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oliveirabruno01

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

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I have a feeling there might be some intersections in this image. I can confidently say that there are no intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#5959ffff b,#ff0303ff c,#ff8686ff d,#0808ffff e,#acacffff f,#ffcacaff g,#ff3636ff ``` ```image e dd dde ade ada edd dd dde ada eda edd dd ade ada edd dd dde ade eda edd dd dde ada eda dd dde eda dd f ade fbb eda bbf dd bbf ade gbc dd gbc dd gbc eda cbg dd cbg ade cbg eda fbb dd fbb ade fbbf dd bbf dd bbf eda gbc dd gbc ade gbc eda cbg dd cbg de cbg fbb fbb bbf fbf cb bb bg fbf cb gb bg fbc cb gb bg fbc cb gb bg fbc cbf gb bg bc cbf gb bg bc fbf gb bg bc ``` <!-- end of image -->

Time to put on my detective hat and find those intersection points! 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,#fb7f7dff b,#0404ffff c,#fe0101ff d,#afafffff e,#fd2b2bff f,#4d4dffff g,#b1d6b0ff ``` ```image acc c aca ae ec c ce ae aca c cc ae gce c eca ae cc c aca ae ec c ce ae aca c ec ae ce c aca ae cc c ace ae ecg c cc ae aca c ec ae ce c aca ae cc c ce ae ac c ae c ae c ae c ae c ae c ae c ae c ae c ae c ae c ae c ae c ae c ae c ae c ae c ae c ae gggggggcgggg ggggggaegggg ggggggcggggg gggggaeggggg gggggcgggggg ggggaegggggg ggggcggggggg gggaeggggggg gggcgggggggg d gggggggggggg dfbbbbbf gggggggggggg ddfbbbbbfd gggggggggggg dffbbbbbfd gggggggggggg dfbbbbbbfd gggggggggggg dfbbbbbffd gggggggggggg ddddddddfbbbbbfdd gggbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbffffd ``` <!-- end of image --> Let's put area A under the microscope. <!-- image --> ```palette Key,Color ,#fffefeff a,#ff7e7eff b,#0000ffff c,#ff0505ff d,#fae9eeff e,#ff2c2bff f,#6363ffff g,#ffacacff ``` ```image dccg ace dccg ace dccg ace dccg ace dccg ace dccg ace dccg ace dccg ace dccg gce dd dffffffffffffffff dbbbbbbbbbbbbbbbb ``` <!-- end of image --> The evidence suggests that this is not an intersection point in area A. My analysis shows there's absolutely no intersections in the image

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff7e7eff b,#0404ffff c,#ff0101ff d,#afafffff e,#ff2c2cff f,#4d4dffff g,#ffceceff ``` ```image g acc c aca ae ecg c gce ae aca c cc ae gce c ecg ae cc c aca ae ecg c gcc ae aca c ecg ae gce c aca ae cc c gce ae ecg c cc ae aca c ecg ae gce c aca ae cc c gce ae ac c ae c ae c ae c ae c ae c ae c ae c ae c ae c ae c ae c ae c ae c ae c ae c ae c ae c ae c ae c ae c ae c ae c d dfbbbbbf ddfbbbbbfd dffbbbbbfd dfbbbbbbfd dfbbbbbffd ddddddddfbbbbbfdd bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbffffd ``` <!-- end of image -->

This is the image I'm working with. The goal is to count the intersections. Zero, Nada.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff3b3bff b,#0a0affff c,#ff8181ff d,#b6b6ffff e,#6464ffff f,#ff0404ff g,#ffc8c8ff ``` ```image e eb eb bb bb bb be be be bd bd bd db db db eb eb eb bb bb bb be be be c bd gf bd f bd fg db aa db cf db gf eb fg eb fc eb aa bb gf bb f bb fg be fa bbbbbbed be cf deebbbbbbed be gf deebbbbbbed bd f debbbbbbbed bd fc debbbbbbd aa cf f fg fc af gf f fg aa cf gf fg fc aa fa gf afg f gfa fg afg fa fa cf cfg gf ff f cfc fc ff aa gfc cf af f gfa fg afg fc gfa cf afg gf ff f cfc fg ff aa cfc cf ff f gfc fg af fc gfaaf af ``` <!-- end of image -->

