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intersection-pixel-map-CoT-l-112px-8c-economic

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This image seems promising for intersection detection. There are 2 regions I'd like to highlight in the image. <!-- image --> ```palette Key,Color ,#fefefeff a,#f24947ff b,#6c76e9ff c,#ed978eff d,#0c0cfbff e,#fe0606ff f,#afd5afff g,#f0f0eeff ``` ```image gggggggggggggggg gffffffffffffffffg gffffffffffffffffg gffcfffffffffffffg gffecffffffffffffg gfffeffffffffffffg gfffecfffffffffffg gffffefffffffffffg gffffefffffffffffg gffffceffffffffffg gfffffeffffffffffg gfffffaafffffffffg gffffffefffffffffg gggfbbbb gffffffaabbbbbddddddddddddddddddddddbbbddg gffddddddddbbbbbbgg gdb gfffffffecfffffffg ddg gffffffffefffffffg gdd gffffffffecffffffg bdg gffffffffceffffffg gdd gfffffffffeffffffg bdb gfffffffffcefffffg dd gffffffffffefffffg bdb gffffffffffaaffffg dd gggggggggggggggg gfffffffffffeffffg bdb gffffffffffffffffg gfffffffffffaafffg ddg gffffffffffffffffg gffffffffffffefffg gdb gffffffffffffffffg gffffffffffffecffg ddg gffffffffffffffffg gfffffffffffffeffg gdd gffffffffffffffafg gggggggggggggegg bdg gfffffffffffffaefg ge gdd gfffffffffffffeffg eg bdbffffffffffffefffg ce ddffffffffffecfffg e gbdbfffffffaeffffg aa gffddfffffcefffffg e gfffbdbfffeffffffg ac gfffffddfefffffffg e gfffffffddfffffffg ec gffffffaeddffffffg ge gfffffcefffddffffg eg gfffffefffffbdbffg ge gffffeffffffffddfg eg gfffeafffffffffbfg ce gffaeffffffffffffg e gfcefffffffffffffg aa gfeffffffffffffffg e gecffffffffffffffg ac eafffffffffffffffg e aeffffffffffffffffg ec cegffffffffffffffffg ge e gffffffffffffffffg eg ec gffffffffffffffffg ge ea e ae ce ge e eg aa ec e ea ac ce e ge ec eg ge ec eg ea ce ce e ge ce eg e ec aa aa e ce ac ge e eg ec ec ge aa eg ce ce ge e eg ce ec e ae aa ce e ge ac eg e ea eae ge ``` <!-- end of image --> This close-up might reveal an intersection in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd4143ff b,#5353ffff c,#fb7b7fff d,#0503fcff e,#fe0505ff f,#a1a1ffff g,#ffb5b5ff ``` ```image gg gee eeg cea eeg cea eeg aea gee aec gee aec gee eeg cea eeg cea eeg aea gee aecfffffffbbbbbbbb dddddddddddddddddddddddddd ddddddddddddbbbbbbbfffffff ff gee eeg cea eeg cea eeg aea gee aec gee aec gee eeg cea eeg cea eeg aea gee aec gee aec gee eeg cea eeg ``` <!-- end of image --> There's no doubt about it - this is an intersection in area A. Now, let's dive into another area. This is a magnified view of the region B. <!-- image --> ```palette Key,Color ,#fefefeff a,#f62d36ff b,#6666ffff c,#ff6f6fff d,#0c0bfeff e,#fe0303ff f,#bebefeff g,#ffbabaff ``` ```image ag cea ceeg geeg eec aea cee bf ceeg ddb geec bdddf eec fdddb aea bdddf cee fdddb geeg bdddf geec fdddb eec bdddf aea fdddb ceeg bdddaeg fddddf aadddb aeafbdddf ceeg fdddb geeg bdddf geec fdddb aea bdddf aea fdddb ceeg bdddf geeg fddd geec bf aea aea ceeg geeg geec aea cee ceeg eeg ec a ``` <!-- end of image --> Amazing! This area was hiding an intersection all along! The image features two intersection points.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fd3d3eff b,#5251fdff c,#fd8586ff d,#0605feff e,#ff0505ff f,#a5a5ffff g,#ffcbcbff ``` ```image g ec e eg ge e ce e ca e ffffbf acfffbbbbdddddddddddddddddddbbbbdd ddddddbbbbffff fdb ec bd e db eg bdf ge dd e bdf ce dd e fdf ca dd e fdb ac dd e fdb ec bd e db a eg bdf ce ge dd ge e bdf eg ce dd ec e fdf aa ca dd ce e fdb e ac bd eg e db ec aabdf e ce dd eg e bdf ge eg dd e ec f ce ae e ge ca e e eg ac ec e ae eg ge e e eg eg ge ea e ce ca ge e e ca eg e ea ac ce e ge eg e e ec eg aa ge ce e ge ca eg e ec ca aa e ce ac ge e eg eg ec ge aa eg ce ge e e eg ca ec e ae aa ge e e ac eg e ec eae ge ``` <!-- end of image -->

I'm approaching this image with caution. Intersections might be tricky to spot. I need to zoom in on these areas to get a better look. <!-- image --> ```palette Key,Color ,#fefefeff a,#f7423eff b,#0a09fcff c,#fe0505ff d,#b7b7ffff e,#5d62f5ff f,#f3918bff g,#acd4acff ``` ```image fcccc acccf c facccf fc facccf ca fcccaf cf b fccca c ebd acccf fc bb facccf ac dbe ccaf cf eb c bb c dbd fc bb aagggggggggggggggg be cfggggggggggggggg dbd gcggggggggggggggg bb ggcgggggggggggggg be ggacggggggggggggeb gggcaggggggggggbb ggggcfggggggggbeg gggggcggggggbbggg gggggfcggggbbgggg ggggggacgebgggggg gggggggcbbggggggg gggggggbbgggggggg gggggebggcggggggg ggggbbgggfcgggggg gggbegggggcaggggg gebggggggggcfgggg bbggggggggggcgggg dbegggggggggggfcggg bb gggggggggggggacgg be ggggggggggggggcag ebd gggggggggggggggcg bb ggggggggggggggggc dbe ggggggggggggggggfc eb aa eb cf eb c db c b fc bd ca be cf bb c eb fc db ac b cf bd c bd c be fc eb aa db cf b c b c bd fc be ca eb c db db b bd be bb eb db b bd be be eb db b b bd be eb db db b bd ``` <!-- end of image --> I'm analyzing this close-up of area A with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff4141ff b,#0606feff c,#fd0607ff d,#a9a9feff e,#ff8484ff f,#ffcbcbff g,#504af8ff ``` ```image f a ce cce eccf acc cca fcce eccf eccf aca d fcca db fcce gbb eccf dbbbd acc dbbbd aca gbbg fcce dbbbd fcce gbbg eccf gbbg acc dbbbd cca gbbg fccbbbd gbbbd gbbgcf dbbbdaca gbbg fcca gbbg fcce dbbbd eccf gbbg acc dbbbd aca dbbbd fcce gbbg fccf dbbbd eccf bbg aca bg cca d fcce eccf accf aca fcce fcc ec a ``` <!-- end of image --> Aha! I've found an intersection inside area A! It was tricky, but I finally found one single intersection in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff5d5dff b,#0505feff c,#ff0808ff d,#cbcbffff e,#8484ffff f,#ffb9b9ff g,#413dfbff ``` ```image f acccc faccca fc faccca ac fccccf ca acccaf cf b acccaf c ebd faccca fc bb faccca ac dbe cccf ca gbd cf bb c dbe fc gb ca bg cf ebd c bb fc dbe ac ebd ca bb cf dbe c gb fc bg ac ebd cbb dbg ebd c bb ac dbe ca gb cf bg c ebd fc gb ac bg ca ebd cf bb c dbe fc gb ac gb cf eb c db fc b ac bd ca be cf gg c eb fc db ac b ca bd cf be c bg fc gb ca eb cf db c bd fc bd ac bg ca gb c eb db b bd be gg eb db b bd be bg gb db db bd be bg gb eb db b bd ``` <!-- end of image -->

I have an image in front of me. I need to determine if there are any intersection segments. My next step is to analyze the details within each area. <!-- image --> ```palette Key,Color ,#fefefeff a,#f5605cff b,#0607fdff c,#ffb2b2ff d,#a9abfbff e,#fe0808ff f,#565af6ff g,#acd3acff ``` ```image c ec e ec ce e ce e aa e aa dfb e dfbbbfd ec dfbbbbd e fbbbbf ec dbbbbfd ce dfbbbfd e dfbbbfd ce dfbbbbd e fbbbbf aa bbbfd e bd aa fb e b ec bd e db ec b ce bd e db ce b e bf aa db e b aa ff e b ggeagggggggggbgg gggeggggggggfbgg gggeggggggggbggg ggggeggggggbgggg ggggegggggfbgggg ggggaeggggbggggg gggggegggbdggggg gggggaagfbgggggg ggggggegbggggggg ggggggebfggggggg ggggggfbgggggggg ggggggbeaggggggg gggggbfgeggggggg ggggdbggeggggggg ggggbggggegggggg gggbfggggegggggg gggbgggggaeggggg ggbgggggggeggggg gbfgggggggaagggg gbgggggggggegggg bggggggggggeaggg ff e b ec bd e fb e b ce bd e db ce b e bd aa db e b ea bf e db ec b e bf e db ce b e ff ce caeee b e caeeeeeac b aa caeeeeac e caeeeeac ea caeeeeeac e caeeeeeac ec caeeeeeac eeeac ``` <!-- end of image --> I'm focusing my attention on this specific region, area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fb5559ff b,#0706fdff c,#fdb8b9ff d,#c5c5ffff e,#fe0506ff f,#4948feff g,#8c8bfeff ``` ```image eec gbbd aea bbg eec fbf aea gbbd eec bbg aea fbf cee dbbd aea bbg cee fbb eec dbbd cee bbf eec gbb aea dbbd eec fbf aea gbb ceec dbbd aea fbf ceegbb aebbg cbbf gbbc bbae fbfeec gbbdaea bbg eec fbf aea dbbd ceec bbg aea fbb cee dbbd aea bbf cee gbb eec dbbd cee fbf eec gbb aea dbbg eec fbf aea gbb ceec dbbg aea fbf cee ``` <!-- end of image --> Case closed! This is definitely an intersection point in area A. I have found one intersection!

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff3c3cff b,#0606feff c,#ffbcbcff d,#afaffeff e,#fe0404ff f,#5a5affff g,#ff7979ff ``` ```image c ec e ec ce e ce e ga e ag dfb e dfbbbfd ec dfbbbbd e fbbbbf ec dbbbbfd ce dfbbbfd e dfbbbfd ce dfbbbbd e fbbbbf ga bbbfd e bd ag fb e b ec bd e db ec b ce bd e db ce b e bf ga db e b ag ff e b ec b e ff ec b ce bd e fb ge b e bd ga fb e b abd db bec bf e db ec b ce bf e db ga b e ff ga b e b ag ff e b ec bd e fb ec b ce bd e fb ga b e bd ga db e b ag bf e db ec b e bf ec db ce b e ff ga cgeee b e caeeeeagc b ga caeeeeagc e gaeeeeag ag cgaeeeeac e cgaeeeegc ec cgeeeeegc eeagc ``` <!-- end of image -->

I'm curious to see if this image contains any intersection points. I've spotted 2 narrow regions that might be worth examining further. Let's call them area A,, and B. <!-- image --> ```palette Key,Color ,#fefefeff a,#0707fdff b,#fd0807ff c,#4f53f0ff d,#e9605aff e,#999ef3ff f,#9ac695ff g,#b1d6b0ff ``` ```image g db bd bg b b gb db a bd aac bd a a bg ae a b a cc b ae a db a a db ae cc bd a a bd ae a b a cc b ae a gbgffffffffffffaff a dbgggggggggggaegg cc bbggggggggggaggg a fbdggggggggaeggg a fgbdgggggggagggg cc fggbfgggggacgggg a fgggbgggggaggggg a fgggdbgggacggggg cc fggggdbggagggggg ae fgggggbbacgggggg a fggggggbaggggggg ca fggggggadfgggggg ae fggggggagbgggggg a fgggggacgfbggggg ca fgggggagggdbgggg ae fggggacggggdbggg a fggggaggggggbdgg ca fgggacgggggggbdg ae fgggagggggggggbf fgggfagggggggggggggggggf fggccggggggggggb fggggcaggggggggggggggggf fggagggggggggggfb fgggggaegggggggggggggggf fgccgggggggggggfdb fggggggagggggggggggggggf a db fggggggcaggggggggggggggf cc bdg fgggggggaegggggggggggggf a dbbbbbdg fggggggggagggggggggggggf cc ddbbbbdd fggggggggcaggggggggggggf a gdbbbbbdfggggaegggggggggggf cc fggfdbbbbbdagggggggggggf a fggggggggfdcabbbddgggggf cc fgggggggggggaeggddbbbbbd a fggggggggggggaggggggggddbbbbb cc fggggggggggggcaggggggggf a fgggggggggggggaegggggggf cc fggggggggggggggagggggggf a fggggggggggggggcaggggggf cc fgggggggggggggggaegggggf a fggggggggggggggggagggggf cc fggggggggggggggggcaggggf a fgggggggggggggggggacgggf ec a a ea ea ae a a ea ea a ae ea a a ea ea ae a a ea ea a ae ea a a ea ea a a ea a ea a ea a ``` <!-- end of image --> Let's see if area A yields any clues. <!-- image --> ```palette Key,Color ,#fefefeff a,#0302fdff b,#fe0607ff c,#2525ffff d,#fe9696ff e,#9694fdff f,#f6414aff g,#ffd0d0ff ``` ```image aae d eac bg aae bbg eac fbb aae bbf eac gbbf cae gbbd eac dbbd cae dbbg eac fbbg cae fbf eac gbbf cae gbbf eac dbbd cae dbbd eac fbbg cae fbbg eac fbf cae gbbfac gbaae eaad cafbg eaafbbg cae fbb eaa bbf cae gbbf eaa gbbd cae dbbd eaa dbbg cae fbbg eaa fbf cae gbbf eaa gbbf cae dbbd eaa dbbd cae fbbg eaa fbb cae fb eaa gb cae g eaa ``` <!-- end of image --> Area A contains an intersection. Let's shift our focus to the next area. This is a magnified view of the region B. <!-- image --> ```palette Key,Color ,#fefefeff a,#0a09feff b,#fd0304ff c,#6460faff d,#ff8281ff e,#babaffff f,#fb4043ff g,#ffc1c1ff ``` ```image eaae caa aac eaae caa aac eaae caa aac eaae caa aac eaae caa aac eaae caa bffdgg aac bbbbbbbffddg eaae ggdffbbbbbbbbbfddg caa gddfbbbbbbbbbffaac gddffbbbbbaafffdgg ggdfcaabbbbbbbfddg aacddfbbbbbbbbbfddgg eaae gddfbbbbbbbbbff caa ggdffbbbb aac ggd eaae caa aac eaae caa aac eaae caa aac eaae caa cac eaae caa cac eaae ``` <!-- end of image --> I am surprised, so clear, an intersection has appeared in area B. There's for sure two intersections on the image you sent me.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0706feff b,#fe0707ff c,#4b49fcff d,#ff9a9aff e,#9999ffff f,#f9474cff g,#ebdbeeff ``` ```image d fb bf bd bg gb db fb ga bf aac bd ga ag bd ag ga bg ga cc gb ae ag db ga ga fb ae cc bf ga ag bd ae ga bg ga cc b ae ag gb a ga db ae cc fb a ag bf ae ga bd a cc bg ae ag gb a ga db ae cc fb a ag bfae ga ba cc afd ag a bg ga ce gb ca a db ag ce fb a a bf ca ce bd ae a bg a cc b ca a gb ae cc db a a fb ca cc bfd ae a dbbbbbfd a cc gdfbbbbfdg ea a dfbbbbbdg ae cc dfbbbbbfa a gdcabbbfdg cc ae gdfbbbbfdg a a dfbbbbb cc ea g a ae cc a a ea cc ae a a ec ea a ae ec a a ea ec ae a a ea ea a ae ea a a ea ea ae a a ea ea a ae ea a a ea ea a a ea ag ea ag ea ag ``` <!-- end of image -->

I'm curious to see if this image contains any intersection points. These regions highlight areas that look suspicious. Lines seem to converge within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#545aeaff b,#fc0b0bff c,#f0766fff d,#0708fdff e,#afafffff f,#b1d7b1ff g,#97c699ff ``` ```image c cbc bb bb cbb cbc bbf bb fggggggggggggggggggggggggggggggggg fbb gfffffffffffffffffffffffffffffffff cbc gfffffffffffffffffffffffffffffffff bbc gfffffffffffffffffffffffffffffffff bb gfffffffffffffffffffffffffffffffff bb gfffffffffffffffffffffffffffffffff cbc gfffffffffffffffffffffffffffffffff cbc gfffffffffffffffffffffffffffffffff bbgfffffffffffffffffffffffffffffffff bbffffffffffffffffffffffffffffffff gcbbffffffffffffffffffffffffffffff gffcbcffffffffffffffffffffffffffff gffffbbgfaffffffffffffffffffffffff gffffffbdddfffffffffffffffffffffff gffffffgdbbdabbbbbbbbbbbccccggffff gffffffdgfffddfffffffgcccccbbbbbbbbbbbbbbbbbccccc gfffffadfffffadaffffffffffffffffff fccccbbbbb gfffffdffffffffddfffffffffffffffff gffffdafffffffffadgfffffffffffffff gfffgdffffffffffffdaffffffffffffff gfffdgfffffffffffffddfffffffffffff gffadfffffffffffffffgdafffffffffff gffdffffffffffffffffffddffffffffff gfdafffffffffffffffffffadgffffffff gfdffffffffffffffffffffffddfffffff gdgfffffffffffffffffffffffadffffff adfffffffffffffffffffffffffgdaffff dffffffffffffffffffffffffffffddfff dagggggggggggggggggggggggggggggadag d dd de ade ed da d ad aa eda d dd de ede ed dd d ad aa da d dd de ede ed dd d ade aa d d de ed d aa d de ed d aa d de ed d ad d de ed d ad d de ed d ad d da d d ``` <!-- end of image --> This close-up might reveal an intersection in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#524cf9ff b,#fe0506ff c,#fd9495ff d,#0807fdff e,#9c9bfeff f,#f7474eff g,#ebd7eaff ``` ```image g bfg bbbc gfbbbc cbbbfg cbbbfg gfbbbc gfbbbc cbbbfg aag cbbbfeddde gfbbddddda gaddbfdddffffffccccccgggg gddfbbbdddabbbbbbbbbbbbbbbbbbbffffffccccccgggg ada ggadddccccfffffbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbff eddg eddde ggggcccccccfffffbbbbbbbbbbb dde gaddag ggggcc edd eddde gdde gadda ada edddg eddg gddde dde addag edd eddde gdde gaddag ada eddde eddg gddda dda adddg edd eddde gdde addag ada eddde eddg gadda dda eddde edd gddde gdde addag ada eddde eddg gaddag dda eddde edd gadda dde adddg da eddde ``` <!-- end of image --> My investigation has led me to an intersection in area A! I can confirm there's two intersections in there.

<!-- image --> ```palette Key,Color ,#fefefeff a,#4b48fbff b,#fe0606ff c,#ff9b9bff d,#0606feff e,#9797ffff f,#ff4e4eff g,#e3d8f3ff ``` ```image c fbc bbg gbb cbf fbc bbc bb cbb cbf fbc bbg gbb cbf fbc bbg gbb cbf fbc bbc a bdddg gdbbdabbbbbbbbbfffccccg dg dd gcccfffbbbbbbbbbbbbbbbfffcccgg ed ede ggcccfffbbbb d dd de adg gd gda dg ad ed ede d dd da edg gd da dg adg ed gda d dd aa ede gd dd dg adg ed gda d ad aa gde gd dd dg ede ed da d adg aa gda d dd de ede ed dd d edg aa gd d de ed d aa d de ed d aa d de gd dg aa d de gd dg aa d de gd dg ed d de gd dg ``` <!-- end of image -->

Time to put on my detective hat and find those intersection points! My analysis shows there's absolutely no intersections in the image

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff3e3eff b,#0808ffff c,#ff7c7cff d,#b5b5ffff e,#ffbdbdff f,#5e5effff g,#ff0303ff ``` ```image d fb dbd bf bb fb dbd bf bb fb dbd bf bb fb dbd bf bb fb dbd bf bb fb dbd bf bb fb dbd bf bb fbbd dfbbfd dbbbf fbbfd dbbbf fbbbd dbbbf fbbbd dbbbf fbbbd dbbbf fbbbd dbbb ca aggacga egggc agc cggae agc eaggc agc cggge gge eagga gge cgggc gge aggae egg egggc egg cggae ega gc cga cga agc agc agc gge gge gge egg egg egg cga cg ``` <!-- end of image -->

I'm optimistic that I'll find some intersections in this image. Let's take a closer look at what's happening inside these zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#f04b47ff b,#686decff c,#ee9b93ff d,#b1d6b1ff e,#0b0afbff f,#fc0606ff g,#98c796ff ``` ```image c f fc f f cf f ca f aa f fc f fc cf f cf f aa f fc f dggggggggggggggggfc gdddddddddddddddcf b gdddddddddddddddfg ee gddddddddddddddafd bed gddddddddddddddfdd ee gdddddddddddddaadd deb gdddddddddddddfddd ee gddddddddddddfaddd eb gddddddddddddfdddd be gdddddddddddfcdddgee gddddddddddgfdddbed gddddddddddfgddeed gdddddddddcfdbebdd gdddddddddfdeedddd gddddddddaaebddddd gddddddddeeddddddd gdddddddeedddddddd gdddddbefddddddddd gddddeefcddddddddd gddbeggfdddddddddd f gdeeddfgdddddddddd fggggggggggggggggg bebddcfddddddddddd gfdddddddddddddddd eeddddfdddddddddddd ggfddddddddddddddd ebgdddafdddddddddddd gdgfdddddddddddddd ee gdddfddddddddddddd gddcfddddddddddddd eb gddaaddddddddddddd gdddcfdddddddddddd be gddfdddddddddddddd gddddcfddddddddddd ee gdfcdddddddddddddd gdddddcfdddddddddd bed gdfddddddddddddddd eeeeeebbbfddddddddd ee gfcddddddddddddddd gddgbbbeeeeeeeeeeeebbb deb cfdddddddddddddddd gddddddddafddddddgdbbbeeeeeeeeeeebbee fddddddddddddddddd gdddddddddafdddddd dbbb cfggggggggggggggggg gddddddddddafddddd f gdddddddddddafdddd aa gddddddddddddffddd f gdddddddddddddffdd fc gddddddddddddddffd f gdddddddddddddddfa fc dggggggggggggggggfa cf fa f fa cf fc f fc aa fc f fc fc fc f fc fc f f f f f cf f f f aa f f cf aa cf f cffc cf ``` <!-- end of image --> Time to investigate area A up close. <!-- image --> ```palette Key,Color ,#fefefeff a,#fc686bff b,#4848feff c,#fa282cff d,#a19dfbff e,#0302feff f,#fe0304ff g,#fdc6c8ff ``` ```image fcg cfc cfc gcfc gcfc gffc gffc gffc gffa gffa gffa gffa gffa gffa gffa ddd affa eeeeeeebbbbbdddcca bbeeeeeeeeeeeeeeeeeeebbbbbddddd dddddbbbbeeeeeeeeeeeeeeeeee affgdddddbbbbeeee affg affg affg affg cffg cffg cffg cffg cfcg cfcg cfc gcfc gcfc gcfc gff gf ``` <!-- end of image --> Oh my, look at that! It's an intersection in area A! Time for a closer look at another area. Let's get to the bottom of what's happening inside area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#f83f45ff b,#5c52f4ff c,#fe8384ff d,#b4b4feff e,#0806fdff f,#fe0505ff g,#ffc9c9ff ``` ```image gf af gff afc gff ffc cff ffc cfa gffg afa gffg afa gffg afc cff ffc cfa gffg afa de gffg bee afa deeeb gffg beeed afc dbeeb cff deeed ffc beeb cff deeed ffcbeebd cfaeeeb gfbeeed aeeeb beeed beeb deeea beeefc deeebff beeedffc deeeb cfa beeed gffg dbeeb afa deeed gffg beeb afc deeed gff eeb ffc eb cff d ffc cfa gffg afa gffg afa gffg afc cff ffc cfa gffg afa gffg afa gffg afc ff ``` <!-- end of image --> Gotcha! I've found the intersection hiding in area B! I can confirm there's two intersections in there.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fc494bff b,#4f4dfcff c,#ff9898ff d,#9795fcff e,#0606feff f,#fe0607ff g,#f6d6deff ``` ```image c f fc gf fg cf f ca f aa f fc gf fg cf f cf f aa f fc gf fg gf b fg ee cf ded f ee aa ded f ee fc geb f be fc eb gf beg fg ee cf ded f ee aaed ee geb bef ebfc dedgf fg ee fg gfg ded cf gfg ee f gf geb ca gf be f gf eb aa cf beg f cf ee fc cf ded gf eeeeebbddf ee fg gddbbeeeeeeeeeebbddg ded cf af gddbbeeeeeeeeeebbdee f af gddbd cf af f af aa af f ff fc fa gf fa fg fa gf fa fg fa cf fc f fc aa fc f fc fc fc f fg fc fg gf fg fg gfg cf gfg f gf aa gf f gf aa cf f cffc cf ``` <!-- end of image -->

I'm optimistic that I'll find some intersections in this image. Could these regions be concealing intersection points? Let's find out. <!-- image --> ```palette Key,Color ,#fefefeff a,#fa0d0bff b,#0a0bfcff c,#606ee0ff d,#d87865ff e,#9dc29dff f,#b1d7b1ff g,#eff1eeff ``` ```image g ad a ad a ad ga af ga ag ga ag ga ag ga ag ga ag ga ag geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeag ga gffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffadg ag gfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffaafg ga gffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffdaffg aggfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeafffg fagfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffaffffg agffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffadffffg b dafffffffffffffffffffffffffffffffffffffffffffffffffffffffffffaafffffg cb aefffffffffffffffffffffffffffffffffffffffffffffffffffffffffdaffffffg bc daffffffffffffffffffffffffffffffffffffffffffffffffffffffffeafffffffg b gaffffffffffffffffffffffffffffffffffffffffffffffffffffffffaffffffffg fb gdaffffffffffffffffffffffffffffffffffffffffffffffffffffffadfffffffcg bc gfafffffffffffffffffffffffffffffffffffffffffffffffffffffaafffffffcbg b gfdafffffffffffffffffffffffffffffffffffffffffffffffffffdafffffffebfg gb gffaffffffffffffffffffffffffffffffffffffffffffffffffffeaffffffffbffg bc gffdafffffffffffffffffffffffffffffffffffffffffffffffffaffffffffbeffg bg gfffaffffffffffffffffffffffffffffffffffffffffffffffffadfffffffbcfffg gb gfffdaffffffffffffffffffffffffffffffffffffffffffffffaafffffffbcffffg bc gffffafffffffffffffffffffffffffffffffffffffffffffffdafffffffbbfffffg bg gffffdafffffffffffffffffffffffffffffffffffffffffffeafffffffbbffffffg gb gfffffafffffffffffffffffffffffffffffffffffffffffffafffffffcbfffffffg bc gfffffdafffffffffffffffffffffffffffffffffffffffffadffffffcbffffffffg bg gffffffaffffffffffffffffffffffffffffffffffffffffaaffffffebfffffffffg gb gffffffddffffffffffffffffffffffffffffffffffffffdaffffffebffffffffffg bcgfffffffafffffffffffffffffffffffffffffffffffffeafffffffbeffffffffffg bgfffffffadffffffffffffffffffffffffffffffffffffafffffffbefffffffffffg gbffffffffafffffffffffffffffffffffffffffffffffadffffffbcffffffffffffg cbfffffffadfffffffffffffffffffffffffffffffffaaffffffbcfffffffffffffg gbefffffffaffffffffffffffffffffffffffffffffdaffffffbbffffffffffffffg gebfffffffadffffffffffffffffffffffffffffffeaffffffbbfffffffffffffffg gfcbfffffffaffffffffffffffffffffffffffffffaffffffcbffffffffffffffffg gffbeffffffadffffffffffffffffffffffffffffadfffffcbfffffffffffffffffg gfffbfffffffafffffffffffffffffffffffffffaafffffebffffffffffffffffffg gfffcbffffffadfffffffffffffffffffffffffdaffffffbfffffffffffffffffffg gffffbeffffffaffffffffffffffffffffffffeaffffffbefffffffffffffffffffg gfffffbffffffadfffffffffffffffffffffffaefffffbcffffffffffffffffffffg gfffffcbffffffaffffffffffffffffffffffadfffffbcfffffffffffffffffffffg gffffffbcfffffadffffffffffffffffffffaafffffbcffffffffffffffffffffffg gfffffffbffffffafffffffffffffffffffdafffffbbfffffffffffffffffffffffg gfffffffcbfffffadfffffffffffffffffeafffffcbffffffffffffffffffffffffg gffffffffbcfffffafffffffffffffffffaeffffcbfffffffffffffffffffffffffg gfffffffffbfffffadfffffffffffffffadffffcbffffffffffffffffffffffffffg gfffffffffcbfffffaffffffffffffffaaffffebfffffffffffffffffffffffffffg gffffffffffbcffffadffffffffffffdafffffbffffffffffffffffffffffffffffg gfffffffffffbfffffafffffffffffeafffffbeffffffffffffffffffffffffffffg gfffffffffffcbffffadffffffffffaeffffbcfffffffffffffffffffffffffffffg gffffffffffffbcfffeafffffffffadffffbcffffffffffffffffffffffffffffffg gfffffffffffffbffffaefffffffaaffffbbfffffffffffffffffffffffffffffffg gfffffffffffffcbfffeaffffffdaffffbbffffffffffffffffffffffffffffffffg gffffffffffffffbcfffaeffffeaffffcbfffffffffffffffffffffffffffffffffg gfffffffffffffffbfffeaffffaefffcbffffffffffffffffffffffffffffffffffg gfffffffffffffffcbfffaeffadfffebfffffffffffffffffffffffffffffffffffg gffffffffffffffffbcffeafaafffebffffffffffffffffffffffffffffffffffffg gfffffffffffffffffbfffadaffffbeffffffffffffffffffffffffffffffffffffg geffffffffffffffffcbffdaffffbeffffffffffffffffffffffffffffffffffffeg ggggggggggggggggggbcggggggbcgggggggggggggggggggggggggggggggggggggg b bc gb bb bc cb bcb gb ``` <!-- end of image --> I'm going to scrutinize area A for any signs of an intersection. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff4a4aff b,#0909ffff c,#5c5cffff d,#ff8e8eff e,#ff0606ff f,#b5b5ffff g,#ffcfcfff ``` ```image a de dee ea ae deg dee geed eea eeg ded d ged e ee ed aee eed deed dee geed ee eea de ee ed deg de ded ee eea fb eed aee fbb dee deeg bbc eed deed bc dea eed bb eed ea cb ee deg cbbf de dee cbbf eg geed bbf da eea fbc geg aee fbc ea eeg fbb aea ged bbb geeg ee cbb aea aee cbbf geeg deeg bbf aea geed fbf aea eea fbb gee ee fbbc ae deg bbc geg ged bbb aa gee cbb geg eea bbf c eeg deeg cbf bf aea eed fbb bbf geeg gea fbbc cbc aea ea fbbc bb geeg ae bbc fbf aed dee bc bc aed geea cb bbf gee aea cbb cbb ae aeeg cbbf bbc ge eeg cbbf fbbf ad ged fbbf cbb de gea bbc fbf ee aee bc cb eed deeg bb bc dee geed cbb bbf eed geea cbbf cbb dee aea cbbf fbbf dee deg fbf cbb ee ged fbc bbc de gee fbb fbb ed aea fbbc cb de aeeg bbc bc ed deeg bbb bb eed gea bbf bbc dee aa cbf fbbf eed aeg cbf cbb dea dee fbb bbc eed geed fbbc fbbf dea geea fbbc bb dea aeeg bbc fbf ee eeg bb cb de ged cb bc geg gea cbf bbf da ae cbb fbb geg aee fbbf bbf eeg geed bbc fbb aea eea fbc cb geeg ea bc bf aea aeg bb fbf geeg deg cbb bbc gee geea cbbf fbbf ae aea cbbf cbb geg aeeg bbf bbc aa deeg fbc fbbf geg eed fbc cbb ea gea fbb fbf aea aeg bbb cb geedee cbb bc aeeed bbf ``` <!-- end of image --> After careful examination, I've determined that there's no intersection in area A. There's definitely not a single intersection on the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff3737ff b,#0909ffff c,#5e5effff d,#ff8e8eff e,#ff0303ff f,#b4b4ffff g,#ffd4d4ff ``` ```image g ad e ed e ed e ed e eg ge eg ge eg ge eg ge eg ge eg e ge ed eg aa ge de e ge de e e ed b de aa fb e de bc de ge b e e fb da ed f bc e aa fb b da de fb fb e ge b bc da e bf b e ed bf fb da aa bc bc e de bc b da ge bb fb e eg cb bc aa ed fb b e aa fb fb aa de b cc e ge b b aa eg bf b e ed bf cc ad aa bc bf e de bc b ad ge cb cb e eg cb bf ad ed fb b e aa fb cb ad de b bf e ge bf b ad eg bf cb e ed bc bf ed aa bc b e de bb cb ed ge cb bf e eg cb b ed ed fb cb e aa fb bf eg de b b ge ge bf fb eg eg bf bf ge ed bc b eg aa bc fb ge de cb bc eg ge cb b ge eg fb fb eg ed fb bc ge aa b b ede b fb ge bf bc bf b bc fb bb bc cb bcb fb ``` <!-- end of image -->

I'm ready to tackle this image and find those intersections! These areas seem to enclose narrow spaces where lines might be close. <!-- image --> ```palette Key,Color ,#fefefeff a,#4345f0ff b,#fa0c0bff c,#e27065ff d,#838fe7ff e,#b0d6b0ff f,#0506fdff g,#eef1f0ff ``` ```image g fd f ad f aa f aa f da f df f df fg df fg gf fg gf fg gf fd gf fd f ad f aa f aa g f gb da bg f ggggggggggggggggggggggggggggggggggggggggggggggbg da geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebc f geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebce df geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbee fg geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeee df geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecbeeee fg geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecbeeeee gf geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebeeeeee fg geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebeeeeeee gf geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebeeeeeeee fg geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebceeeeeeee g gf geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebceeeeeeeeeff fd geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebceeeeeeeeafd gf geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeeeeeedfae fd geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeeeeeeffeee f geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecbeeeeeeafdeeee fd geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecbeeeeeafaeeeeee f geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebeeeeeffeeeeeeee ad geeeeeeeeeeeeeeeeeeeeeeeeeeeeeebeeeeffeeeeeeeeee f geeeeeeeeeeeeeeeeeeeeeeeeeeeeebeeeafdeeeeeeeeeee aa geeeeeeeeeeeeeeeeeeeeeeeeeeeebcedfaeeeeeeeeeeeee f geeeeeeeeeeeeeeeeeeeeeeeeeeebceffeeeeeeeeeeeeeee aageeeeeeeeeeeeeeeeeeeeeeeeeebcffdeeeeeeeeeeeeeeee fgeeeeeeeeeeeeeeeeeeeeeeeeebafaeeeeeeeeeeeeeeeeee daeeeeeeeeeeeeeeeeeeeeeeeecffeeeeeeeeeeeeeeeeeeee feeeeeeeeeeeeeeeeeeeeeeeffeeeeeeeeeeeeeeeeeeeeee dfeeeeeeeeeeeeeeeeeeeeafbeeeeeeeeeeeeeeeeeeeeeee gfeeeeeeeeeeeeeeeeeedfabeeeeeeeeeeeeeeeeeeeeeeee gdfeeeeeeeeeeeeeeeeffebeeeeeeeeeeeeeeeeeeeeeeeee bc gefeeeeeeeeeeeeeeffdebeeeeeeeeeeeeeeeeeeeeeeeeee bbc gedfeeeeeeeeeeeafaeebceeeeeeeeeeeeeeeeeeeeeeeeee cbc geefeeeeeeeeedffeeebceeeeeeeeeeeeeeeeeeeeeeeeeee cbb geedfeeeeeeeffeeeebceeeeeeeeeeeeeeeeeeeeeeeeeeee cbbg geeefdeeeeafdeeeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeee cbbg geeeefeedfaeeeeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeee gbbg geeeefdffeeeeeecbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee gbbe geeeeefeeeeeeecbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee gbbc geeeeeeeeeeeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee bbc geeeeeeeeeeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee bbc geeeeeeeeeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee cbb geeeeeeeeeebceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee cbb geeeeeeeeebceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee cbbggeeeeeeeebceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee ebbeeeeeeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee ebbceeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee geebbccbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee geeeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee ggggggggggggggggggggggggggggggggggggggggggggggg ``` <!-- end of image --> I'm eager to see what's happening in this magnified view of area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#4f4afaff b,#fe0606ff c,#fd8a8bff d,#a1a0feff e,#fa4247ff f,#0606feff g,#f3d3deff ``` ```image cb cbb gbbc gbbe gbbe gbbe ebbg ebbg ebbg cbbg cbbc cbbc gbbc gbbe gbbe gbbe ebbg ebbg ebbg cbbg cbbc cbbc gbbc d gbbe af gbbe dfff gbbe dfffag ebbg gafffd ebbg afffd ebbg dfffag cbbg daffad cbbc gafffd cbbc dfffa gbbc dfffag gbbe gafffd gbbe afffd gbbe dfffag ebbg daffad ebbg gafffd ebbg dfffa cbbg dfffag cbbc gafffd cbbc afffd gbbc dfffa gbbedfffad gbbeafffd gbbafffa d eefffag a effffd fd afffd ff dfffa ffd dffffc dff gafffec ffd afffabc dff dfffabbe ffd dafffdbbe dff afffdgbbe ffd dfffa ebbg dff dfffag ebbg afa gafffd ebbg dff afffd cbbg afa dfffag cbbc dffg daffad cbbc afa gafffd gbbc gffg dfffa gbbe afa dfffag gbbe gffg gafffd gbbe afa afffd ebbg gffd dfffag ebbg afa daffad ebbg gffdafffd cbbg affffa cbbc ffag cbbc gd gbbc gbbe gbbe gbbe ebbg ebbg ebbg cbbg cbbc cbbc gbbc gbbe g gbbe beg gebe bbbeg ebbg gebbbeg ebbg gebbbec ebbg gcbbbec cbbg gcbbbbbbc ``` <!-- end of image --> Eureka! There's definitely an intersection in area A! It was tricky, but I finally found one single intersection in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#4844fbff b,#ff0606ff c,#ff9797ff d,#9090ffff e,#f94349ff f,#0505feff g,#e4d6f1ff ``` ```image g fd f ad f aa f aa f da f df f df fg df fg gf fg gf fg gf fd f fd f ad f aa f aa f gb aa bg f bc da bc f be df be f eb df cb fg cb gf gb fg gb gf bg fg bc g gf bc ff fd be afd f be dfa fd eb ff f cb afg fd cb dfa f gb gff ad b ffg f bg afd aa bc dfa f bcgff aa beafg f bafd da eff f ffg df afe f dfab df gffgb bc fg ffg bg ebe df dfd bc ebe fg gfa bc ebe gf ffg be cbb fg afd be cbbg gf dfa eb cbbg fdff cb gbbc gfg cb bbc gb bbc b ebe bg ebe bc cbb bc cbb be cbbg be gbbc eb gbbccb bb ``` <!-- end of image -->

I'm on the case! Let's uncover any intersections hidden in this image. There are 1 regions I'd like to highlight in the image. <!-- image --> ```palette Key,Color ,#fefefeff a,#0606feff b,#fd0a09ff c,#b7b7feff d,#b2d6b1ff e,#5557faff f,#96c299ff g,#f4716cff ``` ```image dfffffffffffffffffffffd fdddddddddddddddddddddf fdddddddddddddddddddddf fdddddddddddddfdddddddf fddddddddddddbbbbdddddf fdddddddddddgbddgbbgddf fddddddddddgbddddddbbbf fddddddddddbdddddddddgbbg fdddddddddbdddddddddddf gbbd fddddddddbgdddddddddddf bbb fdddddddbgddddddddddddf gbbg fddddddbbdddddddddddddf gbb fdddddgbddddddadddddddf dbbg fddddfbddddddaaeddddddf gbbg fddddbdddddddadafdddddf bbb fdddbfddddddaeddadddddf gbbg fddbgdddddddadddfaddddf gbbd fdbbdddddddafddddeadddf bbg fgbddddddddaddddddaeddf gbbg fbddddddddafdddddddafdf bbb bdddddddddadddddddddadf dbb bfddddddddafdddddddddeaf bgfdddddddfadddddddddddaa bg fdddddddafddddddddddddac gb fddddddfadddddddddddddfa gb ac ca b ca ea b ac ae bg ca ac bg a a gb ca ca gb a ea b ca ae b a ac bd ca a bg a ca bb ca ee gb a ac db ca a b a ca b ca ea bg a ae bg ea ac gb a a gb ee ca b a ea b ee ae a ac ee a a ca ee ee a ac ee a a ca ee ea a ae ee ac a a ee ca a ea ae ae a ac ac a a ca ac ee a ac ac a a ca ac c a ac a ac a ac ca ac ca ac ca a ca a ``` <!-- end of image --> I'm analyzing this close-up of area A with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#0707feff b,#fe0505ff c,#a5a5ffff d,#ffcfcfff e,#5252ffff f,#ff8b8bff g,#ff3f3fff ``` ```image dd dbbgfd bbbbbbgf gbgdfgbbbbfd gbbd dfbbbbgf fbbd dgbbbbgd fbbf fgbbbb dbbf dfbb dbbg f gbg gbbd fbbd fbbf dbbf dbbg gbg gbbd fbbd fbbd aa dbbf caaa dbbg aaaae bbg caacaac gbg aac caac gbbd caa eaa fbbd aac eae fbbf caa aae dbbf aac caac dbbg caa caac gbg aac eaa gbbd eae aae fbbd aac aae fbbf eae caac dbbf aac eaa bbg eae eaa bg aac aae bd eae caac d aac caa eae ea aac e eae aac eae ``` <!-- end of image --> Darn it! This close-up doesn't show any intersections in area A. I can confidently say that there are no intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0505ffff b,#ff0808ff c,#8989ffff d,#ffb1b1ff e,#4343ffff f,#c9c9ffff g,#ff5a5aff ``` ```image d bbbg gb gbbd db bbb b dbbg b gbbd bd dbbg bg dbbg gb gbbd db a dbbg db aae gbbd b a af bbb bd ac a dbbg bg a fa gbbd bb af ea dbbg gb a ac gbbd db af af gbbd b fa a dbb bd af ca bd fa ee bg af ac gb fa a db af fa b fa ca b af ae bd fa af bg af a gb fa fa db a ea db fa ac b a af bd ca a bg a ca bb ca ee gb a ac db ca a b a fa bd ca ca bd a ae bg ce af gb a a db ce fa b a ea b ce ac a af ee a a ca ee ee a ac ee a a fa ee ca a ae ec af a a ec fa a ea ec ac a af ac a a ca ac ee a ac ac a a fa ac f a af a af fa af fa af fa af fa af fa af ``` <!-- end of image -->

I'm optimistic that I'll find some intersections in this image. I have a hunch that these areas might contain the intersections we're looking for. <!-- image --> ```palette Key,Color ,#fefefeff a,#0607feff b,#fc0a0aff c,#9fa6f0ff d,#ed6c63ff e,#febab9ff f,#5859f3ff g,#aed5adff ``` ```image c ac a af a ff a ff a ff a ff a ff gggaggggggggggggg gggfagggggggggggg ggggagggggggggggg ggggfaggggggggggg gggggaggggggggggg gggggfagggggggggg ggggggagggggggggg eddbbbbbbb ggggggcaggggggddbbbbbbbbdee eb gggggddabbbbbbbdd bd edbbbbbbbbdfagggggggg be dde ggggggggagggggggg b ggggggggcaggggggg db gggggggggaggggggg bd ggggggggggagggggg b ggggggggggacggggg b gggggggggggaggggg db gggggggggggacgggg bd ggggggggggggagggg b ac eb a db ac be a b ac eb a bd ac be a b af db a bd ff b a eb ff db a be ff b a eb ff bd a be ff b a db fa bd a b ca eb a gdbggggggggggggg ca ggbdgggggggggggg a gggbgggggggggggg ca gggdbggggggggggg a ggggbbgggggggggg ca gggggbggggggggggcfaa a ggggggbgggggfaaaac ca ggggggdbfaaafcgg a gggcfaaafggggggg ca caaaafgggbggggggg ac faaafcggggggggbgggggg a cfaaaf gggggggggdbggggg ac caaaac ggggggggggbdgggg a faaafc gggggggggggbgggg accfaaaf ggggggggggggbggg aac ggggggggggggbbgg gggggggggggggbdg b eb bd be b db bd b ``` <!-- end of image --> I'm focusing my attention on this specific region, area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0706fdff b,#fe0405ff c,#918efbff d,#fb585cff e,#ffa9a9ff f,#4d47f8ff g,#cfcffeff ``` ```image aag caf aac caf aac caa aac caa aac caa aac caa aac caa aac caa eeed fac eeedddbbbbbbb eeeddaabbbbbbbbbbbbddd eeedddbbbbbbbbaafbbdddeee bbbbbbbbbbbbdddecaag bbbdddeee fac gaag faf gaag faf gaag faf gaag faf gaag faf gaag faf gaag faf ``` <!-- end of image --> Success! This area contains an intersection point! Next up, a closer look at another region. I'm analyzing this close-up of area B with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#0907fdff b,#fe0405ff c,#b2b0fdff d,#ff8282ff e,#fec3c4ff f,#6561fbff g,#ff3c3cff ``` ```image ebbd dbbe gbb gbg ebbd dbbe gbg bbd ebbe dbbe gbg ebbd ebbe dbb cf gbg ccfaaaa ebbd cffaaaaaaaf dbbcfaaaaaaaffc ccfaaaaaaafcc cffaaaaaaafc cfaaaaaaaffcebbe faaaaaaafcc dbbe aaaafc gbg fc bbd ebbe dbb gbg ebbd dbbe gbg bbg ebbd dbbe gbg bbd ebbe ``` <!-- end of image --> Oh my, look at that! It's an intersection in area B! I've identified a total of two intersection points.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0707feff b,#fe0304ff c,#acaafdff d,#ff7676ff e,#ffb7b7ff f,#5957fdff g,#ff3939ff ``` ```image c ac a af a ff a ff a ff a ff a ff a fa a ca a ca a edgbbbbbbb ca edgbbbbbbgdee eb edabbbbbbgde gg edgbbbbbbgdca be gde a b ca db a bd ca b ac b a db ac bd a b ac eb a gg ac be a b ac eb a gg ac be a b af db a bd ff b a eb ff gg a be ff b a eb ff gg a be ff b a db fa bd a b ca eb a db ca be a b ca eb a gg ca be cfaa a b caaaac ca dbfaaafc a cfaaaf ca caaaac b ac faaafc b a cfaaaf db ac caaaac bd a faaafc b accfaaaf eb aac gg be b eb gg be b db bd b ``` <!-- end of image -->

Hmm, I'm not sure what to expect from this image. Let's see if any lines cross. I can confidently say that there are no intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#4b4bffff b,#ff4040ff c,#0606ffff d,#ff0404ff e,#ffbdbdff f,#aaaaffff g,#ff7e7eff ``` ```image fcccca faccaf cc facccf fc acccf ca acccf cc fccca ac fccca fcf fcccaf ca faccaf ac ccf fcf ca cc ac fcf cc ac fcf ca cc fc cf cc ac fcf ca ac fcf ca cc ac fcf ca ac fc ed bdde gddg eddb eddbe bdde gddg gddb eddb bdde gddg gddg eddb bdde bddg dddbbbbbbggggggeeeeee gddg eeeeeeggggggbbbbbbddddddddddddddddddb ``` <!-- end of image -->

This image looks interesting. I wonder if there are any intersections hidden in there? There are 2 areas where the lines seem to converge. We should take a closer look at area A,, and B. <!-- image --> ```palette Key,Color ,#fefefeff a,#f15550ff b,#0707fdff c,#a2a5f7ff d,#fd0707ff e,#f3a39eff f,#525aeeff g,#aed5aeff ``` ```image c b ed bc d d fb ed ed b d ad bc d ad cb de da b d de bc de d cb d d b aa ed bf d ed cb aa ad b d da ff ed de b d de bc ed d fb d d b d ed bc de adgggggggggggggfbg d ddggggggggggggbgg ae daggggggggggbfgg d gdeggggggggcbggg aa ggdggggggggbgggg d gggdggggggbfgggg ea gggedgggggbggggg d ggggadgggbgggggg ed gggggddgffgggggg d ggggggdabggggggg d gggggggbaggggggg de ggggggfbdggggggg d ggggggbggdgggggg de gggggbcggedggggg d ggggfbggggadgggg aa ggggbggggggadggg d gggbfgggggggdagg aa ggcbgggggggggdag d ggbgggggggggggde ed gbfggggggggggggd d gbggggggggggggggd ed b ed d ff ad d b da de bc da d fb de de b d d bc d aa cb ed d b ad aa bc ad d cb da ed b d d bf ed b d b d ff gggggggggggdeggg b gggggggggggdgggg bc ggggggggggdagggg fb ggggggggggdggggg b gggggggggaaggggg bc gggggggggdgggggg cb ggggggggaagggggg b ggggggggdggggggg bc gggggggedggggggg cb gffffcgdgggggggg b gffffbbbbbbbbbbbbbbbbbffffccc bf ggggggdggggggggg ccccfffbbbbbbbbbb ggggggdggggggggg gggggdeggggggggg gggggdgggggggggg ggggdagggggggggg ggggdggggggggggg gggaaggggggggggg gggdgggggggggggg ggadgggggggggggg ggdggggggggggggg ed d ``` <!-- end of image --> I'm now examining the contents of area A in detail. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff3838ff b,#0606feff c,#b5b5ffff d,#fe0405ff e,#fdb5b6ff f,#6868ffff g,#fe7575ff ``` ```image gda dde gda dde edd adg edd adg edd adg edde gda dde gda dde gda dde edd adg fffffccccccedd cbbbbbbbbbbbbbbbbbbbbfffffff ffffffffbbbbbbbbbbbbbbbbbbb adg cccccccffff dde gda dde gda dde gda ade edd adg edd adg edd gdg dde gda dde gda dde ``` <!-- end of image --> Amazing! This area was hiding an intersection all along! Time for a closer look at another area. Let's take a closer look at area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd4b4cff b,#0404feff c,#8481fcff d,#fe0606ff e,#fdadafff f,#3d35f6ff g,#c6c7ffff ``` ```image fbf e cbb d gbbc da fbf dda cbbg edda bbc edde fbf edde gbbg adde bbc add cbf ada gbbg dda fbc edda cbb edde gbbg edde fbf adde cbb add gbbc add fbf dda cbbg eddabbc edfbf cbbe bbfde cbfadde gbbg add fbc dda cbb dda gbbg edda fbf edde cbb edde gbbc adde fbf add cbbg ada bbc dda fbf edda gbbg edde bbc edde cbf add gbbg ad fbc a cbb gbbg ``` <!-- end of image --> My investigation has led me to an intersection in area B! After a long analysis, I found two intersections.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fe4d4eff b,#0707feff c,#9b9bffff d,#fe0707ff e,#fd9799ff f,#5555ffff g,#f1d7e5ff ``` ```image c g gb edg bg dgd fb gd ed b dg ed bc gd ad cb de da b d de bc de dg cb d d b aa gd bf d ed gb ea ad bg d da ff ed de gb d dg bg gd dg fb dg gd b gd ed bc de ad cb d da b ae da bc d de cb aa dg b d gd bf ea ed gb d ad bg ed ad ff dg dab gd be dg fbdg d b d de bc gd d cb ed ae b ad d bc da aa cb de d b dg ed bf dg d gb gd ed bg ed dg ff ad gd b da dg bg da d fb de de b dg d bc gd aa cb ed d b ad aa bc ad d cb da ed b d d bf gd gb dg bg gd ff de b d bg de fb d b aa bc d cb ea b d bc ed cb ffcccgdg b cffffbbbbbbbbbbbbbbbbfffccccg bf dg ggcccfffbbbbbbbbbb gd de d ae d aa d ea d ed dg ``` <!-- end of image -->

I have an image in front of me. I need to determine if there are any intersection segments. I'm going to focus my attention on these specific areas. <!-- image --> ```palette Key,Color ,#fefefeff a,#5356f0ff b,#fd0908ff c,#0707fdff d,#ef6f67ff e,#ababffff f,#99c697ff g,#b0d7b0ff ``` ```image e fggggggggggggggf ce fggggggggggggggg c fggggggggggggggg ce fggggggggggggggg ec fggggggggggggggg c fggggggggggggggg ec fggggggggggggggg c fggggggggggdbggg aa fgggggggggbbgggg c fggggggggbdggggg fggaagggggggggggggggggf fggggggdbfgggggg ggggcgggggggggggggggggf fgggggbbgggggggg ggggcaggggggggggggggggf fggggbdggggggggg gggggcggggggggggggggggf fggdbfgggggggggg bfggggcfgggggggggggggggf fgbbgggggggggggg bbgggfcgggggggggggggggf fbdggggggggggggg gbbgggcgggggggggggggggf dbfggggggggggcggg ggfbdgacggggggggggggggf bbfggggggggggcaggg ggggbbgcggggggggggggggf bd fgggggggggacgggg gggggdbaagggggggggggggf db fgggggggggcggggg gggggggbcgggggggggggggf bb fggggggggcaggggg ggggggggcafgggggggggggf bd fgggggggacgggggg gggggggggcbdggggggggggf db gfffffffcfffffff gggggggggcabbgggggggggf bb ce ggggggggggcgfbdgggggggf bd ac ggggggggggcfggbbggggggf db c ggggggggggfcgggdbdggggf bb ce gggggggggggcgggggbbgggf bd aa gggggggggggacgggggdbggf db c ggggggggggggcggggggfbdf bb c ggggggggggggaagggggggbb bd ca gggggggggggggcggggggggdbd db ec fffffffffffffcafffffffg bb bb c c dbg bd ca ce bb db ec c db bb c ce bd bd ce ec bb db ec c dbd bb c ec bbd ce c ac aa c c ce aa aa c c ce c c ca c ec ec c c ca ec ec c c aa ce c ec aa c c ce ce ac c c c ce ec aa c c ec c c aa aa ec c c ae ca c ec ce c c ce c ec ec c c ce ec ac c c aa ce c aa ae c c c cca c ``` <!-- end of image --> Let's zoom in on area A to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#5849efff b,#fe0505ff c,#0707feff d,#fd8587ff e,#acacffff f,#fd3b3dff g,#fecdcdff ``` ```image ecc aca ecc cce ecc cce ecc cce g aca bfg cce bbbd aca fbbfg ecc dbbbd aca gfbbf ecc dbbbg cce gfbbd ecc dbbfg cce gbbbd ecc fbbfgcce dbbbaca gfbbcce dbaca gfccd acafg eccbbd ccabbf eccdbbbg ccegfbbd eca dbbfg cce gbbbd aca fbbfg cce dbbbd aca gfbbf ecc dbbbg aca gfbbd ecc dbbfg cce gbbbd ecc fbbfg cce dbbbd eca gfbbf cce dbbb aca gfb cce d aca ecc ``` <!-- end of image --> I am surprised, so clear, an intersection has appeared in area A. Let's move forward and inspect another region. I'm analyzing this close-up of area B with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#3d3dffff b,#ff0a0aff c,#0303ffff d,#ff5252ff e,#9f9fffff f,#ff9191ff g,#ffc9c9ff ``` ```image gbf fbbb dbbd gbbbf fbbbg dbbd gbbbf fbbbg dbbd gbbbf fbbbg dbbd gbbbf fbbbg dbbd gbbbf fbbbg dbbd gbbbf ae bbbg aca bd ecce f cce aca ecc cce aca ecc cce aca ecc ecce ``` <!-- end of image --> The evidence suggests that this is not an intersection point in area B. I have found one intersection!

