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oliveirabruno01

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

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The hunt for intersections begins! Let's analyze this image closely. Let's take a closer look at what's happening inside these zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#0b0bfeff b,#fd0c0bff c,#6c6efaff d,#ee776fff e,#dacaeeff f,#b0d7b0ff g,#99c697ff ``` ```image gffffffffffffffg gffffffffffffdff gfffffffffffdbff gffffffffffgbfff gffffffffffbffff gfffffffffbgffff gffffffffbdfffff gfffffffbdffffff gffffffbbfffffff gfffffbbffffffff gffffdbfffffffff gfffdbffffffffff gffgbfffffffffff gffbfffffffffaff gfbgffffffffacff gbdffffffffgafff bdfffffffffaffff bbgggggggggacgggg db ea db ae eb cc b a b ae be ca bd a bd ae bb ca db a db ac eb ea b a be ac be ea bd a bd ac bb ea db ae db ca eb a b ae be ca bd a bd ae bb ca ggggggggggggggf db a ffffffffffffffg db ac ffffffffffffffg eb ea ffffffffffffffg eb a ffffffffffffffg b ac ffffffffffffffg be ea ffffffffffffffg edbd ae ffffffffffffffg eedddbbbbbbbbbbbbbbd cc ffffgdddbbbbbbbbbbbbbbdddde ea fffbbbddddgfffg ae ffffffffffffffg ca ffffffffffffffg a ffffffffffffffg ae ffffffffffffffg ca fffgffffffffffg a fffaafffffffffg ac ffffgaafffffffg ea ffffffcacfffffg a aae ac eaa ea cac a aae ac eaa ea cac ae aae ca eaa a cac ae aae ca eaa a cac ae aae ca eaa a cac ac aae ea aa a cacac aa ``` <!-- end of image --> Let's see if area A yields any clues. <!-- image --> ```palette Key,Color ,#fefefeff a,#0808ffff b,#ff0202ff c,#5050ffff d,#ffc7c7ff e,#b4b4ffff f,#ff8282ff g,#ff3c3cff ``` ```image dddd ddddffffgggggbbbbbbb dbbbbbbbbbbbbbbbbbbbgg dbbbggggffffdddd ace eaaac caaae eaaace eaaac ``` <!-- end of image --> It's a shame, but area A doesn't contain an intersection. Okay, on to the next area of interest. This close-up of area B is like examining a piece of evidence. <!-- image --> ```palette Key,Color ,#fefefeff a,#0e0effff b,#ff0404ff c,#7474ffff d,#ffababff e,#f5d9e2ff f,#ff7474ff g,#ff3737ff ``` ```image fe fbg dbbd dbbf ebbf ebbg egbg gbbe gbbe fbbd fbbd dbbf dbbf ebbg ebbg gbge gbbe fbbe fbbd dbbd dbbf dbbf ebbg egbg eac gbge caa gbbe caae fbbe aac fbbd caa dbbd eaae dbbf aac ebbf caa ``` <!-- end of image --> Hmm, it seems there's no intersection in area B after all. My final answer is: no intersections found.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0505ffff b,#ff0505ff c,#7979ffff d,#ffaaaaff e,#c8c8ffff f,#3535ffff g,#ff5151ff ``` ```image d db db b b bd bg bg gb gb db b b a bd ac bd ea bg a bg fc gb ea db a db ff b a b ae bd cf bd a bg ae gb ca gb a db ac db ea b a b ac bd ea bg a bg ff gb ea gb ae db ff db a b ae bd ca bd a bg ae bg ca gb a db ac db ea b a b fc bd ea ddbd a ddgggbbbbbbbbbbbbgd ff dddgggbbbbbbbbbbbgggddd a bbgggdd ae cf a ae ca e a aa ac eaf ea cac a aa ac eaf ea cac a aae ff eaf ea cac ae aae ff eaf a cac ae fae ca eaa a cac ae fae ca eaa a cac ac fae ea aa a cacfc fa ``` <!-- end of image -->

I'm approaching this image with caution. Intersections might be tricky to spot. I'm going to focus my attention on these specific areas. <!-- image --> ```palette Key,Color ,#fefefeff a,#ea6f65ff b,#4b50f2ff c,#fb0e0cff d,#9ba1f4ff e,#b2d7b1ff f,#0505fdff g,#99c596ff ``` ```image d f fd df f fd df f bb f f bf f fd df f bb f f bf f fd df f bb f f bb f fd df f c fb cc f ac f ac bb ec f c fd c df c f ce fb ca f ca f cc bb cc f ac fd ac df ec f c fd c df c f ce bb ca f ca fd cc df cc f ac c fd ac ca df ec ac f c cc bb c aca eggggggggggggggggggggggggggggggggfggggggggg c ccgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefdeeeeeeeeece acaeeeeeeeeeeeeeeeeeeeeeeeeeeeeebfeeeeeeeeeca gcceeeeeeeeeeeeeeeeeeeeeeeeeeeefeeeeeeeeeca gegcceeeeeeeeeeeeeeeeeeeeeeeeefbeeeeeeeecce geeeccgeeeeeeeeeeeeeeeeeeeeeedfeeeeeeeeccee geeeeecceeeeeeeeeeeeeeeeeeeeefeeeeeeeeaceee geeeeeeacaeeeeeeeeeeeeeeeeeebbeeeeeeeaceeee geeeeeeeecceeeeeeeeeeeeeeeeefeeeeeeeaceeeee geeeeeeeeeacaeeeeeeeeeeeeeefgeeeeeegceeeeee geeeeeeeeeeecceeeeeedbfffffbeeeeeeeceeeeeee geeeeeeeeeeedbffffffbbdeeeeeeeeeeecgeeeeeee geeegbbffffffbdccgeeeeeeeeeeeeeeecgeeeeeeee dbffffffbbgeeeeeeeeecceeeeeeeeeeeeecaeeeeeeeee bfffffbddgeeeeeeeeeeeeeeeeeacaeeeeeeeeeecaeeeeeeeeee d geeeeeeeeeeeeeeeeeeecceeeeeeeecceeeeeeeeeee geeeeeeeeeeeeeeeeeeeeacaeeeeecceeeeeeeeeeee geeeeeeeeeeeeeeeeeeeeeecceeeaceeeeeeeeeeeee geeeeeeeeeeeeeeeeeeeeeeegccaceeeeeeeeeeeeee geeeeeeeeeeeeeeeeeeeeeeeeecceeeeeeeeeeeeeee geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee ``` <!-- end of image --> I'm determined to find out if an intersection exists in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe3939ff b,#5e5cfcff c,#ff0404ff d,#afaefeff e,#fec3c3ff f,#0807feff g,#ff7d7dff ``` ```image dff ffb bff dffd ae ffb ccg bff g accae ffd ec ecccg bfb ecc gccce dff ecca eaccae ffd ecca gcccg bff aca eaccae dffd aca gcccg ffb acce accae bff acce ecccg dffd gcce gccce bfb gcce eaccae dff gccg gcccg ffd eccg eaccae bff eccg gcccg dffd ecca accae ddbbbfffb ecca ecccg ddbbbffffffffffb aca gccce dddbbffffffffffffbbddd aca ddbbffffffffffffbbbdd acce ddbbbffffffffffffbbdd acce dddbbffffffffffffbbdddaccae gcce ddbbbfffffffffffbbbdd gcccg gcce ffffffffffbbdd accae gccg ffbbddd ecccg eccg gccce eccg eaccae ecca gcccg ecca eaccae aca gcccg aca accae acce ecccg acce gccce gcce eaccaegcce gcccccg eaccg eg ``` <!-- end of image --> My analysis confirms the presence of an intersection in area A. I have found one intersection!

<!-- image --> ```palette Key,Color ,#fefefeff a,#fe5555ff b,#3836fcff c,#ff0808ff d,#bebeffff e,#ffb4b4ff f,#0303ffff g,#7a79fdff ``` ```image g f fd gf f fg df f bb f fd gb f fg df f bg f fd gb f fd df f bg df fd gb f fd df f c bg ac df ac f ec gb ec f ec fd c gf ce f ce bg ce df ca f ca bb ac f ac fd ec gf ec f ec fg c df ce f ce bb ce f ca fd ca gf ac f ac c fg ac eca df ec ace f ec cc bb c ace f ce cc fd ce eca gf ce cc f ca eca fg ca ace df ac cc f ac ace bb ac cc f ec eca fd ec cc dgbffffb c dgbfffffbgd c dgbfffffbgdace ce dgbfffffbgd cc ce bfffffbgd ace ca d cc ca eca cc cc ac ecaac ac ``` <!-- end of image -->

I'm on the case! Let's uncover any intersections hidden in this image. I'd describe these as 'hotspots' for potential intersections. <!-- image --> ```palette Key,Color ,#fefefeff a,#0707fdff b,#f47f7aff c,#5d62f5ff d,#b1d7b1ff e,#fb0d0dff f,#96c897ff g,#b5b5ffff ``` ```image g ag a ag ga a ga a cc a cc a ag a ag ga a ga a cc a cc a ag a ag ga a ga a cc a cc a ag a ag ga a ee dfffffcaffffffffffffffd bee fddddddaddddddddddddddf eeb fddddddccdddddddddddddf eeb fdddddddadddddddddddddf beefdddddddacddddddddddddf beebddddddaddddddddddddf ffffffffffffff ffeebddddacdddddddddddf dddddddddddddd fdddeeedddadddddddddddf dddddddddddddd fdddddbeedafddddddddddf dddddddddddddd fdddddddbeeaddddddddddf dddddddddddddd fddddddddddaebddddddddf dddddddddddddd fddddddddddcaeeeddddddf dddddddddddddd fdddddddddddaddbeefdddf dddddddddddddd fdddddddddddccdddbeebdf dddddddddddddd fddddddddddddaddddddeee dddddddddddddd fddddddddddddacdddddddeee dbbbbbbbbbbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedddd fdddddddddddddadddddddf beeeeeebbbbbbbbbbd dddddddddddddd fdddddddddddddacddddddf dddddddddddddd fddddddddddddddaddddddf dddddddddddddd fddddddddddddddafdddddf dddddddddddddd dfffffffffffffffafffffd dddddddddddddd a dddddddddddddd ga dddddddddddddd a dddddddddddddd cc dddddddcaadddd a fffffaaaffffff ac caag a gaac ag gaaa a caag a gaac ga gaac a caag ga caac a gaac cc caag a caac ac gaac a caag agcaac ac ``` <!-- end of image --> I'm eager to see what's happening in this magnified view of area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0706fdff b,#fa5155ff c,#9591faff d,#524cf9ff e,#fd0506ff f,#fea2a2ff g,#e7d8f0ff ``` ```image aac caa aac cad gaag dad gaag dad gaag dac ebg caa eeebf aac fbeeebf caa gbeeeefg aac feeeebg cad fbeeebf gaag fbeeeef dad gbeeeebggaag feeeebdad fbeeeaag gbeaadf gcaaeebg aabeeebf caafbeeebf aac gbeeeef cad feeeebg gaag fbeeebf dad fbeeeef gaag gbeeeefg dad feeee gaag fbe dac g caa aac caa aac cad gaag dad gaag dad ``` <!-- end of image --> Gotcha! I've found the intersection hiding in area A! Time for a closer look at another area. I'm now examining the contents of area B in detail. <!-- image --> ```palette Key,Color ,#fefefeff a,#0808ffff b,#ff3c3dff c,#a9a9ffff d,#5a5affff e,#ff0202ff f,#ffa9a9ff g,#fbdde0ff ``` ```image ggg bbbbbbbbbbeeeeeeeeeeb eeeeeeeeeeeeeeeeeeeeb fffffffffggggggg gdad cdaaaa cdaaaadc ``` <!-- end of image --> It's a shame, but area B doesn't contain an intersection. I have found one intersection!

<!-- image --> ```palette Key,Color ,#fefefeff a,#0505feff b,#ff5555ff c,#8484ffff d,#4242ffff e,#fd0607ff f,#ffa7a7ff g,#c3c3ffff ``` ```image g ac a ag ga a ca a cd a dc a ac a ag ga a ca a cd a dc a ac a ag ga a ca a cd a dc a ag a ag ga a ee ca feef a feef cd eeb a bee dc feef a eef ag beb a bee ag feea aeb cabeb a fee cd feef a eeb dc bee fffffffbbbbbbbeeeeeeeeeeeeeeeeeeeeeeeeeeee a feeeebbbbbbbfffffff ag a ag ga a cd a dd caa a gaad dc daag a caac ag gaad a daag ag caac ga gaad a daag cd caac a gaad dd daag a caac dc gaad a daag agcaac ad ``` <!-- end of image -->

I'm examining this image closely. My goal: find any and all intersections. These spots are like clues. Let's see what they reveal about potential intersections. <!-- image --> ```palette Key,Color ,#fefefeff a,#0203feff b,#fe0707ff c,#bfbfffff d,#f8a4a0ff e,#6264faff f,#fa5553ff g,#b0d7b0ff ``` ```image c eaaac eaae ac eaae ac eaae ac caaae ac caaac ac caaac ac caaac ac caaac ac eaaec ac eaae ac aae ac ac a a ca ca ca ca ca ca ca ca ca ca ca ca ca ca ca ca ca ea ea ea ea ea ea ea ea ea ggggggeagggggg gggggggeaggggg ggggggggeagggg gggggggggegggg gggggggggggggg gggggggggggggg gggggggggggggg gggggggggggggg gggggggggggggg gggggggggggggg gggggggggggggg gggggggggggggg gggggggggfgggg gggggggdbbgggg ggggggbbgggggg ggggbbdggggggg ggfbfggggggggg dbbggggggggggg bbggggggggggggg bbdgggggggggggggg fbd gggggggggggggg dbf gggggggggggggg bb gggggggggggggg bb gggggggggggggg fbd gggggggggggggg dbf gggggggggggggg dbb gggggggggggggg bb gggggggggggggg bbd gggggggggggggg fbf dbf bb bbd fbd bbbbfdd dbf ddffbbbbbbbbbffdd dbb ddffbbbbbbbbbffdd bb ddffbbbbbd ``` <!-- end of image --> I'm analyzing this close-up of area A with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#0404ffff b,#ff0404ff c,#b9b9ffff d,#ffb8b8ff e,#5353ffff f,#ff3434ff g,#ff7575ff ``` ```image eaac eaac eaac eaac eaac eaac eaa ec gd dfbf dfbbbd gbbbg gbbbg dbbbfd dfbbfd dfbbbg gbbbg gbbbfd dfbbfd fbbbd bbg g ``` <!-- end of image --> I had hoped to find an intersection in area A, but there isn't one. After a thorough analysis, I conclude that there are no intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0303ffff b,#ff0505ff c,#ababffff d,#ff9b9bff e,#6060ffff f,#ff4d4dff g,#e9dcf1ff ``` ```image g eaaac eaae ac geaae ac geaae ac gaaac ac caaac ac caaac ag caaac ag caaag ag caaeg gag eaaeg gag aae gag gag gag gag gag gag gag ga ga ga ca ca ca ca ca ca ca ca ca ca ca ca ca ea ea ea ea ea ea ea ea ea ea e d gbb bbg fbd fbf dbf gbb bbg fbd dbf gbb bbg fbd dbf dbb bbg bbd fbd dbf gbb bbg fbd bbbffddg dbf gddffbbbbbbbbbffddg gbb gddfbbbbbbbbbffddg bbg gddffbbbbbd ``` <!-- end of image -->

Based on a first glance, I suspect there could be intersection regions here. There are 1 regions I'd like to highlight in the image. <!-- image --> ```palette Key,Color ,#fefefeff a,#0607fdff b,#f90e0fff c,#999ff3ff d,#e78175ff e,#b1d7b1ff f,#4d54f0ff g,#97c796ff ``` ```image c a ac a a ca a fa a ff a f ac ff a a ac ff ca a a ca ca a a ca ff a a ca ac a a a ac ac ca a a ac ca a a ac ff a a ff ac a a ff ac a a ff a a ca ca a a ff ca a a ff ca a a ac a a ac gggggggggggggggggggggggggggggggggggggagggggg bb a eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecaeeeeee bbbd aceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeeee dbbd aeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefaeeeeeee dbbd afeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeeeee dbbd aeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeffeeeeeeeedbbd afeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeeedbbd eaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeafeeedbbbee effeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaedbbbeeeee eeaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeabbbeeeeeeee eefaeeeeeeeeeeeeeeeeeeeeeeeeedbbageeeeeeeeee eeeaeeeeeeeeeeeeeeeeeeeeeedbbbgaeeeeeeeeeeee eeefaeeeeeeeeeeeeeeeeeegbbbdeefaeeeeeeeeeeee eeeeaeeeeeeeeeeeeeeegbbbdeeeeeaeeeeeeeeeeeee eeeecaeeeeeeeeeeeebbbdeeeeeeeffeeeeeeeeeeeee eeeeeaeeeeeeeeebbbdeeeeeeeeeeaeeeeeeeeeeeeee eeeeecaeeeeebbbdeeeeeeeeeeeeafeeeeeeeeeeeeee eeeeeeagebbbdeeeeeeeeeeeeeeeaeeeeeeeeeeeeeee eeeeeebabdeeeeeeeeeeeeeeeeeaceeeeeeeeeeeeeee eeebbbdaceeeeeeeeeeeeeeeeecaeeeeeeeeeeeeeeee bbbdeeeeaeeeeeeeeeeeeeeeeeaeeeeeeeeeeeeeeeee bbbdeeeeeeeaceeeeeeeeeeeeeeefaeeeeeeeeeeeeeeeee bbbd eeeeeeeeeaeeeeeeeeeeeeeeeaeeeeeeeeeeeeeeeeee bbbd eeeeeeeeeafeeeeeeeeeeeeeffeeeeeeeeeeeeeeeeee bbbd eeeeeeeeeeaeeeeeeeeeeeeeaeeeeeeeeeeeeeeeeeee bbbd eeeeeeeeeeffeeeeeeeeeeeafeeeeeeeeeeeeeeeeeee bbbd eeeeeeeeeeeaeeeeeeeeeeeaeeeeeeeeeeeeeeeeeeee bd eeeeeeeeeeeffeeeeeeeeeaceeeeeeeeeeeeeeeeeeee ggggggggggggagggggggggaggggggggggggggggggggg ff a a ca ca a a ff ca a a ff ca a aac a ``` <!-- end of image --> Let's see if area A yields any clues. <!-- image --> ```palette Key,Color ,#fefefeff a,#0303feff b,#fe0202ff c,#7a7afeff d,#fe9495ff e,#bdbcfeff f,#3731f8ff g,#fb3b3fff ``` ```image eaae fac eaa fac e caa f aac ac caf aa aae fac caf eaa eaae fac fac eaa eaa dg fac fac dgbbb eaa caa dgbbbbgd fac aac dgbbbbgd eaae caf dgbbbbgd faf aae dgbbbbgd eaae cafdgbbbbgd caf eaagbbbgd aae dgfafbgd caf dgbbgaad aae dgbbbbgfac caf dgbbbbbddeaa aae ddbbbbbdd aac caf dbbbbbgd caf aac dgbbbbgd aae caa dgbbbbgd caf fac dgbbbbgd eaae eaa dgbbbbgd faf fac dgbbbbgd eaae eaa dgbbbbgd fac fac dgbbbbgd eaa eaa dgbbbbgd fac fac dgbbbbgd caa eaae dgbbbbgd aae fafgbbbbgd caf dgaabbgd eaae dgbbbfaf faf dgbbbbgdeaae eaae dgbbbbgd caf fac dgbbbbgd aae eaa bbbbgd caf fac bgd aae caa caf aac aac caf caa aae fac caf eaa eaae fac fac eaa eaa fac fac eaae caa fac aac eaae caf faf aae eaae caf ``` <!-- end of image --> Oh my, look at that! It's an intersection in area A! Two intersections have been found!

<!-- image --> ```palette Key,Color ,#fefefeff a,#0505feff b,#ff0303ff c,#7c7cffff d,#ff9a9aff e,#bebeffff f,#4040ffff g,#f8373eff ``` ```image c a ae ea ae ea a cf a fc a c ac ff a a ae cf ea a a cf ca a a ca ff a a ea ac ae a ea ae ae ea a a ae ca a a ac ff a a fc fc a a ff ae a ea cf ae a ca cf a a cf ea a a fc ea a ae ae ea ea ae ae gb a ea gbbd ae a gbbd a cf gbbd ac a gbbd a ff dbbg fc a dbbg a ac dbbg ff a dbbg a agbg cf dbga a dbbbda ca dbbbd ca a gbbd a ea gbbd ff a gbbd a ea gbbd ac ae gbbd a gabd ae gbbdae ea gbbd a a gbbd ae ca gbbd a a gbbd ac ff gbbd a a gbbd fc fc gbbd a a bd ff ae a ea cf ae a ca ca a a cf ea a a fc ea a aae ea ``` <!-- end of image -->

The hunt for intersections begins! Let's analyze this image closely. There are 2 regions I'd like to highlight in the image. <!-- image --> ```palette Key,Color ,#fefefeff a,#0a0bfdff b,#fd0a0aff c,#646decff d,#ec6b62ff e,#98c598ff f,#dec6e6ff g,#b0d7b0ff ``` ```image f bd bf b db bd faa b aafca fb fac a bbgggggggggggggge aa fa begggggggggggggg cac af ebgggggggggggggg aa a edbggggggggggggg caf ac egbdgggggggggggg faa a eggbggggggggggggaaf ca eggdbgggggggggcac af egggbdgggggggaae fa eggggbeggggcacgg ac egggggbgggaagggg a egggggdbcaeggggg ca egggggeaaggggggg a eggggaaebggggggg fa eggcacggdbgggggg af egaagggggbdggggg a cacgggggggbegggg ac aaggggggggggbgggg a cafeggggggggggdbggg ca faa egggggggggggbdgg af aaf eggggggggggggbgg fa f eggggggggggggdbg ac egggggggggggggbd a eggggggggggggggbf gcaeeeeeeeeeeeeee geeeeeeeeeeeeeeeb egagggggggggggggg d db egcaggggggggggggg fbbd bf eggacgggggggggggg fbbf b egggagggggggggggg dbb db egggacggggggggggg bbd bd eggggaggggggggggg fbbd b eggggcagggggggggdbbf fb egggggaeggggggdbbf db egggggeaggggbbdgg bf eggggggacebbdgggg b eggggggdabegggggg db eggggdbbcaggggggg bd eggbbdgggaggggggg b ebbdgggggcagggggg fb dbbeggggggggaeggggg db dbb eggggggggggaggggg bf bbd eggggggggggacgggg b fbbf egggggggggggagggg db dbbf egggggggggggcaggg bbbb eggggggggggggaegg d eggggggggggggeagg egggggggggggggacg geeeeeeeeeeeeeeae cc a fa af a ac a ca af fa ac a cc a fa af a ac a ca af fa ac a cc a ``` <!-- end of image --> Let's zoom in on area A to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#0605feff b,#fe0707ff c,#9898ffff d,#f6424bff e,#4746fdff f,#f1d3e0ff g,#ff9191ff ``` ```image bf bd bbg gbbf dbd fbbg gbbf dbb dbd fbbg gbbf dbd fbbg gbbf ca dbb eaa bbd caaac fbbg feaaef gbbf caaac dbd feaaef fbbg eaaac gbbf caaae dbbfeaaac bdaaac feaaef caaadbf feaaefdbd eaaac fbbg caaae gbbf eaaac dbb caaac bbd feaaef fbbg caaac gbbf eaaef dbd aac fbbg e gbbf dbb bbd fbbg gbbf dbd fbbg gbbf dbb bb fb g ``` <!-- end of image --> As I suspected, there's an intersection within area A. Now, let's turn our attention to the next spot. I'm eager to see what's happening in this magnified view of area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#0605feff b,#fd0607ff c,#8989ffff d,#fd595aff e,#4541faff f,#c8c7feff g,#feb2b3ff ``` ```image faaf eae aac caa aac faaf eae faaf cae aac caa eae faaf eae aac caa aac db faaf gdbbb eae gdbbbdg faaf gbbbbdg cae dbbbbd aac gdbbbbg caadbbbdg gaaebdg dbbbaaf gdbbbbgeae gdbbbdg aac gbbbbdg caa dbbbbd aac gdbbbbg faaf bbbdg eae bdg faaf cae aac caa eae faaf eae faac caa aac faaf eae faaf cae aac caa ``` <!-- end of image --> Aha! I've found an intersection inside area B! After a thorough search, I conclude that there are two intersections.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0404ffff b,#ff0a0aff c,#8383ffff d,#ff5c5cff e,#4443feff f,#c7c7feff g,#feaeaeff ``` ```image g bd bg b db bg faa b eafce gb fae a bd aa fa bg cac af b aa a db eaf ee bg fae a b eaf ca gb fae af bd aa fa b cac ac b aa a dbeaf ee fae a eafb fa fae gb af aa bd a cac b ee aa b a eaf db ca fae bg af eaf b fa f gb ac bd a b ee b a d db fa bbd bg af gbbg b a dbb gb ee bbd bd a gbbg b ca gbbg b af dbb db fa bbd bg acgbbg b gabg gb dbbee bd bbd a b gbbg fa gb gbbg af db dbb a bg bbd ec b gbbg a gb dbb ca bbbd af d fa ac a ee a fa af a ec a ca af fa ac a ee a fa af a ec a ca af fa ac a ee a ``` <!-- end of image -->

This is the image I'm working with. The goal is to count the intersections. The image has some tight areas where segments are too close. I should investigate those closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#0404feff b,#fd0707ff c,#f9a29fff d,#9397f6ff e,#3c3ff3ff f,#f45853ff g,#aed5aeff ``` ```image d a ad da c a bc de b a bc ed b a bc ad b da bc a b de b a cb ed b a cb ad b da cb a b ee cb a b ad ff a b a ff da b a ff ee b a bc ad b a bc a b da bc a b ee bc a b ad b a cb a b da cb a b ee cb a b ad cf a b a ff da b a d ff ee ea b a da ff ad ad b da ae bc a ea b da da bc a ad b ee ae bc a ea bgggggggggggggggggggg ad da bggggggggggggggggggggda ad gbggggggggggggggggggga ae gbggggggggggggggggggee ea gcbggggggggggggggggga da ggbggggggggggggggggee ad ggcbgggggggggggggggag ae gggbggggggggggggggadg ea gggfbggggggggggggdagg cb da ggggbggggggggggggaggg cbbbc adggggfbggggggggggeeggg bbbc aaggggbggggggggggagggg fbbc eagggffggggggggaegggg fbbc gdagggbggggggggaggggg fbbc gggaegffggggggadggggg fbbc ggggaagbgggggdagggggg fbbc gggggeabfggggaggggggg fbbf ggggggdabgggeeggggggg fbbf ggggggggaeggagggggggg fbbf gggggggggaaaeggggggggfbbf gggggggggbeaggggggfbbf ggggggggggbggggfbbfgg ggggggggggbcfbbfggggg gggggggggggbbgggggggg ggggggggggggggggggggg ggggggggggggggggggggg ggggggggggggggggggggg ``` <!-- end of image --> I'm now examining the contents of area A in detail. <!-- image --> ```palette Key,Color ,#fefefeff a,#0807feff b,#fd0204ff c,#ff8484ff d,#b2b2feff e,#5a57fbff f,#f93a3fff g,#ffd1d1ff ``` ```image bf bbg cbf gbbg fbf gbbg fbc gbbg e fbc a gbb ea fbc daa gbb aae fbc daa cbb aad fbc eaa cbb daad bbc eae cbf daa bbc aae cbf daa bbg aad cbf eaa e bbg daad aad cbf eae aaad gbbg daa eaae cbf aae eaae gbbg daa daaad fbf aad daaad gbbg eae eaae fbc daad eaae gbbg eae daaad fbc daa daaadgbb aae eaaefbc daa eaaebb aad daaabc eae daaaf daad eaae eae eaae daa faaadaae cbaaaaa gcf bbeaad gcfbbb cbfdd gcfbbbbfc bbg gcfbbbbfc cbf gcfbbbbfc gbbg cfbbbbfcg cbbbbbbfcg gbbbfcg gcg ``` <!-- end of image --> My investigation has led me to an intersection in area A! After careful examination, I conclude that there is one intersection.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0202feff b,#fe0405ff c,#ff9191ff d,#9191ffff e,#3937fdff f,#fe4949ff g,#ead8ecff ``` ```image d a ad ga c ag fc de b a bc ed b a bc ad gb da bg a gb de bg a gb ed bg ga cb ag b da cb a b ee cf a b ed ff ga b ag ff da b a fc ee b a fc ad b ga bc ag b da bc a gb ee bg a gb ad bg ga gb ag b da cb a b ee cb a b ad cf ga b ag ff da b a d ff ee ea b a dag fc ad gad b ga ae bc ag ea b de dag bc a gad b ee ae bc a ea gb ad dag bg ga gad gb ag ae bg de ea gb a dag b ed gad cb a ae b ad ea cb da gb dag b a gbbbc gad cf de gfbbc ae b a gfbbc ea ff ed gfbbc dag b ga fbbc gad ff ag fbbc ae b da fbbc eafc a fbbc dab ee fbbf ae a cbbf aeed cbbf bea cbbf b cbbf bgcbbfg gbfg ``` <!-- end of image -->

I have an image in front of me. I need to determine if there are any intersection segments. The image is completely devoid of intersections. Zero.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0505ffff b,#ff0707ff c,#9a9affff d,#ff9d9dff e,#ff4c4cff f,#4848ffff g,#ecd8ebff ``` ```image gc gcffaaaaaaaaf gccffaaaaaaaafccg gcffaaaaaaaaffccg faaaaaaaafccg gacg ca fa af ac cag fa aa af gac cag fa aa af gac cag fa aa af gac ca fa af ac cag fa aa af gac ag ge bbeb bbd eb ebd db dbe gbg dbb bd gbb be bbg bb ebd eb ebe eb dbe dbg gbb gbd bbg bd bbd be ebd bb dbe eb dbb db gbbg dbg bbg gbd ebd be be be bb eb db gbg bd be bb eb eb dbg gbd bd be bb eb db dbg gb ``` <!-- 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,#4d50f8ff b,#fe0303ff c,#f69f9bff d,#a1a3fbff e,#0506feff f,#f7413dff g,#aed5adff ``` ```image cggggggggggggggg fbgggggggggggggg gbfggggggggggggg ggbfgggggggggggg gggbcggggggggggg agggbggggggggggg aagggbgggggggggg gegggcbggggggggg gaagggfbgggggggg ggeggggfbggggggg ggaaggggbfgggggg gggegggggbfggggg gggeagggggbcgggg ggggeggggggbgggg ggggeaggggggbggg gggggegggggggbgg gggggedggggggcbg ggggggegggggggfb ggggggedgggggggff e bf ed bc e bc e b de b e cb de cb e fb de bf e bc de bc e b da b e cb cf aa cb cfbbbbc e fb cfbbbfc aa ff cfbbbfc e bf cfbbbfc aa bc cfbbbfc e bc cfbbbfc aa b cfbbbfc e b cfbbbfc ad cbbfc e ed e ed e ed e ed e e de e de e de e de e de e aa e aa dee e deea aa deea e deeed aa aeed e aeed ad aeed e deea ed deea e deee ed eeed e aeed ed aeed e aeea eddeea ea ``` <!-- end of image --> I'm focusing my attention on this specific region, area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#4343ffff b,#ff0606ff c,#ff9494ff d,#9898ffff e,#0505feff f,#ff4545ff g,#f7d3daff ``` ```image cg bbg fbbg gbbf gbbf gbbf cbbc cbbc cbbg fbbg aa fbbg eeg fbf aea gbbf geeg gbbf aea gbbc geeg cbbc aea cbbc dee fbbg aed fbbg dee fbbg aed gbbf dee gbbf aed gbbf dee cbbc aed cbbc dee cbbg eed fbbg dee fbbg eed fbf dee gbbf eed gbbf dea gbbc eed cbbc dea cbbc eed fbb dea fb eed f ``` <!-- end of image --> This close-up reveals that there are no intersections in area A. I can confidently say that there are no intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#4343ffff b,#ff0404ff c,#ffa2a2ff d,#8282ffff e,#0505ffff f,#ff4141ff g,#c1c1ffff ``` ```image c fb bf bc bc a b aa b e cb ad cb e fb ad bf e bf ad bc e b ed b e cb eg cb e fb eg ff e bf eg bc ge bc eg b ge b e cb ge cb e fb ge bf e bc de bc e b da b e cb cf da cb cfbbbbc e fb cfbbbbc aa ff cfbbbfc e bf cfbbbfc aa bc cfbbbfc e bc cfbbbfc ad b cfbbbfc e b cfbbbfc ad cbbfc e ed e eg e eg e eg ge eg ge e ge e ge e de e da e da e da dee e deea aa geea e geeeg ad aeeg e aeed ad deed e deea ed deea e geeag ed geeeg e aeeg eg aeed e deed egdeea gea ``` <!-- end of image -->

This image might have some surprises. Let's look for intersections carefully. I've examined the entire image, and there are zero intersections present.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0505ffff b,#ff0505ff c,#8383ffff d,#ffadadff e,#4040ffff f,#c7c8ffff g,#ff4848ff ``` ```image dddd ggbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbggggd ddddddgbd bbd bb dbb dbg gbg gbd bbd bb dbb dbb dbg gbg gbd bbd bb dbb dbg gbg gbd bbd bbd bb af db fae eaf aa cac aa fae eaf fae eaf aa cac aa fae eaf fae caf aa cac aa fae eaf aa caf ae ea fac aa caf ae ea fac aa caf ae ea fac aa eaf fae aa caf ae ea fac aa caf ae ea fac aa caf ae ea fa ``` <!-- end of image -->

I'm curious to see if this image contains any intersection points. My next step is to analyze the details within each area. <!-- image --> ```palette Key,Color ,#fefefeff a,#0908fdff b,#fe0707ff c,#fca5a4ff d,#5b5ff6ff e,#f55551ff f,#b5b5ffff g,#add4adff ``` ```image f ad a a dd af a da af a da af a fa ad a fa ad a fa dd af a da af a da af a fa ad a fa ad a fa dd af a da af a da af c a eb fa eb ad eb a eb fa eb ad cb a cb fa cb dd cb daa cb faad cb daa b faaf b aad b daaf ggggggggggggggggggggg bc faad ggggggggggggggggggggg bc daa ggggggggggggggggggggg bc faadggggggggggggggggggggg bc aaaggggggggggggggggggg bc gdaadgggggggggggggggg bc ggggaadgggggggggggebb be ggggggdaaggggggcbbbgg be gggggggggaadgbbbggggg be ggggggggggbaaaggggggg be gggggggebbeggdaadgggg be ggggebbeggggggggaaagg bb gebbegggggggggggggdaa bb cbbeggggggggggggggggggg bb cbbe ggggggggggggggggggggg eb cbbbc ggggggggggggggggggggg eb bbbc ggggggggggggggggggggg eb ebbc ggggggggggggggggggggg eb ebbc ggggggggggggggggggggg eb ebbe eb cbbe cbe ``` <!-- end of image --> This close-up of area A is like examining a piece of evidence. <!-- image --> ```palette Key,Color ,#fefefeff a,#0403feff b,#fc0609ff c,#fdaaabff d,#7d7dfeff e,#fe5858ff f,#c1c1feff g,#3c35f8ff ``` ```image d aadf gaaagd fdaaaadf dgaaagf fgaaaad c fdaaaagf cebb fgaaagd cebbbbe fdaaaadf cebbbbbc dgaaagd cebbbbbec fgaaaadfcebbbbbec dgaaagbbbec cebgaaaad cebbbbecdaaaagf cebbbbec fgaaagd cebbbbbc fdaaaadf cebbbbbe dgaaagf cebbbbbec fgaaaad ebbbbbec daaa cebbbbec fg bbbbec bec ``` <!-- 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,#0404feff b,#ff0707ff c,#ffacacff d,#8585ffff e,#fe5656ff f,#c8c8ffff g,#3e3cfcff ``` ```image f gg af fa gg af a da af a da ad a da ad a fa gg af fa gg af a da af a da ad a da ad a fa gg a fa gg af a gg af a da ad c a eb da eb ad eb a eb fa eb gg cb a cb fa cb gg cb gaaf cb faad cb gag cb daad b aag bc daaf bc faad bc gaaf bc faad bc gag bc daaf be faag cbb be daaf cbbb be faadcbbbc be egaa be ebbc daad be ebbe gag bb ebbe daa bb cbbe f bb cbbe eb cbbbc eb bbbc eb ebbc eb ebbc eb ebbe eb cbbe cbe ``` <!-- end of image -->

Hmm, I'm not sure what to expect from this image. Let's see if any lines cross. I've examined the entire image, and there are zero intersections present.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0707ffff b,#ff0303ff c,#9b9bffff d,#ff9191ff e,#5252ffff f,#e7d8efff g,#ff4d4dff ``` ```image c ee ac a ca ae af a ca ae af fa ca ae af fa ea ac af fa ea ac a fa ea ac a ca ee ac a ca ae af a ca ae af fa ca ae af fa ea ac af fa ea ac aaaac ceaaaef caaaac ceaaaef feaaaec ceaaaef feaaaec caaaac feaaaec caaaa f fdg dgbbbbggbbg dgbbbbgd gbbg dgbbbbgdf gbbd fgbbbbgdf gbbd fdbbbbbdf gbbd dgbbbbgf gbbd gd gbbd gbbd fgbbd fgbbd fgbbd fgbbd fgbbd fbbbd fbb ``` <!-- end of image -->

This is the image I'm working with. The goal is to count the intersections. Could these regions be concealing intersection points? Let's find out. <!-- image --> ```palette Key,Color ,#fefefeff a,#0506fdff b,#fa0a09ff c,#b1d7b1ff d,#da6a5dff e,#373fecff f,#99c597ff g,#7a8cdbff ``` ```image c ag a a a a ga a ge a eg a ag a a a a ga a ge a eg a ag a a a a ga a ge a eg a ag a a e a ea cffffffafffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeaf fccccccgaccccccccccccccccccccccccccccccccccccccccccccccccccccccccceacc fcccccccaccccccccccccccccccccccccccccccccccccccccccccccccccccccccaaccc fccccccceeccccccccccccccccccccccccccccccccccccccccccccccccccccccaacccc fccccccccacccccccccccccccccccccccccccccccccccccccccccccccccccccaaccccc fccccccccegcccccccccccccccccccccccccccccccccccccccccccccccccccaecccccc fcccccccccaccccccccccccccccccccccccccccccccccccccccccccccccccaeccccccc fcccccccccagccccccccccccccccccccccccccccccccccccccccccccccccaecccccccc fccccccccccacccccccccccccccccccccccccccccccccccccccccccccccaeccccccccc bd fccccccccccafcccccccccccccccccccccccccccccccccccccccccccccaecccccccccc bb fccccccccccgaccccccccccccccccccccccccccccccccccccccccccccaeccccccccccc bb fcccccccccccacccccccccccccccccccccccccccccccccccccccccccaecccccccccccc dbd fcccccccccccgacccccccccccccccccccccccccccccccccccccccccaeccccccccccccc bb fccccccccccccaccccccccccccccccccccccccccccccccccccccccaecccccccccccccc bbfcccccccccccceeccccccccccccccccccccccccccccccccccccccaeccccccccccccccc dbdccccccccccccacccccccccccccccccccccccccccccccccccccaecccccccccccccccc fbbfccccccccccegcccccccccccccccccccccccccccccccccccagccccccccccccccccc fccbbccccccccccaccccccccccccccccccccccccccccccccccagcccccccccccccccccc fcccdbdccccccccagccccccccccccccccccccccccccccccccagccccccccccccccccccc fcccccbbfcccccccacccccccccccccccccccccccccccccccagcccccccccccccccccccc fcccccccbbccccccafcccccccccccccccccccccccccccccagccccccccccccccccccccc fccccccccdbdccccgaccccccccccccccccccccccccccccagcccccccccccccccccccccc fccccccccccbbfcccacccccccccccccccccccccccccccagccccccccccccccccccccccc fccccccccccccbbccgacccccccccccccccccccccccccagcccccccccccccccccccccccc fcccccccccccccdbdcaccccccccccccccccccccccccagccccccccccccccccccccccccc fcccccccccccccccbbeeccccccccccccccccccccccagccccccccccccccccccccfddbbb fcccccccccccccccccbacccccccccccccccccccccagcccccccccccccfddbbbbbbddfcc fcccccccccccccccccceddccccccccccccccccccafccccccfdbbbbbbbddfcccccccccc fcccccccccccccccccccabbdcccccccccccccccafdbbbbbbbddfcccccccccccccccccc fcccccccccccccccccccagcbbcccccccddbbbbabbddccccccccccccccccccccccccccc fccccccccccccccccccccaccdbbbbbbbbddcfacccccccccccccccccccccccccccccccc fccccccccccccccccccccafcccfccccccccfaccccccccccccccccccccccccccccccccc fccccccccccccccccccccgacccccccccccfacccccccccccccccccccccccccccccccccc fcccccccccccccccccccccaccccccccccfaccccccccccccccccccccccccccccccccccc fcccccccccccccccccccccgaccccccccgacccccccccccccccccccccccccccccccccccc fccccccccccccccccccccccacccccccgaccccccccccccccccccccccccccccccccccccc fcccccccccccccccccccccceecccccgacccccccccccccccccccccccccccccccccccccc fcccccccccccccccccccccccaccccgaccccccccccccccccccccccccccccccccccccccc fcccccccccccccccccccccccegccgacccccccccccccccccccccccccccccccccccccccc fccccccccccccccccccccccccacgaccccccccccccccccccccccccccccccccccccccccc fccccccccccccccccccccccccaeacccccccccccccccccccccccccccccccccccccccccc fcccccccccccccccccccccccccaccccccccccccccccccccccccccccccccccccccccccc fccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc fccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc fccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc ``` <!-- end of image --> I wonder what we'll find inside area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#0808feff b,#fe0505ff c,#e4d7f1ff d,#fb464aff e,#4e4dfeff f,#fe999aff g,#9494feff ``` ```image gaa eac aag ceac aa aaac ga caac cac caac ee caac ae aaac aac caac eag caac gaa caac gaa caae aa aae ga cae cac cae cac caae ae aae aac gae eag gae aag gaae gaa aae aa gae ga gae f ee gaae bd cac aae bbd ae gag cdbbf aac gag fbbd gaa gaag cdbbf aag aag dbbd gaa gag fbbd aa gag dbbdc cac eaag fbbb ee aag cdbbf cac eag cbbdc ae eag dbbf eag eaag cbbdc gaa aag fbbbc aag eag dbbf gaa eag fbbbc ga eaac dbbfcac eaac cf cbbdee aac cffddbbb fbbbac eac cffddbbbbbbbbbd caadf eaa cffddbbbbbbbbbddffc aadbc eaac cfffdbbbbbbbbbbdfffc gaabbf caac cffddbbbbbbbbbddffc aagbbbf caafffdbbbbbbbbbbddffc gaafbbbc cffdaabbbbbbbbddffc ga cbbbf ccffddbbbbbbbbbdaaac cac fbbbbbbbbbbbbddffc caac ee fbbbbddffc caac cac cf caac aac aaec eag caec gaa cae aag caa aa aae ga cae cac cae ee caa ae aae aa gae eag gae gaa gaa gaa aae aaeae gaae caa ``` <!-- end of image --> Incredible, there's actually an intersection in area A! There's for sure two intersections on the image you sent me.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0505ffff b,#fe0a0bff c,#bebeffff d,#ff6a6aff e,#3e39f9ff f,#fdb8baff g,#7c7cffff ``` ```image c ag a ac ca a ca a ge a eg a ac a ac ca a ca a ge a eg a ac a ac ca a ga a ge a eg a ac a ac e ca ea a ea ga ea a ea ge ea a ae eg ae a ae ac ae a ae bd ac ae bbf ca ae fbb a ae dbd ge ae bbf a ag bb ge ag dbd a ag bbf eg ag bb a ag dbd ac ag bbf a ag bb ac ac fbd ca ac bbf a ac bb ge ac fbd a ac bbee ac ffdbbb ba ac fddbbbbbbddf eed ac fddbbbbbbdff adbf afdbbbbbbbdf ac bb fdbbbbabbdf a fbbbbbbbbdf a ac f ca ca ca a ca ge ca a ca ge ca a ca eg ca a ca aga a ``` <!-- 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,#fd0606ff b,#0708feff c,#f8a9a6ff d,#5758f2ff e,#acaefcff f,#f55550ff g,#add5adff ``` ```image c ac a ac ca a ca a ff a ff a ac a ac ca a ca a ff a ff a ac a ac ca a ca a ff a ff a ac a a ca a ca a ff a ff a ac ebb a ebbe a dbb ca bbd gagggggggggggggg ebbe gfaggggggggggggg ebbe ggaggggggggggggg dbb ggffgggggggggggg bbd gggagggggggggggg ebbe bbe gggafggggggggggg ebbe ebbbd ggggaggggggggggg dbb dbbbe ggggacgggggggggg bbd edbbde gggggagggggggggg bbe ebbbd gggggagggggggggg ebbe dbbbegggggcaggggggggg dbb ebbbdgggaggggggggg dbd ggdbbbdagggggggg bbe fa gggggebbbdgggggg ebbe caac gggggggffdbbbdggdbb faa ggggggggaggggdbbd aaf ggggggggafgggggg caac gggggggggagggggg faf gggggggggacggggg caac ggggggggggaggggg faa ggggggggggaggggg aaf ggggggggggcagggg caac gggggggggggagggg faf gggggggggggfaggg caac ggggggggggggaggg faa ggggggggggggffgg aaf gggggggggggggagg caac gggggggggggggafg faf a caac acfaa af ``` <!-- end of image --> I'm determined to find out if an intersection exists in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0304ff b,#0a07fcff c,#ff7c7cff d,#6d68faff e,#c4c2fdff f,#fb383bff g,#ffc2c2ff ``` ```image gaa fac gaa fac caf aag caf aag caf gaag fac gaa fac gaa fac caf aag caf aag caf gaag fac gaa bdde fac bbbbbde gaa eddbbbbbdde fac edbbbbbbddaf eddbbbbbbde edbbbbbbde efbbbbbbbde cafedbbbbbbdde gaag edbbbbbbd fac eddbbb gaa ed fac gaa aac caf aag caf aag caf gaag fac gaa fac gaa aac caf aag caf aag caf gaag fac gaa ``` <!-- end of image --> Area A contains an intersection. There's only one, but is an intersection after all.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0505ff b,#0808ffff c,#ff8989ff d,#6360fbff e,#b5b5ffff f,#fe4949ff g,#ffc7c7ff ``` ```image g ac a ag ga a ca a cf a fc a ac a ag ga a ca a cf a fc a ac a ag ga a ca a cf a fc a ac a ag ga a ca a ff a fc a ag ebb a ebbe ag dbb ga bbd a ebbe ca ebbe a dbb ff bbd a ebbe bbe fc ebbe ebbbd a dbb dbbbe ag bbd edbbde a ebbd ebbbd ag ebbe dbbbe ga dbb ebbbd a bbd dbbbda ebbd fa ebbbd ebbe gaac ffdbbbe dbb faag a edbbd gaaf fc caag a faf ag gaac a faag ag gaaf ga caag a faf cf gaac a faag ff gaaf a caag fc faf a gaac agfaag gaf ``` <!-- end of image -->