I have an image in front of me. I need to determine if there are any intersection segments. I've spotted 1 narrow regions that might be worth examining further. Let's call them area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0909feff b,#fd0c0cff c,#565af7ff d,#f76d6aff e,#96c698ff f,#b2d6b1ff g,#b1b1ffff ``` ```image f dbbb dbbbd eeeeeeeeeeeeeeeeef dbbbf fffffffffffffffffe dbbbd fffffffffffffffffe bbbd fffffffffffffffffe dbbbd fffffffffffffffffe fbbbd fffffffffffffffffe dbbbf fffffffffffffffffe dbbbd fffffffffffffffffe dbbbf fffffffffffffffdbbbd fffffffffffebbbbee fffffffffdbbdffffe fffffffdbbfffffffe fffffdbbfffffffffe fffdbbfffffffffffe fdbbfffffffffffffe dbbfffffffffafffffe dbbffffffffffaacffffe dbb fffffffffcafaffffe dbb fffffffffaffeafffe dbb ffffffffaefffacffe dbb fffffffacfffffaefe dbb ffffffeafffffffafe dbd ffffffaffffffffcae dbd fffffacfffffffffac dbd eeeecaeeeeeeeeeeea dbd a ga dbd ag ac dbd ca ag d a a ag ca cc ag ga a a ga ac ac ga a a a ag ca ca ag a a ag ga cc ac ga a a a ac ca ga ag a a ag ga ca ac a a ag a ca ca a ag a a ac ga ga ac a a ac a ga ca a ag ag a ca ga a ac ag a cc ga ga ca a ag ac a ga ac a ga ca ag a ga ac a ``` <!-- end of image --> Could this be where the intersection is hiding, in area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#0505ffff b,#ff0000ff c,#3c3cffff d,#ff9494ff e,#c4c4ffff f,#ff2121ff g,#8080ffff ``` ```image d dfbb ddfbbbbf dfbbbbbfd dfbbbbfdd dfbbbfd dfbbfd dfbbfd dfbbfd dfbbfd dfbbfd dfbbfd dfbbfd dfbbfd dfbbfd fbbfd ca bfd gaac d eaaaag aaggaae cac cac gaae aag eaag eaae cac gaa gaae cac eaag eaag cac gaae gaa cac eaae aag aag eaae cac gaa eaae cac aag eaa cac ga ``` <!-- end of image --> Unfortunately, there's no intersection inside area A. I can confidently say that there are no intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0909ffff b,#ff0606ff c,#5757ffff d,#ff9292ff e,#e3dbf7ff f,#ff4d4dff g,#a1a1ffff ``` ```image d fbbb dbbbd efbbfe dbbbd efbbfe dbbbd dbbbf fbbbd dbbbf efbbfd dbbbd efbbfe dbbd dbb dbb dbb dbb dbb a dbb aag dbb ca a dbf ea ga dbf ae ac fbf ac ae fbf ga ea fbf a ca fbf ag ag fbf ga a fbf a ga fbf ag ac fbf ca ae d ea ea ae ca cc ag ea a ae ga ac ac ga ae a ea ag ca ca ag a a ae ga cc ac ea ae ae ea ac ca ga ag a a ag ga ga ac a ae ag ea ca ca ea ag ae a ac ga ga ac a ae ag ea ga ca a ag ag a ca ga ea ac ae ae cc ea ea ca ae ag ac a e ga ac ae ea ca ag a ga ac a ``` <!-- end of image -->

I'm approaching this image with caution. Intersections might be tricky to spot. I wonder what's going on inside those areas? Perhaps intersections are hiding there. <!-- image --> ```palette Key,Color ,#fefefeff a,#5354fcff b,#fe0707ff c,#afd6afff d,#f8524fff e,#f6a29eff f,#0707feff g,#a7a8fdff ``` ```image aff f gff aa gff f gff aa gfa f afa fg afa f afa fg afg f ffg fg ffg gf ffg f ff gf gff f gff af gff f gfa aa afa f afa aa afg f ffg fg ffg f ff fg f fg gf f gf f af f aa f aa f fg f fg f fg gf f gf f gf f e aa bb f bd aa db f bb fg ebe f db fg bd f ebe fg bb gf bd f db gf bb f ebe gf db f bd aa ebe cccccfccccccccc bb ccccaaccccccccc bd ccccfcccccccccc db cccfacccccccccc bb cccgccccccccccc ebe ccccccccccccccc bb ccccccccccccccc bd ccccccccccccccc db ccccccccccccccc bb ccccccccccccccc ebe cccbdeccccccccc db ccceddbbbbbbdec bd cccccccccccedbbbbbbde ebe ccccccccccccccc edbbbbbbde bb ccccccccccccccc eedbbbbbdee bd ccccccccccccccc edbbbb ccccccccccccccc ccccccccccccccc ccccccccccccccc ``` <!-- end of image --> I wonder what we'll find inside area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#5555ffff b,#ff0303ff c,#ff8282ff d,#ff4545ff e,#ffc0c0ff f,#0405ffff g,#bebeffff ``` ```image afa gffg afa gffg afa gff afa gff ffa gff gg bddcee ebbbbbbbbddccee eecddbbbbbbbbbbbddccee eeccddbbbbbbbbb eeccddb ``` <!-- end of image --> I don't observe any intersections inside area A. I did not find anything, there's no intersections