<!-- image --> ```palette Key,Color ,#fefefeff a,#4742f9ff b,#ff0909ff c,#0606ffff d,#ff7070ff e,#8888ffff f,#c9c9ffff g,#ffd6d6ff ``` ```image f ce c cf fc c ec c db ea bb c bd ae dbg c bb ce gbd c dbg bg cf bb gbd fc gbd bb c dbg c gbd ec bb ce bb c gbd ec dbaa dbg c bc bb ce aag gbd ec cbd dbg c cebb bb cf c gbd gbd ac cf bb dbg c fc dbg bb cf c bb gbd aa ec dbg dbg fc c gbd bb cf ea bb gbd aa c gbd dbg fc ae bb bb c c dbg gbd ce ce bb dbg ec c dbg bb c cf gbd gbd ce fc bb dbg ec c gbd bb c ec bbd cf c ac ea c c cf ae aa c fc cf cf c aa cf fc fc c c ce ec ec c c aa ce c ec ae c c cf cf ec c c cf cf fc aa c fc ec cf c aa aa fc c c ae ce c fc cf c c ce cf ec fc c c cf ea ec c c aa cf c aa ae fc c cf cca fc ``` <!-- end of image -->

I have an image in front of me. I need to determine if there are any intersection segments. I've spotted 1 narrow regions that might be worth examining further. Let's call them area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0707ff b,#4a47f5ff c,#fbabaaff d,#a2a4fbff e,#fb5250ff f,#0304feff g,#aed5aeff ``` ```image d dbfffffd bfffbd bfb dffffd bff dbfffbd dffd dbfffbd ffb dffffd bfb dbfffbd dffd gggggggggggggggg fffbd dffd gggggggggggggggg bfb gggggggggggggggg bff gggggggggggggggg dffd gggggggggggggggg ffb gggggggggggggggg bfb gggggggggggggggg dffgggggggggggggggg dffbggggggggggggg ggffbggggggggggg ggggbffggggggggg ggggggdffdgggggg gggggggggffbgggg gggggggggggbgggg ggggggggggaggggg gggggggggaeggggg e ggggggggeagggggg ea ggggggggaggggggg ac gggggggagggggggg a ggggggaegggggggg ee gggggeaggggggggg a gggggagggggggggg ca ggggacgggggggggg ae gggeaggggggggggg a ggcagggggggggggg ca ggaggggggggggggg ac ac a ea ca a ac a a ae ee ca a a a ac ee ee a ca ca a ae ac a ea ca a ac a a ae ea ca ac a a ac ee ee a ca ca a ae ac a ea ca ca ac a a ae ca ea ac a a ac ee ae a ca a a ee ac a ea ca ca ac a a ac ca ea ac a a a ea ae ac ca a a ee ac aee ca ``` <!-- end of image --> Time to investigate area A up close. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd0809ff b,#4439f3ff c,#ff5959ff d,#c3c0fcff e,#8681faff f,#0605feff g,#feb3b3ff ``` ```image d fbd ffffe effffed ebfffbd dbfffbe deffffe effffbd dbfffbd dbffffe effffbd ebfff gabe aac caa gaag gaag aac caa gaag aac cac caa gaag aac caa gaag gaag aac caa gaag aac cac caa gaag aac ``` <!-- end of image --> Wow! I can see an intersection so clearly in area A! There's one and only one intersection present in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0505ff b,#4c48faff c,#ff7f7fff d,#aaaaffff e,#ff3e3eff f,#0303ffff g,#fec4c4ff ``` ```image d dbfffffd dbfffbd bfb dffffb bff dbfffbd dffd dbfffbd ffb dffffd bfb dbfffbd dffd fffbd dffd bfb bff dffd ffb bfb dffd dffd bfb bff dffd ffb gb a ac e ca ca a ag ag a ae ee ca a a ga ag ec ee a ga ga a ac ac a ca ca ga ag ag a ac ee ca ag a ga ag ee ee a ga ga a ac ac a ea ca ga ag a a ac ca ca ag a a ag ee ee a ga ga a ec ag a ee ga ga ac a a ac ca ca ag a a ag ee ee ag ga ga a ee ag a ee ga ga ac a a ac ca ca ag a a ag ce ae ag ca a a ee ag aee ga ``` <!-- end of image -->

Based on a first glance, I suspect there could be intersection regions here. These spots mark what I'd call 'danger zones' - areas where intersections are more likely. <!-- image --> ```palette Key,Color ,#fefefeff a,#4d51e4ff b,#f90a0cff c,#0706fcff d,#e36963ff e,#949cedff f,#97c796ff g,#b1d7b1ff ``` ```image e ce c ce c c ec c bffacfffffffffffffffffffffffffffffffffffg gbggcgggggggggggggggggggggggggggggggggggf bdgaaggggggggggggggggggggggggggggggggggf gbggcggggggggggggggggggggggggggggggggggf gbdgaagggggggggggggggggggggggggggggggggf ggbggcgggggggggggggggggggggggggggggggggf ggdbgcaggggggggggggggggggggggggggggggggf gggbggcggggggggggggggggggggggggggggggggf gggfbgcegggggggggggggggggggggggggggggggf ggggbdgcgggggggggggggggggggggggggggggggf gggggbgcfggggggggggggggggggggggggggggggf gggggbdecggggggggggggggggggggggggggggggf ggggggbgcggggggggggggggggggggggggggggggf ggggggdbecgggggggggggggggggggggggggggggf gggggggbgcgggggggggggggggggggggggggggggf gggggggfbacggggggggggggggggggggggggggggf ggggggggbdcggggggggggggggggggggggggggggf gggggggggbaagggggggggggggggggggggggggggf gggggggggbdcgggggggggggggggggggggggggggf ggggggggggbcaggggggggggggggggggggggggggf ggggggggggdbcggggggggggggggggggggggggggf gggggggggggbcegggggggggggggggggggggggggf gggggggggggdbcgggggggggggggggggggggggggf ggggggggggggbceggggggggggggggggggggggggf gggggggggggggbcggggggggggggggggggggggggf gggggggggggggbcggggggggggggggggggggggggf ggggggggggggggbcgggggggggggggggggggggggf ggggggggggggggdcgggggggggggggggggggggggf db gggggggggggggggdcggggggggggggggggggggggf db gggggggggggggggdcggggggggggggggggggggggf bb ggggggggggggggggaagggggggggggggggggggggf bd gggggggggggggggggcgggggggggggggggggggggf bg gggggggggggggggggcaggggggggggggggggggggf db ggggggggggggggggggcggggggggggggggggggggf bb ggggggggggggggggggcdgggggggggggggggggggf bb gggggggggggggggggggcgggggggggggggggggggf bd gggggggggggggggggggcbggggggggggggggggggf gb gggggggggggggggggggfcfgggggggggggggggggf db ggggggggggggggggggggcbgggggggggggggggggf bb ggggggggggggggggggggecdggggggggggggggggf bd gggggggggggggggggggggcbggggggggggggggggf bd gggggggggggggggggggggacbgggggggggggggggf gb ggggggggggggggggggggggcbgggggggggggggggf db ggggggggggggggggggggggaabggggggggggggggf bb gggggggggggggggggggggggcbfgggggggggggggf bd gggggggggggggggggggggggaabgggggggggggggf bg ggggggggggggggggggggggggcbdggggggggggggf db ggggggggggggggggggggggggcabggggggggggggf db gggggggggggggggggggggggggcbdgggggggggggf bb gggggggggggggggggggggggggcebgggggggggggf bd ggggggggggggggggggggggggggcdbggggggggggf bg ggggggggggggggggggggggggggcfbggggggggggf db ggggggggggggggggggggggggggecfbgggggggggf bb gggggggggggggggggggggggggggcgbdggggggggf bb gggggggggggggggggggggggggggecgbggggggggf bd ggggggggggggggggggggggggggggcgbdgggggggf gb ggggggggggggggggggggggggggggaagbgggggggf db gggggggggggggggggggggggggggggcgdbggggggf bb gggggggggggggggggggggggggggggaagbggggggfbd ggggggggggggggggggggggggggggggcgfbgggggbd ggggggggggggggggggggggggggggggcagbdggdbf gggggggggggggggggggggggggggggggcggbgdbgf gggggggggggggggggggggggggggggggcegbbbggf ffffffffffffffffffffffffffffffffcffdfffg c c c ec c ecaeeeee eeaaaaccccccccccccccccccccaaaaeeee eeeeeaaaccccccccccc ``` <!-- end of image --> I'm analyzing this close-up of area A with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#5b56faff b,#fd0608ff c,#0806fcff d,#fc5254ff e,#aaa7fbff f,#800c8aff g,#fdabacff ``` ```image bb ecc dbd cce gbbg ecc dbd cce gb cce bd aca gb ecc bd aca bbg ecc dbd aca bbg ecc gbb cc bbd ec dbd ec gbbg ce dbd ca bbg cce gbb aca bbg cc gbb aca db ecc gbg aca bg cce bb ecc bbg cce gbb ecc dbd cce gbbgaca dbd cce bbgaca bbgac gbbec dbdaa gbbec dbdce bbcc dbcce bacc gbcce bbcce dbfca bbcce dbfca bbcc gbfca bbcc gbcca gbcce dfcc bcc gfc bce gfa dce gca cc gcc cca ecc ccf eccg ccf eccg ccf accg acfd ccb acf eccg acb ecbg cfb ecbd ccbd ccfbg accbb ccfbg acabb ccdbd acabb eccdbd acabbg acabb eccgb ccebd eccgb ccebd eccbbg ccdbd ac bbg aa bbd ec gbb ca dbd cc gbbg aca dbd ecc bbg cce gbb ecc bbg cce gbb cce gbg aca dd cce bg aca bb cc bbg aca gbb ecc dbd aca gbbg ecc dbd gb ec dbb dbbd ce bbg bbd ec gbbgdbg ce dbbbg ``` <!-- end of image --> Gotcha! I've found the intersection hiding in area A! I've found a single intersection point in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#5852f8ff b,#fe0304ff c,#0706fdff d,#ff7d7dff e,#a7a7feff f,#f2303cff g,#ffc2c2ff ``` ```image e ce c ce c c ec c bg ec gb c bd aa b c ff aa b c db ce b c gb ce bg c b c fdec b c dfec b c gbaa bgc baa fdc bae dfc bce gbc bce fc fc fc dc db fc fb gc bf aa bd c gbg ca db c fb cf bf c bd cf gbg cg db cb fb ecd bf cb bd ecf gbg cb fb aab bb cbg bf aab gbg cbd db ceb fb cff bf ceb bd cdb gbg c bg db ecgb fb c bg bf ec b bd c fd gbg aa b db c df fb aa b bf c gb bd ce bg gbg c b fb ce fbb c d ce ec c ec c ecaaeeee eeaaaaccccccccccccccccccccaaaaeeeee eeeeaaaaccccccccccc ``` <!-- end of image -->

Time to put on my detective hat and find those intersection points! There are 1 regions I'd like to highlight in the image. <!-- image --> ```palette Key,Color ,#fefefeff a,#fa0c0bff b,#0505fcff c,#e1796cff d,#3d42eaff e,#b1d7b0ff f,#f0f3eeff g,#8296d5ff ``` ```image c a ac fa af ca a ca a ac a ac fa af fa af ca a cc a ac fa af fa af ca a cc a affffffffffffffffffffffffffffffffffffffffffffffffffffffffff ac faeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef fa fcaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef ae feaceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef fa feeaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef af feecaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefca feeeaceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefa feeeeaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeca feeeeeaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeea deeeeecaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeac b gbgeeeeaceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaf gbg febbeeeeaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeacf fbb feedbeeecaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaef dbf feeeebdeeaceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeef gbd feeeeebbeeaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecaeef fbb feeeeeedbgeaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeef dbf feeeeeeeebdaaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecaeeef gbd feeeeeeeeebbaceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeef fbb feeeeeeeeeegbaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaceeeef dbf feeeeeeeeeeeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeef gbd feeeeeeeeeeeeedbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaceeeeeffbb feeeeeeeeeeeeeeabgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeeedbg feeeeeeeeeeeeeeeabbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeegbd feeeeeeeeeeeeeeeaadbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecaeeeebbef feeeeeeeeeeeeeeeeacgbdeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeedbgeef feeeeeeeeeeeeeeeeeaeebbeeeeeeeeeeeeeeeeeeeeeeeeeecaegbdeeeef feeeeeeeeeeeeeeeeecaeedbgeeeeeeeeeeeeeeeeeeeeeeeeaebbeeeeeef feeeeeeeeeeeeeeeeeeaceeebdeeeeeeeeeeeeeeeeeeeeeeadbgeeeeeeef feeeeeeeeeeeeeeeeeeeaeeeebbeeeeeeeeeeeeeeeeeeeegbdeeeeeeeeef feeeeeeeeeeeeeeeeeeeeaeeeegbgeeeeeeeeeeeeeeeeebbceeeeeeeeeef feeeeeeeeeeeeeeeeeeeeaaeeeeebdeeeeeeeeeeeeeedbgaeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeaceeeeedbeeeeeeeeeeegbdeaceeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeaeeeeeegbgeeeeeeeebbeecaeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeecaeeeeeeebbeeeeedbgeeeaeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeaceeeeeeedbeegbdeeeecaeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeaeeeeeeeegbbbeeeeeeaeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeaeeeeeeeeegeeeeeecaeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeaaeeeeeeeeeeeeeeeaeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeaceeeeeeeeeeeeeaceeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeeeeeeeeeeaeeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeecaeeeeeeeeeeeaceeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeaceeeeeeeeeeaeeeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeeeeeeaeeeeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeecaeeeeeeecaeeeeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaaeeeeeeaeeeeeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaceeeecaeeeeeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeaeeeeeeeeeeeeeeeeeeeef ffffffffffffffffffffffffffffffffcaffacffffffffffffffffffff ac a aac fa ``` <!-- end of image --> I'm determined to find out if an intersection exists in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd0607ff b,#0807fdff c,#fe8d8dff d,#5951f6ff e,#fd4748ff f,#fecfcfff g,#b2b0fdff ``` ```image aaf eae faac caaf eaa aae faac caaf eae faac caaf eaa aae faac caaf faac caa bd ea bbbg ae c gbbbg fac a dbbd aaf ca gbbbg eae aa gbbbd faac cae dbbd caaf faaf gbbbg eaa eae dbbd aae faaf dbbd faac eae gbbg caaf caaf dbd eae aac bbbg faac caa gbbbg caaf aac dbbd eae cae gbbbgaae faaf gbbbdaaf eae dbbdaaf faaf gbbbae eae gbbbdc faaf dbbbf aac gbbbg caa fbbbd aac fdbbbg caa cabbbg faac eadbbd eae faadbbbg aaf gb eae dbbd faf dbbbd aac gbbbg ec gbbbd faaf gbbbd ca dbbbg caa dbb aa dbbbd eae gbbg caa gbbbd faac bbd faac dbbbg caaf dbbbg eae bbbd eae gbbbg faagbbdg faac dbbd eadbbg faaf gbbbg febbbd eaa gbbbg gbbbdg eae dbbd dbbbg faa gbbbg gbbbdc caf gbbbd gbbbdaa ee dbbd dbbbgaac fac gbbbg gbbbd cae aaf dbbd gbbbdg faaf eaa dbbd dbbbg eae aae gbbbg gbbbd faaf faac dbbd gbbbdg eae caaf dbbbg dbbbg caaf eae gbbbg gbbbd aac faac dbbd gdbbdg caa caaf gbbbgdbbbg aac eaa gbbbbbd cae aae dbbg faaf faac g eae caaf faaf eae eae faac faaf eaa caa aae aac faac caa caaf faac eae eae faac faaf caaf eae eaa faaf aae eac faac caa caaf aac eae caa faac faac caaf eae eaa faaf ``` <!-- end of image --> I can confirm that an intersection exists in area A. There are precisely two intersections present in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fe0404ff b,#0806fdff c,#fe8585ff d,#5250fcff e,#fb3b3eff f,#ffc9c9ff g,#b0affeff ``` ```image c a ac fa af fa a ce a ee a ac fa af fa a ce a ee a ac a af fa a ca a ee a af ec fa a ea af ac fa a af ca ca ae a af ce fa a b ee ec b gbg af a gbd bb a ac bb db ca fa bbg bd ac af gbd bb af fa bb dbgfa a dbg bdee ce gbd bbaf a bb gbe ee dbg bb a gbd bb ac bb ebg fa dbg fabb af gbd eedb fa bb afgbd a dbg a bb ce gbd ca dbg a bb ac bd edbg a bb gbd fa gbg bbc ee bd dbga af db gbd af a gbg bb fa ca bb dbg a ac db gbd ca a gbbb a fa g ee ee a af ec a a ca af ac fa a af fa ca ee a af ce a a ca ec ac a aac fa ``` <!-- end of image -->

I have a feeling there might be some intersections in this image. Could these regions be concealing intersection points? Let's find out. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0a0aff b,#0909fbff c,#f26963ff d,#acaff7ff e,#add4acff f,#ffb9b9ff g,#5861ecff ``` ```image c a af fa a ac a af ca a af ac a fa ac a a ca cc a a af fa fa af a a cc ac a a af ca fa a a fa cc af a a af ac fa a a ca d ac a dbbd a fa bb b af af gbd db ca eeeaeeeeeeeeeeee bb db a eeeaceeeeeeeeeee gbd gb ac eeeeaeeeeeeeeeeedbg bg fa eeeecaeeeeeeeeebb bd a eeeeeaeeeeeeegbg bd ca eeeeeeaeeeeebbee b a eeeeeeaceegbdeee db ac eeeeeeeaebbeeeee gbeeeeeeeeeeaeee eeeeeeebbeeeeeee egbeeeeeeeeaeeee eeeeegbgaeeeeeee eebbeeeeeecaeeee eeeebbeecaeeeeee eeebgeeeeeaeeeee eegbgeeeeaeeeeee eeeebdeeeaceeeee ebbeeeeeeeaeeeee eeeeebeecaeeeeee gbeeeeeeeeeaceeee eeeeeebeaeeeeeee dbgeeeeeeeeeeeaeeee eeeeeegbceeeeeee bb eeeeeeeeeeecaeee eeeeeeebbeeeeeee dbg eeeeeeeeeeeeaeee eeeeeeaebbeeeeee bb eeeeeeeeeeeecaee eeeeecaeebgeeeee gbd af eeeeeaeeeebdeeee bg a eeeeaceeeeebeeee ac eeeeaeeeeeeebeee a eeeaeeeeeeeegbee ca eecaeeeeeeeeegbe a eeaeeeeeeeeeeebb fa ac bg af fa bd a a b ac ca b a a db ca af gb a fa bb fa a bg af ca bd a a b ac af b a fa db ca a gb a cc bb fa a bg aaf bd a b b db gb bb bg bd b ``` <!-- end of image --> This is a magnified view of the region A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0404ff b,#0706feff c,#fe797aff d,#b2b2feff e,#f32e3aff f,#febebeff g,#5555ffff ``` ```image cae aac faa eac faaf cae aaf caa db eac gbb faa dbbbg eac dgbbgd faaf gbbbd cae dbbbg aaf gbbbd caa dbbbg eacdgbbgd faebbbd dbbbg gbbbef dbbbgcae gbbbd aac dbbbg caa dgbbgd eac gbbbd faaf dbbbg eae gbbbd faaf dbbbg cae bbgd aac bd caa eac faaf eae faaf cae ``` <!-- end of image --> There is an intersection point visible in this close-up of area A. Let's move forward and inspect another region. Let's get to the bottom of what's happening inside area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd090bff b,#0707feff c,#ff5d5dff d,#c9c7fdff e,#8c8bfdff f,#ffb0b0ff g,#4b45f8ff ``` ```image bbg aaf dbbe caa ebbe faaf ebbd aac gbbd faa gbb aaf bbg cac dbbg faaf dbbe aac ebbe caa ebbd aaf gbbd cac gbb faa bbg aac dbbg caa dbbeaaf ebbac gbbd agbbd caagbb faaf bbg cac dbbg faa dbbe aaf ebbe caa ebbd faaf gbbd aac gbb faa bbg aaf dbbg cac dbbe faaf ebbe aac ebbd caa gbbd aaf gbb ``` <!-- end of image --> Gotcha! I've found the intersection hiding in area B! After a long analysis, I found two intersections.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0404ff b,#0606feff c,#ff7c7cff d,#adadffff e,#ff3838ff f,#ffc6c6ff g,#504dfcff ``` ```image c a af ca a ec fa af ca a af ac fa fa ac af a ce ce a a ac fa fa af a a ee ec a a af ce fa a a fa ee af a a af ec ca a a ce d ec a dbbd fa fa bb b af af gbd db ca a bb db a ec gbd gb ac a dbg bg fa ca bb bd af af dbd bd ce fa bb b a ac gbd db ac a bg db fa bb gb a dbga bg ee bb ca bd a gbd af bd af bb fa b fa gbd ac db a dbg a dbe bb ee gb dbd a afbg bb ca ca bg gbd af a bd bg fa ec b ac a b a af db ce ca gb a a bg fa ac bg af fa bd a af b ec ce b a a db ce ac gb a fa bg fa a bg af ee bd a a b ec af b a fa db ce a gb a ee gg fa a bg aaf bd a b b db gb gb bg bd b ``` <!-- end of image -->

The hunt for intersections begins! Let's analyze this image closely. These regions highlight areas that look suspicious. Lines seem to converge within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#5354fcff b,#f7534fff c,#0707feff d,#fca4a3ff e,#acacfdff f,#fe0505ff g,#aed5aeff ``` ```image gggggggggggggggg gggggggggggggggg gggggggggggggggg gggggggggggdgggg ggggggggbfffgggg gggggbffbggggggg ggbffbgggggggggg dbffbggggggggggggg dfffdgggggggggggggggg dfffd gggggggggggggggg bffb gggggggggggggggg bffb gggggggggggggggg dfffd gggggggggggcgggg dfffd ggggggggggecgggg dfffd ggggggggggcggggg bffb gggggggggaaggggg bffb gggggggggcgggggg bffd ggggggggcggggggg bffd gggggggacggggggg bffd c bffd ce bffb ec bffb c dffb aa dffb c dffb ce dffb ec dfff c dfffd ca fffd ec d c aa c ce ec c ca ec c aa c ce ec c ca c c ac c ce ec c aa c ce ac c e ce cc ec eca c cc aa ece c cc ce ece ac cc c ace ce cc ec ace c ca aa ac c ca ce ac ec eca c cc ca ece ec cc c ece aa cc c ace ce cc ec ace c caca ac ``` <!-- end of image --> Let's put area A under the microscope. <!-- image --> ```palette Key,Color ,#fefefeff a,#6868ffff b,#ff4444ff c,#0b0bffff d,#ff8888ff e,#ffc7c7ff f,#ff0404ff g,#bdbdffff ``` ```image ee dbffb edbfffffd edbffffbde edfffffbde ebfffffbd dbfffffbe dbfffffde fffbde bde ca acc gccg cca acc gccg aca gcc cca acc gccg cca ``` <!-- end of image --> There is no intersection present within area A. I'm extremely confident. No intersections at all.

<!-- image --> ```palette Key,Color ,#fefefeff a,#4040ffff b,#ff5252ff c,#0606ffff d,#ffa3a3ff e,#8282ffff f,#ff0505ff g,#c1c1ffff ``` ```image d dfff bffb bffb dbffd dfffd dfffd bffb bffb dfffd c dfffd gc dfffd c bffb aa bffb c bffd cg bffd ec bffd c bffd ce bffb gc bffb c dffb aa dffb c dffb cg dffb ec dfff c dfffd ce fffd gc d c aa c cg ec c ce gc c aa c cg ec c ae gc cg ea c ce gc c aa c cg ec c g ce ac gc gce c cc aa gce c cc cg ece ec cc c ecg ce ca gc acg c ca aa ac c gca cg ac ec gce c cc ce gce gc cc c ece aa cc c ecg cg cc ec ecg c cace ac ``` <!-- end of image -->

Hmm, I'm not sure what to expect from this image. Let's see if any lines cross. There are 1 regions I'd like to highlight in the image. <!-- image --> ```palette Key,Color ,#fefefeff a,#0809fdff b,#ea7b71ff c,#545af3ff d,#98c49aff e,#b1d7b1ff f,#b7b7ffff g,#fc0c0bff ``` ```image deeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeed deeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee deeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeb deeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedgg deeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeggdc deeeeeeeeeeeeeeeeeeeeeeeeeeeeeggbeca deeeeeeeeeeeeeeeeeeeeeeeeeeebgbeeaae deeeeeeeeeeeeeeeeeeeeeeeeebggeeeaaee deeeeeeeeeeeeeeeeeeeeeeedggeeeeaaeee deeeeeeeeeeeeeeeeeeeeeeggeeeeeaceeee deeeeeeeeeeeeeeeeeeeeggbeeeeeaceeeee deeeeeeeeeeeeeeeeeeggbeeeeeeaceeeeee deeeeeeeeeeeeeeeebggeeeeeeeadeeeeeee deeeeeeeeeeeeeebggeeeeeeedadeeeeeeee deeeeeeeeeeeeeggeeeeeeeedaeeeeeeeeee deeeeeeeeeeeggdeeeeeeeecaeeeeeeeeeee deeeeeeeeeggbeeeeeeeeecaeeeeeeeeeeee deeeeeeebgbeeeeeeeeeecaeeeeeeeeeeeee deeeeebggeeeeeeeeeeeaaeeeeeeeeeeeeee deeedggeeeeeeeeeeeeaaeeeeeeeeeeeeeee deeggdeeeeeeeeeeeeaceeeeeeeeeeeeeeee dggbeeeeeeeeeeeeeaceeeeeeeeeeeeeeeee bgbeeeeeeeeeeeeeeaceeeeeeeeeeeeeeeeee bggdeeeeeeeeeeeeeeadeeeeeeeeeeeeeeeeeee gg deeeeeeeeeeeedadeeeeeeeeeeeeeeeeeeee gg deeeeeeeeeeedaeeeeeeeeeeeeeeeeeeeeee gge eddddddddddcaddddddddddddddddddddddd gggb ca egggb ca bgggb ca bggg aa bggg ac bggb ac bggb ac gggb af egggb af bggge fa bggg fa gb fa ca ca aa aa ac ac ac ac ac ac ac ac ac ac aa aa aa ca ca ca ca ca ca ca ca fa fa fa fa fa fa fa fa a a a af af af af af af af ``` <!-- end of image --> This close-up of area A is like examining a piece of evidence. <!-- image --> ```palette Key,Color ,#fefefeff a,#0909feff b,#ff4141ff c,#5858ffff d,#ffc8c8ff e,#ff8484ff f,#babaffff g,#ff0505ff ``` ```image db dbgg eggge egggbd egggbd c dbgggd ca dbggge caa dbggge caaf egggbd aaaf egggbd faaaf dbggbd faaa dbggge faac dbggge faac egggbd faac egggbd caac egggbd caac dbggge caaf dbggge caaf eggge caaf egggbd aaaf egggbd faaaf dbggge faaaf dbggge faaa bggge faac egggbd faac egggbd faac dbggbd caac dbggge caac dbggge caaf egggbd caaf egggbd caaf dgggbd aaaf dbggge faaaf dbggge faaa eggge faac egggbd faac egggbd faac dbggge caac dbggge caac ggge caaf gbd caaf d caaf aaaf aaaf faaaf faaa ``` <!-- end of image --> I'll move on to the next area. The intersection must be somewhere. I can confidently say that there are no intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0505ffff b,#ff4d4dff c,#7878ffff d,#ffa8a8ff e,#3b3bffff f,#c0c0ffff g,#ff0606ff ``` ```image d gg gg c bgd ea bgb ea dgb aa dgg ae gg ae ggd ac bgd af dgb af dgg faf gg fa ggd ca bgd ca bgb ea dgb ea gg ae gg ae bgd ac bgb ac dgb af dgg faf gg fa ggd fa bggd ca dgggd ea dgggd ea dgggd aa bggb ae bggb ae bggb ac dbggd af dgggd af dgggd faf dggbd fa gb ca ca ea ea ae ae ac ac ac ac ac ae ae ae ae ae ee ea ea ea ea ea ca ca ca ca ca ca fa fa fa fa fa fa fa a a af af af af af af af ``` <!-- end of image -->

I'm approaching this image with caution. Intersections might be tricky to spot. The image has some tight areas where segments are too close. I should investigate those closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#da7361ff b,#4048edff c,#fa0d0aff d,#7d8ce0ff e,#0405fdff f,#b1d7b1ff g,#99c696ff ``` ```image gggggggggggggggggggggggggggggggggaccgggggggggggggggggggggggggggggg fffffffffffffffffffffffffffffffaccfgcfffffffffffffffffffffffffffff fffffffffffffffffffffffffffffaccffffacffffffffffffffffffffffffffff fffffffffffffffffffffffffffaccfffffffccfffffffffffffffffffffffffff fffffffffffffffffffffffffaccffffffffffcaffffffffffffffffffffffffff fffffffffffffffffffffffaccfffffffffffffcgfffffffffffffffffffffffff fffffffffffffffffffffaccffffffffffffffffcfffffffffffffffffffffffff fffffffffffffffffffgccffffffffffffffffffacffffffffffffffffffffffff fffffffffffffffffgccfffffffffffffdeefffffccfffffffffffffffffffffff fffffffffffffffgccgfffffffffffbeebfebfffffcaffffffffffffffffffffff ffffffffffffffccgffffffffffbeebfffffeffffffcgfffffffffffffffffffff ffffffffffffccgfffffffffbeebffffffffdeffffffcfffffffffffffffffffff ffffffffffccafffffffgbeedffffffffffffedfffffacffffffffffffffffffff ffffffffccaffffffdeeedffffffffffffffffeffffffccfffffffffffffffffff ffffffccafffffdeeedfffffffffffffffffffbbffffffcaffffffffffffffffff ffffccaffffdeeedfffffffffffffffffffffffefffffffcgfffffffffffffffff ffccafffdeeegffffffffffffffffffffffffffdefffffffcfffffffffffffffff ccaffbeebfffffffffffffffffffffffffffffffedffffffacffffffffffffffff cafbeebfffffffffffffffffffffffffffffffffffefffffffccfffffffffffffff beebffffffffffffffffffffffffffffffffffffffbefffffffcaffffffffffffff dffffffffffffffffffffffffffffffffffffffffffegfffffffcgfffffffffffff fffffffffffffffffffffffffffffffffffffffffffeffffffffcfffffffffffff fffffffffffffffffffffffffffffffffffffffffffbbfffffffacffffffffffff ffffffffffffffffffffffffffffffffffffffffffffeffffffffccfffffffffff ffffffffffffffffffffffffffffffffffffffffffffdeffffffffcaffffffffff fffffffffffffffffffffffffffffffffffffffffffffedffffffffcgfffffffff ffffffffffffffffffffffffffffffffffffffffffffffefffffffffcfffffffff ffffffffffffffffffffffffffffffffffffffffffffffbbffffffffacffffffff fffffffffffffffffffffffffffffffffffffffffffffffefffffffffccfffffff fffffffffffffffffffffffffffffffffffffffffffffffgefffffffffcaffffff ffffffffffffffffffffffffffffffffffffffffffffffffebfffffffffcgfffff fffffffffffffffffffffffffffffffffffffffffffffffffeffffffffffcfffff fffffffffffffffffffffffffffffffffffffffffffffffffdefffffffffacffff ffffffffffffffffffffffffffffffffffffffffffffffffffedfffffffffccfff fffffffffffffffffffffffffffffffffffffffffffffffffffeffffffffffcaff fffffffffffffffffffffffffffffffffffffffffffffffffffbbffffffffffcgf ffffffffffffffffffffffffffffffffffffffffffffffffffffefffffffffffcf ffffffffffffffffffffffffffffffffffffffffffffffffffffdeffffffffffac gggggggggggggggggggggggggggggggggggggggggggggggggggggedggggggggggcc e ca de c e c e fc bb ac e ca de c ed c e fc bb ac e ca e c ed c e fc de ac ef c e bb e de ed e de e e bb e de ed e bb e e ed e de e e bb e ``` <!-- end of image --> My goal is to determine if there's an intersection inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff8383ff b,#5454ffff c,#ff0404ff d,#b1b1ffff e,#0606ffff f,#fec6c6ff g,#ff3c3cff ``` ```image fgcf fgccccf fcccgfcg acccf fcca cccgf accf accgf gccf acccf gcg acccgf fcc accca acf agccc ccf fccca gcg fgcca fccg fgccc fcca fccca acc fgccc dbbeed gg gcccaf dbeeeeee fcg fgccgf dbeeeebd eb cca fgccgf dbeeeeb eed accf acccg dbeeeebd beb accf accgf dbeeeebd dee cc acccg deeeeed beb fca accgf dbeeebdd deed acf accgf dbeeeeb bee ccf acccg dbeeeebd ee gcg accca dbeeeebd bb fcca agcca deeeeed ed accf gccca dbeeeebd ee acc fgcca deeeeed eeb gc fgcca dbeeebbd deed cg gccca dbeeeeb beb fca gcca deeeeed dee accf cca dbeeeebd be gcg afdeeeeed ded ccg beeeebd be fcc eeed eb acf beb cg eed ccg dee fcca beb accf dee acc be gc de fca eb ccf eed accf bee gcg eeb ccg beb acc eed acf dee gg be cg ded cca eb accf eed gcg beb cc eed fca dee fcf beb ccf be gcg ed fcca de fcc eb acf eed gg eeb cca deed fcc beb ac ``` <!-- end of image --> Area A is clear of intersections, but the search continues. The image is completely devoid of intersections. Zero.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff8f8fff b,#4949ffff c,#ff0303ff d,#8e8effff e,#0505ffff f,#e9d6ebff g,#ff3535ff ``` ```image f gccf acg fc acg ac acg gg acg ca acc cf acc fc fcc ac fccf dee gg fccf deeb ed ca fccf beeb e cf fccf fbeed de fc cca fbeed ef ac cca feeed e gg gca deeed bb ca gca deeef e cf gca deebf fe fc gca deebf ed ac ca beeb e gg beeb de ca d ef cf fe fc bb ac e gg de ca ed cf e fc bb ac ef gg fe ca ed cf e c de ac ef gg e ca bb cf e c fe ac ed gg e ca de cf ef c fe ac bb gg e ca de cf ed c e ac bb gc ef ca fe cf ed c e ac de gc ef c e bb e de ed e de ef fe bb e de ed e bb ef fe ed e de ef fe bb e ``` <!-- end of image -->

Hmm, I'm not sure what to expect from this image. Let's see if any lines cross. Let's take a closer look at what's happening inside these zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#0809fdff b,#ee6b63ff c,#5f68eeff d,#d9c1e6ff e,#98c697ff f,#b1d7b1ff g,#fc0b0bff ``` ```image d ca aca cc ad a a ac cc a a ac da a ac ad a g da ca gb ad ad g da da gd a ac bg da a g a da gb ca ad dg a a g cc ca bb a a g cc da gd a ac bg ac a g a ca gb ad ad dg da a gd ad cc bg da aeeeeeeeeeeeeeeeg a dafffffffffffffgb da acfffffffffffbge a fafffffffffffgfe ca fcafffffffffgbfe a ffaeffffffffgffe cc fffafffffffgeffe a fffacfffffbgfffe cc ffffafffffgffffe a ffffcafffgbffffe ac fffffacfegfffffe a ffffffafgffffffe ad ffffffcagffffffe a fffffffafffffffe ad ffffffgeaffffffe da fffffbgfacfffffe efffffffffffffaee fffffgfffafffffe effffffffffffcafe ffffgbfffcaffffe effffffffffffaffe fffegfffffaefffe efffffffffffcaffe fffgeffffffafffe efffffffffffafffe ffbgfffffffacffe effffffffffcafffe ffgfffffffffaffe effffffffffaffffe fgbfffffffffcafe egbfffffffccffffe bgffffffffffface efggffffffafffffe gfffffffffffffae effggffffacfffffe bgfffffffffffffca efffbgfffaffffffe geeeeeeeeeeeeeeead effffegeacffffffe gd da effffffgafffffffe bg ac effffffaggffffffe g a efffffeafbgfffffe gb ca efffffaeffbgefffe dg ad effffcafffffgbffe g a effffafffffffggfe bg cc efffcaffffffffgge g a efffaffffffffffbg gd da effcafffffffffffegd dg ac effaffffffffffffe gb g a efccffffffffffffe gg gb ca efafffffffffffffe bg g ad eacfffffffffffffe dgd gd a ecffffffffffffffe gb bg ac gg g a bg gb da dgd dg a gb g gg bb gg g bg gd dgd bg gb g gggb bg ``` <!-- end of image --> Let's put area A under the microscope. <!-- image --> ```palette Key,Color ,#fefefeff a,#0504feff b,#fb4043ff c,#8381fcff d,#ffa5a5ff e,#4240fdff f,#c5c5feff g,#fe0505ff ``` ```image eae faaf eac faa eac caa aac caa aac cae aaf cae faaf eae dd faaf dggd eae bggd faaf dggb eac dggb faa dgggd eac bggd caa bggb aac dggb caa dgggd aac bggcae bgaaf eaab faabggd eae bggd faaf bggd eae dggb faaf dggb eac dgggd faa bggd eac bggb caa dggb aac dgggd caa bgg aac bg cae d aaf cae faaf eae faaf eae faaf eac faa eac faa ``` <!-- end of image --> I observe an intersection inside area A. Okay, let's proceed to the next area. Time to investigate area B up close. <!-- image --> ```palette Key,Color ,#fefefeff a,#0908fdff b,#f7373fff c,#5e5effff d,#fcc0c2ff e,#ff7d7dff f,#b2b1feff g,#fe0404ff ``` ```image a b ac eg aaf gg cac bgb aaf dggd faa gge aac egg faaf dggd caa bgb aac egg faa gge cac egb aaf dggd caa bge aac egg faaf dggd caa bgb aaf dggd faa gge cac egb faaf dggd caa bge aac egg faafgge caagb aabd baa egaac dggdaaf bgb caa egg aac gge faa egb cac dggd aaf bge caa egg aac dggd faaf bgb caa dggd aaf gge faa egb cac dggd faaf bgb caa egg aac gge faaf bgb cac dggd aaf bge faa egg aac ggd faa gb ca ``` <!-- end of image --> There is an intersection point visible in this close-up of area B. After a long analysis, I found two intersections.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0404ffff b,#fd4c4eff c,#7e7effff d,#fda4a6ff e,#3d3cfeff f,#c3c3ffff g,#fe0707ff ``` ```image f ca aca ee af a a ec ee a a ac fa a ac af a g fa ce bb af af g fa fa gd a ec dg ca a g a fa gd ce af dg a a g ee ee bb a a g ec fa gd a ac dg ac a g a ca gb af af g fa a g af ee bg fa a g a fa gd fa ac dg a a g ce ce bb a af g ce fa gd a ec dg ec a g a ca gd ec af dg a a g af eeb a a af gda fa dg ac af g a fa gb ca a g af ca g a a bg ee ce g a a gd fa gd ee dg ac gb a g a gg ec bb ce bg a g af dgdac gd fa ga dg ec abg g a fa bg gd ca af dg dg af fa gd g a a gb bb ee ca bg g a a dg gd fa ce gd dg ac a gb g a ee gg bb ca a bg g af ec dgd g a f gb bg ee gg g a bg gd fa dg dg a gd g gb bb bg g dg gd gd dg gb g gggb bg ``` <!-- end of image -->

Hmm, I'm not sure what to expect from this image. Let's see if any lines cross. I'd describe these as 'hotspots' for potential intersections. <!-- image --> ```palette Key,Color ,#fefefeff a,#6063f1ff b,#ed5555ff c,#0a0afdff d,#f7a8a4ff e,#b5b5ffff f,#fd0707ff g,#afd5afff ``` ```image a c ce ac c ce ec c aa c ce ac c ce ec c aa c ce ac c ce ec c ca c ce ac c ce ec c ca c ce ac c ce ec c ca c e ce cc ac ac c ca ce cc ec ac c eca ca cc c ac ce ece ac cc c df ac ce dfffd ece ec bffb ca c bffb cc ca dfffd ece ggggggggggggggggggggcgggggg dfffd ca gggggggggggggggggggcggggggg bffb cc ggggggggggggggggggacggggggg bffb acggggggggggggggggggcgggggggg dfffd cagggggggggggggggcaggggggbfffd gccgggggggggggggacggggbfffg ggacggggggggggggcggbffbgggg ggggcagggggggggcaffbggggggg gggggccgggggbffcdgggggggggg ggggggacggfffgcgggggggggggg gggggggbcbdggacgggggggggggg ggggbffbgccggcggggggggggggg ggfffgggggcccaggggggggggggg bffdggggggggacgggggggggggggg dffbggggggggggggggggggggggggggg dffb ggggggggggggggggggggggggggg bffd ggggggggggggggggggggggggggg dffb ggggggggggggggggggggggggggg dffb ggggggggggggggggggggggggggg bffd dffb dffb ffd ``` <!-- end of image --> I'm focusing my attention on this specific region, area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#7171ffff b,#f54750ff c,#0404feff d,#ff9999ff e,#b4b2fdff f,#fd0405ff g,#3b2ff2ff ``` ```image acc cce gcg ecc cca acg a ecce cg gca ccce acc gcca cce db accg gcg dbfff eccce ecc dbfffffbd gcca cca dbfffffbd accg acg dbfffffbd eccce eccedbfffffdd egcca gcgffffbd accg dbgccffbd eccge dbfffccbd egcce dbfffffgcg acca bffffbd ecc accgbffffd cca dbcccbbd acg bffffgcca ecce dbffffd accg gca dbffffbd eccce acc bffffbd gccacce dbffffd acccg bffffbd ecc ffbd d ``` <!-- end of image --> My analysis confirms the presence of an intersection in area A. There are precisely two intersections present in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#5b58fcff b,#f8474eff c,#0a0afeff d,#ff9d9dff e,#9f9fffff f,#fe0505ff g,#e5d8f2ff ``` ```image e gc cg ac c ce ec c aa gc cg ac c ce ec c aa gc cg ac c ce ec c aa gc cg ac c ce ec c ca gc cg ac c ce ec c ca gc g cg cc ac ecg c gca ce cc ec acg c gce ca cc gc ac cg gce ac cc c df ac ce dfffd ece ec bffbg ca c gbffb cc ca dfffd ecg gc dfffd ca cg bffbg cc ac gbffb ecg c dfffd gca ce dfffd cc ec bffbg acg c gbffb gce caffd cc dffcd ac gffbgcg bcbd ac dffd cc c gffb acce bffd ec dffd gffb bffd dffd gffb bffd dffd gffb ffd ``` <!-- end of image -->

Let's examine this image for potential line intersections. Could these regions be concealing intersection points? Let's find out. <!-- image --> ```palette Key,Color ,#fefefeff a,#0808feff b,#ef5351ff c,#5a5ff3ff d,#eba69dff e,#b9bafeff f,#fc0808ff g,#afd6afff ``` ```image e aa eaecc ca a aa ea ac a eae ea ca ae aa a ac ac eae a ca cc aa a ac ea eae a ca ea aa ae ac a eae ac ca a aa cc ac a eae ca ca a aa ea ac ae eae a ca ae aa a ac cc a ca a ea ff ae fb fd ea bf fb ae ff ff a dfd bf ac ff dfd a dfb fb cc bf ff a fb bf ea bf df a ff fd ea dfd fb ae ff ffgggggggggagggggggggggggggggg dfb gbfggggggggacggggggggggggggggg bf ggdfdgggggggaggggggggggggggggg fb ggggfbggggggccgggggggggggggggg bfd gggggffggggggagggggggggggggggg ff ggggggbfgggggcaggggggggggggggg dfd gggggggdfgggggaggggggggggggggg ff gggggggggfbggggagggggggggggggg fb ggggggggggffgggagggggggggggggg bf gggggggggggffgggaggggggggggggg fb ggggggggggggbfggacgggggggggggg bfd gggggggggggggdfdgagggggggggggg ff gggggggggggggggfbccggggggggggg fd ggggggggggggggggffaggggggggggg gggggggggggggggggbbagggggggggg ggggggggggggggggggdagggggggggg gggggggggggggggggggcabgggggggg ggggggggggggggggggggaffggggggg gggggggggggggggggggggaffgggggg gggggggggggggggggggggacbfggggg ggggggggggggggggggggggaggfdggg ggggggggggggggggggggggacggfbgg gggggggggggggggggggggggagggffg gggggggggggggggggggggggcagggbf ggggggggggggggggggggggggaggggd ggggggggggggggggggggggggcagggg gggggggggggggggggggggggggagggg ggggggggggggggggggggggggggaggg ggggggggggggggggggggggggggacgg gggggggggggggggggggggggggggagg ac a cc a ``` <!-- end of image --> This close-up of area A is like examining a piece of evidence. <!-- image --> ```palette Key,Color ,#fefefeff a,#0505feff b,#f94146ff c,#453ef7ff d,#ff9494ff e,#9190fdff f,#fd0507ff g,#ead1e6ff ``` ```image ffg eac bffd aae bffd eaa dffb cae dffbg eaag gfffd cac gbffd gaag bffb cac dffbg gaae gfffg eac gbffd aae bffd eaa dffb aae dffbg eaag gfffd cac gbffd gaag bffb cac dffbg gaag gfffg eac gbffd aae bffd eaa dffb aae dfffg eaa gfffd cae bffd gaag bffb cac dffbgaag gfffcac gbffaae bfbaa dfaae dbaag gaacd eaafd cacfb gaaffbg cacfffg gaaebffd eac bffb aae dffb eaa dfffg cae gfffd eaag bffd cac dffb gaag dffbg cac gfffg gaae gbff eac bf aae d eaa aae eaag cac gaag cac gaag eac aae eaa ``` <!-- end of image --> The evidence is clear: this is an intersection in area A. There's one and only one intersection present in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0808feff b,#f83940ff c,#5c5cffff d,#ff7f7fff e,#b7b7feff f,#ff0505ff g,#fec5c6ff ``` ```image aa eaecc ca a aa ea ac a eae ea ca ae aa a ac ac eae a ca cc aa a ac ea eae a ca ea aa ae ac a eae ac ca a aa cc ac a eae ca ca a aa ea ac ae eae a ca ae aa a ac cc a ca a ea bfg ae gfbgfd ea bfg fb ae fb bf a dfg df ac ff gfg a gfd fd cc bf ff a fb bf ea dfg dfg a ff fd ea dfg fb ae ff bf a gfd df ac bf gfg a fb fd cc dfg ff a ff bf ea gfd gfg a ff fd ea gfd fb ae bf bf a fb df ac dfg gfg a ff fbcc fd ffa bba gag ead abb abf aedf a gfg cc fb a ff ca bf a g ea ae ea ae a ac a cc a ``` <!-- end of image -->

Here's an image. My task is to find intersections or areas where lines come close together. These regions highlight areas that look suspicious. Lines seem to converge within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#4c52f0ff b,#ee615bff c,#0708fdff d,#feb2b2ff e,#fd0908ff f,#9499f1ff g,#add4adff ``` ```image d ed c e ccf ed c c de aa fc e c ca de aa c e c c bb fc ac e c cf bb fc c e c fc ed c cf e cf c ed c fc de cf ca e c c de af c e c ac bb aa cf e c c bb fa fc e c cf ed fc c e c fc ed c ca b de c c de e c c e de cf ac ed ggegggggggggcggg cf eb ggbbgggggggcaggg c be gggegggggggcgggg fc de gggebgggggaagggg caggggggggggggggge ggggegggggcggggg cgggggggggggggge ggggebgggaaggggg fcggggggggggggeb gggggegggcgggggg gcaggggggggggeeg gggggeggfcgggggg ggcgggggggggbegg ggggggegcggggggg gggcggggggggeggg ggggggefcggggggg gggacggggggegggg ggggggbcgggggggg ggggcfggggebgggg gggggggcgggggggg gggggcgggebggggg ggggggcbbggggggg gggggacgbegggggg ggggggcgeggggggg ggggggcaeggggggg gggggcfgebgggggg gggggggcgggggggg gggggcgggegggggg ggggggefcggggggg ggggaagggebggggg gggggebgcagggggg ggggcgggggeggggg ggggbegggcgggggg gggaagggggeggggg gggbegggggcggggg gggcgggggggegggg gggeggggggacgggg ggacgggggggegggg ggeggggggggcfggg ggcggggggggbeggg gebgggggggggcggg gfcgggggggggeggg eeggggggggggacgg c bb beggggggggggggcag c e eggggggggggggggcg c bb e ggggggggggggggfc c e ed ca cf ed eb c c e be c af e de aa c de e cf aa e ed c c de eb fc fa e be cf c bb de c fc e e c eb ed fc e eb c ed be c e de cf e e c de e cf e ed c de eb aa e be c bb de aa e e c eb ed fc e eb c eee e ``` <!-- end of image --> Let's zoom in on area A to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#362ef6ff b,#fb5a5eff c,#0303feff d,#feb4b4ff e,#fe0708ff f,#8383ffff g,#c4c4feff ``` ```image eed fca bee acf eed fcc beb acf eed gcc beb acf dee gcc beb acf dee gccg eed fca dee ccg eed fca bee ccg eed fca beb ccf eed fca beb acf dee gcc beb acf deegcc eeacf deccg aca gccb fcaed ccbeb fcadeed ccg beb fca dee acf beb fcc dee acf eed gcc dee acf eed gcc beb acf eed gccg beb fca deed ccg beb fca dee ccg beb fca dee ccf eed fca dee acf eed ``` <!-- end of image --> There's no doubt about it - this is an intersection in area A. Moving on to the next area. Let's see if area B yields any clues. <!-- image --> ```palette Key,Color ,#fefefeff a,#3d3bfcff b,#fe5c5cff c,#0504feff d,#ffb3b3ff e,#fe0809ff f,#8784fbff g,#cbcbffff ``` ```image a cf ccg aca b ccf de gccg dee fcc eeb aca eeb gccf bee fccg beed aca deed gccf deeb fccg eeb aca bee ccf beed gccg deed fcc deeb aca eeb gccf bee fccg bee aca deed gccfeed fcceb acc beccf beefccg deed fcc deeb aca eeb gccf bee fccg beed aca deed gccf deeb fccg eeb aca bee ccf beed gccg deed fcc deeb aca eeb gccf eee fccg bee aca eed gccf ed fccg b aca cc gc ``` <!-- end of image --> I observe an intersection inside area B. After a thorough search, I conclude that there are two intersections.