I'm analyzing this image to identify any points where lines intersect. These areas seem to enclose narrow spaces where lines might be close. <!-- image --> ```palette Key,Color ,#fefefeff a,#0707fdff b,#fd0b0aff c,#adadfeff d,#f2756fff e,#b2d7b1ff f,#5251f0ff g,#97c599ff ``` ```image aa faca fa ff ca ac ca a a ca a af ac a ac ca af ff af ac fa a fa ca ca af ca a a a a fa ac ac ac geegaeeeeeeeeeeeeeeeeeeeeeg af geeefaeeeeeeeeeeeeeeeeeeeeg af geeeeafeeeeeeeeeeeeeeeeeeeg fa geeeeeageeeeeeeeeeeeeeeeeeg fa geeeeeeaeeeeeeeeeeeeeeeeeeg ca geeeeeefaeeeeeeeeeeeeeeeeeg ca geeeeeeeafeeeeeeeeeeeeeeeeg a geeeeeeeeaeeeeeeeeeeeeeeeeg a geeeeeeeegaeeeeeeeeeeeeeeeg ac geeeeeeeeeafeeeeeeeeeeeeeeg ac dde geeeeeeeeeeageeeeeeeeeeeeeg af bddbbbbbbbbbddgeeeeeeeaeeeeeeeeeeeeeg af db gdddbbbbbbbbfadgeeeeeeeeeeg fa b geeeeeeeeeegdafbbbbbbbbbddg fa be geeeeeeeeeeeeeaeeeeeeegddbbbbbbbbbd ca bb geeeeeeeeeeeeegaeeeeeeeeeeg ed ca eb geeeeeeeeeeeeeeafeeeeeeeeeg a b geeeeeeeeeeeeeeeageeeeeeeeg a bd geeeeeeeeeeeeeeeeaeeeeeeeeg ac db geeeeeeeeeeeeeeeefaeeeeeeeg ac b geeeeeeeeeeeeeeeeeafeeeeeeg af b geeeeeeeeeeeeeeeeeeaeeeeeeg bd geeeeeeeeeeeeeeeeeegaeeeeeg eb geeeeeeeeeeeeeeeeeeefaeeeeg b geeeeeeeeeeeeeeeeeeeeageeeg bd geeeeeeeeeeeeeeeeeeeeeaeeeg db egggggggggggggggggggggfagge b af b a bd ca db fa b ac bd a db ca b af b a bd a db fa b ac bd a db ca b af b a bd db b be db b b bd db b be bb b b bd db b b ``` <!-- end of image --> Time to investigate area A up close. <!-- image --> ```palette Key,Color ,#fefefeff a,#0605feff b,#fe0505ff c,#8585ffff d,#ff5252ff e,#fda6a7ff f,#463ef6ff g,#c5c5ffff ``` ```image gaag caag faf gaac caag faa aaf gaac caag faf gaac gaag faa faf gaac caag faf aac gaag caa faf gaac caag faf bbddddeee aac bbbbbbbbbbbbbdddeeee gaag eeeedddbbbbbbbbbbbbbbbbfaaeeee eeeedddbbbbbbaafbbbbbbbdddeeee eeeaafdbbbbbbbbbbbbbbbddddeee caag eeeddddbbbbbbbbbbb faf eeeedddb aac gaag caa faf gaac caag faa aaf gaag caag faf gaac gaag faa aaf gaac caag faf aac gaag caa faf gaac ``` <!-- 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,#0606feff b,#ff0808ff c,#8989ffff d,#ff6060ff e,#ffb7b7ff f,#4742f9ff g,#c8c8ffff ``` ```image g aa faga fa ff ca ag ga a ga ca a ac ag a ac ga ac ff af ag fa a fa ca ca ac ga a ga ga a fa ag ag ac a ac ca af af fa ag fa ga ca fa ga ac ga a a ga ag ff ac dde ag ac bddbbbbbbbbbdee a af db eddbbbbbbbbfaee fa b eeafbbbbbbbbddee fa be a eeddbbbbbbbbd ca dd ga ee ga eb ff ga b ag a bd a ag db ca ac b ac ac be a bd ga eb ff b ag be a db ca b ac be a bd ga eb ff b ag be a db ca b af b ag bd ga eb fa b ac be a db ga eb ff b a bd eb b be db eb b bd db b be dd eb b bd db b be ``` <!-- end of image -->

Based on a first glance, I suspect there could be intersection regions here. I need to zoom in on these areas to get a better look. <!-- image --> ```palette Key,Color ,#fefefeff a,#4b50f2ff b,#fc0c0bff c,#a1a3faff d,#ed6b67ff e,#0606feff f,#b1d6b0ff g,#98c599ff ``` ```image c ec e ec ce e d a ce bbbd e e bd dbb e aa db dbb ce e db dbb e aa b fbb ea e b bbf fgggggggggggggeg ec bf bbd gffffffffffffegf e bd bbd gfffffffffffaeff ec bb dbd gfffffffffffefff ce db dbb gffffffffffaafff e fb dbb gffffffffffeffff ce b dbbgfffffffffecffff e b fbbgffffffcefffff aa bd ggbbdffffeffffff e bd gfffbbdfaaffffff gfaafffffffffffbb gfffffbbefffffff fffeffffffffffdb gffffffedbdfffff fffecffffffffgbg gfffffgeffdbbfff ffffeffffffffbfg gfffffefffffdbbg ffffegffffffbgfg gffffaefffffffdbb ffffgefffffbdffg gffffefffffffffffb fffffeffffbbfffg gfffeaffffffffff fffffaeffdbffffg gfffefffffffffff ffffffefdbfffffg gffegfffffffffff ffffffaabffffffg gfaeffffffffffff fffffffefffffffg gfefffffffffffff ffffffbaaffffffg gaaffffffffffffg fffffbdfeffffffg e ffffbbffecfffffg ec fffdbffffefffffg ce ffgbfffffegffffg e ffbffffffgeffffg aa fbgfffffffeffffg e bdffffffffaefffg ec bbffffffffffefffg ce dbfffffffffffaaffg e db ggggggggggggeggf ae b ac e b e ec bf ec e bd e e bb e ce f ce e e aa ce e e ec aa ce e e ac aa e e ec ec e ce e e ce aa e e ce ec e e aa e e ce ac e e aa ec e e ec e ce ce e e aa ce e e ec aa ce e e ac aa e e eec e ``` <!-- end of image --> This is a magnified view of the region A. <!-- image --> ```palette Key,Color ,#fefefeff a,#3c34f6ff b,#fd0608ff c,#7f7fffff d,#ff5151ff e,#0404feff f,#ffa6a6ff g,#c1c1ffff ``` ```image gee aec gee d aec fb cee fbb eeg fbbd cea bbd eeg dbb cea dbb geeg dbbf aec fbbf gee fbbf aec bbd gee bbd aec dbb cee dbb eeg fbbf cea fbbf eegfbbd ceabbd geebd aea dbee fbbaec fbbfgee fbbd aec bbd cee dbb eeg dbb cea dbbf eeg fbbf cea fbbf geeg bbd aec bbd gee dbb aec dbb gee fbbf aec fbbf cea bbd eeg bd cea d eeg cea geeg ``` <!-- end of image --> I can confirm that an intersection exists in area A. Okay, on to the next area of interest. I'm determined to find out if an intersection exists in area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#4b4afeff b,#fe0707ff c,#8d8dffff d,#f3515dff e,#0605feff f,#ffacabff g,#cccbfeff ``` ```image cee geec aea geeg aea cee eec aea geeg aea ceeg eec cee geeg bd aea bbbdf geeg fdbbbdf eec fdbbbdf cee dbbbbf geec dbbbbf aea fbbbbfgeeg fbbbeea fdeebd eedbbbdf aea fdbbbdf geeg fdbbbdf aea dbbbbf ceeg dbbbbf eec fbbbb cee fbb geeg f aea geeg eec cee geec aea geeg aea cee eec aea geeg ``` <!-- end of image --> My investigation has led me to an intersection in area B! My analysis indicates that there are two intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#3d3cfeff b,#fe0808ff c,#8484ffff d,#fb5558ff e,#0404feff f,#ffb3b3ff g,#c8c8ffff ``` ```image g ec e eg ge e d a ce bbbd ge e bd dbd eg ca db dbb ce e fb fbb e ac b fbbf ac e b fbbf e ec bf bbf eg e bd bbd ce eg db dbd e ge db dbd aa e fb dbb e ce b fbb eg e bf fbbf ge ca bf fbbf e e bd bbf aa ac db bbe e fb edbd ec fb ge dbd e b eg dbb eg bf ca fbb ge bd e fb e bd ac ce db ge e fb eg cab ce e e bac aa bd e e db ec eg db e ge fb eg e b ge aa bf e e bf ce ec bd e ge db ca e fb e ca fb ac e b e ec bf eg ge bd e eg bd eg ce f ge e e ac ca e e eg ca ge e e ac aa e e eg ec e ge eg e ge ca e e ca ec e ge ca eg e ce ac e e ac eg e e eg eg ce ge e e aa ca e e ec aa ge e e ac ca e e eec ge ``` <!-- end of image -->

I have an image in front of me. I need to determine if there are any intersection segments. I need to zoom in on these areas to get a better look. <!-- image --> ```palette Key,Color ,#fefefeff a,#f55854ff b,#0807fcff c,#fe0807ff d,#575cf5ff e,#afaffeff f,#fbaba9ff g,#acd3acff ``` ```image e db bb bd bd be eb db db bb fcc bd accafcf be acca c be fcccf fc eb fcccf cf db acca c db facca aa bb fcccf c bd acccf fc be acca gcaggggggggggggg ebe fcccf ggcgggggggggggggeb ccf ggacgggggggggggdb gggcfgggggggggbb ggggcggggggggbbg ggggacggggggbdgg gggggcgggggbdggg ggggggcgggbggggg ggggggcadbgggggg gggggggbbggggggg ggggggbbcggggggg gggggbbgcagggggg ggggbdgggcgggggg gggbdggggacggggg ggbgggggggcggggg dbgggggggggcgggg dbggggggggggcaggg bbggggggggggggcggg bd ggggggggggggfcgg ebd gggggggggggggcag dbbe c dbd ac ebbd cf dbbe c bbd aa ebbe c dbb fc bbd cf ebbe c dbb fc bbd cf ebbe c dbb aa ebbd c ebbe fc d ca c fc cf c aa c fc ca c fc cf c ac c c ca c fc cf c ac cf c aa c ``` <!-- end of image --> Let's take a closer look at area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe5b5bff b,#0404feff c,#fd0809ff d,#3a36faff e,#7f79f9ff f,#ffb6b6ff g,#c6c6feff ``` ```image cca fccf aca ccf fcc aca d fccf gdb acc gbbb cca gbbdg fccf ebbd acc ebbe ccf dbbe fcc dbbe aca gdbbg fccf gbbbg acc gbbd cca ebbd fccebbe adbbe dbbe gdbbcc gbbbgaca gbbd fccf ebbd acc ebbe cca dbbe fccf dbbg acc gdbbg cca gbbdg fccf gbbd aca ebbd ccf ebbe fcc bbe cca bg fccf g acc cca fccf aca ``` <!-- end of image --> The lines cross each other within area A, forming an intersection. I have found one intersection!

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff5252ff b,#0807fdff c,#ff0707ff d,#5252ffff e,#9f9fffff f,#ff9d9dff g,#eed8e9ff ``` ```image e db bb bd be gbe ebg db db bb fcc bd accagcf be gacca c gbe fcccf fc ebg fcccf cf db accag c db gacca aa bb fcccf cg bd fcccg gc be gacca ca gbg fcccf c eb ccf fc db cf bb c bb aa bd cg be gc gbg caeb bb bbc bd cf bd c gbe ac ebg cg eb gc db aa bb c bd fc gbd cf ebbg c dbd ac ebbe cg dbbg gc bbd aa ebbe c dbbg fc bbd cf ebbe c dbbg fc gbbd cg ebbe c dbb aa gbbd cg ebbe gc d cf c fc cf c aa cg gc ca c fc cf c ac cg gc ca c fc cf c ac cg gc aa c ``` <!-- end of image -->

The hunt for intersections begins! Let's analyze this image closely. These areas seem to enclose narrow spaces where lines might be close. <!-- image --> ```palette Key,Color ,#fefefeff a,#e97469ff b,#666cf3ff c,#fc0809ff d,#feb3b3ff e,#97c797ff f,#0809fcff g,#b1d6b2ff ``` ```image a c cd dc c c ac dc c geeceeeeeeeeeeeeg ca eggacggggggggggge c egggcggggggggggge cd egggacgggggggggge dc eggggcgggggggggge c eggggacggggggggge ac egggggcggggggggge c egffbgacgggggggge ca eggefffcgggggggge c egggggefffbggggge cd egggggggcefffbgge dc egggggggacgggfffb c eggggggggcggggggfffb ac eggggggggacggggge bffb c egggggggggcggggge bffb ca egggggggggacgggge bffb c eggggggggggcgggge bffb cd eggggggggggacggge bffb dc egggggggggggcggge bffb c geeeeeeeeeeeaceeg bf ac c gf c dc bf ca c fb c dc fg cd c f dc dc f c c bf ac dc fb c c fb ca dc f c c f cd dc bf dc c effgggggggggcegge dc egfbgggggggacggge c eggfeggggggcgggge dc egggfgggggcagggge c egggbfgggecggggge dc eggggbfggceggggge c egggggfbacgggggge dc eggggggfcggggggge c eggggggafggggggge dc eggggggcefgggggge c egggggcagbfggggge dc eggggecgggffgggge c eggggceggggfbggge dc egggacggggggfegge c egggcggggggggfgge dc eggcaggggggggbfge c geeceeeeeeeeeeffg dc cd fb c dc fg dc c f c ac gf dc c bf c aa fb dc c fb c cd f dc dc f c c bf dc ac ff c c fb dc ca f c c f dc cd gf c dc bf dc c fb c ac fg dc c f cca f dc bf fb fb f ``` <!-- end of image --> I'm now examining the contents of area A in detail. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0e0fff b,#3c37f9ff c,#91006cff d,#ff9494ff e,#9090ffff f,#0000feff g,#e2e1feff ``` ```image aad daa aad daa aad daa aad daa aad daa aad daa aad daa beg aad gfffbeg daa gebffffbegaad gebffffbca gebffffbeg gebffffbeg acbffffbeg daagebffffbeg aad gebffffbeg daa gebffff aad gebf daa g aad daa aad daa aad daa aad daa aad daa aad daa aad ``` <!-- end of image --> An intersection is present within area A. Now, let's dive into another area. Time to investigate area B up close. <!-- image --> ```palette Key,Color ,#fefefeff a,#fa373bff b,#5958fdff c,#fe0404ff d,#fcc3c6ff e,#afafffff f,#0908fdff g,#ff8282ff ``` ```image bff ccg bff gca ffb dccd effb aca effe dccd bffe acg bff gcc ffb ccg ffb gca effe dccd effe aca bff dccd bff acg ffb gcc effbccg effaa bffd afff dccffb acgeffb gcc effe ccg bffe gca bff dccd ffb aca ffb dccd effe acg effe gcc bff ccg bff gca ffb dccd effb aca effe ``` <!-- 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,#f74d54ff b,#403ffeff c,#ff0606ff d,#ffaaaaff e,#8f8fffff f,#0303ffff g,#f3e4efff ``` ```image d c cd dc cg cg ac dc c cg aa dc gc cg cd dc dc cg cg dc ac cg c ffe dc ca gbffag gc gbffe cd cgbffe dc dc gbffe cg cg gbffe aa dc gbffe c cg gbffe ca dc gbffe gc cg gbffe cd dc gbffe dc cg bffe c dc bf aa cg ef c dc bf cd cg fb gc dc fe cd cg f dc dc gf c cg ef aa dc bb c cg fe cd dc fg gc cg gf cg dc ef dc cg bb c dc fe aa cg fg c dc gf cd cg ef gc dc bf cg cg fbdc dc fa cg afg dc cgf cg cd ef dc gc bb cg cg fe dc dc fg cg c gf dc aa ef cg c bf dc cd fe cg gc fg dc cg f cg dc gf dc c ef cg aa fb dc c fe cg cd fg dc gc gf cg cg ef dc dc bb cg c fe dc aa fg cg c gf dc cd ef cg dc bf dc cg fb cg ac fe dc c fg caa gf dc ef bb fe f ``` <!-- 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,#f55651ff b,#0b0bfeff c,#fbadacff d,#7174f7ff e,#fd0706ff f,#add4adff g,#d3d3ffff ``` ```image g bd b db bg gb bd b db bg gb bd b db bg gb bd b db c bg e gb e bd ec b ae db ce bg e gb ec bd ea b ce db e bg ec gb ea bd ae b ce db e bg ec gb ae bd ce b e db ec bg ea gb ce bd e b e db ea bg ae gb ce bd e b ec db aa bg ce gb e bd ec b ffffffffffffffea db fffffffffffffaef bg fffffffffffffeff gb ffffffffffffefff bd fffffffffffeafff b ffffffffffaeffff db fffffffffcefffff bg fffffffffeffffff gbbbbddfffffecffffff fddbbbbbbbbddfff ffffffaeffddbbbbbbbbddg ffffffefffffffff gddbbbbbbbddg fffffeffffffffff gddbbbbbbbddg ffffeaffffffffff ggdb fffaefffffffffff fffeffffffffffff ffefffffffffffff feafffffffffffff eeffffffffffffff ce e ec ea caaeeeee ccaeeeeeeaac caaeeeeeeacc ccaeeeeeeaac eeeeacc ``` <!-- end of image --> I'm determined to find out if an intersection exists in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fb3336ff b,#0704fcff c,#ffbdbdff d,#5652fbff e,#fe0404ff f,#fe7778ff g,#aaa8fdff ``` ```image ee aea feec ceec ceef aea fee feec ceef aea aea feec ceec eef aea fee bbdddggg ceec bbbbbbbbbbbdddggaef gggdddbbbbbbbbbbbbbbdddggg gggddbbbbbbbbbbbbbbbd feec gggdddbbbbb ceef gg eef aea feec ceec ceef aea fee ceec ceef aea aea feec ceec eef aea ``` <!-- end of image --> The close-up clearly shows an intersection point in area A. The image features one single intersection point.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff5353ff b,#2323ffff c,#ffadadff d,#7a7affff e,#ff0606ff f,#0000ffff g,#d3d3ffff ``` ```image g bd f db fg gf bd f db fg gf bd f db fg gf bd f db c fg e gf e bd ec f ae db ce fg e gf ec bd ea f ce db e fg ec gf ea bd ae f ce db e fg ec gf ae bd ce f e db ec fg ea gf ce bd e f e db ea fg ae gf ce bd e f ec db aa fg ce gf e bd ec f ea db ae fg e gf e bd ec f ae db ce fg e gfffbddg ec gddbffffffbdgg ce gddbffffffbddg e gdbffffffbddg e gddbffffffbdg ea gddb ae ce e ec aa ce e ec ea caaeeeee ccaeeeeeeaac caaeeeeeeacc ccaeeeeeeaac eeeeacc ``` <!-- 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,#ff7878ff b,#0303ffff c,#ffaeaeff d,#7878ffff e,#ff0808ff f,#b2b2ffff g,#3e3effff ``` ```image c ee cea ee cea ee cea ee cea ee cea ee cea ee cea ee cea ee cea ee cea ee cea ee eeeeea cea caeeeeeac ee caeeeeeac cea caeeeeeac ee caeeeeeac cea aeeeeeaee ca d f gbbbd fgbbbg dbbbgf dgbbbgf dbbbgf dbbbbgf fgbbbd fdbbbbdf fgbbbd fdbbbbdf dbbbgf fgbbbbd dbbbgf fgbbbgd fgbbbf fgbbbgf fgbbbgf ``` <!-- end of image -->

The hunt for intersections begins! Let's analyze this image closely. I'm extremely confident. No intersections at all.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff5e5eff b,#0505ffff c,#ff0808ff d,#8585ffff e,#ffb4b4ff f,#4343ffff g,#c8c8ffff ``` ```image g bbbg gbbd gb dbbg db fbf ff gbbd bd dbbg b fbf gb gbbd db dbbg ff fbf bd gbbd b dbbg gb fbf db gbbd ff dbbg bd bb b gb db bf bd b gb db bf bg b gb db bf bg b gb db bf bg b gb db bf bg b gb fb bf bg b gb fb bf bg b gb fb bf b ace eca cce cc cce eca cce cc cce eca ecc cc ecc ace ecc cc ecc ace acc cc aca ace aca eca aca cc aca eca cce cc cce eca cce cc cce ace cc cc ecc ace ecc cc ecc ace ecc ca a ``` <!-- end of image -->

This is the image I'm working with. The goal is to count the intersections. I'm extremely confident. No intersections at all.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0404ff b,#0707ffff c,#5a5affff d,#ff8686ff e,#afafffff f,#ff3e3eff g,#ffcacaff ``` ```image d ga a ag ad ff da ga a ag af fa da a ag ad ff da ga a ag ad ff da ga ag ad af fa ga a ag ad ff da ga a ag af fa ga a aafg ag daafg ad daaag ff gaaag da gaaad ga gfaad a gfaad ag gfaad ad faad fa faad da daaf ga daaag g bbe bbbe ebbc cbbc cbbe ebbb ebbc cbbe cbbe eecbbbb ebbc eccbbbbbbcee ebbc eecbbbbbbcce cbbe ecbbbbbbbcee bbbe eccbbbbbbcce ebbbbbce ``` <!-- end of image -->

I'm curious to see if this image contains any intersection points. I've noticed 1 areas of interest. These could be potential intersection zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#0506fdff b,#fc0706ff c,#bdbdfeff d,#afd6afff e,#f82e2bff f,#fe9b9bff g,#6166f3ff ``` ```image f fb b b bf bf be ee fb fb b b ddddddddddddddddddddddddd bf ddddddddddddddddddddddddd bf fddddddddddddddddddddddddd be ebdddddddddddddddddddddddd ee ebddddddddddddddddddddddd fb adebdddddddddddddddddddddd fb cadebddddddddddddddddddddd b agdebdddddddddddddddddddd b daddebddddddddddddddddddd bf dgaddebdddddddddddddddddd bf ddadddebddddddddddddddddd ee ddgadddebdddddddddddddddd eb dddaddddebddddddddddddddd fb ddddaddddebdddddddddddddd fb ddddagddddebddddddddddddd b dddddadddddebdddddddddddd b dddddgadddddebddddddddddd bf ddddddaddddddebdddddddddd bf ddddddgaddddddebddddddddd ee dddddddadddddddebdddddddd eb ddddddddadddddddebddddddd fb ddddddddagdddddddebdddddd fb dddddddddaddddddddebddddd b dddddddddgaddddddddebdddd b ddddddddddadddddddddebddd bf a ddddddddddgadddddddddebdd be ag dddddddddddaddddddddddebd ee ag ddddddddddddaddddddddddeb eb ag ddddddddddddagddddddddddee fb ag dddddddddddddadddddddddddee b ag dddddddddddddgadddddddddd ee b ag a ee bf ag ca ee bf ag ac ee be ag a ee ee ag ag ee fb ag a ee fb ag ga ee b ag a eb ac ca ac ac ac a ac ag ac a ac ga ac a ac ca ac ac ac a ac gg ac a ac ga ac a ac ca a ac ca a ca gg ca a ca ga ca a ca ca ca ac ca a ca gg ca a ca ga ca aga ca ``` <!-- end of image --> I'm going to scrutinize area A for any signs of an intersection. <!-- image --> ```palette Key,Color ,#fefefeff a,#4545ffff b,#ff0808ff c,#c3c3ffff d,#0505ffff e,#ff3838ff f,#ffcbcbff g,#8383ffff ``` ```image ff bbf ebbf ebbf ebbf aa ebbf ddc ebbf ada ebbf ddc ebbf gdd ebbf ddg ebbf cdd ebbf ada ebbf cddc ebbf ada ebbf ddc ebbf gdd ebbf ddg ebbf cdd ebbf ada ebbf cddc ebbf ada ebbf ddg ebbf gdd ebbf ddg ebbf cddc ebbf ada ebbf cddc ebbf ada ebbf ddg ebbf gdd ebbf ddg ebbf cddc ebbf ada ebbf cddc ebbf gda ebbf ddg ebbf gdd ebbf ddg ebbf cddc ebbf ada ebbf cddc ebbf gda ebbf ddg ebbf gdd ebbf adg ebbf cddc ebbf ada ebbf cddc ebb gda eb ddg e gdd adg cddc ada cddc gda ``` <!-- end of image --> Area A does not contain any intersection points. I've examined the entire image, and there are zero intersections present.

<!-- image --> ```palette Key,Color ,#fefefeff a,#3030ffff b,#ff0e0eff c,#bdbdffff d,#0101ffff e,#ff3d3dff f,#ffa4a4ff g,#7171ffff ``` ```image f fb b b bf bf be eb eb fb b b bf bf f be eb eb eb fb dceb fb d eb b ag eb b d eb bf ga eb bf d eb be cd eb eb dc eb fb d eb fb ag eb b d eb b ga eb bf d eb be cd eb be dc eb eb d eb fb ag eb fb d eb b ga eb b d eb bf d cd eb be da dc eb ee da d eb eb da ag eb fb da d eb fb dg ga eb b dg d eb bf dg cd bb bf dg dc bb be dg d bb eb dg ag bb eb dg d bb fb dg ga bb b dg d bb dg cd dc dc dc d dc ag dc d dc ga dc d dc cd dc dc dc d dc ag dc d dc ga dc d dc cd d dc cd d cd ag cd d cd ga cd d cd cd cd dc cd d cd ag cd d cd gd cd dgd cd ``` <!-- end of image -->

I'm analyzing this image to identify any points where lines intersect. Zero, Nada.

<!-- image --> ```palette Key,Color ,#fefefeff a,#3d3dffff b,#ff0a0aff c,#ffacacff d,#0404ffff e,#7d7dffff f,#bebeffff g,#ff5e5eff ``` ```image c bg bc b cb bg bc b cb bg b b gb bg b b gb bg b cb e gb aa bc d b fd cb df gb d bc aa b d cb fd gb cb de bc gbb d b gbb ea cb gbg df bg bbg fd bc bbg de b bbc d cb cbbc ed bg cbb df bc cbb d b gbb ae cb gbg d bg gbg ed b bbg df b bbc d gb bbc aa bg cbbc d b cbb fd b cbb df gb gbb d bbbg aa g d fd de d ea d fd de d ed df d ae d ed df e d edda aa adde d fadde fd fdddf df eddaf d edda aa fadde d fddde fd edddf de eddaf d adda ea fadde d fdddf fdaf ``` <!-- 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,#fd0908ff b,#0607fdff c,#9a9ff2ff d,#f3615cff e,#4649f4ff f,#add4adff g,#ffb8b8ff ``` ```image aa agdd gag a da ga aa a ad ga ag ag gag a da ad aa a ad dd ad a gag ga da a aa ga aa ag ad a gag ad da a fffffffffffffffaa dd ffffffffffffffaa a fffffffffffffadf da ffffffffffffafff a ffffffffffdaffff ga fffffffffaafffff ag b fffbffffaaffffff a bc fffcbffadfffffff ag bc ffffbeadffffffff a be ffffdbffffffffff dd eb fffdafbfffffffff a cb fffdffebffffffff da cb fffffffbefffffff a b ffffffffbfffffff ga b fffffffffbffffff ag bc fffffffffebfffff ga be ffffffffffbcffff ag ee fffffffffffbffff ffafffffffffffeb fffffffffffcbfff ffadfffffffffcbf ee fffafffffffffbff bc fffdafffffffbfff b ffffaffffffbcfff cb ffffdaffffbeffff be fffffafffbefffff b ffffffafebffffff b ffffffaebfffffff cb ffffffcbffffffff bc ffffffbadfffffff b fffffbffafffffff b ffffbcffddffffff eb fffbeffffaffffff bc ffbbfffffdafffff b febfffffffafffff cb cbfffffffffaffff ee cbffffffffffaffff bc bffffffffffffafff b bc ad cb bc a be be dd b eb a b cb da eb cb a bc b ga b b ag cb bc a ee be ag bc be a b eb dd cb cb a ee b da bc b a b bc ga cb bc ag be be ga beb ag b a ad a dd a ``` <!-- end of image --> I'm focusing my attention on this specific region, area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff5353ff b,#0808feff c,#bcbbfdff d,#92016dff e,#5854fbff f,#fe0707ff g,#ffaaaaff ``` ```image gf gff gffa affa affg gfffg gfff gffa affa affg fffg cbe gfffg cbbe gffa cbbc affa ebb affg bbefffg cbbdfg gdbbc affebb affg bbe gffg cbbc gg ebbc ebe bbe cbbc ebb ebe cbbe cbbc ebb bbe cbbc cbbc ebb bbe ``` <!-- end of image --> Yes! I knew it! There's an intersection right here in area A! Now, let's dive into another area. I'm analyzing this close-up of area B with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#f9353bff b,#0707feff c,#b3b2feff d,#ff7171ff e,#5650f8ff f,#fe0404ff g,#ffc0c0ff ``` ```image ffd e gff eb afd cbb gffg cbbe afa cbbe gffg bbe dfa ebb ffg ebb dfa ebbc ffd cbbc gff cbbc afd cbbe gffg bbe afd bbe gffg ebb dfa ebbc ffebbc dabbc cbbe cbbef bbeafd ebb gff ebb afd ebbc gffg cbbc dfa cbbc gffg cbbe dfa bbe ffg bbe dff ebb afd ebbc gff ebbc afd cbbc gffg cbbe afa cbbe gffg bbe dfa ``` <!-- end of image --> The lines cross each other within area B, forming an intersection. Two intersections have been found!

<!-- image --> ```palette Key,Color ,#fefefeff a,#fe3334ff b,#0808ffff c,#b1b0feff d,#ff7a7aff e,#5755fdff f,#ff0303ff g,#ffc3c3ff ``` ```image g ff fdda gfg f df df af fg fa gf fd fg gfg f df ad af f fa da fd f gfg df df f af gf fa fg fd f gfg ad df f af aa fa f fd da gfg f df gf af fg b b fa f bc cb fd fd bc befg f be dbc ad eb af b f eb d eb da cb be f b b gf b b fg bc eb gf be bc fg bb b f eb cb ad cb ee f cb bc da b b f bc cb df bc be fg be bc gf eb b feb eb cb be bad b b f cb bc da eb be f bc be df b eb f cb cb gf ee cb fg bc b f b bc ad cb bc f be be aa b eb f b eb da eb cb f be b gf b b fg cb bc f eb be fd bc be f b eb ad cb cb f be cb da bc b f b bc gf cb bc fg be be gf beb fg b f ad f da f ``` <!-- end of image -->

The hunt for intersections begins! Let's analyze this image closely. I have a hunch that these areas might contain the intersections we're looking for. <!-- image --> ```palette Key,Color ,#fefefeff a,#f1443dff b,#0505fdff c,#fe0202ff d,#d4cdf7ff e,#626ce8ff f,#9dc09dff g,#b1d7b1ff ``` ```image d be b bd b bd db bd db bd db bd db b db b eb b eb b ee b ee b ee a b aa ee cd b c be aa b cd be c b aa bd cd b c bd aa db cd bd c db aa bd c db c bd aa db c b cfffffffebfffffffffffffffffffffffffffffffff aagggggggbggggggggggggggggggggggggggggggggg fcfggggggebgggggggggggggggggggggggggggggggg ffcgggggggbgggggggggggggggggggggggggggggggg fgaaggggggebggggggggggggggggggggggggggggggg fggcfggggggbggggggggggggggggggggggggggggggg fggfcggggggebgggggggggggggggggggggggggggggg fgggaaggggggbgggggggggggggggggggggggggggggg fggggcfgggggeeggggggggggggggggggggggggggggg fggggfcggggggbggggggggggggggggggggggggggggg d fgggggaagggggeegggggggggggggggggggggggggggg dbb fggggggcfgggggbgggggggggggggggggggggggggggg dbbd fggggggfcgggggbeggggggggggggggggggggggggggg dbbd fgggggggaagggggbggggggggggggggggggggggggggg dbbd fggggggggcfggggbegggggggggggggggggggggggggg dbbd fggggggggfcgggggbgggggggggggggggggggggggggg dbbd fgggggggggaaggggbeggggggggggggggggggggggggg dbbd fggggggggggcfggggbggggggggggggggggggggggggg dbbd fggggggggggfcggggbegggggggggggggggggggggggg dbbd fgggggggggggaaggggbgggggggggggggggggggggggg dbbd fggggggggggggcggggbeggggggggggggggggggggggg dbbd fggggggggggggfcggggbgggggggggggggggggggggggdbbd fgggggggggggggaagggbfggggggggggggggggggggfbbd fggggggggggggggcgggfbggggggggggggggggggfbbf fggggggggggggggfcgggbfgggggggggggggggfbbfgg fgggggggggggggggaaggfbgggggggggggggfbbfgggg fggggggggggggggggcgggbfggggggggggfbbfgggggg fggggggggggggggggfcggfbggggggggfbbfgggggggg acc fgggggggggggggggggaaggbggggggfbbfgggggggggg accccad fggggggggggggggggggcggebgggfbbfgggggggggggg gacccad fggggggggggggggggggfcggbgfbbfgggggggggggggg gacccag fgggggggggggggggggggaagebbfgggggggggggggggg dacccag fggggggggggggggggggggcggggggggggggggggggfacccaf fggggggggggggggggggggfcggggggggggggfaccccaf fgggggggggggggggggggggcaggggggfaccccafggggg fggggggggggggggggggggggcggaccccafgggggggggg fggggggggggggggggggggggfccafggggggggggggggf ``` <!-- end of image --> I'm going to scrutinize area A for any signs of an intersection. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff4040ff b,#0606ffff c,#ff0404ff d,#bdbdffff e,#5b5bffff f,#ffd8d8ff g,#ff9191ff ``` ```image ccg dbb gccf bbe aca dbb fccg bbd gccf dbb aca bbd fccg dbb gccf bbd aca ebb fccg bbd gccf ebb aca bbd fccg ebe gccf bbd aca ebe fccg bbd gccf ebe aca dbbd fccg ebe gccf dbbd aca ebe fccg dbbd gccf ebe aca dbb fccg ebe gccf dbb aca ebe fccg dbb gccf bbe aca dbb fccg bbe gccf dbb aca bbd fccg dbb gccf bbd aca dbb fccg bbd gccf ebb aca bbd fccg ebb gccf bbd aca ebe fccg bbd gccf ebe aca bbd de fccg ebe debb gccf dbbd debbbe aca ebe debbbed fccg dbbd debbbed gccf ebe debbbed aca dbbd debbbed fccg ebe debbbed gccf dbb debbbed aca ebe debbbed fccg dbb debbbe gccf ebe debbbe aca dbb debbbe fccg bbe debbbe gccf dbb debbbe aca bbe debbbe fccg dbb debbbe gccf bbeebbbe aca dbbbbe fccg bbe gcc fgaa aca fgaaccccc fccg fggacccccccagf gcc fggacccccccaggf aca fggacccccccaggf fccg ffgacccccccaggf gcc fgacccccccaagf acaaccccccaagf ``` <!-- end of image --> There is no intersection present within area A. Zero, Nada.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff4242ff b,#0606ffff c,#ff0202ff d,#ccccffff e,#6f6fffff f,#ffd8d8ff g,#ff8989ff ``` ```image d be b bd b bd b bd db bd db bd db b db b eb b eb b eb b ee b ee g b aa ee cf b fc be aa b cf be fc b aa bd cf b fc bd aa b cf bd fc db aa bd cf db fc bd aa db cf b fc db aa b cf eb fc b aa eb cf b fc eb aa b cf ee fc b d aa ee dbb cf b dbbd fc ee dbbd aa b dbbd cf be dbbd fc b dbbd aa be dbbd cf b dbbd fc bd dbbd aa b dbbd cf bd dbbd fc b dbbd aa bd dbbd cf db dbbd fc bd dbbd aa db dbbd cf bd dbbd fc db dbbd fgcc aa b dbbd gccccaf cf db dbbd gacccaf fc b dbbd gacccag aa ebbd facccag c facccag fc fgccccgf aa fgccccgf c gccccaf fccaf ``` <!-- 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,#4b4df9ff b,#fe0606ff c,#e85f55ff d,#0606feff e,#adaefdff f,#feb7b6ff g,#aed5aeff ``` ```image f cbb bbc fbbf cbbf cbc fbbc gggggggggggggggg fbbf gggggggggggggggg cbb gggggggggggggggg bbc gggggggggggggggg fbbf gggggggggggggggg cbb gggggggggggggggg bbc gggggggggggggggg fbbf gggggggggggggggg cbbf gggggggggggggggg cbc gggggggggggggggbbc ggggggggggggcbbc ggggggggggcbbggg ffffffccccccccbbcggggg bbbbbbbbbbbbbbbbbbbbbbbbbbcccccccccccggggggg gggggggggggggggg gggggggggggggggg gggggggggggggggg gggggggggggggggg gggggggedggggggg gggggggdadgggggg ggggggdagadggggg ggggggdgggadgggg gggggdgggggdaggg ggggdaggggggdagg ed de d de aa d ed d d ed aa ed d ad d ad aa da d da de de aa de d de de d ad ed d ed de ed ad ad d ad de da ed da d de de de ed d d d de ed ed ed d ad de ad ed da d da da de ed de d d da d ed ed d ed da ad ed ad d da aa da ed de d d aa d d aa d de ``` <!-- end of image --> Let's see what secrets area A holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#2727ffff b,#ff0404ff c,#ff5d5dff d,#0101ffff e,#7272ffff f,#ff9494ff g,#c2c2ffff ``` ```image fcb fbbbb cbbbbc fcbbbbf fcbbbcf fffffffffffcccccccbbbbc bbbbbbbbbbbbbbbbbbbbf cccccccccccccffffff ee gdde addde edaedde gddg eddg ade eddg eda eddg gddg adag ade ada eda ada gddg gdda ade gdde ``` <!-- end of image --> This close-up reveals that there are no intersections in area A. My final answer is: no intersections found.

<!-- image --> ```palette Key,Color ,#fefefeff a,#4141ffff b,#ff0707ff c,#ff6060ff d,#0505ffff e,#8686ffff f,#ffb3b3ff g,#cdcdffff ``` ```image f cbb bbc fbbf cbbf cbc fbbc fbbf cbb bbc fbbf cbb bbc fbbf cbbf cbc fbbc fbbf cbb fffffffffcccccbbc bbbbbbbbbbbbbbbbbbbbbbbbbbccccccccccf gd ded de ed gd ad d da aa da gd de d dg aa dg gd d dg gd aa ed gd ed dg ad aa aa gd da dg de aa dg d dg dg d aa gd d gd dg ed ed ad d aa dg da ed de d de de dg ed d d gd de gd ed ed d ad de ad ed da d de de de gd dg d dg de gd gd gd d ed aa ed gd ad d da aa da gd de dg d aa gd dg aa gd dg ``` <!-- end of image -->

Based on a first glance, I suspect there could be intersection regions here. The image has some tight areas where segments are too close. I should investigate those closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0505ff b,#3b3ef8ff c,#7d84f1ff d,#fbadacff e,#0303ffff f,#f94d4aff g,#afd6afff ``` ```image daad aa a fad da daf da aa fa fad af daf af aa ad fad a daf a aa da fad fa daf fa aa af fad ad daf ad aa a fad da daf da aa fa fad af af af ad a a da da fa af ad ad a a da fa fa af ad ad aggggggggggggg dagggggggggggg faggggggggggg gfagggggggggg ggafggggggggg gggafgggggggg ggggadggggggg gggggaggggggg ggggggagggggg ggggggdaggggg gggggggfagggg ggggggggfgggg ggggggggggggg ggggggggggggg ggggggggggggg ggggggggggggg ggggggggggggg ggggggggggggg ggggggggggggg ggggggggggggg gcccccccccccccbbbbbbbbbgggg eeeeeeeeeeeeeeeeeeeeebbbbbbbbbbccccccccccccccgggg eec eec eec eec bec bec bec bec bec bec beb beb ceb ceb ceb ceb ceb eb ``` <!-- end of image --> This close-up might reveal an intersection in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff0202ff b,#4b4bffff c,#ffcacaff d,#ff8e8eff e,#0000ffff f,#ff5555ff g,#ff2525ff ``` ```image f af aad daad faac faac gag gag caaf caad daad daac faac fagc gag cgaf caaf caad daad daac fag fc bbbbbbbbbbbbbbbbbb eeeeeeeeeeeeeeeeeb ``` <!-- end of image --> There is no intersection present within area A. After a thorough analysis, I conclude that there are no intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0505ff b,#3c3cffff c,#aaaaffff d,#ffaeaeff e,#0303ffff f,#ff4e4eff g,#7272ffff ``` ```image daad aa a fad da daf da aa fa fad af daf af aa ad fad a daf a aa da fad fa daf fa aa af fad ad daf ad aa a fad da daf da aa fa fad af af af ad a a da da fa af ad ad a a da fa fa af ad ad a da da fa af af ad a a da fa f cccccccccccgggggggggbbbbbb eeeeeeeeeeeeeeeeeeeeebbbbbbbbbggggggggccccccc eec eec eec eec bec beg beg beg beg beg beg geb geb geb geb geb geb eb ``` <!-- end of image -->

I'm optimistic that I'll find some intersections in this image. I've examined the entire image, and there are zero intersections present.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff4040ff b,#0707ffff c,#adadffff d,#ff8585ff e,#ff0505ff f,#5c5cffff g,#ffcdcdff ``` ```image c cbbbbf cbbb fbb fbbc cbbc fbbc bbf cbbf fbb cbbf cbbc bbbc bbf fbbc fbbc fbbf cbbf cbbf fbb cbbb cbbc fbbc bbf fbbc fbb f cbbc bbf fbbc cbbf fbb cb eeg aedged aed ee dea ae dea ged dea ea gee ae gee geg geeg ea eeg ae eed deg aed ea aed ee dea deg dea ged dea ee gee de gee ged geeg ee eg ae ged ea ae geg ea ae deg ea ee deg ged ee ae ge ``` <!-- end of image -->

Here's an image. My task is to find intersections or areas where lines come close together. These zones indicate regions where lines appear to be in close proximity. <!-- image --> ```palette Key,Color ,#fefefeff a,#fb1212ff b,#0707fdff c,#a9adf6ff d,#eb9a91ff e,#b1d7b1ff f,#5054eeff g,#96c897ff ``` ```image c ff bc b fb bc b cb ff bc b cb bf b cb ff bc b cb bf b fb cb bb fb cbc bc bb b cbf cb fb bf bf b fbc b bb fb cbc bc bb b cbf cbgggggggggggggggggggggggggggggge fb bfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg bf gbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg fbc gebeeeeeeeeeeeeeeeeeeeeeeeeeeeeg bb gefbeeeeeeeeaadeeeeeeeeeeeeeeeegcbc geebfeeeeeedaeaaeeeeeeeeeeeeeeebb geeebeeeeeeaeeeaaeeeeeeeeeeeegbf geeecbeeeeadeeeedadeeeeeeeeefbeg geeeebfeeadeeeeeeeaaeeeeeeebbeeg geeeeebgaaeeeeeeeeeaaeeeefbceeeg geeeeeebaeeeeeeeeeeedadebbeeeeeg geeeeegfbeeeeeeeeeeeeeabfeeeeeeg geeeeeaebfeeeeeeeeeeebbaaeeeeeeg geeeeadeebeeeeeeeeeebfeedadeeeeg geeeaaeeecbeeeeeeefbeeeeeeaaeeeg geeaaeeeeebfeeeeebbeeeeeeeeaaeeg gedaeeeeeeebgeefbceeeeeeeeeedadg geaeeeeeeeeebebbeeeeeeeeeeeeeeaa gaeeeeeeeeeefbfeeeeeeeeeeeeeeeeaa adeeeeeeeeeeeeeeeeeeeeeeeeeeeeegdad aaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg aa dageeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg aa da egggggggggggggggggggggggggggggge dad a aa a aa ad dad aa aa da aa a dad a aa ad aa ad dad aa aa da aa a dad a aa ad aa aa d da da a a ad aa da a a ad ``` <!-- end of image --> I'm focusing my attention on this specific region, area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe5e5fff b,#0504feff c,#8783fbff d,#ffb9b9ff e,#fe090aff f,#3f3af9ff g,#ccccffff ``` ```image bbg fbb fbf gbbc cbbg fbf gbbc gbbg aad cbb aeeed fbf deeeeea gbbc deea aeeed cbbg deea deeed c fbf eea aeea gfb gbbc aee aeeed cbbb gbbg aeed deeed fbbfg cbb deed aeea gbbbc fbf deea aeeed cbbfg gbbc eea deeed gfbbc cbbg eee aeea cbbbg fbfaee aeeed gfbbf bbfed deeed cbbbc cbbc aeeafbbfg defbb aebbbc eeafbf cbbbed aee gbbc gfbbcaeea aeed cbbg cbbbg aeeed deed fbf gfbbf deeed deed bbc cbbbc aeea deea gbbg fbbfg aeee eea cbbg gbbbc deeed aee fbf cbbfg aeea aeed gbbc gfbbc aeee deed cbbg cbbbg deeed deea fbf gfbbf aee eea bbc cbbbc ae eee gbbfbbfg d aee cbbbc aeed ffg deed eea ea e d ``` <!-- end of image --> I am surprised, so clear, an intersection has appeared in area A. The image features two intersection points.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fc3b3eff b,#0505ffff c,#7e7effff d,#ffadadff e,#ff0202ff f,#3d39faff g,#c2c2ffff ``` ```image g ff bg b cb bc b gb ff bg b cb bc b gb ff bg b cb bc b cb gb bb ff cbg bg bb b gbc cb fb bc bf b cbg gb bb ff gbc bg bb b gbc gb fb ff bf bg cbg b bb cb aed gbc bc de ea bb b e ae gbc gb ed ded fb ff ed ea bf bgaa ae cbg be ded bb dfb abc e bc fbae ed b gbf ded ea gb fbg ea ae ff bf ae de bg cbg ded e b bb ea e cbc ae ed ded ea ea ae ae de ded e ea ed ae ed ded aa ea de ae de ded e ea ed ae ea ded ae ea de ae e ded e ea ed ae ea d ae de e ed ed aa de de e ed ``` <!-- 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,#fe0707ff b,#0808feff c,#f69a95ff d,#6063f8ff e,#aed5aeff f,#fd4f4eff g,#bcbcffff ``` ```image eeeeeeeeeeeeee eeeeeeeeeeeeee eeedeeeeeeeeee eeedbbbdeeeeee eeeeeeedbbbdee eeeeeeeeeeedbbbbg eeeeeeeeeeeeee gdbbbd eeeeeeeeeeeeee gdbbbdg eeeeeeeeeeeeee dbbbbg gggdddb eeeaeeeeeeeeee gbbbbd gggdddbbbbbbbbbbbbbdddgg eeecaeeeeeeeee gdbbbdg gggdddbbbbbbbbbbbbbdddggg eeeeaeeeeeeeee dbbbbbbdddggg eeeecaeeeeeeee eeeeeaeeeeeeee eeeeecaeeeeeee eeeeeeaeeeeeee eeeeeecaeeeeee eeeeeeeaeeeeee eeeeeeecaeeeee eeeeeeeeaeeeee eeeeeeeecaeeee eeeeeeeeeaeeee eeeeeeeeecaeee eeeeeeeeeeaeee eeeeeeeeeefaee eeeeeeeeeeeaee ca a ca a cf a cf a ff a ff a ff a c ff fa a fa ff fa a aa ff aa a af ff af a af ff af a ac ff ac a ac ff ac a ac fc a a a fc ca a ca ac ca a ca ac ca a fa ac fa a fa ac fa a aa ac aa a af ac af a af ac af a ac ac ac a ac ac ac a ac ac a a a ac ca a ca afa a ``` <!-- end of image --> My goal is to determine if there's an intersection inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff0202ff b,#0505ffff c,#ff9494ff d,#4e4effff e,#cfcfffff f,#ff2323ff g,#9292ffff ``` ```image ge ebbbdge edbbbbbbddge egdbbbbbbbdge egddbbbbbbdge egdbbbbb egdb cc caa fac caa fac caa fac caa fac caa fac caa fac caa fac caa fac caa fac caf fac caf fac caf fac caf fac caf fac caf fac caf fac caf ``` <!-- end of image --> No intersection in area A, but I'll keep looking. After a thorough analysis, I conclude that there are no intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0505ff b,#0808ffff c,#ff7a7aff d,#6464ffff e,#ffb6b6ff f,#ff3b3bff g,#aeaeffff ``` ```image g dbbbd dbbbdg gbbbbg gdbbbd dbbbdg dbbbbg ggdddb a gbbbbd ggdddbbbbbbbbbbbbbdddgg ea gdbbbd ggdddbbbbbbbbbbbbbdddgg a dbbbbbbdddgg ea a ea a ea a ea a ea a ca a ca a cf a cf a cf a cf a cf a cf a cf a c cf fa a fa ff fa a fa ff af a af fc af a af fc ac a ac fc ac a ae fc ae a ae fc ae a ea fc ea a ea fc ea a ca fc ca a ca fc fa a fa ac fa a fa ae af a af ae af a af ae ac a ac ae ac a ae ae ae a ae ae ae a ea ae ea a ea aca a ``` <!-- end of image -->

