb cfdbag gcabd ed dacegbf gebfa eagbdc acde efcgbd edb | ed eagdb de de
+feag cfgbed feacbdg cfgade efcdg fcgdab afd dfeac af abedc | cbagfde dbagfc faeg dgabcf
+cdg efgbcd decgfa dcegb dgbf gd ebdcfga adebc gbcfe cefagb | bfecg dgbf gdbf dg
+gab dfceag gdcb bg gbead agdefbc gcabef acged efdba agdceb | gdcb bgdc edbfa bag
+bgafde afdgc gcafed efgdc ceda gdcebfa gdbacf de gbcef edg | edg gde eadfcbg cade
+gdb egcfadb gdef abcfd dg ebfag gadbef abdgf aefbgc cbgaed | fedgba dbegfac bfeagd gefcdba
+gad bdcag becdg gceabd dceafbg fgdeca fcgab ad baed dfcbge | cfaegdb gda ad gaedcfb
+dafbeg eadgbfc fgd bagcf gedb abdfce gafdb fcdgea gd efbda | gebd fdg gaefcd deagcf
+cdbe adefb ecfgbad bfcgad bacdf agcefd efd cdeafb aegfb de | gacebdf bdce fbcagd dcefab
+cb acdgbe bce cdegabf bgdefa aegdb cdbg acbde fcebga fdace | ebc abfdecg ceb gbacdfe
+cg fcedg edfbag ceag fdbec gdc faedcg bdcefag gbafcd dfeag | geca dgfacb cgd cg
+bcafde defac dcage dgfbce gafc cgaedf cgd cg fgcedab gdeab | cdg ebadg aedgcf fagc
+bdec dagbf ecagfb decbfa aefdc aeb dcegfa adefcbg ebadf be | cdbe gfadb eadfc dcbe
+bcgeda fc badfe gbfdaec fcge cfd bedfc cedbg adfgbc dcgebf | cf ebacgfd fgce fdbceag
+gd fgbdea dbg badce gdcab fcagedb fbacg beacfg cgfd dcafbg | fcdg gdcbfa dbg gdfc
+cag cdfa cgade edgcbf fcebga begfcad gfdcae egabd defgc ac | ca agc fgbace gac
+ecabf geacfb eabdcf dec cd bgecfda gfdbce edcba cdaf adgeb | ced aedfgbc dc gbeda
+fbdac ea cadefg fae beag facbe bfgeacd cfdegb bgfec gfecba | agbe ea bafce egbdcf
+bdc dbega abcdg gbcfa dc gcde cgbaefd cdfbae eagdbf ebgadc | adefcb agcfb cdb gced
+ceb ce debfca abgdfe bdaeg cabegd caeg dbgec dcbfg bdecgfa | ce abegd gdfcb fcbdgae
+cafedgb dgf bcfd cgdfbe acedfg gbfed agedb aecgfb bfgec fd | fdgbec feacdg df bgcfe
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