<!-- image --> ```palette Key,Color ,#fefefeff a,#5050ffff b,#ff4141ff c,#0808ffff d,#fd8d8fff e,#ff0505ff f,#9d9bfdff g,#f1d7e5ff ``` ```image g ed c e ccf eg c c ge aa fc e c ca de aa cg e c gc db fc ac e c cf bd fc c e cg fc ed gc cf e cf c eg c fc ge cf ca e c cg de af gc e c ac db aa cf e c c bd fa fc e c cf ed fc c e c fc eg gc ca d ge cg cg de e c gc e de cf ac eg e c cf ed db cf c bb e c fc de bd aa cf ge e c c eg ed aa fc ed ge c ca bb eg fc cg de ge c gc ge efc ac eg dcg cf ed gc c eb cdb fc be c e cfe cf bd c c e efc aa ed ed ca c ge be cg aa eg de gc c ge ge aa fc e eg cf c de ed c fc e bb fc c bb de cf gc e ge c cg bd eg fc c e ed ca cf ed eb cg c ge de gc af eg ge aa c ge e cf aa e eg c c db eb fc fa e be cf c bb de c fc e e c bd eg fc e ed cg ed bb gc ge de cf eg ge c ge eg cf e ed c db bb aa e de c bb ge aa e e c bd ed fc e eb c ebe ge ``` <!-- end of image -->

This image might have some surprises. Let's look for intersections carefully. My final answer is: no intersections found.

<!-- image --> ```palette Key,Color ,#fefefeff a,#8383ffff b,#ff0707ff c,#0404ffff d,#ff5b5bff e,#ffacacff f,#c8c8ffff g,#3e3effff ``` ```image e dbd dbd dbd dbb ebb db ebb dbbd ebb ebbbe ebb dbbde ebbe ebbbd ebbe dbbbe bbe edbbd bbe ebbbe bbe dbbd bbe ebbbd bbd dbbbe bbd ebbbd dbd dbbbe dbd g fcf ca cg gc ac fcf ca cg gc ac fcf cg cc gc acf fca cg cc gc fcf ca cg gc ac fcf ca cg gc ac fcccgf acccca fgcccga fgcccgf accccaf facccga fgcccgf agcccaf facccca fgcc ``` <!-- end of image -->

Based on a first glance, I suspect there could be intersection regions here. These regions highlight areas that look suspicious. Lines seem to converge within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#0506feff b,#f55350ff c,#9fa2f9ff d,#faa19fff e,#acd4acff f,#fd0808ff g,#4649f7ff ``` ```image d ff ffd bfb dff ff bfd dfb ff ffd dfb ff ff bfd dfb ff bfd dfb ff ff bfd dfb ac ff a bfd gg dfb a ff ca ff ac fb a bf ca fb ac bf a ff eggeeeeeeeeeeeee bfd eeaeeeeeeeeeeeee ff eeeaeeeeeeeeeeee dfd eeeageeeeeeeeeee ff eeeeaeeeeeeeeeebfd eeeecaeeeeeeeeff eeeeeaceeeeedfbe eeeeeeaeeeeffeee eeeeeegaeefbeeee eeeeeeeabfeeeeee eeeeeeefaeeeeeee eeeeebfeageeeeee eeeeffeeeaeeeeee eebfeeeeecaeeeee effeeeeeeeaceeee dfdeeeeeeeeeaeeee ffeeeeeeeeeeegaeee dfd eeeeeeeeeeeeaeee ff eeeeeeeeeeeeeaee eeeeeeeeeeeeegge eeeeeeeeeeeeeeae ca ac a ca ac a gg a ca ac a ca ac a gg a a ag a ca ac a ga a a ggcccccccccccccc ggggggggggggaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa ``` <!-- end of image --> Here's a close-up of the area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0505feff b,#fd6162ff c,#8481fbff d,#ffb9b9ff e,#c2c2ffff f,#fe0a0aff g,#403cfaff ``` ```image gag aac caa gag eaae caa aac eaae gag d aac bf caa dfff gag bfffd eaae dfffb caa bfffd gac dfffb eaae bfffd gag dfffb aac bfffd caabffb gagfd bfaac dfffcaa bffb gac dfffb eaae bfffd cag dfffb aac bfffd eaae dfffb gag bfffd eaac fffb caa ffd gag b eaae caa aac eaae gag aac caa gag ``` <!-- end of image --> My analysis confirms the presence of an intersection in area A. After careful examination, I conclude that there is one intersection.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0505ffff b,#fd4445ff c,#a0a0ffff d,#ff9393ff e,#efd7e7ff f,#fe0506ff g,#4b4bffff ``` ```image d eff bfe dfd eff ffe bfd dfb eff bfe dfd eff ffe bfd dfb ff bfe dfb eff ffe bfd dfb ae ff ea bfd gg dfb a eff ca bfe ac efb a bfe ca efb ac bfe a fb gg dfe ae ff ea dfd ag ff a dfd ca ff ac dfd a ff gg efb abfe efa bfegg efb a bfe ca ff ac dfd a ff ga dfd ae ff ea e gg a ca ac a ca ac a gg a ea ac a ca ac a gg ae ea ag a ca ac a ga ae ea ggcccccccccccceeeeee ggggggggggggaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa ``` <!-- end of image -->

Here's an image. My task is to find intersections or areas where lines come close together. Let's take a closer look at what's happening inside these zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0404ff b,#0809fdff c,#f88986ff d,#6669f5ff e,#e1ceeaff f,#add4adff g,#f73e3aff ``` ```image c a ac ea ae ca a cg a gg a ac ea ae ea a cg a gg a ac a ae ea a edd ca edbbbbdbb a edbbbbde bb gg edbbbbde bb a edbbbbde db gc edbbbbde db a edbbbbde db ac dbbbbde db ea de db fffffffffffffaff eb ffffffffffffcaff ebeffffffffffffafff ebfffffffffffggfff ebffffffffffaffff fbffffffffggffff ffbfffffffafffff fffbdffffacfffff ffffbdfffaffffff fffffbdfafffffff ffffffbdafffffff fffffffbdfffffff ffffffggbbffffff ffffffaffbbfffff fffffggfffbbffff fffffafffffbbfff ffffacffffffbbff ffffaffffffffdbf fffaffffffffffdb ffcafffffffffffdb ffafffffffffffffdb fcafffffffffffff eb faffffffffffffff eb ggffffffffffffff eb a ebe ac ebe ag a be cac ae be gac ea bd aae a bd eaa ca bd cag a bd gac gg bd aae a bb aa gc b cag a cac ac gac ea aae ae eaa ca cag a gac cg aae a eaa gc cag a cacac ga ``` <!-- end of image --> Could this be where the intersection is hiding, in area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0404ff b,#0808feff c,#fb7a7eff d,#4e49faff e,#ffc3c3ff f,#b7b7feff g,#fb393cff ``` ```image eaae gag eaae gac caa aac cag aae d cag bb eaae bbb gag bbbf eaae dbbf gac dbbf eaa dbbf aac dbbf caa dbbf aae dbbf cag dbbf eaae dbbf gag dbbd eaae fbbd gac fbbdaa fbbdc cbbd agbbd cagfbbd eaae fbbd gag fbbd eaae fbbb gac fbbb eaa bbbf gac dbbf caa dbbf aac dbbf cag dbbf aae dbbf cag dbb eaae db gag d eaae gac caa aac cag aae cag ``` <!-- end of image --> An intersection is present within area A. One intersection, that's it, but I found it.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0404ff b,#0a0afeff c,#ff7c7cff d,#6c6bfdff e,#ffc0c0ff f,#cdcdffff g,#ff3b3bff ``` ```image c a ae ea ae ea a cg a gc a ac a ae ea a cg a gg a ac a ae ea a fdd ca fdbbbbdbb a fdbbbbdf bb gg fdbbbbdf bb a fdbbbbdf bb gc fdbbbbdf db a fdbbbbdf db ae dbbbbdf db ea df db ae fb ca fb a fb cg fbf a fbf gc bf a bf ae bd ea bd ae bda bd cgbd a bb gc bb a bb ac bb a db ae db ea db a db cg fb a fb gg fb a fbf ac fbf ag a bf cac ae bf gae ea bd aae a bd eaa ca bd cag a bd gac gg bd aae a bb aa gc b eag a cac ae gae ea aa ae eaa ca cag a gac cg aae a aa gc eag a cacae ga ``` <!-- end of image -->

I'm curious to see if this image contains any intersection points. I have a hunch that these areas might contain the intersections we're looking for. <!-- image --> ```palette Key,Color ,#fefefeff a,#0202fdff b,#fa0b0bff c,#717ae7ff d,#b2d7b1ff e,#a3cca3ff f,#2d2af1ff g,#d86b61ff ``` ```image eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeec eddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddea eddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddae edddddddddddddddddddddddddddddddddddddddddddddddddddddddddddacb eddddddddddddddddddddddddddddddddddddddddddddddddddddddddddcabg eddddddddddddddddddddddddddddddddddddddddddddddddddddddddddabbe edddddddddddddddddddddddddddddddddddddddddddddddddddddddddagbde eddddddddddddddddddddddddddddddddddddddddddddddddddddddddffbdde edddddddddddddddddddddddddddddddddddddddddddddddddddddddeabddde edddddddddddddddddddddddddddddddddddddddddddddddddddddddabdddde eddddddddddddddddddddddddddddddddddddddddddddddddddddddafddddde edddddddddddddddddddddddddddddddddddddddddddddddddddddcadddddde eddddddddddddddddddddddddddddddddddddddddddddddddddddeaedddddde eddddddddddddddddddddddddddddddddddddddddddddddddddddacddddddde edddddddddddddddddddddddddddddddddddddddddddddddddddffdddddddde eddddddddddddddddddddddddddddddddddddddddddddddddddbaddddddddde edddddddddddddddddddddddddddddddddddddddddddddddddbaeddddddddde eddddddddddddddddddddddddddddddddddddddddddddddddbacdddddddddde edddddddddddddddddddddddddddddddddddddddddddddddbgaddddddddddde eddddddddddddddddddddddddddddddddddddddddddddddbbadddddddddddde edddddddddddddddddddddddddddddddddddddddddddddgbacdddddddddddde eddddddddddddddddddddddddddddddddddddddddddddgbffddddddddddddde edddddddddddddddddddddddddddddddddddddddddddgbeadddddddddddddde eddddddddddddddddddddddddddddddddddddddddddebdaddddddddddddddde edddddddddddddddddddddddddddddddddddddddddebdacddddddddddddddde edddddddddddddddddddddddddddddddddddddddddbecadddddddddddddddde eddddddddddddddddddddddddddddddddddddddddbedaddddddddddddddddde edddddddddddddddddddddddddddddddddddddddbgdacddddddddddddddddde eddddddddddddddddddddddddddddddddddddddbgdffdddddddddddddddddde edddddddddddddddddddddddddddddddddddddbgdeaddddddddddddddddddde eddddddddddddddddddddddddddddddddddddbbddadddddddddddddddddddde edddddddddddddddddddddddddddddddddddbbddacdddddddddddddddddddde eddddddddddddddddddddddddddddddddddgbddcaddddddddddddddddddddde edddddddddddddddddddddddddddddddddgbdddadddddddddddddddddddddde eddddddddddddddddddddddddddddddddgbdddaedddddddddddddddddddddde edddddddddddddddddddddddddddddddebdddffddddddddddddddddddddddde eddddddddddddddddddddddddddddddebdddeadddddddddddddddddddddddde eddddddddddddddddddddddddddddddbedddaddddddddddddddddddddddddde edddddddddddddddddddddddddddddbedddacddddddddddddddddddddddddde eddddddddddddddddddddddddddddbgdddcadddddddddddddddddddddddddde edddddddddddddddddddddddddddbgddddaddddddddddddddddddddddddddde eddddddddddddddddddddddddddbgddddaeddddddddddddddddddddddddddde edddddddddddddddddddddddddbbddddffdddddddddddddddddddddddddddde eddddddddddddddddddddddddbbddddcaddddddddddddddddddddddddddddde edddddddddddddddddddddddbbdddddadddddddddddddddddddddddddddddde eddddddddddddddddddddddgbdddddacdddddddddddddddddddddddddddddde edddddddddddddddddddddgbdddddcaddddddddddddddddddddddddddddddde eddddddddddddddddddddgbdddddeadddddddddddddddddddddddddddddddde edddddddddddddddddddebddddddaedddddddddddddddddddddddddddddddde eddddddddddddddddddebedddddffddddddddddddddddddddddddddddddddde edddddddddddddddddgbedddddcadddddddddddddddddddddddddddddddddde eddddddddddddddebbbeddddddaddddddddddddddddddddddddddddddddddde eddddddddddddgbbgddddddddacddddddddddddddddddddddddddddddddddde edddddddddgbbgddddddddddcadddddddddddddddddddddddddddddddddddde eddddddebbbedddddddddddeaddddddddddddddddddddddddddddddddddddde eddddgbbgddddddddddddddaeddddddddddddddddddddddddddddddddddddde edgbbgddddddddddddddddffdddddddddddddddddddddddddddddddddddddde bbbedddddddddddddddddcaddddddddddddddddddddddddddddddddddddddde gbbgeeeeeeeeeeeeeeeeeeeeaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee dbbg ac bbb ca gbbg ca dbbg caf bbb caf bg caf caf caf caf caf caf caf caf caf caf caf caf caf caf caf af ``` <!-- end of image --> Time to investigate area A up close. <!-- image --> ```palette Key,Color ,#fefefeff a,#0908fdff b,#fd0809ff c,#6462fdff d,#fdb3b4ff e,#b8b6fdff f,#740b95ff g,#fd595bff ``` ```image e ea caa eaae aacd aadb eadbb eacbbg aabbg caabg aafb caabb eaabbd eaafbd aafbd caabd aabg afg cag eaa aaf faa faae gaac gfaa gfaae daac dbaa dbfae dbbac bbfa bbfaa bbgaae gbbaac bbeaae gbdaac gbdcaa dbbcaae dbbgaae dbbg ac dbbg ca dbbg eae bbb caa bb caae gbd eaae gbd aac gbb caa gbbd eaae dbbd aac dbbg cac dbbg eae bbg ac bg ca bb eaa gb aac gbb cac gbbd caa gbbd eaae dbbd caa dbbg eaae bbg aac dbg ac dbg ca bb eae bbb aa bbb caa gbbd aac gbbd cac gbbd caa bbd eaae dbd aac dbg caa dbb aae dbbg ac bbg ca bbb eaa gbb aac gbbd caa bbd eaae gbd eaac gbd aac dbb caa dbbg aac dbbg aa dbbg eae bbg eac bbb aa bb caa dbbd eaae dgbbbd aac dbbbbgd eaae dgbbbgd eaac gbbbbb aac gbbbbgd caa dgbbbgd aae gbbbbg ac dgbbbbgd ca dgbbbgd eae dgbbbbg aac dbbbbgd caa dbbbbg eaae bbbbd aac ``` <!-- end of image --> I am surprised, so clear, an intersection has appeared in area A. The image features one single intersection point.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0303feff b,#fd090aff c,#7e7dfeff d,#ffa8a8ff e,#c5c3fdff f,#342ef8ff g,#f75159ff ``` ```image c ea a acb cabg abg agb ffb eab ab af ca a ae ff ba ba bac bga gba gbae dbff dbea db a b ac b ca bd a bd ae bd ff bg ea bg a gb ac gb ca gb a db ae db ff b ea b a bd ac bd ca bd a bg ae bg ff bb ea gb a gb ac db ca db a b ae b ff db ea bbb a gbbd ac dbbg ca bbb a gbbd ae dbbg ff bbb ea gbbd a dbbg ac bbb ca gbbd ca dbbg caf gbbd caf bd caf caf caf caf caf caf caf caf caf caf caf caf caf caf caf af ``` <!-- end of image -->

I'm approaching this image with caution. Intersections might be tricky to spot. I need to zoom in on these areas to get a better look. <!-- image --> ```palette Key,Color ,#fefefeff a,#0606feff b,#fc100fff c,#ecedf0ff d,#8a90f2ff e,#e69085ff f,#4246f7ff g,#aed4aeff ``` ```image ecccccccccccccccc bbgggggggggggggggc cbbggggggggggggggc agbegggggggggggggc cagbeggggggggggggc caggbegggggggggggc cdaggbgggggggggggc cgagggbggggggggggc cgdaggebgggggggggc cggagggebggggggggc cggffgggebgggggggc cgggaggggbbggggggc cgggffggggbbgggggc cggggagggggbbggggc cggggadgggggbegggc cgggggaggggggbeggc cgggggadggggggbggc cggggggagggggggbgc cggggggagggggggebc cccccccaccccccceb ac eb da bb a bb da bb f a be da df be ca a bc ac ff cbc ad a cb fa fd eb da a eb a ad eb ad ca bb af ac bb da ca be ca ac be ac da bc ad a bc fa da cb da a cb ccccccccccccccac df ebbc ggggggggggggggadgc a ebbbc gggggggggggggafggc ff ebbbc ggggggggggggfagggc a ebbbc ggggggggggggaggggc fd ebbbc gggggggggggagggggc a ebbbgggggggggadgggggc ad ebbbgggggfaggggggc ca gggebbbgdagggggggc ac ggggggebabgggggggc ca gggggggadebbbegggc ac ggggggafggggebbbec da gggggfaggggggggebbbc ac gggggagggggggggggcebbbc da ggggaggggggggggggc ebbbc a gggadggggggggggggc ebbb df ggffgggggggggggggc e a gdaggggggggggggggc ff gaggggggggggggggg a ac fd af a fa ad ca ca ac ac ad ca ff ac da ca ca ac ac da ad a fa df ca a ac ff ad a ff fd da a ca ad ac a ad afa ca ``` <!-- end of image --> Let's put area A under the microscope. <!-- image --> ```palette Key,Color ,#fefefeff a,#0707ffff b,#ff3b3bff c,#afafffff d,#fecfd0ff e,#ff8888ff f,#5656ffff g,#ff0505ff ``` ```image ggd bggd bgb dggb ffdggb aacdgge faf dgge caa egge faf egge caa eggd faf bggd caa bggd aac bgb caa dggb aac dggb caa dggb aac dgge faf egge aac egge faf eggd aac bggd faf bggd caa bgbd faf dbgb caa dggb faf dggb caa dgge aac egge caa egge aac eggd caa bggd aac bggd faf bggd aac bgb faf dgg aac dg ``` <!-- end of image --> Based on this close-up, I can conclude that there's no intersection in area A. Let's inspect the next region. I'm now examining the contents of area B in detail. <!-- image --> ```palette Key,Color ,#fefefeff a,#0705fdff b,#fc3a3cff c,#e0d3f1ff d,#9393feff e,#ff9090ff f,#4545feff g,#fe0102ff ``` ```image faf faac daac caad caaf faf daac daad caad faf faac daac bec caad gggbec caaf ebggggbec faf ebggggbec daac ebggggbec daad ebggggbaad ebgaaabec faaggggbec daac ebggggbec caad ebggggbec caaf ebggggbe faf ebggg faac eb daad caad aaf faa daac caad caaf faf faac daad caad ``` <!-- end of image --> Amazing! This area was hiding an intersection all along! After careful examination, I conclude that there is one intersection.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0505ffff b,#fe3f40ff c,#cacaffff d,#8484ffff e,#ffababff f,#3f3fffff g,#fe0606ff ``` ```image e bg gb acgb ca ge a ge ca g a g df eg a eg df bg a bg fd gb a gb fd ge a ge ac g a g ac eg ca eg a eg ca bg a bb df gb f a ge da df ge ca a ge ac fd g ad a g fa fd eg ca a eg a ad bg ac a bg af ac gb da ca gb ca ac ge ac ca ge ad a g ff da g ca a eg a df egb ac a eggb af ff eggb da a eggb ca fd eggb a a eggb ad ad eggb ff a eggbeca ac egabe ca aceggbe ac af eggge ca da eggge a ca eggge da a eggge a ad eggg df ff e a da ff a a ac fd ad a da ad ca a a ac ad ca ff ac da ca a a ac da ad a fa df ca a a ff ac a ff fd da a a ad ac a ad afa ca ``` <!-- end of image -->

Time to put on my detective hat and find those intersection points! It's crucial to examine these regions more closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#0606fdff b,#fe0707ff c,#5257f4ff d,#f6a29eff e,#aaabfbff f,#aed5aeff g,#f7534fff ``` ```image e ae a cc a cc a ea a ea db a gbdbd ea bb bb ae bd gb a db bg acffffffffffffff bb gb faffffffffffffff bg dbg facfffffffffffff dbd bb ffafffffffffffff gb dbd ffccffffffffffff bb bb fffaffffffffffffbd gb fffcafffffffffgb bg ffffaffffffffbbf gb ffffcaffffffbgff dbg fffffaffffdbdfff bb fffffeaffgbfffff dbd ffffffafbbffffff bb fffffffagfffffff gb fffffgbaefffffff bg ffffbbffafffffff gb fffbgfffacffffff dbg fdbdfffffaffffff bb gbfffffffacfffff dbd bbfffffffffafffff bb bdffffffffffccffff gb db fffffffffffaffff bg bb fffffffffffcafff gb bg ffffffffffffafff dbg bd ffffffffffffcaff bb fffffffffffffaff dbd ffffffffffffffaf bb ae g a ae a ae a cc a cc a ea a ea a ea ae a ae a ac a cc a cc a ea a eac caaae ecaace eaaac caaae ecaace eaaac caaae ecaace eaaac caaae ecaace eaa ``` <!-- end of image --> I'm determined to find out if an intersection exists in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0404feff b,#fe0a0bff c,#7c7cffff d,#ffb9b9ff e,#bdbcfeff f,#3730f8ff g,#fd6365ff ``` ```image aae caf aac caa fac eaa fac eaa fac eaae faf eaae caf aae caf g aae gb caf dbbb aac dbbbd caa gbbg fac bbbg eaa dbbbd fac gbbb eaa gbbg fac dbbbd eaaedbbbd fafbbg eaabg dbfaf gbbgaae gbbg caf dbbbd aae dbbbd caf gbbg aac bbbg caa dbbbd fac gbbb eaa gbbg fac dbbbd eaae bbbd fac bg eaae g caf eaae caf aae caf aac caa fac eaa fac eaa fac eaa ``` <!-- end of image --> Incredible, there's actually an intersection in area A! It was tricky, but I finally found one single intersection in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0404feff b,#ff0909ff c,#7e7effff d,#ffb4b4ff e,#c4c3feff f,#3c3cffff g,#ff6161ff ``` ```image e fc a fc a cf a ca a ea db ae gbdbd ea bb bb ae bg gbd a gb bg ac bb bb a bg dbg fc dbd bb a gb dbd ff bb bb a bg gbd cf gb bg a bb bb ca bg dbg a dbd bb ea gb dbd aebb bb eag gbd gbae bg bb a bb bg ac dbg dbd a bb gb fc dbd bb a bb bg ff gbd gb a bg bb cf gb bg a dbg bd ca bb a dbd ea bb ae g ea ae a fc a fc a cf a ca a ea ae ea ae a ac a fc a ff a cf a ca a eac caaac efaafe caaac caaac efaafe caaac caaac efaafe caaac caaae efaafe caa ``` <!-- end of image -->

I'm approaching this image with caution. Intersections might be tricky to spot. My next step is to analyze the details within each area. <!-- image --> ```palette Key,Color ,#fefefeff a,#f74440ff b,#0a0afeff c,#fd0506ff d,#7074f5ff e,#f48883ff f,#eacbdfff g,#aed5adff ``` ```image f fbbbb dbf dbbd bb dbbd dbf dbbf bb fbbbf dbd dbbd bb dbbd fbd dbbd bb bbbf bb fbbb dbf dbbd bb dbbd dbd dbbf bb fbbbf fbd dbbdf ggggggggggggggg bb ggggggdbbgggg gggggggggggggggbd ggggggggggggg gggggggggggggdbf ggggggggggggg ggggggggggggbbg ggggggggggggg ggggggggggdbdgg ggggggggggggg gggggggggbbgggg ggggggggggggg gggcgggdbdggggg ggggggggggggg gggecgbbggggggg ggggggggagggg ggggcbdgggggggg gggggggecgggg gggbbcggggggggg gggggggcggggg gggdgacgggggggg ggggggcgggggg ggggggcgggggggg gggggcagggggg gggggggcggggggg ggggacggggggg gggggggaagggggg ggggcgggggggg ggggggggcgggggg gggcggggggggg ggggggggecggggg ggceggggggggg gggggggggcegggg gaagggggggggg ggggggggggcgggg ecggggggggggg ggggggggggacggg cgggggggggggg cf cf c ce aa ac c fc fc c ce ce c aa ec ec cf fc c cf aa ce c ac fc fc ce c c cf ec ca cf ec c fc aa cf c ce fc aa ce ec c c ec cf cf ca c ec aa fc c c fc ce ce aa c ec ec c cf cf c ce aa ac c fc fc c ce ce c aa ec ec cf fc c cf aa ce cac fc ``` <!-- end of image --> I'm focusing my attention on this specific region, area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe5454ff b,#0604fdff c,#fd0709ff d,#7676feff e,#3933f8ff f,#feb6b6ff g,#b9b8fdff ``` ```image g eb gbbb dbbeg gebbd dbbbg gebbd dbbbg ff ebbe fcc gbbbd cca dbbeg fccf gbbbd acadbbeg cbbbd dbbbg ebbeca gbbgfccf g acc cca fccf aca ccf fcc aca fccf acc cca fccf aca ccf fcc aca ``` <!-- end of image --> I can confirm that an intersection exists in area A. Okay, let's direct our attention to the next zone. Let's put area B under the microscope. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff3434ff b,#0707ffff c,#ff0404ff d,#5454ffff e,#ff6f6fff f,#ffb6b6ff g,#a5a5ffff ``` ```image gdbbbbdg gdbbbbdg gbbbbb gdbd ef ecc fccf fcce aca aca eccf fccf cce aca ecc fccf fcce aca aca eccf fccf cce aca ecc fccf ``` <!-- end of image --> Unfortunately, there's no intersection inside area B. I've found a single intersection point in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff4343ff b,#0808ffff c,#fe0506ff d,#5f5fffff e,#ff8383ff f,#ffc3c3ff g,#b2b2ffff ``` ```image g bbbb db gbbd bb dbbd dbg dbbg bb gbbbg gbg gbbd bb dbbd gbd dbbg db bbbg bd gbbb dbg gbbd bb dbbd gbg dbbg bb gbbbg gbd gbbd bb dbb bd db bb dbg bb c gbg fc bb a cbd fc dbc c g ec cf cf ca c ec aa fc c c fc ce ce aa c ec ec c cf cf c ce aa ac c fc fc c ce cf c aa ec ec cf c c cf aa ce c ac fc fc ce c c cf ec ca cf ec c fc aa c c ce fc aa ce fc c c ec cf cf ca c ec aa fc c c fc ce ce aa c ec ec c cf cf c ce aa ac c fc fc c ce cf c aa ec ec cf c c cf aa ce cac fc ``` <!-- end of image -->

I have an image in front of me. I need to determine if there are any intersection segments. My next step is to analyze the details within each area. <!-- image --> ```palette Key,Color ,#fefefeff a,#ed736bff b,#5559f3ff c,#fb0d0cff d,#95c59aff e,#0707feff f,#afafffff g,#b1d6b0ff ``` ```image fe ebb fe e e fe fe e ef fe e ef ef e e eb ef e e bb bb e e fe bb e e fe fe ef e e fe ef e e fe bb ef e e be ef e e fe ef ef e e bb ef e e bb bb e e fe be e e fe fe e ef fe e ef ef e e ef bb e e ef bb e e bb fe e e bb fe e ef dgggggggggbegggd e cc ggggggggggeggggd eb acggggggggggbeggggd e ccggggggggegggggd dgbbgggggggggggd acdgggggdegggggd gggegggggggggggd ggccggggedgggggd gggbeggggggggggd gggccgggeggggggd ggggeggggggggggd acc gggggccedggggggd ggggdegggggggggacc ggggggcegggggggd gggggedggggggccc ggggggebcagggggd ggggggeggggccagd ggggggeggccggggd ggggggebaccagggd gggggbbgggacaggd ggggggaecggggggd gggggeggggggccgd ggggcccbbggggggd ggggbbgggggggaca ggccagggeggggggd ggggeggggggggggcc gccagggggbegggggd gggbeggggggggggdaca accdggggggggegggggd gggegggggggggggd cc acc gggggggggdeggggd ddbedddddddddddg acg cca ggggggggggedgggd e cc cca gggggggggggegggd fe ac acc gggggggggggebggd e cc acc ddddddddddddeddg e ac cca bb ef ca cca e e cc accg be ef ca acc e e cca fe bb ef e e bb ef e e bb bb e e bb e ``` <!-- end of image --> Let's zoom in on area A to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#fa5458ff b,#463ef7ff c,#fe0808ff d,#817ffcff e,#0605feff f,#bdbdffff g,#ffb1b1ff ``` ```image eef deb eef dee eed g fee ca bed cccg fee gccca bed accag fee gcccg bed acca feef gcccg beb acca eef gcccg deb acca eef gccbeb gaeea deeccg eedccca fee acccg bed gccca fee acccg bed gccca fee acccg bed gccca feef acca beb gcc eef a deb eef deb eef dee eed ``` <!-- end of image --> There's no doubt about it - this is an intersection in area A. Right then, let's explore the next spot. I'm determined to find out if an intersection exists in area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe5e5eff b,#4842f9ff c,#fd0708ff d,#8d8dffff e,#0605feff f,#cccbfeff g,#ffbabaff ``` ```image feef beb feef deb eed dee eed dee beb feef beb gac feef gaccc deb gccccag eed acccca dee gaccccg eed gacccag deeccccag aeebca gaccceef gacccagbeb gccccag feef acccca beb gacccca eed accccg dee ccag eed ag dee bed feef beb feef beb feef deb eed dee ``` <!-- end of image --> Oh my, look at that! It's an intersection in area B! There are precisely two intersections present in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fe5556ff b,#3636feff c,#ff0707ff d,#7877feff e,#0303ffff f,#bfbfffff g,#ffaeaeff ``` ```image f de edb fe e e fe fe ef ef fe e ef ef e e bd bd e e db bd e e de db e e fe db ef e e fe bd e e fe bb ef e e db ef e e fe bd ef e e bd ed e e db bd e e db db e e fe fe e ef fe fe ef ef e e ef bd e e bd db e e bd fe e ef db fe e ef db e cc e bd acg fe e cc e db acg fe e ca ef de ac e e gcc caef fe acc ae ef aca bdca e cca e cc bdgccg bd gca aec e cc acabb db gcg cca e e cc gccg db db gcg gcc e e cc acc fe fe acg cca ef e cc gccg e fe acg gccg ed ef ca acc e e ac cca bd ef ca ccg e e ac gccg db bd gca acc e e cca fe bd ef e fe db ef e e db bd e e db e ``` <!-- end of image -->

I have a feeling there might be some intersections in this image. I've spotted 1 narrow regions that might be worth examining further. Let's call them area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0707ff b,#0708feff c,#f49691ff d,#5356f8ff e,#f84f4cff f,#aed5aeff g,#abadfbff ``` ```image g a gb ee b a bg ec bd a db ac gb a b a bg a bd a gb ca b a b ce bg a db ee gb a b ac bg a bd ac db a gb a b ca bg a bd ca db a gb ee b a bg ec bd a gb ac b a b a bg a db a gb ca b a bg ce bd a db ee gb a b ac bg a bd ac db a gb a b fcafffffffffffff bg ffafffffffffffff bd ffeaffffffffffff gb fffaffffffffffff b fffeefffffffffff b ffffafffffffffff bg ffffaeffffffffff db fffffaffffffffff gb fffffacfffffffff b ffffffafffffffffgbg ffffffaffffffdbbbg ffffffcafgbbbdff ffffffdbbbgfffff ca ffdbbbdcafffffff caa gbbbdfffffafffffff caa dbbbgffffffffeeffffff eae gbbbd fffffffffaffffff eae gdbbdg fffffffffeefffff eae dbbbg ffffffffffafffff eae bbbd ffffffffffacffff aac g fffffffffffaffff aac fffffffffffacfff aac ffffffffffffafff aac ffffffffffffafff aac ffffffffffffcaff caa fffffffffffffaff caa ce caa a caa ee caa a eae ac eae a eae aceae ac ``` <!-- end of image --> Could this be where the intersection is hiding, in area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0506ff b,#0907fcff c,#fe8a8aff d,#645ef8ff e,#fe4646ff f,#ffcacaff g,#afafffff ``` ```image faaf eac faa eac caa aac cae aaf cae faaf eae faaf eac faa eac caa aac caa aaf cae aaf eae g faaf gdbbb eae gdbbbbbb faa gdbbbbbbdg eaddbbbbbddg gdbbbbbbdg gdbbbbbbbd gddbbbbbddgcaa gdbbbbbbdg aac bbbbbdg cae bbdg aaf cae faaf eae faaf eac faa eac caa aac cae aaf cae aaf eae faaf eae faa eac caa aac ``` <!-- end of image --> Aha! I've found an intersection inside area A! I've found a single intersection point in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0505ff b,#0808ffff c,#fe8080ff d,#6363ffff e,#ff4040ff f,#ffc5c5ff g,#b9b9ffff ``` ```image d a gb ce b a bg ec bd a db ac gb a b af bg fa bd a db fa b a b ce bd a db ec gb a b ec bg a bd af db fa gb af b fa bg a bd ce db a gb ce b a bg ec bd a db af b a b af bd fa db a gb ca b a bg ce bd a db ec gb a b ac bg a bd af db fa gb a b fa bg a bd ce db a b ee b a bd ec db a gb af b a gbg af dbbbg fa gbbbd dbbbg ca dbbbdca caa gbbbdg a cae dbbbg ce cae gbbbd a eae gdbbdg ec eae dbbbg a eac bbbd ac aac g a aac af aac fa faaf a faaf fa faaf a faaf ce caa a caa ee cae a cae ec eae a eae afeac fac ``` <!-- end of image -->

I'm curious to see if this image contains any intersection points. There are 2 regions I'd like to highlight in the image. <!-- image --> ```palette Key,Color ,#fefefeff a,#403cf9ff b,#fd0606ff c,#ea665fff d,#0606feff e,#97c697ff f,#b2d6b1ff g,#818aedff ``` ```image dd daga da d da gd da d da d ad dg ad d ad ag ad d ad aa ad d ad gd ad d ad fd ad dg gd d gd dg gd d efffffffffffffgde aa effffffffffffgdfe d bbefffffffffffgdffe gd fbbfffffffffgdfffe d ecbbffffffgdffffe gd effcbcfffgdfffffe d effffcbcgdffffffe d effffffcdcffffffe dg efffffgdfbbcffffe d effffedffffbbeffe aa efffedffffffebbfe d effedfffffffffebb ga efedffffffffffffcbb d efdfffffffffffffe cbc gd edffffffffffffffe cbc d deeeeeeeeeeeeeeef cbc d d bbc dg d bbf d bb ag bb d fbb ga cbbc feeeeedeeeeeeeeeeeeeef cbbbf efffffgdfffffffffffffe fbbbc effffffdfffffffffffffe cbbc effffffedffffffffffffe cbbbefffffffdgfffffffffffe fbbbcfffffdfffffffffffe effcbbcffdaffffffffffe efffffcbbbdffffffffffe effffffffcaabcfffffffe effffffffffdfcbbcffffe effffffffffgdfffcbbbee efffffffffffdffffffcbbbc efffffffffffgdfffffffe cbbc effffffffffffdgffffffe cb efffffffffffffdffffffe efffffffffffffdgfffffe feeeeeeeeeeeeeedeeeeef aa d gd d gd d d dg d aa d ga d gd d d dg d ag d ga d ``` <!-- end of image --> This close-up might reveal an intersection in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#302af8ff b,#fe0606ff c,#feaaaaff d,#0303feff e,#c2c2ffff f,#f84e55ff g,#7878ffff ``` ```image g gd gdd gddg gddg gddg gddg bc gddg bbbc eddg cbbbbc eddg cbbbfc eddg cbbbfc eddg fbbbf eddg fbbbf eddg fbbbf eddg cfbbfddg cfddac eddabbbc edda cbbbbc edda cbbbfc edda fbbbfc edda fbbbf edda fbbbf edda cfbbb edda cfb edda c eada eada eada ada ada ada ``` <!-- end of image --> Incredible, there's actually an intersection in area A! Now, let's dive into another area. My goal is to determine if there's an intersection inside area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#4338f3ff b,#fe0506ff c,#ff9090ff d,#0606feff e,#f1cfddff f,#f8464cff g,#9191feff ``` ```image gdd ddg gdd adg gdde ada edde ada e ddg bbfc gda bbbbbfce ddg ecfbbbbbce gdd ecfbbbbbfc adg cfbbbbbfcegdd ecfbbbbbada ecfbbbddfc cfadabbfce eddfbbbbbce gdaecfbbbbbfc ddg cfbbbbbfce gdd ecfbbbbbce ddg ecfbbbbb gdd cfbb ada e edde ada eddg gda ddg gdd ddg ``` <!-- end of image --> Amazing! This area was hiding an intersection all along! There's for sure two intersections on the image you sent me.

<!-- image --> ```palette Key,Color ,#fefefeff a,#3531fbff b,#fe0606ff c,#fe9b9bff d,#0404ffff e,#c5c5ffff f,#fb4f53ff g,#7a7affff ``` ```image e dd daga da d da gd da de aa ed aa de aa d ad ag ad d ad ga ad d ad gd ad d gd ed gd de gd d gd ag gd d gd aa gd d bb gd ga cbb gd d cbf ed ed fbf ed de fbfed d fdc dg ed bbc d ed bb ag ed bb d ed cbb ga ed cbb d ed cbf ed d fbf de de fbc ed de bbc de de bbc d bb ag bb d cbb ga cbbf d cbbbc gd cbbbc de fbbf ed cbbbc de cbbbc d fbbf ag cbbbd caabc d fbbf gd cbbbc d cbbbc ed fbbf de cb d ag d aa d ga d ed de d dg d ag d ga d ed de ed de d ag d ga d ``` <!-- end of image -->

This image seems promising for intersection detection. My next step is to analyze the details within each area. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0706ff b,#0908fdff c,#f8a4a1ff d,#636aefff e,#b0d6b2ff f,#98c699ff g,#f3514bff ``` ```image c a ac ca a gg a ac ca a gg a ac ca a ga a ac a a ca a ag a ac ca a gg a ac ca a gg a ac ca eeeeeeeeeeeeeeeef a eeeeeeeeeeeeeeeef gg eeeeeeeeeeeeeeeef a eeeeeeeeeeeeeeeef edd ac eeeeeeeeeeeeeeeef ddbbbbbddbb ca eeeeeeeeeeeeeeeef edbbbbbbdd bb a eeeeeeeeeeeeeeeddbbbbbbde db ga eeeageefddbbbbbbd db ffffffffffffaffe eeebbbbbddfeeeeef dbfeeeeeeeeeeageef eeeeegaeeeeeeeeef ebeeeeeeeeefaeeef eeeeeegaeeeeeeeef fbfeeeeeeeafeeef eeeeeeecafeeeeeef eebdeeeeegaeeeef eeeeeeeeeaceeeeef eeebdeeeeaeeeeef eeeeeeeeeeageeeef eeeebdeeageeeeef eeeeeeeeeeeaaeeef eeeeebbeaeeeeeef eeeeeeeeeeeeaaeef eeeeeebbfeeeeeef eeeeeeeeeeeeegaef eeeeeegbbeeeeeef ffffffffffffffgaf eeeeeeaedbeeeeef ac eeeeeggeedbeeeef ac eeeeeaeeeedbeeef ag eeeeaceeeeefbeef aa eeecaeeeeeeeebff ga eeeaeeeeeeeeeebd ca eeggeeeeeeeeeeebd ca ffaeeeeeeeeeeeefbd ac ac bb ag ca bb ag a db aa gg db ga a db ca ac eb ac ca b ac a be ag ga bd aa a bd ga ac bd ca a bb caa bb g db db db eb b b ``` <!-- end of image --> Eureka! Let's inspect this close up of area A <!-- image --> ```palette Key,Color ,#fefefeff a,#fd0708ff b,#0505ffff c,#ff5959ff d,#5251fdff e,#aeaafbff f,#fdaeb0ff g,#89097eff ``` ```image eee cc eedddbbbbb faac eeddbbbbbbbbbbbdd faggddbbbbbbbbbbbddeee ebbbbbbbbbdddee bbdggge caaf caac caac faac faaa faaaf aaaf caaf caac faac faac faaaf aaaf caaf caac caac ``` <!-- end of image --> Wow! I can see an intersection so clearly in area A! Hmm, interesting. Let's check out another area. Let's zoom in on area B to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd0607ff b,#0a08fdff c,#fe8182ff d,#5858ffff e,#bab9ffff f,#ffc5c5ff g,#fd4446ff ``` ```image faaf gag d faaf bd aac bbd caa ebbb faaf ebbbe gag bbbe faaf bbbe aac dbbe caa dbbe faaf dbbd gag dbbd faaf ebbd gac ebbd caa ebbd aac ebbbgag ebbbaf bbbe cabbbe aacdbbe cag dbbe faaf dbbd gag dbbd caa ebbd aac ebbd caa ebbd faaf ebbb gag ebbbe faaf bbbe aac dbbe caa dbb faaf db gag d faaf aac ``` <!-- end of image --> Area B contains an intersection. There's for sure two intersections on the image you sent me.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0404ff b,#0706fdff c,#ff8181ff d,#5a5affff e,#b3b3ffff f,#ffc2c2ff g,#ff4040ff ``` ```image c a af fa a gg a af fa a gg a ac fa a cg a ac fa af ca a gc a af ca a gg a af fa a gg a af fa a gg a edd ac eedbbbbbddbb fa eddbbbbbde bb a edbbbbbbde db cg ag eedbbbbbdde db a bbbbbde eb ac ga eb fa ca be af faf be ca af bd a ac bd gc ag bd a ga bbf ga cbb ca a db faf gg db ac a eb ag af eb aa fa be ga a be ca gg bd faf a bd af af bd ac fa bb ag a db ga gg db ga a eb ca ac eb faf fa eb ac a be ag cg be aa a bd ga ac bd ca fa bb faaf bb g db db eb eb ebe b ``` <!-- end of image -->

This image looks interesting. I wonder if there are any intersections hidden in there? I've spotted 1 narrow regions that might be worth examining further. Let's call them area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0808feff b,#fe0808ff c,#5a5ef7ff d,#ed6c64ff e,#babaffff f,#ffc4c4ff g,#afd6afff ``` ```image ffffff bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb bd fffff fbf fb db bb bb bd bf fbf db db bb ggggggggggggggg bd ggggggggggggggg bd ggggggggggggggg fbf ggggggggggggggg fb ggggggggggggggg db ggggggggggggggg bb ggggggggggggggg bb gggggggggggggggbd ggggggggggggggbd gggggggggggggbg gggggggggggdbgg ggggggggggdbggg gggggggggbbgggg ggggggggbbggggg gggggggbdgggggg ggggggbdggggggg ggggdbggggggggg e gggdbgggggggggg ea gggdggggggggggg a ggggggggggggggg ae gggcggggggggggg ae gggcagggggggggg ac ggggacggggggggg ac gggggaggggggggg aa ggggggagggggggg ca ggggggcaggggggg ca gggggggcagggggg ea ggggggggacggggg ea gggggggggaggggg a ggggggggggagggg ae ggggggggggcaggg ae ca ac ac ac ae aa a ca ea ea ca ea ac a ae a a ae ea ae ca ac ac ac ae ca a ca ea ea ca ea ac a ae a a ae ea ae ca ac ac ac ae ca a ca ea ea ca ea ac a ae ae a ae ea ac ca ac ac aa ae ca aca ea ``` <!-- end of image --> I wonder what we'll find inside area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#0909ffff b,#ff0505ff c,#5050ffff d,#ff7272ff e,#a6a6ffff f,#ffb9b9ff g,#ff3a3aff ``` ```image d gb gbb fbbbf fbbg fbbg dbbd gbbd gbbf fgbbf fbbbf fbbg dbbg dbbd gbbd gbbf fbbbf fbbg fbbg dbbd fbbd df ee eaae caa aac aac eaae eaae caa aac aac eaae eaae caa aac aac eaae eaae caa aac ``` <!-- end of image --> It's a shame, but area A doesn't contain an intersection. Zero, Nada.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0707ffff b,#ff0808ff c,#7575ffff d,#ff6d6dff e,#bfbfffff f,#ffc4c4ff g,#4545ffff ``` ```image ffffff bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb bd fffff fbf fb db bb bb bd bf fbf db db bb bd bd fbf fb db bb bb bd bd fbf db db bb bb bd bf fbf e db ea d a ae c ae ga ac ac ag ae gg a ga ea ca ga ea ac ea ae a a ae ea ae ga ac ac ag ae ga a ga ea ca ga ea ac ea ae a a ae ea ae ga ac ac ag ae ga a ca ea ca ga ea ac a ae a a ae ea ac ga ac ac ag ae ga a ca ea ea ga ea ac a ae ae a ae ea ac ga ag ac ag ae ga aca ea ``` <!-- end of image -->