I have an image in front of me. I need to determine if there are any intersection segments. 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,#0606feff b,#fc0505ff c,#add4aeff d,#ec9289ff e,#fa4b48ff f,#9da2f5ff g,#4b4cfbff ``` ```image fa afa fa af a a fa gg b a a db fa fa b a af db fa a b a gg db fa a b a fa de fa af b a a de fa fa b a af ee fa a b a gg ee fa a b a fa ee fa af b a a ee fa gg b a a ed fa fa b a af ed fa a ccbccccccccccacc fa ccbdccccccccfacc a cccbccccccccaccc a cccbdccccccfaccc gg ccccbccccccacccc a ccccbdccccfacccc fa cccccbccccaccccc af cccccbdccfaccccc a ccccccbccacccccc gg ccccccbdcacccccc a cccccccbaccccccc fa cccccccbaccccccc af cccccccabccccccc a cccccccabccccccc ga ccccccacdbcccccc a ccccccaccbcccccc a cccccacccdbccccc ag cccccaccccbccccc a ccccafccccdbcccc fa ccccaccccccbcccc af cccafccccccdbccc a cccaccccccccbccc gg ccafccccccccdbcc a ccaccccccccccbcc fa cafccccccccccebc af a b a af de gg a b a af de a a b af af ee a a b fa af ee af a b a af ee gg a b a af ee fa a b cccccccafccccccc af ed ccccccccaccccccc a b ccccccccgacccccc af ed cccccccccacccccc a b ccccccccccaccccc af bd ccccccccccagcccc a b cccccccccccacccc af bd cccccccccccccccc f b cccccccccccccccc bd cccccccccccccccc b cccccccccccccccc bd ccddeebbbbbbcccc b ddeebbbbbbbbbbbeeddccccccccc bd dddeebbbbbbbbbbeedd cccccccccccccccc bbbbbeeddd cccccccccccccccc cccccccccccccccc cccccccccccccccc cccccccccccccccc ``` <!-- end of image --> Here's a close-up of the area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0101feff b,#ff0303ff c,#d2d1feff d,#fcb1b3ff e,#ff7c7cff f,#fb292cff g,#5450faff ``` ```image dbb gag fbe caac dbb gag fbe caac dbf gag fbe caac ebf gag fbd caac ebf gag bbd caac ebf gag bbd caac ebf gag bbd caac ebf gag bbd caac ebf gag bbd caac ebf gag bbd caac ebf gag bbdaac ebgag faac gag caafd gagbe caacbbd gag fbe caac dbb gag fbe caac dbb gag fbe caac dbb gag fbe caac dbb gag fbe caac dbb gag fbe caac dbb gag fbe caac dbb gag fbe caac dbb gag fbe caac dbf gag fbe caac ebf ``` <!-- end of image --> Wow! I can see an intersection so clearly in area A! Hmm, interesting. Let's check out another area. I'm analyzing this close-up of area B with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#0606ffff b,#ff0303ff c,#a7a7ffff d,#ff8686ff e,#ff4343ff f,#ffc4c4ff g,#5050ffff ``` ```image caa gag aac caa aag caac gag aac caa gag caac gaa aac caa gag ag ffffdddd fffddddeeeebbbbbbbbbbe bbbbbbbbbbbbbbbbbbeeeedd bbbbeeeddddfff ``` <!-- end of image --> I don't observe any intersections inside area B. After careful examination, I conclude that there is one intersection.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0606feff b,#fe0708ff c,#d0d0ffff d,#ffa4a4ff e,#ff5656ff f,#9999ffff g,#4a4affff ``` ```image c fa afa fa ac a a fa gg b a a db fa fa b a af db fa a b a gg db fa ac b a ca db fa af b a a ee fa fa b a ac ee fa ca b a gg ee fa a b a fa ee fa af b a a ee fa gg b a a ee fa ca b a af bd ca a b ac fa bd ca ac b ac ca bd ca gg b ac a bd ca fa b ac ac bd ca a b ac gg bdca a bac ca ba af ab a cab ga acdb ac ca b ca ac db ag ca b a ac db fa ca b ac ac db a ca b gg ac db a ca b ca ac db af ca b a ac db gg a b ac af ee ca a b af af ee a a b fa af ee ac a b a af ee gg a b a af ee fa a b af af ee a a b gg af bd ac a b ca af bd af a b a af bd c b bd b bd ddeebbbbbb b dddeebbbbbbbbbbeeedd bd ddeeebbbbbbbbbbeeddd bbbbbbeedd ``` <!-- end of image -->

I'm examining this image closely. My goal: find any and all intersections. The image has some tight areas where segments are too close. I should investigate those closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#5b67d5ff b,#f70e0eff c,#0908f9ff d,#cb7568ff e,#b1d7b2ff f,#a7cfa7ff g,#eff6efff ``` ```image e cc ca bgcaggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggg gbfcaffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffg gdbecfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfdbfcfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfedbfceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeedbaceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeebbaceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeebbcceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeebbcaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeebbcaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeebdcaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeebdcfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeebdcfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeebdceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeebaceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeebaceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeefbcceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeefbcaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeefbcaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeedbcaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeedbcfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeedbceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeedbceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeebdceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeebaceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeebcceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeebcaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeebcaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeebcaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeebcfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeebceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeebceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeefdceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeefaceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeefcceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedcaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedcaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedcaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedcceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedccfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedbcaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefbccfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebdcaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbccfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbfcaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeccfeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedbefcaeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedbfecceeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefbdeacaeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebdeecceeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeacaeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeecceeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeeacaeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedbeeeecceeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedbfeeeacaeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefbdeeeecceeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebdeeeeacaeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeeeecceeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeeeeacaeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeeeeecceeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedbeeeeeeacaeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedbfeeeeeecceeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefbdeeeeeeacfeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebdeeeeeefcceeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeeeeeeacfefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeeeeeefccfg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeeeeeeeacg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedbeeeeeeeefc gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedbfeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefbdeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebdeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedbfg gffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffdbg ggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggb ``` <!-- end of image --> Here's a close-up of the area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#6461fcff b,#fe4444ff c,#0b08fcff d,#fda3a4ff e,#bdbbfcff f,#fd0406ff g,#9a096dff ``` ```image f eca fb cc ffbace dff ace dfdccc ffecc dfdeca ffdcc bfface bfdcce ffccc bfecc fbeca ffbcca dfbace dfbace ffbcc dfdcc dfdca bfecc bface fface bface bbcc ffcca fgcc dfgca dffcc dface dfcce dfccc bfcc bfgca bfcc bgce ffcce fccc ffca dfgca dfcc fgce dfcce fcc bfca bfca gcc bgce bgce cc fcc dcca gcc dgca dcc gce bccc fcca dfgcc dfgcce bfccc ffdcc dffacce dfbecca ffdecca bfd cce ffdecca dfb ecca dfb acce ffd acce ffd ecc bff acce dfb acce ffb ecca ffd ecca ff ccc bfd ecca ffb cca dff acae ff aca bfd ecc bfd aca dff acc dfb acce dfb ecc bfd ecca ffd acce dfb ccc dfb ecca ff acc ffd acce bff ccc dfb ecc ff acce dfb ecca bff ecc bfd c ffb dff dfb bfd bfd ffb dfb dfb bfd ffd bff df ``` <!-- end of image --> No intersection found in area A, but I won't give up. There's definitely not a single intersection on the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#6866fcff b,#f03442ff c,#0d09faff d,#f87a81ff e,#b3b3ffff f,#fd0607ff g,#ffc3c3ff ``` ```image e cc ca f ca gf ce gf ce gf c dfec dfec bfac bfcc bbca fbca fbce fdce fdc fdc fac fac fcc gfca gfca gfce dfc dfc dbc bbc bcc fcc fca fca fce fc fc bc bc cc gcc gca gca dce dca dcc gfca fcc fdca fbcc ffeca bf cc df eca gfg cc fg eca fd cc fb eca ff cc bf eca df cc gfg ece fg cc fd ece fb cc ff ace bf cc df ace gfg cc fg ace fd cc fb ace ff cc bf ace df c gfg fg fd fb ff bf df gfg f ``` <!-- end of image -->

I'm curious to see if this image contains any intersection points. After a thorough analysis, I conclude that there are no intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#4141ffff b,#ff0707ff c,#0404ffff d,#ff5555ff e,#9191ffff f,#ffa7a7ff g,#d1d1ffff ``` ```image f fddbbbbbbbd ffddbbbbbbbddf ffdbbbbbbbbddf ffdbbbbbbbbdff fbbbddff fbb fbb dbb dbd dbd bbd bbf bbf fbbf fbbf fbb fbb dbb dbd dbd bbd bf a ec gc cg ce aa ec gc cg ce aa ec c cg ce ac ec c ce cg ce ce ce ac cg gc cg c cg cg cg ca gc ac gc gc gc c gc cg ec ca ec ec ec gc ec c ac ce ac aa ac ec ac gc aa cg ca ce ca aa ca ec ca gc ce cg ce ce ce aa ce ec cg c cg cg cg ce cg ac gc ec gc c gc cg gc ca ecac ec ``` <!-- end of image -->

Alright, let's get to work and investigate this image for intersections. There are 1 regions I'd like to highlight in the image. <!-- image --> ```palette Key,Color ,#fefefeff a,#fb0b0aff b,#0707fcff c,#8c98e1ff d,#e96a63ff e,#b1d7b1ff f,#464defff g,#98c896ff ``` ```image c fb bf bf bc bc b b b cb cb cb fb fb bf bf bc bc b b b cb cb fb fb bf bfegggggggggggggggggggggggggggggggggggggggggggg bfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee bceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee gbceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee gebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee geebeeeeeeeaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee geecbeeeeeaaaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee geeecbeeeadeaaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee geeeefbedaeeeadeeeeeeeeeeeeeeeeeeeeeeeeeeeeee geeeeefbaeeeeeadeeeeeeeeeeeeeeeeeeeeeeeeeeeee geeeeeebbeeeeeeageeeeeeeeeeeeeeeeeeeeeeeeeeee geeeeeadbfeeeeeeaeeeeeeeeeeeeeeeeeeeeeeeeeeee geeeedaeebfeeeeeeaeeeeeeeeeeeeeeeeeeeeeeeeeee geeeeaeeeebfeeeeegaeeeeeeeeeeeeeeeeeeeeeeeeee geeeageeeeebbceeeedaeeeeeeeeeeeeeeeeeeeeeeeee geeadeeeeeeeebbeeeedaeeeeeeeeeeeeeeeeeeeeeeee gedaeeeeeeeeeecbbeeeaaeeeeeeeeeeeeeeeeeeeeeee geaeeeeeeeeeeeeecbbeeaaeeeeeeeeeeeeeeeeeeeeee gageeeeeeeeeeeeeeefbfeadeeeeeeeeeeeeeeeeeeeee adeeeeeeeeeeeeeeeeeefbfadeeeeeeeeeeeeeeeeeeee daeeeeeeeeeeeeeeeeeeeeebbddeeeeeeeeeeeeeeeeeee ageeeeeeeeeeeeeeeeeeeeeeebbceeeeeeeeeeeeeeeeee a geeeeeeeeeeeeeeeeeeeeeeeegbbgeeeeeeeeeeeeeeee ad geeeeeeeeeeeeeeeeeeeeeeeeegabbeeeeeeeeeeeeeee da geeeeeeeeeeeeeeeeeeeeeeeeeedacbbeeeeeeeeeeeee a geeeeeeeeeeeeeeeeeeeeeeeeeeedaecbfeeeeeeeeeee a geeeeeeeeeeeeeeeeeeeeeeeeeeeedaeefbfeeeeeeeee ad geeeeeeeeeeeeeeeeeeeeeeeeeeeeeaaeeefbfeeeeeee da geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaaeeeebbceeeee a geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeadeeeeebbceee a geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeadeeeeeebbee ad geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeageeeeeecbb da geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeageeeeeeecbb a geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeeeee cbf a geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegaeeeeeee fbf ad geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedaeeeeee fbc da geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedaeeeee bbc a geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedaeeee b a geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaaeee ad geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaaee da geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeade a geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeead a egggggggggggggggggggggggggggggggggggggggggggae ad a da a a ea a da ad da da da a aa a ad ad ad da ae d a ``` <!-- end of image --> This close-up might reveal an intersection in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#f93439ff b,#0706fdff c,#acabfeff d,#fd7577ff e,#febebeff f,#5853faff g,#fe0405ff ``` ```image f bf bbc cbbc fbbc fbbc fbb fbb bbb bbf age bbf aggge cbbf dggaga cbbf egge aga cbbc ggd egga cbbc aga egga fbbc dgge eggd fbbcegge eggd fbbagd dgge fbba dgge dbbb dgge eggbbb agge ggd bbf agg aga cbbf aga dgge cbbf gga egge cbbf egga ggd cbbc eggd aga cbbfc eggd dgge cbbbfc eggd egge fbbbf dgge ggd fbbbf dgge aga cfbbbf dgge dgge cfbbbc agge egge cbbbbc aga ggd cbbbbc aga aga cbbbfc egga dgge fbbbfc egga egge fbbbf eggd ggd fbbbfeggd aga cfbbbfggd gge cfbbbage ge cbbbbae d cbbbbc cbbbfc fbbbf afbbbf eggfbbbf eggdfbbbc eggdcbbbbc eggd cbbbbc dgge cbbbfc dgge fbbbfc dgge fbbbf agge fbbbf agg cfbbbf aga cfbbbc gga cbbbbc egga cbbbbc eggd cbbbfc eggd fbbbfc eggd fbbbf dgge fbbbf dgge cfbb agge cf agge aga aga egga egga eggd eggd dggd dgge dgge agge agg aga gga egga eggd eggd eggd dgg dg ``` <!-- end of image --> Bingo! This close-up reveals an intersection in area A! Two intersections have been found!

<!-- image --> ```palette Key,Color ,#fefefeff a,#f9343aff b,#0707feff c,#9796fdff d,#ff7979ff e,#f1d8e5ff f,#4949ffff g,#fe0707ff ``` ```image c fb bf bf bc bc be be eb eb cb cb fb fb bf bf bc bc be b eb cb cb fb fb bf bf bc bc be be eb eg eb gaa cb gd ga cb dg gd fbg gd bb ge gdbf ge dg bf eg eg bc eg ge bbe dg gd ebbe dg dg cbb ag eg cbf aa ge cbf ga gd fbcgd dg fbad eg bbc ge ebbe gd egbb dg egcbb eg dg cbf ge dg fbf gd ag fbc dg ga bbc eg gd bbe ge gd ebbe gd ge ebb dg ge cbb eg eg cbf ge eg fbf gd dg fbc dg dg bbc eg ag b ge aa gd ga dg gd eg gd ge ge gd ge dg eg eg eg ge dg gd dg dg ag eg aa ge ga gd gd dg ge d g ``` <!-- end of image -->

I'm on the case! Let's uncover any intersections hidden in this image. My next step is to analyze the details within each area. <!-- image --> ```palette Key,Color ,#fefefeff a,#0202feff b,#f04846ff c,#959dedff d,#ee9a92ff e,#fd0606ff f,#3337f6ff g,#aed5aeff ``` ```image beb e be ed ded de ee e be ed eb de ee e ded ed eb de be e ded bb ee e be e ed bb ee e de ed eb de ee e ded ggggggggggggggggg ed eb ggggggggggggggggg de be ggggggggggggggggg e dedggggggggggggggggg ed eegggggggggggggggg de beggggggggggggggg e ggebggggggggggggg bb gggeegggggggggggg e ggggdedgggggggggg e ggggggebggggggggg bb gggggggbegggfgggg gggggggggggggggge ggggggggdedcagggg cggggggggggggggged ggggggggggeaggggg ffgggggggggggggbe ggggggggggabegggg acggggggggggggeg gggggggggacgggggg gagggggggggggedg ggggggggacggggggg gcagggggggggdegg gggggggafgggggggg ggffggggggggeggg ggggggffggggggggg gggacggggggebggg gggggfagggggggggg ggggagggggdegggg ggggcaggggggggggg ggggcaggggeggggg gggcagggggggggggg gggggffggebggggg gggaggggggggggggg ggggggacgegggggg ggagggggggggggggg gggggggaeggggggg gacgggggggggggggg gggggggbaggggggg afggggggggggggggg gggggggeffgggggg ffgggggggggggggggg ggggggedgacggggg fa gggggbegggaggggg ca gggggeggggcagggg ca ggggedgggggffggg a gggdegggggggacgg a gggegggggggggagg ac ggebgggggggggcag ac gdegggggggggggff ff gegggggggggggggac fa ebgggggggggggggga ca egggggggggggggggca ca egggggggggggggggg ff a ac a a ac ca ac ff af ac fa a ca ca ca ff a ac a a ac ca ac ff af ac fa a ca ca ca ff a ac a a ac ca ac ff af ac ff aca ca ``` <!-- end of image --> I wonder what we'll find inside area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#0404feff b,#fc5d60ff c,#bfbffeff d,#7272ffff e,#fe0909ff f,#3b31f4ff g,#ffb6b6ff ``` ```image b ge c ee f bee ad geeg aac eeb daac bee faf geeg aad beb caac gee daac eeg faf beb aad geeg caac eeb daac bee faf geeg aad eeb caac bee daac geeg faf eeb aad bee caac geeg daacbeb fafee aafg baac gefaac eebfaf bee aad geeg caac eeb daac bee faf geeg aad eeb caac bee daac geeg faf beb aad gee caac eeg daac beb faf geeg aad eeb caac bee daac geeg faf eeb aa bee ca geeg d eeb ee eg b ``` <!-- end of image --> Wow! I can see an intersection so clearly in area A! Time for a closer look at another area. I'm eager to see what's happening in this magnified view of area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#0605fdff b,#fa565aff c,#8889ffff d,#ffacacff e,#fd0709ff f,#4241fdff g,#cdcdffff ``` ```image b eed eeeb beeb deeed beeb beeed deeed beeb deeed deeeb beeb deeed beeb cg beeed caa deeed caac beebaac deaaf gaaaed fafbeeb faag deb faag caag caac gaac gaaf gaaf faf faag faag caag caac gaac gaaf gaaf faf faag faag caag caac gaac gaac aaf af ``` <!-- end of image --> Aha! I've found an intersection inside area B! After a thorough search, I conclude that there are two intersections.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0303ffff b,#fb4245ff c,#a8a8ffff d,#ff8989ff e,#fe0506ff f,#3d3dffff g,#ffccccff ``` ```image g beb e be eg ged de ee e beg ed ged de ee e deg ed eb ge be e ged bb eb ge be eg ged bb ee e deg eg eb de ee e deg ed eb de be e ged ed ee ge deg e geb bb ee ge deg eg eb bb be c e gedca c eg ea ff de abe ac e ac g a ed ac ca de af ff e ff ac ed fa a ge ca ca e ca ff bb a acge a aeg ac ba af eff ff eg ac fa de a ca e ca ca ed ff a de ac a e a ac ed ca af ge ff af e ac fa bb a ca ge ca ca eg ff a ac a a ac ca ac ff af ac fa a ca ca ca ff a ac a a ac ca ac ff af ac fa a ca ca ca ff a ac a a ac ca ac ff af ac fa afa ca ``` <!-- 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,#f56460ff b,#0807fdff c,#fe0908ff d,#5a5ff4ff e,#ffb8b8ff f,#aaaaffff g,#aed4adff ``` ```image a ec c ca ec c ce ac c ce ca ec c ca ac c ce ac ec c ca ec c ce ac c ce ca ec c ca ac c ce ac ec c ca ec c ce ac ggggggggggggggcg gggggggggggggcgg ggggggggggggcagg ggggggggggggcggg gggggggggggcgggg ggggggggggcagggg gggggggggacggggg gggggggggcgggggg dbddgggggcggggggg fbbdgddbbbbbbdgggggg fbbb gggggggcddbbbbbbdf bbbf ggggggcgggggggggddbbbbbdff dbbf gggggcaggggggggg fdbbbbbbdf dbbd ggggacgggggggggg fdbbbbbbdf fbbd ggggcggggggggggg fdbbbb fbbb gggcaggggggggggg bbbf ggacgggggggggggg dbbf ggcggggggggggggg dbbd gcgggggggggggggg fbbd cagggggggggggggg fbbd cc bbf cce ecce ecce ecc ecc acc acc aca aca cca cca cce ecce ecce ecc ecc cc ``` <!-- end of image --> This close-up might reveal an intersection in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff3f3fff b,#0807fdff c,#fe0405ff d,#5d5dfeff e,#fc8588ff f,#a9a9ffff g,#fec8c9ff ``` ```image gcc cce aca eccg gcce aca ecc gccg cce aca eccg gcce aca eccg gcce aca acc bbbddff gccg bbbbbbbbbbddfffgcce ffffddbbbbbbbbbbbbddff ffdddbbbbbbbbbbbddff gcceffddbbbbbbbbbb aca ffddbbb ecc gccg cce aca eccg gcce aca eccg gcce aca acc gccg cce aca eccg gcce ``` <!-- 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,#ff4c4cff b,#0807feff c,#fe0606ff d,#5e5effff e,#ff9494ff f,#acacffff g,#ffd3d3ff ``` ```image e gc cg ca ec c ce ac gc cg aa gc c ce ec c cg aa gc cg ca ec c ce ac gc cg aa gc c ce ec c cg aa gc cg ca ec c ce ac gc cg aa gc c ce ec c dbdf cg fbbdffdbbbbbbdf fbbb gcfdbbbbbbdf bbbf cg fddbbbbbdff dbbf ca fdbbbbbbdf dbbd ec fdbbbbbbdf fbbd c fdbbbb fbbb ce bbbf ac dbbf gc dbbd cg fbbd aa fbbd cc bbf gcce gccg gccg eccg ecc ecc aca aca aca cce cce gcce gccg gccg eccg ecc cc ``` <!-- end of image -->

Hmm, I'm not sure what to expect from this image. Let's see if any lines cross. These regions highlight areas that look suspicious. Lines seem to converge within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#fa0f0dff b,#0d0efbff c,#757eebff d,#f07069ff e,#b0d7b0ff f,#99c698ff g,#eff2efff ``` ```image g ad ga ag ga affffffffffffffffffffg daeeeeeeeeeeeeeeeeeeeg faeeeeeeeeeeeeeeeeeeeg fdaeeeeeeeeeeeeeeeeeeg feaeeeeeeeeeeeeeeeeeeg feadeeeeeeeeeeeeeeeeeg feeaeeeeeeeeeeeeeeeeeg feeadeeeeeeeeeeeeeeeeg feeeaeeeeeeeeeeeeeeeeg feeeafeeeeeeeeeeeeeeeg feeefaeeeeeeeeeeeeeeeg feeeeaeeeeeeeeeeeeeeeg c feeeedaeeeeeeeeeeeeeeg cbfeeeeeaeeeeeeeeeeeeeeg gbceeeedaeeeeeeeeeeeeeg fbbeeeeaeeeeeeeeeeeeeg febbeeeadeeeeeeeeeeeeg feecbeeeaeeeeeeeeeeeeg feeefbceadeeeeeeeeeeeg feeeeebbeaeeeeeeeeeeeg feeeeeebbafeeeeeeeeeeg feeeeeeecbaeeeeeeeeeeg feeeeeeeefbceeeeeeeeeg feeeeeeeeedbbeeeeeeeeg feeeeeeeeeeabbeeeeeeeg feeeeeeeeeedacbeeeeeeg feeeeeeeeeeeaefbceeeeg feeeeeeeeeeeadeebbeeeg feeeeeeeeeeeeaeeebbeeg feeeeeeeeeeeeadeeecbfg feeeeeeeeeeeeeaeeeeebc a feeeeeeeeeeeeeafeeeeebb ad feeeeeeeeeeeeefaeeeeegbb ad feeeeeeeeeeeeeeaeeeeeg cbg ad feeeeeeeeeeeeeedaeeeeg gbc ad feeeeeeeeeeeeeeeaeeeeg bb ad feeeeeeeeeeeeeeedaeeeg bb ad feeeeeeeeeeeeeeeeaeeeg cbg ggggggggggggggggggg ad feeeeeeeeeeeeeeeeadeeg gbc gfeeeeeeeeeeeeeeeeefg ad feeeeeeeeeeeeeeeeeaeeg bb geeeeeeeeeeeeeeeeeeegad feeeeeeeeeeeeeeeeeadeg bb geeeeeeeeeeeeeeeeeeead feeeeeeeeeeeeeeeeeeaeg cbb geeeeeeeeeeeeeeeeeead feeeeeeeeeeeeeeeeeeafg cbbg geeeeeeeeeeeeeeeeeadg feeeeeeeeeeeeeeeeeefag gbbc geeeeeeeeeeeeeeeeadeg feeeeeeeeeeeeeeeeeeeag gbbc geeeeeeeeeeeeeeeaaeeg efffffffffffffffffffda cbbg geeeeeeeeeeeeeeaaeeeg a cbbceeeeeeeeeeeeeaaeeeeg dd gbbceeeeeeeeeeaaeeeeeg a gebbbeeeeeeeaaeeeeeeg ad geeecbbfeeeaaeeeeeeeg a geeeeefbbcaaeeeeeeeeg ae geeeeeeeebbbeeeeeeeeg ga geeeeeeeaaecbbeeeeeeg ag geeeeeeaaeeeecbbceeeg ga geeeeeaaeeeeeeeebbceg a geeeeaaeeeeeeeeeeebbb da geeeaaeeeeeeeeeeeeeecbbg a geeaaeeeeeeeeeeeeeeeg gbbc dd geaaeeeeeeeeeeeeeeeeg bbc a gaaeeeeeeeeeeeeeeeeeg cbbg ad daeeeeeeeeeeeeeeeeeeg cb a daeeeeeeeeeeeeeeeeeeeg ae dageeeeeeeeeeeeeeeeeeeg ga da geeeeeeeeeeeeeeeeeeeg ag da gfeeeeeeeeeeeeeeeeefg ga da ggggggggggggggggggg a da da da a da dd da a da ad da a da ada ga ``` <!-- end of image --> My goal is to determine if there's an intersection inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0404ff b,#4d48f9ff c,#a6a5fdff d,#f93f44ff e,#fd8485ff f,#0706fdff g,#fec8c8ff ``` ```image ae aa dae eaa aae ead aag ead gaag dad gaag dae gaa dae eaa aae ead aag ead gaag dad gaag dae gaa dae eaa aae ead fc aag ffc ead bffb gaag cffb dad cfffc gaag fffc dae bffb gaa cffb dae cfffc eaa fffc aae bffb ead cffb aag cfffcead fffcaag bffbad cfffag cfffe fffc bffb edffb adfffc eadbffc aagbffb ead cffb gaag cfffc dad bffc gaa bffb dae cffb gaa cfffc dae bffc eaa bffb aae cffb ead cfff aag bf ead b gaag dad gaa dae gaa dae eaa aag ead aag ead gaag dad gaa dae gaa dae eaa aag ead aag ead gaag dae gaa da ga ``` <!-- end of image --> Amazing! This area was hiding an intersection all along! Okay, on to the next area of interest. Let's see what secrets area B holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0808ff b,#4640f8ff c,#8684fdff d,#fc3437ff e,#fecfd0ff f,#0605feff g,#c4c4ffff ``` ```image e ea eaa eaad eaad eaad eaad eaad eaad eaad eaad fc eaad fffcg eaad cbfffbg eaad gbfffbc eaad gcffffc eaad cffffbg eaad gbfffbg eaad gbffffceaad cffffbd cffffbg eaadbfffbc eaade gcffffc edade cffffbg edade gbfffbg edade gbffffc edade cffffcg daae cbfff daae gbf daae g daae daae daae daae daae daae daae daae aae ae e ``` <!-- end of image --> My analysis confirms the presence of an intersection in area B. After a thorough search, I conclude that there are two intersections.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fe0808ff b,#3636feff c,#8c8cfeff d,#ff4848ff e,#fe8a8aff f,#0302feff g,#ebd7ebff ``` ```image g ae a ag ga a ea a ed a de a ae a ag ga a c ea cf a gfc ed fb a bf de cfg a gfc ae fb a bfag cfa gfc efb abf edcfg a gfc de fb a bf ae cfg ga gfc a ag fb ae ga bf ae a cfg ae ea gfc ae a fb ae dd bf ae a cfg ae de gfc ae a fb ae ae bf ad ga cfb ad ag cffg ad ga gffc ad a bfb ad ea cffg ad a cffc ad dd gffc ad a bfb ad de cffg ad a gffcad ae ffb ga aa cffg ag aa cffc ga aa gffc a da bfb ea da cffg a da gffc dd da bfb a da cffg de da cf a da ae da ga da ag da ga da a da ea ea a ea dd ea a ea de ea a ea ada ga ``` <!-- end of image -->

This image might have some surprises. Let's look for intersections carefully. Let's take a closer look at what's happening inside these zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd0606ff b,#0405fdff c,#f08f88ff d,#8c96eaff e,#ee4642ff f,#383df4ff g,#aed5adff ``` ```image cae a ea ca ca a ae a aa ac ca a ae ec aa a ca ee ac a aa ca ca a ac ca aa a ea a ac ac aa a ea ec ac a ae ggggggggggggggggg ce eaggggggggggggggggg a cacggggggggggggggg ca gaegggggggggggggg a ggeaggggggggggggg a gggcacggggggggggg a gggggaeggggggdfbg a ggggggaagdfbbbdgg ac gggggdfbbbdgggggg a gdfbbbdggaegggggg ec dfbbbdgggggggaaggggg a dfbbfd gggggggggggcagggg ce dbbbfd gggggggggggggaegg a dbbbfd ggggggggggggggaag ca dbbbfd gggggggggggggggeg a dbbbf ggggggggggggggggg a dbbbf ggggggggggggggggg a fbf a bf ac bf a bd ec bd a b ce db gggggggggggggggag db ggggggggggggggcag fb ggggggggggggggagg fb ggggggggggggggagg bf gggggggggggggaggg bf gggggggggggggaggg bd ggggggggggggacggg bd ggggggggggggagggg b gggggggggggeeggggdb gggggggggggaggggfb ggggggggggeegggfb ggggggggggagggbbg gggggggggcaggbfgg gggggggggaggbfggg gggggggggagbdgggg ggggggggagbdggggg ggggggggabggggggg gggggggebgggggggg ggggggfbggggggggg gggggfbeggggggggg ggggbbagggggggggg gggbfeegggggggggg ggbfgaggggggggggg gbdgcaggggggggggg bdggagggggggggggg bggggagggggggggggg gggacgggggggggggg gggaggggggggggggg ggacggggggggggggg ggagggggggggggggg geegggggggggggggg gaggggggggggggggg eeggggggggggggggg agggggggggggggggg ca a ``` <!-- end of image --> I'm focusing my attention on this specific region, area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0405ff b,#0707feff c,#ff8686ff d,#acacffff e,#f03b49ff f,#4f4bfaff g,#fdccceff ``` ```image a ca aa caa eac gaa eac gaag eae gaag cae aag cae aac caa eac gaa eac gaag eae gaag cae f aag fb cae bbb aac dbbb caa dbbf eac dbbf gaa dbbf eac fbbf gaag fbbd eae fbbd gaagfbbd caebbbd aabbb cebbf ebbf fbbf fbbf fbbe fbbec fbbeag bbbeae dbbbgaag dbbf cae dbbf aag dbbf cae fbbf aac fbbd caa fbbd eac fbbd gaa bbd eac b gaag eae gaag cae aag cae aac caa eac gaa eac gaag eae gaag cae ``` <!-- end of image --> Gotcha! I've found the intersection hiding in area A! Moving on to the next area. I'm going to scrutinize area B for any signs of an intersection. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd0608ff b,#0505feff c,#ff9595ff d,#8e8effff e,#f3444fff f,#4c48fbff g,#e7d2eaff ``` ```image e aeg aaac geaae caaeg caaac geaac caaeg caaac geaac g eaaeg gdfbb caaac gdfbbbbbb geaac gdfbbbbbbfdg eaefbbbbbbfdg gdfbbbbbbfdg gdfbbbbbbfeaac ddfbbbbbbfdg eaae dfbbbbbbfdg caaag bbbbfdg gaaac fdg eaae caaag gaaac eaae caaag gaaa ea c ``` <!-- end of image --> My investigation has led me to an intersection in area B! My analysis indicates that there are two intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fe0606ff b,#0505feff c,#ff8b8bff d,#9a9afeff e,#fb4347ff f,#3e3effff g,#f0d0deff ``` ```image g cae a ea ga cag ag ae ga aa ac cag a ae ec aa a cag ee gac a aa ca cag a gac ga aa ag ea ga gac ac aa a ea ec gac a ae ee ea a gac ca ae a ea ga cag ag ae gfb a ea gfbbbd ac dfbbbd a dfbbbd ae ec dfbbfd aa a dfbbfd cag ce dbbbfd ae a dbbbfd aa ca dbbbfg c a dbbbfg ga dbbbfg ag fbfg a bb ac bf a bd ec bd a gbg ce db a db ca fb a fb ga bf ag bf a bd ac bd a gbg ec db a db ce fb a fb ca bf a bf ga bd agbd abg eb db fbc bba bfce bf a bd ca bd a bg ga ag a ac a ec a ce a ca a ``` <!-- end of image -->

This image seems promising for intersection detection. I'd describe these as 'hotspots' for potential intersections. <!-- image --> ```palette Key,Color ,#fefefeff a,#0606feff b,#fe0605ff c,#b0b0ffff d,#f9aba8ff e,#5154f8ff f,#f45554ff g,#acd4acff ``` ```image ca aca ca ea a ac a a ac ca a ea ee ac a a ee ca a ee ca ac a a ca ca a ee a ac ac a a ca ee ae a ac ee a a ca ca ae a ac ca a ac ea a ae ac a ggggggggggggaggg a gggggggggggeeggg ea gggggggggggagggg ae ggggggggggeegggg a bf ggggggggggaggggg a fbbf gggggggggeaggggg ea fbbfd gggggggggagggggg ac dbbbfggggggggagggggg a dbbbfggggaggggggg ca gggfbbfgaggggggg ea ggggggfaffgggggg ac gggggggagfbbbdgg a ggggggeeggggdbbbd ca ggggggagggggggggfbbf ea gggggeeggggggggg fbbf ac gggggagggggggggg fbbf a ggggeagggggggggg fbd ca ggggaggggggggggg bb ee ggggaggggggggggg dbf ac gggagggggggggggg fbd a gggagggggggggggg bb ca ac dbf ee a fbd ac ee bb a a dbf ca ee fbd ae a bb ac ca dbf a a fbd ca ca bb ae ac dbf a a fbd ac bb a dbf ee bbd a bb ee dbf a bbd ca bb a dbf ca bb ac bb a f ac a ee a ee a ca a ``` <!-- end of image --> I wonder what we'll find inside area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#0303feff b,#fe0606ff c,#bbbbfeff d,#ffa6a6ff e,#3635fdff f,#f44b56ff g,#6f6fffff ``` ```image eag caa eag caa gag caac gae aac gae aac cae eag caa eag fd caa bbbfd gag fbbbbbfd aac dfbbbbbfd gae dfbbbbbfd aac dfbbbbfae dfbaafbfd caafbbbbfdd eag dfbbbbbfd caa dfbbbbbfd eag dfbbbb caa dfb gag aac gae aac gae aac caa eag caa eag caa gag aac gae ``` <!-- 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,#0505feff b,#fd0608ff c,#c4c4ffff d,#ffaeaeff e,#4242ffff f,#ff5858ff g,#8787ffff ``` ```image c ga aca ca ea ac ag a a ac ca a ee eg ag a a ee ca a ee ga ac a a ca ca ac ee a ac ac a a ga eg ae a ac ge a a ga ga ae a ac ca a ac ga a ag ac ac a ca eg ga a ag ge a bf a ca fbbf ga ea fbbbd a ag dbbbd ca a dbbbd ac ca fbbf a ea fabf ag a dbbbd a eg dbbbd ca a dfbbf ee ge fbbf ag a fbbf a ga fbd ca a bb ee ca dbf ac ac fbd a a bb ca ag dbf ee a fbd ac eg bb a a dbf ga ge fbd ee a bb ac ga dbf a a fbd ga ca bb ae ac dbf a a fbd ag bb a dbf eg bbd a bb ge dbf a bbd ga bb a fbf ca bb ac bb a f ag a eg a ge a ca a ``` <!-- end of image -->

Based on a first glance, I suspect there could be intersection regions here. 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,#f74f4bff b,#0808feff c,#f59f9bff d,#b0b0ffff e,#add5adff f,#fd0506ff g,#595df7ff ``` ```image cffc f ffc cf afa f afa cf aff eeeeeeeeeeeeeefee cff eeeeeeeeeeeeeefee cffc eeeeeeeeeeeeefcee ffc eeeeeeeeeeeeefeee ffc eeeeeeeeeeeefceee afa eeeeeeeeeeeefeeee afa eeeeeeeeeeefaeeee aff eeeeeeeeeeefeeeee cff eeeeeeeeeeaaeeeee cffc eeeeeeeeeefeeeeee ffc eeeeeeeeeaaeeeeee ffc eeeeeeeeefeeeeegbb afa eeeeeeeeaaeegbbbebg afa eeeeeeeefbbbgeeee b aff eeeeegbbbgeeeeeee b cff eegbbbefeeeeeeeee gb cf gbbgeeecfeeeeeeeee bd dbbbdeeeeeefeeeeeeeeee b gbbbd eeeeecfeeeeeeeeee gb gbbg eeeeefeeeeeeeeeee bd dbbbd eeeeefeeeeeeeeeee b gbbbd eeeefceeeeeeeeeee db bg eeeefeeeeeeeeeeee bg eeefceeeeeeeeeeee b eeefeeeeeeeeeeeee b eefaeeeeeeeeeeeee gb eefeeeeeeeeeeeeee bd eaaeeeeeeeeeeeeee b efeeeeeeeeeeeeeee gb aa bd f b ca db f bg cf b f db cf gb f bd cf b f gb f bd fc b f db fc bg f b ac db f gg aa bd f b aa gb f bd ca b f db cf bg f b cf db f gg f bd fc b f gb fc bd f b fc db f bg ac b f db aa gg f bd aa b f gb cf bd f b db bg b ``` <!-- end of image --> Let's put area A under the microscope. <!-- image --> ```palette Key,Color ,#fefefeff a,#fc3d40ff b,#0504feff c,#ffc3c3ff d,#a2a2ffff e,#fe7d7dff f,#fe0404ff g,#5045f4ff ``` ```image cff afe cffc afa cffc efa ffc efa ffc efa ffc efa ffe eff afe cff afe cff afe cff afe cffc afa cffc efa d ffc ddgbb efa dgbbbbbg ffc dgbbbbbgd efggbbbbbgd dgbbbbbgd dgbbbbbgd dgbbbbbgae dgbbbbbgddeff dgbbbbbgd afe bbbbgd cff gdd afe cff afe cff afe cffc afa cffc efa ffc efa ffc efa ffc eff ffe cff afe cff afe cff afe cffc ``` <!-- end of image --> My investigation has led me to an intersection in area A! I have found one intersection!