<!-- image --> ```palette Key,Color ,#fefefeff a,#3333ffff b,#ff0707ff c,#7272ffff d,#ff5b5bff e,#ffb2b2ff f,#0303ffff g,#babaffff ``` ```image g cffg f gff ca gff f gfa ac cfa f cfa fc cfc f afc fg afc gf afg fg ffg gf ffg f gff gf gff f gff ca gfa f cfa ca cfa f cfc ac afc f afg ac ffg f ff fg gf fg gf f gf f ca f ca f ac f ac f fg f fg gf f gf f ca f e ca bb f bd ac dbe f bb ac ebd f db fg bd f ebe fg bb gf bd f db gf bb f ebe ca bb f bd ca dbe f bb ac ebd f db ac bb g ebe bb bd dbe bb ebe bde db eddbbbbbdde bd edbbbbbbdee ebe edbbbbbbde bb eddbbbbbdde bd edbbbb ``` <!-- 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,#444debff b,#fa0a0aff c,#0505fdff d,#e77065ff e,#b1d7b1ff f,#8e97ebff g,#9bc396ff ``` ```image e bdgggggggggggggggggggggggggggggggggggg cbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee cbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee cbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee gcbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee ecbgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee efcbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eecbdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeaabeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeecdbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeaabeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeecdbeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeecabgeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeeecebeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeeecfbdeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeeeecebeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeeeecgdbeeeeeeeeeeeeeeeeeeeeeeeeeee eeeeeefcebeeeeeeeeeeeeeeeeeeeeeeeeeee eeeeeeecedbeeeeeeeeeeeeeeeeeeeeeeeeee eeeeeeefcebgeeeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeceebeeeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeaaebdeeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeceebeeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeaaedbeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeceebeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeecfedbeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeceebgeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeecfeebeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeegceebdeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeeceeebeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeefceedbeeeeeeeeeeeeeeeeeee eeeeeeeeeeeeeceeebeeeeeeeeeeeeeeeeeee eeeeeeeeeeeeefceedbeeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeceeebgeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeaaeeebeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeeceeebdeeeeeeeeeeeeeeee eeeeeeeeeeeeeeeaaeeebeeeeeeeeeeeeeeee eeeeeeeeeeeeeeeeceeedbeeeeeeeeeeeeeee eeeeeeeeeeeeeeeecfeeebeeeeeeeeeeeeeee eeeeeeeeeeeeeeeeeceeedbeeeeeeeeeeeeee eeeeeeeeeeeeeeeeecfeeebgeeeeeeeeeeeee eeeeeeeeeeeeeeeeegceeeebeeeeeeeeeeeee eeeeeeeeeeeeeeeeeeceeeebdeeeeeeeeeeee eeeeeeeeeeeeeeeeeefceeeebeeeeeeeeeeee eeeeeeeeeeeeeeeeeeeceeeedbeeeeeeeeeee eeeeeeeeeeeeeeeeeeeaceeeebeeeeeeeeeee eeeeeeeeeeeeeeeeeeeeceeeedbeeeeeeeeee eeeeeeeeeeeeeeeeeeeeaaeeeebgeeeeeeeee eeeeeeeeeeeeeeeeeeeeeceeeeebeeeeeeeee eeeeeeeeeeeeeeeeeeeeeaaeeeebdeeeeeeee eeeeeeeeeeeeeeeeeeeeeeceeeeebeeeeeeee eeeeeeeeeeeeeeeeeeeeeecfeeeedbeeeeeee eeeeeeeeeeeeeeeeeeeeeeeceeeeebeeeeeee eeeeeeeeeeeeeeeeeeeeeeecgeeeedbeeeeee eeeeeeeeeeeeeeeeeeeeeeegceeeeebgeeeee eeeeeeeeeeeeeeeeeeeeeeeeceeeeeebeeeee eeeeeeeeeeeeeeeeeeeeeeeefceeeeebdeeee ddbbb eeeeeeeeeeeeeeeeeeeeeeeeeceeeeeebeeee edbbbbbbdd eeeeeeeeeeeeeeeeeeeeeeeeeaaeeeeedbeee ddbbbbbbde eeeeeeeeeeeeeeeeeeeeeeeeeeceeeeeebeee ddbbbbbdd eeeeeeeeeeeeeeeeeeeeeeeeeeaaeeeeedbee edbbbbbbdd eeeeeeeeeeeeeeeeeeeeeeeeeeeceeeeeebggddbbbbbbde gggggggggggggggggggggggggggcaggggggbbdd c cf c c fc c fc c fa c aa c cf c ffffaaacccccccccc cf ffffaaaccccccccccccccaaffff ccccccccaaffff ``` <!-- end of image --> Let's see what secrets area A holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#5250fcff b,#fd090aff c,#0706feff d,#ff5e5eff e,#ffa6a6ff f,#9b9afdff g,#e7d8efff ``` ```image bb bbd ccbg ccbd gccb acce gccb acbd gcbbg aabd fcbbe cabb ccbbe fccbbd ccfbbg fcadbd gccfbbe acadbb gccgbb acaeb gccgbd acfebg ccfbbe fccdbb cc bbe fc ebb cf bbd aa ebbg gcg dbd ca gbbe aca bbe gccg ebb acf bbd fcc ebb ccf db fcc gbe ccf db fca be ccf bb gccg ebbg aca dbd gccg gbbe aca dbb fcc bbe ac ebb fc bbd cf ebbg cf gbb ca db ccf be aca eb gccg bd aca bbg gccg dbd aca gbbe fcc dbb fcc ebb ccf bbd fcc ebbg ccf dbd fca gbbe gcc dbb ac bb gcg eb aa bd ca bd cc bbe ccf dbb fcc bbe ccf ebb fcc bbd ccf ebbg fca dbd aca dbb gccg bbe aca ebb gccg bb acf ebg fcc dd cc gbe fc bb cf bbe cf bbd ca ebbg ccg dbd aca gbbe gccg dbb aca bbe gccg ebb acf bbd ccf dbd fcc gbb ccf db fca be gccf eb aca bd gcc bbg ac dbd gcg gbbe fcg gbbe cf ebb cc bbd ccf ebbg fcc dbd ccf gbbe fca dbb gccg gbb aca eb aca ebg gccg bd aca bbe fcc dbbb ``` <!-- end of image --> This isn't an intersection in area A, but I'm not discouraged. I'm extremely confident. No intersections at all.

<!-- image --> ```palette Key,Color ,#fefefeff a,#5959feff b,#f92a30ff c,#0707feff d,#ff7070ff e,#ffb8b8ff f,#aaaaffff g,#fe0202ff ``` ```image e bd cb cb cb fcg cge fcg cbd aag cdb aag ceg cfge c g cfbd c g c db fc g c eg fc ge c g aa bd c g aa db c g cf eg c ge cf g c bd c g fc db c g fc eg c ge aa g c bd aa g c db cf g c eg cf ge c g c bd fc g c db fc g c eg aa ge c g aa bd c g cf db c g cf eg fc ge c g fc bd edbggg c g edbgggggde aa db edgggggbde c g edbgggggbde aa eg edbgggggde c ge edgggggbde cf ggbde c cf c c fc c fc c aa c aa c cf c fffaaaccccccccccc cf fffaaacccccccccccccccaaaffff ccccccccaaafff ``` <!-- end of image -->