Here's an image. My task is to find intersections or areas where lines come close together. These zones are intriguing. I bet there's something interesting happening within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0605ff b,#0404feff c,#f19790ff d,#8b93eeff e,#403fefff f,#aed5adff g,#f14640ff ``` ```image dbbe b dbbe ffffffffffffffaf ee dbbd fffffffffffffggf b ebbd fffffffffffffaff bd ebbd ffffffffffffacff b dbbe ffffffffffffafff bd dbbe fffffffffffaffff b dbbd ffffffffffcaffff b ebbd ffffffffffafffff db ebbdfffffffffggfffff b bbbfffffffaffffff de fdbbefffagffffff b ffffebbeafffffff ee fffffffebbdfffff b ffffffcaffebbdff ed ffffffafffffdbbf b fffffgafffffffff bd fffffaffffffffff b ffffggffffffffff b ffffafffffffffff db fffacfffffffffff b fffaffffffffffff db ffafffffffffffff b fcafffffffffffff ee faffffffffffffff b ggffffffffffffff ed a b gc bd a b ac b ca db a b ca db a b gg ee a c ffffffffffffffbf ac ggfffffffffffffeef a agffffffffffffbff a acffffffffffbdff ca faffffffffffbfff a ffaffffffffbdfff cg ffcaffffffdbffff a fffgafffffbfffff gc ffffgafffdbfffff a fffffagffbffffff ac ffffffaceeffffff a fffffffabfffffff a fffffffeefffffff ca fffffffbcaffffff a ffffffbdfgafffff gg ffffffbfffgaffff a fffffbdffffagfff ac ffffdbffffffacff a ffffbffffffffaff ac fffdbfffffffffaf ca fffbffffffffffca a ffeefffffffffffga cg ffbfffffffffffffga a feefffffffffffff ag gg fbffffffffffffff ac a bd a ac b a a bd a a b ca ca b ga a ag gg ac a ac ac a a a ac ca ca ga a ag ca ac a ac gg a a aac ca ``` <!-- end of image --> Let's see if area A yields any clues. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0707ff b,#0404feff c,#fdafb0ff d,#8383ffff e,#403af8ff f,#c6c5feff g,#fd5658ff ``` ```image fbbf ebe fbbf ebd fbb g ebd ac dbb aac bbd gaac dbe gaa bbf aaa dbe aag fbbf caag ebe caac fbbf caac ebd gaac fbb gaa ebd gaa dbb aag bbd caag dbe caag bbf caac dbe gaacbbf gaebe gbbf ebeg fbbaag ebdcaag dbb caac bbd gaac dbb gaac bbd gaa dbe aag fbbf aag ebe caag fbbf caac ebe gaac fbbf gaac ebd gaa dbb aag bbd aag dbb caa bbd ca dbe c fbbf ebe fbbf ebe fbbf ``` <!-- end of image --> Amazing! This area was hiding an intersection all along! Okay, let's proceed to the next area. This close-up might reveal an intersection in area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0606ff b,#0706feff c,#ff8f8fff d,#9c9bfdff e,#524df9ff f,#f5d3ddff g,#fc4649ff ``` ```image fac gag faaf gag caaf aac caa faac gag faaf gag faaf gac caa aac caa faac gag bef faaf bbbbdf gag debbbbed caaf debbbbed aac debbbbed caa fdbbbbbegac febbbbbdf debbbbed gagdebbbbed faaf debbbbed gac fdbbbbbed caa febbbb aac ded caa faac gag faaf gag caaf aac caa aac cag faaf gag faaf gag caaf aac caa faac ``` <!-- end of image --> The evidence is clear: this is an intersection in area B. I can confirm there's two intersections in there.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fe0606ff b,#0404ffff c,#ff9191ff d,#9494ffff e,#4640f8ff f,#edd2e4ff g,#ff4545ff ``` ```image f dbbef b dbbe a ee dbbd gg b ebbd a bd febbd ac b fbbef fa bd dbbe af fb dbbd ca bf ebbd a db febbd gg b fbbbf a de dbbe ac b dbbea ee ebbd b fa ebbd ed a fbb b ca bd a fb gg bf a db ac b fa db af b ca ee a b gg ed a b gc bd a fb ac bf fa db af b ca db a b gg ee a f b ac gg ee fa ag b af ac bd ca af fb a fa bf cg ca fb a ca bf gc gg db a ag b ac acee fa ab af ee ca bfa a bd ca gg b ga a bd ag ac fb ac fa bf af af db a ca b fa a de ca cg b ga a ee ag gg b ac a bd af ac b a fa bd fa af fb ca ca bf ga a ag gg ac a af ac a a fa af ca fa ga a ag ca ac a af gg af a faac ca ``` <!-- end of image -->

I have a feeling there might be some intersections in this image. There are 1 areas where the lines seem to converge. We should take a closer look at area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0708fdff b,#fe0202ff c,#b0b0ffff d,#f8a19dff e,#5a5df3ff f,#f7403cff g,#acd4adff ``` ```image c caae a eaae ca eaac a caae a caae ac eaac a caaa ee caae a eaac bf ee aaa fb a caae fb ca eaac db a aaa bd ca caae bd a eaac bf a aaac fb ac ca fb ggggggggggggaggg db gggggggggggaeggg bd gggggggggggagggg bd ggggggggggeegggg bfggggggggggaggggg bbggggggggeaggggg fbgggggggagggggg gdbggggggagggggg gggbdgggaggggggg ggggbfggaggggggg gggggbfaeggggggg ggggggbagggggggg ggggggaebggggggg ggggggagdbgggggg gggggeegggbdgggg gggggagggggbfggg ggggeaggggggbfgg ggggaggggggggbbg ggggagggggggggfb gggagggggggggggfb gggaggggggggggggdbd ggaegggggggggggg bd ggaggggggggggggg bfd gaeggggggggggggg dfbbbfd a dfbbbfd ee dfbbbfd a dfbbbfd ca dfbbbfd a dfbbbfd ca dfbbbfd ac dfbbbfd a dfbb ac a ee a ee a ca a ca ac a ac a ee a ee a ca a ca ac a ac a ee a ee a ca a ``` <!-- end of image --> Let's zoom in on area A to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#0706feff b,#fe0808ff c,#9491fcff d,#ffababff e,#504cfbff f,#fa4d52ff g,#ccccfeff ``` ```image caa aac caa eac gaa eae gaag eae aag f cae bb aac bbbd caa fbbd aac fbbd caa fbbf eac dbbf gaa dbbb eae dbbbd gaag fbbd eae fbbd aag fbbf cae dbbf aac dbbfaa dbaac caabd eaebbd gaagfbbf eae dbbf gaag dbbb eae dbbbd aag fbbd cae fbbd aac fbbf caa dbbf aac dbbb gaa dbbb eac fb gaag f eae gaag eae aag cae aac caa aac gaa ``` <!-- end of image --> As I suspected, there's an intersection within area A. It was tricky, but I finally found one single intersection in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0606ffff b,#fe0303ff c,#9c9cffff d,#ff9f9fff e,#5654fcff f,#ff3c3cff g,#dcd4f6ff ``` ```image g caae a caac ga eaac ag gaae ga caae ac eaac a gaaag ec caae a eaac bf ee gaaag fb a caae fb ca eaac db a gaaag gbd ga caae bd ag eaac bf ga geaag fb ac ca fb a db ec gbd a bd ee bf a bb ca fb a db ga gbd ag bd ga bfac ba eeb a db ee gbd a bd ca bf a bb ga fb ag db a gbg ac bd a bfd ee dfbbbfd a dfbbbfd ee dfbbbfd a dfbbbfd ca dfbbbfd a dfbbbfd ga dfbbbfd ag dfbbbfd a dfbb ac a ee a ee a ca a ga ag a ac a ee a ee a ca a ga ag a ac a ee a ee a ca ag ``` <!-- end of image -->

I'm approaching this image with caution. Intersections might be tricky to spot. The image has some tight areas where segments are too close. I should investigate those closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#ef4740ff b,#0b0cfdff c,#666eedff d,#e89287ff e,#fd0605ff f,#99c59aff g,#b1d7b1ff ``` ```image d e ed de e aa e ed de e aa e ed e e de e ed e e de e aa e ed de e aa e ed de e aa e b ed b e b e bg da bc e bc ed bc e bc e bb de bb e cb ad cb ed e cb ee e cb ae de gb de e b ed aa b ea e b eegggggggggggggggggggggggggggggggggggggggged b faeggggggggggggggggggggggggggggggggggggggdef bg fgfedggggggggggggggggggggggggggggggggggggegf bc fgggeaggggggggggggggggggggggggggggggggggaagf bc fggggeegggggggggggggggggggggggggggggggggeggf bc fgggggaegggggggggggggggggggggggggggggggedggf bc fggggggdedggggggggggggggggggggggggggggdegggf bb fggggggggeagggggggggggggggggggggggggggeggggf bb bb fgggggggggeegggggggggggggggggggggggggaaggggf cb gbb fggggggggggaeggggggggggggggggggggggggegggggf cb cbc fgggggggggggdefgggggggggggggggggggggedgggggf cb bbcgggggggggggggeagggggggggggggggggggfeggggggfcb bbgggggggggggggeeggggggggggggggggggefggggggcb ffbbggggggggggggaeggggggggggggggggaeggggggfb fggcbcgggggggggggdefggggggggggggggeggggggfbf fggggbbcgggggggggggedggggggggggggeaggggggbgf fggggggbbfggggggggggeaggggggggggfeggggggbfgf fgggggggfbbggggggggggeegggggggggefgggggbfggf fgggggggggcbbgggggggggaegggggggdegggggbcgggf fgggggggggggcbcggggggggfedgggggegggggbcggggf fgggggggggggggbbfggggggggeagggaaggggbcgggggf fggggggggggggggfbbggggggggeeggeggggbcggggggf fggggggggggggggggcbbgggggggaeedgggbbgggggggf gffffffffffffffffffcbcffffffdefffbbffffffffg bbg bb bb cb gbb cb cbccb bb ``` <!-- end of image --> This close-up of area A is like examining a piece of evidence. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff3c3cff b,#0808ffff c,#5b5bffff d,#ff7f7fff e,#fe0505ff f,#ffc4c4ff g,#b7b7ffff ``` ```image ea e eeef de faeed fee aeed aea deea feef feeef eed faeef dee aeed feef deea aea feeaf feef feeef aed aeed dee deea eed deeaf aea feeef feef aeed aed deed dee deea eed feeef dea faeed feef aeed aea deea dee feeef eed faeef dea bg aeed feef bbcg deea aea cbbbc feeaf feef cbbbc feeef eed g gcbbbg aeed dea gb gbbbcg deea feef gbb cbbbc deeaf aea gbbc cbbbc feeef feef bbb gcbbbg aeed aed bbb gbbbbg aeed dee bbb gbbbc deea feef cbbg cbbbc feeef aea cbbg gcbbbg faeed feef cbbg gbbbbg aeed aed cbbg gbbbcg deea dee cbbg cbbbc feeef eed cbbg gcbbbg faeef dea gbbg gbbbbg aeed feef gbbc gbbbcg deea aed gbbc cbbbc deeaf dee gbbc cbbbc feeef eed gbbc gcbbbg aeed dea gbbc gbbbcg deeaeef gbbc cbbbc deeea bbc ``` <!-- end of image --> This isn't an intersection in area A, but I'm not discouraged. After a thorough analysis, I conclude that there are no intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff3838ff b,#0909ffff c,#5e5effff d,#ff7f7fff e,#ff0404ff f,#ffc6c6ff g,#b5b5ffff ``` ```image d e ef fe e aa e ef fe e da e ed fe ef da e ad fe ef de e ad e ef de e aa e ef fe e aa e b ed bg fe bg e bg da bg e bc ed bc fe bc ef bb de cb e cb ad cb ed e cb ea ef gb ae de gb def e gb ed aa b ea e b ae ef bg de fe bg fef e bg ea aa bc ee e bc de ed bc fef fe bb ed e bb bb ee da cb gbb ae e cb cbc fef ed cb bbg ed fe gb bb ea ef gb gbb ae da gb cbc def e b cbg fed ad b bb ea fe bg gbb ae ef bg gbc de de bg cbg fef e bg bbg ea ad bc bb ee e bc gbc deef bc cbc fe bb bbg cb bb cb gbb cb cbccb bb ``` <!-- end of image -->

This image looks interesting. I wonder if there are any intersections hidden in there? My next step is to analyze the details within each area. <!-- image --> ```palette Key,Color ,#fefefeff a,#6d76ebff b,#fe0303ff c,#0a0bfcff d,#e6877bff e,#eef0efff f,#b0d6b0ff g,#f43933ff ``` ```image d effffffffffffffffffffffffffffffffffffffdbe effffffffffffffffffffffffffffffffffffffbfe efffffffffffffffffffffffffffffffffffffbffe effffffffffffffffffffffffffffffffffffbdffe efffffffffffffffffffffffffffffffffffggfffe effffffffffffffffffffffffffffffffffdbffffe effffffffffffffffffffffffffffffffffbffffae efffffffffffffffffffffffffffffffffbfffffce effffffffffffffffffffffffffffffffbdffffcae efffffffffffffffffffffffffffffffbgffffacfe effffffffffffffffffffffffffffffgbfffffcffe efffffffffffffffffffffffffffffdbfffffccffe efffffffffffffffffffffffffffffbffffffcfffe effffffffffffffffffffffffffffbffffffcafffe efffffffffffffffffffffffffffbdfffffacffffe bd effffffffffffffffffffffffffggffffffcfffffe bd efffffffffffffffffffffffffdbffffffcafffffe bd efffffffffffffffffffffffffbfffffffcffffffe be effffffffffffffffffffffffbfffffffcaffffffe be efffffffffffffffffffffffbdffffffacfffffffe ebe effffffffffffffffffffffbgfffffffcffffffffe ebe efffffffffffffffffffffgbfffffffcaffffffffe eb effffffffffffffffffffdbffffffffcfffffffffe eb effffffffffffffffffffbffffffffcffffffffffe db efffffffffffffffffffbffffffffacffffffffffe db effffffffffffffffffbdffffffffcfffffffffffe db efffffffffffffffffggffffffffcafffffffffffe gb effffffffffffffffdbfffffffffcffffffffffffe gb effffffffffffffffbfffffffffcfffffffffffffe gg efffffffffffffffbfffffffffacfffffffffffffe gg effffffffffffffbdfffffffffcffffffffffffffe bg efffffffffffffbgfffffffffcaffffffffffffffe bg effffffffffffgbffffffffffcfffffffffffffffe bd efffffffffffdbffffffffffcffffffffffffffffe bd efffffffffffbffffffffffacffffffffffffffffe bd effffffffffbfffffffffffcfffffffffffffffffe be efffffffffbdffffffffffcafffffffffffffffffe be effffffffggffffffffffacffffffffffffffffffe ebe efffffffdbfffffffffffcfffffffffffffffffffe ebe efffffffbfffffffffffccfffffffffffffffffffe eb effffffbffffffffffffcffffffffffffffffffffe eb efffffbdfffffffffffcaffffffffffffffffffffe db effffbgfffffffffffacfffffffffffffffffffffe db efffgbffffffffffffcffffffffffffffffffffffe db effdbffffffffffffcaffffffffffffffffffffffe gb effbfffffffffffffcfffffffffffffffffffffffe gb efbfffffffffffffcffffffffffffffffffffffffe gb ebdffffffffffffacffffffffffffffffffffffffe gg ggfffffffffffffcfffffffffffffffffffffffffe bg dbeeeeeeeeeeeeecaeeeeeeeeeeeeeeeeeeeeeeeee bg eb ec bd be ce bbd ac d c ca ec ce ac c ca ec ce aa c e cf cca ac acca c acce ca eccce ec acca ce accf ac eccce c acca ca acca ec eccce ce acca ac acca c eccceca fcc ``` <!-- end of image --> I'm going to scrutinize area A for any signs of an intersection. <!-- image --> ```palette Key,Color ,#fefefeff a,#5554ffff b,#ff0505ff c,#0707ffff d,#ff8383ff e,#ffc5c5ff f,#ababffff g,#ff3d3dff ``` ```image d eb ebb gbg gbb dbbe dbbe ebbd bbg gbg gbbe dbbe ebbd ebbd gbg f gbb c dbbe fc dbbe cc ebbd aca bbg fccf gbg cca gbbe fcc dbbe ccf ebbd aca ebbd fcc gbg cca gbb acc dbbe ccf dbbe aca ebbd fcc bbg ccf gbg acc gbbe fccf dbbe aca ebbd fcc ebbd ccf gbg acc gbb fccf dbbe aca dbbe fcc ebbd ccf bbg aca gbg fccf gbbe cca dbbe fcc ebbd ccf ebbd aca gbg fccf gbb cca dbbe acc dbbe ccf ebbd aca bbg fcc gbg cca gbbe acc dbbe fccf ebbd aca ebbd fcc gbg ccf gbb acc dbbe fccf dbbe aca ebbd fcc bbg ccf gbg aca gbbe fccf dbbe cca ebbd fcc ebbd ccf gbg aca gbb fccf dbbe cca dbbe fcc ebbd ccf bbg aca gbg fcc gbbe cca dbbe acc ebbd ccf ebbd aca gbg fcc gbb ccf dbbe acc dbbe fccf ebbd aca bbg fcc gbg ccf gbbe acc dbbe fccf ebbd aca ebbd fcc gbg ccf gbb aca dbbe fccf dbbe cca ebbd fcc bbg ccf bg aca ``` <!-- end of image --> I'll move on to the next area. The intersection must be somewhere. I did not find anything, there's no intersections

<!-- image --> ```palette Key,Color ,#fefefeff a,#4848ffff b,#ff0505ff c,#0505ffff d,#ff9393ff e,#e6d2eaff f,#9494ffff g,#ff4141ff ``` ```image d db b be bd gg db eb e b c bd cf bg ec gb c db aa b c be cf bd fc bd gg c bd db aa bd eb c be b ce be bd fc be bg c eb gb aa eb db ec eb b ce db be fc db bd c db gg cf gb db ec gb eb ce gb b aa bg bd c bg bg cf bg gb ec bd db c bd b aa bd be c be bd cf be gg fc be db c eb eb aa eb b c eb bd cf db bg fc db gb c db db aa gb b ec gb be ce gb bd fc bg gg c bg db cf bg eb ec bd b ce bbd fc d c cf ec ce aa c cf ec c aa c e cf cca fc fccf c acce aa ecca c fccf ce accf fc eccae c fcca aa accf ec eccce ce fcca fc accf c eaccecf fcc ``` <!-- end of image -->

Here's an image. My task is to find intersections or areas where lines come close together. The image has some tight areas where segments are too close. I should investigate those closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#fb5250ff b,#0707feff c,#fe0808ff d,#5a5afeff e,#f6a4a0ff f,#b1b1ffff g,#aed5adff ``` ```image f bb dbf fbd bd bb bb dbf fbd fbd dbf bb bb dbf dbf fbd bb bb fbd dbf bb fbd fbd bb dbf dbf bb fbd dbf bb bb dbf fbd fbb bb bb fbd dbf dbf fbb bb bb dbf dbd bb bb fbd bb bbdbd ggggggggbggggggg gggggggggggggggg gggggggggggggggg gggggggggggggggg gggggggggggggggg gggggggggggggggg gggggggggggggggg gggggggggggggggg gggggggggggggggg gggggggggggggggg cccccccccccaaaaaaaaaeeeeeeeeeegggggggggggggg eeeeeeeeeeeaaaaaaaaacccccccccggggggg gggggggggceggggg ggggggggggcegggg gggggggggggceggg ggggggggggggcagg gggggggggggggcag ggggggggggggggca gggggggggggggggca ggggggggggggggggca gggggggggggggggg cc gggggggggggggggg cc gggggggggggggggg ac gggggggggggggggg ac ac ac ec ec ec ec c c ce ce ce ce ca ca ca ca cc cc ac ac ac ac ec ec ec ec c ce c ``` <!-- end of image --> Let's zoom in on area A to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff3030ff b,#0505ffff c,#ff0202ff d,#4747ffff e,#ffcbcbff f,#c1c1ffff g,#ff8787ff ``` ```image dbbbbdf fdbf eeeeeeeeeee ccccccccccccccccccae aaaaaacccccccccccccae eacce acce acce acce acce accg gccg gccg gccg gccg gcc gc g ``` <!-- end of image --> After careful examination, I've determined that there's no intersection in area A. Zero, Nada.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff4545ff b,#0808ffff c,#ff0707ff d,#5c5cffff e,#ffc9c9ff f,#b2b2ffff g,#ff8989ff ``` ```image f bb dbf fbd bd bb bb dbf fbd fbd dbf bb bb dbf dbf fbd bb bb fbd dbf bb fbd fbd bb dbf dbf bb fbb dbf bb bb dbf fbd fbb bb bb fbd dbf dbf fbb bb bb dbf dbd bb bb fbd bb bbdbd fb ccccccccccaaaaaaaaggggggggeeeeeee eeeeeeeggggggggaaaaaaaacccccccce ce ce cg cg cg ca ca ca cc cc ac ac ac gc gc gc ec ec ece ece ce ce cg cg cg ca ca ca cc ac ac ac ac gc gc gc ec ec ece ce c ``` <!-- end of image -->

I'm optimistic that I'll find some intersections in this image. I'd describe these as 'hotspots' for potential intersections. <!-- image --> ```palette Key,Color ,#fefefeff a,#f45450ff b,#0707fdff c,#afd6afff d,#989df4ff e,#f6a9a4ff f,#5157f2ff g,#fe0706ff ``` ```image d fbbbbbfd dfbbbbbfd dfbbbbbfd dfbbbbfd dfbbbbbfd dfbbbf fbb dbbd bbf dbbd bbf fbb cccccccccccccccccccccccc dbbd cccccccccccccccccccccccc bbbccccccccccccccccccccccc fbbdcccccccccccccccccccc cccbbfcccccccccccccccccc cccccfbbcccccccccccccccc cccccccdbbfccccccccccccc ccccccccccbbbccccccccccc ccccccccccccfbbdcccccccc cccccccccccccccbbfcccccc cccccccccccccccccfbbcccc cccccccccccccccccccdbbfc ccccccccccccccccccccccbb cccccccccccccccccccccccc cccccccccccccccccccccagg cccccccccccccccccegggacc ccccccccccccccagggeccccc ccccccccccegggaccccccccc cccccccagggecccccccccccc ccccgggacccccccccccccccc agggaccccccccccccccccccc aggaccccccccccccccccccccccc eggge cccccccccccccccccccccccc aggae cccccccccccccccccccccccc eggga cccccccccccccccccccccccc aggge cccccccccccccccccccccccc agga cccccccccccccccccccccccc ga cccccccccccccccccccccccc ga cccccccccccccccccccccccc ag cccccccccccccccccccccccc ag cccccccccccccccccccccccc eg cccccccccccccccccccccccc g cccccccccccccccccccccccc g cccccccccccccccccccccccc ge cccccccccccccccccccccccc ge cccccccccccccccccccccccc ga ag ag eg g g ge ge ga ag ag eg eg g ge ge ga ga ag eg eg g g ge ga ga ag eg eg g g ge ``` <!-- end of image --> I'm determined to find out if an intersection exists in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff5555ff b,#0606ffff c,#c7c7ffff d,#8888ffff e,#ffa8a8ff f,#4646ffff g,#fe0505ff ``` ```image fd bbbdc dbbbbfc cfbbbbd cdbbbbfc dfbbbfd cfbbbbdc dbbbbfc cfbbbbd cdbbbbfc dfbbbfd cfbbbbdc dbbbbfc cfbbbbd cdbbbbfc dfbbbfd cfbbbbdc dbbbbfc cfbbbbd cdbbbb dfb c ea eaggg eaaggggga eagggggaee eeagggggae eaggggggae eagggggae eaggggggae eagggggae eaagggggae eagggggaee eeagggggae eagggggaae eagggggae ggggae ae ``` <!-- end of image --> Area A doesn't meet the criteria for an intersection. After a thorough analysis, I conclude that there are no intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff3333ff b,#0504ffff c,#ff7272ff d,#a0a0ffff e,#ffbcbcff f,#4e4effff g,#ff0303ff ``` ```image d fbbbbbfd dfbbbbbfd dfbbbbbfd dfbbbbfdd dfbbbbbfd dfbbbf fbb dbbd bbf dbbd bbf fbb dbbd fbf dbbd bbf fbb dbbd fbf dbbd bbf fbb dbbd fb agg egggc cggae eaggc cggge eaggc cggge aggae egggc cggae eaggc cggae aggc gc ga aa cg eg eg g ge gc ga aa cg eg eg g ge gc gc aa cg eg eg g ge ge gc aa cg cg eg g ge ge gc aa ag cg eg g ge ge ``` <!-- end of image -->

This image looks interesting. I wonder if there are any intersections hidden in there? I need to zoom in on these areas to get a better look. <!-- image --> ```palette Key,Color ,#fefefeff a,#5660ebff b,#e66a5eff c,#b1d7b2ff d,#ddbedfff e,#fd0b0aff f,#0909fdff g,#9ecb9fff ``` ```image d ffa afd ff ff dfd dfd fa ff ff dfa dfd af fa ff gffggggggggggggggggggggggggggggggggg afd gcafgccccccccccccccccccccccccccccccg ff gcccfacccccccccccccccccccccccccccccg dfa gccccffccccccccccccccccccccccccccccg ff gcccccafgccccccccccccccccccccccccccg fa gcccccccfacccccccccccccccccccccccccg afd gccccccccffccccccccccccccccccccccccg ff gcccccccccafgccccccccccccccccccccccg dfd gcccccccccccfacccccccccccccccccccccg ff gccccccccccccffccccccccccccccccccccg dfa gcccccccccccccafgccccccccccccccccccg af gcccccccccccccccfacccccccccccccccccg ff gccccccccccccccccffccccccccccccccccg afd gcccccccccccccccccafgccccccccccccccg ff gcccccccccccccccccccfacccccccccccccg dfa gccccccccccccccccccccffccccccccccccg ff gcccccccccccccccccccccafgccccccccccg fa gcccccccccccccccccccccccfacccccccccg fd gccccccccccccccccccccccccffccccccccg gcccccccccccccccccccccccccafgccccccg gcccccccccccccccccccccccccccfacccccg gccccccccccccccccccccccccccccffccccg gcccccccccccccccccccccccccccccafgccg gcccccccccccccccccccccccccccccccfacg gccccccccccccccccccccccccccccccccffg gcccccccccccccccccccccccccccccccccaf gccccccccccccccccccccccccccccccccccg gccccccccccccccccccccccccccccccccccg deeeeeeeeebbbbbbbggcccccccccccccccccccccccccg e ddbbbbbbeeeeeeeeeeeeeeeeeeeeeeeebbbbbb ed gcccccccccccccccccccccccccgggbbbbbbe eb gccccccccccccccccccccccccccccccccccg be gccccccccccccccccccccccccccccccccccg be gccccccccccccccccccccccccccccccccccg de gccccccccccccccccccccccccccccccccccg e gccccccccccccccccccccccccccccccccccg ed gccccccccccccccccccccccccccccccccccg eb gccccccccccccccccccccccccccccccccccg be gccccccccccccccccccccccccccccccccccg de gccccccccccccccccccccccccccccccccccg e gccccccccccccccccccccccccccccccccccg e gccccccccccccccccccccccccccccccccccg ed gccccccccccccccccccccccccccccccccccg eb gccccccccccccccccccccccccccccccccccg be gccccccccccccccccccccccccccccccccccg de gccccccccccccccccccccccccccccccccccg e gccccccccccccccccccccccccccccccccccg ed gccccccccccccccccccccccccccccccccccg eb gccccccccccccccccccccccccccccccccccg eb gccccccccccccccccccccccccccccccccccg be gccccccccccccccccccccccccccccccccccg de gccccccccccccccccccccccccccccccccccg e gccccccccccccccccccccccccccccccccccg ed gccccccccccccccccccccccccccccccccccg eb gccccccccccccccccccccccccccccccccccg ee gccccccccccccccccccccccccccccccccccg be gccccccccccccccccccccccccccccccccccg de gccccccccccccccccccccccccccccccccccg e gccccccccccccccccccccccccccccccccccg ed gggggggggggggggggggggggggggggggggggg eb ee be de e ed eb ee be de e ed ``` <!-- end of image --> I'm now examining the contents of area A in detail. <!-- image --> ```palette Key,Color ,#fefefeff a,#5151ffff b,#ff5555ff c,#ffa1a1ff d,#cacaffff e,#ff0404ff f,#0909ffff g,#9191ffff ``` ```image gfffd dfffg affa gffd dffg ffa gfffd dfffg affa dfffg affa gfffd dfffg affa gfffd dfff afa gffd fffg affa gfffd dfffg affa gfffd dfffg affa gfffd dfffg gffd dffg ffa gfffd dfffg affa gfffd dfffg affa gfffd dfffg affa gfffd dfff afa gffd fffg affa gfffd aff gf d bbbbbbbbccccccccc eeeeeeeeeeeeeeeeeeeeeeeeeeebbbbbbbbbccccccccc cccccccbbbbbbbbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbbbbbbbcccc cccccccccbbbbbbbbeeeeeeeeeeeeeeeeeeeeeeeee cccccccccbbbbb ``` <!-- end of image --> Based on this close-up, I can conclude that there's no intersection in area A. I'm extremely confident. No intersections at all.

<!-- image --> ```palette Key,Color ,#fefefeff a,#4242ffff b,#ff4343ff c,#ff8686ff d,#aeaeffff e,#ff0404ff f,#0505ffff g,#ffc6c6ff ``` ```image d ffa af af ff dfd dfd fa ff af dfa dfd af fa fa af dfd dfd ff fa dfd af af dfd fa fa afd af ff dfd dfd fa ff af dfa dfd af fa fa af dfd dfd ff fa dfd ff af dfd fa fa fd ff dfd fa ff dfd fa ff df geeeeeeebbbbccccggg e ggggccccbbbeeeeeeeeeeeeeeeeeeeebbbbcccc eg gggccccbb eb be ce ge e eg eb be ce ge eg ec eb be ge e eg ec eb be ge e eg ec bb ce ge e eg ec bb ce ge e eg ec bb ce ge e eg ``` <!-- end of image -->

I'm curious to see if this image contains any intersection points. I've spotted 2 narrow regions that might be worth examining further. Let's call them area A,, and B. <!-- image --> ```palette Key,Color ,#fefefeff a,#3c41f6ff b,#ef6361ff c,#0505feff d,#e3cbe6ff e,#aed4adff f,#8489f4ff g,#fc0b0bff ``` ```image d fc cfa aa c c fc af cd c dc cf cf c c cf af dc c cd aa dc c cd fc fc c c dc fc cd c c fa cf c c aa aa c c af fc c c cf dc c cd cf dc dc cf cd c g dc aa dg cd c bg fc fa gb c c gd fc fc g c cd bg fa dc ggeeeeeeeeeeceee cf egbeeeeeeeeaaeee c eegeeeeeeeeceeee af eeegeeeeeeaaeeee c eeebgeeeeeceeeee fa eeeegbeeecfeeeee c eeeeegeeeceeeeee fc eeeeeegecfeeeeee cd eeeeeebgceeeeeee dc eeeeeeecbeeeeeee cf d eeeeeefcgbeeeeee eeeceeeeeeeeeeee gg eeeeeeceegeeeeee eeecaeeeeeeeeeee dgb eeeeefceeegeeeee eeeeceeeeeeeeeee gg eeeeeceeeebgeeee eeeeaaeeeeeeeeeegb eeeefceeeeegbeee eeeeeceeeeeeeeggd eeeeceeeeeeegeee eeeeefceeeeeegbe eeeaaeeeeeeeegee eeeeeeceeeeggeee eeeceeeeeeeeebge eeeeeefceegbeeee eeaaeeeeeeeeeegg eeeeeeecbgeeeeee c gb eeeeeeegceeeeeee af gd eeeeeggecfeeeeee c dg eeeeggeeeceeeeee cf bg eeggeeeeeaaeeeee c gb eggeeeeeeeceeeee cd gd bgeeeeeeeeefceeee dc g ggeeeeeeeeeeeceeee cd dg bgd eeeeeeeeeeefceee dc bg gg eeeeeeeeeeeeceee c gb bgd eeeeeeeeeeeeecee fc gd gg cf c g bgd c fa bg gg aa c gb bgd c gd gg fa g bgd c dg gg fc bg bgd cd gb gg dc gbgd cf g c af c fa c ``` <!-- end of image --> Let's zoom in on area A to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#3c34f6ff b,#fd5a5bff c,#0303feff d,#c0bffeff e,#fdaeb0ff f,#7b7bffff g,#fe0809ff ``` ```image bgg dccd ggb fca ggb dccd egge aca bgge dccd bgg acf ggb dcc egge acf egge dcc bgg acf ggb fcc ggb ccf egge fca bgge ccd bgg fca ggb ccd eggbfca eggccd baca dccb acagb dccegge acf egge dcc bgg acf ggb dcc eggb acf egge fcc bgg ccf bgg fca ggb ccd egge fca egge ccd bgg fca ggb dccd ggb aca egge dccd bgg ``` <!-- end of image --> I observe an intersection inside area A. Let's move forward and inspect another region. My goal is to determine if there's an intersection inside area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#4f4afaff b,#fb3e41ff c,#0706fdff d,#ebd8ecff e,#ff9292ff f,#9493feff g,#fe0404ff ``` ```image fcc ccf fcc ccf fccd aca dccd aca d dccf eg fca dbgg ccf eggge fcc dbggbd ccf eggge fccd dbggbd aca eggge dccd dbggbd aca eggge dccbggbd accge dbgccf egggacc dbggbd ccf eggge fccd dbggbd aca eggge dccd dbggbd aca eggge dccd dbggbd aca ggge dccf gbd fcc e ccf fcc acf fccd aca dccd aca ``` <!-- end of image --> I am surprised, so clear, an intersection has appeared in area B. The final answer is: two intersections found.

<!-- image --> ```palette Key,Color ,#fefefeff a,#4141ffff b,#fb585bff c,#0505ffff d,#c7c7ffff e,#ffc0c0ff f,#8282ffff g,#fe0909ff ``` ```image d fc cfa aa c c fc af cd c dc cf cd c c cd af dc c cd aa dc c cd fc dc c c dc fc cd c c fa cf c c aa aa c c af fc c c cf dc c cd cd dc dc cf cd c g dc aa eg cd c bg dc fa gb c c ge fc dc g c cd eg fa dc gb c cf ge aa c g c af eg af c bg c fa gb cf c ge c fc g cd cd egc dc cb cd e dcge c gg c g af egb fc eg c gg c bg aa egb fc gb c gg c ge fc egb fa g c gg c eg dc egb aa bg cbg c gb egc af g bg cf c eg egb c cf bg bge aa c gb gb c cd ge bge fc dc g gb c cd eg bge dc dc bg gg cd c gb bge dc fc ge gg cf c g bge c fa eg gg aa c gb bge c ge gg fa g bge c eg gg dc bg bge cd gb gg dc gbge cf g c af c fa c ``` <!-- end of image -->

This image seems promising for intersection detection. It's crucial to examine these regions more closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#0a0afcff b,#f12f2fff c,#6770ebff d,#d98370ff e,#fe0101ff f,#b1d7b1ff g,#95c69bff ``` ```image c a af ca a cc a af fa a cc a ac fa a ca a ac a a ca a ac a a ca a ac a a ca a ac a a ca a ac a de gggggggggggggggggggggggggggggggggggggggggggaggggggf beb ffffffffffffffffffffffffffffffffffffffffffcaffffffg deed ffffffffffffffffffffffffffffffffffffffffffafffffffg beb fffffffffffffffffffffffffffffffffffffffffacfffffffg deed fffffffffffffffffffffffffffffffffffffffffaffffffffg beb ffffffffffffffffffffffffffffffffffffffffacffffffffdeed fffffffffffffffffffffffffffffffffffffffcafffffffbeb fffffffffffffffffffffffffffffffffffffffafffffdeedfg ffffffffffffffffffffffffffffffffffffffaafffbebffffg ffffffffffffffffffffffffffffffffffffffafdeedffffffg fffffffffffffffffffffffffffffffffffffabebfffffffffg fffffffffffffffffffffffffffffffffffdbadfffffffffffg fffffffffffffffffffffffffffffffffbebafffffffffffffg ac ffffffffffffffffffffffffffffffdeedfcafffffffffffffg aa ffffffffffffffffffffffffffffbebffffaffffffffffffffg aa fffffffffffffffffffffffffdeedfffffacffffffffffffffg cac fffffffffffffffffffffffbebfffffffgafffffffffffffffg aa fffffffffffffffffffffdedfffffffffaffffffffffffffffg aa ffffffffffffffffffffeeffffffffffcaffffffffffffffffg cac ffffffffffffffffffdedfffffffffffafffffffffffffffffg aagffffffffffffffffeeffffffffffffacfffffffffffffffffg aafffffffffffffdedffffffffffffgaffffffffffffffffffg fcacffffffffffeeffffffffffffffafffffffffffffffffffg fffaagffffffdedffffffffffffffcafffffffffffffffffffg ffffgaaffffeeffffffffffffffffaffffffffffffffffffffg ffffffcacdedffffffffffffffffacffffffffffffffffffffg ffffffffaagffffffffffffffffgafffffffffffffffffffffg ffffffbedfaafffffffffffffffagfffffffffffffffffffffg fffffebffffcacffffffffffffcaffffffffffffffffffffffg fffbedfffffffaagffffffffffafffffffffffffffffffffffg ffebfffffffffffaaffffffffacfffffffffffffffffffffffg bedfffffffffffffcacfffffgaffffffffffffffffffffffffg ebfffffffffffffffffaagfffagffffffffffffffffffffffffg befffffffffffffffffffffaafcafffffffffffffffffffffffffg eb fffffffffffffffffffffcaaffffffffffffffffffffffffffg be fffffffffffffffffffffffgffffffffffffffffffffffffffg eb ffffffffffffffffffffffffffffffffffffffffffffffffffg be gfffffffffffffffffffffffffffffffffffffffffffffffffg eb be eb ``` <!-- end of image --> I wonder what we'll find inside area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#3937fcff b,#fa565bff c,#7a77fcff d,#feafafff e,#fe0909ff f,#c1c2ffff g,#0404feff ``` ```image cga fggf agc cgg ggc cga fggf aga fgg ggc cga fggf aga dbe fggf deeee ggc dbeeeebd cga deeeebd fggf dbeeeebd aga deeeebd fggf dbeeeebd agc deeeebd cggdbeeeebd fggbeeebd dagaeebd deeggbd dbeeeggc deeeeecgg dbeeeebd ggf deeeeed aga dbeeeebd fggf deeeeed agc dbeeeebd cgg deeeeed ggf dbeeeebd cga deeeeed fggf beeebd agc deeed cgg beeb ggc deeed cga beeb fggf deeed agc f dbeeb cgg gaf deeed ggc gggc dbeeb cga fagggf beeed fggf faggaf deeeb agc cgggc beeed fgg fagggf deeeb ggc faggaf beeed cga cgggc deeeb fggf agggf beeed aga faggaf deeeb fgg cgggc beeed ggc agggbeb cga bgggaf fggf deeecgggc aga beeed agggc fggf deeeb faggaf ggc beeed cgggc cga deeeb cgggc fggf beeed faggaf aga deeeb cgggc fggf beeed cgggc agc deeeb faggaf cgg beeed cgggc fggf deeeb cgggc aga eeed faggaf fggf eb cgggc agc d cgggc cgg faggafggf cgggga cggf ff ``` <!-- end of image --> The close-up clearly shows an intersection point in area A. I can confirm there's two intersections in there.

<!-- image --> ```palette Key,Color ,#fefefeff a,#3333ffff b,#fa3237ff c,#8080ffff d,#ff9393ff e,#ff0101ff f,#d6d1faff g,#0404feff ``` ```image c g gf cg g aa g gf fg g aa g gc fg g ca g gc fg gf ca g gc fg gf ca g ac fg gf cg g ac fg gf cg g ac g de gf beb cg deed g beb aa deed g beb gf deed cg beb g deed aa beb g deed gbeb dbgd bebg gc deed aa ggf beb g fga deed gc cgc beb fg agf ded g fga ee ca cgc ded g agf ee gc fgg ded fg cgc ee gf agf ded ca fgg ee g cgcded gc ggf fg dedfgg gf eb cgc ca bed agf g eb fgg ac bef cgc fg eb agf gf bef gg cg eb cgg bef f eb be feb be eb ``` <!-- end of image -->

Here's an image. My task is to find intersections or areas where lines come close together. I wonder what's going on inside those areas? Perhaps intersections are hiding there. <!-- image --> ```palette Key,Color ,#fefefeff a,#f28882ff b,#4e56eeff c,#fc0e0dff d,#0707fcff e,#aeaefeff f,#b1d7b1ff g,#98c699ff ``` ```image e bd bd ed bd bd ed dd ed ede ed bd d db de ede de dd de db db ede db dd db db dd bd dd dd bdggggggggggggggggggggggggggggg edb bdffffffffffffffffffffffffffff bd gbdfffffffffffffffffffffffffff dd gfbdffffffffffffffffffffffffff ede gffbdfffffffffffffffffffffffff bd gfffgdffffffffffffffffffffffff dd gffffgdgffffffffffffffffffffff ede gffffffdgfffffffffffffffffffff bd gfffffffdgffffffffffffffffffff db gffffffffdbfffffffffffffffffffede gfffffffffdbfffffffffffffffffdd gffffffffffdbfffffffffffffffdb gfffffffffffdbffffgaffffffbdgf gfffffffffffaddcccccgffffddfff gffffgaccccccaddffffcfffdbffff accccccaafffffffddfffgcbdgfffff accccccagffffffffffffffbdfffddfffffff aacccccaa gffffffffffffffffbdgdbccffffff cccca gfffffffffffffffffbdfffccfffff gfffffffffffffffffffffffcaffff gffffffffffffffffffffffffcafff gfffffffffffffffffffffffffcfff gfffffffffffffffffffffffffgcff gffffffffffffffffffffffffffacf gfffffffffffffffffffffffffffcc gffffffffffffffffffffffffffffcc gfffffffffffffffffffffffffffffca gfffffffffffffffffffffffffffff ca gfffffffffffffffffffffffffffff c gfffffffffffffffffffffffffffff c fggggggggggggggggggggggggggggg ac ac cc ca ca c c ac ac cc ca ca c c ac ac cc ca ca c c ac ac cc ca ca c c ac ac cc ca ca c ``` <!-- end of image --> Here's a close-up of the area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fc5759ff b,#4342feff c,#fd0708ff d,#0604fdff e,#8583fdff f,#feb1b2ff g,#c0c0ffff ``` ```image dg ddg bddg bddg bdde edde edde edde eddb gddb gddb gddb gddb gdddg gdddg bddg bddg bddg bddg bdde edde edde gb edde edd eddb bddb gddb gddde gddb fff edddg gddb ffaacccccf bddb ffadddcccccccccccf gddde ffaaccccccdddaaaff acc eddbg ffaaccccccccccaaffdddg acc bddb ffaaccccccccccaaff bddg cca gddde aaccccccccccaaff bddg fccaeddbg ccccccaaff bddg fcddde aff bddg gddde bdde eddbccf bddegbdde acc edddddg acc eddb cca ge fcca fcca fccf accf acc acc cca fcca fcca fccf accf acc ac c f ``` <!-- end of image --> There is an intersection point visible in this close-up of area A. After a thorough search, I conclude that there are two intersections.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff5c5cff b,#3f3fffff c,#ff0808ff d,#0504fdff e,#8484feff f,#ffb2b2ff g,#c5c5ffff ``` ```image e bd bd gd ed bd ed db gd gdg gd bd gdg db dg edg dg bd de db de edg db dd db de db edg bd dd bd gde bd bd ed dd ed gde gd bd gd db gdg gde dg bd dg db de edg de bd db db db ff edg fddcccccf dd facccccafdd c db facccccaf bd fcedg facccccaf bd dd facccccaf edgdeac cccaf ed ca ca cf c fc fc ac ca ca cf c fc fc ac ca ca cf c c fc ac cc ca cf c c fc ac cc ca cf c c fc ac cc ca cf c c fc ac ac ca cf c ``` <!-- end of image -->

Hmm, I'm not sure what to expect from this image. Let's see if any lines cross. These zones indicate regions where lines appear to be in close proximity. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd0707ff b,#0b0bfdff c,#f1a099ff d,#b0d6b0ff e,#98c698ff f,#6a72eeff g,#f35752ff ``` ```image ga agg gg a a ca gg a a a ac ac a a ac ag a a ac gg ca a a ca ca a a ca ca ac a a gg ac a a gg gg a a bf gg ca bf a a bf ac ca bf a ac bf ac a bb edddddddddddeade ac bb edddddddddddaedd a bbeddddddddddcaddd gg bbddddddddddadddd a bbddddddddcadddd ga efbdddddddaddddd a edfbdddddgaddddd ca eddfbddddadddddd a edddfbddgadddddd a eddddfbdaddddddd ac edddddebgddddddd a eddddddabddddddd gg edddddagdbeddddd a edddddadddbedddd gg eddddagddddbfddd a eddddaddddddbfdd gaeeeeeeeeeeeeed edddacdddddddbfd daedddddddddddde eddeadddddddddbf deadddddddddddde eddaeddddddddddbf ddacddddddddddde edcaddddddddddddbf dddaddddddddddde edaddddddddddddd bb dddagdddddddddde ecaddddddddddddd bb ddddadddddddddde daeeeeeeeeeeeeee bb ddddggddddddddde ca bb dddddaddddddddde a fb dddddgadddddddde gg fb ddddddaddddddefffbbbbb a fb ddeffbbbbbbbbbbff gg fb fffbbbbbbbbbffeacdddddde a fb fffbbbbbbbbfff ddddddddadddddde ac dbbbfff ddddddddagddddde a dddddddddaddddde ac dddddddddggdddde a ddddddddddadddde ac ddddddddddgaddde a dddddddddddaddde a dddddddddddcadde ca ddddddddddddacde a dddddddddddddade ca eeeeeeeeeeeeeagd a a ca gg a a ga a ca a a ac a gg a gg a ``` <!-- end of image --> I'm going to scrutinize area A for any signs of an intersection. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0506ff b,#0706fdff c,#ff7c7cff d,#a5a5ffff e,#fbbec1ff f,#5656feff g,#fe4243ff ``` ```image aae cag eaae gag eaae gag eaae bd gac bbd eaa fbbd gac fbbd eaa fbbd aac fbbd caa fbbd aac fbbd caa fbbd aae dbbf cag dbbf aae dbbf cag dbbf eaae dbbf gag dbbfaae dbbbg ebbb gabbb eaaebbb gac bbb eaa bbbd aac fbbd caa fbbd aac fbbd caa fbbd aae fbbd cag fbbd aae fbbd cag dbbf eaae dbb gag db eaae d gag eaae gac eaa gac eaa ``` <!-- end of image --> The close-up clearly shows an intersection point in area A. Next up, a closer look at another region. Could this be where the intersection is hiding, in area B? <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0303ff b,#0302feff c,#fd6e70ff d,#aeaeffff e,#feb6b7ff f,#4c4cffff g,#ff3232ff ``` ```image eaa gac eaa gac eaae cag aae cag aae eaa gac eaa gac eaae cag aae cag aae caa gac eaa ddd gacddddffffbbbbbb ddddffffbbbbbbbbbbbbbbbff fffbbbbbbbbbbbbbbbffffdddd bbbbbbbffffddddeaae dddd cag aae cag gac eaa gac eaae gac eaae cag aae cag aac eaa gac eaa gac eaae cag aae ``` <!-- end of image --> I observe an intersection inside area B. My analysis indicates that there are two intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fe0505ff b,#0808feff c,#ff8282ff d,#b4b4ffff e,#ffc4c4ff f,#5c5cffff g,#fe4040ff ``` ```image e ca acg gg a a ca gc ae a ea ac ae a a ae gc a a ae gg ea a ae ca ea a a ea ca ae a a cg ac a a gg gg a a bd gc ca bd a a bf ac ea bf a ae bf ae a bf ea ac bb ae a bb ea gg bb a a fb ea cg fb a a fb ca ea fb a ae db cg ea db a ac dbg a ab gc gc bd a a bd cg ac bd a a bd ca ae bf ae ea bf ea ae bf ae ea bf a a bb gc ca bb a a bb gg cg fb a a fb ca cg fb a ddffbbbbb a fb ddffbbbbbbbbffdd gg db ddffbbbbbbbbffddae a db ddffbbbbbbbbffdd a gc dbbbffdd ac a a ac gg a a ae ca ea a ae ea ea ae a a ca ac a a cg gg a a cg a ea ae ea ac a gc a cg a ``` <!-- end of image -->

This is the image I'm working with. The goal is to count the intersections. I've spotted 1 narrow regions that might be worth examining further. Let's call them area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#7073f8ff b,#f83637ff c,#fe0404ff d,#0a0afeff e,#e1c9e6ff f,#acd4acff g,#f47f7aff ``` ```image e add dd ad dde d ada ed dd de dde d ada da edd d dde aa ada d edd ad dde de ada ed edd da dde d ada aa edd d dde ad c ada d gc edd ed c dd de ce da d bb da ec d c ad cg d gc ed c de ce d bb da ec d c aa cg d gc ad c de ce fffdfffffffffbbf fffdaffffffffcff ffffdfffffffcfff ffffdafffffcgfff fffffdffffgcffff fffffadfffcfffff ffffffdffcgfffff fffffffdbbffffff fffffffdbfffffff fffffffcdfffffff ffffffcgdaffffff fffffgcffdffffff fffffcfffadfffff ffffcgffffdfffff fffbbfffffadffff fffcfffffffdffff ffcfffffffffdfff fcgfffffffffdaff gc d c aa b ce d gcg bb ad cc ec de ecb c ed bce cg da ecb gc d gcg c da cc ce d gcg bb ad bc ec d ecb c ed bce cg de cc gc d gcg c da cc ce d ecg bb ad bce ec d ecb c ed gce cg de cc gc ed gcg c da cc ce d ecbbb e bc ``` <!-- end of image --> Let's put area A under the microscope. <!-- image --> ```palette Key,Color ,#fefefeff a,#8280fcff b,#ff4a4aff c,#fd0608ff d,#0605feff e,#c2c1feff f,#ffa1a1ff g,#4841f7ff ``` ```image gdg ccf edde bcb adg fcc dda fccf add ccb dda bcc edd fccf gdg ccf edde bcb gdg fcc dde fccf add ccb dda bcc edd fccf gda ccf eddebcb gdgcc eddcf gdd bcdda fccadd ccf gda bcb edde fcc gdg fccf edde ccb adg bcc dda fccf add ccf dda bcb edd fcc gdg fccf edde ccb gdg bcc dde fccf add ``` <!-- end of image --> Oh my, look at that! It's an intersection in area A! One intersection, that's it, but I found it.