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff3b3bff b,#0707feff c,#ffbcbcff d,#ababffff e,#ff7979ff f,#fe0404ff g,#5555feff ``` ```image c effc f ffe cf afe f afa cf efa fc eff cf cffc fc cffc f ffe fc afe f afa ae efa f eff ae cffc f cffc aa ffe f dbb afe ea gbbg bg afa fgbbg b efa dbbbd b eff gbbgdf gb cf gbbg cf bd dbbbd f b gbbbd cf db gbbg fc bd dbbbd f b dbbbd fc db bg f bg fc b f b ae gb f bd ae b f gb ea bd f b ea db f bg ef b f b cf gg f bd cf b fc gb f bd fc b f db fc bg f b ae db f gg ae bd f b ea gb f bd ea b f db cf bg f b cf db f gg cf bd fc b f gb fc bd f b fe db f bg ae b f db ae gg f bd ea b f gb ea bd f b db bg b ``` <!-- end of image -->

This image looks interesting. I wonder if there are any intersections hidden in there? These spots mark what I'd call 'danger zones' - areas where intersections are more likely. <!-- image --> ```palette Key,Color ,#fefefeff a,#fb4442ff b,#5456f0ff c,#fd0606ff d,#acadffff e,#aed5aeff f,#ed9b93ff g,#0708fdff ``` ```image d bgg bgb ggb dggd dgg bgg ggb dggd dggd bgg bgb ggd dggd bgg bgb ggb eeeeeeeeeeeeeeeeeeeeeee dggd eeeeeeeeeeeeeeeeeeeeeebggd eeeeeeeeeeeeeeeeeeeebgg eeeeeeeeeeeeeeeeeeegbee eeeeeeeeeeeeeeeeeegeeee eeeeeeeeeeeeeeeeebgeeee eeeeeeeeeeeeeeeeegeeeee eeeeeeeeeeeeeeeegbeeeee eeeeeeeeeeeeeeeegeeeeee eeeeeeeeeeeeeeegeeeeeee eeeeeeeeeeeeeebgeeeeeee eeeeeeeeeeeeeegeeacceee eeeeeeeeeeeeegbccfefcee eeeeeeeeeefccgfeeeeeace eeeeeeefcccfgeeeeeeeeac eeeefcccfeebgeeeeeeeeeca efcccfeeeeegeeeeeeeeeeecf fcccfeeeeeeegbeeeeeeeeeee cf fcccfeeeeeeeeeegeeeeeeeeeeee c fcca eeeeeeeeegeeeeeeeeeeeee c fcca eeeeeeeebgeeeeeeeeeeeee fc fcca eeeeeeeegeeeeeeeeeeeeee fc fcca eeeeeeegbeeeeeeeeeeeeee ac a eeeeeeegeeeeeeeeeeeeeee aa eeeeeegeeeeeeeeeeeeeeee ca eeeeebgeeeeeeeeeeeeeeee cf eeeeegeeeeeeeeeeeeeeeee c gd c dg c g fc bb ac g ac gd ca dg cf g cf bb c g c gd fc dg fc g ac bb ca g cf gd cf dg c g c bb fc g fc gd ac dg aa g ca gb cf g c gd c dg c g fc gb ac g ac gd ca dg cf g cf gb c g g ``` <!-- end of image --> Eureka! Let's inspect this close up of area A <!-- image --> ```palette Key,Color ,#fefefeff a,#fc6062ff b,#4a42f7ff c,#fe0708ff d,#8a8afeff e,#cbc9fdff f,#ffb4b4ff g,#0505feff ``` ```image d edgg ebgggg ebgggbe egggbe bgbe egge ggd dgg egge bgb egge ggd dgg egge bgb dgge ggd dgg egge faa bgb aacccca dggeacccccaacca ggbccccaf fcca fabggccaf fccf facccggaf accf facccccbgb accf facccccafdgge acc facccccaf ggd cc facccccaf dgb c facccccaf egge f facccccaf bgb facccccaf dgg ccccaf ggd caf bgb egge bgb dgg ggd bgb egge bgb dgg ggd bgb egge bgb dgg eggd bgb ``` <!-- end of image --> Success! This area contains an intersection point! There's one and only one intersection present in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff4848ff b,#4e4afbff c,#fe0707ff d,#9595ffff e,#e7d6eeff f,#ffa3a3ff g,#0606feff ``` ```image d dgg bgb eggd eggd dgge bgb ggb eggd dgge bgg bgb eggd dggd dgge bgb ggb eggd dgge bgg egb ge dg g gd eg ge dg g eacc gbccf fc eccgf fc fcccfge ac fcccf bg ca fcccf g ca fcccf gd cf fccce eg ce fccae ge c fccae bb ec fccae g fc fccae gd ac a eg aa g ca bb cf g ce gd c dg ec g fc bb ac g ac gd ca dg cf g cf bb ce g ec gd fc dg fc g ac bb ca g ca gd cf dg ce g ec bb fc eg fc ge ac dg ca g ca bb cf eg ce ge c dg ec g fc gb ac eg ac ge ca dg cf g cf gd c eg ge ``` <!-- end of image -->

I'm examining this image closely. My goal: find any and all intersections. These zones are intriguing. I bet there's something interesting happening within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd0908ff b,#0c0cfeff c,#ffaeaeff d,#6570e7ff e,#b0d6b0ff f,#ef5d5aff g,#99c398ff ``` ```image c ac a ac ca a ca a ff a ff a ac a ac ca a ca a ff a ff a ac b a bbb ac b db ca b b a b bd ca b bb a b bb ff b db eggaggggggggggggeb eb geeafeeeeeeeeeegb bd geeeaeeeeeeeeegb bd geeeafeeeeeeegbg bb geeeeaeeeeeedbee db geeeeageeeedbeee db geeeegaeeedbeeee be geeeeeaeedbeeeee bd geeeeefadbeeeeee bb geeeeeefbeeeeeee bb geeeeedbfeeeeeee db geeeedbeaeeeeeee b geeedbeeafeeeeee bd geeeeeeeeeeeeeeg geedbeeeeaeeeeee bb eeeeeeeeeeeeeeeg gedbeeeeeafeeeee bbeeeeeeeeeeeeeeega gdbeeeeeeeaeeeee dbeeeeeeeeeeeeefa dbeeeeeeeeageeee dbgeeeeeeeeeeaag dbeeeeeeeeegaeeee eebdeeeeeeeeafeg dbgeeeeeeeeeeaeeee eeebdeeeeegageeg db geeeeeeeeeefaeeg eeeebbeeefaeeeeg db a eeeeebbeaaeeeeeg db ff eeeeeedbfeeeeeeg bb a eeeeefagbdeeeeeg bb ff eeeeaaeeebdeeeeg bb a eeeaaeeeeebbeeeg bb ac egafeeeeeeebbeeg bb a faeeeeeeeeeedbeg bb a aaeeeeeeeeeeeegbg ca afeeeeeeeeeeeeeeebd a cac eeeeeeeeeeeeeeegb ca fa eeeeeeeeeeeeeeeg a aa ggggggggggggggge ff af a ca af aa a af ac cac a fa a aa ca af a cac ca fa a aa ff af a ca ac aa a af acac a ``` <!-- end of image --> This is a magnified view of the region A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0707ff b,#0101ffff c,#ff8a8aff d,#6861f8ff e,#a6a5feff f,#f94a4fff g,#ffc5c5ff ``` ```image gaag faf gaa fac gaa e aac eb caa ebb aac ebbd caf ebbd aag ebbd faf ebbd gaag ebbd faf ebbd gaa ebbd fac ebbd gaa ebbd aac ebbd caa ebbd aadbbd cfbbd ebbd ebbdf ebbdaag ebbd faf dbbd gaa dbbd fac dbbe gaa dbbe aac dbbe caa dbbe aag dbbe caf dbbe aag dbbe faf dbbe gaag dbbe faf bbe gaa be fac e gaa aac caa ``` <!-- end of image --> As I suspected, there's an intersection within area A. Now, let's turn our attention to the next spot. Let's take a closer look at area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd0809ff b,#0504feff c,#ffacacff d,#3c37f9ff e,#c4c3fdff f,#fd5253ff g,#7f7ffeff ``` ```image e be bbg c gbbg fa gbbd faa ebbde caaac ebbbe caaa dbbg faaf dbbg faac gbbd caaac ebbd caaf ebbbe faaf edbbe caaac dbbg caaac gbbdaaf gbbdf caabbde caaaedbbe faaf dbbg faac gbbg caaac gbbd caaf ebbde faaf ebbbe caaac dbbg caaac dbbg faaf gbbd faaf ebbd aaac ebbb aa edb f d ``` <!-- end of image --> Eureka! There's definitely an intersection in area B! My analysis indicates that there are two intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0606ff b,#0707ffff c,#fe8788ff d,#5b5bffff e,#bfbefdff f,#fb4043ff g,#ffc7c7ff ``` ```image g ac a ag ga a ca a cf a fc a ac a ag ga a ca a cf a fc a ac d a bdb ag be db ga be ebe a be bd ca eb bd a eb bb cf eb db a eb ebe fc eb be a eb bd ac eb bb a eb db ag eb eb ga eb ebe a eb bd caeb bb fb db ebf db db a ebe db fc bd db a bd db ag bb ga db a db ca db ag ebe aa db ga be af db a bd gag db ca bb fa db a db aa db cf ebc db a caebe db fc fa bd bb a af bb bb ag gac db bb a ca db bb ag aa ebe e ga af bd a gag b cf fa a aa ff ac a cag fc fa a af ag gac a ca ag aa ga af a gag cf fa a aa ff ac a cag fc fa a af acac ga ``` <!-- end of image -->

This image might have some surprises. Let's look for intersections carefully. Could these regions be concealing intersection points? Let's find out. <!-- image --> ```palette Key,Color ,#fefefeff a,#f65753ff b,#0909feff c,#6369f3ff d,#fd0909ff e,#ffb1b1ff f,#aed4acff g,#b9b9ffff ``` ```image e ad dd da ede ad dd da de ed ad dd da ede ed ad dd da ede ad dd b da cbg de bb ed gbc ad cb dd bb da gbg ede cb ed bb ad gbg dd bb da bc ede cbg ad bb dd bc da cb de bb de gbc da cb ad bb fffffffffffffffad gbg fffffffffffffffd cb ffffffffffffffdf bb fffffffffffffdff gbg ffffffffffffdaff bb cg fffffffffffddfff bc cbbbbbc ffffffffffadffff cbg gcbbbbcg ffffffffffdfffff bb cbbbbbcffffffffdffffff bc gcbbbbccfdfffffff cb fffffcbbbbbcffff bb ffffffddffccbbbbcg gbc fffffadfffffffffcbbb fffffdffffffffff ffffdfffffffffff fffdffffffffffff ffdaffffffffffff fddfffffffffffff adffffffffffffff edfffffffffffffff dffffffffffffffff deffffffffffffffff da ad ed ed d de da ad ed ed d de da ad ed ed d de ``` <!-- end of image --> I'm analyzing this close-up of area A with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#fc2c2fff b,#0604fdff c,#544ef8ff d,#ff0303ff e,#ffc4c4ff f,#fa7479ff g,#a19efbff ``` ```image e ed ad ada fdde fdde eddf eddf ada ada fdde fdde eddf eddf ada cgg ada bbbbbccg fdde gcbbbbbbbbccgg fdde ggccbbbbbbbbbcg ggcbbbbbbbbccgg aafccbbbbbbbbccg ada ggcbbbbbbb fdde ggccb fdde eddf eddf ada ada fdde fdde eddf eddf ada ada fdde fdde eddf ddf da a ``` <!-- end of image --> Success! This area contains an intersection point! My investigation reveals that there is exactly one intersection in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff3434ff b,#0a0affff c,#6b6bffff d,#ff0303ff e,#ffc3c3ff f,#ff7c7cff g,#b9b9ffff ``` ```image f ad da df ede fd ad da df ede ad dd da ede fd ad da df ede fd ad b da cbg df bb ede gbc ad cb dd bb da gbg ede cb fd bb ad gbg da bb df bc ede cbg fd bb ad bc da cb df bb de gbc df cb aa bb fd gbg ed bb d bb de gbg df bb cg aa bc cbbbbbc fd cbg gcbbbbcg ed bb cbbbbbc d bc gcbbbbcg de cb cbbbbbc bb aa gcbbbbcg gbc fd cbbb ed d de df aa fd ed d de df aa fd ed d de df aa fd ed d de df aa fd ed d de ``` <!-- end of image -->

I'm approaching this image with caution. Intersections might be tricky to spot. These spots are like clues. Let's see what they reveal about potential intersections. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0606ff b,#5156f4ff c,#f9a3a1ff d,#aaacfaff e,#0707feff f,#f6504eff g,#acd3acff ``` ```image caa aa ca cac ac aa a fac fa caf a aa a cac ff aa a fac ca caf ac aa a cac ca aa ac fac a af ff e aa a e caf a ed aa af eb fac a eb af ca be aa ac de af a de fa e ac ed a ed ff eb a be ggaggggggggggggbe ggafggggggggggde gggaggggggggggeg gggfaggggggggegg ggggacggggggedgg gggggagggggebggg gggggfagggebgggg ggggggaggbeggggg gggggggabegggggg gggggggfeggggggg gggggggeaggggggg ggggggegcagggggg gggggebggafggggg ggggebggggaggggg gggeegggggfagggg ggbegggggggacggg gbegggggggggaggg geggggggggggffgg eggggggggggggagg eggggggggggggggag ed af eb a be ca be ac de a e fa e ac ed a eb ff eb a be ca de ac de a e ca ed ac ed a eb ff eeb a beed a deeb ff eee a beed deeb deee beed deeb deeb beed deeb deeb eed ``` <!-- end of image --> Let's see what secrets area A holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0606ff b,#322df9ff c,#fea3a3ff d,#c1c1ffff e,#0403feff f,#f8474dff g,#7373ffff ``` ```image caac g faa ge aac dee caa deeg faf deeb aac beb caa beb faf geed aac geed caa deed aaf deeg caac deeg faf beb aac beb caa beed faf geed aacgeed cafeeg feeg deebc bebaa beb aaf geed caac geed faf geed aac deeg caa deeg faf eeb aac beb caa bee faf geed caac geed faa deeg aac deeg caa deeg faf beb aac eb caa ed faf ``` <!-- end of image --> My investigation has led me to an intersection in area A! My investigation reveals that there is exactly one intersection in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fe0505ff b,#4e4effff c,#ff9292ff d,#9e9effff e,#0606ffff f,#fd4547ff g,#eed6e6ff ``` ```image g caa aa ca cac ac gaa a fag ff gaf ag aa ga cac ff aa a fag ca gaf ac aag a cac ca aa ag fac a g gaf ff ge aag ag eg cac ga ed aa af eb fac a eb gaf ca be fag ac de af a ge ca e ag eg ga ed ff eb a be ga be ac de a ge ca eg ac ed a ed ff eb ag be gade fe ea egca ed ac eb a bb ca be ag de a ge ff e ag eg ga ed ac eb a be ca de ac de a ge ca eg ag ed ga eb ff eb a be ga de ac ge a e ca eg ac ed a eb ff geeb ag beed ga deeb ff geeeg a beed deeb geebg beed deeb geeb beed deeb geeb eed ``` <!-- end of image -->

The hunt for intersections begins! Let's analyze this image closely. I wonder what's going on inside those areas? Perhaps intersections are hiding there. <!-- image --> ```palette Key,Color ,#fefefeff a,#e4433dff b,#0909fbff c,#5b68e3ff d,#d38f7aff e,#eff5efff f,#fc0706ff g,#b1d7b1ff ``` ```image e bc b bc b cc b cc b cb b cb d be ef gb fe be df aeeeeeegbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee f dfggggggbgggggggggggggggggggggggggggggggggggggggggggggggggggggggggge fd efgggggggbggggggggggggggggggggggggggggggggggggggggggggggggggggggggge df edfggggggbcgggggggggggggggggggggggggggggggggggggggggggggggggggggggge f egfdggggggbgggggggggggggggggggggggggggggggggggggggggggggggggggggggge fd eggfggggggbcggggggggggggggggggggggggggggggggggggggggggggggggggggggge df eggfdggggggbggggggggggggggggggggggggggggggggggggggggggggggggggggggge f egggfggggggbcgggggggggggggggggggggggggggggggggggggggggggggggggggggge aa egggaaggggggbgggggggggggggggggggggggggggggggggggggggggggggggggggggge ef eggggfggggggbcggggggggggggggggggggggggggggggggggggggggggggggggggggge fe eggggdfggggggbggggggggggggggggggggggggggggggggggggggggggggggggggggge aa egggggfggggggccgggggggggggggggggggggggggggggggggggggggggggggggggggge ef egggggdfggggggbgggggggggggggggggggggggggggggggggggggggggggggggggggge fe eggggggfdgggggcbgggggggggggggggggggggggggggggggggggggggggggggggggggedf egggggggfggggggbgggggggggggggggggggggggggggggggggggggggggggggggggggef egggggggfdgggggcbggggggggggggggggggggggggggggggggggggggggggggggggggfd eggggggggfggggggbgggggggggggggggggggggggggggggggggggggggggggggggggdf eggggggggaagggggcbggggggggggggggggggggggggggggggggggggggggggggggggfe egggggggggfggggggbgggggggggggggggggggggggggggggggggggggggggggggggfde egggggggggdfgggggcbgggggggggggggggggggggggggggggggggggggggggggggdfge eggggggggggfggggggbgggggggggggggggggggggggggggggggggggggggggggggfgge gb eggggggggggdfggggggbgggggggggggggggggggggggggggggggggggggggggggfagge cb egggggggggggfdgggggbggggggggggggggggggggggggggggggggggggggggggdfggge bb eggggggggggggfggggggbgggggggggggggggggggggggggggggggggggggggggfgggge ebc eggggggggggggfagggggbggggggggggggggggggggggggggggggggggggggggaagggge cbe egggggggggggggfggggggbgggggggggggggggggggggggggggggggggggggggfggggge bb egggggggggggggaagggggbcgggggggggggggggggggggggggggggggggggggfdggggge bc eggggggggggggggfggggggbggggggggggggggggggggggggggggggggggggafgggggge gbe eggggggggggggggdfgggggbcgggggggggggggggggggggggggggggggggggfgggggggecb egggggggggggggggfggggggbggggggggggggggggggggggggggggggggggfdgggggggbb eggggggggggggggggfgggggbcggggggggggggggggggggggggggggggggdfgggggggbc eggggggggggggggggfdgggggbggggggggggggggggggggggggggggggggfggggggcbge egggggggggggggggggfgggggccggggggggggggggggggggggggggggggfdgggggbbgge egggggggggggggggggaagggggbgggggggggggggggggggggggggggggdfgggggbcggge eggggggggggggggggggfgggggccggggggggggggggggggggggggggggfggggcbggggge eggggggggggggggggggafgggggbgggggggggggggggggggggggggggfagggcbgggggge egggggggggggggggggggfgggggcbgggggggggggggggggggggggggdfgggbbggggggge egggggggggggggggggggdfgggggbgggggggggggggggggggggggggfgggbcgggggggge eggggggggggggggggggggfdggggcbgggggggggggggggggggggggaagcbgggggggggge egggggggggggggggggggggfgggggbgggggggggggggggggggggggfgbbggggggggggge egggggggggggggggggggggfdggggcbgggggggggggggggggggggfdbcgggggggggggge eggggggggggggggggggggggfgggggbggggggggggggggggggggaabgggggggggggggge eggggggggggggggggggggggaagggggbgggggggggggggggggggbbggggggggggggggge egggggggggggggggggggggggfgggggbggggggggggggggggggbbgggggggggggggggge egggggggggggggggggggggggdfgggggbggggggggggggggggbaggggggggggggggggge eggggggggggggggggggggggggfgggggbggggggggggggggcbfgggggggggggggggggge eggggggggggggggggggggggggdfgggggbggggggggggggbbfdgggggggggggggggggge egggggggggggggggggggggggggfdggggbcggggggggggbcdfggggggggggggggggggge eggggggggggggggggggggggggggfgggggbggggggggcbggfgggggggggggggggggggge eggggggggggggggggggggggggggfdggggbcggggggbbggfagggggggggggggggggggge egggggggggggggggggggggggggggfgggggbgggggbbggdfggggggggggggggggggggge egggggggggggggggggggggggggggaaggggbcgggbcgggfgggggggggggggggggggggge eggggggggggggggggggggggggggggfgggggbgcbggggaagggggggggggggggggggggge eggggggggggggggggggggggggggggdfggggbbbgggggfggggggggggggggggggggggge egggggggggggggggggggggggggggggfgggggcgggggfdggggggggggggggggggggggge egggggggggggggggggggggggggggggdfgggggggggafgggggggggggggggggggggggge eggggggggggggggggggggggggggggggfdggggggggfggggggggggggggggggggggggge egggggggggggggggggggggggggggggggfgggggggfdggggggggggggggggggggggggge egggggggggggggggggggggggggggggggfagggggdfgggggggggggggggggggggggggge eggggggggggggggggggggggggggggggggfgggggfggggggggggggggggggggggggggge eggggggggggggggggggggggggggggggggaagggfdggggggggggggggggggggggggggge egggggggggggggggggggggggggggggggggfggdfgggggggggggggggggggggggggggge egggggggggggggggggggggggggggggggggdfgfggggggggggggggggggggggggggggge eggggggggggggggggggggggggggggggggggffaggggggggggggggggggggggggggggge eggggggggggggggggggggggggggggggggggdfgggggggggggggggggggggggggggggge eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee ``` <!-- end of image --> Let's see what secrets area A holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd3d3eff b,#0807feff c,#5755fcff d,#fe8283ff e,#ffc4c4ff f,#fe0505ff g,#a7a6feff ``` ```image ffe bc dfa bbg ff cbc ad cbc efe bbg fa cbc ffe bbg afa cbb dfa gb ffd bg dff gb af bg efe bb efe gbb fa cbc ffe gbb dff cbc ffd gbb dff cb eff cc af bg efe bc da bbg fd cbc ffd cbb eff bbg afd gbb d effe bb ef afa gb af dfa gb ffd ff bg fa df bb efe ad cbc fd efe gbb df fa cbc eff afa cbc dff ffe gbb effe dfa cbc afa ffd bb ff dff cb efd efe cc dfe aa bg ff efe bb afa fa bbg effe ffe gbb ffd ffd gbb ffe dff bbg fd afd gbb df eff bb efe af gb af c efe bc dff bb fd bc afa cbc ff bb dffe cbc ffd cbc ffd gbbb eff gbb afa gbbb afd cbc ffe bbc afa cbc da gbbg effe bb efe cbbc dfa cb af cbbc ff bg dff gbbg df cb effe gbb ad bg afa cbb fa bbg ffd gbbbg ffe gbb fa bbc afa bbg dfe cbc ffe gbb fd gbbg dfa bbg af gbbb dff bbc ffdbbg af gbb dfabbg efe cb efcbb aa gb abbbc efe cc bbbg ffe bc cbc dff bbg bbb ffd cbc gbbbf dff bbg cbbbfa afd cbc bbcffe eff bbg gbbgffd efe bb cbbceffe da gb bbbg ffd fd bg gbbg fa ff gb cbc efe ffd bg cbb ad afd bbg bbb eff effe gbb cbc afa afa bbc bbg dff effe gbb gbbb effd dfa cbc cbbc afa df cbbbg fd ad gbb aa ef g efe fa ff ffe dfa afa effe dfa dff ffd ffe dff fa af df efe efd efe dff fa ffd ffe afa dff effe ffd ffd afdffe efffd aff ``` <!-- end of image --> Area A contains an intersection. It was tricky, but I finally found one single intersection in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fa3338ff b,#0a09feff c,#6868ffff d,#ff7a7aff e,#febdbdff f,#fe0303ff g,#c0c0ffff ``` ```image g bc b bc b cc b cc b cb b gb d b f gb fe b da a gb f da bg fe f gb df ef bg f fe b fd f bg ef fd b f f bc ad aa b ef f bc f da b aa f cc f ef b fe fe cc da f b f ad cb fe f b df aa cb f f b fd df gb ef f b f gb ef gb ad cb fe bg ef bb f gb f gbc ad bg aa cb f b f bb da bg fe bc f b da gbg ef bc f cb fe b fe bb ef bc df gbc fe b f cb f cc fd bb ad b ef bc f cc f gbg da b ad cb f cb ef bb ef b f gbc fe cb aa cb f b f bb fd gb febc f b dabg aa gb bb f bg bb da gb gba f bg cbf ef b bbfd fe bg bcef f b gbg f ad bc cb ad f b bb ef aa bc gbc f f b cb aa df cbb f f c fe ef da fe f f fe ad df f f da fd f ef ef f fad ef ``` <!-- end of image -->

I'm ready to tackle this image and find those intersections! I wonder what's going on inside those areas? Perhaps intersections are hiding there. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0706ff b,#0a0bfdff c,#f7a39fff d,#bcbcfeff e,#f6534fff f,#aed5aeff g,#6669f7ff ``` ```image ffffffffffffffff ffffffffffffffff ffffffffffffffff fffffffffffgffff fffffffffbbbffff ffffffgbbgffffff ffffbbbfffffffff fgbbgfffffffffff dbbbffffffffffffff gbbdffffffffffffffff dbbg fffffffffffcffff gbbd fffffffffffaffff dbbg ffffffffffaeffff bbb fffffffffcafffff gbbg fffffffffaffffff bbb ffffffffeeffffff gbbd ffffffffafffffff dbbg fffffffacfffffff gbbd ffffffcaffffffff dbbg ffffffafffffffff gbbd fffffeefffffffff dbg fffffaffffffffff bb ffffacffffffffff dbg fffeafffffffffff bb fffaffffffffffff dbg ffaeffffffffffff bb ffafffffffffffff dbg faffffffffffffff gb eaffffffffffffff bg afffffffffffffff gbd aefffffffffffffff bb affffffffffffffff gbd a ffffffffffffffff bb ea ffffffffffffffff gbd a ffffffffffffffff bb ac ffffffffffffffff gbd ca bb a gbd ee bb a gbd ac bb ca dbg a bb ee dbg a b ac ca a ee a ac ca a ae a a ea a ac ca a ee a ac ca a ee a ac ca a ee a ac ca a ae cc a eaaaaaaecc a ceaaaaaaecc ca ceaaaaaaecc a ceaaaaaaecc ac ceaaaa ``` <!-- end of image --> I'm determined to find out if an intersection exists in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff0505ff b,#0707ffff c,#ff8181ff d,#adadffff e,#ff4040ff f,#ffc3c3ff g,#5958ffff ``` ```image dd gbbg dgbbbbg dgbbbbgd dgbbbbd dgbbbbgd dbbbbbd dgbbbbgd gbbbbgd dgbbbbgd bbbbgd bbg d f fae eac caa aac eae faaf eac caa faaf eae faaf aac caa faaf eae faaf aac cae faaf eae caa aac cae faaf eae caa aac eae faaf eac caa aac eae faaf aac caa faaf eae faaf aac aa af e f ``` <!-- 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,#ff0606ff b,#0707ffff c,#ff8e8eff d,#a9a9ffff e,#ff4c4cff f,#ffcbcbff g,#5151ffff ``` ```image d gbb dbbd bbb dbbd bbg gbbd dbbg f gbbd a dbbg ac gbb fa dbbd a bbg ee gbbd a dbbg af gbbd ca dbbg a gbbd ee dbg a bb af dbg ca bb a dbg ee gb fa bg af gb ca bg a gb ac bg fa gbd af bb ea gbd a bb ac gbd fa bb a dbd ee bb a dbd ac bb fa dbd a bb ee dbd a g af ca a ee a af ca a ac fa af ca a ac fa a ee a ac fa a ee a af ca a ee a af ca a ee cf fa eaaaaaaecf af fceaaaaaaecf ca fceaaaaaaecf a fceaaaaaaecf ac fceaaaa ``` <!-- end of image -->

Let's examine this image for potential line intersections. These spots are like clues. Let's see what they reveal about potential intersections. <!-- image --> ```palette Key,Color ,#fefefeff a,#0809faff b,#fc0605ff c,#d18f79ff d,#5e6bd9ff e,#b2d7b1ff f,#a3cca3ff g,#ea4138ff ``` ```image fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff feeeeeeeeeeeeeeeeeeeeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeebgggeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeebgeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeebbeeecbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeegbeeeeebfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef ad feeeeeeeeeeeeeeeegbeeeeeecbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef daad feeeeeeeeeeeeeeegbeeeeeeeebceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef daad feeeeeeeeeeeeeegbeeeeeeeeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef daaa feeeeeeeeeeeeegbeeeeeeeeeeebgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef eaaadeeeeeeeeeeegbeeeeeeeeeeeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef daaadeeeeeeegbeeeeeeeeeeeeeeggeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef feefaaadeeecbeeeeeeeeeeeeeeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef feeeeefdaadbeeeeeeeeeeeeeeeeecbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef feeeeeeeecdaadfeeeeeeeeeeeeeeebfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef feeeeeeecbeeedaaafeeeeeeeeeeeecbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef feeeeeecbeeeeeeedaaafeeeeeeeeeebceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef feeeeecbeeeeeeeeeeedaaadeeeeeeefbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef feeeefbeeeeeeeeeeeeeeefadeeeeeeebceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef feeefbeeeeeeeeeeeeeeeeeeafeeeeeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef feefbfeeeeeeeeeeeeeeeeeefaeeeeeeeggeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef fefbfeeeeeeeeeeeeeeeeeeeefaeeeeeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef febfeeeeeeeeeeeeeeeeeeeeeedaeeeeeecbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef fbceeeeeeeeeeeeeeeeeeeeeeeedaeeeeeebfeeeeeeeeeeeeeeeeeeeeeeeeeeeeef bceeeeeeeeeeeeeeeeeeeeeeeeeedaeeeeecbeeeeeeeeeeeeeeeeeeeeeeeeeeeeef bceeeeeeeeeeeeeeeeeeeeeeeeeeeeaaeeeeebceeeeeeeeeeeeeeeeeeeeeeeeeeeef bcfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeadeeeefbeeeeeeeeeeeeeeeeeeeeeeeeeeeef bc feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeadeeeebceeeeeeeeeeeeeeeeeeeeeeeeeeef bc feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeadeeeebeeeeeeeeeeeeeeeeeeeeeeeeeeef bc feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeafeeeggeeeeeeeeeeeeeeeeeeeeeeeeeef bc feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefafeeebeeeeeeeeeeeeeeeeeeeeeeeeeef bg feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefaeeeggeeeeeeeeeeeeeeeeeeeeeeeeef bg feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedaeeebeeeeeeeeeeeeeeeeeeeeeeeeef bg feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedaeecbeeeeeeeeeeeeeeeeeeeeeeeef bg feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedaeebfeeeeeeeeeeeeeeeeeeeeeeef bg feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaaefbeeeeeeeeeeeeeeeeeeeeeeef bg feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeadebceeeeeeeeeeeeeeeeeeeeeef gb feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeadebeeeeeeeeeeeeeeeeeeeeeef e feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeadggeeeeeeeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeafbeeeeeeeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaggeeeeeeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefabeeeeeeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedabeeeeeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedafeeeeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedaeeeeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaaeeeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaaeeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebadeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebadeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeggafeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebeafeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecbfaeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebffaeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecbedaeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebcedaeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefbeeaaeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebceeaaeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebeeeadeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeggeeeadeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebeeeeafeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecbeeeeafeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebeeeefaeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecbeeeefaeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebceeeedaef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefbeeeeedaf feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebceeeeeaa feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebeeeeeea feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeggeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeggeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecbeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebfeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefbeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebcef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeggf feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebf feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegg ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffb ``` <!-- end of image --> I wonder what we'll find inside area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#0706fdff b,#fe0505ff c,#fc7f81ff d,#534cf8ff e,#b0b0ffff f,#fec8c8ff g,#fb363aff ``` ```image fbf fbbg bbbbf fbg bb fbb cb bg cb ggf bc bb gb gbf fbf gbf cg gbf bg gbf bb bbf gc cbf fbf aaad bb bbf eaaaad cbc gbg edaaad cbc fbb eaaaad cbc bc edaaadgc cb gdaaade bb fbc daaade gb fbc ddaaae fbf fbg daaade fbf fbg daaaae bg bbg eaaae cb fbg eaae bc bb da bc fbg da bbf gg ad gbg bb ead cb gbf ead bf gbb eae bc bbf dae bb gbf aae gb b da gg f ad fbf aa bbf ead cbg aa cb dae gc dae fbf daa bb aa gb ead cg aa bc eae gb aae fb daa gc da bg aa bbf ead bb ead cb aa bc eae bc aaebb dafbf dacg aabg eadbc eadb eaaf dac aa aa cad caa gad gbaae fbdaa fbfdae bg aa bbcaa gb ead fb aa fbf eae bg aae cb dae bc da cb aa bb ead gb ead gg eaa fbf eae bg dae cbg da bb da gc aa fbf ead bb aae cb eaa fbf dae bc a bb d fbb gb fbf fbf bg cb gc bc bb gb cg bc bbc cbb fbf gg fb b ``` <!-- end of image --> Case closed! This is definitely an intersection point in area A. There are precisely two intersections present in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0807fdff b,#fe0505ff c,#fe7475ff d,#5b56f9ff e,#b6b6ffff f,#fec1c1ff g,#fe3535ff ``` ```image f bb bgcg bg b gg fb gb bf ad gb fb daad gb bf daad gb b eaaae cb gc eaaae cb b eaaae cb cg edaad cb b daadb cb fdaad b fb daade fb fb eaaae bf fb eaaae b fb eae gc fb ae b b a gg bf ea b bf ea cg bf da b bf da fb bf aa bf bf ad b bf ad bc bc ae b bc ae gc bc a b bc ea cg bg ea b bg da fb bg da bf bg aa fb gg ad bf gg ad b f aegc aeb acg eab eab eaf da aa ad gad bae cgae b a cb a b ea fb ea bf da b da bc ad b ad gg ae b ae cg a b a fb ea bf ea b da bc da b a gc b cg b fb bf fb bf b gc b cg b ``` <!-- end of image -->

Hmm, I'm not sure what to expect from this image. Let's see if any lines cross. After a thorough analysis, I conclude that there are no intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0505ffff b,#ff0606ff c,#8484ffff d,#ff5353ff e,#ffafafff f,#ccccffff g,#3e3effff ``` ```image e eedbbbbbbbd eeddbbbbbbbdee eddbbbbbbbdde eedbbbbbbbddee ebbbbbdee db db bb bd bd be ebe eb db db bb bd be be eb fa eb aga db ca ga bb a gg bd gc ag bd fa ag be af ac ebe ca ac eb a af db ac af db fa af bb af fa bd cg fa bd a fa be ac ca eb fa ca eb af ga d cg ga a gg ac ag fa ag a ac gg ac a af ac af fa af a fa gg fa a fa ac ca fa ca a ga gg ga a gg af ag fa ag a ac gg ac a af af af ca a a fa gg fa a fa af ca ca ca a ga gc g a af ca a gc fa af ca a ac fa af ``` <!-- 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,#fa3f3dff b,#0808fdff c,#a5a5ffff d,#fbaaa8ff e,#acd4acff f,#fe0303ff g,#595aefff ``` ```image af dfdf f fd fd f aa aa df f f df fd fd aa f df aa f f fd df aa fd df f f aa fd f aa df df fd f f fd aa aa f df df f fd fd f aa aa df f f f fd fd aa f df df f fd fd f aa aa df f b f df cb fd fd bb aa f bg df eeaaeeeeeeeeeeee cbc f eeefeeeeeeeeeeeegb fd eeedfeeeeeeeeeebb aa eeeefdeeeeeeeebg df eeeeefeeeeeegbee f eeeeeaaeeeebbeee fd eeeeeefeeebbeeee aa eeeeeedfebgeeeee df eeeeeeegbeeeeeee f eeeeeebbfeeeeeee fd eeeeebgeaaeeeeee eeegbeeeefeeeeee eebbeeeeeefeeeee ebbeeeeeeefaeeee bgeeeeeeeeefeeee gbeeeeeeeeeeeafeee bb eeeeeeeeeeeefeee bg df cbc fd gb f bb df bc fd cb f bb aa bg f cbc df gb fd bb f bg aa cb f gbb df cbbbc fd cbbbc f cbbbc aa gbbg f gbbg cbbbc cbbbc cbbbc gbbg gbbg bbc ``` <!-- end of image --> Time to investigate area A up close. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff5d5dff b,#0707feff c,#b1b1ffff d,#ffb6b6ff e,#8f1483ff f,#ff0808ff g,#5050ffff ``` ```image afa dffd aff ffa dff c afa gb dffd gbb aff cbbbc ffa cbbbc dffd gbbg afa gbbc ffd cbbbc aff gbbg ffa gbbg dffdcbbbc afebbbc ebbg gbbe cbbbefa cbbg dffd gbbg afa cbbbc ffd cbbbc dff gbbg ffa gbbg dffd cbbbc aff cbbg ffd gbbg dff bbbc afa bbc dffd g aff ffa dff ``` <!-- end of image --> There's no doubt about it - this is an intersection in area A. There's one and only one intersection present in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff3636ff b,#0707feff c,#a6a6ffff d,#ffb5b5ff e,#ff7272ff f,#ff0202ff g,#534efaff ``` ```image d af dfef f fd fd f aa ae df f f df fd fd aa f df aa f f fd df aa fd df f f aa fd f aa df df fd f f fd ea aa f df df f fe fd f aa ea df f f df fd ae aa f df ef f fd fd f aa ae df f b f df cb fd fd bb aa f bg df ae cbc f f gb fd df bb aa fd bg df f cb f aa gb fd f bg aa dfcbc df gb f bbf fd bg ea cbc f gb df bg fe bc f gb ea bb f bg df cbc ae gb f bb ef bc fd cb f bb ae bg f cbc ef gb fd bb f bg ae cb f gbb df cbbbc fd cbbbc f cbbbc aa gbbg f gbbg cbbbc cbbbc cbbbc gbbg gbbg bbc ``` <!-- end of image -->

Hmm, I'm not sure what to expect from this image. Let's see if any lines cross. I'm going to focus my attention on these specific areas. <!-- image --> ```palette Key,Color ,#fefefeff a,#f25351ff b,#0405feff c,#949af3ff d,#f3aba6ff e,#fd0707ff f,#444af3ff g,#afd6afff ``` ```image d ae ae ee ee ea ea ea ed ed ed de de de ae ae ae ee ee ea ea ea ed ed ed de de de ae gggggggggggggggggggggggae f ggggggggggggggggggggggaeg cbbc bc gggggggggggggggggggggeegg bbf fbf ggggggggggggggggggggeeggg fbbc cbbc gggggggggggggggggggeagggg cbbf bbf ggggggggggggggggggeaggggg fbb cbbc gggggggggggggggggeagggggg cbbc bbf ggggggggggggggggeaggggggg cbbf fbb gggggggggggggggedgggggggg fbbc cbbc ggggggggggggggegggggggggg cbbc fbf gggggggggggggeggggggggggg bbf cbbc gggggggggggdeggggggggggggfbbc bbfgggggggggdeggggggggggcbbf fbbggggggdegggggggggfbbgg ggcbbfgggegggggggfbbfgggg gggggfbbegggggcbbfggggggg gggggggabbcgfbbcggggggggg ggggggedggbbfgggggggggggg gggggedgggggggggggggggggg ggggeaggggggggggggggggggg gggeagggggggggggggggggggg ggeaggggggggggggggggggggg geagggggggggggggggggggggg eeggggggggggggggggggggggg aegggggggggggggggggggggggg aeggggggggggggggggggggggggg ae ggggggggggggggggggggggggg de ggggggggggggggggggggggggg de ggggggggggggggggggggggggg de e e e ed ed ed ea ea ea ee ae ae ae de de de e e e ed ed ``` <!-- end of image --> I'm now examining the contents of area A in detail. <!-- image --> ```palette Key,Color ,#fefefeff a,#fc3033ff b,#0807feff c,#b1b1ffff d,#ff6c6cff e,#fe0404ff f,#5d59faff g,#ffbfbfff ``` ```image de dee aeeg aeeg aeeg aeeg gaeag geea geea geea geea geed deed deed deed deeg aeeg aeeg aeeg aeeg gaeag geea geea geea geea cb bfc geed cfbbb bbbbc geed cfbbbbfc cfbbbbfc geed cfbbbbfc cbbbbfc geea cfbbbbfc cfbbbbf geea fbbbbbc fbbbbfc aea cfbbbbfc cfbbbbfea cfbbbbfc fbbbbfc cbbbbbf aabbbbbc cfbbbbfc aeegcfbbbbbbbbfc deeg cbbbbfc deeg cc deeg deeg deed geed geed geed geed geea geea aea aea aea eeg eg g ``` <!-- end of image --> Oh my, look at that! It's an intersection in area A! The image features one single intersection point.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fb3c3fff b,#0605feff c,#a6a6ffff d,#ff8989ff e,#fe0404ff f,#5252ffff g,#ffc9c9ff ``` ```image d ae ae ae ea ea ea ed ed eg geg geg ge de de ae ae ae ea ea ea ed ed eg geg geg ge de de ae f ae cbbc bc ae bbf fbb ea fbbc cbbc ea cbbf bbf ea fbb fbbc ed fbbc cbbf ed cbbf fbb eg fbbc cbbc geg cbbf fbf geg bbf cbbc ge fbbc bbf ge cbbf fbbc ge fbb cbbf ge cbbc fbbe cbbf abbc fbbc eg bbf eg ed ed ea ea aa ae ae de de ge ge ge e eg eg ed ed ed ea ea aa ae ae de de ge ge ge e eg eg ed ``` <!-- end of image -->

Hmm, I'm not sure what to expect from this image. Let's see if any lines cross. These spots mark what I'd call 'danger zones' - areas where intersections are more likely. <!-- image --> ```palette Key,Color ,#fefefeff a,#0606fdff b,#fd0706ff c,#9a9df7ff d,#f14946ff e,#fca6a5ff f,#4a4ef3ff g,#aed5aeff ``` ```image ggggggggggggggggggggggg ggggggggggggggggggggggg ggggggggggggggggggggggg ggggggggggggggggggggggg ggggggggggbbbgggggggggg gggggggggdbgdbdgggggggg ggggggggdbggggbbggggggg gccfffffaaaaggggbbggggg ccccffffaaaaaaaaaaaaaaaaaaafffffdcggagggggdbdggg ffffcccc ggggggbgggggaggggggbbgg gggggbggggggafgggggggbb ggggbegggggggaggggggggdbe gggbdggggggggffgggggggg bb ggbdggggggggggagggggggg ebd gdbgggggggggggcaggggggg dbe dbgggggggggggggacgggggg bb ebgggggggggggggggagggggg ebd bggggggggggggggggafggggg dbe b a bb be ca ebe be a bb bd ca ebd bd ac dbe db a bb eb ff ebd eb a dbe b ca bb b a ebd be a dbe be ac bb bd a eb bd ff db a eb ca eb ac b a b ff be a be ca bd a dd ca db ac eb a eb ff b a ca a a ac a ff a ca ac a ff a ca a a ac a ff a ca ac a ac a ff a ca ac a ff a ca a a ac a ff 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,#ff0505ff c,#abaafdff d,#f63a43ff e,#ffd0d0ff f,#5959feff g,#ff8989ff ``` ```image ee ebbd ebbbbbg dbdedbbde dbbe gbbbg dbbe edbbbg gbbe edbbde gbbg gbbbg ccccccccfffffffaaaaaaaa edbbbe aaaaaaaaaaaaaaaaaaaaaaaaf ebbbde aaafffffffffccdddccc caa gbbbg ebbd faf edbbde dbd aac gbbbde dbbe faa gbbb dbbe aac edb gbbe caa g gbbg faf gbbg caac ebbg faf ebbd aac ebbd caa dbd aaf dbbe caa dbbe faf gbbe caac gbbg faa bbg aac ``` <!-- end of image --> The evidence is clear: this is an intersection in area A. I have found one intersection!

<!-- image --> ```palette Key,Color ,#fefefeff a,#0505feff b,#fd0a0bff c,#8484feff d,#ff6262ff e,#ffb8b8ff f,#4141feff g,#cbcbfeff ``` ```image e bbb db ebd db bbe gggccccffaaaf bb gccccfffaaaaaaaaaaaaaaaaaafffcccbgggag dbd fffccccggg b ga bb be ac ebb be a dbe bd ff bb bd a ebd db ga dbe db ag bb eb a ebd eb fc bbe b a bb be cf dbd be a bb bd ga ebb bb ac dbe db a bb db ff ebd eb a dbe eb ca bb b ag ebd be ga bbe be ac bb bd a db bb ff db a db ga eb ag b a b fc be a be ca bd ag bb ga db ac db a eb ff b a ca ag ga ac a cf a ga ag a fc a ca ag ga ac a ff a ca ag ga ac a cf a ga ag a ff a ca ag ga ac a ff a ``` <!-- end of image -->

I'm optimistic that I'll find 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,#0808feff b,#fd0a09ff c,#575cf5ff d,#ef665fff e,#ffbabaff f,#aeaffcff g,#aed5aeff ``` ```image d ggggggggggggggggggggdb gggggggggggggggggggdba ggggggggggggggggggdbca ggggggggggggggggggbgag gggggggggggggggggbgccg ggggggggggggggggbggagg gggggggggggggggbggacgg ggggggggggggggbgggaggg gggggggggggggbgggagggg ggggggggggggbdggcagggg gggggggggggbdgggaggggg ggggggggggbdgggcaggggg gggggggggbdggggagggggg ggggggggbdggggacgggggg gggggggbbgggggaggggggg ggggggbbgggggafggggggg bd gggggbbggggggagggggggg bb ggggbbggggggaggggggggg bb gggdbggggggcaggggggggg db ggdbgggggggagggggggggg ebe gdbgggggggccgggggggggg bd dbggggggggaggggggggggg bb ebggggggggacggggggggggg db eb fa ebe eb af bd b fa bb b a bb be cc db be a ebe be ac bd be a bb bd af db bd fa eb bd a be bd ca bd bb a bb bb cc db db a ebe db af bd db fa bb db a db eb fa eb eb a ebe eb cc bdeb a bb af a af fa a ca a ac a af fa a c fa cac a caf cc aa a faa af cac a aaf af aa fa fac a caf cc aaf a aa ac fac a caf af aa fa faa a fac ca caf a aa cc faa a cacaf aa ``` <!-- end of image --> Let's see what secrets area A holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#0707feff b,#fe0505ff c,#5454ffff d,#ff4444ff e,#ffc5c5ff f,#aaaafeff g,#fb8588ff ``` ```image g gb gbb gbbg ebbga ebbdfa ebbd aa ebbd cac ebbd aaf ebbd cac ebbd faa bbd aac dbb faa dbbe aaf dbbe caa dbbe aaf dbbe cac dbbe faaf dbbe cac gbbe faa gbbg aaf gbbg faa gbbg aaf gbbg cac ebbg faaf ebbd cac ebbd faa ebbd aac ebbd faa ebbd aaf ebbd caa bbd aaf dbb cac dbbe faaf dbbe cac dbbe faa dbbe aaf dbbe faa dbbe aaf gbbe cac gbbg faaf gbbg cac gbbg faa gbbg aac ebbg faa ``` <!-- end of image --> I'll move on to the next area. The intersection must be somewhere. There's definitely not a single intersection on the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0404ffff b,#ff0909ff c,#7c7cfeff d,#ff6262ff e,#ffb8b8ff f,#c3c3ffff g,#3b3cffff ``` ```image d db eba ebca eb a eb gg b a b ac be fa be af be fa be a bd cg bd a bd gc bd a bb af bd bb fa bb db a bb db ca db db a ebe db gg bd eb a bb eb ac db eb fa ebe eb af bd b ca bb b a bb be cg db be a ebe be gc bd be a bb bd af db bd fa eb bd a be bd cg bd bb a bb bb gc db db a ebe db af bd db fa bb db af db eb ca eb eb a ebe eb gg bdeb a bb ac a af fa a cg a gc a af fa a c ca cac a gaf gg aa a fag ac cac fa gaf af aa fa fag a cac cg aaf a faa gc cag a gac af aaf fa faa a cag ca gaf a aa gg fag a cacac ga ``` <!-- end of image -->

Hmm, I'm not sure what to expect from this image. Let's see if any lines cross. The image has some tight areas where segments are too close. I should investigate those closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#5860eeff b,#f90e0fff c,#ec6e65ff d,#0808fdff e,#d3beeaff f,#b1d7b1ff g,#99c39aff ``` ```image e da de ed aa de d ad de d ad de d ed da d ed da d ed da de ed ad de d ad de d ad de d fadgggggggggggggggggggggggggggggggggggg gfdafffffffffffffffffffffffffffffffffff gffdfffffffffffcbffffffffffffffffffffff gffgdfffffffffbbcbfffffffffffffffffffff gfffdafffffffbcffcbffffffffffffffffffff gffffdfffffcbgffffcbfffffffffffffffffff gffffgdfffbbfffffffcbffffffffffffffffff gfffffdafbbfffffffffcbfffffffffffffffff gffffffdbcfffffffffffbbffffffffffffffff gfffffcbdfffffffffffffbbfffffffffffffff gffffbbfadfffffffffffffbbffffffffffffff gfffbbfffdgfffffffffffffbbfffffffffffff ea gfgbcfffffdffffffffffffffbbffffffffffff adddda gcbfffffffadffffffffffffffbbfffffffffff eadddae bbfffffffffdaffffffffffffffbcffffffffff eadddae bbfffffffffffdfffffffffffffffbcfffffffffeadddda ebegfffffffffffadfffffffffffffffbcffffaddddae cb gffffffffffffdafffffffffffffffbddddagff bb gfffffffffffffdffffffffffgaddddbcffffff bc gfffffffffffffadffffgaddddafffffbcfffff ebe gffffffffffffffdaddddagffffffffffbgffff cb gfffffffffffffffagffffffffffffffffbgfff bb gffffffffffffffffffffffffffffffffffbgff bc gfffffffffffffffffffffffffffffffffffbff cbe gfffffffffffffffffffffffffffffffffffgbg bb gffffffffffffffffffffffffffffffffffffgb bb gfffffffffffffffffffffffffffffffffffffgb bc eb cb eb bb cb bb cb cb cb cb cb bb bb bb bb bc bc bc bc bc bc be be b ``` <!-- end of image --> Time to investigate area A up close. <!-- image --> ```palette Key,Color ,#fefefeff a,#5855fbff b,#fe0405ff c,#fe8181ff d,#0807fdff e,#acacfeff f,#fb383bff g,#fec5c5ff ``` ```image edde ada dda edde cc add fbbc dda gfbbbbc edde gbbbgcbbc add cbbf cbbc dda fbbc cbbc edde gfbbc cbbc add gbbfg cbbc dda cbbf cbbg edde fbbc cbbg add gbbbg fbbg ada cbbfg fbbg ddecbbf fbbg eddbbc fbbg gdddg fbbg cbbdde fbbg fbbfedde fbbg gfbbc ada fbf gbbbg dda fbf cbbf edde gbbf fbbc add gbbf gfbbc dda gbbf gbbbg edde gbbf cbbf add gbbf fbbc dda gbbf fbbg edde gbbf bfg add gbbc f dda gbbc edde gbbc eaa edd cbbc eeaddddd ada cbbc eeaddddddddae dde cfaddddddddaee edd eaadddddddaae ada eeadddddddaafbc dde eeaddddddddaee cbbg edde eeaadddddddaee cbbg add eaadddddddaae fbbg ddaadddddddaae fbbg edddddaaee fbbg eaee fbbg fbbg fbbg fbbg fbf fbf gbbf gbbf gbb gb ``` <!-- 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,#5454feff b,#fe0607ff c,#fe8181ff d,#0606feff e,#acacffff f,#f8393fff g,#ffc5c5ff ``` ```image e aa d d aa de d ad de d ad de d ed de d ed da d ed aa d d aa de d ad de d ad de d ed da d fb ed bbcb da bc cb d gbg cb ed fb cb aa bf fb dbc fb cbd fb fb aa fb bf de bf a gbc d bf edddda cb ad bf eadddae bb de bf eadddae bf d bc adddde gbg ed bc edddda cb de fddddae bb d eadddafc bf ed eadddde bg gbg dadddda bg fb ae bg bb bg bc b cbg gb fb gb bf gb gbc gb cbg gb fb cb bf cb cb cb fb fb fb fb bf bf bf bf bc bc bc bc bg bg b ``` <!-- end of image -->

Let's examine this image for potential line intersections. I have a hunch that these areas might contain the intersections we're looking for. <!-- image --> ```palette Key,Color ,#fefefeff a,#3d40f8ff b,#f95351ff c,#9293fcff d,#feb1b0ff e,#fe0706ff f,#add4acff g,#0404feff ``` ```image d eee be deb eb bed bed ee ee deb ded bed ee ee ded deb ee bed deb ee ee deb deb bed be ee eb deb bed bed ffffffffffffffff ee ee ffffffffffffffff bed dee ffffffffffffffff ee bed ffffffffffffffff ded eeffffffffffffffff ee deeffffffffffffff deb fbebffffffffffff ee fffeefffffffffff deb fffffeefffffffff be ffffffbebfffffff eb ffffffffeeffffff ffffffffffeeffff fffffffffffgffff fffffffffagaffff fffffffagaffffff fffffagaffffffff fffcggffffffffff ffggffffffffffff ggffffffffffffff ggc ggc agc aga cga cga cgg gg gg ggc agc agc cga cga cgg gg gg gc cg gg ga gc cg ag ga gc cg ag ga gc cg ag ga gc cg ag ga gc cg ag ga gc cg ag gg gc ``` <!-- end of image --> This close-up of area A is like examining a piece of evidence. <!-- image --> ```palette Key,Color ,#fefefeff a,#6261fdff b,#fe4546ff c,#b9b8feff d,#ff7a7aff e,#fe0808ff f,#ffbabaff g,#0909feff ``` ```image b eed beeef feeeb deeed fbeeef feeebf deeed fbeeef feeebf deeed beeef feeebf deeed beeef feeb cga cgggg caggga caggga aggga agggac agggac cggggc cggggc cggggc caggga caggga aggga ``` <!-- end of image --> There is no intersection present within area A. My final answer is: no intersections found.