This image might have some surprises. Let's look for intersections carefully. I wonder what's going on inside those areas? Perhaps intersections are hiding there. <!-- image --> ```palette Key,Color ,#fefefeff a,#4d51f8ff b,#fd0a09ff c,#f36e69ff d,#a1a3fbff e,#0707feff f,#aed5aeff g,#ffb8b8ff ``` ```image ded e ed aa ea e ea aa ea e ea aa ea e ee aa ee e ae ed ae e ae ed ae e ae ed de e de ed de e de ed de e e ed e de ed e ed de ed e ed de ed e ea de ea e ea de ea e ea da ee e ee aa ae e ae aa ae e ae aa de e de aa de e de ed de e ed e ed e ed e ed de ffffffffffffefffff ffffffffffffefffff fffffffffffeffffff ffffffffffdeffffff ffffffffffefffffff fffffffffdefffffff fffffffffeffffffff ffffffffaeffffffff fffbbfffefffffffff ffffcbbaefffffffff ffffffcebfffffffff ffffffaecbbfffffff ffffffefffcbbfffff fffffaafffffcbbfff fffffeffffffffcbbf ffffaaffffffffffcbb ffffefffffffffffffgbbg fffaafffffffffffff gbbg fffaffffffffffffff gbbg ffffffffffffffffff bbg ffffffffffffffffff bbg bbg bbc bbc bbc bbccccgggg gccccbbbbbbbbbbbbbbbbbbbbbbccccgggg ggggcccccbbbbbbbbbbb ``` <!-- end of image --> I'm analyzing this close-up of area A with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#4848ffff b,#fe0e0eff c,#ff9696ff d,#8282feff e,#0504feff f,#cbcbffff g,#950871ff ``` ```image aea feef aea feef aea feef aed feef aed fee aed fee aed dee eed dee cc eed cbbbc dee cbbbbc eed cbbbbcdee cbbbeed cgeebc eegbbbc dea cbbbbc eef cbbbbc dea cbbbbc feef cbbbbc dea cbbbbc feef cbbbbc aea cbbbb feef cbb aea c feef aea feef aea feef dd ``` <!-- end of image --> I observe an intersection inside area A. There's only one, but is an intersection after all.

<!-- image --> ```palette Key,Color ,#fefefeff a,#4343ffff b,#fe0a0aff c,#ff6c6cff d,#8282feff e,#0505ffff f,#c7c7ffff g,#ffb6b6ff ``` ```image f ded e ed da ed e ea aa ea e ea aa ea e ee ad ae e ae ad ae e ae ed de e de ed de e de ef fe e fe ef fe fe fef ef ef fe ef ef ef fe ef e ed fe ed e ed de ea e ea de ea e ea da ee e ae da ae e ae aa ae e de aa de e de ad de e fe ad fe e f ed e ed e ef fe ef fe ef fe ef fe e fe e de bc e cbbde ceb dacbb e cbb da gbb e gbb aa gbb e gbbg aa gbbg d gbbg bbg bbg bbg bbc bbc bbc bbccccgggg gccccbbbbbbbbbbbbbbbbbbbbbbccccgggg ggggcccccbbbbbbbbbbb ``` <!-- 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,#5c5efbff b,#fd0808ff c,#0808feff d,#f66661ff e,#adaffaff f,#ffc2c2ff g,#add4adff ``` ```image f bbbd dbf dbbf bb fbbd fbd dbbf db fbbd bb dbbf fbd fbbd db dbbf bb fbbd fbf dbbf bb fbbd bd dbb gggggggggggggggg dbf fbbd gggggggggggggggg bb dbb ggggggggggggggggfbd fbbd gggggggggggggggdbf ac dbb ggggggggggggggbb acaca fbbd gggggggggggggbdg ecc c bb gggggggggggdbggg ecc ec ggggggggggbbgggg ecc ca ggggggggdbdggggg cc c gggggggbbggggggg cce c ggggggbbgggggggg cce ac ggggdbgggggggggg aca ce gggbbggggggggggg aca c ggbdgggggggggggg aca ac gbgggggggggggggacc ce gggggggggggggecc c ggggggggggggccgg ec ggggggggggccgggg ca ggggggggcceggggg c ggggggccaggggggg ec aca ca aca c ca ec aa c c ac ce c ac ce c ec ca c ec ca c ec aa ce c ac ce c ac ce c ec ca c ec ca c c aa ce c ac ce c ec ce c ec ca c ``` <!-- end of image --> I wonder what we'll find inside area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#5555ffff b,#ff0606ff c,#0707ffff d,#ff4343ff e,#b5b5ffff f,#ffceceff g,#ff8c8cff ``` ```image f gb dbb fbbbg gbbbf dbbd fbbbg gbbdf fdbbd fbbbg gbbdf fdbbg gbbbf dbbdf fdbbg gbbbf dbbd fbbbg gbbdf fdbbd fbbbg fbdf f e eac eaccc eaccca accca acccae acccae ecccae ecccce ecccce ``` <!-- end of image --> Based on this close-up, I can conclude that there's no intersection in area A. Zero, Nada.