<!-- image --> ```palette Key,Color ,#fefefeff a,#6a6affff b,#fc3c3eff c,#fe0505ff d,#0a0afeff e,#bebeffff f,#ffc4c4ff g,#ff8181ff ``` ```image e edd dd ad dde d eda ed dd de dde d ada da dd d dde aa ada d edd ed dde de ada ed edd de dde d ada aa edd d dd ad c ada d gc edd ed c dd de cf da d bb da fc d c ad cg d gc ed c de cf d bb da fc d c aa cg d gc ed c de cf ed bb de fc d c aa cg d gc ad c d cf edbb db cd cgda gc d c ad cf d bb ed fc de c d cg da gc d c aa b cf d gcg bb ed cc fc de fcb c ed bcf cg de cb gc d gcf c aa cc cf d gcg bb ad cc fc d fcb c ed bcf cg de cc gc d gcg c da cc cf d fcb bb ad bcf fc d fcb c ed bcf cg de cc gc d gcg c da cc cf d fcbbb e bc ``` <!-- end of image -->

I have an image in front of me. I need to determine if there are any intersection segments. My next step is to analyze the details within each area. <!-- image --> ```palette Key,Color ,#fefefeff a,#0808fdff b,#fb0a0bff c,#5b5febff d,#f57571ff e,#b1d7b1ff f,#afaffeff g,#96c49bff ``` ```image c a af a af fa a ca a cc a af a af fa a ca a cc a af a af fa a fa c a ca cc af a a ac ca a af af a fa ca a af fa a a ca cc af a d a ac bb fa a bb af af bd a a be fa af db ac fa bb a a bb fa ca bd ac a be a cc db fa a db ac af bb a a bd fa af bd cc fa db a geeeeeeeeeeeeeeeeeeeeeeeeeeeeeageeeeeeeebbg ageeeeeeeeeeeeeeeeeeeeeeeeeeeecaeeeeeeeebbeg caeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeeeeebdeeg ageeeeeeeeeeeeeeeeeeeeeeeeeecceeeeeeebdeeeg gaeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeeedbeeeeeg gcaeeeeeeeeeeeeeeeeeeeeeeeeaceeeeedbeeeeeeg geageeeeeeeeeeeeeeeeeeeeeeeaeeeeebbeeeeeeeg geeaeeeeeeeeeeeeeeeeeeeeeeageeeebbeeeeeeeeg geecaeeeeeeeeeeeeeeeeeeeegaeeeebdeeeeeeeeeg geeeageeeeeeeeeeeeeeeeeeeaeeedbgeeeeeeeeeeg geeeeaeeeeeeeeeeeeeeeeeecaeedbeeeeeeeeeeeeg geeeecaeeeeeeeeeeeeeeeeeaeebbeeeeeeeeeeeeeg geeeeeaceeeeeeeeeeeeeeeccebbeeeeeeeeeeeeeeg geeeeeeaeeeeeeeeeeeeeeeaebdeeeeeeeeeeeeeeeg geeeeeecaeeeeeeeeeeeeeacbgeeeeeeeeeeeeeeeeg geeeeeeeaceeeeeeeeeeeeabeeeeeeeeeeeeeeeeeeg geeeeeeeeaeeeeeeeeeeeabeeeeeeeeeeeeeeeeeeeg geeeeeeeecaeeeeeeeeebaeeeeeeeeeeeeeeeeeeeeg geeeeeeeeeaceeeeeeebageeeeeeeeeeeeeeeeeeeeg geeeeeeeeeeaeeeeegbcaeeeeeeeeeeeeeeeeeeeeeg geeeeeeeeeecaeeedbeaeeeeeeeeeeeeeeeeeeeeeeg dddddddddbbbbbbbbbbbbbbbbbbbbbbbacbbbecaeeeeeeeeeeeeeeeeeeeeeeg ddddddddddee geeeeeeeeeeeeaeeeeaeeeeeeeeeeeeeeeeeeeeeeeg geeeeeeeeeeeegaeeaceeeeeeeeeeeeeeeeeeeeeeeg geeeeeeeeeeeeeaceaeeeeeeeeeeeeeeeeeeeeeeeeg geeeeeeeeeeeeeeaaceeeeeeeeeeeeeeeeeeeeeeeeg geeeeeeeeeeeeeegaeeeeeeeeeeeeeeeeeeeeeeeeeg geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg ``` <!-- end of image --> I'm analyzing this close-up of area A with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#0404feff b,#fd090aff c,#7a78fcff d,#feaaabff e,#3830f6ff f,#c1c0fdff g,#fd5a5cff ``` ```image faaf d eac gb caa gbb aac bbbd cae dbbbd f aaf dbbb e cae gbbg ac faaf gbbg aaf eae bbbd eae faaf dbbbd aac eac dbbb faaf faa gbbg eae eac gbbg aac caa bbbd faaf aaf dbbbd cae cae dbbb aac faaf gbbg faaf eae gbbg cae faaf gbbd eac eac dbbbd faaf faa dbbb caa eac dbbg eac caa gbbg faaf aac gbbd caa cae dbbbd eac faaf dbbb faaf cae dbbg caa faaf gbbg eae eac gbbd faaf faafbbbd caa eacbbb eae caabbg faac aagbg caaf caabd eae faabd faac deaed caaf dbaaf eae gbeae aac gbbaaf faaf bbbeac eae dbbbcaa aac dbbg aac faaf gbbg cae dddddddddddddggggggggggeaeggbbbbbbd aaf bbbbbbbbbbbbbbbbbbbbbbbbaaebbbbbbd cae bbbbgggggggggggggggdddddcaaddddd faaf cae eae aac faaf faaf eac cae faa eac eac faafcaa caaaaf eaae faaf ff ``` <!-- end of image --> I observe an intersection inside area A. There are precisely two intersections present in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0404feff b,#fe0506ff c,#7e7cfdff d,#ffa3a3ff e,#3c38fbff f,#c0c0ffff g,#fc5356ff ``` ```image c a af fa af fa a ce a ec a ac a af fa a ce a ee a ac a af fa a ca c a ee ee af a a ec ce a af af a fa ca af af ca a a ca ce ac a d a ec gb ca a bb ac af bg a fa dbd fa af db ac fa gb a a bb fa ce bg ac a bd a ec db fa a gb ee ac bb a a bg fa af bd ee fa db af a gb fa ce bb ee a bg af ee bd a a db ee ac gb af a bb a af bg ce fa bd af a db a ca gb ca a bb af ee bg a a bd ca ecb ac ab a ag ca ba ac baf a dbca fa gb a dddggggggggbbbbbbbbbbbbbbbbbbbbbaebbb ce gggggdddddddd a a fa ec ec a aaf fa ``` <!-- end of image -->

Alright, let's get to work and investigate this image for intersections. I'm going to focus my attention on these specific areas. <!-- image --> ```palette Key,Color ,#fefefeff a,#5f5ffeff b,#fe0605ff c,#f75d59ff d,#aed6aeff e,#0909feff f,#f9aaa8ff g,#b7b7ffff ``` ```image a e eg ae e ea ge e aa e eg ae e ea ge e aa e eg ge e ea ge e ae e eg ge e ea ge e ae e eg ge e eg ea eg e ea eg ea ae ea e ee eg ee ge ae e ae aa ae e ge eg ge ae geg e eg eg eg ge ea e ea aa ea e ee eg ee ae ae e ae ea ae ge ge e ge aa ge e eg eg eg ge eg e ea ea ea ge ea e eeae ddddddeedddddddd dddddddddddddddd dddddddddddddddd dddddddddddddddd dddddddddddddddd ffcc dddddddddddddddd ffccbbbbbbbbbbccf dddddddddddddddd ffccbbbbbbbbbbccff ddddddddfcccbbbbbbbbbbccff ffffcccccbbbbbbbbbbbbbbbbbbbcccfddd bbbbbbbbbbbcccccffff dddddddddddddddd dddddddddddddddd dddddddddddddddd dddddddddddddddd ``` <!-- end of image --> I wonder what we'll find inside area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#4d4dffff b,#ff0202ff c,#ff7373ff d,#ff3737ff e,#0707ffff f,#ffa5a5ff g,#fbcfd3ff ``` ```image eeeeeg aeea aa gg ggffcccdddbbbbb ccccdddddddbbbbbbbbbbbbbbbbbbbd bbbbbbbbbbbbbbbbbdddcccffgg ccccfffffggggg ``` <!-- end of image --> Darn it! This close-up doesn't show any intersections in area A. I've examined the entire image, and there are zero intersections present.

<!-- image --> ```palette Key,Color ,#fefefeff a,#4040ffff b,#ff0606ff c,#ff5c5cff d,#8383ffff e,#0606ffff f,#ffadadff g,#c7c7ffff ``` ```image d e eg de e ed ge e aa e eg de e ed ge e aa e eg de e ed ge eg aa e eg de e ad ge eg da e ed ge e eg aa ed ge ed eg ea de ea e ea ed ae ge ae e ae aa de e de eg ge de geg e eg ed eg ge ed e ed aa ea e ea eg ee de ae e ae ed de ge de e ge aa geg e geg eg eg de ed e ed ed ea ge ea e eeaa ae ffcc ffccbbbbbbbbbbccf ffccbbbbbbbbbbccff ffccbbbbbbbbbbccff ffffcccccbbbbbbbbbbbbbbbbbbbccff bbbbbbbbbbbcccccfffff ``` <!-- end of image -->

Alright, let's get to work and investigate this image for intersections. These spots are like clues. Let's see what they reveal about potential intersections. <!-- image --> ```palette Key,Color ,#fefefeff a,#0606feff b,#fe0808ff c,#5354fdff d,#f85b58ff e,#ffb1b1ff f,#b0b0ffff g,#afd5aeff ``` ```image f caaa faaaf fa faaaf cc caac af faaac a faaaf ca caac af faaac a faaaf fa caacf ac caac a f a ca af a fa ac a fa ca af a fa ac a fa cc af a ca af a fa cc af a e ca bbbd af dbbbe a ebbbd fa dbbbe ac edbbde a ebbbd a dbbbe ca ebbbd af dbbbe a edbbd fa ebd ac bb a ebe fa bb cc db af bd a bb fa ebe ac bd a db fa ebe cc bb af dbe a bd gggggggggcagggg bb ggggggggggagggg ebe ggggggggggggggg bb ggggggggggggggg db ggggggggggggggg ebd ggggggggggggggg bb ggggggggggggggg dbe ggggggggggggggg bd ggggggggggggggg bb ggggggggggggggg ebdgggggggggggggg bbggggggggggggg gdbgggggggggggg gggbdgggggggggg ggggbbggggggggg gggggdbgggggggg gggggggbbgggggg ggggggggbbggggg ggggggggggbgggg ggggggggggggggg ggggggggggggggg ggggggggggggggg ``` <!-- end of image --> My goal is to determine if there's an intersection inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0f0fffff b,#ff0202ff c,#6262ffff d,#ff6161ff e,#ff9e9eff f,#ffceceff g,#ff2727ff ``` ```image caa aac ac e bd bbgf fgbbd dbbgf ebbbe fgbbd dbbgf fgbbe dbbd ebbgf fgbbd dbbgf ebbbe fgbbd ebbgf fgbg de ``` <!-- end of image --> It's a shame, but area A doesn't contain an intersection. I can confidently say that there are no intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0505ffff b,#ff0707ff c,#7f7fffff d,#ff5656ff e,#ffb0b0ff f,#c3c3ffff g,#3f3fffff ``` ```image f gaaa faaac fa caaaf gg gaag af fgaac a caaaf ca gaagf ac fgaac a caaaf fa caagf gg gaac af f fa ga af a ca ac a fa gg af a ca ac a fa gg af a ca ac a fa gg af a e ca bbbd ac dbbbe a ebbbd fa dbbbe ag edbbde af ebbbd fa dbbbe gg ebbbd af dbbbe a edbbd ca ebd ac bb a ebe fa bb gg db af bd a bb ca ebe ac bd a db fa ebe gg bb af dbe a bd ca bb a ebe bb db ebd bb dbe bd db ebe bb db bd bb ebe bd db eb ``` <!-- end of image -->

Time to put on my detective hat and find those intersection points! My next step is to analyze the details within each area. <!-- image --> ```palette Key,Color ,#fefefeff a,#0607fdff b,#fd0506ff c,#aaacfaff d,#ee9b93ff e,#4f57f0ff f,#afd6afff g,#f54946ff ``` ```image c ea ea ca ca ac ac ae ae aa ea ea ca ca ac ac ae ae aa ea ea ca ca ac ac ae ae aa ea ea ca ca ffffffffffffffffffffffffffff acffffffffffffffffffffffffffff aafffffffffffffffffffffffffff eaefffffffffffffffffffffffff dbbb ffaaffffffffffffffffffffffff dgbbg ffffaaffffffffffffffffffffff gbbbd fffffeaeffffffffffffffffffffgbbbd fffffffaafffffffffffffffdbbbg fffffffffaafffffffffdbbbgdff ffffffffffeaeffffgbbbdffffff ffffffffffffaabbbgffffffffff fffffffffdbbbgaaffffffffffff fffffdgbbgdffffeaeffffffffff ffgbbbdffffffffffaacffffffff bbbgffffffffffffffffaafffffff bdffffffffffffffffffffeaefffff b ffffffffffffffffffffffaacfff b ffffffffffffffffffffffffaaff db fffffffffffffffffffffffffeae db fffffffffffffffffffffffffffaac db ffffffffffffffffffffffffffff aa db ffffffffffffffffffffffffffff cae gb eac gb aa gb cae bb eac bg aa bg cae bg e bg bd bd bd b b db db db db gb gb gb gb bb bg bg bg bd bd ``` <!-- end of image --> Eureka! Let's inspect this close up of area A <!-- image --> ```palette Key,Color ,#fefefeff a,#0403feff b,#fe0506ff c,#9393ffff d,#ffa7a7ff e,#4946fcff f,#c5c5ffff g,#fa5156ff ``` ```image e aac eaaef caaae eaaac feaaef caaae eaaac feaaef caaae eaaac ddg feaaef dgbbbb caaae dgbbbbbbgd eaaac dggbbbbbgdd feaaef ddgbbbbbggd caaae dgbbbbbbgd eaaac dgbbbbbbgd feaaabbbbbgdd ddgbgaaaegd dgbbbbbbgeaaac dgbbbbbbgd feaaef dggbbbbbgdd caaae ddgbbbbbbgd eaaac dgbbbbbbgd feaaef dgbbbbbbgdd caaae bbbbggd eaaac bgd feaaef caaae eaaac feaaef caaae eaaac feaaef caaa ea f ``` <!-- end of image --> Wow! I can see an intersection so clearly in area A! My investigation reveals that there is exactly one intersection in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0404ffff b,#fe0506ff c,#ababffff d,#ff8989ff e,#4b4bfeff f,#ffcacaff g,#fe4344ff ``` ```image c ea ea ca ca ac ac ae ae aa ea ea ca ca ac ac ae ae aa ea ea ca ca ac ac ae ae aa ea ea ca ca ac aa cae dbbb eac fgbbgf aa fgbbbf cae dbbbd eac dbbbg aa fgbbgf cae fgbbbd eabbbd dbbbgaa fgbbgf cae fgbbbd eac bbbd aa bf cae fbf eac fbf aa fb cae db eac db aa db cae gb eac gb aa gb cae bb eac bg aa bg cae bg e bd bd bd bf bf fbf fb fb db db db gb gb gb bb bg bg bg bd bd ``` <!-- end of image -->

Let's examine this image for potential line intersections. These zones indicate regions where lines appear to be in close proximity. <!-- image --> ```palette Key,Color ,#fefefeff a,#a3a5fcff b,#fd0b0aff c,#0807feff d,#f16b65ff e,#ffc4c4ff f,#5556f5ff g,#add4adff ``` ```image a c ca c c ac c fc c ff c ca c ca ac c ac c ff c ca c ca e ac bd c b ac eb c bd ff b c eb cf bd c b ca eb ac bd c be ac eb c dd ff be c eb ff db c be ca b c db c be ac b c db fc be c b ff db c be ca b c db ca be ac b c db ac be c b ff db c ebb be ca ebbe b c dbb db ca dbb be ac bbd b c ebbd a db ac ebbe fcf be c dbbe acca b ff dbb acca db c bbd ccf bd cf bbd fcc bgggggggggggcggggggg ebbe acca dbgggggggggcaggggggg ebbe ccf gbdggggggggcgggggggdbb fcc ggbgggggggcggggggbbb acca ggdbgggggfcggggbbdgg ccf gggbdggggcgggbbdgggg fcc ggggbgggfcdbbggggggg acca ggggdbggcbbggggggggg ccfggggbbcfggggggggggg fccgggdcgggggggggggg ggfccacfgggggggggggg gggggccggggggggggggg gggggggggggggggggggg gggggggggggggggggggg gggggggggggggggggggg ``` <!-- end of image --> Let's get to the bottom of what's happening inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#9b9bffff b,#fe0405ff c,#0907fcff d,#fb3e42ff e,#fa8d92ff f,#534ef9ff g,#f2dae6ff ``` ```image bg acc bd cca bbe acc ebbg gcca dbd fcf gbbe gccg ge ebbg fcf gdbb dbd accg edbbbd gbbe ccf edbbbdg ebbg acc ebbbbeg dbd cca gebbbbe gbbe acc gdbbbde ebbg gcca gdbbbde dbd fcf edbbbdg gbbe gccebbbbeg ebbg fccbbbeg dbd geccbbe fg gbbdbccfe ccfa ebbdccg fcccca eecca gaccccfg acc accccfagcca afcccccf gfccca aa ``` <!-- end of image --> There is an intersection point visible in this close-up of area A. I've found a single intersection point in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#9999ffff b,#ff0707ff c,#0706feff d,#fe4f4fff e,#ff9a9aff f,#4c4afcff g,#ecd7eaff ``` ```image a c ca gc cg ac c af c ff c ca gc cg ac c ac c ff c ca gc ca g gc bd cg b ac gb c bd ff bg c gb ca dd c bg ca gb gc dd cg bg ac gb c dd ff bg c gb ff dd c bg ca gb gc dd cg bg ac gb c db af bg c b ff db c bg ca b gc db cg be ac b c db ac be c b ff eb c gbb be ca ebbg b c ebbg eb ca dbd be gc bbd b cg gbbe a eb ac ebbe fcf be c ebbg accg b ff dbb gcca eb c dbd fcf be ca gbbe accg b c gbbe acca eb ca ebbg ccf be gc dbb fccg b cg dbd acca eb ac bbd ccf be c gbbe fccg b ffebbg acca eb cbbg gccf bbcf fcc dc accaca gcc ``` <!-- end of image -->

Alright, let's get to work and investigate this image for intersections. These areas seem to enclose narrow spaces where lines might be close. <!-- image --> ```palette Key,Color ,#fefefeff a,#4e51e6ff b,#e06d65ff c,#949fe6ff d,#f90b0cff e,#b1d7b1ff f,#9ac695ff g,#0708fcff ``` ```image e ddd bdde fffffffffffffffffffffffffffffffffffffffffffffffe bddb eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef bddb eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef eddd eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef ddde eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef bddb eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef bddb eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef bddb eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef ddd eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefddde eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecgeeeeeeeeebddb eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegageeeeebddbef eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeagegaebdddeeeef eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegeefgddfeeeeeef eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeageddbgeeeeeeeef eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegedfeeageeeeeeef eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaaddeeeegceeeeeef eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegfdeeeeeegeeeeeef eeeeeeeeeeeeeeeeeeeeeeeeeeeeeegadeeeeeeecgeeeeef eeeeeeeeeeeeeeeeeeeeeeeeeeeeeegdbeeeeeeeegaeeeef eeeeeeeeeeeeeeeeeeeeeeeeeeeeegadeeeeeeeeeegfeeef eeeeeeeeeeeeeeeeeeeeeeeeeeeeegdeeeeeeeeeeeegeeef eeeeeeeeeeeeeeeeeeeeeeeeeeeegdbeeeeeeeeeeeeageef eeeeeeeeeeeeeeeeeeeeeeeeeeeegdeeeeeeeeeeeeeegaef eeeeeeeeeeeeeeeeeeeeeeeeeeegdeeeeeeeeeeeeeeeegef eeeeeeeeeeeeeeeeeeeeeeeeeecgfeeeeeeeeeeeeeeeecgf eeeeeeeeeeeeeeeeeeeeeeeeeegdeeeeeeeeeeeeeeeeeeag eeeeeeeeeeeeeeeeeeeeeeeeecgeeeeeeeeeeeeeeeeeeeegc eeeeeeeeeeeeeeeeeeeeeeeeegfeeeeeeeeeeeeeeeeeeeefg eeeeeeeeeeeeeeeeeeeeeeeebgeeeeeeeeeeeeeeeeeeeeefcg eeeeeeeeeeeeeeeeeeeeeeebgeeeeeeeeeeeeeeeeeeeeeef ga eeeeeeeeeeeeeeeeeeeeeeeageeeeeeeeeeeeeeeeeeeeeef g eeeeeeeeeeeeeeeeeeeeeedgeeeeeeeeeeeeeeeeeeeeeeef g eeeeeeeeeeeeeeeeeeeeebaaeeeeeeeeeeeeeeeeeeeeeeef ag eeeeeeeeeeeeeeeeeeeeedgeeeeeeeeeeeeeeeeeeeeeeeef gc eeeeeeeeeeeeeeeeeeeedgaeeeeeeeeeeeeeeeeeeeeeeeef g eeeeeeeeeeeeeeeeeeebdgeeeeeeeeeeeeeeeeeeeeeeeeef cg eeeeeeeeeeeeeeeeeefdgaeeeeeeeeeeeeeeeeeeeeeeeeef aa eeeeeeeeeeeeeeeeeedfgeeeeeeeeeeeeeeeeeeeeeeeeeef gc eeeeeeeeeeeeeeeeedbgceeeeeeeeeeeeeeeeeeeeeeeeeef g eeeeeeeeeeeeeeeefdegeeeeeeeeeeeeeeeeeeeeeeeeeeef cg eeeeeeeeeeeeeeeedegceeeeeeeeeeeeeeeeeeeeeeeeeeef ga eeeeeeeeeeeeeeedbcgeeeeeeeeeeeeeeeeeeeeeeeeeeeef g eeeeeeeeeeeeeebdegeeeeeeeeeeeeeeeeeeeeeeeeeeeeef g eeeeeeeeeeeeeedecgeeeeeeeeeeeeeeeeeeeeeeeeeeeeef ag eeeeeeeeeeeeedbegeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef gc eeeeeeeeeeeebdeageeeeeeeeeeeeeeeeeeeeeeeeeeeeeef g eeeeeeeeeeeedeegeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef cg eeeeeeeeeeedfeageeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef aa eeeeeeeeeeddeegeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef gc eeeeeeeeefdeeaaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef g eeeeeeeeedeeegeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef cg eeeeeeeedbeegaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef ga eeeeeeebdeeegeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef g eeeeeeedeeegaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef g eeeeeedbeeegeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef ag eeeeebdeeegceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef gc eeeeedeeeegeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef g eeeedfeeegceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef cg eeeddeeecgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef ga eefdeeeegeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef g eedeeeecgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef g edbeeeegeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef cg bdeeeeageeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef gc deeeeegeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef g dbeeeeageeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef g g ag aa gc g g aa cg g a gc g gc g g cg g ``` <!-- end of image --> This close-up of area A is like examining a piece of evidence. <!-- image --> ```palette Key,Color ,#fefefeff a,#5b59fdff b,#fd5354ff c,#6a0b9eff d,#fd0709ff e,#fda5a6ff f,#b0affdff g,#0706fdff ``` ```image aa e fgga bdd ggggf ebdddd ggf ag bddddbe fgg ga ebdddbe ggf fgfbdddde gg ggdddbe gf ebdggce aa ddddeggf gf bdde fggf fgg dde gga agabdb fggf fggfdd agg agaede ag fgg db ga agabd fgf ggaddb gga fggbdd fggf ggadde fggf ggdde agg gcdb gga agdd fggf gcde agg ggd ga agce fgf fggd gg agcd gga fggde fgg agcb fg fggb a fgge ggc gg ega cg bgf ecg bcga edggf dcga bdggf edcga ddggf dcga edgga ddgg bddga eddfg ddegf bdbfg edd gg ddb ggf dd aga ede ggf db aga bd fggf edd aga ddefggf edd gg dde ga bdb fg bdd ga dde fg db gg bd fgg ede ggf bdb ggf edd aga dde ggf bdb aga edd fggf edde aga ddb ggf ede fg db aa bd fg edd gg dde fgg bdb ggf edd fgg ddb agg bdd ggf dde aga db ggf bd aga ede ggf dd ga edd aa edde fg ddb ag bdd fgg edde gga ddb fgg dd ggf db ggf bd agg edd ggf ``` <!-- end of image --> I've cracked the case! This area contains the intersection. My analysis indicates that there are two intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#3f39f8ff b,#f74a52ff c,#7b79fdff d,#fd0607ff e,#fdacaeff f,#bbbafeff g,#0505feff ``` ```image e eddd bdde bdde eddb eddb bdde bdde bddb eddb eddd bdde fg bdde gcg eddb cg gc eddb g gdde ca ddeg g de aa aabb gf ged g acd fg gdb aa gcd gf gd g gbe cg gd gc gd g fge fg gb aa fg gf g g bg fg eg gc aa gf dg g eaa cg dg gc dac g bdg fg dgc aa d g gf bbgf g ed g cg d gf gc defg g ed g fg d fg cg de g gc bd cg g d g fg de ca aa bb g gf ed aa g d g cg db ac gc ed g g d gc fg de g aa bd gf gf d g g de gf fg bb fg aa ed g gf d fg g db g cg ed cg gc d g g de ca fg g aa aa gf g g ac fg g a gc g gf g gf fg g ``` <!-- end of image -->

I'm on the case! Let's uncover any intersections hidden in this image. I've examined the entire image, and there are zero intersections present.

<!-- image --> ```palette Key,Color ,#fefefeff a,#3d3dffff b,#ff0505ff c,#ff9a9aff d,#9a9affff e,#0303ffff f,#e3d6f2ff g,#ff4949ff ``` ```image ddffff aaaeeeeeeeeeeeeeeeeeeeeeeeeeeeeaaaaad ffffdddded ef fe de aa ed ef e fe ae aa ed ef fe de ae ea ed e fe de aa ed ef e de ae ea ed ef fe de aa ea ef e fe de aa ed ef fe de ae ea ed ef fe de aa ed ef e gbbbbc cbbc cbbbc gbg fgbbg cbbc cbbbc gbb cbbbc cbbc fgbbg gbbf cbbgf cbbc cbbbc gbbf fgbbg cbbc gbbgf gbbf cbbbc cbbg fgbbg gbbf gbbgf cbbg cb bbf ``` <!-- end of image -->

This image might have some surprises. Let's look for intersections carefully. I've spotted 1 narrow regions that might be worth examining further. Let's call them area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#f65a56ff b,#0708fdff c,#fe0808ff d,#595ef4ff e,#feb0b0ff f,#b2b2feff g,#aed5aeff ``` ```image e ca c aa c aa c ec c ec c ec ce c ce c ca c aa c ac c c c ec ce c ce ec ca ce ca c cc ce ac c ac ce ec c ec aa ec c c aa c c ce ec ce c ca ec ca c ca ec ac ce ac c ac ce ec c ec ca c c c aa ce c ce aa ca c ca ec ca c ac ec ac ce ac f c ec bbf ce ec bb c c fbb ggcagggggggggggg c dbd gggcggggggggggggce bbf gggcaggggggggggce bb ggggcgggggggggca fbb ggggaagggggggcag dbd gggggcggggggccgg dbf gggggacggggccggg bb ggggggcgggacgggg fbb ggggggacgacggggg fbd gggggggcacgggggg dbf ggggggggcggggggg bbf gggggggggggggggg bb gggggggggggggggg fbbggggggggggggggg dbdggggggggggggg ggbbgggggggggggg ggggbbgggggggggg gggggdbbgggggggg gggggggdbbbbbbddf fddbbbbbbbbddf ffddbbbbbbbddff fddbbbbbbbbddf ffddbbbb ``` <!-- end of image --> Could this be where the intersection is hiding, in area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#ff3f3fff b,#0606ffff c,#ff0505ff d,#4d4effff e,#ffc0c0ff f,#afafffff g,#ff8282ff ``` ```image ccg gcc ccg gcc acg ecc g acg gc ecce gcc aca eccg ecce eccg aca ecca ecce ecca gca cca cce aca gca acc ccg acce gcc acce ccg gcce ecc gcce acg gccg eccgccg acccg ecca gg df bbd dbbbf fdbbbf fbbbdf fbbbd dbbbd fdbbbf fbbbdf ``` <!-- end of image --> Area A does not contain any intersection points. I'm extremely confident. No intersections at all.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff4545ff b,#0707ffff c,#ff0606ff d,#5c5cffff e,#ffc0c0ff f,#b1b2ffff g,#ff8181ff ``` ```image e cg c aa c ga c gc c ec ce ec ce c cg c ag c aa c ga c c ce gc ce c cg ec cg ce ca ec ca ce ac c ac cg gc c ec ag ec c c aa ce c ce gc ce c cg ec ca ce ca ec ac ce ac c gc cg ec c ec ag c c c aa ce c ce ga cg c ca gc ca c ac ec ac ce gc f ec ec bbf ce ec bb c c fbb cg c dbd c ce bbf ag ce bb c cg fbb aa ca dbd c ca dbf gc ac bb c ac fbb ec gc fbd cgc dbf ec bbf bb fbd dbd bbf bb fbb dbbbbbddff fddbbbbbbbbddf ffddbbbbbbbddff fddbbbbbbbbddf ffddbbbb ``` <!-- end of image -->

I'm examining this image closely. My goal: find any and all intersections. I wonder what's going on inside those areas? Perhaps intersections are hiding there. <!-- image --> ```palette Key,Color ,#fefefeff a,#0606feff b,#fe0505ff c,#bdbdffff d,#fba5a3ff e,#f94d4aff f,#afd6b0ff g,#6c6efbff ``` ```image d eb eb db db db bd bd bd be be be bb eb eb fffffffffffffff db fffffffffffffff db fffffffffffffff db fffffffffffffff bd fffffffffffffff bd fffffffffffffff bd fffffffffffffff be fffffffffffffff be fffffffebbbffff be fffdbbbefffffff bb ebbbdffffffffff eb dbbbeffffffffffffff eb dbbbe fffffffffffffff db ebbbd fffffffffffffff db dbbbd fffffffffffffff db dbbbe ffffffffffaffff bd ebbed fffffffffafffff bd ebbbd ffffffffagfffff bd dbbbe fffffffagffffff bebbed aa d ga ca ca a ac ag ag ga ga ag ca ag a ag ac ag ac ag ag ag aa ag ga ag ca ac a ac a ac ac ac ag ac aa ac ga ac ca ac ca ac a ac ac ac ag ac ag a ga a ga a ca ca a ca ac ca ag ca ag ca ga ca ga ca ca ca a ca ac ca ac ca ag ca aa caga ga ``` <!-- end of image --> I'm determined to find out if an intersection exists in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0808ffff b,#ff0404ff c,#bfbfffff d,#ff8d8dff e,#ff4848ff f,#ffd1d1ff g,#5353ffff ``` ```image f fdebe fdebbbbbe debbbbbbedf fdebbbbbedf fdebbbbbedf fdebbbbbbedf bbbbbedf bedf c cag caag aag gaa gaac gaac caac ``` <!-- end of image --> No intersection in area A, but I'll keep looking. My analysis shows there's absolutely no intersections in the image

<!-- image --> ```palette Key,Color ,#fefefeff a,#0404ffff b,#ff0505ff c,#9898ffff d,#ffa0a0ff e,#ff4a4aff f,#dcd4f6ff g,#5151ffff ``` ```image d eb eb db db db fbf bd bd be be be bb eb eb db db db fbf bd bd be be dbbb be debbef bb ebbbd eb dbbbd eb dbbbef db febbbd db dbbbd f db dbbbe fa fbf febbed af bd ebbbd af bd dbbbe ac bebbed ag d ga ca fa a af ac ag ga ca ag fa ag a ag af ac ac ac ag ac ga ac ga ac ca ac fa ac af ac ac ac ag ac ag af ga af ca af fa af af af af af ac af ag faf ga faf ca faf fa faf a fa af fa ac fa ag fa ga fa ca fa fa fa fa ca af ca ac ca ag ca ga caga ca ``` <!-- end of image -->

The hunt for intersections begins! Let's analyze this image closely. These zones are intriguing. I bet there's something interesting happening within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#fc0504ff b,#5665deff c,#cd826fff d,#a2caa5ff e,#b1d7b2ff f,#e43c35ff g,#0505fdff ``` ```image e gb g bb g bb g bg g eg g g a ge ca acdddddgdddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddda aeeeeegbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeac aceeeeegeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeca daeeeeegbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeead dffeeeeegeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeffd deaeeeeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedaed deffeeeeegeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaded deeaeeeeebgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeffeed deecaeeeeegeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeed deeeaeeeeebgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaceeed deeecaeeeeegeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecaeeeed b deeeeadeeeebgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeedbg deeeedaeeeeegdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaceeeeebg deeeeeaceeeedgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecaeeeeebg deeeeedaeeeeegdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeebgd deeeeeeaceeeedgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeafeeeebged deeeeeeeaeeeeegbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedaeeeebgeed deeeeeeefceeeeegeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeadeeebgeeed deeeeeeeeaeeeeegbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeffeeebgeeeed deeeeeeeeffeeeeegeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedaeeebgeeeeed deeeeeeeeeaeeeeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeadeebgeeeeeed deeeeeeeeecfeeeeegeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefaeebgeeeeeeed deeeeeeeeeeaeeeeebgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeebgeeeeeeeed deeeeeeeeeecaeeeeegeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeacebgeeeeeeeeed deeeeeeeeeeeadeeeebgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecaebgeeeeeeeeeed deeeeeeeeeeecaeeeeegeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaebgeeeeeeeeeeed deeeeeeeeeeeeaceeeebgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeacbgeeeeeeeeeeeed deeeeeeeeeeeedaeeeeegdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecabgeeeeeeeeeeeeed deeeeeeeeeeeeeaceeeedgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeabgeeeeeeeeeeeeeed deeeeeeeeeeeeeeaeeeeegdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefcgeeeeeeeeeeeeeeed deeeeeeeeeeeeeefceeeedgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedfgeeeeeeeeeeeeeeeed deeeeeeeeeeeeeeeaeeeeegbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefgeeeeeeeeeeeeeeeeed deeeeeeeeeeeeeeeffeeeeegeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecgeeeeeeeeeeeeeeeeeed deeeeeeeeeeeeeeeeaeeeeegbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebgeeeeeeeeeeeeeeeeeeed deeeeeeeeeeeeeeeeffeeeeegeeeeeeeeeeeeeeeeeeeeeeeeeeeeedgceeeeeeeeeeeeeeeeeeed deeeeeeeeeeeeeeeeeaeeeeebbeeeeeeeeeeeeeeeeeeeeeeeeeeedgaeeeeeeeeeeeeeeeeeeeed deeeeeeeeeeeeeeeeecaeeeeegeeeeeeeeeeeeeeeeeeeeeeeeeedgaeeeeeeeeeeeeeeeeeeeeed deeeeeeeeeeeeeeeeeeadeeeebgeeeeeeeeeeeeeeeeeeeeeeeedgaceeeeeeeeeeeeeeeeeeeeed deeeeeeeeeeeeeeeeeecaeeeeegeeeeeeeeeeeeeeeeeeeeeeedgcaeeeeeeeeeeeeeeeeeeeeeed deeeeeeeeeeeeeeeeeeeadeeeebgeeeeeeeeeeeeeeeeeeeeedgeaeeeeeeeeeeeeeeeeeeeeeeed deeeeeeeeeeeeeeeeeeedaeeeeegdeeeeeeeeeeeeeeeeeeedgeafeeeeeeeeeeeeeeeeeeeeeeed deeeeeeeeeeeeeeeeeeeeaceeeebgeeeeeeeeeeeeeeeeeedgddaeeeeeeeeeeeeeeeeeeeeeeeed deeeeeeeeeeeeeeeeeeeeeaeeeeegdeeeeeeeeeeeeeeeedgdeadeeeeeeeeeeeeeeeeeeeeeeeed deeeeeeeeeeeeeeeeeeeeeaceeeedgeeeeeeeeeeeeeeedgdeffeeeeeeeeeeeeeeeeeeeeeeeeed deeeeeeeeeeeeeeeeeeeeeeaeeeeegdeeeeeeeeeeeeedgdedaeeeeeeeeeeeeeeeeeeeeeeeeeed deeeeeeeeeeeeeeeeeeeeeeffeeeedgeeeeeeeeeeeedgdeeadeeeeeeeeeeeeeeeeeeeeeeeeeed deeeeeeeeeeeeeeeeeeeeeeeaeeeeegbeeeeeeeeeedgdeefaeeeeeeeeeeeeeeeeeeeeeeeeeeed deeeeeeeeeeeeeeeeeeeeeeeffeeeeegeeeeeeeeedgdeeeaeeeeeeeeeeeeeeeeeeeeeeeeeeeed deeeeeeeeeeeeeeeeeeeeeeeeaeeeeegbeeeeeeedgdeeeaceeeeeeeeeeeeeeeeeeeeeeeeeeeed deeeeeeeeeeeeeeeeeeeeeeeecaeeeeegeeeeeedgdeeecaeeeeeeeeeeeeeeeeeeeeeeeeeeeeed deeeeeeeeeeeeeeeeeeeeeeeeeadeeeebbeeeedgdeeeeaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeed deeeeeeeeeeeeeeeeeeeeeeeeecaeeeeegeeedgdeeeeaceeeeeeeeeeeeeeeeeeeeeeeeeeeeeed deeeeeeeeeeeeeeeeeeeeeeeeeeadeeeebgedgdeeeecaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeed deeeeeeeeeeeeeeeeeeeeeeeeeedaeeeeegdgdeeeeeaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeed deeeeeeeeeeeeeeeeeeeeeeeeeeeaceeeebgdeeeeeffeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeed deeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeeeeeeeedaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeed deeeeeeeeeeeeeeeeeeeeeeeeeeeeaceeeeeeeeeeadeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeed deeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeeeeeeffeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeed deeeeeeeeeeeeeeeeeeeeeeeeeeeeeffeeeeeeeeaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeed deeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeeeeaceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeed deeeeeeeeeeeeeeeeeeeeeeeeeeeeeeffeeeeecaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeed deeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeeaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeed deeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecaeeeaceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeed deeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeadecaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeed dddddddddddddddddddddddddddddddddcadadddddddddddddddddddddddddddddddddddddddd aac a ``` <!-- end of image --> I'm going to scrutinize area A for any signs of an intersection. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe090aff b,#312bf9ff c,#fb5b5eff d,#7c7cfeff e,#feaeaeff f,#ccccfeff g,#0303feff ``` ```image ae ggf ae gg a aa dg a aae gd ea aa gd ca ea gg eaa ea fgf aa ac bd ae aae fgf cc aa ggf aa ca dgb caa ae fgg aae ae gd ca aa db eae ea gg aa ac bgd eae ea fgg cc aae fgf aa b cac bd cac g ca gb ac dgf ae gg ca dgg ca dg eae ggf aa db aa dgf aa gd eae dgg ac bgd ea dgd ea dgg aa dgd ac bg cac gg cac bd ae dgd aa fgf ca dgg ae gg aa dgd ca dg caa dgd ae fgf aae gg aae fgf ca dgd eaa gb eae dgg aa ggd ca ggd cc bg ae dgd eae dg cc dgg aa fg aa dgd ca gd caadgd ae ggf aaegg ae fgg cadgd aa dg eadgg eaa db acgd aa gf agd ea gb cgg ea dg cgd ac bd cgg ca gd fgb ae gg fgb ca bgd fgge aa bg fgba aae fgf fgbae aa fgf fgba ea gb fgbae cc gg fggca ac gd fgb ac aae db fgb ca aa gg fgb aa ca bgd fgb caa ae fgg fgg aae ae fgf fgb ea aa bd fgb ae aa fgf fgg ca cc ggf fgb ae ea dgb fbb ca aae dg fgb aa cac gd fbbf caa aa db fbgf aae ae gg fgbf ca ca bg bbf eae aa bd gb eaa aa fgf bbf aae ea gd bgf ac ea dgb ggf ac ac fgg bgf ca cac gf bgg ac aa db ggf ca ca gggf eae ca bg eaa ae aae aac ea eaa ae aa ca cc ac eae ca ac eae ca caa ae aae ae ea aa ae aae ca aa aac ``` <!-- end of image --> Case closed! This is definitely an intersection point in area A. There's one and only one intersection present in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fd090bff b,#5454ffff c,#fa6064ff d,#9190feff e,#feafafff f,#d5d5ffff g,#0404ffff ``` ```image f gd g bb g bb g dg g dg gf fg a gf ea ae fg a a gd ac ae g ea a gd a ac g ac a bb a cc g a a bb ca ca g a a dg ae ea g ca b a dg a bg ea gf ae bg ae fg ea bg a gf a bg ae fg ac bg a gd ea bg ac g a bg a gd cc bg cc g a dg a bb ae dg ca g ca dg a bb a dg ea g ae dg a dg ea dg ea g a dg ae dg acdg a gf eadg ae fg adg a gf acg ac fg ag a gd ag cc g cg a gd dg ca g fge a bb fga ea g fga a bb fgae ea g fgea ae dg fg a a g fg ac ae dg fg ea a gf fg a ac fg fg cc a gf fgf a cc fg fgf ae a gd fgf ca ca g fgf a a gd fgf ae ea g fgf ea a bb gf a ea g gf ac ae bb gf ea a g gf a ae dgf ac a a ac a a ca cc a a ae cc ca a a ea ae a ea ea a aac a ``` <!-- end of image -->

I'm analyzing this image to identify any points where lines intersect. There are 1 regions I'd like to highlight in the image. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd0707ff b,#4b3ee7ff c,#f8a09dff d,#f44f4dff e,#9c9ffaff f,#0303feff g,#aed5aeff ``` ```image c a ac ca a ca a dd a ac a a ca a dd a ac a ac ca a dd a dd a ac ca a ca a dd a ac a c a da ca ad a ac dd a a a ac ca a da ac ad ca ac a a dd a a ca ad da a ad ac ac ca a a a ca ca a da dd ad a ac ac a a a a ca ca da a ad dd ac a a ac a a cagggggggggggggggggaggg dagggggggggggggggcaggg gadggggggggggggggagggg ggadggggggggggggddgggg gggaggggggggggggaggggg ggggaggggggggggadggggg ggggcagggggggggagggggg gggggdagggggggacgggggg gggggedbbffffbaggggggg eebbffffffffbbbggggbfffffbeg eebbfffffffbbee ggggggggagggdagggggbbffffbe bfffffffbbee gggggggggaggaggggggggg ebfffffee e gggggggggcaadggggggggg eefffffbe ggggggggggdagggggggggg ebffffbe gggggggggggggggggggggg ebffffbee gggggggggggggggggggggg ebfff gggggggggggggggggggggg gggggggggggggggggggggg gggggggggggggggggggggg ``` <!-- end of image --> I wonder what we'll find inside area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#ff0606ff b,#5a55faff c,#fca1a3ff d,#ff5151ff e,#bebcfdff f,#0606feff g,#830580ff ``` ```image aad dad caac caa caac dad daa caa daa aac aad caa aad aac caac dad caac caac daa dad daa caa aad aac aad caa caac aac caac dad daa aac daa eee dad eeegggbbffffffffbbgge eeeebbbbfffffffffffffffffffffffffbbbee fffffffffffffbbbggcee ebggffffffffffbbee ffbbbbeee caac aac eebbbfffffff daa daa eebbf daa aac aad dad aad caa caacdad caaaa daac dd ``` <!-- end of image --> An intersection is present within area A. Two intersections have been found!

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0707ff b,#4847fdff c,#ffa4a4ff d,#ff5151ff e,#a6a6ffff f,#0303ffff g,#8e1887ff ``` ```image c a ac ca a ca a dd a ac a a ca a dd a ac a ac ca a dd a dd a ac ca a ca a dd a ac a c a da ca ad a ac dd a a a ac ca a da ac ad ca ac a a dd a a ca ad da a ad ac ac ca a a a ca ca a da dd ad a ac ac a ca a a ca ca da a ad dd ac a a ac a a ca ac da ca ad a ac dd a a a ac ca a da ac eggbffffbg eebbffffffffbgg egbffffbe eebbfffffffbbee a da ebffffbe bfffffffbbee a a ebfffffbe e cadd ebfffffbe da ebffffbe ebffffbee ebfff ``` <!-- end of image -->

Let's examine this image for potential line intersections. There are 1 areas where the lines seem to converge. We should take a closer look at area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#5f65e0ff b,#fc0b09ff c,#b1d7b1ff d,#9cc19aff e,#0809fcff f,#e66c60ff g,#eef4f0ff ``` ```image f bb gdddddddddddddddddddddddddddddddddddddddddddddddddddddddbf gcccccccccccccccccccccccccccccccccccccccccccccccccccccfbdg gccccccccccccccccccccccccccccccccccccccccccccccccccccbbccg gcccccccccccccccccccccccccccccccccccccccccccccccccccbbcccg gcccccccccccccccccccccccccccccccccccccccccccccccccdbfccccg gccccccccccccccccccccccccccccccccccccccccccccccccfbccccccg gcccccccccccccccccccccccccccccccccccccccccccccccbbcccccccg gcccccccccccccccccccccccccccccccccccccccccccccdbfccccccccg gccccccccccccccccccccccccccccccccccccccccccccfbdcccccccccg gcccccccccccccccccccccccccccccccccccccccccccbbcccccccccccg gccccccccccccccccccccccccccccccccccccccccccbfccccccccccccg gccccccccccccccccccccccccccccccccccccccccfbdcccccccccccccg gcccccccccccccccccccccccccccccccccccccccbbcccccccccccccccg gccccccccccccccccccccccccccccccccccccccbbccccccccccccccccg gccccccccccccccccccccccccccccccccccccdbfcccccccccccccccccg gcccccccccccccccccccccccccccccccccccfbcccccccccccccccccccae gccccccccccccccccccccccccccccccccccbbccccccccccccccccdaeeag gccccccccccccccccccccccccccccccccdbfccccccccccccccaeeeaccg gcccccccccccccccccccccccccccccccfbdccccccccccccaeeedcccccg gccccccccccccccccccccccccccccccbbccccccccccdeeeacccccccccg gcccccccccccccccccccccccccccccbfccccccccaeeeaccccccccccccg gcccccccccccccccccccccccccccfbdcccccdeeeaccccccccccccccccg gccccccccccccccccccccccccccbbccccaeeeacccccccccccccccccccg gcccccccccccccccccccccccccbbccaeeedccccccccccccccccccccccg gcccccccccccccccccccccccdbaeeeaccccccccccccccccccccccccccg gccccccccccccccccccccccaeeedcccccccccccccccccccccccccccccg bfc gccccccccccccccccccdeeeacccccccccccccccccccccccccccccccccg gfbbbbbbfg gcccccccccccccccaeeeabfccccccccccccccccccccccccccccccccccg cfbbbbbfc gcccccccccccccaeadcfbdcccccccccccccccccccccccccccccccccccg gfbbbbbffdccccccccccccecccbbcccccccccccccccccccccccccccccccccccccg gffbbbbbfdccccceaccbfccccccccccccccccccccccccccccccccccccccg gccccdfbbbbbeecfbdcccccccccccccccccccccccccccccccccccccccg gccccccccccdebbbcccccccccccccccccccccccccccccccccccccccccg gccccccccccecccccccccccccccccccccccccccccccccccccccccccccg gccccccccceacccccccccccccccccccccccccccccccccccccccccccccg gccccccccaeccccccccccccccccccccccccccccccccccccccccccccccg gccccccccecccccccccccccccccccccccccccccccccccccccccccccccg gcccccccedcccccccccccccccccccccccccccccccccccccccccccccccg gcccccceaccccccccccccccccccccccccccccccccccccccccccccccccg gcccccaecccccccccccccccccccccccccccccccccccccccccccccccccg gccccceccccccccccccccccccccccccccccccccccccccccccccccccccg gcccceaccccccccccccccccccccccccccccccccccccccccccccccccccg gcccaecccccccccccccccccccccccccccccccccccccccccccccccccccg gccdeccccccccccccccccccccccccccccccccccccccccccccccccccccg gccecccccccccccccccccccccccccccccccccccccccccccccccccccccg gceacccccccccccccccccccccccccccccccccccccccccccccccccccccg gaeccccccccccccccccccccccccccccccccccccccccccccccccccccccg geccccccccccccccccccccccccccccccccccccccccccccccccccccccdg ecggggggggggggggggggggggggggggggggggggggggggggggggggggggg ea ge eg ea ae ge eg ea ae e ec ae ge eg ea ae ge eg ea ce e ec ae ge eg ea ae ge eg ``` <!-- end of image --> I'm eager to see what's happening in this magnified view of area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#5955faff b,#fe0506ff c,#fec3c3ff d,#acaafcff e,#0807feff f,#f83d43ff g,#fe8282ff ``` ```image gb cfbb cbbbc gbbf fbbg cbbbc gbbfc fbbf cbbbg gbbbc fbbf cfbbg cbbbc gbbf fbbg cbbbc gbbfc fbbf cbbbg gbbbc fbbf cfbbg cbbbc gbbf fbbg cbbbc gbbfc fbbg cbbbg gbbfc fbbf cfbbg dae cbbbc daeeee gbbf daeeeeeead cfbbg daeeeeeadd cbbbc daaeeeeead gbbfc daeeeeeaad fbbg daeeeeead cbbbc daeeeeeead gbbfc daeeeeead fbbf daeeeeeead cfbbg daeeeeeadd bbbc ddaeeeeead gbf daeeeeeead cfbg daeeeeead cbbb daeeeeeead gbbf daeeeeeadd cbbbdaeeeeaad gbfeeeeeed daeeeeeead daeeeeead daeeeeeead daeeeeeefbf ddaeeeeeadfbbg deeeeeead cbbbc deeead gbbf eea fbbg gc aea cbbbc bbbbffgcc aee gbbfc ffbbbbbbbbbfggc deed fbbg ccgffbbbbbbbbbffgcc eea cbbbg cggfbbbbbbbbbfaeec gbbbc ccgffbbfeebbbbbbf deeafbbbbg eea c aee deed eea aea aee deed eea aee deed deed eea aee deed eea aea dee deed eea aee deed eed aea aee deed eea aee deed deed eea ``` <!-- end of image --> The lines cross each other within area A, forming an intersection. After a long analysis, I found two intersections.