<!-- image --> ```palette Key,Color ,#fefefeff a,#3736feff b,#ff4747ff c,#8d8dffff d,#ff9999ff e,#ff0606ff f,#ebdaedff g,#0202ffff ``` ```image f feee bef deb feb bed bef ee ee deb ded bed ee ee ded deb ee bed ded ee be deb feb bed bef eef feb feb bef bed ee eef ded feb ee bed ded eef ee fee ded ded ee eef feb fee bef ded eb eef fee a agc cga cga cga fgg fggf ggf agc agc agc cga cga fgg fggf ggf ggc agc agc cga cga cgg fggf ggf fgc cg ag ga fgc cgf ag ga fgc cgf ag ga fgc cgf ag ga fgc cgf ag ga fgc cgf ag ga gc cgf ag ga gc ``` <!-- end of image -->

This is the image I'm working with. The goal is to count the intersections. I need to zoom in on these areas to get a better look. <!-- image --> ```palette Key,Color ,#fefefeff a,#0808feff b,#f74947ff c,#a7a9faff d,#5055f6ff e,#f39e9bff f,#fe0404ff g,#aed5aeff ``` ```image c a ac a a ca a da a dd a ac a ac ca a ca a dd a ac a ac ca a ca a dd a ad a ac ca ffffbe a ebfffffbe ca ebfffffbe a ebfffffbe dd eebfffffbe a eebfff dd efe a ff ggggggggggggadg bf ggggggggggggagg efe gggggggggggaggg fb ggggggggggcaggg bfggggggggggagggg efegggggggdagggg gfbggggggaggggg ggbfggggddggggg gggefeggagggggg gggggfbadgggggg ggggggbaggggggg ggggggaefeggggg a gggggcaggfbgggg cac gggggaggggffggg aa ggggdagggggbfgg da ggggaggggggggfb cac gggddgggggggggff aa gggagggggggggggef da ggadggggggggggg fb cac ggagggggggggggg ff aa gacgggggggggggg bf da ca fe cac a ff aa ca bf da a fe cac dd ff aa a bf da ad efe cac a fb aa ac bf da ca efe cac a f aa ca da a cac dd aa a da dd cac a aaac da ``` <!-- end of image --> My goal is to determine if there's an intersection inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0605fdff b,#fd4f50ff c,#c1c1ffff d,#433ef9ff e,#fcacaeff f,#fe0606ff g,#827efaff ``` ```image aac gad caac dad caac dag caa e aag fb gaa ffb aag efffe gad bffb caac bffb dad efffe caac bffb dad bffb caa efffe dag bffe gaa bffb aag effdad ebaag daafb caaefffe dad efffe caac bffb dag efffe gaa efffe aag bffb gaa efffe aac efffe gad bffb caac eff dad ef caac dag caa aag gaa aac gad caac ``` <!-- end of image --> I am surprised, so clear, an intersection has appeared in area A. There's one and only one intersection present in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0808ffff b,#fd494aff c,#c8c8ffff d,#4c4cffff e,#fda7a8ff f,#ff0404ff g,#9090ffff ``` ```image g a ag ca ac ga a gd a dd a ag ca ac ca a ga a dd a ag a ac ca a ga a dd a ag a ac ca ffffbe ac ebfffffbe ga ebfffffbe a eebfffffbe dd eebfffffbe a eebfff dd efe a ff ag bf ca efe ac fb ga bf a efe gd fb a bf dd efe a fbag ba aefe a ca fb cag a ff aa ga efe da a fb cag dd ff aa a ef da ag fb cag a ff aa ac bf da ca fe cag a ff aa ga bf da a efe cag dd ff aa a bf da ag efe cag a fb aa ac bf da ca efe cag ac f aa ga da a cag dd aa a da dd cag a aaag da ``` <!-- end of image -->

This image might have some surprises. Let's look for intersections carefully. I'm going to focus my attention on these specific areas. <!-- image --> ```palette Key,Color ,#fefefeff a,#5a66e5ff b,#f90a0aff c,#0808fcff d,#aeaefeff e,#b1d7b1ff f,#e16e60ff g,#99c598ff ``` ```image d cd c cd dc c dc c aa c aa c cd c c cd ac dc c c cd dc ac c c aa cd c ac aa c c cd cd dc c c cd cd dc dc c c e dc gggggggggggggggggggggggggggggggggggggggggggggggggggcagggggggbb c eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaceeeeeeebbe aa eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeceeeeeegbfee c eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecaeeeeefbeeee aa eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaceeeeebbeeeee c eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeceeeegbfeeeeee cd eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecaeeefbeeeeeeee c eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegceeebbeeeeeeeee cdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeceeebfeeeeeeeeee dceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecaefbgeeeeeeeeeee cgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegcebbeeeeeeeeeeeee dceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecebbeeeeeeeeeeeeee ceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecabfeeeeeeeeeeeeeee aaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegcbeeeeeeeeeeeeeeeee eceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecbeeeeeeeeeeeeeeeeee ecaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegcceeeeeeeeeeeeeeeeeee eeceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefbceeeeeeeeeeeeeeeeeeee eecaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbcgeeeeeeeeeeeeeeeeeeee eeeceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegbfaceeeeeeeeeeeeeeeeeeeee eeecgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefbeeceeeeeeeeeeeeeeeeeeeeee eeegceeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeecgeeeeeeeeeeeeeeeeeeeeee eeeeceeeeeeeeeeeeeeeeeeeeeeeeeeeebfeeaceeeeeeeeeeeeeeeeeeeeeee eeeeaceeeeeeeeeeeeeeeeeeeeeeeeefbgeeeceeeeeeeeeeeeeeeeeeeeeeee eeeeeceeeeeeeeeeeeeeeeeeeeeeeebbeeeecgeeeeeeeeeeeeeeeeeeeeeeee eeeeeaaeeeeeeeeeeeeeeeeeeeeeebbeeeeaceeeeeeeeeeeeeeeeeeeeeeeee eeeeeeceeeeeeeeeeeeeeeeeeeefbfeeeeeceeeeeeeeeeeeeeeeeeeeeeeeee eeeeeecaeeeeeeeeeeeeeeeeeebbeeeeeecgeeeeeeeeeeeeeeeeeeeeeeeeee bbbbbf eeeeeeeceeeeeeeeeeeeeeeeebbeeeeeeaceeeeeeeeeeeeeeeeeeeeeeeeeee efbbbbff eeeeeeecaeeeeeeeeeeeeeegbfeeeeeeeceeeeeeeeeeeeeeeeeeeeeeeeeeee ffbbbbffeeeeeeeeceeeeeeeeeeeeefbeeeeeeeecaeeeeeeeeeeeeeeeeeeeeeeeeeeee fbbbbbffeecgeeeeeeeeeeebbeeeeeeeeaceeeeeeeeeeeeeeeeeeeeeeeeeeeee eeegfbbbbcfgeeeeeeegbfeeeeeeeeeceeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeecfbbbbbfgfbeeeeeeeeeecaeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeaceeeegfbbeeeeeeeeeeaceeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeceeeeeeeeeeeeeeeeeeceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeaaeeeeeeeeeeeeeeeecaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeceeeeeeeeeeeeeeeaceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeecaeeeeeeeeeeeeeeceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeeceeeeeeeeeeeeecaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeecaeeeeeeeeeeeaceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeeeceeeeeeeeeeeceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee gggggggggggggcggggggggggcagggggggggggggggggggggggggggggggggggg dc dc c c dc ca c dc aa c c ca cd dc c c cca c ``` <!-- end of image --> I'm determined to find out if an intersection exists in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#3734fcff b,#fd090aff c,#0303feff d,#c2c2feff e,#ffb6b6ff f,#fc5d60ff g,#7e7bfcff ``` ```image dcc f ccg fb aca ebbb dccd fbbbe ccg bbf dccd ebbe ccg fbbf gca ebbbe dccd ebbbe ccg fbbf gca bbbf ccd bbbe cg fbf ga fbf dcd ebbb ac fbbbe dccd ebbbe acg ebbbe g gcc fbbf c dccd ebbe cg aca ebbe ca gcc fbb ccd dccgbbbf gca acabbbe ccd gccbbf gca dccbbf dccd acabe dcc ccg ac ebca dc ebfcd ag fbbcg ga ebbbac cd ebbbgcc ca fbbfdccg ccd bbbf aca gca bbbe gccd dccd fbf ccg dcc ebbb dccd acg fbbbe ccg dcc fbbf aca acg ebbbe dccd gca ebbbe ccg ccd fbbf gca gca ebbe ccd ccd ebbe cg gca fbb ga dccd bbbf dcd acg ebbbe cc acg fbbf dccd dcc ebbbe acg ac bbbe gca gc fbf dccd cd ebbe acg ga ebbb gcc e cd fbbf dccd bbbffe ca ebbbe acg bbbbbbbbffe ccd ebbbe gcc effbbbbbbbbffacg fbbf dccd effbbbbbbccffee bbbf aca dccffbbbbbbbbffee fbf dcd acg eefbbbbbbbbbb aa gca eeffbbbe gc ccd dcc gca aca ccd gcc gca dccg dccd aca acg gccd dcc dccg acg aca acg ccg gca aca cc dccd gc ccg cd ca ``` <!-- end of image --> Eureka! There's definitely an intersection in area A! Two intersections have been found!

<!-- image --> ```palette Key,Color ,#fefefeff a,#3d3cfdff b,#fd0709ff c,#0605feff d,#b8b8ffff e,#ffaeaeff f,#fd5a5bff g,#7979ffff ``` ```image d cd c cd dc c dc c ga c ag c cd c c cd gc dc c c cd dc gc c c ga cd c gc ag c c cd cd gc c c cd cg dc dc c c e dc cg fb c dc bb ga c ebe c cg fb ag dc bb c c bf cd cg fb c dc bb cd c bf dc ag ebe c dc bb gc c bf c aabe ga dcb c cf ag eca c fbc cd bbc c bfaa cd fb c dc bb cd c bf aa ga ebe c c bb cd ga bf ga c ebe c ag fb cd bbbbfe c bb gc efbbbbfe cd ebe c efbbbbfe c fb cd efbbbbfe cd bb gc ebbbbcfe bf c cfbbbbbfefb cd ga efbb gc c c ga cd c gc ag c c cg cd dc c c c cg dc dc c c ga cg c dc ga c c cg ag dc c c cca c ``` <!-- end of image -->

I'm ready to tackle this image and find those intersections! It's crucial to examine these regions more closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#0405feff b,#ec605eff c,#3940f0ff d,#eff0eeff e,#fc0c0bff f,#afd5afff g,#808be9ff ``` ```image g a ag da ad ga a gc a cc a ag da ad ga ad ga a cc a ag da ad da ad ga dddddddddddddddddda dfffffffffffffffffcc dfffffffffffffffffad dffffffffffffffffacd d dffffffffffffffffafd eee dfffffffffffffffagfd be bef dfffffffffffffffaffd de ee dffffffffffffffafffd e bed dfffffffffffffgafffd ed ee dfffffffffffffaffffd eb beddffffffffffffccffffd be eeffffffffffffafffffd fe beffffffffffccfffffd de dfeeffffffffaffffffd ed dffbeffffffagffffffd eb dffffeeffffafffffffd be dfffffbeffaffffffffd be dfffffffebaffffffffd de dffffffffaeffffffffd ed dfffffffccfeeffffffd fffffffffffffffffff eb dfffffffafffbefffffd dfffffffffffffffffffd ee dffffffccfffffeefffd dfffffffffffffffffffdbe dffffffafffffffbeffd dfffffffffffffffffffde dfffffagfffffffffeed dfffffffffffffffffffed dfffffafffffffffffeed dffffffffffffffffffeb dffffagffffffffffffdeb dfffffffffffffffffeed dfffgafffffffffffffd bed dffffffffffffffffbefd dfffaffffffffffffffd deb dffffffffffffffffeffd dffgaffffffffffffffd eed dfffffffffffffffefffd dffafffffffffffffffd deb dffffffffffffffebfffd dfccfffffffffffffffd eed dfffffffffffffebffffd dfaffffffffffffffffd deb aafffffffffffbefffffd dagffffffffffffffffd eed dgacfffffffffeffffffd dafffffffffffffffffd deb dffcagffffffefffffffd agfffffffffffffffffd e dffffaaffffeffffffffd daffffffffffffffffffd dfffffgacfebffffffffd addddddddddddddddddd dfffffffcabfffffffffd ga dfffffffbeaaffffffffd a dfffffffeffgacffffffd cc dffffffefffffcagffffd a dfffffebfffffffaafffd cg dffffeefffffffffgacfd da dfffbeffffffffffffcag ag dfffefffffffffffffffaad da dffeffffffffffffffffddac ad dfebffffffffffffffffd gag ga deefffffffffffffffffd aad a beffffffffffffffffffd daa gc bfffffffffffffffffffd gag a dfffffffffffffffffffd cad cg dfffffffffffffffffffd daa a dfffffffffffffffffffd gacag dfffffffffffffffffffd ca dfffffffffffffffffffd fffffffffffffffffff ``` <!-- end of image --> Let's see if area A yields any clues. <!-- image --> ```palette Key,Color ,#fefefeff a,#0908feff b,#fb373aff c,#5d5bfcff d,#b3b3ffff e,#fe0404ff f,#ffc3c3ff g,#fb7a7dff ``` ```image f fe be beb geef feef feeg eeb beb geef geef feeg eeb ac beb aaad geef daaaad geef daaac feeg caaad feeg dcaaad beb daaac bee caaac geef dcaaad feeg daaac feeg caaacbeb dcaaab gaaacd feecaaac feeg caaad beb daaacd beb caaac geef caaad feef daaacd feeg daaac eeb caaad beb daaaad geef daaa geef ca feeg d eeb beb geef geef feeg feeg beb bee geef eeg bg ``` <!-- end of image --> Eureka! There's definitely an intersection in area A! Moving on to the next area. Eureka! Let's inspect this close up of area B <!-- image --> ```palette Key,Color ,#fefefeff a,#0504feff b,#fb6467ff c,#4140fdff d,#c6c6ffff e,#fe0a0aff f,#ffbabaff g,#8583fcff ``` ```image d c da ca gaa aag gac aad cac daad cac daad cag gaa aag gaa aad gac daad f cac eb daad eeef cag feeeb gaa beeef aag feeeb gaa beeef aag feeeb gac beeef daad feeeb cac beeef daad feeeb cag beebaa feaac gaaeef aageeeb gac beeef daad feeeb cac beeef daad feeeb cac beeef daad feeeb cag beebf gaa feeeb aag bee gac fe aad cac daad cac daad cag gaa aag gaa aad gac daad cac daad cag gaa aag gaa aag ac ad c d ``` <!-- end of image --> The close-up clearly shows an intersection point in area B. The final answer is: two intersections found.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0505ffff b,#fa4e52ff c,#4141ffff d,#cbcaffff e,#fe0707ff f,#ffbfbfff g,#8585ffff ``` ```image g a ag da ad da a gc a cc a ag da ad da a ga a cc a ag a ad da a ga a cc a cg f a eee ad be bef da fe ee ad e bef ga ef ee a eb bef gc be ee a fe bef cg e ee a ef bef ag eb ee da be bef ad fe eba e aef ef gc eb ef a bef bb cc eb fe a bef fe ag eb e da bef ef ad feb eb da be be a feb fe ga be e a feb ef cc be eb a feb aa be ag ee gac fe a feb cad e ad e aa ef da gac eb a cab ga feaa a e dac cc ef cag a eb aa cg be dac a fe gag ad e aad da ef dac ad ef gag ga bb aad a be daa gc b gag a cad cg daa a gacag ca ``` <!-- end of image -->

Let's examine this image for potential line intersections. I can confidently say that there are no intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#5050ffff b,#ff0808ff c,#0707ffff d,#ff8e8eff e,#a6a6ffff f,#ff5050ff g,#ffcacaff ``` ```image g bbbb gbbd dbd dbbg bb fbb gbf bbf fbg gbbd bb dbbg dbd fbb bb bbf gbf gbbd fbg dbbg gbb fbb fbd bbf bb gbbd dbf dbbg bbg fbb gbf d fbg bb dbd bb gbf fbg bb dbd bb gbf fbg b c cecc ce ecc ca eca ca aca ac aca ec ace ec cce c cce c cc ce ecc ca ecc ca eca ac aca ec aca ec ace c cce ce cce ce cc ca cc ac ecc ac ecc ec eca c ac c ce ce ca ac ac ec c c ce ce ca ac ec ec c c ce ``` <!-- end of image -->

This is the image I'm working with. The goal is to count the intersections. I need to zoom in on these areas to get a better look. <!-- image --> ```palette Key,Color ,#fefefeff a,#5c60e5ff b,#fa090aff c,#99c39aff d,#b1d7b1ff e,#ea7369ff f,#b7b8feff g,#0909fcff ``` ```image a g gf fg gf fg g ag g aa g gf g gf fg g ag g aa g ga g gf fg g fg g aa g ga b g bb gf bb fg be g be fg be g be ga aa bd gf g b g ga b fg g db ag gf eb gg fg eb ga gf eb gf dcccccccccccccccccccccccccccccccccccccagcccccccbb g cdddddddddddddddddddddddddddddddddddddgdddddddbbd fg cddddddddddddddddddddddddddddddddddddagddddddbbdd ag cddddddddddddddddddddddddddddddddddddgddddddbbddd ga cdddddddddddddddddddddddddddddddddddgadddddbedddd gf cdddddddddddddddddddddddddddddddddddgdddddbeddddd g cddddddddddddddddddddddddddddddddddgaddddbedddddd g cddddddddddddddddddddddddddddddddddgddddbeddddddd fg cdddddddddddddddddddddddddddddddddgcdddbcdddddddd ag cddddddddddddddddddddddddddddddddcgddcbcddddddddd ga cddddddddddddddddddddddddddddddddgddcbddddddddddd gfcdddddddddddddddddddddddddddddddagdebdddddddddddd gcdddddddddddddddddddddddddddddddgdebddddddddddddd fgddddddddddddddddddddddddddddddaaebdddddddddddddd agdddddddddddddddddddddddddddddgebddddddddddddddd cggdddddddddddddddddddddddddddgabdddddddddddddddd cdgaddddddddddddddddddddddddddgbddddddddddddddddd cddgcddddddddddddddddddddddddgbdddddddddddddddddd cdddgdddddddddddddddddddddddbgddddddddddddddddddd cdddcgdddddddddddddddddddddbgdddddddddddddddddddd cddddagdddddddddddddddddddbagdddddddddddddddddddd cdddddgadddddddddddddddddbegddddddddddddddddddddd cddddddgadddddddddddddddbeagddddddddddddddddddddd cdddddddgddddddddddddddbcdgdddddddddddddddddddddd bbeee cdddddddcgdddddddddddcbcdgadddddddddddddddddddddd deeebbbbbbbbbbeeecdddddddagdddddddddcbdddgddddddddddddddddddddddd deebbbbbbbbbbggeeecdddebdddgaddddddddddddddddddddddd cdddddddddcgaebbbbbbdddcgdddddddddddddddddddddddd cdddddddddddgcdddddddddgcdddddddddddddddddddddddd cddddddddddddgddddddddagddddddddddddddddddddddddd cddddddddddddcgdddddddgdddddddddddddddddddddddddd cdddddddddddddagdddddagdddddddddddddddddddddddddd cddddddddddddddggddddgddddddddddddddddddddddddddd cdddddddddddddddgaddgaddddddddddddddddddddddddddd cddddddddddddddddgcdgdddddddddddddddddddddddddddd cddddddddddddddddcggadddddddddddddddddddddddddddc fg ``` <!-- end of image --> I wonder what we'll find inside area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#3b33f7ff b,#fd0709ff c,#7978fdff d,#fdb2b3ff e,#fd5759ff f,#c0bffeff g,#0504feff ``` ```image agc e fgg eb agc ebb cgg bbbd ggc bbbd cga dbbb fggf dbbb cga dbbe fggf dbbe agc dbbe fgg dbbe agc dbbe cgg ebbe ggc ebbd cga ebbd ggf ebbd cga ebbd fggf ebbd aga bbbd fggf bbbd agc dbbb fgg dbbb ggc dbbe cga dbbe f ggf dbbe a cga dbbe ga fggf ebbe ggc aga ebbe fggf fggfebbd cggf agcebbd agg fggebbd aga ggabbd gga cggbbd fggc ggbbd cggf cggb cggf dgge aga daga aga dbggf fggc dbagc fggc dbbgg cggf dbbggc cggf ebbcgg aga ebbeggc gga ebbdcga fggc ebbdfggf fggf ebbd cga cggf ebbd fggf agg bbbd agc aga bbbd fgg fggc dbbb agc fggc dbbb cgg edddd cggf dbbe ggc bbbbbbbbbeeeeedddd cggf dbbe cga eeebbbbbbbbbbbbbbbbbbaggeeedddd dbbe ggf ddddeeeebbbbbbggabbbbbbbbbbbeeebbe cga ddggaeeebbbbbbbbbbbe fggf fggc dddded aga cggf fggf cggf agc aga fgg gga ggc fggc cga fggf ggf cggf cga agg fggf aga aga fggc fggf fggc agc cggf fgg cggf ggc aga cgg agaggf ``` <!-- end of image --> Eureka! There's definitely an intersection in area A! The final answer is: two intersections found.

<!-- image --> ```palette Key,Color ,#fefefeff a,#443ef8ff b,#fe0708ff c,#8683fcff d,#ffb2b2ff e,#fc595cff f,#cacaffff g,#0505feff ``` ```image c g gc fg gf fg g ca g aa g gc fg gf fg g cg g aa g gc g gf fg g cg g aa g ac e g bb gf bb fg be gf be cg be f g bd ga ca bd gf g bd g ac db fg g db cg gc db aa fg eb gc gf eb gf fg eb g g bb fg ca bb cg g be ga aa be gc g be gf gc bd fg fg bd cg gf bd ag fg bd ga g db gf cg db g g db fg aaeb cg geb aa gab gc gb gf ge g bg fg bg ag bcg ga bdg gc bdaa gf bd g bbeedd fg db ac ddeebbbbbbbbbbeedd cg db g ddeebbbbbbbbbagedd db gf dgaebbbbbb fg gf gf g cg fg g cg ca aa g gc ac gf g ggc fg ``` <!-- end of image -->

I'm examining this image closely. My goal: find any and all intersections. After a thorough analysis, I conclude that there are no intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff3d3dff b,#0909ffff c,#5e5effff d,#ff8080ff e,#ff0404ff f,#aeaeffff g,#ffc4c4ff ``` ```image f fbb bc fbb cbc cbb bbf cbb bb cbc fbb cbc fbc cbc cbc cbc bbf bbc bbf bbc bb bbf fbb bbf cbc bbf cbf fbbf bbf fbbf bb fbb fbb fbb fbc fbb cbc fbb bbf cbb bbcbb fc eeadg eggdaeeeeeeadg ed gdaeeeeeeadg ea gdaeeeeeeadg ae gdaeeeeeeadg ge gdaeeeeee e eg ed ea de ge e eg ed aa de ge e eg ed aa de ge e eg ed aa de ge e eg ed aa de ge e eg ed aa de ge e eg ``` <!-- end of image -->

The hunt for intersections begins! Let's analyze this image closely. I need to zoom in on these areas to get a better look. <!-- image --> ```palette Key,Color ,#fefefeff a,#0708fcff b,#fb0b0aff c,#4c57e7ff d,#b1d7b1ff e,#df6f60ff f,#91a2dcff g,#99c795ff ``` ```image f a a cc f a ac a a ac fa fa a dggggggggggggggggggggggggggggggggggggggggggggggggggaggggb a gdddddddddddddddddddddddddddddddddddddddddddddddddacdddbe ac gddddddddddddddddddddddddddddddddddddddddddddddddfaddddbd a gddddddddddddddddddddddddddddddddddddddddddddddddaddddbgd fa gdddddddddddddddddddddddddddddddddddddddddddddddacdddebdd a gddddddddddddddddddddddddddddddddddddddddddddddfaddddbddd a gddddddddddddddddddddddddddddddddddddddddddddddaddddbeddd af gdddddddddddddddddddddddddddddddddddddddddddddacdddgbdddd a gddddddddddddddddddddddddddddddddddddddddddddcaddddbddddd ca gddddddddddddddddddddddddddddddddddddddddddddaddddebddddd a gdddddddddddddddddddddddddddddddddddddddddddafddddbdddddd a gddddddddddddddddddddddddddddddddddddddddddcaddddbedddddd af gddddddddddddddddddddddddddddddddddddddddddaddddgbddddddd a gdddddddddddddddddddddddddddddddddddddddddafddddbdddddddd cc gddddddddddddddddddddddddddddddddddddddddcaddddebdddddddd a gddddddddddddddddddddddddddddddddddddddddadddddbddddddddd fa gdddddddddddddddddddddddddddddddddddddddafddddbeddddddddd af gddddddddddddddddddddddddddddddddddddddcaddddebdddddddddd a gddddddddddddddddddddddddddddddddddddddadddddbddddddddddd cc gdddddddddddddddddddddddddddddddddddddafddddbeddddddddddd a gddddddddddddddddddddddddddddddddddddccdddddbdddddddddddd fa gdddddddddddddddddddddddddddddddddddfadddddbgdddddddddddd af gdddddddddddddddddddddddddddddddddddadddddebddddddddddddd a gddddddddddddddddddddddddddddddddddacdddddbdddddddddddddd cc gdddddddddddddddddddddddddddddddddfadddddbedddddddddddddd a gdddddddddddddddddddddddddddddddddadddddgbddddddddddddddd be fa gddddddddddddddddddddddddddddddddacdddddbgddddddddddddddd b af gdddddddddddddddddddddddddddddddfadddddebdddddddddddddddd b a gdddddddddddddddddddddddddddddddaddddddbddddddddddddddddd eb cc gddddddddddddddddddddddddddddddacdddddbeddddddddddddddddd bb a gdddddddddddddddddddddddddddddfadddddgbdddddddddddddddddd be fa gdddddddddddddddddddddddddddddaddddddbddddddddddddddddddd b afgddddddddddddddddddddddddddddacdddddebddddddddddddddddddd b agdddddddddddddddddddddddddddcaddddddbdddddddddddddddddddd eb ccdddddddddddddddddddddddddddaddddddbedddddddddddddddddddd be addddddddddddddddddddddddddafdddddebddddddddddddddddddddd bd caddddddddddddddddddddddddcaddddddbdddddddddddddddddddddd b gafdddddddddddddddddddddddaddddddebdddddddddddddddddddddd db gdaddddddddddddddddddddddafddddddbddddddddddddddddddddddd eb gdacddddddddddddddddddddcaddddddbeddddddddddddddddddddddd be gddaddddddddddddddddddddaddddddebdddddddddddddddddddddddd b gddcaddddddddddddddddddafddddddbddddddddddddddddddddddddd b gdddafddddddddddddddddcaddddddbeddddddddddddddddddddddddd eb gddddaddddddddddddddddadddddddbdddddddddddddddddddddddddd bb gddddacddddddddddddddafddddddbgdddddddddddddddddddddddddd be gdddddadddddddddddddcaddddddebddddddddddddddddddddddddddd b gdddddcaddddddddddddadddddddbdddddddddddddddddddddddddddd b gddddddadddddddddddadddddddbedddddddddddddddddddddddddddd eb gddddddfadddddddddacddddddgbddddddddddddddddddddddddddddd be gdddddddacdddddddfadddddddbgddddddddddddddddddddddddddddd bd gddddddddadddddddadddddddebdddddddddddddddddddddddddddddd b gddddddddcadddddacdddddddbddddddddddddddddddddddddddddddd db gdddddddddaddddfadddddddbeddddddddddddddddddddddddddddddd ebgdddddddddfadddadddddddgbdddddddddddddddddddddddddddddddd beddddddddddacdacdddddddbddddddddddddddddddddddddddddddddd bgddddddddddafadddddddebddddddddddddddddddddddddddddddddd gbddddddddddcaddddddddbdddddddddddddddddddddddddddddddddd gebddddddddddfdddddddbedddddddddddddddddddddddddddddddddd gdbbddddddddddddddddebddddddddddddddddddddddddddddddddddd gddbedddddddddddddddbdddddddddddddddddddddddddddddddddddd gdddbddddddddddddddbedddddddddddddddddddddddddddddddddddd gddddbdddddddddddddbddddddddddddddddddddddddddddddddddddd gddddebdddddddddddbeddddddddddddddddddddddddddddddddddddd gdddddbbdddddddddebdddddddddddddddddddddddddddddddddddddd gddddddbeddddddddbddddddddddddddddddddddddddddddddddddddd gdddddddbdddddddbeddddddddddddddddddddddddddddddddddddddd gdddddddgbddddddbdddddddddddddddddddddddddddddddddddddddd gddddddddebddddbgdddddddddddddddddddddddddddddddddddddddd gdddddddddbeddebddddddddddddddddddddddddddddddddddddddddd gddddddddddbgdbdddddddddddddddddddddddddddddddddddddddddd dgggggggggggbbegggggggggggggggggggggggggggggggggggggggggg db ``` <!-- end of image --> This is a magnified view of the region A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0909ffff b,#ff0404ff c,#6262ffff d,#ffc4c4ff e,#ff8282ff f,#ff3a3aff g,#b8b8ffff ``` ```image caa e gaag db aa bb gag be ac ff ca dbd aac ebb caa dbbd aag fbf ac bbd gag ef gaa dbd cac fb caa ebb gaag bbe aa bbd gag bf ac eb ca be aac dbb caa fbe aag ebb ac bbe gag dbd aa fe caa eb gaag dbb aa dbbd gag bbe ac ebf ca bbd aag eb cac be aa eb gag dbb ca ebb gaa bbe aac bf caa dbd ac eb ca dbb gag fbf aa dbbd caa bbe aac dbd aa ff gag dbd ac bb gaa dbbd aac fbf caa bb aag be cc dbd g gag fb a gaa ebb ac cac bbe ca gaag bbd ag aac be ga aa eb ac gag dbd cac ca dbb aag gaa bbe caa aac ebf aa caa bbd cc ac ebd ag ca be aa gag eb aac aa dbb cac gaag ebb aa aac bbe ca aa bf ac gag dbd gag ac fe aag gaa bb caa aag fbf aac cac dbbd gaa aa fbe gag cc bbd ca ca bf ac gaa dbd aa aac be gaag aag dbb caa ac fbf aac ca ebb gaa gag bbe gag caa dbd f ca gaag fe be ag aac eb bb aa aa bb fb gaaac dbbd bf caa fbe bbe aa bb dbbd g dbd fb dbd bf bb dbe ebb bbd dbbd fbf bbd dbb be dbe ef ebd dbd bb fb dbbe bbe dbb ebf ebd bbd ff be bbe be ebbd fb ebbd dbb fbf fbe dbe bbd ebd bf ``` <!-- end of image --> No intersection found in area A, but I won't give up. I did not find anything, there's no intersections

<!-- image --> ```palette Key,Color ,#fefefeff a,#0404ffff b,#ff0a0aff c,#3939ffff d,#ffb9b9ff e,#ff6565ff f,#7d7dffff g,#c9c9ffff ``` ```image f ga ag cc g ga cf a a cc fa ga ag a b ga af be cf ga b a a bd fa af eb ag fa b ga a be af af db a fa b fc a eb ag ag b ga fa bd af a db a ag b fc fc ee a a b ga ag bd af cc db a ga b cc ag ee a cc b ga ga bd ag ag db a cc b cc ga be a a b be ga cf bd b ag ga eb b a a b eb cc af be be a ga db bd fa a b b ag af eb db a fa b eb cf a bd be a af db bd fa fa b b ag a ee db a ag b eb cf fa bd be a a db bd fa ag b b ag cc be db ga a b bb cf ag bd bd a cc eb b fc ga b db ag ag be eb ga cc db be af ga bd bd a a eb b fc cc b db a ga be eb ga a db be af af b bd aga eb b fa b db g bd eb db be b b ee b b eb bd be db bd b b be db b eb bd be eb bd b bbe db ``` <!-- end of image -->

This image looks interesting. I wonder if there are any intersections hidden in there? These spots mark what I'd call 'danger zones' - areas where intersections are more likely. <!-- image --> ```palette Key,Color ,#fefefeff a,#3f48ebff b,#e95349ff c,#0506fdff d,#fb0707ff e,#d59d8cff f,#8493e1ff g,#b1d7b1ff ``` ```image ggggggggggggggggggggggggggggggggggggggggggggggggggggggg ggggggggggggggggggggggggggggggggggggggggggggggggggggggg ggggggggggggggggggggggggggggggggggggggggggggggggggggggg gggggggggggggggggggggggggggggggggggeggggggggggggggggggg ggggggggggggggggggggggggggggggggggbdggggggggggggggggggg ggggggggggggggggggggggggggggggggggdcdgggggggggggggggggg gggggggggggggggggggggggggggggggggdcacgggggggggggggggggg ggggggggggggggggggggggggggggggggedcgecggggggggggggggggg ggggggggggggggggggggggggggggggggdcfggdcgggggggggggggggg gggggggggggggggggggggggggggggggbdcgggedcggggggggggggggg gggggggggggggggggggggggggggggggdaaggggdecfggggggggggggg ggggggggggggggggggggggggggggggdbcggggggdgcfgggggggggggg ggggggggggggggggggggggggggggggdaaggggggdbgcfggggggggggg gggggggggggggggggggggggggggggdecggggggggdggcfgggggggggg ggggggggggggggggggggggggggggbdfcggggggggbbggcaggggggggg ggggggggggggggggggggggggggggdgcggggggggggdgggcagggggggg gggggggggggggggggggggggggggdbfcggggggggggbdgggcaggggggg gggggggggggggggggggggggggggdgcggggggggggggdggggcagggggg ggggggggggggggggggggggggggdegcggggggggggggedggggccggggg gggggggggggggggggggggggggedgcfgggggggggggggdeggggccgggg gggggggggggggggggggggggggdggcgggggggggggggggdgggggacggg ggggggggggggggggggggggggbbgcfgggggggggggggggdbgggggacgg ggggggggggggggggggggggggdggcgggggggggggggggggdggggggacg gggggggggggggggggggggggdegaagggggggggggggggggbbggggggac ggggggggggggggggggggggedggcgggggggggggggggggggdgggggggfc ggggggggggggggggggggggdggaagggggggggggggggggggbdgggggggfc gggggggggggggggggggggbbggcgggggggggggggggggggggdggggggg fc gggggggggggggggggggggdggfcgggggggggggggggggggggedgggggg c ggggggggggggggggggggdeggcgggggggggggggggggggggggdeggggg c gggggggggggggggggggedggfcggggggggggggggggggggggggdggggg c gggggggggggggggggggdgggcgggggggggggggggggggggggggdegggg cf ggggggggggggggggggbdgggcggggggggggggggggggggggggggdgggg cf ggggggggggggggggggdgggcfggggggggggggggggggggggggggbbggg cf gggggggggggggggggdbgggcggggggggggggggggggggggggggggdggg cf ggggggggggggggggedgggcfggggggggggggggggggggggggggggbdgg ca ggggggggggggggggdegggcggggggggggggggggggggggggggggggdgg ca gggggggggggggggbdgggaaggggggggggggggggggggggggggggggedg ca gggggggggggggggdggggcggggggggggggggggggggggggggggggggde ca ggggggggggggggdbgggaagggggggggggggggggggggggggggggggged cc ggggggggggggggdggggcggggggggggggggggggggggggggggggggggde ac gggggggggggggdegggfcgggggggggggggggggggggggggggggggggggd ac ggggggggggggedggggcggggggggggggggggggggggggggggggggggggbb ac ggggggggggggdggggfcgggggggggggggggggggggggggggggggggggg d ac gggggggggggbbggggcggggggggggggggggggggggggggggggggggggg bb fc gggggggggggdgggggcggggggggggggggggggggggggggggggggggggg d fc ggggggggggdeggggcfggggggggggggggggggggggggggggggggggggg ed fc gggggggggedgggggcgggggggggggggggggggggggggggggggggggggg d fc gggggggggdgggggcfgggggggggggggggggggggggggggggggggggggg d ggggggggbbgggggcggggggggggggggggggggggggggggggggggggggg de ggggggggdgggggaaggggggggggggggggggggggggggggggggggggggg d gggggggdegggggcgggggggggggggggggggggggggggggggggggggggg de ggggggedgggggaagggggggggggggggggggggggggggggggggggggggg d ggggggdggggggcggggggggggggggggggggggggggggggggggggggggg bb gggggbdgggggfcggggggggggggggggggggggggggggggggggggggggg d gggggdggggggcgggggggggggggggggggggggggggggggggggggggggg ed ggggdbgggggfcgggggggggggggggggggggggggggggggggggggggggg d gggedggggggcggggggggggggggggggggggggggggggggggggggggggg ed gggdgggggggcggggggggggggggggggggggggggggggggggggggggggg de ggbdggggggcfggggggggggggggggggggggggggggggggggggggggggg d ggdgggggggcgggggggggggggggggggggggggggggggggggggggggggg de gdbggggggcfgggggggggggggggggggggggggggggggggggggggggggg d gdgggggggcggggggggggggggggggggggggggggggggggggggggggggg bb deggggggaaggggggggggggggggggggggggggggggggggggggggggggg d edgggggggcgggggggggggggggggggggggggggggggggggggggggggggg ed dgggggggaagggggggggggggggggggggggggggggggggggggggggggggg d c ed fa d c d fc de c d c bb c d c bd cf d c ed af d c d aa de c d fa bb c d fc bb c d ``` <!-- end of image --> I'm focusing my attention on this specific region, area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#5953f9ff b,#fa4549ff c,#0707feff d,#fe0606ff e,#fe9495ff f,#a8a7fdff g,#f6d3dcff ``` ```image gg bddb dbbd dcca eaccce edca fca gddcf cca bdac bcc ddac bdccg ddcc gdcccg gdfcc bbccc bbaca gdeacf ddaca dde ccf eddccg edd accf gddeca bde acc bdb cf edd acf db cf gdg cca ed fc bb fcca gde cc gde fcc gdd ccf dde fca bdbfcc edd cca eddgaca dde fcca dde cc edd fcc gdg gcg gdg gccg bb aa bb ccc edg cf gdg ccg dd ac db ccf dde fcc edd accf db ccf dde acc edg fcc edd acf de ccf bd acf gdd ca bb ac bdb fc gdg f gddg aa db dd ac edd gde cc dde bb aca edd gdg ccf bd edd cf bb dde fc gdg bdb cf db ddg fc dde edg fcc dd de aca ed ed gccg be gdd aca edg eddg ca ddg dde cf bdb dd fc gdde bb fc dd edg cc ed dd fcc de edd aca edg db aca dd gdg ccg bd bb ca gd ed cf b bdb cf gddg fc bdb cc ddg fcc bb fcc gdg aca bd cc dde gcg edd aa dde cf db ac de fcc ed ccf gdd cc bdb cf bde aa dd fc gde ac gdg aca bd ccf edd aca dde ccf ddg cf db fc edg cf de fc gdd fcc bdb aca ddg gccg de aca gde ca bd cf gdd fc edd fc dde cc db fcc gdg aca ed aca dd ccg ``` <!-- end of image --> The lines cross each other within area A, forming an intersection. After careful examination, I conclude that there is one intersection.

<!-- image --> ```palette Key,Color ,#fefefeff a,#5959feff b,#fe3f3fff c,#0808feff d,#fd0506ff e,#fd8182ff f,#a9a9ffff g,#fec7c8ff ``` ```image g ed dcb dcac gdc ec dcf dc edc gdc daa dgcf dec d cf gdaa be cf dgc d cf edfc bb ca d c d ca befc ed ca d c d ca dg c gd cc ed cf dg cc d c d ac bb cf de ac d c d ac dg aa bb ac gd c d fc d aa ed fc bb c d fc d fc gd fc de c dg c gd fc gd cf d c de cf eb c d cf d cf bb cf de c d ca gd cf eb ca dg c d ca ed aa gd ca d c dg cc be aa gd cc d c de cc dg fc d ac ed c be ac d fc d ac bb c eb ac d c d fc dg cf ed fc gd c dg fc d cf gd bb c dg d aa d de c be gd aa d d c bb eb fc d d c ed de fc d gd c gd dg c dg ed cf d d c de be cf d d c bb dg aa d ed c ed d aa d c gd fc dg c gd fc de c d fc bb cf d c eb cf d c gd aa dg c gd aa de c d fc be c d fc eb c d ``` <!-- end of image -->

Alright, let's get to work and investigate this image for intersections. I have a hunch that these areas might contain the intersections we're looking for. <!-- image --> ```palette Key,Color ,#fefefeff a,#1518f6ff b,#ec453cff c,#fd0504ff d,#d88e7cff e,#6e79eaff f,#b1d7b1ff g,#96c897ff ``` ```image f aa a a ea ae fggggggggggggggggggggggggggggggggggggggggggggggggggggggggggg a gffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa a gfffffffffffffffffffffffffffffffffffffffffffffffffffffffffaa ea gffffffffffffffffffffffffffffffffffffffffffffffffffffffffaaf ae gfffffffffffffffffffffffffffffffffffffffffffffffffffffffaaff a gffffffffffffffffffffffffffffffffffffffffffffffffffffffaafff ea gfffffffffffffffffffffffffffffffffffffffffffffffffffffaaffff ae gffffffffffffffffffffffffffffffffffffffffffffffffffffaafffff a gfffffffffffffffffffffffffffffffffffffffffffffffffffaaffffff a gffffffffffffffffffffffffffffffffffffffffffffffffffaafffffff ea gfffffffffffffffffffffffffffffffffffffffffffffffffaaffffffff ae gffffffffffffffffffffffffffffffffffffffffffffffffaafffffffff a gfffffffffffffffffffffffffffffffffffffffffffffffaaffffffffff fa gffffffffffffffffffffffffffffffffffffffffffffffaafffffffffff aa gfffffffffffffffffffffffffffffffffffffffffffffaaffffffffffff af gffffffffffffffffffffffffffffffffffffffffffffaafffffffffffff a gfffffffffffffffffffffffffffffffffffffffffffaaffffffffffffff ea gffffffffffffffffffffffffffffffffffffffffffaafffffffffffffff ae gfffffffffffffffffffffffffffffffffffffffffaaffffffffffffffff a gffffffffffffffffffffffffffffffffffffffffaafffffffffffffdbcc a gfffffffffffffffffffffffffffffffffffffffaafffffffffdccccbdff eagffffffffffffffffffffffffffffffffffffffaaffffdbccccbdfffffff aefffffffffffffffffffffffffffffffffffffaadbccccbgffffffffffff affffffffffffffffffffffffffffffffffdbaacbdffffffffffffffffff eafffffffffffffffffffffffffffgbccccbaaffffffffffffffffffffff gaafffffffffffffffffffffdbccccbdfffaafffffffffffffffffffffff gfagfffffffffffffffdbccccdffffffffaaffffffffffffffffffffffff gffaffffffffffffcccbdffffffffffffaafffffffffffffffffffffffff gffeaffffffffffcdfffffffffffffffaaffffffffffffffffffffffffff gfffaeffffffffcbfffffffffffffffaafffffffffffffffffffffffffff gffffafffffffdcfffffffffffffffaaffffffffffffffffffffffffffff gffffgaffffffcfffffffffffffffaafffffffffffffffffffffffffffff gfffffaaffffcgffffffffffffffaaffffffffffffffffffffffffffffff gffffffaeffcbffffffffffffffaafffffffffffffffffffffffffffffff gfffffffafbcffffffffffffffaaffffffffffffffffffffffffffffffff gfffffffeacffffffffffffffaafffffffffffffffffffffffffffffffff gffffffffaafffffffffffffaaffffffffffffffffffffffffffffffffff gfffffffcdagfffffffffffaafffffffffffffffffffffffffffffffffff gffffffbcffaffffffffffaaffffffffffffffffffffffffffffffffffff gfffffdcfffeaffffffffaafffffffffffffffffffffffffffffffffffff gfffffcfffffaeffffffaaffffffffffffffffffffffffffffffffffffff gffffcdffffffafffffaafffffffffffffffffffffffffffffffffffffff gfffbcfffffffgafffaaffffffffffffffffffffffffffffffffffffffff gffdcfffffffffaafaafffffffffffffffffffffffffffffffffffffffff gffcfffffffffffaaaffffffffffffffffffffffffffffffffffffffffff gfcdffffffffffffafffffffffffffffffffffffffffffffffffffffffff gbbfffffffffffffffffffffffffffffffffffffffffffffffffffffffff dcffffffffffffffffffffffffffffffffffffffffffffffffffffffffff cfffffffffffffffffffffffffffffffffffffffffffffffffffffffffff cdfffffffffffffffffffffffffffffffffffffffffffffffffffffffffff cbgfffffffffffffffffffffffffffffffffffffffffffffffffffffffffff dc gfffffffffffffffffffffffffffffffffffffffffffffffffffffffffff c gfffffffffffffffffffffffffffffffffffffffffffffffffffffffffff c gfffffffffffffffffffffffffffffffffffffffffffffffffffffffffff cb gfffffffffffffffffffffffffffffffffffffffffffffffffffffffffff dc gfffffffffffffffffffffffffffffffffffffffffffffffffffffffffff c gfffffffffffffffffffffffffffffffffffffffffffffffffffffffffff c gfffffffffffffffffffffffffffffffffffffffffffffffffffffffffff cd gfffffffffffffffffffffffffffffffffffffffffffffffffffffffffff bc gffffffffffffffffffffffffffffffffffffffffffffffffffffffffffg c c cd bc c c cd bb dc c cd bb dc c cf ``` <!-- end of image --> I'm focusing my attention on this specific region, area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#3232feff b,#fd5f60ff c,#fd0809ff d,#d1d1feff e,#7f7efeff f,#0908feff g,#feb2b2ff ``` ```image a af aff affd affd affd affd ffd afd afd aff affd affd affd affd affd affd affd affd affd affd affd affd ffd afd afd aff affd affd affd affd affd affd g affd ggbbccc affd ggbcccccccc affd gbbcccccccbbgg affd ggbccccccccbbg affd ggbcccccccbbgg e affdgbbccccccccbgg fd gffccccccccbbg fa ggbccffccccbgg ffe gbbccccccffbgg dffd gbbccccccccbbaff effd ggbbcccccccbgg affd afa ggbccccccccbgg affd dffe gbbccccccccbbgg affd effd ggbbcccccccbbg affd afa ggbccccccccbgg affd afe cccccccbbgg affd dff bccbbg affd efd gccg affd aa gccg affd ffd bcc affd eff bccg affd afa ccg ffd dffe cb afd effd bc afd afa bc aff ffe gcc affd dffd ccb affd effd ccb affd afa bcc affd dffegccg affd effccb affd effb affd bffa affd gccffe affd gccbeffd affd bcc dffe affd gccg dffd affd gccg eff ffd ccb af afd bcc dfe afd bccg efd aff gccg fa affd ccb afe affd cc dffe affd bcg effd affd gcg afa affd cc dffe affd bcc dffaffd bcc efffd gccg aad ccb bcc gccg ccb cb c g ``` <!-- end of image --> There is an intersection point visible in this close-up of area A. The image features two intersection points.