<!-- image --> ```palette Key,Color ,#fefefeff a,#4444ffff b,#ff0808ff c,#0606ffff d,#ff6565ff e,#c8c8ffff f,#ffc1c1ff g,#8585ffff ``` ```image f bbbd dbf dbbf bb fbbd fbd dbbf db fbbd bb dbbf fbd fbbd db dbbf bb fbbd fbf dbbf bb fbbd bd dbb dbf fbbd bb dbb fbd fbbd dbf ac dbb bb gcacg fbbd fbd gca c bb db ecc ec bb ecc aa fbf cce ce bb cce ec bd ccg aa dbf acg ce bb aca c bd gca gc bf gca cg ecc c ecc gc cce cg cce c acg ec acg ca gca c ca ec aa ce ec aa ce c gc cg c gc cg c ec ca c ec aa ce c ac ce c gc cg c gc cg c ec aa ce ec aa ce c gc ce c gc cg c ec cg c ``` <!-- end of image -->

The hunt for intersections begins! Let's analyze this image closely. After a thorough analysis, I conclude that there are no intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff3e3eff b,#0d0dffff c,#b2b2ffff d,#ff8080ff e,#ff0505ff f,#ffcfcfff g,#6060ffff ``` ```image c gbbbgc cbbbbg cgbbbbc cgbbbgc gbbbbg cgbbbgc cbbbbgc gbbbbbbbbbbgggggggggggggggcccccccccccccc ccccccccccccccgggggggggggggggbbbbbbbbbbbbbbb de fede ef ed ed ef ae fe fe de e ed ed ef aa fe fe de e ed ef ef aa fe de de e ed ef e ea fe de ae fe ed ef e ed fe de aa fe ed ef e ed fe ae aa fe ed e e ed fe aa aa fe ef e e ef fe aa aa de ef e e ef de ea aa de ef fe e ef de ed aa de ef fe e e de ed ea aa ef d e de ed ef fe de ed ef fe de ed e ``` <!-- 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,#fe0908ff b,#0909feff c,#fbacabff d,#a1a6f6ff e,#aed5aeff f,#f75854ff g,#5754f7ff ``` ```image aa caca a ff a ac af a fa ca ca af a a ac a af fa ca ac a a a ca ac af fa ac ca a a fa ac af af a fa ca a fa a ac ac a fa ca ca af a a ac a af fa fa ac ca a a ca ac ff fa ac ca a a ca ac af af a fa a ca fa a ac ac a af ca ca af a gd eaeeeeeeeeeeeeeeee ac bdbbbg eeaeeeeeeeeeeeeeee af bd gbbbd eefaeeeeeeeeeeeeee b dbbbg eeeafeeeeeeeeeeeee b gbbbd eeeeaeeeeeeeeeeeee b dbbbg eeeeeaeeeeeeeeeeee b gbbbd eeeeefaeeeeeeeeeee db dbbbg eeeeeeaceeeeeeeeee db gbbbdeeeeeeeaeeeeeeeeee db dbbbgeeeefaeeeeeeeee db eegbbbdeafeeeeeeee db eeeeedbbbgeeeeeeee db eeeeeeeeegbbbdeeee db eeeeeeeeeefadbeeee db eeeeeeeeeeeafeeeee gb eeeeeeeeeeeeaeeeee gb eeeeeeeeeeeecaeeee gb eeeeeeeeeeeeefeeee gb eeeeeeeeeeeeeeeeee gb eeeeeeeeeeeeeeeeee gb eeeeeeeeeeeeeeeeee gb eeeeeeeeeeeeeeeeee bb bb bb bb bg bg bg bg bg bg bg bd bd bd ``` <!-- end of image --> Let's take a closer look at area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0909ff b,#0706fdff c,#fdb0b1ff d,#a9a9ffff e,#8f0372ff f,#ff5a5aff g,#5654fdff ``` ```image caac caac faa aaf caac faa faf aaf caac faa aaf caac caa faa aaf caac faa d aaf bbgd caac bbbbbbgd caac ddgbbbbbgd faa dgbbbbbbgd aaf ddgbbbbbgdcaac dgbbbbbbee ddgbbbbbgd dgbbbbbbgd caegbbbbb faa dgbg aaf caac caac faa aaf caac faa fc ``` <!-- end of image --> There's no doubt about it - this is an intersection in area A. After careful examination, I conclude that there is one intersection.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0606ff b,#0b0bffff c,#ff8989ff d,#b1b1ffff e,#fec9c9ff f,#ff4545ff g,#615dfaff ``` ```image e fa caea a ff ae ae ac a fa ca ea af a ae ae ea af fa ca ac ea a ae ea ac ff fa ae ea a a ca ae ac af a ca ea ea ff a ae ac a ff ca ea af a ae ae ea af ca ca ac ea a a ea ac ff ff ae ca a a ca ae ac af a fa ea ea fa a ac ac a ff ea ca ff a bd ae ae bdbbbg a ac bd gbbbd ca bd dbbbg ac b gbbbd a b dbbbg ea db gbbbd ff db dbbbg ae db gbbbd a db dbbbg ca db gbbbd af db dbbbge db gbbbd db fadb gb ac gb a gb ea gb f gb gb gb bb bb bb bb bb bb bg bg bg bg bg bg bg bd bd ``` <!-- end of image -->