<!-- image --> ```palette Key,Color ,#fefefeff a,#4139f6ff b,#ff0606ff c,#ffababff d,#8683fbff e,#0404ffff f,#ff5555ff g,#c7c6feff ``` ```image c bb bf cbc fb bb cbc fb bb bf cb bb bf cbc fb bf cbc fb de bb gaeeag bf deeed fb deeag bb gaeed bf deeeg cbc gaeea fb deeed bf aeeag cbdeeed aeeag bfc gaeea cfbbbbfc deeedbc cfbbbbbfc deag fb cfbbbbbfc e bb cfbbbbbfc eg bf cfbbbbbaa cbc gefbb e ed de e eg aa ge e ed ae ge e ed de e eg aa ge e ed de ge eg ea de e eg aa ge e ed de e eg aa ge e eg aa ge e ed de e eg ``` <!-- end of image -->

This image looks interesting. I wonder if there are any intersections hidden in there? I have a hunch that these areas might contain the intersections we're looking for. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0707ff b,#0a0afeff c,#f6605cff d,#a3a6f7ff e,#feb9b9ff f,#aed4aeff g,#5858f4ff ``` ```image e eaa a eaa ea eac ae cac a aae ae aae a aa cc eaa a cac cc cac a aae ea aae a eaa ea eaa ae cac bg a cac bb ae aae gb a aae gb cc eaa db a eaa db cc cac bd a cac bd ffffffffffffcaff aae bg ffffffffffffafff aa bg ffffffffffffafff e bbfffffffffffaffff bbffffffffffaffff gbffffffffacffff fgbfffffffafffff ffdbfffffacfffff ffffbffffaffffff fffffbdfccffffff ffffffbgafffffff fffffffbgfffffff fffffffabbffffff fffffffafbbfffff ffffffafffbbffff ffffffaffffgbfff fffffacfffffgbff fffffafffffffdbf ffffacfffffffffbd ffffafffffffffffbd fffccfffffffffff bg fffaffffffffffff bg ffcaffffffffffff bb ffafffffffffffff bb ea gb ae gbg a gbbd ae bbb a dbbg cc gbbd a bbb cc dbbg a gbbd ea dbbg a dbbd ea gbbd ae dbbg a gbbd ae bbb a dbbg cc gbbd a bbb cc d a ea a ea ae a ae a cc a cc a ea a ``` <!-- end of image --> Could this be where the intersection is hiding, in area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0404ff b,#0808feff c,#ff7a7aff d,#b5b5ffff e,#ffbbbbff f,#f7383fff g,#5951f7ff ``` ```image caf aae caf fac eaa fac eaa fac eaae d caf bd aae bbd caf gbbd aae gbbg caa gbbg fac dbbg eaa dbbg fac dbbb eaa dbbbd fac bbbd eaae gbbd caf gbbd aae gbbdcaf gbbgae dbbg fbbg eafbbg facdbbb eaa dbbbd fac bbbd aae gbbd caf gbbd aae gbbg caf gbbg aae dbbg eaa dbbg fac dbbb eaa dbbb fac bb eaa g fac aae caf aae caf aae eaa fac eaa ``` <!-- end of image --> Case closed! This is definitely an intersection point in area A. My investigation reveals that there is exactly one intersection in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0505ff b,#0909feff c,#ff7a7aff d,#aaaaffff e,#ffbdbdff f,#ff3f3fff g,#5955fbff ``` ```image e caa a eaa ea caf ae cac a fae ae aae a aa fc eaa a caf cf fac a fae cf aae a eaa ea eaf ae caf bg a fac bb ae fae gb a aae gb fc eaa db a eaf db cf caf bd a fac bd ca aae bg a aa bg ea e bb ae bb a gb ae gb a db fc db a bd cf bda bg abg ea bb ae gb a gb ae db a db fc bd a bd cf bg a bg ea bb a bb ea gb ae gbg a gbbd ae bbb a dbbg fc gbbd a bbb cf dbbg a gbbd ea dbbg a dbbd ea gbbd ae dbbg a gbbd ae bbb a dbbg fc gbbd a bbb cf d a ea a ea ae a ac a fc a cf a ea a ``` <!-- end of image -->

I have a feeling there might be some intersections in this image. These areas seem to enclose narrow spaces where lines might be close. <!-- image --> ```palette Key,Color ,#fefefeff a,#4649f8ff b,#f8706dff c,#fd0808ff d,#0606feff e,#e5d2ebff f,#add4adff g,#9092faff ``` ```image e gda d ade gd eda d dd ed gdg de dd ed ade dg eda d dd dg gdg d dd ag gde d da aa ad d edg ga dd d gde gd da d ade ed eda de dd ed gdg de dd d ade dg eda d ad ag gdg d dd aa gde d da ga ad d e gd d gd de ed de ed dg d dg d ag d aa d ga d gd d ed de ed de d dg d ag fffffffffffdffffff ffffffffffaaffffff ffffffffffdfffffff fffffffffaafffffff fffffffffdffffffff ffffffffgdffffffff ffffffffdfffffffff fffffffgdfffffffff fffcccfdffffffffff fffffbcdcbffffffff ffffffdffcccbfffff ebc ffffffdfffffcccbff ebccccbe fffffdgffffffffbccb ebccccbe fffffdffffffffffffbccce ebccccbe ffffdaffffffffffff bccce ebccccbe ffffdfffffffffffff ecccb ebccccbe fffaafffffffffffff ecccb bccccbe fffaffffffffffffff ebccb bccccbe ffffffffffffffffff bccb bccccbe ffffffffffffffffff bcccbe ``` <!-- end of image --> Could this be where the intersection is hiding, in area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#3730f7ff b,#ff5050ff c,#fc0507ff d,#0303feff e,#ffa9a9ff f,#b6b5feff g,#706ffdff ``` ```image adg fdd adg fdd gdg fddf gda ddf gda ddf gda ddf fda adf fdd adg fdd cbe adg ecccccbefdd ebccccadg ebcddccbe gdacccccbe ddf ebcccccbe gda eebccccbee ddf ebcccccbe gda ebccccc ddf ebcc gda e ddf fdd adg fdd adg fdd adg fdd gg ``` <!-- end of image --> Aha! I've found an intersection inside area A! The image features one single intersection point.

<!-- image --> ```palette Key,Color ,#fefefeff a,#4444ffff b,#ff6b6bff c,#fe0607ff d,#0505feff e,#ffc8c8ff f,#c6c6ffff g,#8686ffff ``` ```image f gda d ad fd fdg d dd fd gdf df dd d adf df fda d ad dg fdg d dd ag gdf d da aa ad d fdg ga dd d gdf gd da d ad fd fdg df dd fd gdf df dd d adf dg fda d ad ag fdg d dd aa gdf d da ga ad d f gd d fd d fd df d df d dg d ag d aa d ga d gd d fd df fd df d dg d ag d aa d ga d gd d fd ccced ecdce dfecccb ebc d ebccb ebccccb df bccb ebccccbe d bccbe ebccccbe ag bccce ebccccbe d eccce ebccccbe ag ecccb bccccbe a bccb bccccbe bccb bccccbe bcccbe ``` <!-- end of image -->

I'm on the case! Let's uncover any intersections hidden in this image. These zones indicate regions where lines appear to be in close proximity. <!-- image --> ```palette Key,Color ,#fefefeff a,#feb4b3ff b,#0808fdff c,#fc0707ff d,#9ea3f5ff e,#aed5adff f,#4f56e8ff g,#e65b52ff ``` ```image d bf b db b b bd b fb b db bd b ff b db bd b ff b db bd c b cgc bf gc ac b c ac db ca ac b ac ac b c ac bd gg ac b c ac fbeeeeeeeeeeecge c ebeeeeeeeeeegcee ca edbeeeeeeeeeceee ca eebfeeeeeeecgeee ca eeebeeeeeeeceeee ca eeeffeeeeeceeeee ca eeeebeeeegceeeee ca eeeeeeeeeeeeeeee eeeedbeeeceeeeee ca eeeeeeeeeeeeeeee d eeeeebdecgeeeeee cgeeeeeeeeeeeeeeee dbb eeeeeebeceeeeeee cgeeeeeeeeeeeeeee dbb eeeeeeffeeeeeeee cgeeeeeeeeeeeeee bb eeeeeegbeeeeeeee ecgeeeeeeeeeeeee bbd eeeeeecfbeeeeeee eecgeeeeeeeeeeebbd eeeeecgebdeeeeee eeecgeeeeeeeefbf eeeegceeebeeeeee eeeecceeeeefbfee eeeeceeeebfeeeee eeeeecceefbbeeee eeecgeeeeebeeeee eeeeeecgbbeeeeee eeeceeeeeefbeeee eeeeeebbceeeeeee eeceeeeeeeebeeee eeeebbdecceeeeee egceeeeeeeeebeee eebbfeeeecceeeee eceeeeeeeeeebfee fbfeeeeeeegceeee cgeeeeeeeeeeebee fbfeeeeeeeeeegceee aceeeeeeeeeeeefbe dbb eeeeeeeeeeeegcee c b dbb eeeeeeeeeeeeegce gc db bb eeeeeeeeeeeeeegc c bd bbd eeeeeeeeeeeeeeegc ca b bbd eeeeeeeeeeeeeeeeac ac ff fbd eeeeeeeeeeeeeeee ac c b fbf eeeeeeeeeeeeeeee ac gg db dbf ac c bdbb ac ca b ac ac ac c c cg ac c gc c ca ac c gg c ca ac c cg c ca ``` <!-- end of image --> Let's see what secrets area A holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#fcb0b2ff b,#0504feff c,#fe0909ff d,#8484ffff e,#c7c6feff f,#413af7ff g,#fe5d5eff ``` ```image fbf cc ebbe gcc dbf acca bbd gcg dbb acc fbd cca ebbe gcc fbf acca bbd ccg dbb acc fbd cca ebbe gcg fbf acca ebbe ccg dbb gcc bbd cca ebbe gcg fbf acc ebbe ccg dbf gcc bbdacca dbbgcg fbfc ebba gfbf accbbd ccgdbb gcc fbd cca ebbe gcg fbf acc bbd ccg dbb gcc fbd acca ebbe gcg fbf acc ebbe cca dbb gcc bbd acca ebbe ccg fbf gcc ebbe cca dbf gcg bbd acca dbbe ccg fbf gcc ebbe ``` <!-- end of image --> Success! This area contains an intersection point! Now, let's turn our attention to the next spot. Let's see if area B yields any clues. <!-- image --> ```palette Key,Color ,#fefefeff a,#ffb9b9ff b,#0404feff c,#fe0707ff d,#7f7fffff e,#c7c4fbff f,#4136f4ff g,#fc5456ff ``` ```image g cg ccg accg accg accg accg accg accg e accg efb accg efbbb accg dbbbde accg dbbbfe accg dbbbfe accc dbbbfe accc efbbbd accgfbbbd efbbbd dbbbfca dbbbfeccca dbbbfe ccca dbbbfe gcca efbbbd gcca efbbbd gcca efbbbd gcca dbbbd gcca bbfe gcca fe gcca gcca gcca gcca gcc gc g ``` <!-- end of image --> There's no doubt about it - this is an intersection in area B. I can confirm there's two intersections in there.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff9898ff b,#0404feff c,#ff0404ff d,#8b8bffff e,#ebd6e9ff f,#3c39fbff g,#fc4648ff ``` ```image e fd b db be eb bd b df be eb bd b ff b db bd b ff b db be ec eb cgc fd ac ac b c ac db ca ac be ec ac eb c ec bd gg ec b c ece df ca ece be ac ece eb c ece bd gg ce b ec ca ff ce ca b ac ca db c ca d bd ca ca dbf bec ca ebb ffe cg ebbe gb cg bbe cdb cg fbd ca be cg fbd ac eb cg dbf c fd cg dbf gg b cgbb ec db ebbg ce be bbe gc ac eb fbd gc c bd fbd gc ca b dbf gc ec df dbf gc ce be ebb gc gg eb ebbe ac c bd bbe ac ca b fbd ac ac ff fbd ac c b dbf ac gg db dbf ac c bdbb ec ce be ec ac ece c ec ca ec ce gg c ca ac c gg c ca ac c gg ec ce ``` <!-- end of image -->

I'm on the case! Let's uncover any intersections hidden in this image. I have a hunch that these areas might contain the intersections we're looking for. <!-- image --> ```palette Key,Color ,#fefefeff a,#fb0c0cff b,#6468e8ff c,#0909fcff d,#e8746aff e,#b1d7b1ff f,#99c498ff g,#efefeeff ``` ```image g gbccc bcccb bc gbccbg c ecccb bc bcccg cg gcccbg gc bcccb ce gbccbg gc bcccb cb gbcccg c ccb bb ffdafffffcfffffffffffffffffffffffffffffffffffff geeadaeeeebceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg geadeaaeeeeceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg gfaeeeafeeefceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg gafeeeeaeeeecfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg daeeeeedaeeeeceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg aeeeeeeeaaeeecbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg adeeeeeeeeadeeeceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg gageeeeeeeeeaeeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg aggeeeeeeeeefaeeeceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg da geeeeeeeeeeaaeebceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg a geeeeeeeeeeeadeeceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg ad geeeeeeeeeeeeaeebceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg ga geeeeeeeeeeeefaeecfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg ag geeeeeeeeeeeeedaeeceeeeeeeeeeeeeeeeeeeeeeeeeeeeeg da geeeeeeeeeeeeeeadecbeeeeeeeeeeeeeeeeeeeeeeeeeeeeg a geeeeeeeeeeeeeeeafeceeeeeeeeeeeeeeeeeeeeeeeeeeeeg ad geeeeeeeeeeeeeeeeaecbeeeeeeeeeeeeeeeeeeeeeeeeeeeg ga geeeeeeeeeeeeeeeedaeceeeeeeeeeeeeeeeeeeeeeeeeeeeg ag geeeeeeeeeeeeeeeeeadbceeeeeeeeeeeeeeeeeeeeeeeeeeg da geeeeeeeeeeeeeeeeeeafceeeeeeeeeeeeeeeeeeeeeeeeeeg a geeeeeeeeeeeeeeeeeeeabceeeeeeeeeeeeeeeeeeeeeeeeeg ad geeeeeeeeeeeeeeeeeeedacfeeeeeeeeeeeeeeeeeeeeeeeeg ga geeeeeeeeeeeeeeeeeeeeadceeeeeeeeeeeeeeeeeeeeeeeeg ag geeeeeeeeeeeeeeeeeeeeeacbeeeeeeeeeeeeeeeeeeeeeeeg da geeeeeeeeeeeeeeeeeeeeeeaceeeeeeeeeeeeeeeeeeeeeeeg a geeeeeeeeeeeeeeeeeeeeeedcbeeeeeeeeeeeeeeeeeeeeeeg ad geeeeeeeeeeeeeeeeeeeeeeeaceeeeeeeeeeeeeeeeeeeeeeg ga geeeeeeeeeeeeeeeeeeeeeeeebceeeeeeeeeeeeeeeeeeeeeg ag geeeeeeeeeeeeeeeeeeeeeeeeeceeeeeeeeeeeeeeeeeeeeeg da geeeeeeeeeeeeeeeeeeeeeeeeebceeeeeeeeeeeeeeeeeeeeg a geeeeeeeeeeeeeeeeeeeeeeeeeecaeeeeeeeeeeeeeeeeeeeg ad geeeeeeeeeeeeeeeeeeeeeeeeeefcdeeeeeeeeeeeeeeeeeeg ga geeeeeeeeeeeeeeeeeeeeeeeeeeecaeeeeeeeeeeeeeeeeeeg ag geeeeeeeeeeeeeeeeeeeeeeeeeeeecaeeeeeeeeeeeeeeeeeg da geeeeeeeeeeeeeeeeeeeeeeeeeeeecbaeeeeeeeeeeeeeeeeg a geeeeeeeeeeeeeeeeeeeeeeeeeeeeecadeeeeeeeeeeeeeeeg ad geeeeeeeeeeeeeeeeeeeeeeeeeeeeebcafeeeeeeeeeeeeeeg ga geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeceaeeeeeeeeeeeeeeg ag geeeeeeeeeeeeeeeeeeeeeeeeeeeeeebcdaeeeeeeeeeeeeeg da geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeceadeeeeeeeeeeeeg a geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefceafeeeeeeeeeeeg ad geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecfeaeeeeeeeeeeeg ga geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecedaeeeeeeeeeeg ag geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecbeaaeeeeeeeeeg da geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeceeadeeeeeeeeg a geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeaeeeeeeeeg ad geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeceedaeeeeeeeg ga geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebceeaaeeeeeeg ag geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeceeeadeeeeeg da geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebceeeaeeeeeg a geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecfeefaeeeeg ad geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeceeedaeeeg ga geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecbeeeadeeg ag geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeceeeeaeeg da geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecbeeefaeg a geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeceeeedag ad ffffffffffffffffffffffffffffffffffffffffbcffffag ga c ag ec cg gc cb c cb c bc c ``` <!-- end of image --> Time to investigate area A up close. <!-- image --> ```palette Key,Color ,#fefefeff a,#f83a41ff b,#5b55f8ff c,#0906fcff d,#fe8686ff e,#afacfcff f,#fe0405ff g,#ffc9c9ff ``` ```image dffa bcc ffffd cce dfadffg ecc gffg aff ccb afa afa ecc dff gffd bcb ffd dffg ecce dfa aff bcb gffg afa cce afa gffd bcc dff gffg cce ffd dffg ecc fa afa cce fg gffd ecc a gffd bcb dffg ecc afa bcb ffa ecce gffd bcb dffg cce afa bcc ffa cce gffd ecc dffg ccb aff ecc afa bcb gffd ecce dffg bcb dffg cce afa bcc gffd cce gffg ecc dffg ccb afa ecc gffd bcb gffd ecce dffg bcb afa cce ffa bcc gffd cce dffgecc aff ccb afaecc gffdbcb dffecce affbcb afacc gffbc dffce dfac afce gfcc gccb acc accb acce dcce bcc ccb eccd ccbg ecca bcca eccfd bccfg ccaf bccfa ccafd eccffg ccbffg eccafa bcbffd ecceffd bcbdffg cceafa bcc ffa ccegffd ecc dffg ccb afa ecc ffa bcb gffd ecce dffg bcb aff cce afa bcb gffd cce dffg ecc dffg cce afa ecc gffd bcb gffg ecc dffg bcb afa ecce gffd bcb gffd cce dffg bcc afa cce ffa ecc gffd ccb dffg ecc aff bcb afa ecce gffd bcb dffg cce aff bcc afa cce gffd ecc dffg ccb dffg ecc afa bcb gffd ecce gff bcb df ``` <!-- end of image --> Gotcha! I've found the intersection hiding in area A! The image features one single intersection point.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fa2b2fff b,#534ef9ff c,#0605feff d,#ff7c7cff e,#a8a7feff f,#fe0303ff g,#fecfd0ff ``` ```image bccc eccce bb bccbe c ecccb ec bccce c ebccb ec eccce ce bccb c eccce cb bccbe c ccb bb df c fdf ec ad aa c f fg ec fg f ce df gf c f aa ce ad fg c f f bb fg gf c df aa ec f fd c ad f ec f gf ce fg df c df fd ce f fg c ad gf bb f df c fg adbc df fgc f fec ad dfc gf aac fg fce df fc f gcb ad ac gf bb fg c df ec f ca ad ecd gf cag fg cf df cbf f cfd ad bbfg gf cgf fg ecdf df c aa f ec fg ad ce f gf c df fg ce aa da c fg f bb f ad c gf gf ec aa fg c fd da ec f f ce gf ad c da gf ce fd fg c fg da bb gf f c df ad bb a gf c fg ec c c ce c bb c bb c ``` <!-- end of image -->

I'm analyzing this image to identify any points where lines intersect. Let's take a closer look at what's happening inside these zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#f84d4aff b,#0a0afdff c,#f89f9cff d,#666cf2ff e,#fe0706ff f,#abd3abff g,#b7b7ffff ``` ```image c ce e ec aa g ce dbbg e dbd b e dbd b ea dbb gb ae dbb db e gbb db e gbb bb ec gbb bd aa gbb bd ce gbb bg e gbb b ec bbg b ea bbg gb ce bbg gb e bbg db e bbg bbffffffffffffeaf bbg bbffffffffffaeff bbd fbdffffffffcefff bd ffbdfffffffeffff fffbffffffecffff ffffbffffeafffff fffffbffaeffffff fffffdbfefffffff ffffffdbffffffff ffffffebbfffffff fffffaefbbffffff fffffefffbdfffff ffffefffffbdffff fffecffffffbffff ffeaffffffffbfff fceffffffffffbff fefffffffffffdbf efffffffffffffdb ea db ae bb e bd e bd ec bg ae b ce b e gb ec gb ea db ce bb e bd e bd ec bg ae bg ce b e ec cea ee cec ee aec cea ee cec ee aec ea ee cea ee aec ee ae cea ee cec ee aec ea ``` <!-- end of image --> Let's zoom in on area A to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#f7454cff b,#0505feff c,#fe9d9dff d,#8e8effff e,#fe0707ff f,#e5d6efff g,#3f3af9ff ``` ```image gbbf feec fgbg eea fbbg aee fbbg ceef fbbd ceec dbbd feea dbbd aea dbbf aeef gbbf ceec gbbf feec gbg eea fbbg aee fbbg ceef fbbd ceec dbbdfeea dbbaea dbbaf cgbbf feegbbf aea gbgf aeef fbbg ceec fbbg feec fbbg eea dbbd aee dbbd ceef dbbd ceec gbbf feea gbbf aea gbbf aeef fgbg ceec fbbg feec fbbg eea fbb ``` <!-- end of image --> My analysis confirms the presence of an intersection in area A. There's one and only one intersection present in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff4040ff b,#0b0afeff c,#ff8585ff d,#6e6effff e,#ff0505ff f,#ffc7c7ff g,#c2c2ffff ``` ```image c fe e ef aa g ce dbbg e dbd b ef dbd gb ec dbb gb ce dbb db fe dbb db e gbb bb ec gbb bd aa gbb bd fe gbb bg e gbbg bg ef gbbg b ea bbg gb ce bbg gb fe bbg db ef bbg bb ec bbd bd ae bbd bd fe bd bg e bg ef b aa gb ce gb e dbf ebb ae bb fe bd e bd ec bg aa b ce gb e gb ef db ea db ce bb fe bd e bd ec bg aa bg fe b e gb ef db ea db ce bb fe bd ef bd ec bg ae bg fe b e ef fea ee cec ee aef fea ee cec ee aef fea aef cec ee cec fea aef fea ee cec ee aef ea ``` <!-- end of image -->

Time to put on my detective hat and find those intersection points! The image has some tight areas where segments are too close. I should investigate those closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#fb0b0bff b,#0b0afaff c,#b1d7b1ff d,#ffbabaff e,#6a75e5ff f,#98c698ff g,#d36c66ff ``` ```image d ag afcccccccccccccccccccccccccccccccccccccccf gacccccccccccccccccccccccccccccccccccccccf fagccccccccccccccccccccccccccccccccccccccf fcaccccccccccccccccccccccccccccccccccccccf fcgacccccccccccccccccccccccccccccccccccccf fccafccccccccccccccccccccccccccccccccccccf fcccaccccccccccccccccccccccccccccccccccccf fcccaacccccccccccccccccccccccccccccccccccf beccccacccccccccccccccccccccccccccccccccccf bfcccfaccccccccccccccccccccccccccccccccccf fbccccagcccccccccccccccccccccccccccccccccf febccccacccccccccccccccccccccccccccccccccf fcbbcccgaccccccccccccccccccccccccccccccccf fccbecccagcccccccccccccccccccccccccccccccf fcccbecccacccccccccccccccccccccccccccccccf fccccbcccgaccccccccccccccccccccccccccccccf fccccfbcccafcccccccccccccccccccccccccccccf fcccccebccfacccccccccccccccccccccccccccccf fccccccbbccagccccccccccccccccccccccccccccf fcccccccbeccaccccccccccccccccccccccccccccf fccccccccbfcgacccccccccccccccccccccccccccf fcccccccccbccagccccccccccccccccccccccccccf fcccccccccebccaccccccccccccccccccccccccccf fccccccccccbbcgacccccccccccccccccccccccccf fcccccccccccbecafccccccccccccccccccccccccf fccccccccccccbfcaccccccccccccccccccccccccf fcccccccccccccbcaacccccccccccccccccccccccf fcccccccccccccfbcacccccccccccccccccccccccf fccccccccccccccebfaccccccccccccccccccccccf fcccccccccccccccbbagcccccccccccccccccccccf fccccccccccccccccbeacccccccccccccccccccccf fcccccccccccccccccbgaccccccccccccccccccccf fcccccccccccccccccfbagcccccccccccccccccccf fccccccccccccccccccebacccccccccccccccccccf fcccccccccccccccccccbbaccccccccccccccccccf bb fccccccccccccccccccccbgccccccccccccccccccf ebb fcccccccccccccccccccccbacccccccccccccccccf bbe fccccccccccccccccccccccbgccccccccccccccccf ebbc fccccccccccccccccccccccebccccccccccccccccf bbe fcccccccccccccccccccccccebcccccccccccccccf ebbe fccccccccccccccccccccccccbbccccccccccccccf bbb fcccccccccccccccccccccccccbecccccccccccccf ebbe fcccccccccccccccccccccccccgbcccccccccccccf bbb fccccccccccccccccccccccccccabccccccccccccf ebbe fcccccccccccccccccccccccccccgbcccccccccccf ebb fcccccccccccccccccccccccccccabbccccccccccf cbbe fccccccccccccccccccccccccccccabecccccccccf ebb fccccccccccccccccccccccccccccgabfccccccccf bbe fcccccccccccccccccccccccccccccagbccccccccfebbc fccccccccccccccccccccccccccccccaebcccccfbbe fccccccccccccccccccccccccccccccgaebccebbef fcccccccccccccccccccccccccccccccagbbbbcccf fccccccccccccccccccccccccccccccccacecccccf fccccccccccccccccccccccccccccccccgaccccccf fcccccccccccccccccccccccccccccccccaccccccf fcccccccccccccccccccccccccccccccccfagccccf fcccccccccccccccccccccccccccccccccccaagccf fcccccccccccccccccccccccccccccccccccccaagf fccccccccccccccccccccccccccccccccccccccfaad aad aad aad aad aad daad daad daa daa daa daa daa daa daa daa gaa gaa gaa ga ``` <!-- end of image --> Let's see if area A yields any clues. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd4d4fff b,#0908fdff c,#bcbafdff d,#fea5a6ff e,#5e5cfcff f,#fd0708ff g,#7e0e8dff ``` ```image fa ffd aff ffd dff afa ffd dff afa aff ffa dffd afa ff df aa e fd be ff bbc ffa ebbc dffd ebb aff bbe ffd cbbe dff cbbc afa ebbc ffd ebb dff bbe afa cbbe dffd cbc ffa ebc dffd bb afa bbe ffd cbbe dff cbbc afa ebbc ffd ebb dff bbe ffa cbbe dffd cbbc aff ebbc ffd ebb dff ebb afa bbe ffd cbbe dff cbbc afa ebbc dff ebb af cbbe dfd cbbc fa ebbc ffd ebb dff bbb afa bb ffd cbe dff cbc ffa bbcdffd ebb aff bbe ffd cbbedff cbbcafa ebbcffd ebbdff bbeafa cbbeffd cbbgff ebbffd ebbfa bbgfd cbbgf cbbga ebbfd ebbf bbba cbbgd cbbg ebb ebc bb cbe bbe gbbc dgbbc agbb fbbe agbbc fgbbc dfgbb afbbb ffbbe dfabbe ffgbbc dffebbc afaebb ffdbbe dffcbbe c afacbbc cebb ffdebbc cebbbb dff ebb ebbbbec afa bbb ebbbbec dffd bbbbbec aff cbbec ffa cc dffd ffd dff afa dffd dfffd ffffd dffffd dffffd dffff ``` <!-- end of image --> I've cracked the case! This area contains the intersection. The final count is: one intersection.

<!-- image --> ```palette Key,Color ,#fefefeff a,#f83339ff b,#0806fdff c,#b2b2feff d,#ffc2c2ff e,#5b55f8ff f,#fd0406ff g,#fc8184ff ``` ```image d ag f df fg f gf fd f aa bc f bc df b fg cb f eb gf be fd bc f b aa cb fd eb df be ag bc f b df b fg cb f eb ga be fd bc f b aa cb f ebdf befg bcf bgf bfd cbf eba cbb be ebbc bf cbbe bg ebbc cb bbe eb cbbc be bbe bc cbbc gb ebb fb cbbe ab ebb abb cbbe fbe ebbc dfbc cbbe fgb ebbc fcb bbe gfeb ebbc fdbbbe f c aa f dfg afg ffg ffd ffd ffd ffd ffd dffd dffd dffd dff dff dff dff dff gff gff gfa gfa gfa gfa gf ``` <!-- end of image -->

Time to put on my detective hat and find those intersection points! I've noticed 1 areas of interest. These could be potential intersection zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#0a09fdff b,#fe0808ff c,#f8a6a2ff d,#6165f7ff e,#a7aaf9ff f,#f95754ff g,#add4adff ``` ```image e ad a da a a ad cb a fbbcbf da bbf bb ae bbc bb gggagggggggggggg cbbc fbc gggadggggggggggg fbb bb ggggaggggggggggg fbf cbf ggggdagggggggggg bbf fbc gggggaggggggggcbbc bb ggggggagggggfbbg cbf ggggggadggfbbggg fbc gggggggabbfggggg bb ggggggbaaggggggg cbf gggcbbcgaggggggg bb gfbbggggeagggggg bb fbfgggggggadggggg fbc bbfggggggggggaggggg bb c ggggggggggdagggg cbf gggggggggggagggg fbc gggggggggggeaggg bb ggggggggggggadgg cbf a fbc dd bb a cbf ea fbc ae bb a cbf dd b a ea ae a ad a ea ae a ad a ea a a ad a da a a ad a da a ea ae a da daa eaae aad daa eaae aad daa eaae aad daa eaae aad daa eaae aad daa eaae aad da ``` <!-- end of image --> Here's a close-up of the area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0404feff b,#fd090aff c,#fc5e61ff d,#433cf8ff e,#cfcfffff f,#8f8fffff g,#fdb4b6ff ``` ```image faae dad eaae fad aaf faae dad eaae fad aaf faae gc dad gbbb eaae gbbbbc dad cbbbbc aaf gcbbbbg faa gcbbbcg dadbbbbcg caabbc gcbbdad gcbbbbgaaf gbbbbcg faa gbbbbcg dad cbbbbc eaae gcbbbbg dad bbbcg eaaf bcg faa daf eaae dad eaaf faa daf eaae dad eaaf ``` <!-- end of image --> Bingo! This close-up reveals an intersection in area A! One intersection, that's it, but I found it.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0a09fdff b,#ff0505ff c,#ff8888ff d,#6464ffff e,#b1b1ffff f,#ff4141ff g,#ffcacaff ``` ```image e ad a da ae a ad cb a fbfcbc da fbf bbg a gbbc gbf ea cbbg cbc ad cbb bb a fbf gbf da bbc fbc a gbbc bb ea cbbg gbf ae fbf fbg afbf bb gbaa cbc cbbg a fbg cbb ea gbb fbf ae cbc bbc a bb g dd gbf a fbc ea bb ae gbf a fbg dd bb a cbf ea fbg ae bb a cbc dd b a ea ae a ad a ea ae a ad a da ae a ad a da a ea ad a da a ea ae a da daa eaae aad daa eaae aad daa eaae aad daa eaae aad daa eaae aad daa eaae aad da ``` <!-- end of image -->

Based on a first glance, I suspect there could be intersection regions here. Could these regions be concealing intersection points? Let's find out. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0606ff b,#0506feff c,#f69c98ff d,#454af4ff e,#9b9ff6ff f,#f34848ff g,#acd4acff ``` ```image e c b aa be caca eb a a b ac a dd ca ac b a a be ac ff eb ca a b a ff dd ac a b fa ca be a a eb ac a b ff ac dd a a b a ff be ff a b a ca b a a eb ff ca b ca ac be a a b af ac b ca a eb a ff b e ac a dd dd ca ca b be a a be b ac ca eb b ca gggacgggggggbggg gdbggggggggggagg ggggaggggggddggg ggbdggggggggacgg ggggafgggggbgggg gggbgggggggfaggg gggggaggggbegggg ggggbggggggagggg gggggffggebggggg ggggebggggacgggg ggggggaggbgggggg gggggbdggfaggggg ggggggcaddgggggg ggggggbegagggggg gggggggabggggggg gggggggbaggggggg gggggggbfggggggg gggggggfbggggggg ggggggebacgggggg gggggggadbgggggg ggggggbggagggggg ggggggaggbdggggg gggggddggafggggg gggggffgggbggggg gggggbggggaggggg gggggagggggbgggg ggggbdggggffgggg ggggaggggggdbggg ggggbggggggagggg gggafgggggggbdgg gggbgggggggcaggg ggcagggggggggbeg ggdbggggggggaggg ggagggggggggggbg b a af eb be ac ca dd b a a be b ff ac b eb a ca b b cf a db bd a bd b ca b be ac b eb a eb b ac dd dd a be b ff b be a eb eb ca db b a be dd ca b b ac b be a eb eb ac bd b a be dd ff b b a eb be ca ddeb a bb ca d ac a fc a ff a ``` <!-- end of image --> This is a magnified view of the region A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0909ff b,#0404feff c,#f75a62ff d,#7979feff e,#bfbffeff f,#3833f9ff g,#feb5b5ff ``` ```image ebbe gaag dbbe aac fbf caa bbd gaag ebbe aac dbbe caa fbf gaag fbf aac ebbd caa dbbe gaag dbb aac fbf caa ebbd gaag ebbe aac dbbecaa fbfaag bbfc cbbd gacbbe aagfbb cac fbf gaa ebbd gaag ebbe cac dbbe caa fbf gaag bbd aac ebbe caa dbbe gaag fbf aac fbf caa ebbd gaag dbbe aac dbb ``` <!-- end of image --> My analysis confirms the presence of an intersection in area A. Onward to the next region of interest. Let's see if area B yields any clues. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0606ff b,#0806fdff c,#fb9396ff d,#514bf9ff e,#9292ffff f,#f94045ff g,#e2d1eeff ``` ```image faf bbe gaac dbb caf gbbg aac dbd caa ebbg aac bbe caag ebb faf gbbe gaag dbd faf ebbg gaac bbe caf ebb aac gbbe caa dbd facbbg cabbe dbb gbbfg dbbaf gbbgaac bbd caa ebb aac gbbe caa dbd fac gbbg caag dbd faf ebb gaag bbe faf dbd aac gbbg caa dbd aac ebbg caa bbe faf ``` <!-- end of image --> Aha! I've found an intersection inside area B! There are precisely two intersections present in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fe0505ff b,#0808feff c,#ff7f7fff d,#5b5bffff e,#b3b3ffff f,#fa3a3fff g,#ffc1c1ff ``` ```image d c b aa be gaca eb a ag b ac ga dd ca ag b a a be ac fc eb ca a b a cf dd ag a b ca ga be a ag eb ag ga b ff ac db a a b ag ff bd ff a eb ga cf b a a db ff ga b ga ag bd a a b ac ac be ga a eb a ff b e ac a bd db ga ca b be a a be b ac ga eb eb ca ag b db a a dd bd ag fc b be ca a be b a ff eb eb ag a b bd cf cadd be a ab bag bf fb ebag gadb b a ag bd dd fc ff b b a ga b be cf a db eb a ff bd b ga ga be db ag a b b ga ac eb bd ac ga db eb a a be b fc ac b db a ca eb b cf f db bd a bd b ga be be ag b eb a eb b ac bd dd a be b ff b be a eb eb ca db b a bd dd ga b b ag b be a db eb ac bd b a be dd ff b b a eb be ca dbeb a bb ga d ag a fc a cf a ``` <!-- end of image -->

I'm approaching this image with caution. Intersections might be tricky to spot. There are 1 regions I'd like to highlight in the image. <!-- image --> ```palette Key,Color ,#fefefeff a,#f55752ff b,#4f54f6ff c,#9a9ef7ff d,#fca6a4ff e,#fe0807ff f,#add4adff g,#0606feff ``` ```image d e ed e e de e ae e aa e ed e gg ed cgb de bgb e bgc de ggc e gg aa gg e cgg ed cgb e bgb ed bgc de ggc e gg ffffffffffffaeff gg ffffffffffffefff cgg fffffffffffaafff cgb fffffffffffeffff bgb ffffffffffeaffff bgc ffffffffffefffff ggc fffffffffedfffff ggggbc fffffffffeffffff ccbggggggbcc ffffffffefffffff cbgggggggbcffaefffffff ffcbbggggggbbcff ffffffaefffbbggggggbbc ffffffefffffffff cbbggggg fffffeafffffffff fffffeffffffffff ffffeaffffffffff ffffefffffffffff fffeffffffffffff ffdeffffffffffff ffefffffffffffff faefffffffffffff e aa e ed e ed de e de e aa e ed e ed de e de e aa e ea e ed de eeead e deeeed de daeeea e aeeead aa deeeed e daeeea aa aeeead e deeeed ed daee ``` <!-- end of image --> I'm analyzing this close-up of area A with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff5f5fff b,#4c4afcff c,#adabfdff d,#86148cff e,#fe0909ff f,#ffb1b1ff g,#0404feff ``` ```image eea fee eef aee eef aea feef aea fee eea fee eef aee eef aea feef aea fee ccc eea gggggbbbccc fee bbggggggggggggbdddc cccbbggggggggggggbbbccc cddbbbgggggggggggg aea cccbbbgggg feef c aea fee eea fee eea aee eef aee eef aea feef aea fee eea fee eef aee ``` <!-- end of image --> Oh my, look at that! It's an intersection in area A! One intersection, that's it, but I found it.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff4040ff b,#4646ffff c,#9898ffff d,#ff8585ff e,#ff0505ff f,#ffc6c6ff g,#0404ffff ``` ```image d e ed fe ef fe e da e aa e ed fe gb ef cgb fe bgc e bgc de ggc e gg aa gg e cgg ed cgb e bgb ef bgc fe ggc e gg de gg e cgg aa cgb e cgb ad bgc e bgc ef ggggbc fe ccbggggggbcc ef cbbgggggbbc de ccbggggggbcc da cbggggggbcc e ccbggggg ad e ed fe ef fe e da e aa e ed e ef fe e de e aa e ed e ef fe e de e aa e ad e ef f fe eeeaf ef daeeed de faeeedf e deeeaf da deeeed e faeeed ad fdeeeaf e deeead ed faee ``` <!-- end of image -->

This image seems promising for intersection detection. These zones are intriguing. I bet there's something interesting happening within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#3e45e7ff b,#f90d0cff c,#b2d7b2ff d,#a2cba1ff e,#7d8be1ff f,#d96f64ff g,#0506fcff ``` ```image eg g g cg cg g eg g ag ge ga ddddddddddddddddgdddddddgeddddddddddddddddddddddddddddddddddddddddd dccccccccccccccaaccccccccgecccccccccccccccccccccccccccccccccccccccc dccccccccccccccgccccccccccgcccccccccccccccccccccccccccccccccccccccc dcccccccccccccaaccccccccccdgccccccccccccccccccccccccccccccccccccccc dcccccccccccccgccccccccccccegcccccccccccccccccccccccccccccccccccccc dccccccccccccegcccdbccccccccagccccccccccccccccccccccccccccccccccccc dccccccccccccgcccbbbbccccccccgacccccccccccccccccccccccccccccccccccc dcccccccccccegcfbfccfbccccccccgeccccccccccccccccccccccccccccccccccc dcccccccccccgdbbcccccfbccccccccgecccccccccccccccccccccccccccccccccc dccccccccccdgbdcccccccdbdcccccccgcccccccccccccccccccccccccccccccccc dcccccccccfgfccccccccccdbfccccccdgccccccccccccccccccccccccccccccccc dcccccccdbbgcccccccccccccbfccccccegcccccccccccccccccccccccccccccccc dccccccbbdaaccccccccccccccbfccccccagccccccccccccccccccccccccccccccc dccccfbfccgccccccccccccccccbbccccccgacccccccccccccccccccccccccccccc dcccbbcccaacccccccccccccccccbbccccccgaccccccccccccccccccccccccccccc dcbbfccccgcccccccccccccccccccfbccccccgecccccccccccccccccccccccccccc fbbcccccegccccccccccccccccccccfbccccccgdccccccccccccccccccccccccccc bbcccccccgccccccccccccccccccccccfbdccccdgccccccccccccccccccccccccccc fbfdccccccegcccccccccccccccccccccccdbdccccegcccccccccccccccccccccccccc bb dccccccgdcccccccccccccccccccccccccbfccccagccccccccccccccccccccccccc bb dcccccdgcccccccccccccccccccccccccccbfccccggcccccccccccccccccccccccc fbf dcccccgeccccccccccccccccccccccccccccbbccccgaccccccccccccccccccccccc bb dcccccgccccccccccccccccccccccccccccccbbccccgecccccccccccccccccccccc bb dccccaacccccccccccccccccccccccccccccccbbccccgdccccccccccccccccccccc fbf dccccgcccccccccccccccccccccccccccccccccfbcccdgccccccccccccccccccccc bb dcccaaccccccccccccccccccccccccccccccccccfbdccegcccccccccccccccccccc fbc dcccgccccccccccccccccccccccccccccccccccccdbdccagccccccccccccccccccc bf dccegccccccccccccccccccccccccccccccccccccccbfccagcccccccccccccccccc dccgccccccccccccccccccccccccccccccccccccccccbfccgaccccccccccccccccc dcegcccccccccccccccccccccccccccccccccccccccccbbccgecccccccccccccccc dcgdccccccccccccccccccccccccccccccccccccccccccbbccgdccccccccccccccc dcgccccccccccccccccccccccccccccccccccccccccccccbbcdgccccccccccccccc dgecccccccccccccccccccccccccccccccccccccccccccccfbcegcccccccccccccc dgcccccccccccccccccccccccccccccccccccccccccccccccfbcegccccccccccccc aaccccccccccccccccccccccccccccccccccccccccccccccccdbdagcccccccccccc gccccccccccccccccccccccccccccccccccccccccccccccccccdbfgaccccccccccc eaccccccccccccccccccccccccccccccccccccccccccccccccccccbfgecccccccccc gdcccccccccccccccccccccccccccccccccccccccccccccccccccccbbgdccccccccc egdccccccccccccccccccccccccccccccccccccccccccccccccccccccbbgccccccccc g dcccccccccccccccccccccccccccccccccccccccccccccccccccccccbbgcccccccc g dccccccccccccccccccccccccccccccccccccccccccccccccccccccccffgccccccc g dcccccccccccccccccccccccccccccccccccccccccccccccccccccccccfagcccccc g dccccccccccccccccccccccccccccccccccccccccccccccccccccccccccfgaccccc ge dcccccccccccccccccccccccccccccccccccccccccccccccccccccccccccdgacccc g dcccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccgdccc ae dcccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc g dcccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc ea dcccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc g dcccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc eg dcccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc g dcccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc g dcccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc g dcccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc g dcccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc ge dcccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc g ddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddd ae g ea g eg g g g g ge g ae g ea g eg g ``` <!-- end of image --> Let's take a closer look at area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#3935faff b,#fd0709ff c,#ffaeaeff d,#c4c3fdff e,#7a7afeff f,#f74b53ff g,#0504feff ``` ```image gd dga eg dge dgg eggd age egg dgg agd age aa ga gge gd dgge ea egg gd egd ag fbbbc ga dgg bbbfbbc gga age cfbfc fbb dgg ge bbbf cbf egd dgdfbbc bbf ggd eabbc cbbf aggd gbbf cbb aga cbgg bbc dga cbfga fbbc dge fbbgge fbb gge cbbbdgg fbf eggd fbbc gg bbf ag cbbb ge cbbb aa cbbbc dgd cbbc dga fbbc ea bbc gge fbbc eg fbb egg cbbf gg fbf egd bbbf ega cbf ag fbbc age bbf ga bf age cbbc dgg c gg bbc dge ge bbc egd dgd fbbc ggd gd cbf aga eg cbf dgg gg bbf dge age bbc ggd dgg fbc eggd age bbc agg gg fbb ag dgd cbf dge ea bbf gge gd cbbb eggd eg cbbc egg egg bbc aa age fbbc ga gg fbb gge ge cbf dgg ae bbb egd dgd cbbb ggd eg bbc aga gg fbc aga ggd fbb dge egg cbf dge age cbf ggd ge cbbb agg dg bbc ag ae fbcdga dgd bbcdge gg fbbegg ga cbfegd gd cbfag g bbbga fbgge bfgg fbfgd fbagd cgga bgga cfgg fge gg ad ``` <!-- end of image --> Yes! I knew it! There's an intersection right here in area A! There are precisely two intersections present in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#3f3cfcff b,#fe0505ff c,#ffa7a7ff d,#c5c4feff e,#837ffbff f,#f94247ff g,#0505feff ``` ```image d egd g g dg dg gd eg g ag gd ga g ge ae gd g g ea dg g eg ea cf ag g bbfb ga dg fbc fb ge gdbf cb gd gb cb g cge bc dg bbg bc eg fbcae bf ag cbf g bf aa bb ea fb ge fbc g fb gd cbf eg cb g bb g cb dg fbc dg bc dg cbf gd bc eg bb g bf aa cbc gd bf ge bb g bb gd fbc ae fb gd cbf g cb g bb ea cb dg fbc g bc eg bf eg bc aa g bf ga dg bf ge gd bb gd g fb g gd fb dg g cb eg ae cb ag g bcga ea bcge g bfgd eg bfg g ffg dg ffg gd cag g cga ge ge g g ae g ea g eg g dg gd g ge g ae g ea g dg g dg gd g ge g ae g ea g dg g ``` <!-- end of image -->

I'm ready to tackle this image and find those intersections! Let's take a closer look at what's happening inside these zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#595cf2ff b,#fe0201ff c,#0707fdff d,#eb9c93ff e,#f73231ff f,#b1b2feff g,#afd6afff ``` ```image fc cfc fc cf c c c ac cf cf c c aa ac c cf aa c c aa fc c c fc fc ca cf c c fc cf ca c c aa fc c cf aa c c ac fc cf c c fc ac cf cf c c cf aa c c aa fc c ca aa c c fc fc cf c c fc fc cf cf c c cf ac c cf aa c c aa aa c c c fc aa c c fc fc cf ca c c cf fc c cf aa c c ac aa ggggcagggggggggggg c gggggcgggggggggggg fc gggggacggggggggggg c ggggggcggggggggggg fc gggggggcgggggggggg ggggggggggggcggggg gggggggacggggggggg ggggggggggggcggggg ggggggggcggggggggg gggggggggggcaggggg gggggggggcgggggggg gggggggggggcgggggg gggggggggcaggggggg ggggggggggaagggggg ggggggggggcggggggg ggggggggggcggggggg gggggggggggcgdgggg gggggggggacggggggg gggggggggdecabgggg gggggggggcgggggggg gggggdebbbdgcggggg ggggggggacgggggggg gdebbbdgggggacgggg ggggggggcggggggggg debbbdggggggggggcgggg gggedgggcggggggggg debbed gggggggggggggggggg gggdebbceedggggggg debbed gggggggggggggggggg gggggggcgdebbbbedg debbed gggggggggggggggggg ggggggcagggggggdebbbbed debbed gggggggggggggggggg ggggggcggggggggggg debbbbed debbed gggggggggggggggggg gggggaaggggggggggg debbbbed debbed gggggggggggggggggg gggggcgggggggggggg debbbbebbed gggggggggggggggggg ggggacgggggggggggg d gggggggggggggggggg ggggcggggggggggggg gggggggggggggggggg gggacggggggggggggg gggcgggggggggggggg gggggggggggggggggg gggggggggggggggggg gggggggggggggggggg ``` <!-- end of image --> Let's zoom in on area A to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#8989ffff b,#fc0507ff c,#0404feff d,#ffb1b1ff e,#ff5959ff f,#cacaffff g,#453ef8ff ``` ```image fccf gcg fccf acg ccf acg cca acc gca fcc gca fccf gcg fccf acg ccf acg cca acc gca fcc gca eedd fccf dbbbbbbeegcg deebbbbbccbbeedd ddgcgbbbbbbbbeedd ccf ddeebbbbbbbbbeedd acg ddeebbbbbbb cca ddeeb acc gca fcc gca fccf gcg ccf acg ccf acg cca acc gca fcc aa ``` <!-- end of image --> My analysis confirms the presence of an intersection in area A. Onward to the next region of interest. This close-up might reveal an intersection in area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#7b7afeff b,#fe0505ff c,#0605feff d,#ffa1a1ff e,#f9474cff f,#bebcfcff g,#423bf8ff ``` ```image acc gcg fccf acc gca fccf acc cca fccf gcg cca fccf gcg cca acc gcg fccf acc gcg fccf acc gca fccf dd accebbe ddebccgbbe ddebbbbbeccf ddebbbbbbed gcg ddebbbbbbed cca ddebbbbbbed fccf ebbbbbbed gcg bbbed ca d ``` <!-- end of image --> I can confirm that an intersection exists in area B. There are precisely two intersections present in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#8383ffff b,#fd0203ff c,#0505feff d,#ffa6a6ff e,#ff3737ff f,#c5c5ffff g,#413efbff ``` ```image f ac cac fc ca cf c c ac cf cf c c ga gg c cf ag c c gg ag c c fc fc ga cf c c fc cf ca c c ga ac c ca ag c c ac ac cf c c fc gg cf cf c fc cf gg c c ga fc c ga ag c c fc ac ca c c fc ac cf cf c c ca ac c cf ga c c gg ag cf c fc ac gg c c fc fc cf ca c c ca fc c ca ga c c ac ag cf c c ac ac c cf fc c cf gg c cf ca fc c gg ga c c fc d ag decgb c debbbd c fc debbbd ac c debbbd c ed fc debbed debbcbed debbed c debbbbed debbed ca debbbbed debbed c debbbbed debbed ga debbbbed debbed c debbbbebbed ag d c fc c ``` <!-- end of image -->

I'm analyzing this image to identify any points where lines intersect. My final answer is: no intersections found.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0505ff b,#0808ffff c,#ff8f8fff d,#5b5bffff e,#b4b4ffff f,#ff4a4aff g,#ffc7c7ff ``` ```image e bbb bd ebd be dbe be bb eb ebb eb dbd db bbe db bb bb ebd bb dbe bd bb bd ebb be dbd ebe bbe eb bb eb ebd db dbe db bb bb ebb bd dbd bd bbe be bb be ebd eb dbe eb bb db eb db bb bb bd bd be be faa ca caa ca gaag ga gaag a aac ag aac ag faf ac faf af caa af caag fa gaag fa gaac ca aac ga faf ga faf a faf ag caa ag caag ac gaag af gaac af aa fa fa ca ga ga a ag ag ac af af fa fa ca ga ga a ag ag ``` <!-- end of image -->

I'm ready to tackle this image and find those intersections! These zones indicate regions where lines appear to be in close proximity. <!-- image --> ```palette Key,Color ,#fefefeff a,#f15e57ff b,#0405fdff c,#fe0908ff d,#5156f5ff e,#feb9b9ff f,#8d94f0ff g,#afd6afff ``` ```image a ec c c ce ca cc ac ec c ce ce ca ac ac ec c ce ce ca ac ec ec c ce ca ca ac ec ec c ce ca cc ac ec c c ce ca ac ac ec c ce ce ca gggggggggggggggggggggg ac gggggggggggggggggggggg ec gggggggggggggggggggggg ec gggggggggggggggggggggg c gggggggggggggggggggggg ce gggggggggggggggggggggg cce gggggggggggggggggggggg ecce gggggggggggggggggggggg ecce gggggggggggggggggggggg ecce gggggggggggggggggggggg ecc ggggggggggggggggggggggecc ggggggggggggggggggggacc b ggggggggggggggggggaccg bbbf ggggggggggggggggaccggg dbbf ggggggggggggggacaggggg dbbf ggggggggggggacaggggggg dbbf ggggggggggccaggggggggg dbbf ggggggggccaggggggggggg dbbf ggggggccaggggggggggggg dbbf ggggccaggggggggggggggg dbbf ggccaggggggggggggggggg dbbd eccgggggggggggggggggggg dbbd cgggggggggggggggggggggg dbbd gggggggggggggggggggggg fbbd gggggggggggggggggggggg fbbd gggggggggggggggggggggg fbbd gggggggggggggggggggggg fdbbbd gggggggggggggggggggggg fdbbbbdf gggggggggggggggggggfdbbbbbf gggggggggggggfdbbbbbdg ggggggggdbbbbbdfgggggg ggdbbbbbdfgggggggggggg bbbdfgggggggggggggggggg gggggggggggggggggggggg gggggggggggggggggggggg ``` <!-- end of image --> This close-up might reveal an intersection in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff7a7aff b,#0606ffff c,#ff0404ff d,#5a5affff e,#ffbdbdff f,#ababffff g,#ff3b3bff ``` ```image ac accc acccge acccge acccge eacccge egcccge egcccge egcccge egcccae egcccae egccca egccca agccca acccca acccca acccca acccge acccge acccge eacccge cccge cge ffdd ffddbbbbbb ffddbbbbbbbbbddf ffddbbbbbbbbbddff ffddbbbbbbbbbddff ffddbbbbbbbbbddff fddbbbbbbbbbddff fdbbbbbbbbbddff bbbbbddff dff ``` <!-- end of image --> After careful examination, I've determined that there's no intersection in area A. I did not find anything, there's no intersections