<!-- image --> ```palette Key,Color ,#fefefeff a,#3534feff b,#ff3f3fff c,#ff0404ff d,#ff8787ff e,#9d9dffff f,#0d0cfdff g,#ffc6c6ff ``` ```image e aa fe f ef fe f a f af aa af fe af f af ef af aa af f af f af ef af fe af f af ef af aa af fe af f af ef af fa af f af dbcc f af dbcccbd af af gdccccbg fe afgbccccdg f dbffcbd ef gdccccbaf aa gbccccdg af fe dbcccbd af f cccbd af ef cg af fe cb af f dc af f c af aa cg af fe cd af f dc af efc af fa af cdf af bc f af gc ef af c fe af cd f af bb ef af gc aa af c faf cg a bb dc c cg bb dc c cg cb dc gc cg cd dc gc c cd bc gc c cd bb gc c cg bb dc c cg ``` <!-- end of image -->

Alright, let's get to work and investigate this image for intersections. These spots mark what I'd call 'danger zones' - areas where intersections are more likely. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd0707ff b,#0809fbff c,#e6998cff d,#5359f2ff e,#f04e47ff f,#afd6afff g,#a6a8fbff ``` ```image g db gb gb gb gb gb gb gb gb gb b b b b b b bg bg bg bg bg bg bg bg bg bd bd fffffffffffffffffffcafffffffffffffffbd fffffffffffffffffffacafffffffffffffbd ffffffffffffffffffacffacffffffffffbdf fffffffffffffffffeaffffacffffffffbdff fffffffffffffffffaffffffacffffffbdfff ffffffffffffffffacfffffffaeffffbbffff fffffffffffffffeafffffffffaeffbbfffff fffffffffffffffafffffffffffaebbffffff ffffffffffffffafffffffffffffbbfffffff fffffffffffffaeffffffffffffbbaaffffff ffffffffffffcaffffffffffffbbffeafffff ffffffffffffaffffffffffffbbffffeaffff fffffffffffaefffffffffffdbffffffeafff ffffffffffeafffffffffffdbffffffffcaff ffffffffffafffffffffffdbffffffffffcaf fffffffffacffffffffffdbffffffffffffca ffffffffeaffffffffffdbfffffffffffffffa gggggggdddddbbbbbbbbbbbbbbbbbbbbbffffffffffffffff ac bbbbbbbddddddgggdggffffafffffffffffffffffffffffffffff ac ffffffaefffffffffffffffffffffffffffff ac fffffcaffffffffffffffffffffffffffffff ae fffffafffffffffffffffffffffffffffffff ae ffffaefffffffffffffffffffffffffffffff aa fffcaffffffffffffffffffffffffffffffff aa fffafffffffffffffffffffffffffffffffff ea ffacfffffffffffffffffffffffffffffffff ea feaffffffffffffffffffffffffffffffffff ca a ca a ca ee a a a a ac ae ac ca ac a ae ac ae ca ae a aa ac ea ea ea a ea a c ee ca a ac ca a ac ea a a ``` <!-- end of image --> I wonder what we'll find inside area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0405ff b,#0706fdff c,#fe8384ff d,#4f4ffeff e,#ff3e3eff f,#fdc6c7ff g,#bab8fdff ``` ```image cc g caae gb faaaae gbb eaefaaef gbbd caaf faaaf gbbd faac eaaf gbbd eae eaaf gbbd caa eaaf gbbd faaf eaac gbbd aac eaac gbbd eae caac gbbd faaf caac gbbd aac caac gbbd eae caae gbbd caaf faae bbd faac faaegbbb eae faabbb caa fbbbf faaf bbbaaf eae bbbgeaaf caa dbbg eaaf faaf dbbg eaaf aac dbbg eaaf eae dbbg eaac caaf dbbg caac faac dbbg caac eae dbbg caac caaf dbbg caae faac dbbg faae eae dbbg faae caa dbbg faae faaf dbbg faa aac dbbg fa eae dbbg f caagggggggggggggdddddddddbbg ddddbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbg bbbbbbbbbbbbbbbbbbbbbbddddddddddddddggggg ggggggggg caaf faac eae caa faaf eae caa faaf aac eae caaf faac eae caaf faac ``` <!-- end of image --> Amazing! This area was hiding an intersection all along! The image features two intersection points.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fe0505ff b,#0908feff c,#ff8888ff d,#5f5fffff e,#ff4040ff f,#ffc9c9ff g,#b4b4ffff ``` ```image d db db gb gb gb gb gb gb gb gb gb b b b b bg bg bg bg bg bg bg bg bg bd bd bd ca bd afaf bd ac af bd ca af bd a ac bd af ac bd ee ae bb fa aebb a bb ee bbea fa bb ea a db ea ac db ca ca db ca a db fa af db faf ee db faf ggggggdddddddbbbbbbbbbbbbbbbbbbbb af bbbbbbbdddddddgggggg af ac ee ac fa ae a ae ac ae ca ea a ea ac ea ca ca a ca af fa ee fa fa faf a af ae ac fa ac a ae ac ae ca ae a aa af ea ee ea fa ca af c ee fa a ac ca a ac ca a af ``` <!-- 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,#5e61f4ff b,#f74e4aff c,#0404feff d,#aed5aeff e,#f9a19eff f,#dddafbff g,#fe0606ff ``` ```image dddddddddddddddd dddddddddddddddd dddddddddddddddd dddddddddddddddd ff dddddddddddddddd eebggggggb dddddddddddddddd ebggggggbe bg dddddddddddddddbbgggggbee ege dddddddebggggggbe gg dbggggggbedddddd bgf dcaddddddddddddd gb ddccdddddddddddd gg dddccddddddddddd ege ddddacdddddddddd gb ddddddcddddddddd bg dddddddcaddddddd ege ddddddddccdddddd gg dddddddddccddddd bgf ddddddddddacdddd gb ddddddddddddcddd gg fca ege ca gb cc bg ac ege fcf gg fca bgf ca gb cc gg ac ege fcf gb fcf bg ca fge cc gg ac egf acf gb fcf gg ca eg cc ac ac fcf fcf fcf fcf fcf fcf fcf fcf fcf fcf fcf fcf fcf fcf fcf fcf fcf fcf fcf fcf fcf fcf fcf fcf fcf fcf fcf fcf fcf fcf cf cf cf cf cf cf cf cf cf cf cf cf cf c ``` <!-- end of image --> Let's see if area A yields any clues. <!-- image --> ```palette Key,Color ,#fefefeff a,#5756feff b,#f63f47ff c,#0a08fdff d,#ff8282ff e,#fec2c2ff f,#b3b3feff g,#fe0404ff ``` ```image ee eddbbgggg eeddbbggggggggggb eedbbgggggggggggbddee ebbggggggggggbbddee ecbgggbbdee fcca fcca fcccf fcccf accf acca fcca fccc fcccf accf acca acca fccc fcccf cccf acca acca fcca fcccf ``` <!-- 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,#6463feff b,#fe3737ff c,#0404ffff d,#ff7575ff e,#ffbdbdff f,#d9d9ffff g,#ff0303ff ``` ```image e edbggggggb edgggggbde bg edbgggggbde egd edbgggggde gg bgggggbde dge ca gd cc gg ac dge ac gb fcf bg ca egd cc gg cc dge ac gd fcf bg ca ege ca gb cc bg ac egd fcf gg fca dge ca gb cc bg ac ege fcf gb fcf bg ca egd cc gg ac dge acf gb fcf bg ca eg cc ac ac fcf fcf fcf fcf fcf fcf fcf fcf fcf fcf fcf fcf fcf fcf fcf fcf fcf fcf fcf fcf fcf fcf fcf fcf fcf fcf fcf fcf cf cf cf cf cf cf cf cf cf cf cf cf cf cf cf c ``` <!-- end of image -->

Alright, let's get to work and investigate this image for intersections. The image is completely devoid of intersections. Zero.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0606ff b,#0707ffff c,#ff7373ff d,#5959ffff e,#adadffff f,#ffbcbcff g,#ff3f3fff ``` ```image ee eeeedddbbbbbbbbbbbbbbbbd eeeedddbbbbbbbbbbbbbbbbdddeeee eeeedddddbbbbbbbbbbbbbbbbbbbbbbdddeee bbbbbbbdddddeeeee a ag ga ca fa fa a af af ac ag ga ca fa fa a af af ac ag ga ca fa fa a af af ac ag ga ca fa fa a af af ac ag ga f ca gaagf fa faaagf fa caaac a caaac af fgaaaf af fgaagf ac faaagf ag caaac ga caaac ca fgaa ``` <!-- end of image -->

Here's an image. My task is to find intersections or areas where lines come close together. These spots mark what I'd call 'danger zones' - areas where intersections are more likely. <!-- image --> ```palette Key,Color ,#fefefeff a,#0808fdff b,#fd0d0cff c,#b0b0ffff d,#ee7c76ff e,#98c698ff f,#5b60f5ff g,#b2d7b1ff ``` ```image c cfaaa faaac geeeeeeeeeeeeeeeeeeeeeeeeeee faaaf eggggggggggggggggggggggggggg caaaf eggggggggggggggggggggggggggg caaafc eggggggggggggggggggggggggggg cfaaac eggggggggggggggggggggggggggg faaac egggggggggggdbegggggggggggfaaaf eggggggggggdbgbbggggggfaaafe egggggggggbbgggdbbfaaafegggg eggggggggbbgggeaaaadgggggggg egggggggbbggeaafgggbbdgggggg eggggggbbgggaegggggggbbegggg egggggbdgggeagggggggggebbggg eggggbdggggaggggggggggggdbbg egggbdggggfaggggggggggggggdbd egebegggggagggggggggggggggggbbg edbggggggfaggggggggggggggggg bb dbgggggggagggggggggggggggggg gbb dbeeeeeeefaeeeeeeeeeeeeeeeeee dbd bb a bbd bb ff bb bb a bb bd af dbb bd a dbd bd ac bbd bg a bb b ac bb db ca dbd db a dbd db ca bb bb a bb bb ca d bb a bd fa bd a bd ff b a gb af db a b ac a ac a ac ca a ca a fa a ff a ff a af a ac a ac ca a ca a ca a fa a ff a ff a ac a ac a ac ca a ``` <!-- end of image --> Let's get to the bottom of what's happening inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0706fdff b,#ff0404ff c,#ababfeff d,#ff3f3fff e,#fdc9caff f,#5951f6ff g,#f98489ff ``` ```image ee gbbde cfa gbbbbbde cffaaaa gbbgedbbbg ccfaaaaaafc dbbg edbbbg cfaaaaaafc dbbg edbbdecfaaaaaafcc dbbe gfaaaaaafcc dbbe cffaaaaaafge ebbbe cfaaaaaafcedbbbg ebbde aaaafc edbbbg ebbd faf gbbbde ebbd caac gbbbde gbbd faf gbbbg gbbg caa edbbbg gbbg faf edbbde dbbg caa gbbbde dbbg aaf gbbb dbbe caa edb edbbe aac e ebbbe caa ebbde aac ebbd faa gbbd aac gbbd faf bbg aac ``` <!-- end of image --> My investigation has led me to an intersection in area A! One intersection, that's it, but I found it.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0605feff b,#ff0808ff c,#8989feff d,#fc5759ff e,#ffb2b2ff f,#4848ffff g,#c9c9ffff ``` ```image g gfaaa gfaaac caaac caaafg gaaafg gfaafg gfaaac ebe caaac db bb caaaf db ebbcaaafg bb gfaaad bb gaac dbe bd ag bb bd ga ebb be a ebd be ca dbd ebe a bbe eb cf bb eb a ebb db ff dbd db a dbe bb ff bbe bb a bb bd ac ebd bd a dbd be ac bbe be ga bb eb ag ebb eb ga ebd db ag dbe db ga bbe db a bb bb ca e bd a bd cf bd a be ff be a eb fc eb a d ac a ag ga ag ga a ca a ca a ff a ff a ac a ac a ag ga ag ga a ca a cf a ff a fc a ac a ag ga ag ga ag ``` <!-- end of image -->

Let's examine this image for potential line intersections. Let's take a closer look at what's happening inside these zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#f25957ff b,#535cecff c,#0708fdff d,#fba9a8ff e,#fe0504ff f,#a6a9f8ff g,#aed4adff ``` ```image f c cf bc e c eae cf e de fc ed de c e de cf ed de fc e de c aa de cb e de fc aa de c e de bb aa de c e de c de de bc e de c de de cf e de ggggggggggggbcgg de deggggggggggggcggg e deggggggggggcbggg e geggggggggbcgggg ed ggegggggggcggggg e gggegggggcbggggg ed ggggegggfcgggggg e gggggeggcggggggg ed ggggggecbggggggg e gggggggcgggggggg aa ggggggcgeggggggg e gggggbcggegggggg aa gggggcggggeggggg e ggggcfgggggegggg aa gggbcgggggggeggg e gggcgggggggggegg de ggcbggggggggggeg e gbcgggggggggggge de gcgggggggggggggge e cbgggggggggggggg e de fc e e c e e cb e ed c e e c e ed bb e e c e ed cf e e bc aa c e cf aa fc e c aa cf e fc de c e cb de fc e c de bb e c de cf ed bc gggggggggggegggg c ggggggggggedgggg cf ggggggggggeggggg fc gggggggggeaggggg c gggggggggegggggg cf ggggggggeagggggg fbcccc ggggggggeggggggg fbcccccbf gggggggaaggggggg ffbcccccbf gggggggeggggggbbcccccbf ggggggaabcccccbb gggcccccbfgggggg gggggaeggggggggg gggggegggggggggg ggggaegggggggggg ggggeggggggggggg gggdeggggggggggg gggegggggggggggg gggggggggggggggg gggggggggggggggg gggggggggggggggg ``` <!-- end of image --> I'm focusing my attention on this specific region, area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fa7478ff b,#5e5effff c,#0605feff d,#feb0b1ff e,#fd0304ff f,#b1b0feff g,#fa2b2fff ``` ```image aeg eed aeg eed aeg eed aeg ged deg gea dee gea dee gea dee gea dee aea ffb eed ffbbbccccc aeafbbccccccccccbb ffbbccccccccccbbbff fcccccccccbbff ccbbfged aeg eed aeg eed deg gea dee gea dee gea dee aa ``` <!-- end of image --> My investigation has led me to an intersection in area A! Let's shift our focus to the next area. I wonder what we'll find inside area B? <!-- image --> ```palette Key,Color ,#fefefeff a,#f7363dff b,#3c39fcff c,#0404feff d,#fcccceff e,#fe0808ff f,#8181ffff g,#c5c5ffff ``` ```image bcf fcc a gccg ea bcb eea fcc deea gccf deea bcb deea fccg deea ccf deea bcb deea gccg deea ccf deea fcb deea gccg deea bcf deea fcc deea gccg deeabcb deacc dcca bcbea fccdeea ccf deea bcb deea gccg deea ccf deea fcb deea gccg deea bcf deea fcc deea gccg deea bcb deea fcc deea gccf dee bcb de fccg d ccf bcb ``` <!-- end of image --> Incredible, there's actually an intersection in area B! The final answer is: two intersections found.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fc5356ff b,#4b4bfeff c,#0606ffff d,#ffa6a6ff e,#ff0404ff f,#9a9affff g,#f4dae4ff ``` ```image f gc cg bc ge c eae cf e de fc ed de c e de cf ed de fc e de c aa de cb e de gc aa de c e de bb aa de gc e de cg de de bb e de c de de cf eg de fc ge de c eg de cf ge de fc ed ge c ge ge cf ed ge fc e ge c ed gebb e gc aa cge e bb ge aa c geg e cf geg aa fc geg e c geg de cf geg e fc geg de c geg e cf geg de fc geg eg c geg ge bb geg eg gc geg ge cg geg ed bb geg e c geg ed cg ge e bc aa c e cf aa fc e c aa cf e fc da c e cb de gc e cg de bb eg gc ge cg eg bc ge c ed cf e fc ed c e cf ad fbcccc e fbcccccbfg aa gfbccccbff e fbcccccbf aabcccccbfg ccccbfg aa e de e de eg ``` <!-- end of image -->

This image looks interesting. I wonder if there are any intersections hidden in there? Could these regions be concealing intersection points? Let's find out. <!-- image --> ```palette Key,Color ,#fefefeff a,#0505fdff b,#fc0907ff c,#b1d7b1ff d,#8999deff e,#e46256ff f,#9dc494ff g,#454befff ``` ```image feebbbbbbbeffffffffffffffffffffffffffffffffffffffffff eebbbbbbefccccccbeccccccccccccccccccccccccccccccccccccccccc cebbbbbbee fccccccccccbbcccccccccccccccccccccccccccccccccccccccc cebbbbbbee fcccccccccccbbccccccccccccccccccccccccccccccccccccccc bbbbbbec fccccccccccccebcccccccccccccccccccccccccccccccccccccc fcccccccccccccebccccccccccccccccccccccccccccccccccccc fccccccccccccccfbfccccccccccccccccccccccccccccccccccc fccccccccccccccccbfcccccccccccccccccccccccccccccccccc fccccccccaccccccccbeccccccccccccccccccccccccccccccccc fcccccccagadcccccccbecccccccccccccccccccccccccccccccc fcccccccaccaacccccccbbccccccccccccccccccccccccccccccc fccccccadcccgacccccccbbcccccccccccccccccccccccccccccc fccccccaccccccagccccccebccccccccccccccccccccccccccccc fcccccadcccccccaaccccccebcccccccccccccccccccccccccccc fcccccacccccccccdadcccccfbfcccccccccccccccccccccccccc fccccadcccccccccccagcccccfbfccccccccccccccccccccccccc fcccdacccccccccccccgaccccccbecccccccccccccccccccccccc fcccadccccccccccccccdagcccccbeccccccccccccccccccccccc fccdacccccccccccccccccaacccccbbcccccccccccccccccccccc fccacccccccccccccccccccgadccccbbccccccccccccccccccccc fcdacccccccccccccccccccccagccccebcccccccccccccccccccc fcacccccccccccccccccccccccaaccccebccccccccccccccccccc fdaccccccccccccccccccccccccdadcccfbfccccccccccccccccc facccccccccccccccccccccccccccaacccfbfcccccccccccccccc daccccccccccccccccccccccccccccgaccccbeccccccccccccccc accccccccccccccccccccccccccccccdagcccbecccccccccccccc daccccccccccccccccccccccccccccccccaacccbbccccccccccccc afcccccccccccccccccccccccccccccccccgadccbbcccccccccccc dafcccccccccccccccccccccccccccccccccccagccebccccccccccc a fccccccccccccccccccccccccccccccccccccgaccebcccccccccc da fcccccccccccccccccccccccccccccccccccccdadcfbfcccccccc a fcccccccccccccccccccccccccccccccccccccccaacfbfccccccc da fccccccccccccccccccccccccccccccccccccccccgaccbecccccc a fccccccccccccccccccccccccccccccccccccccccccagcbeccccc da fcccccccccccccccccccccccccccccccccccccccccccaacbbcccc a fccccccccccccccccccccccccccccccccccccccccccccdadbbccc dg fccccccccccccccccccccccccccccccccccccccccccccccaaebcc a fcccccccccccccccccccccccccccccccccccccccccccccccgaebf dg fccccccccccccccccccccccccccccccccccccccccccccccccdagb a aa gg d a gg a gg a gg a gg a gg a gd a gd a ad a ad a ad a ad a ad a ad a ad a a a a a a a a da a ``` <!-- end of image --> I wonder what we'll find inside area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#0404feff b,#ff0808ff c,#feb3b4ff d,#7c7cfeff e,#fe5c5cff f,#c9c9feff g,#4040feff ``` ```image cceeebbbbbc ccceebbbbbbbbbbbbbbe bbbbbbbbbbeeecc ebbe bbbeeccc cbbe cbbe cbbb cbbbc bbbc ebbc ebbe ebbe cbbe cbbe cbbb cbbbc bbbc ff ebbc aad ebbe daaagf ebbe aadaaad cbbe dag gaag cbbe aaf daaaf cbbb dag fgaad cbbbc faaf daagf bbbc dag faaaf ebbc faaf fgaad ebbe dag daagf ebbe faaf faaad cbbe dag gaag cbbe faaf daaaf cbbb gag fgaad cbbbc faaf daagf bbbc gag faaad ebbc faaf fgaag ebbc gag daaaf ebbe faaf faaad cbbe gag gaagf cbbe faaf daaaf cbbb gag fgaad cbbbc faaf daagf bbbc gad faaad ebbc faaf gaag ebbc gad daaaf ebbe faaf fgaad cbbe gad daagf cbbe faaf faaaf cbbb gad fgaad cbbbc faa daagf bbbc gad faaad ebbc faa gaag ebbc gad daaaf ebbe aa fgaad ebbe ad daagf cbbe a faaad cbbb d fgaag cbbbc daaaf bbbc faaad ebbc gaagf ebbc daaaf ebbe fgaad ebbe daagf cbbe faaad cbbb gaag cbbbc daaaf bbbc fgaad ebbc daagf ebbc faaaf ebbe fgaag ebbe daagf cbbe faaad cbbb gaag cbbbc daaaf bbbc fgaad ebbc daagfebbc faaadebbe gaagebbe daaacbb ``` <!-- end of image --> This close-up reveals that there are no intersections in area A. My final answer is: no intersections found.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0606feff b,#ff0404ff c,#fea2a3ff d,#8a89fdff e,#ff4747ff f,#ccccffff g,#4949ffff ``` ```image ceebbbbbbc ccebbbbbeec be cebbbbbbec bb ccebbbbbecc eb bbbbbeec eb cb cb bc a bc adad be a aa bb af gaf eb fa fag eb af aa cb fa daf cb af ag bc fa ga bc af fad be fa aa be af daf eb fa ag eb af aa cb fa dad cb a aa bc fa ga bc a fad be da aa be a daf eb da ag eb a ga cb da fad cb a aa bc da gaf bc a fag be da aa be a dafbb dg ageb a gacb dg fadb a aa gg d a gg a gg a gg a gg a gd a gd a gd a ad a ad a ad a ad a af a af fa af fa af fa af fa af fa af fa af ``` <!-- end of image -->

This image might have some surprises. Let's look for intersections carefully. My next step is to analyze the details within each area. <!-- image --> ```palette Key,Color ,#fefefeff a,#e94543ff b,#0a0cfbff c,#fd0606ff d,#edf1efff e,#df9384ff f,#5f6ae9ff g,#b0d6b0ff ``` ```image d bf bd db fb bf b db bf bd db fb bf b db bf bd ddbddddddddddddddddddddddddddddddddddddddddddddd dggfbggggggggggggggggggggggggggggggggggggggggggggd dgggbfgggggggggggggggggggggggggggggggggggggggggggd dggggbgggggggggggggggggggggggggggggggggggggggggggd dgggggbggggggggggggggggggggggggggggggggggggggggggd dgggggbbgggggggggggggggggggggggggggggggggggggggggd g dggggggbgggggggggggggggggggggggggggggggggggggggggd bb dgggggggbgggggggggggggggeeaagggggggggggggggggggggd fbf dgggggggfbggggeeaccccccccaaceggggggggggggggggggggd dbb dgggeeaccbaccccaeeggggggggggcggggggggggggggggggggd fbd deeaccccccccaeeggbgggggggggggggggggecgggggggggggggggggggd dbb cccaaed dggggggggggbgggggggggggggggggacggggggggggggggggggd bbd dggggggggggbbgggggggggggggggggcagggggggggggggggggd dbf dgggggggggggbggggggggggggggggggceggggggggggggggggd bbd dggggggggggggbggggggggggggggggggcggggggggggggggggd fbf dggggggggggggfbgggggggggggggggggecgggggggggggggggd bb dgggggggggggggbfgggggggggggggggggacggggggggggggggd fbg dggggggggggggggbggggggggggggggggggcagggggggggggggd dbb dgggggggggggggggbggggggggggggggggggceggggggggggggdfbd dgggggggggggggggbbggggggggggggggggggcggggggggggggbf dggggggggggggggggbggggggggggggggggggecgggggggggbbd dgggggggggggggggggbggggggggggggggggggacggggggfbfgd dgggggggggggggggggfbggggggggggggggggggcaggggbbgggd dggggggggggggggggggbfggggggggggggggggggcegfbfggggd dgggggggggggggggggggbgggggggggggggggggggcbbggggggd dggggggggggggggggggggbgggggggggggggggggfbagggggggd dggggggggggggggggggggbbgggggggggggggggbbgacggggggd dgggggggggggggggggggggbgggggggggggggbbggggcagggggd dggggggggggggggggggggggbgggggggggggbfggggggcgggggd dggggggggggggggggggggggfbggggggggbbgggggggggcggggd dgggggggggggggggggggggggbfgggggfbfggggggggggecgggd dggggggggggggggggggggggggbggggbbgggggggggggggaaggd dgggggggggggggggggggggggggbgfbfgggggggggggggggcegd dgggggggggggggggggggggggggbbbggggggggggggggggggcgd dddddddddddddddddddddddddddddddddddddddddddddddc ec aa ce cd dc ec ca ce cd dc ac ca cd c ec ac ce cd dc ec ac ce cd dc ec aa ce c ``` <!-- end of image --> Let's get to the bottom of what's happening inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fa5559ff b,#0706feff c,#fe0707ff d,#e0d4f2ff e,#fea3a3ff f,#9393feff g,#4b49fdff ``` ```image dbbf fbbd gbg dbbf fbbd gbb bbg dbbf fbbd gbg dbbf fbbd gbb bbg deeeaaaa dbbf deeeaaaccccccccccca fbbd deeeaaacccccccccccccccaaaeecce gbgeaaacccccccccccccccaaaeeed accd deeeaaaccccbbaccccccccaaaeeed acc eaaaccccccccccccccabbaeeed cca cccccccccaaaeeed gbb dcca aaeeed bbg ecce dbbf accd fbbd acc gbg cca dbbf dcce fbbd ecce gbb accd bbg acc dbbf cca fbbd ecce gbg ecce dbbf accd fbbd aca gbb dcca bbg ecce dbbf ecce fbbd accd gbg cca d dbbf dcca fb fbbd ecce dbbb gbb ecce gbbbf bbg acc fbbbg dbbf cca dgbbbd fbbd dcca fbbbf gbg ecce dgbbgd dbbf accd fbbbf fbbd acc dgbbgd gbb ccgbbbf bbg fbbbgd dbbf gbbbce fbbd fbbbgaccd gbg dgbbgd acc dbbf fbbbf cca fbbd dgbbgd dcce gbb fbbbf ecce bbg dbbbgd accd dbbf gbbbf acc fbbd fbbbg cca gbg dgbbbd ecce dbbf fbbbf ecce fbbd dgbbgd accd gbb fbbbf aca bbg dgbbgd dcca dbbf fbbbf ecce fbbfbbbgd ecce gbbbbf accd ``` <!-- end of image --> An intersection is present within area A. My analysis indicates that there are two intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fa5256ff b,#0505feff c,#fd0809ff d,#c5c5ffff e,#ffaaaaff f,#8181ffff g,#3c3dffff ``` ```image d gg bd b fb bf b db gg bd b fb bf b db gg bd b fb bf b db gg d bd bb b eeaa fbf fb eeaccccccccaece bb eeaccbaccccaee c gbd eeaccccccccaee b ec dbg ccccaee db ac gbd gg ca dbg bd ce bb b c fbf fb ec bb bf ac fbd b ca bb db ce gbd gg c dbg bd ec gb b ac dbf fb ca bb bf ce fbf b cbb db gbc gg dbg ac bd gbd ce b dbg c fb bb c bf fbf ec b bb aa db fbf ce gbb c d c ec ca ce c ec ac ca ce c ec ac ca ce c ec ac ca ce c ec ac ca c c ec aa ce c ``` <!-- end of image -->

The hunt for intersections begins! Let's analyze this image closely. The image has some tight areas where segments are too close. I should investigate those closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#979cf4ff b,#fb0a0aff c,#0607fdff d,#febfbfff e,#add4adff f,#ef6760ff g,#4a4df4ff ``` ```image d bbd dbd b fb db bb fb dbf fb fb bf bb bf bf bd dbd b fb db a bb fb ga dbd fb c fb bf gg bb bf eeeceeeeeeeeeeee bf bd eeeggeeeeeeeeeeedbd b eeeeceeeeeeeeeebb db eeeegceeeeeeeebb db eeeeeceeeeeeebfe fb eeeeeaceeeefbeee bf eeeeeeceeebbeeee bf eeeeeeacebfeeeee bd eeeeeeecbeeeeeee b eeeeeebbceeeeeee db eeeeebbecaeeeeee db eeeebfeeeceeeeee fb eefbeeeeecaeeeee bb ebbeeeeeeeceeeee bf eeeeeeeeeecgeeee bd eeeeeeeeeeeceeee b eeeeeeeeeeeggeee db eeeeeeeeeeeeceee db gg fb c bbeeeeeeeeeeeeec gg ebfeeeeeeeeeeece c eebfeeeeeeeeecee ac eeebeeeeeeeecaee c eeeebeeeeeecaeee ac eeeefbeeeecaeeee c eeeeefbeecgeeeee ac eeeeeebbcgeeeeee c eeeeeeecgeeeeeee c eeeeeecgbfeeeeee ca eeeeecgeebeeeeee c eeeecgeeeebeeeee ca eeecceeeeeebeeee c eecceeeeeeefbeee ga egceeeeeeeeebbee c gceeeeeeeeeeebfe gg gceeeeeeeeeeeeebf c gceeeeeeeeeeeeeeeb gg ac c ac ac ac c ac ac ac c c ac c c c c c ca c c ca ca ca c ca ca ca c ca gg cg c cg gg cg c cg gg cg c cc ac gc c gc ac gc c gc ac ac cgc c ``` <!-- end of image --> I'm going to scrutinize area A for any signs of an intersection. <!-- image --> ```palette Key,Color ,#fefefeff a,#7f7fffff b,#fd0a0bff c,#0404feff d,#ffbbbbff e,#bfbffeff f,#ff5c5cff g,#3b32f6ff ``` ```image ecce gcg ecce acg cce acg cce db acg fbb cca fbbf acc dbbbd cca dbbbd acc fbbf gca dbbbf ecc dbbbd gca fbbf ecc fbbf gcgbbbd eccbbd fgcg dbbbcce dbbbdacg fbbf ecce fbbf acg dbbbd cce dbbbd acg fbbf cce dbbbd acg dbbbd cca bf acc gca ecc gca ecc gca ecce ``` <!-- end of image --> Gotcha! I've found the intersection hiding in area A! Okay, on to the next area of interest. Let's zoom in on area B to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#8986fbff b,#fd0809ff c,#0505feff d,#feb1b1ff e,#cbcbffff f,#ff5555ff g,#3f39f8ff ``` ```image bbd fbb e bbb g bbf gc dbbf gcc dbbd gcce dbbd gcce fbbd gcce fbb gcce fbb gcce bbf gcce dbbf acce dbbd acca dbbd acca fbbd acca fbb acca fbbacca bbcca accg eccgbf eccgdbbd eccg fbbd eccg fbb eccg fbb eccg bbf eccg dbbf eccg dbbf gcg dbbd gcce fbbd gcce fbbd gcce fbb gcce bbf gcce bbf gcce dbbf cce dbb ``` <!-- end of image --> An intersection is present within area B. The image features two intersection points.

<!-- image --> ```palette Key,Color ,#fefefeff a,#7373ffff b,#fd0607ff c,#0303feff d,#ffb4b4ff e,#bcbcffff f,#ff4f4fff g,#3533fdff ``` ```image d bbd dbd b fb db bb db bd fb fb bf bb bd bf bd dbd b fb db e bf db ga dbd fb c fb bf ga bb bd c bf bd ag dbd b c fb db ag bf db c dbd fb ec fb bf c bb bf ec bf bd cbd b fbc db bf ce db dbd c fb fb ce bf bb c bf ga bd c b ga b c db ag fb c ff c ag bf ce c bd ce ag b ce c b ce ec db ce c fb ca ec fbca ce cg ec cabd ce cg bd c cg b ca gg db c gg fb ga gc fb c gc bf ga ac bd c ac b ag ac c ac ag ec c ec ec ec c ec ec ec ce c ec ce ce ce c ce ce ce c ce ga ca c ca ga ca c ca gg cg c cg ag gg c gg ag gc c gc ec ac c ac ec ac cac ec ``` <!-- 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,#f3504aff b,#494aedff c,#f0a19aff d,#9aa1eeff e,#fd0706ff f,#aed5aeff g,#0807fcff ``` ```image ffffffffffffffffff ffffffffffffffffff ffffffffffffffffff fffffffffffffbffff ffffffffffffggffff fffffffffffgbcffff fffffffffdgdefffff ffffffffbgfeffffff fffffffggfceffffff fffffdgdffefffffff ffffbgfffaefffffff fffggffffeffffffff ffgbffffaaffffffff bgffffffefffffffff ggffffffeafffffffff gbfffffffeffffffffff dg ffffffecffffffffff gg fffffcefffffffffff gb fffffeffffffffffff dgd ffffaeffffffffffff bg ffffefffffffffffff gb fffaafffffffffffff dgd fffeffffffffffffff bg ffeaffffffffffffff gg ffefffffffffffffff gd fecfffffffffffffff bg ce gg e gb ce dg e gg aa gb e dgd ec bg e gb ec c dgd e aa bg e ec gg ce e gb e ce gd aa ae dg e ec dg aa e bg e e gg ec aeffffffffffffffff gb e eafffffffffffffff gd e efffffffffffffffdg ce fefffffffffffffbg e faefffffffffffgg aa ffeafffffffffggf e fffecfffffffgbff aa ffffeffffffgdfff e ffffcefffdgfffff ec fffffaefbgffffff e ffffffeggfffffff ec ffffffggffffffff ce fffffgbcefffffff e ffffgdffaeffffff ce ffdgfffffeafffff e fbgfffffffefffff aa ggfffffffffeffff e gbffffffffffaefff ec gdffffffffffffeaff e dgd fffffffffffffecf ec dg ffffffffffffffef ce bg ffffffffffffffce e gg fffffffffffffffea ce gb ec e e aa ce e ae ec ec e e ec e e ae e ea ce e e e aa ce e aa aa ec e eec ce ``` <!-- end of image --> I'm focusing my attention on this specific region, area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd393aff b,#6060feff c,#ffbfbfff d,#b7b7ffff e,#fe0505ff f,#fb797cff g,#0a09fdff ``` ```image c e ea eef ceec feec aea eea ceef feec g aee dgg aea dggg ceef bggb ceec bggb fee bggd aea gggd ceef dgggd ceec dggg feec bggb aea bggb eef bggd ceegggd fgggd dggga bggbaea bggb ceef bggd feec dgggd fee dgggd aea dggb ceef bggb ceec bggb feec gggd aea dgggd eef dggg ceec ggb feec gb aea b eea ceef feec aee ae ce c ``` <!-- end of image --> My investigation has led me to an intersection in area A! Let's shift our focus to the next area. Here's a close-up of the area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#fc3336ff b,#6257f3ff c,#ffbfbfff d,#bcbafcff e,#fe0303ff f,#ff7979ff g,#0b09fcff ``` ```image bd bgg dgggb dggga bgggec dgggbea dgggdeec bggb aea bggb ceec dgggd aef bgggd cee bggb aef dgggd fee dgggd eef bggb fea dgggd ceec dgggd fea bggb ceec dgggb aef dgggd cee bggb aef bggb fee ggd eef gd fea eec fea ceec aef ceec aef fee eef fea eec fea ceec aea ceec aef cee aef fea eec fea ``` <!-- end of image --> Incredible, there's actually an intersection in area B! After a thorough search, I conclude that there are two intersections.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff3535ff b,#5350fcff c,#ffbebeff d,#aeadfeff e,#ff0303ff f,#ff7777ff g,#0907fdff ``` ```image b gg ggc dgde bg ec gb ce dgd e bg fa gg e gd af bg e gg ef gb e dgd ec gg ce gb e dgd fa bg e gb aa dgd e bg af gg e gd ec bg ce gg e gb fe dgd e gg fa gb e dgd af bg e gb ec c dgd ce aa bg ec ec gg ce e gb e ce gd fa aa dg e ef bg af e bg e ce gg ec fe gb ce ef gd ec ec dg ce e bg e fe gg fa aa gb e ec gb af e gd e ce dg ef aa bg e egg ec gg ce gbce e dgd fe fa dg ef e bg ec aa gg e e gb fe af gd aa e dgd ec ec dg e ce bg ce e gg aa fe gb ec e e fa ce e aa af ef e e ec ce ce fe ec ef ce ec e e fa fe e aa af ec e eec ce ``` <!-- end of image -->

I'm ready to tackle this image and find those intersections! There's definitely not a single intersection on the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#9d9dffff b,#ff0404ff c,#0303ffff d,#ff9999ff e,#4949ffff f,#ff4848ff g,#f3d8e4ff ``` ```image gd gddffbbbbbbbbbf gddffbbbbbbbbbffddg gddffbbbbbbbbbffddg gbbbbffddg bg ff b bd db b ff gb bg db b bd gb bg ff b bd db b ff gb bg db b bd gb bg ff b bd db b ff gb bg db b bd gb bg ff b bd db b ff gb bg db b bd gb bg ff b bd db b eccceeeaaag gcce gaaaeeecccccccccccceeeaaag acca gaaaeeecccccccccccceeeaa ece gaaaee acca eccg gcce acca ece acca eccg gcce acca ece acca ccg ``` <!-- end of image -->

I'm approaching this image with caution. Intersections might be tricky to spot. I've examined the entire image, and there are zero intersections present.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0303ff b,#0606ffff c,#9f9fffff d,#ff8c8bff e,#5050ffff f,#ffc8c8ff g,#ff4444ff ``` ```image f aaaaaaaagddf ad fdgaaaaaaggdf faf fdgaaaaaaagdf da fdggaaaaaagdf ga fddgaaaaaa ga ag ag ad faf da ga aa ag ad faf faf da ga aa ag ad faf da ga ga ag ag ad faf da g bc bb cbe ebc bb bb cbe ebc bb cbe ebc bb bb cbe ebc bb cbe ebc bb ccce bb ccceebbbbbbbbbbbbbeec cbe ccceebbbbbbbbbbbbbeeccc ebbbbbbbeeccc ``` <!-- end of image -->

This is the image I'm working with. The goal is to count the intersections. These regions highlight areas that look suspicious. Lines seem to converge within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#0b0bfeff b,#f84c49ff c,#696bf9ff d,#fe0404ff e,#faa3a1ff f,#bebeffff g,#aed5aeff ``` ```image gggggggggggggggg gggggggggggggggg gggggggggggggggg ee gggggggggggggggg bddddddddbbee gggggggggggggggg eebbddddddddbbee gggggggggggggggg eebbddddddddbbbegggggggg ggggebbddddddddddddddddddbbbeeeee gggggggggggggggg eeeebbbbdddddddddddddddddbb gggggggggggggggg eee gggggggggggggggg gggggggggggggggg gggggggggggggggg gggggggggggggggg gggggggcgggggggg ggggggaagggggggg ggggggagaggggggg gggggacgacgggggg ggggcagggagggggg ggggaggggcaggggg ca af a a ac ca fa af af a ca ca a af ac fa a ac af a fa fa a ac ca a a fa ac af fa a af ca ca af a a ac ca a a af fa fa ac a a cc fa a ac ac a fa ca a af ca a a ca ac af a a af cc fa a a fa cc ac a a af fa fa ac a a ca ca a af ac a a ca af af fa a a ac cc a a fa af ac fa a a fa ca af a a ac ca f af a ca af fa ac a ``` <!-- end of image --> My goal is to determine if there's an intersection inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0808ffff b,#ff3b3bff c,#6060ffff d,#ff0303ff e,#ffbfbfff f,#b6b6ffff g,#ff7e7eff ``` ```image gggeee dddddddddbbbgggeeeee ggbbbdddddddddddddddddddddbbbbb eeegggbbbbddddddddddddd eeeeeeg ff faaf caaa faaaac aacfaaf caa caa aaf aac cac faaf faaf caa ``` <!-- end of image --> After careful examination, I've determined that there's no intersection in area A. The image is completely devoid of intersections. Zero.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0505ffff b,#ff4949ff c,#8585ffff d,#ff0303ff e,#ffa5a5ff f,#c8c8ffff g,#4141ffff ``` ```image ee bddddddddbbee eebbddddddddbbee eebbddddddddbbeee eebbdddddddddddddddddbbbeeeee eeeebbbbdddddddddddddddddbb eee c ga afa af ac fa a a ca gg ac a a ac ca fa af af a ca gg a af gg fa a gg af a fa fa a ac gg a a ca ac ac fa a af ca ca af a a gc gg a af af fa fa gg a a gg fa a ac ac a fa ca af af ca a a cg gc af a a af gg fa a a fa gg ac a a ac fa fa ac af a ca ca a af gc a a gg af af ca fa a gg gg a a fa ac ac fa a a ca cg ac a a gc ca f af a gg af fa gg a ``` <!-- end of image -->