I'm analyzing this image to identify any points where lines intersect. Could these regions be concealing intersection points? Let's find out. <!-- image --> ```palette Key,Color ,#fefefeff a,#f34641ff b,#0607fdff c,#5e61e4ff d,#ef958dff e,#fd0606ff f,#97c699ff g,#b1d7b1ff ``` ```image ae eaa e e ed de de e e e ed ed aa e ge ad fgggggggggggggefggggggggggeggggggggggggggggf fggggggggggggeagggggggggggaagggggggggggggggf fgggggggggggdegggggggggggggegggggggggggggggf fgggggggggggeggggggggggggggdeggggggggggggggf fggggggggggedgggggggggggggggeggggggggggggggf bbcg fgggggggggaeggggggggggggggggdegggggggggggggf cbbbbcg fggggggggfeggggggggggggggggggedggggggggggggf cbbbbcg fggggggggeggggggggggggggggggggeggggggggggggf cbbbbcfggggeaggggggggggggggggggggeagggggggggggf fgcbbbbceggggggggggggggggggggggegggggggggggf fgggggfcbbbbcfgggggggggggggggggaaggggggggggf fgggggedgggfcbbbbcfgggggggggggggeggggggggggf fggggaegggggggggfcbbbbcgggggggggaegggggggggf fgggfegggggggggggggggfbbbcfggggggegggggggggf fgggefgggggggggggggggggggcbbbcgggdeggggggggf fggeaggggggggggggggggggggggggcbbbcedgggggggf fgdeggggggggggggggggggggggggggggfbbbcfgggggf fgeggggggggggggggggggggggggggggggggecbbbcggf fedgggggggggggggggggggggggggggggggggegggcbbbg aeggggggggggggggggggggggggggggggggggaagggggcbbbc eggggggggggggggggggggggggggggggggggggegggggf cbbbc efggggggggggggggggggggggggggggggggggggaeggggf cbbbg aafgggggggggggggggggggggggggggggggggggggeggggf gbbbc de fgggggggggggggggggggggggggggggggggggggdegggf cbbbc e fggggggggggggggggggggggggggggggggggggggefggf cbb ed fggggggggggggggggggggggggggggggggggggggfeggf de fgggggggggggggggggggggggggggggggggggggggedgf e fggggggggggggggggggggggggggggggggggggggggegf e gffffffffffffffffffffffffffffffffffffffffeag aa e de aa e e ed de de e e e e ed aa e de ad e e ed aa de e a de e de ed e ed e aa e de e de e e ed e aa e da e de e e ed e ad e aa e ``` <!-- end of image --> Could this be where the intersection is hiding, in area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#fa3b3fff b,#0404feff c,#524af7ff d,#fec0c1ff e,#fe0505ff f,#ff7c7cff g,#a1a1ffff ``` ```image deef aef aea dee fee aef deed deed eef aea aea deed feed fea deef eef aea fee fee aef deed dee eef aef aea deed feed aea deef deed aea fea fee eed cgg deed fee bbbbbcgg eef eef gcbbbbbbbccgg aea dee ggcbbbbbbbccaed aef ggcbbbbbbbccgg deed accbbbbbbbccg aea fee ggcbbbbbbbccg deed deed gccbbbbbbbccg fea eef gccbbbbbbbccg eed aea gccbbbbbbbcg fee deed gccbbbbbccg eef deef ggcbbbbbcg fee aea gcbbbbbbcg aef feed gcbbbbbccg deed deed ggcbbbbbcg aea eea gcbbbbbbcgdeed fee gcbbbbbbca deed gccbbbbbcg eef gcbbbbbbcg aea eeccbbbbbcgg feed fee gccbbbbbcg deed aef gcbbbb aea dee ggc fee aef deed deed eef aea ea deed ed fea f eef fee aef dee aef deed aea deed fea eed fee eef dee ``` <!-- end of image --> Yes! I knew it! There's an intersection right here in area A! Two intersections have been found!

<!-- image --> ```palette Key,Color ,#fefefeff a,#f93339ff b,#0808feff c,#6a67fbff d,#ffc1c1ff e,#fe0404ff f,#ff7575ff g,#c2c2feff ``` ```image d ae defa e e ef de fe ed e de ed ed aa e de af e e ef fa fe e e fe ed e bbcg aa de gbbbbcg de ed cbbbbcg e e cbbbbcg ef af cbbbbca e gabbbbcg aa ed gcbbbbcg e fa gcbbbbg fa de gbbbcg e ed cbbbc de af cbbbged de gbbbcg e ecbbbc ed e cbbbg fe af gbbbcg e e cbbbc ed fa gcbbbg aa e gbbbc de de cbbbc e ed gcbb ef de fe ed e e ed af aa e de fa e e ef de fe ed e de ed ed aa e de af e e ef fa fe e a fe e de ed e ef e aa e fa e de ed e ef e af e fa e de ed de ed e af e fa e ``` <!-- end of image -->

I'm approaching this image with caution. Intersections might be tricky to spot. My final answer is: no intersections found.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0b0bffff b,#ff0606ff c,#ff9898ff d,#6363ffff e,#adadffff f,#f1dce9ff g,#ff4b4bff ``` ```image e fdaaa eaaad eaaadf daaae eaaad fdaade daaae eaaadf fdaaae daaad eaaadf daaae ad aa da ea g fa fb af b ae bc ad cb aa b da bc ea cb fa b af bf ae gg ad fb aa bf da bg ea cb fa b af bc ae cb ad b aa bc da gb ea fb fa bf af gg ae fb ad bf aa bg da cb ea b fa bc af cb ae b ad bc aa gb da fb ea bf fa gg af fb ae bf bg cb b bc cb b bc gb fb bf gg fb bf bg bc cb fgbbgc b cbbbgf bc cbbbc cb fgbbbc b cbbbgf bc cbbbc gb fgbbbc fb cgbbgf bf cbbbc gg fgbb ``` <!-- end of image -->