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff7f7fff b,#0808ffff c,#ff0404ff d,#6a6affff e,#ffc1c1ff f,#c1c1ffff g,#ff3e3eff ``` ```image a ec ec c ce ca gg ac ec c ce ce cg gc ac ec c ce ca cg gc ac ec c ce ca gg gc ec ec c ce ca gg ac ec c ce ce cg gg ac ec c ce ca cg gc ac ec c ce cce ecce ecce ecce ecc acc acc fb acg fbbbf acg fbbbf gcg bbbf gcg dbbd gca dbbd gca dbbd cca dbbd cca dbbd cce dbbd ecce dbbd ce dbbd dbbd dbbd dbbd fdbbbd fdbbbbbd fdbbbbbdf fdbbbbbdf fdbbbbbdf fdbbbbbdf bbbdf ``` <!-- end of image -->

This image might have some surprises. Let's look for intersections carefully. The image is completely devoid of intersections. Zero.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0404ff b,#0505ffff c,#ff7d7dff d,#a4a5ffff e,#ff3737ff f,#ffc2c1ff g,#5353ffff ``` ```image dd gbbbbbbbbbbbbbbbbbgggdddd ddddgggbbbbbbbbbbbbbg gbbg dbbbd dgbbg gbbgd dbbbd gbbg gbbbd dbbbd gbbg dbbbd dbbbg gbbg dbb ca afaf af af ac af ca af fa af a ac ac ac ca ac fa ac a ae ac ae ca ae fa ae a ea ac ea ea ea fa ea a ea ac ca ee ca fa ca a ca ac fa ee fa fa fa a fa af faf ee af fa af a af af af ee ac fa ac a ac af ac ee ae fa ae a ae af ae ee ee fa ea a e af ee ca a af ``` <!-- end of image -->

I have an image in front of me. I need to determine if there are any intersection segments. There are 1 regions I'd like to highlight in the image. <!-- image --> ```palette Key,Color ,#fefefeff a,#0606fdff b,#fe0504ff c,#a6a9f9ff d,#fa4b49ff e,#f9a09eff f,#5458f7ff g,#acd4acff ``` ```image c cfaaaaaf cffaaaaafc cfaaaaaafc cffaaaaafcc cfaaaaaafc faaaaafcc ff a af a ac a ac ca a ca a ca a ff a ff a af a ac a ac ca a ca a ca a ff a ff a ggggggggggggafgg ggggggggggggaggg gggggggggggafggg gggggggggggagggg d ggggggggggacgggg ebb ggggggggggaggggg ebbegggggggggagggggg ebbeggggggcagggggg gbbdggggaggggggg gggbbdgfaggggggg gggggdbagggggggg ggggggfabbgggggg ggggggaggebbgggg gggggffgggggbbeg gggggaggggggggbbe ggggafggggggggggdbd ggggaggggggggggg dbd gggafggggggggggg ebb gggagggggggggggg ebbe ggacgggggggggggg ebbe ggaggggggggggggg bbe gagggggggggggggg dbd ca dbb a ebbe ca bbe a dbd ff ebb a ebbe ff bbd a dbd af ebbe a ebbe ac dbd a dbb ac ebbe bbe dbd ebb ebbe bbd db ``` <!-- end of image --> This close-up might reveal an intersection in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0505feff b,#fd090aff c,#8585ffff d,#fd6162ff e,#feb3b3ff f,#443df8ff g,#c7c7ffff ``` ```image fac caa aac caa aac caf aag caf gaag faf gaag faf e gaag bde fac bbbbe gaa dbbbbe fac dbbbbd caa ebbbbd aac ebbbbde caa edbbbdeaac edbbfaa daabbe cafbbbbd gaag ebbbbd faf ebbbbde gaag edbbbde faf edbbbbe gaag dbbb fac db gaa fac caa aac caa aac caf aag caf gaag faf gaag faf ``` <!-- end of image --> Wow! I can see an intersection so clearly in area A! One intersection, that's it, but I found it.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0404ffff b,#ff0808ff c,#8585ffff d,#ff6262ff e,#ffb4b4ff f,#4140feff g,#c5c5ffff ``` ```image g gcfaaaaaf gcfaaaaafcg gcfaaaaafcg gcfaaaaafcg cfaaaaaacg faaaaafcg ff a fc a ac a ag ga ag ga a ca a cf a ff a fc a ac a ag ga ag ga a ca a cf a ff a fc a ac a d ag dbb ga ebbe ag ebbe ga bbd a bbd ca dba cfbb a ebbe ff ebbe a bbd fc bbd a dbb ac dbb a ebbe ag ebbe ga bbd ag bbd ga dbb a ebbe ca bbd a dbd cf dbb a ebbe ff bbd a dbb fc ebbe a ebbe ac bbd a dbb ag ebbe bbd dbd dbb ebbe bbd db ``` <!-- end of image -->

This image seems promising for intersection detection. These spots are like clues. Let's see what they reveal about potential intersections. <!-- image --> ```palette Key,Color ,#fefefeff a,#3f41eaff b,#fc0a09ff c,#0505fdff d,#e45e57ff e,#b1d7b1ff f,#808edfff g,#d9aa98ff ``` ```image eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeee eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefceeee eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecgeeee eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecdeeeee eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecaeeeeee eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeacdeeeeee eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefcbeeeeeee eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecbeeeeeeee eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecddeeeeeeee eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecabeeeeeeeee eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeacbeeeeeeeeee eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefcdbeeeeeeeeee eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecebeeeeeeeeeee eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecfbgeeeeeeeeeee eeeeeeeeeeeeeeeeeeeeeeeeeeeeeecadbeeeeeeeeeeee eeeeeeeeeeeeeeeeeeeeeeeeeeeeeacebeeeeeeeeeeeee eeeeeeeeeeeeeeeeeeeeeeeeeeeeecebdeeeeeeeeeeeee eeeeeeeeeeeeeeeeeeeeeeeeeeeecegbeeeeeeeeeeeeee eeeeeeeeeeeeeeeeeeeeeeeeeeecfebeeeeeeeeeeeeeee eeeeeeeeeeeeeeeeeeeeeeeeeecaebdeeeeeeeeeeeeeee eeeeeeeeeeeeeeeeeeeeeeeeefcegbeeeeeeeeeeeeeeee eeeeeeeeeeeeeeeeeeeeeeeeeceebeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeeeeeeeeeeeceedbeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeeeeeeeeeecfeebeeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeeeeeeeeeaaeebgeeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeeeeeeeefceedbeeeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeeeeeeeeceeebeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeeeeeeeceeebdeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeeeeeecfeegbeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeeeeeaceeebeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeeeefceeebdeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeeeeceeegbeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeeeceeeebgeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeecaeeedbeeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeaceeeebeeeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeeefceeeebgeeeeeeeeeeeeeeeeeeeeeeeee cc eeeeeeeeeeeeeceeeedbeeeeeeeeeeeeeeeeeeeeeeeeee fca eeeeeeeeeeeecfeeeebeeeeeeeeeeeeeeeeeeeeeeeeeee fca eeeeeeeeeeecaeeeebdeeeeeeeeeeeeeeeeeeeeeeeeeee acf eeeeeeeeeeaceeeegbeeeeeeeeeeeeeeeeeeeeeeeeeeee acf eeeeeeeeefceeeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeee cc eeeeeeeeeceeeeebdeeeeeeeeeeeeeeeeeeeeeeeeeeeee cc eeeeeeeecfeeeegbeeeeeeeeeeeeeeeeeeeeeeeeeeeeee ecc eeeeeeecaeeeeebgeeeeeeeeeeeeeeeeeeeeeeeeeeeeee fca eeeeeeaceeeeedbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee fca eeeeefceeeeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee acf eeeeeceeeeeebgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee acf eeeecfeeeeedbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee cc eeecaeeeeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee cc eeaceeeeeebdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee cc efceeeeeegbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee fca eceeeeeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee fca cfeeeeeebdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee acf caeeeeeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee acffceeeeeeebgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee cc eeeeeedbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeeebgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeedbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeebdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eegbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee ebdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee ebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee bgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee dbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee beeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee bg gbbb dbbbg gbbbd dbbbg gbbbd dbbbg gbbbd dbbbg gbbbd dbbbg bbd ``` <!-- end of image --> I'm focusing my attention on this specific region, area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#5650f9ff b,#fe4344ff c,#0807fdff d,#fe8485ff e,#fd0506ff f,#acacfeff g,#fec6c7ff ``` ```image g ac fca cc acd fccg cca cce fceb cceg ace acee fcced caeg acbe cceed fcaeb cadeg accbe ccfee ca de ac geg cc be fca eed cc eb ccf ed fcf be ca ee cc de fcf geg cc dee cca eed cc eb fcf ed cc de ac ed fcf de cc geg aa dee ac eed ccf geg ca ed ac ee cc eb fcf de ac be acc ee fca bb ca geg ac ee fcf eeg fca eb acc ged ccf be fcf ee cc bb cc geg fcf dee cc eeg cca eb fcf ged fcf be ca ed ac bb fcf geg ca dee aa eeg fcc de ccf ged ca be ac ed cc bb ca ee ac dee acc eeg fcf de ca ged c ee f ed db be ee bb deg ee eeg ed geg be ee bb deg beb eeg ed eg ``` <!-- end of image --> My analysis confirms the presence of an intersection in area A. I've found a single intersection point in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#6260fcff b,#f9282dff c,#0b09fdff d,#ff6d6dff e,#fe0202ff f,#b4b3feff g,#feb7b7ff ``` ```image a fc cg cb cc acg fce ce cbd cae ace fcbb c e cfeg cadb ac e fc eg c ge cf e ca bd ac ge c e c db cf e cc eg fc de c e c ed ca ge ac e fc bd c ge cf e ca db ac e fc eg cc c de fcc cf e aca ca ed aca ac ge ccf fc e ccf c bd cc cf e fcc ca eg fcc ac db aca fc e aca c eg ccf cf de ccf ca e cc ac ed fcc fc ge fcc c e aca cf bd aca ca e ccfac eg cc db e eg ge e bd ge e bb e eg db e eg gbee deebg gbeed deebg gbeed deebg gbeed deebg gbeed deebg eed ``` <!-- end of image -->

Time to put on my detective hat and find those intersection points! These zones are intriguing. I bet there's something interesting happening within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#0707fdff b,#fb0a09ff c,#545bf2ff d,#e16761ff e,#b9b9feff f,#b1d7b1ff g,#97c29aff ``` ```image e eae a ae ea a ae ea gfffffffffffgaffffgaffffffffffffffffffffffffffg gfffffffffffagfffffgaffffffffffffffffffffffffff gfffffffffffafffffffcafffffffffffffffffffffffff gffffffffffacffffffffcaffffffffffffffffffffffff gffffffffffaffffffffffcafffffffffffffffffffffff gfffffffffccfdbbdffffffcaffffffffffffffffffffff gfffffffffabbbgfdbbfffffaafffffffffffffffffffff gfffffffddadffffffdbbdfffaaffffffffffffffffffff gffffdbbdafffffffffffbbbffacfffffffffffffffffff gfdbbbffgafffffffffffffdbbgacffffffffffffffffff bbbgffffagfffffffffffffffgbbacfffffffffffffffff dbbdfffffffafffffffffffffffffffdadffffffffffffffff dbbd gffffffacfffffffffffffffffffffabbdfffffffffffff fbbd gffffffafffffffffffffffffffffffagbbbfffffffffff bbb gfffffacffffffffffffffffffffffffaffdbbgffffffff dbbd gfffffafffffffffffffffffffffffffgafffgbbdffffff dbbd gffffccffffffffffffffffffffffffffgafffffdbbffff fbbd gffffaffffffffffffffffffffffffffffgaffffffdbbdf bb gfffcafffffffffffffffffffffffffffffcaffffffffbbb fgggagggggggggggggggggggggggggggggggcagggggggggdbbf ea ca bbd ae ca dbb a aa fbbd ae ac bb a ac cc ac a ae cc ae a ae ea ae a a ea ea ae ea a ea ae ea a ca cc ca a ca cc aa a ac ea ac a ac ea a ae a ae a cc a cc a ea a ea ae a ae a cc a cc a ea a ea ae a ae a cc a cc a ea a ``` <!-- end of image --> Let's zoom in on area A to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#0606feff b,#fe0808ff c,#a19efbff d,#fe5d5eff e,#9e0262ff f,#feb1b1ff g,#4c4bfdff ``` ```image aa aag gag aag aac caag cag caag aac caag caa caac aac caac caa caac gac caac caa gaac gag gaac aa ff gaac gag fdbbbbdf gaa aacfdbbbbbbbbbdf gaa cagbbbbbdf fdbbbbd gaa faaebbdf dbbbbdf aag fdbeaadf fdbbbbf aag fdbbbbaac fdbbbbdf aag fbbbbbdcaa fbbbbdf caag fdbbbbdf gac fdbbbbd caag fdbbbbdf caa dbbbbdfcaag fdbbbbbd gag fdbbbbcaac fbbbbbdf aa fdbbbeaac bbbdf gag fbbeaac df aac fdeaaed cag gaaebdf aac gaaebbbf caa gaadbbbbdf aac gaa fbbbbdf caa gaa fdbbbbd gac aaa dbbbbdf caa aag fdbbbbf gag aag fdbbbbdf aa aag fbbbbdf gag caag fdbbbbd aac caag dbbbbdf cag caag fdbbbbf aac caac fdbbbbd caa caac fbbb aac caac fd ``` <!-- end of image --> Gotcha! I've found the intersection hiding in area A! There's for sure two intersections on the image you sent me.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0605feff b,#fd0405ff c,#8080ffff d,#f8444bff e,#c4c4feff f,#ffa4a4ff g,#4141ffff ``` ```image e cae a ae ea a ae ea a ea ae ea a ca gc ca a ga cg fbbd ga adbbf dbb ga ddaf fbbf ag fbbda dbd ag fbbd ea fbbfac dbbf ae bbac dbbf a dad fbbd ae abbf fbbd a aedbd dbbf gc a fbbf dbbf a ea bbd fbbd cg ea dbb fbbd a ea fbbf bbf ca ca dbd a ca fbbf ea ga bbd ae ga dbb a gg fbbf ae ag db a ag gc ac a ac cg ae a ae ca ae a a ea ea ae ea a ea ae ca a ca gc ga a ga cg ag a ag ca ag a ac ea a ae a ac a gc a cg a ca a ea ae a ac a gc a cg a ea a ea ae a ac a gc a cg a ea a ``` <!-- end of image -->

The hunt for intersections begins! Let's analyze this image closely. I did not find anything, there's no intersections

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0606ff b,#0404ffff c,#ffaeaeff d,#7878ffff e,#ff5555ff f,#bfbfffff g,#3737ffff ``` ```image f gb db db fb db fb bb fbf fbd bf gb bf fbg bd gb bd bg bg dbf bg bg bg dbf gb bb gb fbd db bb db fbd fb gb fb bg fbf gbf bf bg bf dbf bd bb bd dbf bg bb bg fbd bg gb gb fbd gb gb db bg db dbf fb bg fbdbf fb a eac aa cac aa cac aa cae ea ae eac aa eac aa cac aa cae aa ae ea ae eac aa cac aa cac aa cae aaaaaaaaeeeccc ea ccceeeaaaaaaaaaaaaeeeccc ae ccceeeaaaaaaa ``` <!-- end of image -->

I'm approaching this image with caution. Intersections might be tricky to spot. Zero, Nada.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0606ff b,#0606ffff c,#ff9090ff d,#5959ffff e,#ffd1d1ff f,#ff4545ff g,#aeaeffff ``` ```image c ea ae ff ea a ac ca a ac fa a ae ff ea a af ca a ac ca a ae ff ea ae ff ea a ac ca a ac ae ca eac a af ae aa ff fa ea cae ae eac af af ea aa a fa ac cae ca eac a af ac aa fa fa a ca ae eae ff af ea aa a fa af ca ca eae a ac ac af ca fa a ca ae eae ff ac ea af ae faff ca ggdddbbbbbbbddggg gggddbbbbbbbbbbbbddggg ggdddbbbbbbbbbbbddggg ddbbbbbbbbbbbdddgg ggdddbbbbbbbbbbbddggg ggg ggdddbbbbbb ``` <!-- end of image -->

Alright, let's get to work and investigate this image for intersections. The image has some tight areas where segments are too close. I should investigate those closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#0808fcff b,#fd0506ff c,#f3908bff d,#a6abf5ff e,#5158edff f,#ef4941ff g,#aed5aeff ``` ```image c fc b cb b b bc b cb b b bc b cf b b bc b ff b cb bc b ff b cb bc b ea ff da a b a da cb ad ea bc ea ae b da ad ff a a gggbgggggggggaeg a gggcbgggggggeagg da ggggbcggggggaggg ea gggggbgggggagggg ae gggggffgggaegggg ad ggggggbggeaggggg a ggggggcbgagggggg da gggggggbadgggggg da gggggggaaggggggg ea ggggggdabfgggggg ae ggggggaggbgggggg ad gggggaeggfbggggg a ggggeaggggbggggg da ggggaggggggbgggg ea gggagggggggbfggg ae ggaeggggggggbggg ad geagggggggggfbgg a a b a a b da ae bc ea da b ae a cf gggaeggggggggggggggggg ad b ggggaggggggggggggggggg ee b gggggagggggggggggggggg da bc gggggeaggggggggggggggg a b ggggggeagggggggggggggg ad fbcc gggggggaeggggggggggggg ea ccfbbbbbbbfcc ggggggggadgggggggggggg da ccfbbbbbbbffcggggggagggggggggggg a gcffbbbbbbbafcggggggggg ad ggggggggggeafbbbbbbbffc ea gggggggggggaagggggggcffb a ggggggggggggaegggggggg a gggggggggggggadggggggg ae ggggggggggggggaggggggg da ggggggggggggggdagggggg a gggggggggggggggeaggggg ad ggggggggggggggggaagggg ae gggggggggggggggggaeggg da ad a a ad da ea ae ad a ``` <!-- end of image --> I'm determined to find out if an intersection exists in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0806fdff b,#fe0708ff c,#feadadff d,#8787feff e,#4747feff f,#f95055ff g,#c6c6feff ``` ```image fbf eaa cbbc daag fbb gaad bbc eae cbb daa fbf gaag cbbc aad fbb eae bbc daag cbb gaad fbf aae cbbc eaa fbf daag bbc gaad cbb aae fbfeaa cbfaag faad eaac daabb gaagbbf aad cbbc eae fbf daag bbc gaad cbb aae bbf eaa cbbc daag fbf gaad bbc aae cbb eaa bbf daag cbb gaad fbf eae bbc daa fbb ``` <!-- end of image --> Area A contains an intersection. Alright, let's concentrate on the next area. I'm now examining the contents of area B in detail. <!-- image --> ```palette Key,Color ,#fefefeff a,#0909feff b,#ff0101ff c,#fc7174ff d,#babaffff e,#5e59faff f,#f32b37ff g,#ffc0c0ff ``` ```image daad eaad eaa aaa aae daae daad eaad eaa aae daae daae daad eaad bffcccggg eaa bbbbbbbbbbbffcccggg aae gggcccffbbbbbbbbbbbbfaaeccggg gggcccffbbbfaafbbbbbbffcccggg ggeaacffbbbbbbbbbbbbbffcc eaad gggcccffbbbbbbb eaa gggcc aae daae daad eaad eaa aaa aae daae daad eaad eaa aae daae ``` <!-- end of image --> I can confirm that an intersection exists in area B. Two intersections have been found!

<!-- image --> ```palette Key,Color ,#fefefeff a,#0807feff b,#fe0506ff c,#fe8989ff d,#a6a6ffff e,#5351fdff f,#ff4040ff g,#efd6e5ff ``` ```image g fc b cb bg gb bc b cb bg gb bc b cf bg gb bc b ff b gb bc b ff b gb bc g b eag ff daga b a da cb ad ea bg ea ae b ga ad ff a ag b ad ga cb ea da bg ga ea b ag ae ff ae ad b da a cb a ga bad da ea ea dafc ae a b ad ad cb a ea bg da ga gb ea a bc ae ad b ad ea cb ag ga bg a ag gb da ae bc ea da b ae a cf ad ad bg ag ee gb ga da bc da a b ea ad fbccg ae ea ccfbbbbbbbfccg ad ga gccfbbbbbbbfccg a a gccfbbbbbbbaccg ad geafbbbbbbbfccg ea ea gccfb ga ae ag ad ae a da da a ea ad ae ee ad da ag a a ad da ea ae ad a ``` <!-- end of image -->

I'm approaching this image with caution. Intersections might be tricky to spot. There are 1 areas where the lines seem to converge. We should take a closer look at area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0809feff b,#fc0b0aff c,#95a2e5ff d,#ed7974ff e,#5759f1ff f,#b1d7b1ff g,#96c995ff ``` ```image c ae a ca ac a ee a ca ac a ea a a ae a a ac ca ac ac ac a ac ee ac a ac ca ac ac ae a ae ea ae a ae a ae ae ae a aa ca aa ac aa a aa ee ea a ea ca ea ac ea a fgggggggggggggggggggggggggggggg ea eagffffffffffffffffffffffffffffff ea agffffffffffffffffffffffffffffffca afffffffffffffffffffffffffffffea aefffffffffffffffffffffffffffca gaffffffffffffffffffffffffffcaf geaffffffffffffffffffffffffcaff gfacffffffffffffffffffffffcafff gffafffffffffffffffffffffcaffff gffaefffffffffffffffffffcafffff gfffafffffffffffffffffffaffffff gfffcafffffffffffffffffafffffff gffffacfffffffffffffffaffffffff gfffffaffffffffffffffafffffffff gfffffeaffffffffffffacfffffffff gffffffaffffdffffffacffffffffff gffffffcafdbdbbgffacfffffffffff gfffffffaebfffgbbacffffffffffff gfffffffbaffffffadbbfffffffffff gffffffbdeaffffacffdbbdffffffff gffffdbfffacffaeffffffbbbffffff gfffbbfffffafaefffffffffdbbdfff gffbbffffffaaefffffffffffffbbbf gdbdffffffffcffffffffffffffffdbb bbffffffffffffffffffffffffffffffbbd bbffffffffffffffffffffffffffffff dbb bdgffffffffffffffffffffffffffffff dbbd db gffffffffffffffffffffffffffffff bbb bb gffffffffffffffffffffffffffffff dbbd bd gffffffffffffffffffffffffffffff bbd db gffffffffffffffffffffffffffffff dbbf bb gffffffffffffffffffffffffffffff bbd bb gffffffffffffffffffffffffffffff dbb bd gffffffffffffffffffffffffffffff dbb db gffffffffffffffffffffffffffffff bb gffffffffffffffffffffffffffffff bd fgggggggggggggggggggggggggggggg db bb bb bd db bb bd ``` <!-- end of image --> Let's see what secrets area A holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#0505feff b,#fd0708ff c,#cacaffff d,#feadadff e,#413af7ff f,#8887feff g,#fc585bff ``` ```image c e ac aa f aaf fa caac faa eae faaf caaf caae faa caae eaf caae caac caae eae caae aaf caae faac caae eae caae caac caae faa caae aaf caae caac caae eae ceae caaf eaac faa eaac eaf eaac caac eaac eae eaac aaf eaac faa ggd eaac eae gbbbbd eaac caac dbbbgbbbbgd eaac fae gbbg dbbbbgd eaac aaebbg dgbbbeaac faabd deaabgd dbeae faagbbbbg gbbgaaf faaf gbbbbgd bbbd faa faaf dgbbbbd dbbbd eaf faaf dgbbbbgd gbbg caac faaf dbbbbgd gbbg eae faaf dgbbbbg dbbbd aaf faaf dbbbbgd dbbbd faafaaf dgbbbbg gbbg eaaaf gbbbbgd bbbd caaf dgbbb dbbbd cf dgb gbbg gbbg bbd bd ``` <!-- end of image --> I've cracked the case! This area contains the intersection. I've identified a total of two intersection points.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0404ffff b,#fe0505ff c,#c6c6ffff d,#ffaeaeff e,#3d3afcff f,#8484ffff g,#fc5154ff ``` ```image c ef a fa ac a ee a ca af a fe ac ca ef a a ac fa ac ac ac a ac ee af a af ca af af af a af fe ae ac ae ca ae ef ae a ae fa ee ac ea a ea ee ea a ea ca ea af ea a fa fe fa ac fa ca fa af fa a ca fa ca ac ca a ca ee ca a ca ca ca af ac a ac ee ac a g ac ca dbgbbd ac aeb dbbac ba agbb bdfa af dbbd gb ac af gbg bb a af dbbd bg eaf bbg dbd f gbbd gb dbbg bb gbb bd dbbd gb gbg bb dbbd bg bbg dbd gbbd gb dbbg bg gbb dbd dbb gb bb bg dbd gb bg dbd gb bb bg ``` <!-- end of image -->

This image looks interesting. I wonder if there are any intersections hidden in there? I need to zoom in on these areas to get a better look. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd0605ff b,#0808faff c,#d38c7bff d,#b1d7b1ff e,#96c699ff f,#5a67e0ff g,#e8433fff ``` ```image d aceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeed adddddddddddddddddddddddddddddddddddddddddddddddddde acddddddddddddddddddddddddddddddddddddddddddddddddde caddddddddddddddddddddddddddddddddddddddddddddddddde daddddddddddddddddddddddddddddddddddddddddddddddddde dcadddddddddddddddddddddddddddddddddddddddddddddddde ddadddddddddddddddddddddddddddddddddddddddddddddddde ddggddddddddddddddddddddddddddddddddddddddddddddddde dddaddddddddddddddddddddddddddddddddddddddddddddddde dddggdddddddddddddddddddddddddddddddddddddddddddddde ddddadddddddddddddddddddddddddddddddddddddddddddddde ddddacddddddddddddddddddddddddddddddddddddddddddddde beddddaddddddddddddddddddddddddddddddddddddddddddddde dbddddacdddddddddddddddddddddddddddddddddddddddddddde bfdddcadddddddddddddddddddddddddddddddddddddddddddde dbddddadddddddddddddddddddddddddddddddddddddddddddde dfbdddcaddddddddddddddddddddddddddddddddddddddddddde ddbedddaddddddddddddddddddddddddddddddddddddddddddde dddbdddggdddddddddddddddddddddddddddddddddddddddddde dddbfdddadddddddddddddddddddddddddddddddddddddddddde a ddddbdddggddddddddddddddddddddddddddddddddddddddddde gg ddddfbdddaddddddddddddddddddddddddddddddddddddddddde da dddddbfddacdddddddddddddddddddddddddddddddddddddddde a ddddddbdddadddddddddddddddddddddddddddddddddddddddde ac ddddddfbddaeddddddddddddddddddddddddddddddddddddddde ga dddddddbddcaddddddddddddddddddddddddddddddddddddddde a dddddddebddaddddddddddddddddddddddddddddddddddddddde a ddddddddbfdcadddddddddddddddddddddddddddddddddddddde ac dddddddddbddadddddddddddddddddddddddddddddddddddddde ca dddddddddfbdggddddddddddddddddddddddddddddddddddddde a ddddddddddbedaddddddddddddddddddddddddddddddddddddde a ddddddddddebdggdddddddddddddddddddddddddddddddddddde ag dddddddddddbfdadddddddddddddddddddddddddddddddddddde ca ddddddddddddbdacddddddddddddddddddddddddddddddddddde a ddddddddddddfbdaddddddddddddddddddddddddddddddddddde ad dddddddddddddbeaedddddddddddddddddddddddddddddddddde gg ddddddddddddddbcadddddddddddddddddddddddddddddddddde ca ddddddddddddddbfadddddddddddddddddddddddddddddddddde a dddddddddddddddbcaddddddddddddddddddddddddddddddddde ac dddddddddddddddfbaddddddddddddddddddddddddddddddddde gg ddddddddddddddddbcgdddddddddddddddddddddddddddddddde da dddddddddddddddddbadddddddddddddddddddddddddddddddde a dddddddddddddddddfbgddddddddddddddddddddddddddddddde ac ddddddddddddddddddbaddddddddddddddddddddddddddddddde ga ddddddddddddddddddebcdddddddddddddddddddddddddddddde a dddddddddddddddddddbgdddddddddddddddddddddddddddddde a ddddddddddddddddddddbeddddddddddddddddddddddddddddde ac ddddddddddddddddddddfbddddddddddddddddddddddddddddde ca dddddddddddddddddddddbedddddddddddddddddddddddddddde a dddddddddddddddddddddcbdddddddddddddddddddddddddddde a ddddddddddddddddddddddbfddddddddddddddddddddddddddde ag ddddddddddddddddddddddgbddddddddddddddddddddddddddde ca dddddddddddddddddddddddgbdddddddddddddddddddddddddde a dddddddddddddddddddddddgbeddddddddddddddddddddddddde ad ddddddddddddddddddddddddabdddddddddddddddddddddddddegg ddddddddddddddddddddddddabfddddddddddddddddddddddddca dddddddddddddddddddddddddabdddddddddddddddddddddddda dddddddddddddddddddddddddafbddddddddddddddddddddddac dddddddddddddddddddddddddcabfddddddddddddddddddddgge ddddddddddddddddddddddddddadbdddddddddddddddddddcade ddddddddddddddddddddddddddcafbddddddddddddddddddadde dddddddddddddddddddddddddddadbdddddddddddddddddacdde dddddddddddddddddddddddddddggebdddddddddddddddgaddde ddddddddddddddddddddddddddddadbfdddddddddddddeadddde ddddddddddddddddddddddddddddgcdbdddddddddddddaddddde dddddddddddddddddddddddddddddadfbdddddddddddagddddde dddddddddddddddddddddddddddddacdbedddddddddgadddddde ddddddddddddddddddddddddddddddaddbdddddddddaddddddde ddddddddddddddddddddddddddddddaddbfdddddddaeddddddde dfffffbbbb ddddddddddddddddddddddddddddddcaddbddddddagddeeffffffbbbbbbbbbbbbbbbbbffffdd dddddddddddddddddddddddddddddddaddfbbbbbbbbbbbbbffffdd dddddddddddddddddddddddddddddddcadddddddadddddddddde ddddddddddddddddddddddddddddddddaddddddacdddddddddde ddddddddddddddddddddddddddddddddggddddagddddddddddde dddddddddddddddddddddddddddddddddadddcadddddddddddde dddddddddddddddddddddddddddddddddgcddaddddddddddddde ddddddddddddddddddddddddddddddddddadacddddddddddddde ddddddddddddddddddddddddddddddddddaagdddddddddddddde dddddddddddddddddddddddddddddddddddaddddddddddddddde ddddddddddddddddddddddddddddddddddddddddddddddddddde ddddddddddddddddddddddddddddddddddddddddddddddddddde ddddddddddddddddddddddddddddddddddddddddddddddddddde ``` <!-- end of image --> Time to investigate area A up close. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0809ff b,#0b09fcff c,#fd5e60ff d,#bebdfdff e,#feb1b2ff f,#6867feff g,#8c1f91ff ``` ```image a ea ae aa ca cc ea aa aa ae cc ac aa ea ac ae f aa ff ca dbd ae bb ea dbd ac bd aa bb ea dbd ca fb ae bb aa bb ca fb cc bf ea bb ae dbd aa fb ca bb cc fb ae fb aa bf ca fb ae bf ea bf aa bb aa bf ae dbd cc bb ac fb aa dbdea bb ae fb ae bf ac bbca bbea ffea dbdae bbaa dbca dbgc bbae dbaa fba bbe bba fbc bg fbe dbg bg bb ebd gb bb gb cgb eabf egbb abb aabf cacbd cabb c eadbd a eadbd ca acbb cae aadbd ac ea fb ca cc bb aa aefb ac acdbd ca ca bf aa ea bb ac ea dbd eae ae fb aa aa bb ca ca fb eae cc fb aa ea bf cae aa fb aa ddddfff aa bfdddffffbbbbbbbbbbbbb ae bbfffffggddd ea aa ac eae aa eac ea aa cc eae ac ca aa aa ea ac aaa ae e ``` <!-- end of image --> Wow! I can see an intersection so clearly in area A! The final answer is: two intersections found.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fe0506ff b,#0706fdff c,#fb7a7eff d,#b3b2fdff e,#fec0c0ff f,#5b59fdff g,#f73a41ff ``` ```image e ac a ae ea a ea a cg a gc a ae b a db ae bf ea b a db ea bd a b cg ff a a b gc gg db a ea bd ae a b a ac ff ae ga b ea ea db a a bd ca ac b a ca fb cg a b a ae b gc ac bf a ca b ae a db a ae bdae gg bea ea ffa a bca ae dba gg bcg ea ba a fbc ac ba ga dbe ea bg a be ac fb ca bd a cb ae bf ac cb ca gb a gbd ae ab gg aff ea ab a adb ae eabd gg a b ea cgfb a a b ac cgdb ga a bf ea gc b a a fb ac ae bd ca a b a ae ff ae dddffffbbbb ea b ac dddffffbbbbbbbbbbbbbbbbffffdddd a dbbbbbbbbbbbbffffddd cg a a ae cg gg a ea gc a a ae aag a ``` <!-- end of image -->

I'm ready to tackle this image and find those intersections! The image has some tight areas where segments are too close. I should investigate those closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#5358f4ff b,#fc0809ff c,#0606feff d,#a8a8ffff e,#f86a66ff f,#fec4c4ff g,#add4adff ``` ```image d dccccd c daccca dc acccad c dccccd c daccca cd acccad c dccccd cd daccca c acccad aa dccccd c da aa c dc c dc c c cd c ggggggggggggcagg ggggggggggggcggg gggggggggggaaggg e gggggggggggcgggg ebbe ggggggggggaagggg ebbe ggggggggggcggggg ebbe gggggggggacggggg ebbe gggggggggcgggggg ebbegggggggcgggggg gbbbegggcggggggg ggggbbbgcggggggg gggggggcbbgggggg gggggggcgebbbggg ggggggcaggggebbbf ggggggcggggggggebbe gggggaaggggggggg ebbe gggggcgggggggggg ebf ggggacgggggggggg bf ggggcggggggggggg bf gggacggggggggggg bf gggcgggggggggggg bf gggcgggggggggggg bf ggcggggggggggggg bf c be cd be c be ad be c be aa be c be da be c be dc bb c bb dc bb cd bb c bb cd bb c eb aa eb c eb aa eb c eb dc eb c eb dc eb c eb c fb cd fb c fb cd fb c fb aa fb c fb aa fbf c bf dc bf c bf b ``` <!-- end of image --> I'm focusing my attention on this specific region, area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#4c46f8ff b,#fd0506ff c,#0606feff d,#9493ffff e,#fe4a4bff f,#fd9697ff g,#e3d4f0ff ``` ```image dcc ccd dcc acd gccg aca gccg aca gccg dca ccd dca ccd dcc ccd dcc f acd bbef gccg ebbbbef aca gfebbbbef gccg gfbbbbbef aca gfbbbbbefccg gebbbacag feccbbbfg dccebbbbbfg ccd febbbbefg dcc febbbbefg acd febbbbe dcc febb acd gf gccg aca gccg aca gccg dca ccd dcc ccd dcc acd dcc acd gccg aca ``` <!-- end of image --> There is an intersection point visible in this close-up of area A. There's one and only one intersection present in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#3f3fffff b,#fd0809ff c,#0404feff d,#8484ffff e,#ff6262ff f,#febcbcff g,#c6c6ffff ``` ```image g dccccd c gacccd gc gdcccag cg dcccad gc gacccd cg gdcccag c dcccad cd gacccd c gdcccag ad dcccad c ga da c dc c gc cg gc cg c ad c ad e c ebbe da ebbe c ebbe dc ebbe c ebbf gc fbbbf cg fbbbfc fcbbf c fbbbf ad fbbe c ebbe aa ebbe c ebf da bf c bf dc bf c bf gc bf cg bf c bf cg be c be ad be c be aa be c be da be c be gc bb c bb gc bb cg bb c bb cd bb c eb ad eb c eb aa eb c eb da eb c eb gc eb c fb gc fb cg fb c fb cd fb c fb ad fb c fb da fb c bf da bf c bf b ``` <!-- end of image -->

Here's an image. My task is to find intersections or areas where lines come close together. I'd describe these as 'hotspots' for potential intersections. <!-- image --> ```palette Key,Color ,#fefefeff a,#f56864ff b,#0606feff c,#a8a8ffff d,#aed4adff e,#ffb9b9ff f,#fe0a0aff g,#5153fbff ``` ```image gbbbg cbbbc gb gbbbc cbc gbbg bb cbbbc gb gbbbc bg gbbg bb cbbbc cbc gbbbc bg gbbg gb bbbc cbc c bb gb bg bb cbc bg gb cbc bb gb bg bb cbc bg gb cbc dddbbddddddddd ddddgbdddddddd ddddddbgdddddd dddddddbbddddd ddddddddgbdddd dddddddddddddd dddddddddfdddd ddddddddfddddd dddddddfdddddd ddddddfddddddd dddddfdddddddd ddddfadddddddd dddfaddddddddd ddfadddddddddd dfaddddddddddd fadddddddddddd faddddddddddddd fadddddddddddddd ff ff ff af af af af af ef ef ef ef ef f f a fe aff fe aff fe aff fe aff fe eff fa eff fa eff fa eff fa effe fa effe ff effe ff effe ff ffe af ffe af ffe af ffe af ffeaf ff ``` <!-- end of image --> Let's see what secrets area A holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff5353ff b,#0707ffff c,#9898ffff d,#ff9a9aff e,#efdae9ff f,#ff0808ff g,#4e4effff ``` ```image egbbg cbbbe ebbbc gbbge cbbbc egbbg gbbge cbbbc egbbg cbbb ebc e efd effa efffe efffe efffe affe affe affe affe affe affd affd affd affd dffd dffd dffd dffd dffa dffa dffa ffa ``` <!-- end of image --> Darn it! This close-up doesn't show any intersections in area A. I can confidently say that there are no intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff3a3aff b,#0606ffff c,#a3a3ffff d,#ff8b8bff e,#fdcfd1ff f,#ff0505ff g,#5151ffff ``` ```image gbbbg cbbbc gb cbbbc cbc gbbg bb cbbbc gb gbbbc bg gbbg bb cbbbc cbc gbbbc bg gbbg gb bbbc cbc e bb gb bg bb cbc bg gb cbc bb gb bg bb cbc bg gb cbc bb gb bg bb cb e ef efe fe fe fe fe fd fd fd fd fa fa fa aa af af af af df df df df ef ef ef ef fe d fe dfa fe dfa fe dfa fd dff fd dff fd dff fd dff fa effe fa effe fa effe fa effe aa effe af effe af effe af ffd df ffd df ffddf ff ``` <!-- end of image -->

I'm approaching this image with caution. Intersections might be tricky to spot. These zones are intriguing. I bet there's something interesting happening within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0606ff b,#0a0afdff c,#f8a9a6ff d,#afb0feff e,#f75552ff f,#add4adff g,#666af7ff ``` ```image c a ac a a ca a ea a ee a ac a ac ca a ca a ee a ac a ac ca a ca a ee a ae a ac ca a ca a bbbd ee dbbbg a gbbbd ee dbbbg a gbbbd fffffffffffffaef dbbbg fffffffffffffaff gbbbd ffffffffffffafff dbbbg fffffffffffcafff gbbbd fffffffffffaffff dbbbg ffffffffffeaffff gbbbd ffffffffffafffff dbbb fffffffffeefffff dbbbfffffffffaffffff dbbbfffffaeffffff ffgbbbffafffffff fffffgbbbfffffff ffffffcagbbbffff ffffffaffffgbbbf fffffeafffffffgbbg fffffaffffffffff gbbg ffffeeffffffffff gbbg ffffafffffffffff gbbg fffaefffffffffff gbbg fffaffffffffffff gbbg ffacffffffffffff gbbg fcafffffffffffff g faffffffffffffff ca a ee a ae ac a ceaae ac eaaec ca caaac a ceaae ca eaaec a caaac ee ceaae a eaaac ee caaac a eaae ac eaa ``` <!-- end of image --> I'm going to scrutinize area A for any signs of an intersection. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0404ff b,#0000feff c,#ff7b7bff d,#9090ffff e,#ff3a3aff f,#fdbcbdff g,#4237f3ff ``` ```image aaf cae faaf eae faaf eac faa eac caa aac cae aaf eae faaf eac faa d eac bbgd caa gbbbbgd aac dgbbbbgd cae dgbbbbgd aaf dgbbbbggae dgbbbbgd ggbbbbgd faafdgbbbbgd eac dgbbbbgd faa dgbbbbgd aac dgbbb cae dg aaf cae faaf eae faaf eac faa aac caa aaf cae faaf eae faaf eac faa ``` <!-- end of image --> Eureka! There's definitely an intersection in area A! I have found one intersection!

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0404ff b,#0404ffff c,#ff8484ff d,#9c9cffff e,#ff3f3fff f,#ffc9c9ff g,#5252feff ``` ```image c a ac fa af fa a ce a ee a ac fa af fa a ca a ee a ac a af fa a ca a ee a ec a af fa af ca a bbgd ce dbbbd a gbbgd ec dbbbg a gbbbd ac dbbbg fa gbbbd af dbbbg fa gbbbd a dgbbg ce dbbb a dbbg ee dbbg a dbbg ac dbbg fa dbbg fadbbg a dbbg ca dbbg a dbbg ee dbbg a dbbg ac gbbg a gbbg af gbbg fa g a ca a ee a ec ac a feaac af caaef fa caaac af feaac ca caaef a caaac ce feaac a caaef ec caaac a feaae ac caa ``` <!-- end of image -->

Here's an image. My task is to find intersections or areas where lines come close together. I need to zoom in on these areas to get a better look. <!-- image --> ```palette Key,Color ,#fefefeff a,#0405fdff b,#fb0b0aff c,#818fe2ff d,#db7b6aff e,#a3cda3ff f,#3f45f0ff g,#b2d7b2ff ``` ```image eeeeeeeeeedbbbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eggggggdbbbecabggggggggggggggggggggggggggggggggggggggggge egggdbbbegggaffbgggggggggggggggggggggggggggggggggggggggge eebbbdgggggcagabdggggggggggggggggggggggggggggggggggggggge bbbdggggggggaegcabdgggggggggggggggggggggggggggggggggggggge dbbdegggggggggeagggaebgggggggggggggggggggggggggggggggggggggge dbbd egggggggggacgggeadbggggggggggggggggggggggggggggggggggggge dbbd egggggggggagggggacbbgggggggggggggggggggggggggggggggggggge dbbd eggggggggacggggggagbdggggggggggggggggggggggggggggggggggge dbbb eggggggggagggggggffgbegggggggggggggggggggggggggggggggggge gbbb egggggggffggggggggagebgggggggggggggggggggggggggggggggggge bbbg egggggggagggggggggfagdbggggggggggggggggggggggggggggggggge bbg eggggggffggggggggggaggbdgggggggggggggggggggggggggggggggge eggggggagggggggggggcaggbdggggggggggggggggggggggggggggggge egggggcaggggggggggggacggbggggggggggggggggggggggggggggggge egggggagggggggggggggeaggdbgggggggggggggggggggggggggggggge eggggcaggggggggggggggacggbbggggggggggggggggggggggggggggge eggggaegggggggggggggggagggbdgggggggggggggggggggggggggggge egggeaggggggggggggggggffgggbeggggggggggggggggggggggggggge egggacgggggggggggggggggagggebggggggggggggggggggggggggggge egggaggggggggggggggggggcagggdbgggggggggggggggggggggggggge eggfcgggggggggggggggggggaegggbdggggggggggggggggggggggggge eggaggggggggggggggggggggcaggggbdgggggggggggggggggggggggge egffgggggggggggggggggggggacggggbgggggggggggggggggggggggge egagggggggggggggggggggggggaggggdbggggggggggggggggggggggge ecfgggggggggggggggggggggggafggggbbgggggggggggggggggggggge eagggggggggggggggggggggggggagggggbdggggggggggggggggggggge cagggggggggggggggggggggggggffgggggbegggggggggggggggggggge aeggggggggggggggggggggggggggagggggebgggggggggggggggggggge gagggggggggggggggggggggggggggcagggggdbggggggggggggggggggge acggggggggggggggggggggggggggggaegggggbdgggggggggggggggggge aeggggggggggggggggggggggggggggeaggggggbdggggggggggggggggge acegggggggggggggggggggggggggggggacggggggbggggggggggggggggge a eggggggggggggggggggggggggggggggaggggggdbgggggggggggggggge fc eggggggggggggggggggggggggggggggffggggggbbggggggggggggggge a egggggggggggggggggggggggggggggggagggggggbdgggggggggggggge ff egggggggggggggggggggggggggggggggfagggggggbeggggggggggggge a eggggggggggggggggggggggggggggggggagggggggebggggggggggggge cf eggggggggggggggggggggggggggggggggcagggggggdbgggggggggggge a egggggggggggggggggggggggggggggggggacgggggggbdggggggggggge ca egggggggggggggggggggggggggggggggggeaggggggggbdgggggggggge a eggggggggggggggggggggggggggggggggggacggggggggbgggggggggge a egggggggggggggggggggggggggggggggggggaggggggggdbggggggggge ag egggggggggggggggggggggggggggggggggggffggggggggbbgggggggge a eggggggggggggggggggggggggggggggggggggagggggggggbdggggggge ac eggggggggggggggggggggggggggggggggggggcagggggggggbegggggge a egggggggggggggggggggggggggggggggggggggaeggggggggebgggggge fc egggggggggggggggggggggggggggggggggggggcagggggggggdbggggge a eggggggggggggggggggggggggggggggggggggggacgggggggggbdgggge cf egggggggggggggggggggggggggggggggggggggggaggggggggggbdggge a egggggggggggggggggggggggggggggggggggggggafggggggggggbggge ca eggggggggggggggggggggggggggggggggggggggggaggggggggggdbgge a eggggggggggggggggggggggggggggggggggggggggffggggggggggbbge ga egggggggggggggggggggggggggggggggggggggggggagggggggggggbde a egggggggggggggggggggggggggggggggggggggggggcagggggggggggbe a eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeeeeeeeeeb ac ga d a ac fc a a ff ff a a cf cf a a ca ca a a a a ac a a a ff ac a a ca fc a a a ff ac a a cf fc a a ca ff a a ``` <!-- end of image --> This is a magnified view of the region A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0404feff b,#fe0809ff c,#807ffeff d,#fea8a8ff e,#fd5657ff f,#3c3bfdff g,#c4c4feff ``` ```image dbbd debbbbb debbbbedabe debbbbed cafbe debbbbed faabbd debbbbbd gaaafbb debbbbbed facaaebb debbbbbed gaa caabbe dbbbbbed fac aacbbd ebbbbed gaag caadbbd bbed faf facebb d gaag gaagbbe caf faf bbe aag gaagdbbd caf caf ebb aag aac ebb caa caa bbe fac fac dbbd gaa gaa dbbd fac fac ebb gaa gaag bbe fac faf bbe gaag gaag dbbd caf caf ebb aag aac ebb caf caa bbe aag fac dbbd aac faf ebb caa gaag bbe fac caf bbe gaa aag dbbd fac caa ebb gaa aac ebb fac caa bbe gaag fac dbbd caf gaag dbbd aag faf ebb caf gaag bbe aag caf bbe caf aac dbbd aac caa ebb gaa fac ebb fac gaa bbe gaa fac dbbd fac gaag dbbd gaag faf ebb faf gaag bbe gaag caf bbe caf aac dbbd aag caa ebb caf fac ebb aag gaag bbe caa faf dbbd fac gaag dbbd gaa caf ebb fac aag bbe gaa caf bbe fac aac dbbd gaag caa ebb faf fac ebb aag gaag bbe af faf dbbd ag gaag dbbd f caf ebb c aac bbe caa bbe fac dbbd gaa ebb fac ebb gaag bbe faf dbbd gaag dbb caf eb aac be caa be fac bbd gaag ebb faf ebb gaag bbe caf dbbd aag dbbd caf ebb aac bbe fac dbbd gaag ebb faf ebb gaag bbe caf dbbd aac dbbd caa ebb fac bbe gaa bbe fac dbbd gaag ebb faf ebb gaag bbe caf dbbd aac dbbd caa ebb fac bbe gaa bbe fa dbbd gag ebb cf ebb ag bbe af dbbd aac dbbd caa ebb fac bb gaag b ``` <!-- end of image --> No intersection in area A, but I'll keep looking. Zero, Nada.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0404ffff b,#fe0808ff c,#8181ffff d,#ffaaaaff e,#ff5454ff f,#3d3cfeff g,#c5c5feff ``` ```image dbbb dbbe cab dbbb affb dbbbd ga abe ebbd ag cabd ebbd ga agb ebbd ag gadb ebbe a aceb dbbe fc a bd dbbe a fc b dbbb fc a b dbbbd a cf eb bbd cf a be a ga bd ca ag b a a db ga ac eb ag a bd a ff b ag a b a ca eb fc a be a ga bd ff ag b a a db cf fc eb a a bd ga cf b a a b ga ca eb ag ag be a ga bd ac ac b a a db fc fc eb a a bd cf cf b a a b cf ga eb a ag be ga a bd a ac b ga a db ag ff eb a a bd ac ca b a a b fc ga eb a ag be cf a bd a fc b ca a db a cf eb ga a bd ag ca b ga ag b ag ga d a ac fc a a fc fc a a cf cf a a ga ca ag a a ga ac ag a a ff ag a a ca fc a a ga ff ag a a cf fc a a ga cf a a ``` <!-- end of image -->