Let's examine this image for potential line intersections. These regions highlight areas that look suspicious. Lines seem to converge within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#e16f64ff b,#0606fdff c,#fa0b0bff d,#8795e3ff e,#b1d7b0ff f,#4448eeff g,#eff3efff ``` ```image ge geaacccccccc geaaccccccccaag geaaccccccccaag geaaccccccccaag gccccaag ggggggggggggggggggggggggggggggggggcg geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecg geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecag geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeceg geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecaeg geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeceeg geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecaeeg geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeceeeg geeeeeeeeeeeeeeeeeeeeeeeeeeeeeecaeeeg geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeceeedb geeeeeeeeeeeeeeeeeeeeeeeeeeeeecaeeebfb geeeeeeeeeeeeeeeeeeeeeeeeeeeeeceeedbgff geeeeeeeeeeeeeeeeeeeeeeeeeeeecaeeebeg bd geeeeeeeeeeeeeeeeeeeeeeeeeeeeceeeffeg bg geeeeeeeeeeeeeeeeeeeeeeeeeeecaeeebeeg gb geeeeeeeeeeeeeeeeeeeeeeeeeeeceeebfeeg db geeeeeeeeeeeeeeeeeeeeeeeeeeaaeeebeeeg ff geeeeeeeeeeeeeeeeeeeeeeeeeeceeebdeeeg bd geeeeeeeeeeeeeeeeeeeeeeeeeaaeedbeeeeg bg geeeeeeeeeeeeeeeeeeeeeeeeeceeebeeeeeg gb geeeeeeeeeeeeeeeeeeeeeeeeaceedbeeeeeg db geeeeeeeeeeeeeeeeeeeeeeeeceeebeeeeeeg fb geeeeeeeeeeeeeeeeeeeeeeeaceeffeeeeeeg bd geeeeeeeeeeeeeeeeeeeeeeeceeebeeeeeeeg bg geeeeeeeeeeeeeeeeeeeeeeaceebfeeeeeeeg gb geeeeeeeeeeeeeeeeeeeeeeceeebeeeeeeeeg db geeeeeeeeeeeeeeeeeeeeeaceebdeeeeeeeeg fb geeeeeeeeeeeeeeeeeeeeeceedbeeeeeeeeeg bf geeeeeeeeeeeeeeeeeeeeaceebeeeeeeeeeeg bg geeeeeeeeeeeeeeeeeeeeceedbeeeeeeeeeeg b geeeeeeeeeeeeeeeeeeeaceebeeeeeeeeeeeg db geeeeeeeeeeeeeeeeeeeceeffeeeeeeeeeeeg fb geeeeeeeeeeeeeeeeeeeceebeeeeeeeeeeeeg bf geeeeeeeeeeeeeeeeeeceebfeeeeeeeeeeeeg bd geeeeeeeeeeeeeeeeeeceebeeeeeeeeeeeeeg bg geeeeeeeeeeeeeeeeeceebdeeeeeeeeeeeeeg gb geeeeeeeeeeeeeeeeecedbeeeeeeeeeeeeeeg db geeeeeeeeeeeeeeeeceebeeeeeeeeeeeeeeeg bf geeeeeeeeeeeeeeeecedbeeeeeeeeeeeeeeeg bd geeeeeeeeeeeeeeecaebeeeeeeeeeeeeeeeeg bg geeeeeeeeeeeeeeeceffeeeeeeeeeeeeeeeeg gb geeeeeeeeeeeeeecaebeeeeeeeeeeeeeeeeeg db geeeeeeeeeeeeeecebfeeeeeeeeeeeeeeeeeg ff geeeeeeeeeeeeecaebeeeeeeeeeeeeeeeeeeg bd geeeeeeeeeeeeecebdeeeeeeeeeeeeeeeeeeg bg geeeeeeeeeeeecadbeeeeeeeeeeeeeeeeeeeg gb geeeeeeeeeeeecebeeeeeeeeeeeeeeeeeeeeg db geeeeeeeeeeecadbeeeeeeeeeeeeeeeeeeeeg ff geeeeeeeeeeecebeeeeeeeeeeeeeeeeeeeeeg bd geeeeeeeeeecaffeeeeeeeeeeeeeeeeeeeeeg bg geeeeeeeeeecebeeeeeeeeeeeeeeeeeeeeeeg gb geeeeeeeeecabfeeeeeeeeeeeeeeeeeeeeeeg db geeeeeeeeecebeeeeeeeeeeeeeeeeeeeeeeeg fb geeeeeeeeaabdeeeeeeeeeeeeeeeeeeeeeeeg bd geeeeeeeecdbeeeeeeeeeeeeeeeeeeeeeeeeg bg geeeeeeeacbeeeeeeeeeeeeeeeeeeeeeeeeeg gb geeeeeeecdbeeeeeeeeeeeeeeeeeeeeeeeeeg db geeeeeeacbeeeeeeeeeeeeeeeeeeeeeeeeeeg fb geeeeeecffeeeeeeeeeeeeeeeeeeeeeeeeeeg bf geeeeeacbeeeeeeeeeeeeeeeeeeeeeeeeeeeg bg geeeeecbfeeeeeeeeeeeeeeeeeeeeeeeeeeeg b geeeeacbeeeeeeeeeeeeeeeeeeeeeeeeeeeeg db geeeecbdeeeeeeeeeeeeeeeeeeeeeeeeeeeeg fb geeeacbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg b geeecbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg geeaabeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg geecbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg geaffeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg gecbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg gebfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg gcbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg gbdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg cbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg bggggggggggggggggggggggggggggggggggg ``` <!-- end of image --> This is a magnified view of the region A. <!-- image --> ```palette Key,Color ,#fefefeff a,#f74047ff b,#0404feff c,#fe0405ff d,#9593fcff e,#fd9798ff f,#433df9ff g,#efd8e8ff ``` ```image a gc cc ca gce ce ec cc eca ecc cce cc ce ce ec ac d ace db cc bb ce bf ecg gbd gcg gbg ac fb gcc dbb gccg dbb aca bbd ccg bf ca gbd aa gbg gcg fb ac dbb gcc bbd gcce bd eca df cce gbd ce gbb ea fbf ce dbbg ec bbd ecc bd cce df cc gbd ce fb ae fbf ec dbbg ac bbd ace bd eccg df ace gbd ccg fb gcg fbf aa bbg gcg bd gcc bd aca db gccg gbb aca fbf ca fbf gcg bbg aa bd gcg db gcc db eca gbb cce fbf ce fbf ea bbg ce bd ec db ecc db ccegbb ecc fbf cc bf ce dbg ec fd ae db ac dbf eccgbbd acefbf gccgbbg ccgdbg ca fd gcgdb gcgdbf acgbbd gccfbf acabbg cadbg gcgfd aadb gcebb gccbbd ecabf ccebg ccdbg cafb cdbb eabbd ecbbd ccbf ecabg cabg cbb eabb abbd acbd ecff acbg gcfb cbbd abb gbbd gcbd aff ``` <!-- end of image --> This close-up reveals that there are no intersections in area A. I'm extremely confident. No intersections at all.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fc5659ff b,#0605feff c,#fd0607ff d,#8383ffff e,#ffb1b1ff f,#423ffcff g,#c3c3ffff ``` ```image e eaaccccccca eaacccccccaaee eaacccccccaaee eaacccccccaaee ecccaaee ce c ce c ce c ce c ce c gb ce bdb c db ff aa b bd c ff b aa b gb c bd db aa b ff c bg bd aa gb bg c b b aa db db c b ff aa ff bd c b bg ec bd b c b gb ec bg fb c gb bd ec b bg c db b ec b gb c ff fb ec b bf c bd bg ec b b ce bg gb c gb db ce b bf c db bg ce b b c ff gb ce b db c fd ff ce b bd c bg b cegb gb c b db cadb ff c b bd aaff bg c b b aafd db c b fb aabg bd cgb bg aab b cdb gb aab fb cff bd acb bg cfd b ecb gb cbg fb ecb b cbg eab cb eff cb ebd cb ebg cb bg ``` <!-- 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,#1a1afdff b,#ed544cff c,#e99b91ff d,#fc0707ff e,#656aceff f,#b1d7b1ff g,#98c698ff ``` ```image fffffffffffffffffffffffffffffffg fffffffffffffffffffffffffffffffg fffffffffffffffffffffffffffffffg fffcfffffffffffffffffffffffffffg fffdbffffffffffffffffffffffffffg fffadffffffffffffffffffffffffffg ffffacfffffffffffffffffffffffffg ffffeafffffffffffffffffffffffffg fffffaeffffffffffffffffffffffffg fffffgaffffffffffffffffffffffffg ffffffeafffffffffffffffffffffffg ffffffgaeffffffffffffffffffffffg fffffffdaffffffffffffffffffffffg fffffffgeafffffffffffffffffffffg ffffffffdaeffffffffffffffffffffg a ffffffffcdaffffffffffffffffffffg aa fffffffffdeafffffffffffffffffffg aa fffffffffcdaeffffffffffffffffffg aa ffffffffffdfaffffffffffffffffffg aa ffffffffffcdeafffffffffffffffffg aa fffffffffffdfaeffffffffffffffffg aa fffffffffffbdfaffffffffffffffffg aa ffffffffffffdfeafffffffffffffffg aa ffffffffffffbdfaeffffffffffffffg aa fffffffffffffdffaffffffffffffffg aa fffffffffffffbbfeafffffffffffffg aa ffffffffffffffdffaeffffffffffffg aa ffffffffffffffbbffaffffffffffffg aa fffffffffffffffdffeafffffffffffg aa fffffffffffffffbbffaeffffffffffg aa ffffffffffffffffdfffaffffffffffg aa ffffffffffffffffbbffeafffffffffg aa fffffffffffffffffdfffaeffffffffg aa fffffffffffffffffdbfffaffffffffg aa ffffffffffffffffffdfffeafffffffg aa ffffffffffffffffffdbfffaeffffffg aa fffffffffffffffffffdffffaffffffg aa fffffffffffffffffffdcfffgafffffg aa ffffffffffffffffffffdffffaeffffg aa ffffffffffffffffffffdcffffaffffg aa fffffffffffffffffffffdffffgafffg aa fffffffffffffffffffffdcffffaaffg aa ffffffffffffffffffffffdfffffaffg aa ffffffffffffffffffffffdcffffgafg aa ffffffffffffffffffffffgdfffffaag aa fffffffffffffffffffffffdgfffffag aa fffffffffffffffffffffffcdfffffga aa ffffffffffffffffffffffffdffffffaa aa ffffffffffffffffffffffffcdfffffga aa fffffffffffffffffffffffffdfffffg a aa fffffffffffffffffffffffffcdffffg aa aa ffffffffffffffffffffffffffdffffg a aa ffffffffffffffffffffffffffcdfffg a aa fffffffffffffffffffffffffffdfffg ea aa fffffffffffffffffffffffffffbdffg a aa ffffffffffffffffffffffffffffdffg a aa ffffffffffffffffffffffffffffbdfg ea aa fffffffffffffffffffffffffffffdfg aaa fffffffffffffffffffffffffffffbbg a ffffffffffffffffffffffffffffffdg ffffffffffffffffffffffffffffffbb d bb d bb d dc d dc d dc d dc d dc d d dddbc ccbdddddddbc ccbddddddbbc ccbddddddbcc cbbddddddbcc cbdddd ``` <!-- end of image --> I'm eager to see what's happening in this magnified view of area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#4f4dfdff b,#fc5659ff c,#fea9a9ff d,#fd0809ff e,#a9a7fcff f,#0705fdff g,#710e9cff ``` ```image cc cdd ddc agd effdc affd ffgc effb affc ffg effe gff ffa gff bff dfe bgf dfa bffe cgff dffa ddffe bdgff cddafa bdbffe bdbafa cddeffe ddbeff cdd afa ddc ffe cdd eff ddc afa cdd ff ddc ef cdd aa ddc fe cdd ff ddc afa ddc eff bdb afa dd ffe bd eff dc afa bb ffe dc effe db afa ddc ffe bdb effe ddc afa bdb ffa bdb af cdd fa bdb efe cdd ff bdb ffa cdd effe bdb aff cdd ffa ddc effe cdd aff ddc ffa cdd effe cdd ffa ddc effe cdd aff dd ffa cd effe dc aff bd af dc efe db ef ddc fa bdb ffe ddc eff bdb afa bdb eff ddc afa bdb ff cdd ef bdb a cdd bdb cdd bdb cdd bdb cdd cdd ddc cdd dd cd dc cd dc dd ddc cdd ddc bdb bdb ddc bdb dd bd d ``` <!-- 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,#312efbff b,#ff4444ff c,#ff8b8bff d,#fe0405ff e,#9995fbff f,#0c0cfeff g,#f8ccd2ff ``` ```image g dc fd fc af fe gf af gfe df gaf dfe f gdf fa def fa gdfe fa d f fa cdef fa d fe fa cd f aa d ef aa cb fe aa d f aa cb ef aa d fe aa bb f aa d ef aa bb fe aa d f aa bc ef af d fe af bc f af d ef af bc ae af d f af dc ef af d aa af dc f af d gf af dg aa af gd f af dg gf af gd aa af dg f af gd f af dg aa af gd f af d f af cd aa af d fg af cd f af d aa af cb fg af d f af cb aa af d faf cb f d bb d bb d bc d bc d dc d dc d dg d dg gd dg gdddbcg gcbddddddbbcg gcbddddddbccg gcbddddddbcg gccbddddddbcg gcbdddd ``` <!-- end of image -->

This is the image I'm working with. The goal is to count the intersections. My next step is to analyze the details within each area. <!-- image --> ```palette Key,Color ,#ffffffff a,#0906f8ff b,#f70c0dff c,#5862d6ff d,#b1d7b1ff e,#eff6efff f,#d0655bff g,#84047bff ``` ```image eddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddde eddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddde eddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddde cddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddde caaddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddde bfcaacdddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddde efbbbaaadddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddde edddfbbgaacddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddde edddddddbbaaaddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddde eddddddddddfgaacdddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddde edddddddddddddfaaafddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddde eddddddddddddddddcaagfdddddddddddddddddddddddddddddddddddddddddddddddddddddddddde edddddddddddddddddddaagbbfdddddddddddddddddddddddddddddddddddddddddddddddddddddde edddddddddddddddddddddcaagbbfddddddddddddddddddddddddddddddddddddddddddddddddddde eddddddddddddddddddddddddaacfbbbdddddddddddddddddddddddddddddddddddddddddddddddde eddddddddddddddddddddddddddcaadfbbbfdddddddddddddddddddddddddddddddddddddddddddde edddddddddddddddddddddddddddddaacddbbddddddddddddddddddddddddddddddddddddddddddde edddddddddddddddddddddddddddddddcaadfbdddddddddddddddddddddddddddddddddddddddddde edddddddddddddddddddddddddddddddddcaabdddddddddddddddddddddddddddddddddddddddddde edddddddddddddddddddddddddddddddddddacbddddddddddddddddddddddddddddddddddddddddde eddddddddddddddddddddddddddddddddddddafbdddddddddddddddddddddddddddddddddddddddde edddddddddddddddddddddddddddddddddddddabdddddddddddddddddddddddddddddddddddddddde edddddddddddddddddddddddddddddddddddddcabddddddddddddddddddddddddddddddddddddddde eddddddddddddddddddddddddddddddddddddddagfdddddddddddddddddddddddddddddddddddddde edddddddddddddddddddddddddddddddddddddddabdddddddddddddddddddddddddddddddddddddde eddddddddddddddddddddddddddddddddddddddddabddddddddddddddddddddddddddddddddddddde eddddddddddddddddddddddddddddddddddddddddaafdddddddddddddddddddddddddddddddddddde edddddddddddddddddddddddddddddddddddddddddabdddddddddddddddddddddddddddddddddddde eddddddddddddddddddddddddddddddddddddddddddabddddddddddddddddddddddddddddddddddde eddddddddddddddddddddddddddddddddddddddddddcafdddddddddddddddddddddddddddddddddde edddddddddddddddddddddddddddddddddddddddddddagdddddddddddddddddddddddddddddddddde eddddddddddddddddddddddddddddddddddddddddddddabddddddddddddddddddddddddddddddddde edddddddddddddddddddddddddddddddddddddddddddddafdddddddddddddddddddddddddddddddde edddddddddddddddddddddddddddddddddddddddddddddcadddddddddddddddddddddddddddddddde eddddddddddddddddddddddddddddddddddddddddddddddagddddddddddddddddddddddddddddddde edddddddddddddddddddddddddddddddddddddddddddddddafdddddddddddddddddddddddddddddde edddddddddddddddddddddddddddddddddddddddddddddddcadddddddddddddddddddddddddddddde eddddddddddddddddddddddddddddddddddddddddddddddddagddddddddddddddddddddddddddddde edddddddddddddddddddddddddddddddddddddddddddddddddafdddddddddddddddddddddddddddde eddddddddddddddddddddddddddddddddddddddddddddddddddadddddddddddddddddddddddddddde eddddddddddddddddddddddddddddddddddddddddddddddddddcaddddddddddddddddddddddddddde edddddddddddddddddddddddddddddddddddddddddddddddddddacdddddddddddddddddddddddddde eddddddddddddddddddddddddddddddddddddddddddddddddddddadddddddddddddddddddddddddde eddddddddddddddddddddddddddddddddddddddddddddddddddddfaddddddddddddddddddddddddde edddddddddddddddddddddddddddddddddddddddddddddddddddddaadddddddddddddddddddddddde eddddddddddddddddddddddddddddddddddddddddddddddddddddddadddddddddddddddddddddddde eddddddddddddddddddddddddddddddddddddddddddddddddddddddfaddddddddddddddddddddddde edddddddddddddddddddddddddddddddddddddddddddddddddddddddgadddddddddddddddddddddde eddddddddddddddddddddddddddddddddddddddddddddddddddddddddacddddddddddddddddddddde eddddddddddddddddddddddddddddddddddddddddddddddddddddddddbaddddddddddddddddddddde edddddddddddddddddddddddddddddddddddddddddddddddddddddddddbadddddddddddddddddddde eddddddddddddddddddddddddddddddddddddddddddddddddddddddddddgaddddddddddddddddddde eddddddddddddddddddddddddddddddddddddddddddddddddddddddddddbacdddddddddddddddddde edddddddddddddddddddddddddddddddddddddddddddddddddddddddddddbadddddddddddddddddde eddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddgaddddddddddddddddde eddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddbacdddddddddddddddde edddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddbadddddddddddddddde edddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddfbaddddddddddddddde eddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddbcadddddddddddddde edddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddbacddddddddddddde edddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddfbaddddddddddddde eddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddbfadddddddddddde edddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddbacddddddddddde edddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddfbaddddddddddde eddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddbfadddddddddde edddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddbcaddddddddde edddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddfbacdddddddde eddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddbfadddddddde edddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddbdaddddddde edddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddfbcadddddde eddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddbdacddddde edddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddbdaddddde edddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddfbcadddde eddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddbdacddde edddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddbdaddde edddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddbbdadde eddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddbdcade edddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddbdace edddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddbfdae eddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddbdde edddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddbde edddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddbfe eddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddbe eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee ``` <!-- end of image --> Let's get to the bottom of what's happening inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0704fbff b,#fc0609ff c,#5140edff d,#f9a5aaff e,#a29efaff f,#fb565aff g,#9d0f70ff ``` ```image e caae eaaae bbbfdaaac fbbbfgaaae dfbbgcaae dfbbgaaae dbbaaac dbgaace gaaagd caaabfd eaaagbfd eaaagbbf aaacbbbbd eaaacbbbbd ecaaedbbbbfd caaae fbbbfd eaaac ffbf eaace bb eaaaebd caaeb aabb acb eaff aabb eagb acb aabf cab acf eabb cab aab cabf eag aaf agb eag caf agd aa aad eaf aa eag cad aa ead ac aa ac dae ca dac aa aa gae daa gae dga aa gae bac daae bca dbac dbaa faa bgae fbaa dgae bga dbaa fgae bbac fbaa dbcc bfac bbaa ffcc bdae fbca bdac bfaa bbca bfeae dbdaa bbeae dbdea bfaa bbeae bf ac dbdaa bb ca dbd ac bdea bb cc bd aa db ca bb ea db a bd bb dbd fb b ``` <!-- end of image --> Case closed! This is definitely an intersection point in area A. My analysis indicates that there are two intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0a06faff b,#fb0408ff c,#6058f6ff d,#f7a4abff e,#b1aefcff f,#fa4d51ff g,#86057dff ``` ```image e caa bfeaac fbbfcaa dbbgaae dfbaaa fgaae daaad caagf aagbbd caagbbf eaacfbbf caaedbbbd eaac dfb caa ff eaab acb aff ab cab agf ab eab caf ab ab eaf ag ab ead ca ag ad ea ag ad a ca ac a fa ac ae fa ga ac fa ba ga fae ba dga bac ba dba bca bae dba bda bac dbae bda bca dbac bda bea fbca bdae b a ffea bdac b a ff a b ca b ae ff a b db bf b ``` <!-- end of image -->

This image seems promising for intersection detection. I'd describe these as 'hotspots' for potential intersections. <!-- image --> ```palette Key,Color ,#fefefeff a,#0808feff b,#fe0706ff c,#b5b5ffff d,#f85350ff e,#fba4a2ff f,#5b60f5ff g,#acd4acff ``` ```image f a e ac dd ca b ac eb ca be a b fa db a b ff b a bd ac b a eb ac be ca b a dd fa b a eb ff be a b af dd a b ac eb ca be a b ca eb a be ff b a dd af b a eb ac be ca b a dd ca b a eb ff be a b af db a b ac b ca bd ac b ca eb a be fa b a dd ff b a eb ac be a b ac db ca b gggggggggggggaggg b ggggggggggggfaggg bd ggggggggggggagggg b gggggggggggffgggg eb gggggggggggaggggg be ggggggggggafggggg b ggggggggggagggggg ddgggggggggaggggggg dbbbbdegggaggggggg aa ggggdbbbaddgggggg caac gggggggfaedbbbbdg caac gggggggagggggggdbbbbde aac ggggggffggggggggg edbbbbe aac ggggggagggggggggg edbbbbde aaf gggggafgggggggggg dbbbbde aaf gggggaggggggggggg edbbbbe faf ggggafggggggggggg ed faf ggggagggggggggggg faa gggaggggggggggggg faa ggfaggggggggggggg caa a caa ff caac a caac af aac a aacac aa ``` <!-- end of image --> I'm focusing my attention on this specific region, area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0504feff b,#fd0608ff c,#8282ffff d,#fd595aff e,#feababff f,#423cf8ff g,#c9c8fdff ``` ```image fac caa aac caa aag caf gaag faf gaag fac caa aac caa aac caf e gaag bbbddee faf dbbbbbbbbdee gaag eddbbbbbbbbddefac eedbbbbbbaaddee eedaafbbbbbbdde caageddbbbbbbbbddee aac eedbbbbbbb caf eeddb gaag faf gaag faf gaag fac caa aac caf aag caf gaag faf gaag ``` <!-- end of image --> Oh my, look at that! It's an intersection in area A! The image features one single intersection point.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0606feff b,#ff0707ff c,#9797ffff d,#fe5253ff e,#ffa1a1ff f,#4b4bffff g,#e3d5f1ff ``` ```image c a e ac dd ga b ag eb ca be a b cf db a bg ff gb a bd ac b ga eb ag be ca b a dd ca b a eb ff be a b ac dd ga bg ag gb ga be ag b ca eb a bg ff gb a dd ac b a eb ac be ga b ag dd ca b a eb ff be a b ff db a bg ac gb ga bd ag b ca eb a be cf b a dd ff b a eb ac be ga b ag db ca bg a gb ca bd a b ff eb a be ac b ga ddg ag dbbbbde ga aag ebbbade gaag caedbbbbdg gaac a gdbbbbde gaac ff edbbbbe aac a edbbbbdg aac ac gdbbbbde faf a edbbbbe faf ac ed faf ga faf ag caa ca caa a caag ff caag a gaag ff gaac a gaacac aa ``` <!-- end of image -->

This image seems promising for intersection detection. These spots mark what I'd call 'danger zones' - areas where intersections are more likely. <!-- image --> ```palette Key,Color ,#fefefeff a,#f15452ff b,#4d52f5ff c,#0607fdff d,#fe0808ff e,#a0a4f6ff f,#f8a4a1ff g,#aed5afff ``` ```image f fd fd d d df df da da ad ad fd fd d d df df da dd ad fd fd d d d df df da dd ad fd fd d d df df da cb da ce ad c ad c fd ec fd bc d cb d cegggggggggggggggggggg df cgggggggggggggggggggg df cggggggggggggggggggg da ecgggggggggggggggggg da b gbcggggggggggggggggg ad cc ggccgggggggggggggggg fdd ece gggcbggggggggggggggg add bc ggggcegggggggggggggg dda cb gggggcgggggggggggggfddf ece ggggggcggggggggggadd cc ggggggbcgggggggddagg cb gggggggbcgggfddagggg bc ggggggggcbaddggggggg cc ggggggggdcaggggggggg ece ggggggddagcggggggggg bc gggaddfggggcgggggggg cb gaddgggggggecggggggg ece ddaggggggggggbcgggggg cc fddfgggggggggggggcbggggg cb add ggggggggggggggcbgggg bc dda gggggggggggggggcgggg cc f ggggggggggggggggcggg ece ggggggggggggggggecgg bc gggggggggggggggggbcg cb ggggggggggggggggggcc ece gggggggggggggggggggcb cc ggggggggggggggggggggce cb c bc c cc ec ece bc bc cb cb ce ece c cc c cb ec ``` <!-- end of image --> This close-up of area A is like examining a piece of evidence. <!-- image --> ```palette Key,Color ,#fefefeff a,#f04f5dff b,#3936fcff c,#0404feff d,#fe0909ff e,#c2c2feff f,#ffa3a3ff g,#7878ffff ``` ```image e ce cb bcb eccg eccg gcce gcce bcc bcb eccb eccg ecce gcce bcce bcb ccb fd eccg addd eccg faddddf gcce fddddaf gcce adddda bcb faddddf bcb fddddaf eccg adddda eccadddf faaccaf fddddbcce faddddf bcc fadddaf bcb fddddaf eccb adddda eccg faddddf ecce fddddaf gcce ddda bcce df bcb ccb eccg eccg gcce gcce bcb bcb eccg eccg gcce gcce bcc bc c e ``` <!-- end of image --> My investigation has led me to an intersection in area A! There's only one, but is an intersection after all.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fb4b4eff b,#4e4effff c,#0606ffff d,#ff0707ff e,#a5a5ffff f,#ff9a9aff g,#efdbeaff ``` ```image f fd gd gd dg df df da da ad ad fd gd gd dg df df da da ad fd fd gd gdg dg df df da ad ad fd fd gd dg dg df g da cb da ce ad cg ad gc fd ec fd bc gd cb dg ce dg cg df gc da ec da b bc ad cc cb fdd ece ce add bc ce gdda cb c fddf ece gc addg cc ec dda gcb bc fddf bcg cbfddg cc aca ece gddf cg bc fddg gc cb ada ec ece gddf bc cc fddf cb gcb add ce bcg dda cg cc g c ece ec bc bc cb bb ece cb cc ce gcb c bcg gc cc ec ece bc bc cb cb ce ece cg cc gcgcb ecg ``` <!-- end of image -->

Based on a first glance, I suspect there could be intersection regions here. I've noticed 1 areas of interest. These could be potential intersection zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#f35c57ff b,#676cf5ff c,#fe0808ff d,#0a0afdff e,#ffadadff f,#bcbcfeff g,#aed4adff ``` ```image e acce ccce eccc ecca acca acce acce eccce ecca ecca acca acce ccc ca ca ce c c ec ac cc ca ce c c ec ac ac ca ce ce c ec ec ac ca ca ce c c ec ac ac cagggggggggggggg gcaggggggggggggg ggcggggggggggggg gggcgggggggggggg ggggcggggggggggg ggggacgggggggggg gggggacggggggbdddd ggggggcabdddddbg gggbdddddbgggggg fbddddbggggcggggggg fbddddbfgggggggggcgggggg fdddddb ggggggggggcggggg bddddbf ggggggggggacgggg fbddddbf gggggggggggacggg bdddbf ggggggggggggccgg fdd gggggggggggggcag dd ggggggggggggggca bdf c fdb c dd ec ddf e bdb fdd ddf bdb fdd dd bdf fdb dd ddf bdb fdd dd bdb dd ``` <!-- end of image --> Let's put area A under the microscope. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe3c3dff b,#5654fcff c,#ff0504ff d,#0503fdff e,#fd8687ff f,#aeaefeff g,#ffcacaff ``` ```image ca cca gcca gcce ecce eccg accg acc aca gcca gcce gcce eccg eccg accg fbbd aca ffbbdddddd gccaffbbdddddddbbff ffbddddddddbbff fbbddddddddbbf ffbbddddddddbffecce ddddddbbff eccg dbbff accg aca aca gcca gcce ecce eccg accg accg aca gcca gcce gcce ecc ``` <!-- end of image --> There's no doubt about it - this is an intersection in area A. The final count is: one intersection.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fe4445ff b,#4d4cfdff c,#ff0505ff d,#0505ffff e,#ff9090ff f,#a4a4ffff g,#ffccccff ``` ```image e acce gaccg gccag ecca ecca acce acce gcccg gcca ecca ecce acce gacc ca ce cg c gc ec ac aa ca ce cg c gc ec ac ca ce cg c gc ec ac ca ce cg cg gc gc ec aa ca ce cg c gc ec ac fbddd cafbdddbf fddddbf fbddddbf cg fbddddf c fbdddbf gc fddddbf ec fbddddbf ac bdddb aa fdb ca dd ce bdf cg fdb c dd gc bdf e fdb dd dd bdf fdb dd bdf fdb dd ddf fdb fdd dd bdf db ``` <!-- 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,#0505feff b,#f55f5aff c,#aeaefeff d,#fe0808ff e,#feb4b4ff f,#5458f6ff g,#acd4adff ``` ```image c caaaaaafc a ccfaaaaafcc ca cfaaaaaffc a cfaaaaaafc a ccfaaaaafcc ac cfaaaaaff a cf ff a ff a ca a ca a a ac a ff a ff a ca a ca ac a ac db gggggggggggagggg ddb ggggggggggffgggg bdb ggggggggggaggggg bdd gggggggggffggggg bdd gggggggggagggggg eddggggggggfagggggg eddggggggaggggggg ggddbgggaggggggg ggggddbagggggggg ggggggdabggggggg ggggggafbdbggggg ggggggagggbddggg gggggffgggggbddg gggggaggggggggbdd ggggffggggggggggedde ggggaggggggggggg edde gggfaggggggggggg dde gggagggggggggggg dde gggagggggggggggg dd ggaggggggggggggg bde a dd ac edb a dd ff edb a bde ff dd a bde ca dd a edb ca dd ac edb a bde ac dd a bde ff dd a edb ff dd a edb ca bde a dd ca bde ac dd a edb ac dd a edb ff b a ff a ca 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,#ff5f5fff c,#8b8bfeff d,#fd0809ff e,#ffb6b6ff f,#4641faff g,#cbcbfeff ``` ```image aac caa fac gaa fac gaa faf gaag caf aag caf aac db caa dddbe fac ebdddbe gaa ebdddbe fac ebdddde gaag bdddde faf bddddbgaag edddfaf edaadb caadddbe aacebdddbe caa ebdddbe fac ebdddde gaa bdddde fac bdddd gaag edd faf e gaag caf aag caf aac caa fac gaa fac gaag faf ``` <!-- 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,#0505ffff b,#ff5e5eff c,#8888feff d,#fe0909ff e,#ffb2b2ff f,#4545ffff g,#c9c9ffff ``` ```image g caaaaaafc a gcfaaaaafcg ga gcfaaaaafcg ag gcfaaaaafc a gcfaaaaafcg ag gcfaaaaafc a gc fc a ff a ca a ga ag a ag a fc a cf a ca a ga ag a ac db a ddb fc bdb a bdd cf bdd a edd ca edde a dde ga ddeag dab acbdb a bdd fc bdd a edd cf edde a edde ca dde a dde ga dd ag bde a dd ac edb a dd fc edb a bde cf dd a bde ca dd a edb ga dd ag edb a bde ac dd a bde fc dd a edb cf dd a edb ca bde a dd ga bde ag dd a edb ac dd a edb fc b a cf a ca a ``` <!-- end of image -->

The hunt for intersections begins! Let's analyze this image closely. Could these regions be concealing intersection points? Let's find out. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd0707ff b,#5d66ebff c,#0607fdff d,#fda8a8ff e,#9ac398ff f,#b0d6b1ff g,#ed574fff ``` ```image d ad a ad da a da a gg a gg a ad a ad da a da a gg faeeeeeeeeeeeeee eggfffffffffffff efafffffffffffff a efagffffffffffff ad effaffffffffffff gg effaefffffffffff da effeafffffffffff a efffafffffffffff efffffffffffffffffae b efffgaffffffffff fffffffffffffffffage bccb effffaffffffffff ffffffffffffffffgafe bccf effffggfffffffff ffffffffffffffffaffe ccceffffafffffffff fffffffffffffffaeffe bccbffggffffffff ffffffffffffffagfffe effbccbaffffffff fffffffffffffgaffffe efffffbccbffffff fffffffffffffafffffe efffffffacccefff ffffffffffffaefffffe efffffffaefeccce fffffffffffagffffffe efffffffeaffffbccb ffffffffffgafffffffe effffffffaffffff bccb fffffffffeaffffffebbbcc effffffffgafffff bccb ffeebbbcccccccccccbbbf efffffffffafffff ccc fbbbcccccccccccbbbeagfffffffffe efffffffffggffff fccccccccccccbbbf fffffffgaffffffffffe effffffffffaffff ffffffeafffffffffffe effffffffffagfff ffffffaffffffffffffe efffffffffffafff fffffagffffffffffffe efffffffffffadff ffffgafffffffffffffe effffffffffffaff fffeaffffffffffffffe effffffffffffaef fffafffffffffffffffe effffffffffffeae ffagfffffffffffffffe a fgaffffffffffffffffe da eafffffffffffffffffe a affffffffffffffffffe gg ageeeeeeeeeeeeeeeeeef a gg gd da a a ad ad a ag a da da a a ad da ag a da gg a a ad gd ag a ga ad a a a a ag da ga a a da a a ad gg ga a da gd a a ad aaa a ``` <!-- end of image --> This close-up might reveal an intersection in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0505ff b,#6359f4ff c,#0806fcff d,#ff8a8aff e,#ffcbcbff f,#b5b5feff g,#fd4b4dff ``` ```image eaae gag eaae gad eaa gad daa aad dag aae dag eaae gag eaae gad eaa aad daa aad dag aae dag f eaae ccbf gag cccccf eaae fbccccbf gad fbccccbf eaa bcccccbgad fbcccccbf fbccccbf bcccccbf aabbccccbf gag fbcccccbf eaae fbcccccb gag fbccc eaa fb gad eaa aad daa aad dag aae gag eaae gag eaa gad eaa aad daa aad dag aae gag eaae gag ``` <!-- end of image --> Area A contains an intersection. Moving on to the next area. This close-up might reveal an intersection in area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0607ff b,#4f4fffff c,#0504feff d,#ff8f8fff e,#ffcdcdff f,#aba9fdff g,#fb4649ff ``` ```image g da eaa gag gaa daae eaad aag gaa daae eaad aag gaa daae eaad aag gag daae eaad eaag gag daae eaad eaad ffff gagfffbbbbbcccccccc fffffbbbbcccccccccccccccccccccbb bccccccccccccccccccccbbbbbfffff cccccccbbbbbfffffaad ff gag gaae daae eaad gag gaa daae eaad aag gaa daae eaad aag gaa daae eaad aag gag daae eaad eaag gag aae ``` <!-- end of image --> Eureka! There's definitely an intersection in area B! The final answer is: two intersections found.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fe0505ff b,#6363feff c,#0808ffff d,#ff7f7fff e,#ffc4c4ff f,#b3b3ffff g,#ff3c3cff ``` ```image e ad a ae ea a ea a dg a gd a ad a ae ea a da a dg a gd a a ae ae a gg ae ea ea a a ae b da gg bccb a da bccf dg a fcccf a ae fccb gd ag bccba da bccf a acccf ae ae fccc ad ea fccb da a bccb ea ffbbcc da bccf ffbbcccccccccccbbff a cccf ffbbbcccccccccccbbffad dg fccccccccccccbbbff da a f ea gd a a ad ae ga a ea ae a ea ad a gg dg ea a a dg ae a gg gd ea a a ae ae a gg ae da ea a a ae dg ag a da dg a a ae gd ad a da ae a a ae ae ad ea da a ea dg a a ad dg ga a ea gd a a ad agg a ``` <!-- end of image -->

Let's examine this image for potential line intersections. These zones are intriguing. I bet there's something interesting happening within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0909ff b,#0505fdff c,#f4645fff d,#6168e8ff e,#c7c7ffff f,#add4acff g,#feb3b2ff ``` ```image g ag a ag ga a ga a cc a cc eb a beb ag db ebe a a b ebe ac ag dd be ga ga b be a a be be cc ga eb be a a be be ag cc eb be ca a b be a cc db be ag a b be ca ag dd be a a b be ag ag bd be ga ga b be a a be be ac ga eb be ga a b bdfffffffffffafff cc db bdfffffffffacfff a b fbdffffffffaffff cc dd ffbdffffffafffff ffffafffffffbfff fffbdffffcafffff ffffacfffffbdfff ffffbdfffaffffff fffffafffffbffff fffffbdfafffffff fffffaffffbdffff ffffffbdafffffff ffffffafffbfffff fffffffbdfffffff ffffffaffbffffff ffffffacbdffffff ffffffcadbffffff fffffcaffbdfffff fffffffabfffffff fffffaffffbdffff fffffffdbfffffff ffffacfffffbdfff fffffffbafffffff fffcafffffffbdff ffffffbdacffffff fffafffffffffbdf ffffffbffaffffff ffacffffffffffbd fffffbdffacfffff ffaffffffffffffbd fffffbffffafffff faffffffffffffffbd ffffbfffffafffff ac bd fffdbffffffaffff a bd fffbfffffffaffff a bd ffdbfffffffcafff ca bd b a a bd dd cc ag bd b a ca b be ac a eb a ag be ag ga eb a a b a ac db ga ga b a a dd ga ac b a ga bd cc a b a cc be ac a eb a ag b ag ca db a a b a ag dd ga ca b a a bd ga ag b a ga be cc a a ac ac ga a a aac a ``` <!-- end of image --> I'm now examining the contents of area A in detail. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd090aff b,#0404feff c,#fca7a9ff d,#7c7bffff e,#bcbcffff f,#ff6060ff g,#3c2ff1ff ``` ```image caa ebbe aac gbd caa ebb aac gbd faa dbb aac bbd faf dbg aa bbe faf dbg caa ebbe faf gbd caa ebb aac gbd caa dbb aacbbd fagbg abbe gbg ebba gbgaf ebbcaa gbd faf ebb caa bbd aac dbg caa bbe aac dbg faa ebbe aac gbg faf ebbe aa gbd faf ebb caa gbd faf dbb caa bbe aac ``` <!-- end of image --> As I suspected, there's an intersection within area A. Moving on to the next area. Could this be where the intersection is hiding, in area B? <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0707ff b,#0000ffff c,#feb0b0ff d,#7070ffff e,#9999ffff f,#ff5656ff g,#85168fff ``` ```image e caac be aaf bbe faa dbbe caac dbbe faf dbbe caa dbbe aac dbbe faf dbbe caa dbbe aac dbbe faf dbbe caac dbbe aaf dbbe faa dbbe caac dbbe aaf dbbgaa dbbgc gbbe fagbbe caacdbbe faf dbbe caa dbbe aac dbbd faf ebbd caa ebbd aac ebbd faf ebbd caac ebbd aaf ebbd faa ebbd caac ebbd aaf ebb faa eb caac e ``` <!-- end of image --> Aha! I've found an intersection inside area B! I can confirm there's two intersections in there.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0606ff b,#0505feff c,#ff8888ff d,#6965fbff e,#bbbbffff f,#ff4545ff g,#fec8c8ff ``` ```image g ac a ag ga a ca a cf a fc eb a beb ac db b a a b b ff ag dd be ga ga b be ag a be be ff ca b be a a be be ag cf eb be ca a b be a fc db be ag a b be ca ac dd be a a b be ac ag bd be ca ga b be a a be be ac ca eb be ga a b be a cf db be ff a b be ga fc dd be ag a b be ff ac bd be a a b be ag ag be bda ga eb bd a b agbd caeb ca bd ab a bd db ac bd ba ga bd bdfc a bd b a ac bd be ag ga bd eb a a bd be ag ff bd eb ga ga bd b a ag bd db ca ff bd b a a bd dd ff ag bd b a ca b be fc a b a ac be ag ca eb a a b ag ac db ga ga b a a dd ca ac b a ga bd ff a b a ff be fc ga eb a ag b ag ff db a a b ag ag dd ga ca b a a bd cf ac b a ca be ff a a ac fc ga a a aaf ga ``` <!-- end of image -->

I'm curious to see if this image contains any intersection points. I need to zoom in on these areas to get a better look. <!-- image --> ```palette Key,Color ,#fefefeff a,#fb0b0aff b,#0b0bfaff c,#e07164ff d,#6673deff e,#f0f3eeff f,#b2d7b1ff g,#a1cba0ff ``` ```image d dbbbe eggggggggggggggggggggggggggggggggggggggggggggggggggggggge dbbbde egfffffffffffffffffffffffffffffffffffffffffffffffffffffge edbbbd egffffffffffaffffffffffffffffffffffffffffffffffffffffffge ebbbde egfffffffffaagfffffffffffffffffffffffffffffffffffffffffge dbbbd egffffffffcagafffffffffffffffffffffffffffffffffffffffffge edbbbe egffffffffaffacffffffffffffffffffffffffffffffffffffffffge dbbbdfffffffacfffaffffffffffffffffffffffffffffffffffffffffge edbbbdffcaffffcafffffffffffffffffffffffffffffffffffffffge egffdbbbbgfffffagffffffffffffffffffffffffffffffffffffffge egfffffadbbbdffgaffffffffffffffffffffffffffffffffffffffge egffffcafffgbfffacfffffffffffffffffffffffffffffffffffffge egffffafffffdbfffafffffffffffffffffffffffffffffffffffffge egfffacffffffbdffcaffffffffffffffffffffffffffffffffffffge egffgaffffffffbfffaffffffffffffffffffffffffffffffffffffge egffafffffffffdbffcafffffffffffffffffffffffffffffffffffge egfacffffffffffbgffacffffffffffffffffffffffffffffffffffge eggaffffffffffffbfffaffffffffffffffffffffffffffffffffffge egagffffffffffffbbffacfffffffffffffffffffffffffffffffffge eaaffffffffffffffbgffafffffffffffffffffffffffffffffffffge eafffffffffffffffgbffcaffffffffffffffffffffffffffffffffge agffffffffffffffffbdffagfffffffffffffffffffffffffffffffge cagfffffffffffffffffbffgafffffffffffffffffffffffffffffffge eaegfffffffffffffffffdbffacffffffffffffffffffffffffffffffge aeegffffffffffffffffffbdffaffffffffffffffffffffffffffffffge ca egfffffffffffffffffffbffcafffffffffffffffffffffffffffffge a egfffffffffffffffffffdbffagffffffffffffffffffffffffffffge af egffffffffffffffffffffbgfgaffffffffffffffffffffffffffffge ca egffffffffffffffffffffgbffacfffffffffffffffffffffffffffge a egfffffffffffffffffffffbdffafffffffffffffffffffffffffffge ac egffffffffffffffffffffffbffcaffffffffffffffffffffffffffge ca egffffffffffffffffffffffdbffaffffffffffffffffffffffffffge a egfffffffffffffffffffffffbdfcafffffffffffffffffffffffffge ac egffffffffffffffffffffffffbffacffffffffffffffffffffffffge ea egffffffffffffffffffffffffdbffaffffffffffffffffffffffffge ae egfffffffffffffffffffffffffbdfacfffffffffffffffffffffffge ac egffffffffffffffffffffffffffbffafffffffffffffffffffffffge ea egffffffffffffffffffffffffffdbfcaffffffffffffffffffffffge ae egfffffffffffffffffffffffffffbgfagfffffffffffffffffffffge ac egfffffffffffffffffffffffffffgbfgafffffffffffffffffffffge ea egffffffffffffffffffffffffffffbdfacffffffffffffffffffffge ae egfffffffffffffffffffffffffffffbffaffffffffffffffffffffge ca egfffffffffffffffffffffffffffffdbfcafffffffffffffffffffge ea egffffffffffffffffffffffffffffffbdfagffffffffffffffffffge ae egfffffffffffffffffffffffffffffffbfgaffffffffffffffffffge ca egfffffffffffffffffffffffffffffffdbfacfffffffffffffffffge a egffffffffffffffffffffffffffffffffbgfafffffffffffffffffge af egffffffffffffffffffffffffffffffffgbfcaffffffffffffffffge ca egfffffffffffffffffffffffffffffffffbbfaffffffffffffffffge a egffffffffffffffffffffffffffffffffffbfcafffffffffffffffge ac egffffffffffffffffffffffffffffffffffgbfacffffffffffffffge ca egfffffffffffffffffffffffffffffffffffbdfaffffffffffffffge a egffffffffffffffffffffffffffffffffffffbfacfffffffffffffge ac egffffffffffffffffffffffffffffffffffffdbfafffffffffffffge ea egfffffffffffffffffffffffffffffffffffffbdcaffffffffffffge a egffffffffffffffffffffffffffffffffffffffbfagfffffffffffge ac egffffffffffffffffffffffffffffffffffffffdbgafffffffffffge ea egfffffffffffffffffffffffffffffffffffffffbgacffffffffffge ae egfffffffffffffffffffffffffffffffffffffffgbfaffffffffffge egffffffffffffffffffffffffffffffffffffffffbdcafffffffffge egfffffffffffffffffffffffffffffffffffffffffbfagffffffffge egfffffffffffffffffffffffffffffffffffffffffdbgaffffffffge egffffffffffffffffffffffffffffffffffffffffffbdacfffffffge egfffffffffffffffffffffffffffffffffffffffffffbfafffffffge egfffffffffffffffffffffffffffffffffffffffffffdbcaffffffge egffffffffffffffffffffffffffffffffffffffffffffbgaffffffge egfffffffffffffffffffffffffffffffffffffffffffffbcafffffge egfffffffffffffffffffffffffffffffffffffffffffffbbacffffge egffffffffffffffffffffffffffffffffffffffffffffffbgaffffge egffffffffffffffffffffffffffffffffffffffffffffffgbacfffge egfffffffffffffffffffffffffffffffffffffffffffffffbdafffge egffffffffffffffffffffffffffffffffffffffffffffffffbcaffge egffffffffffffffffffffffffffffffffffffffffffffffffdbagfge egfffffffffffffffffffffffffffffffffffffffffffffffffbdafge egffffffffffffffffffffffffffffffffffffffffffffffffffbacge egffffffffffffffffffffffffffffffffffffffffffffffffffdbage egfffffffffffffffffffffffffffffffffffffffffffffffffffbcae egggggggggggggggggggggggggggggggggggggggggggggggggggggbae bd b ``` <!-- end of image --> Let's see what secrets area A holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0506ff b,#0606feff c,#fe8586ff d,#5250fcff e,#fec8c8ff f,#b6b5fdff g,#fe4444ff ``` ```image g eaaae aagag aa aac gg ga ca eae bdf aa gg dbbbbbf cae aa fdbbbbdfeac aac fbbbbbd eaa aadbbbbd eae ag fbbbf cg ac bd aa ga bbf gag eaa dbd eaa aa fb ac eae dd ca ac fbf ac eaa bbd ga gag fbb eae aa db ca gg fbf aae ca bd gag eaa bbf eaa aae db ac eac fbf ca ae bd aae a bb gag g db aa fb gc bd eae bbf ag bb caa fbf aa db eae bbf eae dbd ag bb aa dd gg fbf eae bbd aac fbb caa db ga fb gg bd eae bb aa dd eaa fbf ga bb eae fbb ac db aa bf gag bd ga bbf ac bb ac fbf aae db gag bbf ca dbd ac bb eae dd aa fbf ca bb ac fbb ag db aae bf gag bd ca bb gc bd ag fbf aae bb caa fbb eae db gg bf eae bd aac bbfcaa dbb ga fbf gg dd ac bf aa dbdeaa bb ga dd ca fbf ac bb aa fbbeae db cg bf ac bdgag bbeaa db ga fbfca bb ac bbfaae dbeaa bfca bdeae bbfag dbbaae fbfaa ddca bfgg dbdag fbbaac dbcaa fbfae bbgg bbda dba ``` <!-- end of image --> Yes! I knew it! There's an intersection right here in area A! There's only one, but is an intersection after all.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fe0303ff b,#0807feff c,#fd7677ff d,#5958fdff e,#febdbdff f,#afaffeff g,#ff3333ff ``` ```image f dbbdf fbbbd dbbbf a fbbbd aae dbbbf ca a fdbbdf a gc fbbbd ae a dbbbf ca cg fbbbb ae adbbbf ea ea fb ac a fb a gc bf cg ea b a a db ea gc bf ae ea b a a dd gg gg b a a fb ea ae bd ae cg b a a fb gc ae bf a cg b cg a db ae ae bf ea ca b ac a dd a ac b cg ea fb a a bf ea ac b ae ea fb a a bf gg gc b a ea dd ea a b ae gg fb a a bd gc ae b a gg fb cg a bf ae ae b ea cg db ac a bf a ae b cg ca dd a a b ea ac fb ae ea bd a a b gg ac fb a ea bfea a b ae gc db a ea b gc a b a bdcg b ae fbea bfac b a dbcg bfa bea ddae b a fbgg bda bea fbae bfa bgc dba bcg ba dd b ``` <!-- end of image -->

I'm curious to see if this image contains any intersection points. These zones indicate regions where lines appear to be in close proximity. <!-- image --> ```palette Key,Color ,#fefefeff a,#ee7068ff b,#0809fdff c,#fd0a09ff d,#b5b5ffff e,#ffb0b0ff f,#6166f4ff g,#aed5aeff ``` ```image d fbbbbf dfbbbbfd fbbbbfd dbbbbbd dfbbbbfd dfbbbbfd fbbbbf bf bf bd bd bd b b db db db fb fb fb bb bb bf bf bf ec bd ceca bd ca cc bd ec ac b c ece b ca cc db ec ac db c ece db ca cc fb ec ac fb c ece fb ca ccgggggggggggbbggggggggggggggg ec ccgggggggggggbbgggggggggggggg c gacaggggggggggbfggggggggggggg ca gggccggggggggggbfgggggggggggg ec ggggccggggggggggbfggggggggggg c gggggacagggggggggbfgggggggggg ca gggggggccgggggggggbgggggggggg ec ggggggggccgggggggggbggggggggg c gggggggggacgggggggggbgggggggg ca gggggggggggccggggggggbggggggg ec ggggggggggggccggggggggbgggggg c gggggggggggggacgggggggfbggggg ce gggggggggggggggcaggggggfbgggg ec ggggggggggggggggccggggggfbggg c gggggggggggggggggacggggggfbgg ce gggggggggggggggggggcagggggbbg ac ggggggggggggggggggggccgggggbb c gggggggggggggggggggggacgggggb ce gggggggggggggggggggggggcagggg ac ggggggggggggggggggggggggccggg c gggggggggggggggggggggggggacgg ce gggggggggggggggggggggggggggca ac ggggggggggggggggggggggggggggc c ce ac c ce ac c ce ac c ce ac c ce ac c ce ac c ce ``` <!-- end of image --> Time to investigate area A up close. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff7676ff b,#0808feff c,#ff0404ff d,#b0b0ffff e,#ffbfbfff f,#5050ffff g,#ff3737ff ``` ```image a fbb cge fbb ccce bbb gcca bbf accge bbf eccce dbbf gcca dbbf accg dbbf eccce dbbf gcca dbbd accg dbbd eccce fbbd egcca fbbd accg fbbd eccce fbbd egcca fbbd accg fbb eccce fbb egcca bbb accg bbf eccce dbbf egcca dbbf accg dbbf accge dbbf egcca dbbf gccg dbbd accge dbbd egcca fbbd gcca fbbd accge fbbd eccce fbbd gcca fbbd accge fbb eccce bb gcca b accge eccce gcca accge eccce gcca accge eccce gcc ac ``` <!-- end of image --> This close-up reveals that there are no intersections in area A. I'm extremely confident. No intersections at all.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff6868ff b,#0505ffff c,#ff0909ff d,#8d8dffff e,#ffb2b2ff f,#4c4cffff g,#cdcdffff ``` ```image d fbbbbdg gfbbbbfg gdbbbbfd dfbbbfd gfbbbbdg gfbbbbfg gdbbbbf bf bd bd bg bg bg gb gb gb db db fb fb fb bf bf bf bd ec bd ceca bg ca cc bg ec ac bg c ece gb ca cc gb ec ac gb c ece db ca cc db ec ac fb c ece fb ca cc fb ec ac bf c ece bf ca cc bf ec cc bd c ece bd ca ca bg ec cc bg c ece bg ca ca gb ec cc gb c ece gb ce ca db ec cc db c ece fb ce ca fb ac cc fb c ace b ce ca ac cc c ac ce ca ac c c ce ac c ce ac c ce ac c ce ac c ce ac c ce ac c ce ``` <!-- end of image -->