I'm on the case! Let's uncover any intersections hidden in this image. I need to zoom in on these areas to get a better look. <!-- image --> ```palette Key,Color ,#fefefeff a,#f6a29eff b,#0606feff c,#fe0706ff d,#4e52f0ff e,#a1a5f6ff f,#add5adff g,#f6534fff ``` ```image gc e cgg be c c b cg ac be ac c b c c b ca ca eb gc c b c gg eb ca c b gg ac ed c c b c ac dd cg ca b ac c de c ca b ca c be ac gg b c c be ca ac b gg c ffbfffffffffffcf ac ffebfffffffffcff ca fffbffffffffcgff c fffdbffffffacfff gg ffffbffffffcffff c ffffddffffcgffff gg fffffbfffgcfffff c fffffddffcffffff ac ffffffbfcaffffff c ffffffbdcfffffff c fffffffbffffffff ca ffffffcbefffffff c fffffcgfbfffffff gg ffffacffbeffffff c ffffcffffbffffff ac fffcgffffbffffff c ffgcfffffebfffff ac ffcfffffffbfffff ca fcafffffffdbffff c gcfffffffffbffff ca cffffffffffddfff c c b gg gg dd c ac b ac c be c ca b ac ac be ca c b c ca be cg gc eb c g b gg eb c b ac eb c b c dd ca b c dd gg b c be gc b c be ac b ca b c eb ca b c eb ffffggfffffffff b fffffcfffffffff ed fffffgcffffffff b ffffffcffffffff dd ffffffacfffffff b fffffffcaffffff dd ffffffffcffffff b ffffffffcgfffff be fffffffffcfffff b eeeedddbbbbbbbbffff be eeeedddbbbbbbbbbbbbbbbbdddddeeffffffcffff bbbbbbbbddddeee fffffffffffffff fffffffffffffff fffffffffffffff fffffffffffffff ``` <!-- end of image --> This close-up might reveal an intersection in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff8585ff b,#0908feff c,#fe0505ff d,#655ef8ff e,#b5b5ffff f,#fecbccff g,#fa393eff ``` ```image ebb fcc dbd gcg ebb accf bbd fcca ebb gcg bbe acc ebb fccf bbe cca dbb gcg bbe accf dbd fcca bbe gcg dbd accf ebbe fcca dbd gcg ebb acc dbd fccf ebbfcca bbdcg ebbcf fbbd ggbb accbbe fccadbb gcg bbe acc dbd fccf bbe cca dbd gcg ebbe accf dbd fcca ebb gcg dbd accf ebb fcca bbd gcg ebb acc bbe fccf ebb cca bbe gcg dbb accf bbe ``` <!-- end of image --> Amazing! This area was hiding an intersection all along! Onward to the next region of interest. I wonder what we'll find inside area B? <!-- image --> ```palette Key,Color ,#fefefeff a,#ff5f5fff b,#0707ffff c,#ff0909ff d,#5d57f8ff e,#b0adfcff f,#ffb7b7ff g,#790085ff ``` ```image cca fccf aca fccf acc ccf acc cca fcc aca fccf aca ccf acc ccf fcc cca fcc aca eeeeeggde ddddddbbbbbbbbbbbbbbbbd bbbbbbbbbbbbbbbbbdddggd ddeeeeeee acc af ``` <!-- end of image --> An intersection is present within area B. There's for sure two intersections on the image you sent me.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff7979ff b,#0707feff c,#ff0303ff d,#5c59fcff e,#afafffff f,#fec0c0ff g,#ff3535ff ``` ```image f gc e fcag be c c b ga fc be fc cf b c fc b ca ca eb ac c b c ga eb cf c b gg ag dd fc c b c fc dd ga cf b fc c dd c ga b ca c be ac gg b c c be cf ac b gg c b fc fc eb c cf b ga c eb fc ga b c c dd ca ag b ac c dd c fc b cf cf bdg fc fb ca cbe c gg b ga fc be c c eb ag ca b c ac eb fc c b cf cf eb c ag b ca c dd c cf b gg gg dd c fc b ac c be c ca b fc ac be cf c b c cf be ga ag eb c a b ag eb c b fc eb cf b fc dd cf b c dd ga b c be ag b c be fc b cf be c eb ca b c eb gg b c db ac b c dd fc b cf dd c b ga be c b eeeddddbbbbbbbb be eeeedddbbbbbbbbbbbbbbbbddddeee c bbbbbbbbbdddeeee ``` <!-- end of image -->