I'm examining this image closely. My goal: find any and all intersections. I'm going to focus my attention on these specific areas. <!-- image --> ```palette Key,Color ,#fefefeff a,#0a0bfdff b,#fc0809ff c,#9095f4ff d,#e8695eff e,#feb5b5ff f,#b0d7b0ff g,#96c59aff ``` ```image c ac a ac a ac a ac a ac a ac a ac a ac a ac a ac a ac a ac a ac a ggggaggggggggggggggggg ffffgaffffffffffffffff fffffagfffffffffffffff fffffgafffffffffffffff ffffffagffffffffffffff ffffffgaffffffffffffff fffffffagfffffffffffff bbd fffffffgafffffffffffff edbbbd ffffffffagffffffffffff dbbbdgfffffgaffffffffffff fdbbbbdffagfffffffffff fffffdbbbbafffffffffff fffffffffgabbbdfffffff ffffffffffcaffdbbbdgff fffffffffffaffffffdbbbbe fffffffffffcafffffffffebbbbe ffffffffffffafffffffff ebb ffffffffffffcaffffffff ebe fffffffffffffaffffffff bb fffffffffffffcafffffff dbe ffffffffffffffafffffff bb ffffffffffffffcaffffff dbe fffffffffffffffaffffff bb fffffffffffffffcafffff dbe ggggggggggggggggaggggg bb ca dbe a bb ca db a bd ca db a ebd fggggggggggggggg ca bb gfffffffffffffff a ebd gfffffffffffffff ca bb gfffffffffffffff a ebd gfffffffffffffff ca bb gfffffffffffffff a ebdfffffffffffffff ca bbffffffffffffff a gdbdffffffffffff ca gffbbfffffffffff a gfffdbdfffffffff ca gfffffbbffffffff a gffffffdbdffffff ca gffffffffbbfffff a gfffffffffdbgfff cac gfffffffffffbfff caaaaaac gfffffffffffffff ccaaaaacc gfffffffffffffff caaaaaacc gfffffffffffffff ccaaaaaac gfffffffffffffff ccaaaaaacffffffffffff ggcaaaaaacgfffff gfffffffcaaaafff gfffffffffffffff fggggggggggggggg ``` <!-- end of image --> I'm analyzing this close-up of area A with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#0201fdff b,#fe0303ff c,#5552fcff d,#fc4345ff e,#fdc0c1ff f,#cbcbffff g,#fc8386ff ``` ```image cac faaf cac faaf cac faaf cac faaf cac faaf cac faaf cac faaf cac faaf cac faaf dge cac bbbbdge faaf gdbbbbbbdge cac egdbbbbbbdge faaf egddbbbbbbdgecac egdbbbbbdaae egdbbaacbdge egaabbbbbdge cacgddbbbbbbdge faaf egdbbbbbbdge cac egdbbbbbbdg faaf egdbbbb cac egd faaf cac faa cac faa cac faa cac faa cac faa cac faa cac faa cac faa ``` <!-- end of image --> Case closed! This is definitely an intersection point in area A. Moving on to the next area. Time to investigate area B up close. <!-- image --> ```palette Key,Color ,#fefefeff a,#0505ffff b,#ff0606ff c,#a4a4ffff d,#ff4646ff e,#ff8a8aff f,#f8d1d7ff g,#5252ffff ``` ```image e bdf bbbe fdbbdf ebbbe fdbbdf ebbbe fdbbdf ebbbe fdbbdf ebbbe fdbbd ebbbf fdbbd ebbbf fbbbd ebbbf fbbbe dbd ff c aaaggccf aaaaaaaaaaggcc cccggaaaaaaaaaggccf ccggaaaaaaaaaaggc fccggaaaaag ccgc ``` <!-- end of image --> No luck this time. Area B doesn't have an intersection. My investigation reveals that there is exactly one intersection in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0303feff b,#fd0809ff c,#8989ffff d,#ff5f5fff e,#ffafafff f,#c4c4ffff g,#2c2cffff ``` ```image f gc a gc a gc a ac a ac a ac a af a af a af a af a af a af fa af fa af fa af fa af fa af bbd fa edbbbd af dbbbde fa ebbbbe af edbbba eabbbd fa dbbbde a ebbbbe fa ebbbbe a ebb fa ebe a bb fa dbe a bb fa dbe a bb fa dbe a bb ca dbe a bd ca db a bd ca db a ebd cg bb a ebd cg bb a ebd cg bb a ebd cg bb a ebe cg bb a ebe cg bb a dbe cg bb a dbe cgf b cgaaaagcf fcaaaaagc fcgaaaagcf fcgaaaagcf cgaaaaacf fcgaaaagcf fcaaa ``` <!-- end of image -->

I'm approaching this image with caution. Intersections might be tricky to spot. I've noticed 1 areas of interest. These could be potential intersection zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#ed645bff b,#0b0bfbff c,#787fefff d,#fc0a0aff e,#ffb9b9ff f,#b1d7b1ff g,#98c796ff ``` ```image a ed d d ed de da da d ad ed ed aa d de de d da ad dd de ed d ed ad d de de d da ed ad da ed d d ed de da da d ad ed ed da d d de ed da aa ad de ed d fgggggggggggggggggggggggggggggggf d ad gfffffffffffffffffffffffffffffffgde de gfffffffffffffffffffffffffffffffda d gffffffffffffffffffffffffffffffdd ad gfffffffffffffffffffffffffffffadg degfffffffffffffffffffffffffffffdfg dgffffffffffffffffffffffffffffdffg edfffffffffffffffffffffffffffdaffg dafffffffffffffffffffffffffddfffg gdffffffffffffffffffffffffadffffg gadffffffffffffffffffffffgdfffffg gfdafffffffffffffffffffffdffffffg gffdffffffffffffffffffffdaffffffg gffgdfffffffcbbcfffffffdafffffffg gfffdafffffcbfgbbbbcffadffffffffg gffffdffffgbffffffcbbbbgffffffffg gffffgdfffbffffffffffdcbbbcfffffg gfffffddfbffffffffffdgffffcbbbcfg gffffffdbgfffffffffdaffffffffcbbbbf gffffffbdfffffffffadffffffffffffgcbbbc gfffffbcadfffffffadfffffffffffffg cbbbc gffffbcffdgffffffdffffffffffffffg cbbbc gfffbcffffdfffffdgffffffffffffffg cbbbc gffbbfffffadfffdafffffffffffffffg cbbbc gfbbfffffffdafddffffffffffffffffg cbbbc gbbfffffffffdadfffffffffffffffffg b bbffffffffffadffffffffffffffffffg cbfffffffffffffffffffffffffffffffg cbgfffffffffffffffffffffffffffffffg cb gfffffffffffffffffffffffffffffffg fb gfffffffffffffffffffffffffffffffg b gfffffffffffffffffffffffffffffffg b gfffffffffffffffffffffffffffffffg b gfffffffffffffffffffffffffffffffg b gfffffffffffffffffffffffffffffffg bc bc bc bc bb bb bb cb cb cb cb b b b b bf bc ``` <!-- end of image --> I'm focusing my attention on this specific region, area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fc3b3dff b,#0807fdff c,#b1affdff d,#fe0404ff e,#ffc3c3ff f,#5754fbff g,#fe7e7eff ``` ```image a gd gdd eddg edda ada adde g gdde de eddg da eddg ddg ada gdde add ada gdde ddg eddg edde eddg ada ada ddg add edde gdde gdd edde adg cfc eddg edde cbbbbfcc dda gdd cbbfbbbbbbfc ada ada cbbf ccfbbbbbbfc gdde edde cbbf cffbbbbbffcgdde gdd cbbf cfbbbbbbbf ada cbbf cfbbbbbbfc eddg bbf adaffbbbbbffc gdde bbb adde cfbbbbbbfcc ada bbb gdde cfbbbbbbfc eddgfbb eddg ccfbbbbbb gdbbbc eddg cffbb fbbc ada c fbbag add fbbcdde gdde fbbc ada eddg cbbc ddg eddg cbbc edde ada cbbf gdd add cbbf adg gdde cbbf edde edde cbbf gdd eddg bbf ada dda bbf edde ada bbb gdd gdde fbb adagdde fbb eddddg fbbc gdda bbc ga bc c ``` <!-- end of image --> My analysis confirms the presence of an intersection in area A. There's for sure two intersections on the image you sent me.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fd3a3bff b,#0706fdff c,#b1b1ffff d,#fe0404ff e,#ffbfbfff f,#5756feff g,#ff7e7eff ``` ```image g ed d d ed de aa dg d aa ed ed aa d de de d dg aa aa de gd d ed gd d de dg d aa gd gd dg ed d d ed de dg da d gd ed ed aa d d de ed dg aa ad de ed d d aa de de dg d aa gd gd de d d d gd dg dg aa d gd ed ed dg d d de ed cbbc da aa cb cfbbbc gd d cb cbbbb ed b dfbbbf aa b de fbbbc dbc dg cfbbfc ba ad cbbbf bcaa ed fbbbc bc de d cfbbbc bf d de cbbbfc bf gd dg cbbbf bf de aa fbbbc fb dgd cf fb gd fb fb cb cb cb b b bc bc bc bf bf bf bb fb fb fb cb cb cb b b bc bc bc ``` <!-- end of image -->

I'm approaching this image with caution. Intersections might be tricky to spot. I've spotted 1 narrow regions that might be worth examining further. Let's call them area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#f5625eff b,#0606ffff c,#fe0909ff d,#9797ffff e,#feb3b3ff f,#4041f2ff g,#add5adff ``` ```image d bbb fbbd fbbd dbbd dbbf dbbf bbbd fbbd fbbd dbbf dbbf dbbf fbbd fbbd fbbd bbf bbd bbd bbd bbd bbd bbd bbd gggggggggggggggg fbd gggggggggggggggg fbd gggggggggggggggg fbd ggggggggggggggggfbd ggggggggggggggfbd gggaggggggggfbfg gggacgggggfbfggg ggggcaggfbfggggg gggggcfbfggggggg ggggfbfggggggggg gggbfgcagggggggg gggggggcgggggggg ggggggggcggggggg ggggggggacgggggg gggggggggcaggggg ggggggggggcggggg ggggggggggacgggg gggggggggggcaggg ce c ac ce c ec ca ce c ac ca c ec ec ac cc ce cce c aca ec ecc ca cc c cce ec aca ac ecc ce cc c ace ec eca ca ecc c cc c ace ac eca ce cc c cce ec aca ca eca ce cc c cce ac aca ce ecc c cc ece ``` <!-- end of image --> I'm now examining the contents of area A in detail. <!-- image --> ```palette Key,Color ,#fefefeff a,#fb6d70ff b,#0301fcff c,#ff0404ff d,#cccafdff e,#fcb3b5ff f,#534ffaff g,#fa3337ff ``` ```image df dfbb ae dfbbbf ecce dfbbbf gcg dfbbbfd cca dfbbbfd ecce dfbbbfd acc dfbbbfd gcgfbbbfd dbbbbfd dfbbbfe dfbbbfacg dbbfd cca dd ecce acc gcg cca ecce acg gca ecce acc gcg cca ecce acc gcg ``` <!-- end of image --> The close-up clearly shows an intersection point in area A. One intersection, that's it, but I found it.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff7575ff b,#0707ffff c,#ff0303ff d,#9898ffff e,#ffbabaff f,#4f4bfbff g,#ff3232ff ``` ```image d bbb fbbd fbbd dbbf dbbf dbbf bbbd fbbd fbbd dbbf dbbf dbbb bbbd fbbd fbbd bbf bbd bbd bbd bbd bbd bbd bbd bbd fbd fbd fbd fbd a fbf gg fbf ce fbf cfbf fbf bf ga c c ag ce c ec gg ce c ac ca c ec gg ce c ac ca c ec ec gg cc ce gce c aca ac ecg ca cc c gce ec aca gg ecg ce cc c gce ec aca ga ecc c cce c gca ag ecg ce cc c gce ec aca gg ecg ce cc c gce ac aca ca ecg c cc ece ``` <!-- end of image -->

Time to put on my detective hat and find those intersection points! I wonder what's going on inside those areas? Perhaps intersections are hiding there. <!-- image --> ```palette Key,Color ,#fefefeff a,#474bf7ff b,#fd0707ff c,#0607feff d,#ffb2b2ff e,#9da2f4ff f,#acd4acff g,#f35d57ff ``` ```image g db b bd gb db b bd gb db b bd gb db b bd ca gb aca db ecc b ecc bd ecc gb ecce db cce b cce bd cce gb cca db aca b aca bd aca gb ecc db ecc b ecc bd ecce gb cc db ac fffffffffffffffb acffffffffffffffbg acffffffffffffgbf cafffffffffffbff fcafffffffffbfff ffcafffffffbgfff fffcafffffgbffff ffffceffffbfffff fffffceffbffffff ffffffcebgffffff fffffffcbfffffff fffffffbcfffffff ffffffbffcffffff fffffbgffecfffff ffffgbffffecffff ffffbffffffecfff fffbffffffffacff ffbgfffffffffacf fgbfffffffffffac fbfffffffffffffac bfffffffffffffffcc bgfffffffffffffff ca gb ca db ca dgb ce dggbbbbbgg ce ddgbbbbbbgd ce dgbbbbbbgdd ce dggbbbbbggd c bbbbgd c c ec ec ec ec ac ac ac ca ca ca ca ce ce ce c ``` <!-- end of image --> My goal is to determine if there's an intersection inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#5656feff b,#fe0909ff c,#0807fdff d,#fe9091ff e,#a7a7ffff f,#ffcacaff g,#fb4c50ff ``` ```image g db fbb c bbg cc gbb ccc dbbf cca fbbd cca bbg ecca gbb ecca dbbf ecca fbbd ecca bbg ecca gbb ecce dbbf ecce fbbd acce bbg acce gbb acce dbbf accefbbd accgbg accg dccc fbbccc bbg ccc gbb cca dbbf cca fbbd ecca bbg ecca gbb ecca dbbf ecca fbbd ecce bbg ecce gbb ecce dbbf acce fbbd acce bbg acc gbb ac dbbf a fbbd bbg gbb ``` <!-- end of image --> As I suspected, there's an intersection within area A. The final count is: one intersection.

<!-- image --> ```palette Key,Color ,#fefefeff a,#5959ffff b,#fe0707ff c,#0909ffff d,#ff9191ff e,#b1b1ffff f,#ffcbcbff g,#fd4e50ff ``` ```image d fb b bd gb fb b bd gb fb b bd gb fb b bd ca gb acc fb acc b ecc bd ecc gb ecce fb ecce b cce bd cce gb cca fb aca b aca bd acc gb acc fb ecc b ecc bd ecce gb ecc fb ac b ac bd cc gb ca fb ca b ca bd ca gb ce fb ce b cebd cg fbc b c bd ec gb ec fb ec b ac bd ac gb ac fb ac b cc bd ca gb ca fb ca dgb ca fdgbbbbbgdf ce fdgbbbbbbgd ce dgbbbbbbgdf ce fdgbbbbbgdf c bbbbgd c c ec ec ec ac ac ac ac cc ca ca ca ce ce ce c ``` <!-- end of image -->

Time to put on my detective hat and find those intersection points! I've spotted 2 narrow regions that might be worth examining further. Let's call them area A,, and B. <!-- image --> ```palette Key,Color ,#fefefeff a,#0607fdff b,#e54243ff c,#a7aaf9ff d,#e6968aff e,#aed5aeff f,#5156f3ff g,#fd0505ff ``` ```image fa aff ff a a ca ff a a ca ac ac a a ac af a a ac ff ca a a ca ca a gg a ca ggd ca ac dgg a eeaeeeeeeeeeeeee dgg ff eeafeeeeeeeeeeee bgb a eeeaeeeeeeeeeeee ggb ff eeeffeeeeeeeeeee ggd a eeeeaeeeeeeeeeee dggd ff eeeefaeeeeeeeeee dgg a eeeeeaeeeeeeeeebgb ac eeeeecaeeeeeebgb a eeeeeeaeeeeggbee ac eeeeeeeadggdeeee a eeeeeedabdeeeeee ac eeeebggeaeeeeeee ca eebgbeeeffeeeeee a ggbeeeeeeaeeeeee ca ggdeeeeeeeefaeeeee a dggd eeeeeeeeeeaeeeee eeeeeeeeeeeeeeeefaeeeeee dgg eeeeeeeeeecaeeee eeeeeeeeeeeeeeeeaeeeeeee bgb eeeeeeeeeeeaeeee eeeeeeeeeeeeeeefaeeeeeee dggd eeeeeeeeeeeeaeee eeeeeeeeeeeeeeeaeeeeeeee bgg eeeeeeeeeeeeafee eeeeeeeeeeeeeeffeeeeeeee ggb eeeeeeeeeeeeeaee eeeeeeeeeeeeeeaeeeeeeedggd ff eeeeeeeeeeeeeafeeeeebgbe a eeeeeeeeeeeeeaeeedggdeee ff eeeeeeeeeeeeafebggeeeeee a eeeeeeeeeeeeaggbeeeeeeee ca eeeeeeeeeebabdeeeeeeeeee a eeeeeeeeggbaeeeeeeeeeeee ca eeeeedggdeaceeeeeeeeeeee ac eeebggeeeeaeeeeeeeeeeeee a dggbeeeeeaeeeeeeeeeeeeee af dggdeeeeeecaeeeeeeeeeeeeee a d eeeeeeeeaeeeeeeeeeeeeeee ff eeeeeeefaeeeeeeeeeeeeeee a eeeeeeeaeeeeeeeeeeeeeeee ca eeeeeefaeeeeeeeeeeeeeeee a eeeeeeaeeeeeeeeeeeeeeeee ca ff ac a a ff ac a a ac ff a a ac ca a a ac ca ca ac a a ca ac a a ca ff a a fa a ca a a ac a ff a ff a ``` <!-- end of image --> Let's see what secrets area A holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#0908fdff b,#f9383eff c,#5e54f4ff d,#fec6c6ff e,#aaaaffff f,#ff8282ff g,#fe0303ff ``` ```image eaa aae eaa aae caa aae cac aae cac eaae d cac fbg eaa dfgggg cac fbgggbf eaa dfggggbd aac dbgggbf eaa fggggbd aae dbggggfd eaa fbgggbf aacggggfd caaggbf fbaabbd dbggcaad fbgggbaae dfggggfdcac dbgggbf aae dfggggbd cac dbggggf eaae fbgggbd cac dfggggfd eaa bgggbf cac ggbd eaa f aac eaa aae eaa aae eaa aae caa aae ``` <!-- end of image --> The lines cross each other within area A, forming an intersection. Now, let's scrutinize the next spot. I'm determined to find out if an intersection exists in area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#0605feff b,#f14451ff c,#8d8dfeff d,#ff9696ff e,#e0d1efff f,#4646ffff g,#fe0607ff ``` ```image aac caa aac caae fac eaae faf eaae faf eaac caa aac caa e fac ebg eaae dbggg faf dggggbe eaae dggggd faf ebggggd eaacebgggbd caagggbd dbaabbe dgggbaa dggggd fac ebggggd caae ebgggbd faf dbgggbe eaae dggggbe faf gggd eaae gd caf aac caa aac caae faf eaae faf eaae caf aac caa ``` <!-- end of image --> Success! This area contains an intersection point! After a long analysis, I found two intersections.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0505feff b,#f7535bff c,#7f7fffff d,#ffaeaeff e,#c3c3ffff f,#4242ffff g,#ff0707ff ``` ```image e ca acf ff a a ca fc ae a ea ac ae a a ae fc a a ae ff ea a ae ca ea a gg a ea dggd ca ae dggd a a bgg cf ac bgb a a ggb ff ff ggd a a dggd fc ca dgg a a bgg ac ea bgb a ae ggb ae adggd a dabd ae bgg a ea bgb ff ae ggb a ea ggd cf a dggd a ca dgg ea a bgg ae cf dggb ea a bggd ac ff ggb a a dggd fc fc bgb a a dggd cf ac bgg a aggb ca babd ae ggba ea dggd ae ae bgg ea a dggb ae fc bggd ea a b a ff ca a a ca cf a a ea ff ae a a fc ac a a ac ff a a ae ca a a ae ea ea ae ae a ea ac a a ca ff a a cf a ea ae ea ae a fc a cf a ``` <!-- end of image -->

I'm analyzing this image to identify any points where lines intersect. I'd describe these as 'hotspots' for potential intersections. <!-- image --> ```palette Key,Color ,#fefefeff a,#0a0bfeff b,#fe0909ff c,#ffaeaeff d,#6166f3ff e,#ff5d5dff f,#babaffff g,#afd6afff ``` ```image f daaf faa a aa a aaf fa dad fa fad da faa da aaf aa daf aa dad ad faa ad aa af aaf af dad a fad a faa fa aa fa aaf da dad da faa aa a ad ad ad af af a fa fa fa da da aa ad ggadgggggggggggggggg gggadggggggggggggggg ggggadgggggggggggggg gggggagggggggggggggg ggggggaggggggggggggg gggggggagggggggggggg gggggggdaggggggggggg ggggggggdagggggggggg gggggggggdaggggggggg ggggggggggaagggggggg gggggggggggaaggggggg ggggggggggggadgggggg gggggggggggggadggggg ggggggggggggggadgggg ccccccccceeeeeeeeebbbbbbbbbbbbbbbbbbbbbbbbbagggg bbbbbeeeeeeeeeccccccccc gggggggggggggggggggg be gggggggggggggggggggg bc gggggggggggggggggggg cb gggggggggggggggggggg eb gggggggggggggggggggg bb gggggggggggggggggggg be gggggggggggggggggggg be gggggggggggggggggggg cbc gggggggggggggggggggg cb gggggggggggggggggggg eb gggggggggggggggggggg bb gggggggggggggggggggg be gggggggggggggggggggg bc gggggggggggggggggggg cbc gggggggggggggggggggg eb eb bb be bc cb eb bb bb be bc cb eb bb be be ``` <!-- end of image --> My goal is to determine if there's an intersection inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0504feff b,#fe0909ff c,#fcb4b6ff d,#8181ffff e,#fc6b6eff f,#c0c0ffff g,#473cf4ff ``` ```image faag faag faad faad daad daaf daaf gaaf gaaf gaa gag aag faag faag faad faad daad daaf daaf gaaf gaaf gaa gag aag faag faag faad faad daad cccccccccccccccceeeeeeeeeeegaae bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbgaa bbbbbbbbbbbbeeeeeeeeeeeeeeeeeeegc ``` <!-- end of image --> Gotcha! I've found the intersection hiding in area A! I've found a single intersection point in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0404ffff b,#fe0909ff c,#ffaeaeff d,#7e7effff e,#ff5d5dff f,#c5c5ffff g,#3737ffff ``` ```image f daaf fag af aa a gaf fa dad fa dag da faa ga aaf ga gad ag dad ag fag ad aa af gaf af gad a dag fa faa fa aaf fa gaf da dad ga fag gg g ag ad ad af af a fa fa da da ga gg ag ad ad af af a fa fa da da ga gg ag ad ad ccccccccceeeeeeeeebbbbbbbbbbbbbbbbbbbbbbbbba bbbbbeeeeeeeeeccccccccc be bc cb eb bb be be cbc cb eb bb be bc cbc eb eb bb be bc cb eb bb bb be bc cb eb bb be be ``` <!-- end of image -->

Time to put on my detective hat and find those intersection points! There are 2 areas where the lines seem to converge. We should take a closer look at area A,, and B. <!-- image --> ```palette Key,Color ,#fefefeff a,#0809fdff b,#fc0f0eff c,#b7b6ffff d,#ea7872ff e,#5c5ff2ff f,#95c49aff g,#b1d6b0ff ``` ```image e a ac ca ac ca a ea a ee a ac a ac ca a ea a ee a ae a ac e ca ea a ac ca a a ee ee a a ca ae ae dbd a a bb bb ac ca bb dbd ca ac bb bb gffffffffffffaff a bb dbd fgggggggggggeagg ea bb bb fgggggggggggaggg ac bd gbd fggggggggggeaggg a bd bbfggggggggggagggg ee bd bbggggggggaegggg fafffffffffffffg bd fbbgggggggaggggg gfaggggggggggggfbg fggbbggggaeggggg ggaegggggggggggb fgggbbfgfagggggg gggaggggggggggbf fgggggbbafgggggg gggfagggggggfbgf fggggggdadgggggg ggggaegggggdbggf fggggggagbbggggg gggggaggggdbgggf fgggggeaggdbdggg gggggeaggdbggggf fgggggagggggbbgg ggggggafdbgggggf fggggaeggggggdbd gggggggabggggggf fggggagggggggggbb ggggggbeaggggggf fgggaeggggggggggdbd gggggbbgafgggggf fgggaggggggggggg bb ggggbbgggagggggf fggafggggggggggg gbd gggbbggggaeggggf fgfagggggggggggg bb ggbbggggggaggggf gfafffffffffffff bd gbbgggggggfagggf ea bb bdgggggggggaeggf a bb bdgggggggggggaggf ee db bdggggggggggggeagf a bb bg fggggggggggggaef ae db bg a a b ea ac b ac ca gb a a db ee ca b a a ca ee ae a a ae ca a ae ac a ca ca a ac ca a a ea ee ac a a ae ee a aac ca ``` <!-- end of image --> Let's put area A under the microscope. <!-- image --> ```palette Key,Color ,#fefefeff a,#0505feff b,#ff0707ff c,#9494ffff d,#fb4246ff e,#443bf6ff f,#ecdaedff g,#fb9599ff ``` ```image faac caaf eae faac caaf eae fd faac fdb caa fbbb aac fbbbf caaf fbbdf eae fbbd faac gbbd caaf gbbd eae gbbd faac gbbd caaf gbbd eae gbbg faac gbbg caadbbg eaebg daag dbeae dbbgaac fdbbf caaf fdbbf eae fbbbf faac fbbbf caaf fbbdf eae fbbdf faac gbbd caaf gbbd eae gbbd faac gbbd caa gbbd aac bbg caaf bg eae g faac caaf eae faac ``` <!-- end of image --> Aha! I've found an intersection inside area A! Let's move forward and inspect another region. Let's put area B under the microscope. <!-- image --> ```palette Key,Color ,#fefefeff a,#0908feff b,#fe0404ff c,#a4a1fcff d,#fd3d3fff e,#5c57f9ff f,#eddbedff g,#fa8f93ff ``` ```image caaf aae caaf aac caa faac eae faac f eae bg caaf bbdf aae gbbbg caaf fdbbdf aac gbbbg caa fdbbdf faac gbbbg eaa fdbbdf faac gbbbg eae fdbbdcaaf gbbaae gaadg aaebbd caafgbbbg aac fdbbdf eaa gbbbg faac fdbbdf eae gbbbg faaf fdbbdf eae gbbbg caaf fdbb aae gb caa f aac eaa faac eae faaf eae caaf aae ``` <!-- end of image --> I can confirm that an intersection exists in area B. The image features two intersection points.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0404feff b,#ff0808ff c,#bcbcffff d,#fc5053ff e,#3a37fcff f,#7575ffff g,#ffb0b0ff ``` ```image f a ac ca ac ca a fe a ef a af a ac ca a fe a ee a af a ac f ca fe a ac fa a a ee fe a a ca ef af dbg a a db bb ac ca bb gbg ca ac bb bb a a bd gbd ca fa bd bb a ac bd gbd fe a bd bb a ee bg gbd ef a bg db a ca bg bd ac ef bg dbg ca a b bbac ca gb dag af gb a bb a gb fe dbg fa gb a bb acdb ef gbg ab a bb dee af gbd db ac a bb bb a ac gbd bb ee ca bb bd a a gbd bd ca fe db bd af a bd bd a ee dbg bg ca a bb bg ac af db bg a a bg fa ac gb ac ca gb a a gb ee fa d a a ca fe ef a a ef ca a af ac a ca fa ac ac ca a a fe fe ac a a ef ee a aac ca ``` <!-- end of image -->

I'm ready to tackle this image and find those intersections! These zones indicate regions where lines appear to be in close proximity. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0908ff b,#0707feff c,#aeaffdff d,#f7615dff e,#add5adff f,#febfbfff g,#5256f6ff ``` ```image c bbbbbgc cbc gbbbbg bb cgbbbbg bg cgbbbbc cbc cgbbbgc eeeeeeeeeeeeeeee bb cgbbbgc eeeeeeeeeeeeeeee bg cgbbbgceeeeeeeeeeee cbc eegbbbbgeeeeeeee bb eeeeeeegbbbbgeee bg eeeeeeeeeeeegeee cbc eeeeeeeeeeeeeeee bb eeeeeeeeeeeeeeee bg eeeeeeeeeeeeaeee cbc eeeeeeeeeeaadeee bb eeeeeeeeaadeeeee bg eeeeeeaadeeeeeee cbc eeeeaadeeeeeeeee bb eeaadeeeeeeeeeee bg faadeeeeeeeeeeeee cbc faaeeeeeeeeeeeeeeee bb faaf eeeeeeeeeeeeeeee bg faaf eeeeeeeeeeeeeeee cbc faaf eeeeeeeeeeeeeeee bb faa eeeeeeeeeeeeeeee bg faa eeeeeeeeeeeeeeee cbc faa eeeeeeeeeeeeeeee bb daa eeeeeeeeeeeeeeee c daa daa dad dad dad dad aad ad da fa a af ad da fa a af ad da fa a af ad da fa a af ad da fa a af ad da fa a af ad da fa a af ad da fa a af ad da fa a af ``` <!-- end of image --> This close-up might reveal an intersection in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff0303ff b,#0505ffff c,#bbbbffff d,#ff2727ff e,#8a8affff f,#ff9595ff g,#4a4affff ``` ```image bgec bbbbbbgec ceggbbbbbbbgec ceggbbbbbbbgec cegbbbbbbbggec cegbbbbbbbgge cegbbbbg cee fdf fdaad fdaaaf fdaaaf fdaaaf fdaaaf fdaadf fdaadf faaadf faaadf faaadf faaadf faaadf aaadf adf f ``` <!-- end of image --> No intersection found in area A, but I won't give up. My final answer is: no intersections found.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0808ff b,#0707ffff c,#c6c6ffff d,#ff5d5dff e,#8f8fffff f,#ffbabaff g,#4f4fffff ``` ```image c bbbbbgc ebc ebbbbec bb cgbbbbe bg cgbbbbe ebc cgbbbge bb cgbbbge bg egbbbgc ebc ebbbbgc bb ebbbbg bg ce ebc bb bg d ebc aad bb aad bg aad ebc aaf bb aaf bg aaf ebc faaf bb faaf bg faaf ebc faa bb faa bg faa ebc faa bb daa c daa dad dad dad dad dad aad ad da fa a af ad da fa a af ad da fa a af ad da fa a af ad da fa a af ad da fa a af ad da fa a af ad da fa a af ad da fa a af ``` <!-- end of image -->

I'm analyzing this image to identify any points where lines intersect. The image has some tight areas where segments are too close. I should investigate those closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#f55955ff b,#0505feff c,#4448f7ff d,#fe0606ff e,#fcaaa9ff f,#9f9ffeff g,#add4acff ``` ```image e da d ed de d ad d d aa d ed de d ad de d aa d ed de d ad de d aa d ed de d ed de d aa d ed da d ed de d aa d f ed cbc da fbc d fbb edgggggggggggggggg fbb daggggggggggggggg fbb dggggggggggggggg fbb adgggggggggggggg fbb gdgggggggggggggg ead fbbf ggdggggggggggggg eaddddae bbf ggdagggggggggggg eaddddae bbf gggdgggggggggggg eaddddae bbf gggadggggggggggg eadddddae bbf ggggdaggggggggggeadddddae bbf gggggdggggeadddddae bbfgggggadddddagggg cbcgggggggggggggg gcbcgggggggggggg gggcbcgggggggggg gggggcbbgggggggg fbbf bbc cbb fbbf cbc fbbf bbc cbb fbbf cbc fbbf bbc cbb fbbf bbc fbbf fbbf cb ``` <!-- end of image --> I'm now examining the contents of area A in detail. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff3939ff b,#0303ffff c,#5555ffff d,#ff0404ff e,#ffbabaff f,#c6c6ffff g,#ff7474ff ``` ```image e d dg dde gda ddg edd ada edde gdd adg edde gda ddg edde ada edde gdd eegad adg eggaddddddd edde eggaddddddddaagee gdddddddddaagee c dddaagee bbc e cbbbcf fcbbbcf fcbbbcf fcbbbcf fcbbbcf fcbbbbf ``` <!-- end of image --> The evidence suggests that this is not an intersection point in area A. I can confidently say that there are no intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff3f3fff b,#0a0affff c,#6c6cffff d,#ff0404ff e,#ffbcbcff f,#bdbdffff g,#ff7c7cff ``` ```image e ag d ed de d ga de d aa d ed dg d gd de d aa d ed dg d gd de d aa d ed dg d gd de d aa d ed dg d gd de d aa d c ed cbb dg cbb d cbb gd cbb de fbb d fbb aa fbbf d ead fbbf ed gaddddag fbbf ag gaddddae fbbf d egaddddae bbf ed egaddddae bbf de egdddddge bbc d egdddddge bbc gddddage bbc e bbc cbc cbb cbbf bbc cbbf fbbc bbb cbbf fbbc cbb fbbc bbc cbbf fbbc cbb fbbf bbc cbbf fbbc cb ``` <!-- end of image -->

I have an image in front of me. I need to determine if there are any intersection segments. These areas seem to enclose narrow spaces where lines might be close. <!-- image --> ```palette Key,Color ,#fefefeff a,#0808feff b,#f84c49ff c,#5b5df8ff d,#f59893ff e,#fe0303ff f,#add4aeff g,#b8b8ffff ``` ```image aa accc ag a gag ga ga a ca ga ca ag aa a ac ac ac a ag cc gag a ga ga ca a ca ga aa ag ac a ac ac ag a gag cc ga a ca ca ca a aa ga ac ag ac a ag ag gag a ga cc ca a ca ca aa a g ga ag ga ag a ac a cc a ga a ga ag a ac a cc a ga a ga ag eeeebd a dbeeeeebd ac dbeeeeebd a dbeeeeebd cc dbeeeeebd fffffaffffffffffff dbeeeebd fffffcafffffffffff dbeeeebd ffffffafffffffffff dbeeeebd fffffffaffffffffff deeeeed fffffffaffffffffff dbeeeebdffffffffafffffffff dbeeeebdffacffffffff ffffdbeeeabdffffff fffffffffaceeeeebf ffffffffffaffffdbf ffffffffffcaffffff fffffffffffaffffff fffffffffffcafffff ffffffffffffafffff fffffffffffffaffff fffffffffffffacfff a ac a cc a ``` <!-- end of image --> I'm eager to see what's happening in this magnified view of area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0706feff b,#fa3035ff c,#5c53f6ff d,#ffb3b3ff e,#fe0102ff f,#ff7070ff g,#b7b7ffff ``` ```image gaag cac aag caa aag gaa aac gaa cac gaag cac d aag eeebfdd caa beeeeeeebbfdd aag ddfbbeeeeeeebffcaa ddfbeeeeeeaacffd dffbbaaeeeeebfdd cacfbeeeeeeebbfd gaag ddfbbeeeeb cac ddff aag caa aag gaa aac gaa cac gaag cac gaag cac ``` <!-- end of image --> Success! This area contains an intersection point! It was tricky, but I finally found one single intersection in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0505ffff b,#ff4d4dff c,#7b7bffff d,#ff9c9cff e,#fe0303ff f,#3f3dfcff g,#c1c1ffff ``` ```image g aa accf ag a gag ca ca ag ca ga fa ag aa a af fc ac a ag ff gag a ga ca ca a fa ga aa ag af a ac ac ag a gag ff ga a ca ca fa a aa ga af ag ac a ag ac gag a ga fc ca a fa cf aa a g ga ag ga ag a fc a cf a ca ag ga ag a fc a ff a ca a ga ag eeeebd a dbeeeeebd ac dbeeeeebd a dbeeeeebd ff dbeeeeebd a dbeeeebd ca dbeeeebd a dbeeeebd ga deeeeed ag dbeeeebd a dbeeeebd ac dbeeeabd ffbeeeeb a db cf a ga ag ga ag a fc a cf a ``` <!-- end of image -->

I'm examining this image closely. My goal: find any and all intersections. It's crucial to examine these regions more closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd0707ff b,#6a72edff c,#f09891ff d,#97c798ff e,#f34a45ff f,#0b0afbff g,#b1d7b1ff ``` ```image bff f bf fb fb f ff f bfb bf ff f bf bb fb f ff fb gfb gf ff f bfg dggggggggggggggggg bf ff dggggggggggggggggg f bf dggggggggggggggggg fb fb dggggggggggggggggg f ff dggggggggggggggggg f bfb dggggggggggggggggg bf ff dggggggggggggggggg f bf dggggggggggggggggg bb fb dggggggggggggggggg f ffdggggggggggggggggg fb gfbgggggggggggggggg f dffggggggggggggggg f dgbfdggggggggggggg gddddddddddddddd bf dgggffgggggggggggg dggggggggggggggg f dggggffggggggggggg dggggggggggggggg fb dgggggdfbggggggggg dggggggggggggggg f dgggggggffgggggggg a dgggggggggggggggfg dggggggggbfbgagggg ca dggggggggggggggbf dggggggggggffagggg aedggggggggggggggf dggggggggggeffgggg adgggggggggggggbf dgggggggggcagggggg agggggggggggggfg dggggggggdaggggggg eagggggggggggfbg dggggggggagggggggg dacgggggggggdfgg dgggggggadgggggggg dgagggggggggfdgg dggggggacggggggggg dgcagggggggbfggg dgggggaegggggggggg dggaeggggggfgggg dggggaaggggggggggg dgggagggggfbgggg dgggeagggggggggggg dggggaggggfggggg dggcaggggggggggggg dggggeaggfbggggg dgdagggggggggggggg dgggggacbfgggggg dgaggggggggggggggg dggggggafggggggg dacggggggggggggggg dggggggbfggggggg aegggggggggggggggg dggggggfaegggggg aeggggggggggggggggg dgggggfbgadggggg eadggggggggggggggggg dggggdfgggaggggg ca dggggggggggggggggg dggggfdgggeagggg ca dggggggggggggggggg dgggbfgggggacggg a dggggggggggggggggg dgggfgggggggaggg a gddddddddddddddddd dggfbgggggggcagg ac dggfgggggggggaeg ac dgfbggggggggggad ae ddfgggggggggggga ea dfgggggggggggggea ca bfggggggggggggggac ca fggggggggggggggg a a fbggggggggggggggg ca a fdggggggggggggggg ee ac f dggggggggggggggg a ae bf dggggggggggggggg a ae f dggggggggggggggg ea ea gddddddddddddddd ac ca a a ca a ee a a ac a ae ca ee ac ea a ca ca a ee a a ac a ac ca ae ac ea aea ca ``` <!-- end of image --> This close-up might reveal an intersection in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd0708ff b,#5b56faff c,#ff9292ff d,#a3a3ffff e,#ff4b4bff f,#0808feff g,#efd5e5ff ``` ```image d f df gff g bfb e dffg ac ffb aag dff eaa ffd aae bff gaac gffd caag bfb eae dffg gaac ffb caag dff eaa gffd aae bfb gaac dffg caag bfb eae dffg gaac ffd caag bff eaa gffd aae bfb gaac dffg caagffb eabff gaffd bffg gffaa bfbaae dffggaac ffd caag bff eae gffd gaac bfb caag dffg eaa ffb aae dff gaac ffd caag bff eae gffd gaac bfb caag dffg eaa ffd aae bff gaac gffd caag bfb eae dffg gaa ffb ca dff e ffd bff ffd fb fg b ``` <!-- end of image --> I've cracked the case! This area contains the intersection. Let's shift our focus to the next area. Let's put area B under the microscope. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd0607ff b,#433ef9ff c,#ff9b9bff d,#8e8dfeff e,#ff4b4bff f,#0605fdff g,#ecd6e8ff ``` ```image d fbg fffd bffbg dfffd gbffb dfffg gfffd bffbg dfffd gbffb dfffd gbffd dffbg dfffd bffbg g dfffd gae gbffbgaae dfffae gfffd eabffb caacdfd caac g caac gaae gaae eae eaag eaag caac caac caac gaae gaae eaa eaag eaag caac caac gaae gaae gaae eaag eaag eaag caac caac aae ae e g ``` <!-- end of image --> I am surprised, so clear, an intersection has appeared in area B. There's for sure two intersections on the image you sent me.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0909ff b,#4b47fbff c,#ffa3a3ff d,#9696ffff e,#ff5555ff f,#0605feff g,#e9d9eeff ``` ```image g bfb f bfg fd gfb gf ff fg dfd df ff f bfg bb gfb f bf fd dfd gf ff fg dfg db fb f bfg fd gfb gf ff fg dfd df ff f bfg bb gfb f bf fd dfd gf ff fg dfg df fb f bfg bb gfb gf ff a fg dfd a ca df ffe ae f ebf ag bb ca g ga f ga ea fd a ac gf ag a fg ac ca df ae ae f ea ag bb ea ga f ca ea fd ga acdf ag af ac bf ac fae ae fd ag ea gf ga ea fg ea ca df ac ga f a ag bb ca ac f ae ae fd ag ae gf ga ea fg ea ca bb ac ca f a ga fd ca ag gf ae ac fg ag ae df ga ae f ea ea ac ca a ga ca a ae ag ag ac ga ae ea aa ac ea a ca ca ga ee a ag ag a ac ea ae ac ea aea ca ``` <!-- end of image -->

I'm ready to tackle this image and find those intersections! These zones are intriguing. I bet there's something interesting happening within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0606ff b,#0506fdff c,#999df6ff d,#fca9a7ff e,#4a48f3ff f,#acd4acff g,#f74946ff ``` ```image d da a a ad ag ga da a a ad ag ga da a a c ad ebbbe ag cbbbec ga cebbbc da cebbbe a cbbbec a cebbbc ad ebbbe ag cbbbec ga cebe da ebc ffffffffffffffaf bbc fffffffffffffaff bb ffffffffffffadff cbbffffffffffagfff ebefffffffgaffff ffbbcffffgafffff ffffbbfffaffffff fffffcbbafffffff fffffffebeffffff ffffffagfbbcffff fffffgaffffbbfff ffffgaffffffcbbf ffffafffffffffebe fffaffffffffffffebc ffadffffffffffff bb fagfffffffffffff bb ga cbe da ebc da bb a bb ad cbe ag ebc ga bbc da bb da c a ad dad ga aa dad ga ag dad ga ag dad ga ag dad ga ag dad ga ag dad aa ag dad aa ag dad aa ag ``` <!-- end of image --> Let's put area A under the microscope. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff0808ff b,#0505feff c,#9595ffff d,#fc9fa1ff e,#4b42f6ff f,#e9d5ebff g,#fb4f52ff ``` ```image faag aag gaaf gaaf daad c daad bef faag bbbef aag febbbc gaaf febbbc gaaf cbbbef daad cbbbef daad ebbbc faag febbbc aag cebbegaaf cbbbef debbbe daadebbbc faag febbbc aag cbbbef gaaf cbbbef gaaf febbbc daad febbbc daad cbbbe faag cbb aag fe gaa gaaf daad daad faag ``` <!-- end of image --> Aha! I've found an intersection inside area A! There's one and only one intersection present in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0606ff b,#0404ffff c,#9898ffff d,#ffa3a3ff e,#4944faff f,#ecd9ebff g,#ff4848ff ``` ```image d da fa af ad ag ga da fa af ad ag ga da fa af c ad ebbbef ag cbbbec ga cebbbc da febbbef fa cbbbec af cebbbc ad febbbef ag cbbbec ga cebe da ebc fa bbf af fbb ad cbe ag ebc ga bbc da fbb fa cbeaf ebe ag ebc ga bbf da fbb fa cbe af ebc ad bbf ag fbb ga cbe da ebc fa bbf a fbb ad cbe ag ebc ga bbf da fbb fa c a ad fad ga aa dad ga ag dad ga ag dad ga ag dad ga ag dad ga ag dad aa ag daf aa fag daf aa ag ``` <!-- end of image -->

I'm approaching this image with caution. Intersections might be tricky to spot. These spots mark what I'd call 'danger zones' - areas where intersections are more likely. <!-- image --> ```palette Key,Color ,#fefefeff a,#4e56efff b,#fa0a0aff c,#919de6ff d,#e26660ff e,#b1d7b1ff f,#9ac696ff g,#0809fdff ``` ```image c gc g aa g aa g cg g cg g cg g g gc g gc g gc g g d aa ag db g ag db aa cg dbffffffffgffffffffffffffffffffffffffffffffffffff g bbeeeeeeeageeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee g ebbeeeeeeegeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee g eebbeeeeeecgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee gc eeebdeeeeeegeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee gc eeeebdeeeeecgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee ga eeeeebdeeeeegceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee gg eeeeeebdeeeefgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee ag eeeeeeebfeeeegceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee cg eeeeeeeebfeeeegeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee cg eeeeeeeeebfeeegceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee g eeeeeeeeeebeeeegeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee g eeeeeeeeeefbeeegaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee g eeeeeeeeeeefbeeegeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee gc eeeeeeeeeeeedbeeaaeeeeeeeeeeeeeeeeeeeeeeeeeeeeee ga eeeeeeeeeeeeedbeegeeeeeeeeeeeeeeeeeeeeeeeeeeeeee ga eeeeeeeeeeeeeedbeageeeeeeeeeeeeeeeeeeeeeeeeeeeee ag eeeeeeeeeeeeeeedbegeeeeeeeeeeeeeeeeeeeeeeeeeeeee ag eeeeeeeeeeeeeeeedbageeeeeeeeeeeeeeeeeeeeeeeeeeee cg eeeeeeeeeeeeeeeeebbgeeeeeeeeeeeeeeeeeeeeeeeeeeee cg eeeeeeeeeeeeeeeeeebdgeeeeeeeeeeeeeeeeeeeeeeeeeee g eeeeeeeeeeeeeeeeeeebgeeeeeeeeeeeeeeeeeeeeeeeeeee g eeeeeeeeeeeeeeeeeeeebgeeeeeeeeeeeeeeeeeeeeeeeeee gc eeeeeeeeeeeeeeeeeeeeegdeeeeeeeeeeeeeeeeeeeeeeeee gc eeeeeeeeeeeeeeeeeeeeeegdeeeeeeeeeeeeeeeeeeeeeeee ga eeeeeeeeeeeeeeeeeeeeeegbdeeeeeeeeeeeeeeeeeeeeeee ga eeeeeeeeeeeeeeeeeeeeeeegbdeeeeeeeeeeeeeeeeeeeeee ag eeeeeeeeeeeeeeeeeeeeeeegabfeeeeeeeeeeeeeeeeeeeeeag eeeeeeeeeeeeeeeeeeeeeeeegebfeeeeeeeeeeeeeeeeeeecg eeeeeeeeeeeeeeeeeeeeeeeegaebfeeeeeeeeeeeeeeeeecg eeeeeeeeeeeeeeeeeeeeeeeeegeebeeeeeeeeeeeeeeeeegf eeeeeeeeeeeeeeeeeeeeeeeeeaaefbeeeeeeeeeeeeeeegfe eeeeeeeeeeeeeeeeeeeeeeeeeegeefbeeeeeeeeeeeeegcee eeeeeeeeeeeeeeeeeeeeeeeeeeageedbeeeeeeeeeeegaeee eeeeeeeeeeeeeeeeeeeeeeeeeeegeeedbeeeeeeeeegaeeee eeeeeeeeeeeeeeeeeeeeeeeeeeeageeedbdeeeeeeggeeeee eeeeeeeeeeeeeeeeeeeeeeeeeeeegeeeeebbdeeeageeeeee eeeeeeeeeeeeeeeeeeeeeeeeeeeecgeeeeeebbdageeeeeee eeeeeeeeeeeeeeeeeeeeeeeeeeeeegeeeeeeeedgdeeeeeee eeeeeeeeeeeeeeeeeeeeeeeeeeeeecgeeeeeefgebbdeeeee eeeeeeeeeeeeeeeeeeeeeeeeeeeeeegceeeeegeeeedbdeee eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegeeeegceeeeeedbbe eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegceegceeeeeeeeedbb eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegegaeeeeeeeeeeeedbb eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeggaeeeeeeeeeeeee dbb eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegeeeeeeeeeeeeee dbb eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee ebb eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee ebb eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee bbe ffffffffffffffffffffffffffffffffffffffffffffffff bbe bbd bbd bbd bbd dbd dbd db ``` <!-- end of image --> Let's get to the bottom of what's happening inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#3931f6ff b,#fd0809ff c,#c2c2feff d,#fa5256ff e,#feaeaeff f,#7d7bfdff g,#0404feff ``` ```image bbe fga dbb ggc bbb fga bbb ggf bbb fgg bbd agf ebbd cgg ebbd agf ebbd cgg ebbd agf ebbd cggc ebbd agf ebbe cggc ebbe aga dbbe cggc dbbe fga dbbe ggc dbbe fga dbbe ggc dbbe fga dbb ggf bbb fgg bbb agf bbd cgg bbd agf ebbd cgg ebbd agf ebbd cggc ebbd aga ebbd cggc ebbd fga ebbe cggc ebbe fga dbbe ggc dbbe fga dbbe ggc dbbefga dbbeggf dbbfgg dbbagf bbdgg bbagf bbgg bagf ebggc eaga eggd agad cggbd fgabe ggbbe fgabbe ggfbbe fggdbbe ggfdbbe fgg dbbe agf dbbe cgg dbb c agf dbb cg cggc bbb cgg agf bbb aga cggc bbd aga aga ebbd aggc cggc ebbd fggc fga ebbd fggc ggc ebbd fggf fga ebbd cggf ggc ebbd cggf fga ebbe cgga ggf ebbe gga fgg dbbbe aga agf ebbbbe aggc fgg ebbbbe aggc agf ebbbbe fggc cgg ebbbbe fggc agf ebbbdggf cggc edggad agf cggabbbd cggc cgga edbbbd aga aga edbbbde cggc aga edbbbde fga aggc edbbbde ggc fggc edbbbde fga fggc dbbb ggc fggc db fga cggf ggf cggf fggcgga aggga cgga aa ``` <!-- end of image --> The lines cross each other within area A, forming an intersection. The final answer is: two intersections found.

<!-- image --> ```palette Key,Color ,#fefefeff a,#3737ffff b,#fd080aff c,#c1c1ffff d,#f85960ff e,#ffb0b0ff f,#7a7afeff g,#0404feff ``` ```image c af g af g fa g fa g fg g cg gc cg gc g gf g af g a d af ag db g fg db fa cg db g cg bb fa g bb g gc bd cg gc bd g gf bd cg ga be gc aa be cg ag be gc fg be g cg b gf cg b g g b af gc eb g gc eb aa gf eb g ga db fa aa db g fg dbfa fg dbg cg bdg g bg g bg gc gd gf cgd gf gbe aa gbe ag gfbe fg g be cg af b cg g b g aa eb gc g eb gc fa eb gf g eb ga fg dbe aa g bbe ag cg bbdfg gc dgd cg cg dbd gc g dbd g gc dbd gc gc dbb g gf dbb aga ebb a ebb ebb ebbe ebbe bbe bbe bbe bbd bbd dbd dbd db ``` <!-- end of image -->