This image looks interesting. I wonder if there are any intersections hidden in there? It's crucial to examine these regions more closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#0909feff b,#fa3130ff c,#b5b5feff d,#f7817dff e,#fd0303ff f,#afd4adff g,#5f63f6ff ``` ```image c caaa caaa ga aaac a gaac ca gaag a caag ca caag ac e caaac a ed gaac ag bb gaag a be gaag gg de caag a fe aaac ca e c a e ca ef ac ed a eb ag bb a be gg de a fe ga e a e ca ed ac ed fffafffffffffffeb fffagfffffffffbb ffffaffffffffbef ffffagffffffdeff fffffaffffffefff fffffgaffffeffff ffffffafffefffff ffffffgafedfffff fffffffaedffffff fffffffbafffffff ffffffbeagffffff fffffbeffaffffff ffffdefffagfffff ffffefffffafffff fffeffffffgaffff ffeffffffffaffff fedffffffffgafff edffffffffffafff ebffffffffffffaff bb ac de a de ag e a e gg e a ed ca ed a bb ca be ac de a be ag bed a bed gg bed a bed ga bed a bed ca bed ac bed a bed ac bed a bed gg bed a bed ga bed a bed ca bed ac bed ca ed ac a ag a gg a ``` <!-- end of image --> Let's put area A under the microscope. <!-- image --> ```palette Key,Color ,#fefefeff a,#0606feff b,#ff4c4cff c,#9b9bfeff d,#ff9595ff e,#fd0708ff f,#f3d8e3ff g,#4941f7ff ``` ```image gag f faac fe caa fee aac bee caa beef gac beef caaf deed gag deed faaf deed gag feeb faac feeb cag feeb aac beef caa beef aac beef caaf deed gagdeed caaeed gagb feaac feegag beefaac beef caa beef aac deed caa deed gag deed caaf feeb gag feeb faac feeb gag beef aac beef caa beef aac deed caa deed gac eed caaf eb gag ``` <!-- end of image --> I am surprised, so clear, an intersection has appeared in area A. After careful examination, I conclude that there is one intersection.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0606ffff b,#fe3132ff c,#9393ffff d,#ff8282ff e,#fe0203ff f,#decfefff g,#4b4bffff ``` ```image f caaa faagf gg faaaf a gaac ca gaac af caag fa caag ac e faaaf a eb gaac ac bb gaac a be caag gg de caag a fe aaaf ca fe f af ef fa ef af ed a eb ac bb a be gg de a fe ca e a ef fa ef af ed fa eb ac bb a de gg de a fe cg e a ef ca ed aed ba bbac de a de gg fe a e gg ef a ed ca ed af eb fa bb ac de a de ac fe a e gg ef a ed ca ed af bb fa be af de a be ac bed a bed gg bed a bed ca bed a bed fa bed af bed fa bed ac bed a bed gg bed a bed cg bed a bed ca bed af bed fa ed ac a gg a gg a ``` <!-- end of image -->

This image might have some surprises. Let's look for intersections carefully. My next step is to analyze the details within each area. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0808ff b,#0404ffff c,#7e80faff d,#f9a9a6ff e,#b2b2feff f,#add4afff g,#f95c59ff ``` ```image d gaag a gaa ad daad a daag a gaa ga daad a aag ag gaa a daad ad aag da gaa a daad gg aag a gaa ad daad da aag a gaa gg daad a aa ad da a ga a ad a a da a ag a ad da a gg e a bbc ad bc bc da be bc a be bc gg be bc a be bc ad eb bc da eb bc a eb bc ga eb bc a cb bc ag cb bc a cb bc ad cb bc fffffffffgafff cb bc fffffffffaffff bb bc ffffffffagffff bb be ffffffffafffff bb be fffffffadfffff bb be ffffffdaffffff bb be ffffffafffffff bc be fffffggfffffff bc be fffffaffffffff bc be ffffagffffffffbc be fffdaffffffffbe be fffaffffffffbc be fffffffffffbff be ffffffffffbfff be fffffffffbffff be ffffffffbfffff be ffffffcbffffff be eb be cb be cb be c be be be be be be be be be b ``` <!-- end of image --> I'm going to scrutinize area A for any signs of an intersection. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff0404ff b,#0707ffff c,#3131ffff d,#ff7373ff e,#d4d4ffff f,#ffb8b8ff g,#ff3636ff ``` ```image gad daa aaf dag faaf gad faa aad dag faaf gag faa aad dag faaf gag faaf gad daa aaf dag faaf gad c faa cb ff cbb cbbe ecbbe ecbbe ecbce ebbce ebbce ebbc ebbc ebbc ``` <!-- end of image --> The evidence suggests that this is not an intersection point in area A. My final answer is: no intersections found.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0404ff b,#0404ffff c,#7f7fffff d,#ff8282ff e,#b6b6ffff f,#ffc8c8ff g,#ff3e3eff ``` ```image f daad a gag ad daaf fa faad af gag da daaf a faad gd gag a daaf af faad da gag a daaf gg faad a gag af daaf fa faad a gaa gg daaf a faa ad fa a dg a ad fa af da a gd a af da a gg e a bbc af bc bc fa be bc a be bc gg be bc a be bc ad eb bc fa eb bc af eb bc dg eb bc a cb bc ad cb bc fa cb bc af cb bc da cb bc a bb bc gg bb bc a bb be af bb be fa bb be a bc be gg bc be a bc be ad bc be fa be be a be be be be be be eb be eb be eb be eb be cb be cb be c be be be be be be be be be b ``` <!-- end of image -->

This is the image I'm working with. The goal is to count the intersections. Could these regions be concealing intersection points? Let's find out. <!-- image --> ```palette Key,Color ,#fefefeff a,#0809fdff b,#fd0808ff c,#6970f2ff d,#eb5853ff e,#b1d7b2ff f,#f1a49eff g,#96c699ff ``` ```image eggggggggggggggggggggge geeeeeeeeeeeeeeeeeeeeeg gegeeeeeeeeeeeeeeeeeeeg geaceeeeeeeeeeeeeeeeeeg geeaeeeeeeeeeeeeeeeeeeg geeaceeeeeeeeeeeeeeeeeg geeeaeeeeeeeeeeeeeeeeeg geeeaceeeeeeeeeeeeeeeeg geeeeaeeeeeeeeeeeeeeeeg geeeeageeeeeeeeeeeeeeeg gebbeeaeeeeeeeeeeeeeeeg geedbdageeeeeeeeeeeeeeg geeeebbaeeeeeeeeeeeeeeg geeeeefadeeeeeeeeeeeeeg geeeeeegabfeeeeeeeeeeeg geeeeeeeagbbeeeeeeeeeeg geeeeeeegaedbdeeeeeeeeg geeeeeeeeaeeebbgeeeeeeg geeeeeeeecaeeegbbeeeeeg geeeeeeeeeaeeeeedbdeeeg geeeeeeeeecaeeeeeebbeeg geeeeeeeeeeaeeeeeeefbdg geeeeeeeeeecaeeeeeeeedbf geeeeeeeeeeeaeeeeeeeeegbb geeeeeeeeeeecaeeeeeeeeg fbd geeeeeeeeeeeeaeeeeeeeeg bb geeeeeeeeeeeecaeeeeeeeg bb a dbf ca bb a fbd cc dbf a bb cc fb a fb cc db a db cc bd a bd ac bf a b ac b a fb ac fb a db ac bb a bd ae bf a bf ae b a b a fb a db a db a bd a bf ea bf a b ea b a fb ca fb a db ca bd a bd ca bf a b ca bgggggggggggggggggg a gbeeeeeeeeeeeeeeeee cc edbeeeeeeeeeeeeeeee a eedbeeeeeeeeeeeeeee cc eeebbeeeeeeeeeeeeee a eeeebdeeeeeeeeeeeee cc eeeeebdeeeeeeeeeeee a eeeeeebfeeeeeeeeeee cc eeeeeeebeeeeeeeeeee a eeeeeeeebeeeeeeeeee ac eeeeeeeefbeeeeeeeee aaaaaaaaaaaaccce eeeeeeeeedbeeeeeeee ecccaaaaaaaaaaaaaccccgeeeeeedbeeeeeee ecccaaaaaaaaaaaaaeeee eeeeeeeeeeeebdgeeee eeeeeeeeeeeeebfeeee eeeeeeeeeeeeeebeeee eeeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeeeeee ``` <!-- end of image --> This close-up might reveal an intersection in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0404feff b,#fd0708ff c,#8484ffff d,#fb4b4fff e,#b7b6feff f,#ffa7a7ff g,#3a2ff3ff ``` ```image ee eaa gac caa aac cag aae cag aae cag aae cag aae cag aae df cag fbbbf aae fbbbd cag dbbbf aae fdbbdgag fbbbaae dbgag fdaad gagbf eaabbbf gagbbbd eaaedbbbf gac fdbbdf eaa fbbbd gac dbbbf eaa fbbbd gac fbbbf eaa dbbbf gac fbbbd eaa dbbbf gac fdbbdf eaa fbbbd gac dbbbf eaa fbbbd gac fbb caa d gac caa aac cag aae cag aae cag ``` <!-- end of image --> Case closed! This is definitely an intersection point in area A. Moving on to the next area. Could this be where the intersection is hiding, in area B? <!-- image --> ```palette Key,Color ,#fefefeff a,#0605feff b,#fd0506ff c,#5a5affff d,#f94146ff e,#abaafeff f,#fdcccdff g,#fd8b8cff ``` ```image dbbf dbd fbbd fbbd fbbg gbbg gbbf dbbf dbbf dbb bbd fbbd fbbg gbbg gbbg gbbf dbbf dbbf dbd fbbd fbbd fbbg gbbg gbbf dbbf cccceeeee dbbf aaaaaaaaaaaaaaaccccceeedbdf eecccccaaaaaaaaaaaaaaaaaaaaaaaac eeeeeccccccaaaaaaac fbbgeee gbbg gbbg gbbf dbb df ``` <!-- end of image --> Bingo! This close-up reveals an intersection in area B! There are precisely two intersections present in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0404feff b,#fe0808ff c,#7e7effff d,#fc575aff e,#bebefeff f,#ffadadff g,#4040ffff ``` ```image e ac a ae a ae a ae bb a dbfae bba fad eabf aebb ea fbd a bb ea bb a dbf ea bb a fbd ca dbf a bb ca fbd a bb cg bb a dbf cg bb a fbd cg dbf a bb gg fb a fb gc db a db gc bd a bd gc bf a b gc b a fb ac fb a db ae bb a bd ae bf a bf ae b a fb ae fb ea db ae db ea bd a bd ea bf a b ea b a fb ea fb a db ca bd a bd cg bf a bf cg b a fb cg fb a db cg db a bd gg bf a bf gc b a b gc fb aaaaaaaaaaaggccee db eeccggaaaaaaaaaaaggccee db eeccggaaaaaaaaaaag bde bf b ``` <!-- end of image -->

I'm on the case! Let's uncover any intersections hidden in this image. The image has some tight areas where segments are too close. I should investigate those closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd0808ff b,#0708feff c,#f2aaa4ff d,#9c9efbff e,#f56762ff f,#aed5aeff g,#4d4cf3ff ``` ```image d db b bd bg db b b bd gb db b bd bg db b b bd gb db b bd bg db b b ae bd a gb ca db ae b a bd ca bg ae db a b ca b ae bd a gb ca db ae b a bd ca bg ae db a b ca b ae bd a gb ca db ae b afffffffffffffff bd eaffffffffffffff bg faefffffffffffff db ffafffffffffffff b ffcaffffffffffff b fffaefffffffffff bd ffffafffffffffff gb ffffcaffffffffff db ca fffffaefffffffff dgb aa ffffffaffffffffdgbbbd aa ffffffcafffgbbbbd aac fffffffgbbbgdfff eae fffgbbbgafffffff caa dgbbbgffffcaffffff caa dbbbbdfffffffffaefffff aa gbbbgd ffffffffffafffff aac gbbbg ffffffffffcaffff eae bd fffffffffffaefff cae ffffffffffffafff caa ffffffffffffcaff aa fffffffffffffaef aac ffffffffffffffaf eac ffffffffffffffca eae fffffffffffffffae caa a aa ca aac ae eac a eae ca caa ae aa a aa cac ``` <!-- end of image --> I'm eager to see what's happening in this magnified view of area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0000ff b,#0706fdff c,#ffbcbcff d,#a9a9feff e,#fb676aff f,#fe1f1fff g,#5750f8ff ``` ```image ac af fae caac eaf fae caac eaf fae caac eaf fae caac eaf fae caac eaf fae caac eaf d fae dgbbb caac ddgbbbbbbb eaf ddgbbbbbbggd dgbbbbbbbgdd dgbbbbbbbgdd ddgbbbbbbbgeaf ddgbbbbbbggd fae bbbbbgdd caac bgdd eaf fae caac eaf fae caac eaf fae caac eaf fae caac eaf fae caac eaf fae caa ea f ``` <!-- end of image --> I am surprised, so clear, an intersection has appeared in area A. The final count is: one intersection.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fe0909ff b,#0706feff c,#ffb8b8ff d,#8080ffff e,#ff6b6bff f,#c1c1ffff g,#4742faff ``` ```image d fb b bf gg db b bf bd gb fb b bf bg db b bf bd gb fb b bf bg db b bf ae bd a gb ca fb ae b a bf ca bg ae db a b ca bf ae bd a gb ca fb ae b a bf ca bg ae db a fb ca b ae bd a gb ca fb ae b a bf ca bg ae db a fb ca b ae bd a gb ca fb ca ae fgb caa a fgbbbd aac ca dbbbgf aac gbbbgf eae fgbbbda caa fgbbbd ca caa dbbbgf ae aa dbbbgf a aac fgbbbdf ca eae bd ae eae a caa ca aa ae aac a eae ca eae ae caa a aa ca aac ae eac a eae ca caa ae caa a aac cac ``` <!-- 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,#f35b55ff b,#666eedff c,#feb0b0ff d,#fd0807ff e,#b0d6b2ff f,#090afdff g,#98c697ff ``` ```image a d dc d dc cd d ad d aa d dc d dc cd d ad d aa d d dc cd d dc dc d cd aa egggggggggggdggge d geeeeeeeeeeadeeeg cd geeeeeeeeeedeeeeg dc geeeeeeeeeaaeeeeg gegdeeeeeeeeeeeg geeeeeeeeedeeeeeg geeaaeeeeeeeeeee geeeeeeeedaeeeeeg geeedeeeeeeeeeee geeeeeeeedeeeeeeg geeegdeeeeeeeeee geeeeeeedgeeeeeeg ebbbbbff geeeedaeeeeeeeee ebbbbffffffffffffffffbbbbee geeeeedeeeeeeeee bbbffffffffffffffffbbbbbgeedgeeeeeeeg geeeeeadeeeeeeee ebbffffffffbbbe geeeeeadeeeeeeeeg geeeeeedeegbbfffffffffbbe geeeeedeeeeeeeeeg gbbfffffffffbbge geeeeadeeeeeeeeeg fffbbbeeeedaeeeeee geeeedeeeeeeeeeeg geeeeeeeedeeeeee geeedaeeeeeeeeeeg geeeeeeeeadeeeee geeedeeeeeeeeeeeg geeeeeeeeedeeeee geedaeeeeeeeeeeeg geeeeeeeeegdeeee eggdgggggggggggge geeeeeeeeeedaeee dc geeeeeeeeeeedeee cd geeeeeeeeeeeadeg d dc ad d d da aa d d ad dc dc d d dc da cd d d cd ad dc d d aa aa d d dc cd d dc dc d cd aa d d cd cd d dc aa d d aa da d d cd dc dc cd d d aa cd d d cd aa dc d d aa ad d ddc cd ``` <!-- end of image --> Let's see what secrets area A holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#f73a42ff b,#4d3eefff c,#ff8787ff d,#ff0505ff e,#9998feff f,#0303ffff g,#f5cfd8ff ``` ```image cdd ddc gddg ada gddc cdd adc gddg ada gddc cdd adc gddg ada gddc cdd geeeebbbfff geeebbbffffffffffffff eeeebbbffffffffffffffbbbeeeeg fffffffffffbbbebaag fbbbeeeg ddc cddg ada gddg cda ddc cddg ada gddg cda ddc cddg ada gddg cdd ``` <!-- end of image --> I am surprised, so clear, an intersection has appeared in area A. Let's continue our search in the next region. Let's put area B under the microscope. <!-- image --> ```palette Key,Color ,#fefefeff a,#f6565fff b,#4e4effff c,#ff9f9fff d,#fd090aff e,#8d8dfeff f,#0503fcff g,#ead9edff ``` ```image ada cddg ddc cdd ddc add gddc ada gddg ada cddg dda cdd ddc add gddc gggadaeeeebbbbbbfff eebbbbbffffffffffffffffffffffff fffffffffffffffffbbbbeeeeeegggg beeeeeegggg cddg dda cdd ddc cdd gddc ada gddc ada cddg dda cddg ddc cdd gddc ``` <!-- end of image --> Yes! I knew it! There's an intersection right here in area B! After a long analysis, I found two intersections.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff4141ff b,#5a5affff c,#ff8585ff d,#ff0505ff e,#aeaeffff f,#0707ffff g,#ffc2c2ff ``` ```image c d dc gd dg gd d ca d aa d dc d dg gd d cd d aa d d dc cd d dg dg d gd aa d d cd gd d dg aa d d aa ac d d gd dg eeeebbbff dc eeebbbbfffffffffffffffbbbeee d eebbfffffffffffffffbbbbeee dg aa eebffffffffbbeee cd d ebbffffffffbee d eebffffffffbbee ca fffbee dc d d ac ca d d dc gd gd dc dg d gd cd d dg ca gd d dc aa d d cd dc dg d d dg ac gd d d cd cd dg d d aa aa d d dc cd d dg dg d gd aa d d cd gd d dg aa d d aa ac d d gd dg dc gd d dg aa cd d d gd ca dc d d ac ca d ddc gd ``` <!-- end of image -->

I'm on the case! Let's uncover any intersections hidden in this image. I'm going to focus my attention on these specific areas. <!-- image --> ```palette Key,Color ,#fefefeff a,#0808feff b,#fe0505ff c,#5f62f8ff d,#fbaba9ff e,#b5b5ffff f,#f64f4bff g,#add4aeff ``` ```image e ae a ae ea a ea a cc a cc a ae a ae d ea db a b ea b a bd cc bd a bd cc bf a bf ae bf a fb ae fb ea db a db ea db a b cc b a bd cc bd a bd ae bf a bf ae bf ea fb a fb ea db a db cc db a b cc b a bd ae bd a bd ae bf a ea bf cae a bf aa ea fb ac a fb ca cc db aa a db eac ggggacggggggggggg db ca gggggaggggggggggg b aa gggggacgggggggggg b eae ggggggagggggggggg bd aa ggggggagggggggggg bd ac gggggggaggggggggg bd eae gggggggagggggggggbf aa gggggggcagggggggbf ac gdffffbbabbbbbbbf cae dddffbbbbbbbbbbbbfffdggccggggggg aa bbbbbbffddd gggggggggaggggggg ac gggggggggacgggggg ca ggggggggggagggggg aa ggggggggggacggggg eae gggggggggggaggggg ca gggggggggggaggggg aa ggggggggggggagggg eae ggggggggggggagggg aa ca ac a eae cc aa a ac ac cae a aa aeac a ``` <!-- end of image --> I'm analyzing this close-up of area A with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#0303feff b,#fe0404ff c,#7f7cfcff d,#ffa5a5ff e,#c1c1ffff f,#fc5255ff g,#3d34f5ff ``` ```image gac eaa gac eaa gac cag aae cag aae cag eaae gac eaa gac eaa gac cag d aacddddfffffbbbbb dddddfffffbbbbgagbbbbbbbbbbbbbb bbbbbbbbbbbbbbbbaafffffddddd bbfffffddddd cag eaae gac eaa gac eaa aac cag aae cag aae cag eaae gac eaa gac eaa ``` <!-- 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,#0505ffff b,#ff0505ff c,#8282ffff d,#ffacacff e,#c8c8ffff f,#ff4e4eff g,#3f3fffff ``` ```image e ac a ae ea a ca a cg a gc a ac a ae d ea db a b ca b a bd cg bd a bd gc bf a bf ac bf a fb ae fb ea db a db ca db a b cg b a bd gc bd a bd ae bf a bf ae bf ea fb a fb ca db a db cg db a b gc b a bd ae bd a bd ae bf a ea bf cae a bf aa ca fb eac a fb cae cg db aa a db eac gc db ga a b ag ae b eac a bd ga ae bd ag ea bd cae a bf aa cg bf ag ddfffbbabbbbbbbf cae dddffbbbbbbbbbbbfffddd cg aa bbbbbbffddd a eac gc cae a aa ae eac a ga ae ag ea eae a ga cg ag a cae gg aa a ag gc cae a aa acac ea ``` <!-- 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,#fc0e0dff b,#0808fdff c,#b4b5feff d,#f07d76ff e,#b1d6b0ff f,#545ae5ff g,#96c797ff ``` ```image daa aa da dad a b aa da cb aa a bfgggggggggggggge dad a beeeeeeeeeeeeeeg aa ad fbeeeeeeeeeeeeeg dad a ebfeeeeeeeeeeeeg aa ad eebeeeeeeeeeeeeg aa a eefbeeeeeeeeeeegdad da eeebfeeeeeeeeeeaa a eeeebeeeeeeeeaag da eeeefbeeeeedaaeg a eeeeebgeeeaaeeeg a eeeeeebedadeeeeg ae eeeeeefbaeeeeeeg a eeeeeaabeeeeeeeg ad eeedadegbeeeeeeg a eeaaeeeebfeeeeeg dd dadeeeeeebeeeeeg a aaeeeeeeeegbeeeeg da a eeeeeeeeeebfeeeg a eeeeeeeeeeebeeeg ea eeeeeeeeeeefbeeg a eeeeeeeeeeeebfeg a eeeeeeeeeeeeebeg ad eeeeeeeeeeeeefbg a ggggggggggggggbg ad b a fb da bc a b da ff a b a cb ad bf a b ad cb eagggggggggggggg bc gdaeeeeeeeeeeeee b geaeeeeeeeeeeeee cb gedaeeeeeeeeeeee bc geeaeeeeeeeeeeee b geegaeeeeeeeeeee fb geeeadeeeeeeeeee cb bc geeeeaeeeeeeeeee cbbbc b geeeeadeeeeeeeeecbbbc ff geeeeeaeeeeeefbbbc b geeeeedaeefbbfee cb geeeeeefbbfeeeee bf geeefbbfaeeeeeee b gfbbfeeeaeeeeeee cb cfbbfeeeeeegaeeeeee bf cbbbc geeeeeeeeadeeeee b cbbbc geeeeeeeeeaeeeee cb cbbbc geeeeeeeeeadeeee bc cbbbc geeeeeeeeeeaeeee b fbbf geeeeeeeeeeaaeee fbbf geeeeeeeeeeeaeee geeeeeeeeeeedaee geeeeeeeeeeeeaee geeeeeeeeeeeedag ae a ad a ad a da a da a a ad a ad a da a ``` <!-- end of image --> Time to investigate area A up close. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0808ff b,#0303feff c,#babaffff d,#f84f55ff e,#fda2a4ff f,#706cfbff g,#312efcff ``` ```image gbf cbbc fbg bbf cbbc fbg bbf cbbc gbg bbc fbb gbf cbbc fbb ea gbf daa cbbc eaaae fbg eaaad gbf daaae cbbc eaaad fbg daade bbf daaae cbbeaaad gbgaae eabbf edaadbb daaae gbg eaaad cbbc daaae fbb eaaae gbf eaaad cbbc daaae fbg eaaad gbf aaae cbbc ae fbg bbf cbbc fbg bbf cbbc gbg bbc fbb gbf cbbc fbb gb ``` <!-- end of image --> I've cracked the case! This area contains the intersection. Okay, let's proceed to the next area. I'm analyzing this close-up of area B with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0404ff b,#0404feff c,#9999ffff d,#fc7a7dff e,#fec1c1ff f,#4940f6ff g,#fc393cff ``` ```image gag eaae dag aae dag aad daa gad eaae gag eaae dag aae dag aad daa gad eaa c gad cfbb eaae cfbbbbf gag cfbbbbfc eaaeccbbbbbfc dfbbbbbfc cfbbbbbfc cfbbbbbfga cfbbbbbfc gad cfbbbbbcc eaa fbbbbfc gad bbfc eaae c gag eaae dag aae daa aad eaa gad eaae gag eaae dag aae dag aad daa gad ``` <!-- end of image --> Bingo! This close-up reveals an intersection in area B! There's for sure two intersections on the image you sent me.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0303ff b,#0908feff c,#afafffff d,#ff6e6eff e,#ffb9b9ff f,#5c56f9ff g,#fe2f2fff ``` ```image e eaa aa dg dae a b ag ea cb gae a bf ead ea b aa ae cb dae a bc eag gd b ga a cb dad dg bc aa a b gae da fb eag a bc aa ea b dad ae fbg a gab gd ead cb a aa bf gd dae b a eag cb dg g bf a b ea cb ae bc a b ae fb a bc gd b a fb dg bc a b ea ff ae b ea cb ae bf a b gd cb a bc dg b a cb ea bc a b ea fb ae cb bc a cbbbc b gd cbbbc ff a cbbbc b dg fbbf cb fbbf bf fbbfg b fbbf a cb fbbc ea bf cbbbc ae b cbbbc a cb cbbbc gd bc cbbbc a b fbbf gd fbbf a dg a ea ae a ae a gd a dg a ea ae ea ae a gd a dg a ``` <!-- end of image -->

I'm examining this image closely. My goal: find any and all intersections. These areas seem to enclose narrow spaces where lines might be close. <!-- image --> ```palette Key,Color ,#fefefeff a,#0606fdff b,#ed6a62ff c,#8189efff d,#fc0707ff e,#dbc7eaff f,#b0d6b0ff g,#4142f4ff ``` ```image c a ac ea ae ca a gg a ac a ae ea a ca a gg a ac ea ae ea a cg a gc a ac ea ae ca a ac gg a a ea ac ca a ac ae ae ea a a ca ca gg a ae gg a a ea ac ga ea ac ae ae ea ea a ca cg ag a ae gc a a ca ac gg ea ac ae a ca ea a ga gg ac a ae ac dde ea a eddb ca ae bddb fffffffagfffffffffffffffffffcaff ddde ffffffffacffffffffffffffffffafff eddb fffffffffafffffffffffffffffcafff bddbfffffffffcaffffffffffffffffaffff dddffffffffgaffffffffffffffggffff fbddbffffffacfffffffffffffafffff ffffbddbffffaffffffffffffacfffff fffffffdddfffafffffffffffaffffff fffffffffbddbgafffffffffacffffff ffffffffffffbdagfffffffcafffffff fffffffffffffffaddfffffaffffffff ffffffffffffffffabdddbgaffffffff ffffffffffffffffcaffbbadddddbbff fffffffffffffffffagffggfffffbbddddddbe ffffffffffffffffffacfaffffffffff ebbdddddbbe fffffffffffffffffffaacffffffffff ebddddddbbe fffffffffffffffffffcafffffffffff ebbddddddbe ffffffffffffffffffffffffffffffff ebbddd ffffffffffffffffffffffffffffffff ffffffffffffffffffffffffffffffff ffffffffffffffffffffffffffffffff ``` <!-- end of image --> I'm analyzing this close-up of area A with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#0504feff b,#ff5959ff c,#7876fcff d,#fa060aff e,#bebefeff f,#feafafff g,#3b35f9ff ``` ```image gag gag gag eaae eaac gac eaae eaa caa aac gag caa eaac aae eaae cag dbf caae eaae ddddbf gag gag fbddddbf aac eaae fbddddbf eaac gac fbddddbf caae eaa fbdddddf gaa aac fbddddbf gag cag fbddddbf eaac aae fbdddddf eaae cag fbddddbfcaae eaae fbddddgag gac fbdddaag eaa fbdaadbf gac caadddbf caa gaadddddf aac aagfbddddbbbfcag eaac fbdddddaaddbbfff caae fbbgagdddddddddbbbff caa eaae ffbbbdddddddddd gag gac fffbbddd eaac eaa eaae aac caaecaa gagaae aaag eaae ee ``` <!-- end of image --> Aha! I've found an intersection inside area A! The image features two intersection points.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0404feff b,#ff5959ff c,#807ffeff d,#fe0505ff e,#c0c0ffff f,#feb4b4ff g,#3f3dfdff ``` ```image c a ae ea ae ca a gg a gc a ae ea a ca a gg a ac a ae ea a cg a gc a ae ea ae ca a ac gg a a ea gc ca a ac ae ae ea a a ca ca gg a ae gg a a ea ac ga a ac ae a ea ea a ca cg ag a ae gc a a ea ae gg ea ae ae a ca ea a ga gg ac a ae gc ddf a a fddb ca ae bddf gg ea bddf ae a fddb a ca bddf ea a bddf gg gg fddb ac a bddf a ac bddf ea a fddbca ae bdag ea addf a afddbbcg ca fbadddddbff gg gc ffbddddddbf ae a fbbdddddbbf aae fbddddddbff ea ffbddddddbf fbbddd ``` <!-- end of image -->

Time to put on my detective hat and find those intersection points! These spots mark what I'd call 'danger zones' - areas where intersections are more likely. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0808ff b,#3e40f2ff c,#f69a96ff d,#0101ffff e,#add5acff f,#fa4644ff g,#8888feff ``` ```image c fa af af ac ac ac a a a ca ca fa fa af af ac ac ac a a a ca ca fa fa ff af af ac ac a a a ca ca ca fa fa af aa fa ca ac ac af aa fa ca ac ac af aa fa ca ac ac eeeeeeeeeeeeeeee afeeeeeeeeeeeeeeee b aaeeeeeeeeeeeeeee bdb faeeeeeeeeeeeeee bdb ecaeeeeeeeeeeeebdb eeeaceeeeeeeebdb eeeeafeeeeebdbee eeeeeaaeebdbeeee eeeeeeabdbeeeeee eeeeebdbaeeeeeee eeebdbeecaeeeeee ebdbeeeeeeaceeee bdbeeeeeeeeeafeee bdgeeeeeeeeeeeeaaee bdg eeeeeeeeeeeeeaae bdg eeeeeeeeeeeeeefa bdg eeeeeeeeeeeeeeeca bdg eeeeeeeeeeeeeeee ac bdg af gg bdg aa bbdddddddbgg bdg fa ggbdddddddbgg bdg c ggbdddddddbbgg bdg ggbbddddg ``` <!-- end of image --> Here's a close-up of the area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd0507ff b,#5551fbff c,#ffc6c6ff d,#0200fdff e,#ff7a7aff f,#ff3939ff g,#d2d2feff ``` ```image ac aac faae eaae eaaf caaf g caaac gbd cfaac gbddd faae gbdddbg eaae gbdddbg eaaf gbdddbg caaf gbdddbg caaacgbdddbg cfaddddbg gbdddbg gbdddbaae gbdddbg eaaf gbdddbg caafc gbdddbg caaac gbdddbg cfaac gbdddbg faae dddbg eaae dbg eaaf g caafc caaac cfaac faa ea e ``` <!-- end of image --> Amazing! This area was hiding an intersection all along! The final count is: one intersection.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0404ff b,#4743fbff c,#ffc1c1ff d,#0101ffff e,#ff7a7aff f,#ff3636ff g,#8787ffff ``` ```image c fa ff af ae ac ac ac a ca ca ea ea fa ff af ae ae ac ac a ca ca ea ea fa ff af ae ae ac ac a ca ca ea ea fa ff af aa fa ea cac ae af aa fa ea cac ae af fa fa ca cac ae af b fa bdb ea bdb ca bdb cac bdb ae bdb af bdb fbdb bdba bdb ca bdb cac bdg ae bdg af bdg fa bdg ea bdg cac bdg ac bdg ae gg bdg af bbdddddddbgg bdg fa ggbdddddddbgg bdg e ggbdddddddbbgg bdg ggbbddddg ``` <!-- 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,#e7635aff b,#4244ecff c,#fc0808ff d,#9199efff e,#b1d6b0ff f,#0505fdff g,#9dc497ff ``` ```image d df f f fd fd bb bf df f f fd fb bb bf df f f fd fb geeeeeeeeeeeeeeeeeebfeeeeeg eeeeeeeeeeeeeeeeeebfeeeeeeg eeeeeeeeeeeeeeeeedfeeeeeeeg eeeeeeeeeeeeeeeeefeeeeeeeeg acc eeeeeeeeeeeeeeeefeeeeeeeeeg acccca eeeeeeeeeeeeeeefdeeeeeeegacccae eeeeeeeeeeeeeefbeeegaccccag eeeeeeeeeeeeebfaccccageeeeg eeeeeeeeeegabfccaeeeeeeeeeg eeeeeeaccccafeeeeeeeeeeeeeg eaacccageeefeeeeeeeeeeeeeeg accccaeeeeeeefgeeeeeeeeeeeeeeg cccca eeeeeeeeefdeeeeeeeeeeeeeeeg ca eeeeeeeefbeeeeeeeeeeeeeeeeg ac eeeeeeebfeeeeeeeeeeeeeeeeeg c eeeeeebfeeeeeeeeeeeeeeeeeeg c eeeeedfeeeeeeeeeeeeeeeeeeeg ca geeegfgeeeeeeeeeeeeeeeeeeeg ac fe ec fd c fb ce bf ca df ac df c f c f ca fd geeeeeeeeeeeeeeeeeac fb geeeeeeeeeeeeeeeegce bf geeeeeeeeeeeeeeeecge df geeeeeeeeeeeeeeecaee df geeeeeeeeeeeeeeaceee df geeeeeeeeeeeeegceeee dffb geeeeeeeeeeeeeceeeee bff geeeeeeeeeeeecaeeeee dffd geeeeeeeeeeeaceeeedffb geeeeeeeeeegceeebffg geeeeeeeeeecebffbeee geeeeeeeeecffbeeeeee geeeeeeebffdeeeeeeee geeeedffbceeeeeeeeee gegffbeeceeeeeeeeeee bffdeeecgeeeeeeeeeee dffbeeeeecaeeeeeeeeeeee ffb geeeeaceeeeeeeeeeeee fd geeegceeeeeeeeeeeeee geeecgeeeeeeeeeeeeee geecaeeeeeeeeeeeeeee geaceeeeeeeeeeeeeeee ggceeeeeeeeeeeeeeeee gceeeeeeeeeeeeeeeeee caeeeeeeeeeeeeeeeeee acggggggggggggggggggg ec c ce ca ec c ce ``` <!-- end of image --> Time to investigate area A up close. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff7e7eff b,#544df8ff c,#fd0607ff d,#a7a6fdff e,#febebeff f,#0605fdff g,#fb3e42ff ``` ```image c gc acc ecce cca gcg acc ecce ecca gcg gcc acce ecca ccg gcc acce ecca ccg gcg dbf acce dffff ecce dbffffbd cca dbffffbd gcg dfffffd accdbffffbd ecbffffbd dfffffd dbffffbd dbfffffg dbffffbcce dbffffbdecca bffffbd ccg dbffffbd gcc dbffffbd acce fffbd ecca fbd ccg gcg acce ecce cca gcg acce ecce ecca gcg acc ecce ecca gcg gcc acce ecca ccg ``` <!-- end of image --> My analysis confirms the presence of an intersection in area A. Next up, a closer look at another region. Let's zoom in on area B to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff5757ff b,#5958feff c,#fd0607ff d,#babaffff e,#fea9aaff f,#0807feff g,#9a268bff ``` ```image dffb ffb fff bff bffd dffd dffb dffb ffb bff bff bffd dffd eaa dffb eeaccccc dffb eaacccccccae ffb eeacccccccaee bffeeacccccccaae bffcccccccaee eeacgffcccaae eaaccccgffgee eeacccccccagffb eeacccccccaae dffb eaacccccccaee ffb acccccccaae bff ccccaee bffd ee bffd dffd dffb dffb ffb bff bffd bffd dffd dffb dffb ``` <!-- end of image --> Aha! I've found an intersection inside area B! The final answer is: two intersections found.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fc5f61ff b,#332ef9ff c,#fe0809ff d,#b4b4ffff e,#ffb3b3ff f,#0303feff g,#6d6bfdff ``` ```image g df f f fd fg bb gf df f f fd fg bb gf df f f fd fg bb gf df f eacc f acccca fd eacccae fg acccce bbecccca eabfcae accccaf eacccae f acccce f cccca fd ca fg ac bb ec gf c df ce f ac fd ec fd c fg ce bb ca gf ec df c f ce fd ca fd ac fg c bb c gf ca df ac gf ec dffg c bffd ce gffg ac dffb ec bffd c gffg cffb bffd dffgc dffb c gffd ce dffg ca bfb ac fd c c ca ac ec c ce ac ec c ce ca ec c ce ``` <!-- end of image -->

I'm curious to see if this image contains any intersection points. I've examined the entire image, and there are zero intersections present.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0606ffff b,#ff0505ff c,#9090ffff d,#ffa6a6ff e,#4444ffff f,#ff5050ff g,#d2d2ffff ``` ```image d fbbbbbbffd dffbbbbbbfdd dfbbbbbbbfdd ddfbbbbbbffd ddfbbbd dbbbd fbbf fbbf dbbbd dbbbd fbbf fbbfd dbbbd dfbbf fbbf dbbbd dbbbd c fb eae a aa ag ea ca ea a ca ee ca a gag ac gag ga ac ag ac ce ae a ae ac aa ga ea ag ea ca ca a ca ee gag a gag ag ac ca ac a ae ee ae a aa ac ea ga ea ag ca ca ca a gag ac gag ga ac ag ac ca ae a ae ee aa a ea ac ea ga ca a ca ee ga a ac ga ag ca a ec ga ag ca a ee a ac ga a ee a ac ga ag ``` <!-- end of image -->

I'm examining this image closely. My goal: find any and all 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,#fd0706ff b,#0b0cfcff c,#ed9e96ff d,#8b93eeff e,#98c798ff f,#ed5850ff g,#b1d7b1ff ``` ```image c caaaf a faaac ca faaac a caaaf ca caaac a faaac ca caaaf a caaac a faaac a cfaaf a caaaf ac faaa a c ac a ac a ac a fc a b ff bdbb a db bb ff b dbb a bd dbb eeeeeeeeeeeeeeeeeeeeeeff b dbb ggggggggggggggggggggggae b dbb gggggggggggggggggggggfae db dbb gggggggggggggggggggggage b dbb ggggggggggggggggggggfage bd dbb ggggggggggggggggggggagge db dbb gggggggggggggggggggcagge b dbb gggggggggggggggggggaggge bb dbb ggggggggggggggggggcaggge b dbb ggggggggggggggggggagggge bd dbb gggggggggggggggggcagggge db dbb gggggggggggggggggaegggge b dbb ggggggggggggggggeagggggebd dbb ggggggggggggggggaegggggeb dbb ggggggggggggggggaggggggb dbb gggggggggggggggacgggggdb dbb gggggggggggggggaggggggbe dbb ggggggggggggggacgggggbde db ggggggggggggggagggggdbge gggggggggggggafgggggbgge gggggggggggggagggggbbgge ggggggggggggafgggggbggge ggggggggggggagggggbdggge gggggggggggafggggdbgggge gggggggggggagggggbggggge ggggggggggffggggbdggggge ggggggggggaggggebgggggge gggggggggffggggbegggggge gggggggggaggggdbggggggge ggggggggffggggbgggggggge ggggggggaggggbdgggggggge gggggggfagggdbggggggggge gggggggaggggbgggggggggge ggggggfagggbbgggggggggge ggggggaggggbggggggggggge gggggcagggbdggggggggggge gggggagggdbgggggggggggge ggggcagggbggggggggggggge ggggagggbdggggggggggggge gggcaggebgggggggggggggge gggaeggbegggggggggggggge ggeaggdbggggggggggggggge ggacggbgggggggggggggggge ggaggbdgggggggggggggggge gacgdbggggggggggggggggge eaggbgggggggggggggggggge acgbbgggggggggggggggggge aggbggggggggggggggggggge afgbdggggggggggggggggggge c db b bd b b ``` <!-- end of image --> Could this be where the intersection is hiding, in area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0404ff b,#0707ffff c,#ff7f7fff d,#a7a7ffff e,#5050ffff f,#ff3b3bff g,#ffc0c0ff ``` ```image c a ca aa caf aag caf aag caf aac caa aac caa fac gaa fac gaa fac gaa fac gaa fac gaag faf gaag faf gaag caf aag caf aag e caf db aag eb caf dbb aag bbd caf ebe aag dbbd caf bbe aac dbb caa bbd fac ebe gaa dbb fac bbd gaa ebb fac dbbd gaa ebe fac dbb gaa bbd fac ebe gaa dbbd fac bbe gaag dbb faf bbd gaag ebe caf dbb gaag bbd caf ebb aag dbbd caf ebe aag dbb caf bbd aag ebe caf dbbd aag bbe caf dbb aac bbd caa ebe aac dbb caa bbd fac ebb gaa dbbd fac ebe gaa dbb fac bbd gaa ebe fac dbbd gaa bbe fac dbb gaag bbd fac ebe gaag dbb faf bbd gaag ebb caf dbbd aag ebe caf dbb aag bbd caf ebe aag dbbd caf bbe aag dbb caf bbd aag ebe caf dbb aac bbd caa ebb fac dbbd ``` <!-- end of image --> I had hoped to find an intersection in area A, but there isn't one. The image is completely devoid of intersections. Zero.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0707ff b,#0808ffff c,#ff9d9dff d,#a7a7ffff e,#5a5affff f,#ff5555ff g,#f1dae7ff ``` ```image g caaafg a faaac ca gfaaac a caaafg ca caaac ag gfaaac ca caaafg ag caaaf ga gfaaac ag cfaafg ga caaaf ag faaa ga g ac a ac a ac a fc a bg ff bdbbg a db dbbg ff b dbbg a be dbbg ff gb dbbg a bg dbbg cf eb dbbg a b dbbg ca bd dbb a db dbb ca b dbb a ee dbb ca b dbb ag bd dbb ga db dbb ag b dbb ga be dbb ag gb dbb ga bg dbb ac eb dbb ga b dbb ac bd db a db ac b a ee ac b a bd ff db a b ff be a gb ff bg a eb ff b a bd ca db a b ca ee a b ca bd a db ca b ag be ga gb ag bg ga eb ag b ga bd ac db a b ac ee a b ac bd c db b be gb bg ``` <!-- end of image -->

I'm analyzing this image to identify any points where lines intersect. My next step is to analyze the details within each area. <!-- image --> ```palette Key,Color ,#fefefeff a,#090afdff b,#fd0908ff c,#5a5cf4ff d,#f65652ff e,#f2a39dff f,#b4b4feff g,#add4adff ``` ```image f ca afa af ca ca ac a af af a fa fa a ca af af fa a a fa d ac ca b fa ac b a af dd ac a b fa fa be a ca db cc af b a a be af fa eb ca ca b a ac be af af eb ca a b a fa bd af ca b fa af b a gaggggggggggdbgg ac ggagggggggggbggg fa ggcagggggggbeggg a gggacgggggdbgggg ac ggggagggggbggggg fa gggggagggbeggggg a gggggcagdbgggggg cc ggggggaabggggggg a gggggggacggggggg af ggggggebaggggggg ca ggggggbggagggggg a gggggbdggcaggggg af gggggbggggacgggg ca ggggbggggggagggg a gggdbgggggggaggg af gggbggggggggcagg fa ggbegggggggggaag a db af ac b a fa be fa a eb ca ac b ac fa bd af ggggggagggggggg eb a gggggacgggggggg b fa gggggaggggggggg dd ac ggggagggggggggg b af gggcagggggggggg b a gggcggggggggggg db fa gggbegggggggggg b f ggggbbggggggggg be gggggebdggggggg eb gggggggbbeggggg b gggggggggbbgggg be ggggggggggdbdgg eb ggggggggggggbbg b ggggggggggggggbb bd gggggggggggggggdbe eb ggggggggggggggg bb b ggggggggggggggg ebd dd dbe b bb b ebd db bb b bb be dbe eb bb b ebd be dbe eb bb b ebdbd db ``` <!-- end of image --> I'm determined to find out if an intersection exists in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0404ffff b,#ff0606ff c,#9191ffff d,#ff4141ff e,#ffc8c8ff f,#ff8585ff g,#4242ffff ``` ```image gag caa aac gag caa aac gag caa aac gag caa cc e ebbe ebbbde fbbbf edbbde fbbbd fbbbf edbbde fbbbf dbbbf edbbde fbbbf edbbbe ebbbd fbb ed ``` <!-- end of image --> Hmm, it seems there's no intersection in area A after all. Time to investigate another area. My goal is to determine if there's an intersection inside area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#0303feff b,#fe0606ff c,#837ffaff d,#f94e53ff e,#ffababff f,#cdccfeff g,#3732faff ``` ```image caaf bbe gag dbd gag ebb faac bbe caaf dbb caaf ebbe gag bbd faac dbb faac ebbe caaf dbd gag ebb gag bbe faac dbd caaf ebb caaf bbe gagdbd faagbe faac ddaaf ebbgag bbd gag dbb faac ebbe caaf dbd caaf ebb gag bbe faac dbd faac ebb caaf bbe gag dbd gag ebbe faac bbd caaf dbb caaf ebbe gag ``` <!-- end of image --> I've cracked the case! This area contains the intersection. I have found one intersection!

<!-- image --> ```palette Key,Color ,#fefefeff a,#0404feff b,#fe0707ff c,#6e6cfcff d,#ff5454ff e,#ffaeaeff f,#b9b9ffff g,#3535feff ``` ```image f ga afa af ca cg ac a af af a ca fa a gg ac af fa a a fa d ac ca eb fa ac b a af dd gc a b fa fa be a gg db gg af b a a be af fa eb cg ca b a ac be af af eb ca a b a fa bd af gg eb fa af b a a dd ac fa b fa ca be a ac db gc af b fa a be a fa eb gg ggb a ac af eba cg b fa a dd ca af b ac ca b af a dd a af b fa fa be gg a db af ac b a fa be fa a eb ca gc b ac fa bd af a eb a gg b fa a dd gg af b af cg b a c db fa be b c bb be ebd db dbe b bb be ebd eb bb b ebb bd dbe eb bb b ebd dd dbe b bb be ebd db bbe b bb be dbe eb bb b ebd be dbe eb bb b ebdbd db ``` <!-- end of image -->