I'm on the case! Let's uncover any intersections hidden in this image. I've spotted 2 narrow regions that might be worth examining further. Let's call them area A,, and B. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0707ff b,#0707fdff c,#f9a9a6ff d,#494ef0ff e,#aed5aeff f,#f35651ff g,#8e94efff ``` ```image c ac a ac a a ca a ca a ff a ff a ac a ac ca a ca a cf a ff a fc a ac a ac ca a ca a ff a ff a ac a ac a eeeeeeeegdeeee a gdbbbbbbddeeee ca ggdbbbbbbdgeeeeeeeeeee a ggdbbbbbbdg eeeeeeeeeeeeee ca gdbbbbbbdg eeeeeeeeeeeeee eeeaeeeeeeeeeeee gdbbbbbbdg eeeeeeeeeeeeee eeeffeeeeeeeeeee gbbbdg eeeeeeeeeeeeee eeeeaeeeeeeeeeeedb eeeeeeeeeeeeee eeeeffeeeeeeeeebb eeeeeeeeeeeeee eeeeeaeeeeeeeebb eeeeeeeeeaeeee eeeeeafeeeeeebde eeeeeeefafeeee eeeeeeaeeeeebdee eeeeeeaaeeeeee eeeeeeaceeebgeee eeeefaceeeeeee eeeeeeeaeebeeeee eeeaaeeeeeeeee eeeeeeeagbeeeeee eaaeeeeeeeeeee eeeeeeedbeeeeeee cafeeeeeeeeeeee eeeeeedbaeeeeeee aaeeeeeeeeeeeeee eeeeebbefaeeeeee cac eeeeeeeeeeeeee eeeebbeeeaeeeeee aa eeeeeeeeeeeeee eeebdeeeeffeeeee fac eeeeeeeeeeeeee eebdeeeeeeaeeeee aa eeeeeeeeeeeeee ebgeeeeeeeffeeee fa eeeeeeeeeeeeee beeeeeeeeeeaeeee caf eeeeeeeeeeeeee gbeeeeeeeeeeeafeee aa gb eeeeeeeeeeeeaeee cac db eeeeeeeeeeeeacee aa bb eeeeeeeeeeeeeaee fac bd a aa bd ca fac bg a caf bg ca aa b a caf gb ff aa gb a fac db ff aa bb a fac bd afaf bd a bg ``` <!-- end of image --> Let's see if area A yields any clues. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff0606ff b,#0909feff c,#fe8787ff d,#5b57fbff e,#ffc9c9ff f,#f33e49ff g,#b9b8fdff ``` ```image caa aac caf aae caf eaae faf eaae fac b eaa gbb fac gbbb eaa gbbd aac gbbd caa dbbd aac dbbd caf dbbg aae dbbg caf bbbg eaae gbbbg faf gbbb eaagbbd ffbbd dbbd dbbfc dbbdaa dbbg aac bbbg caa gbbbg aac gbbb caf gbbd aae gbbd caf dbbd eaae dbbd faf dbbg eaae dbbg fac bbbg eaa bbg fac b caa aac caa aae caf aae caf ``` <!-- end of image --> I can confirm that an intersection exists in area A. Let's shift our focus to the next area. I'm focusing my attention on this specific region, area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff0606ff b,#0303ffff c,#ff8686ff d,#4848ffff e,#f2cdd9ff f,#ff4242ff g,#9595ffff ``` ```image eggdg eggdddbbbbbbd egggddbbbbbbbbbbbddgg bbbbbbbbbbddggge bbddggge cac efaaf caaac efaafe caaac eaaaf faaae caaac efaafe caaac efaafe caaac eaaafe aaae ac e ``` <!-- end of image --> The evidence suggests that this is not an intersection point in area B. I have found one intersection!

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0404ff b,#0909ffff c,#ff7e7eff d,#6564feff e,#ffc0c0ff f,#ff3d3dff g,#bbbbfeff ``` ```image e ac a ae ea a ea a cf a cf a fc a ae a ae ea a ea a cf a ff a fc a ae a ae ea a ea a cf a fc a fc a ae a gd ae gdbbbbbbdd ea gddbbbbbbdg a gddbbbbbbdg ca gddbbbbbbdg a ggdbbbbbbdgg cf dbbbddg a db fc bb a bb a fc bd cac a bd aa ae bg fae a gbg eaf agb fae db eaf dba aa bb ca cac bb a aa bd cf cae bd a af bg fc fae gbg a eaf gb ac aa db a cac db ae aa bb ea cae bb a af bd ea fae bd a eaf bg cf aa gbg a cac gb cf aa db a cae db fc af bb a fae bb acaf bd a bd ``` <!-- end of image -->

Here's an image. My task is to find intersections or areas where lines come close together. I'm extremely confident. No intersections at all.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff4e4eff b,#3c3cffff c,#bbbbffff d,#ff0505ff e,#ffa8a8ff f,#7c7cffff g,#0303ffff ``` ```image e addd eadda eddde adda eddde addde eadda eddde adda eddde addae eadda ddde dd ade edd dd ade eda dd ade eda dd ade eda dd ade eda dd ade eda dd ade eda a cfb ccfbgggggggbfc cffbgggggggbfcc cfbbgggggggbfc cfbgggggggbbfc fgbffc fgb fgb cgg cgg cgg cgg ggc ggc ggc ggc bgf bgf bgf bgf fgb fgb fgb gb ``` <!-- end of image -->

Alright, let's get to work and investigate this image for intersections. Could these regions be concealing intersection points? Let's find out. <!-- image --> ```palette Key,Color ,#fefefeff a,#f84542ff b,#0404feff c,#6467f8ff d,#f58c87ff e,#fe0505ff f,#f6cdd5ff g,#afd5afff ``` ```image ggggggggggggggg gggcbbbbcgggggg cbbcggggcbbgggg cbbcgggggggggcbbcg cbbc gggggggggggggbbc cbbc gggggggggggggggcbbf cbbc ggggggggggggggg fbbc cbbc ggggggggggggggg cbb cbbc ggggggggggggggg cbbc cbbc ggggggggggggggg bbc cbbc ggggggggggggggg cbbf cbbc ggggggggggggggg fbbc cbbc gggggaegggggggg cbb c gggggedeggggggg gbbc ggggaagaagggggg bbc ggggegggegggggg cbbf gggaaggggeggggg fbbc gggegggggaegggg cbb ggedggggggedggg gbbc ggeggggggggeggg b gedggggggggdegg geggggggggggeag edgggggggggggeg feggggggggggggge eggggggggggggggae feggggggggggggggged efggggggggggggggg e de ggggggggggggggg de e ggggggggggggggg ea da ggggggggggggggg ef e ggggggggggggggg fe aa ggggggggggggggg aa e ef aa e e de ad ed e e ed fe e aa ef ef fe e ef de fe ed ef e de fe e aa de ef e fe da ae e ed aa e e de ad ea e ef ed fe e aa ed ef fe e ef de fe ed ef e fe fe e aa de ef e e da de e ed aa e e fe aa aa e ef ad fe e ae ed e e ef fe ef fe ef ``` <!-- end of image --> Time to investigate area A up close. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff4646ff b,#0909ffff c,#6868ffff d,#ff8484ff e,#fe0505ff f,#ffccccff g,#b9b9ffff ``` ```image gg gcbbbbg gcbbbbbbbbbcg gcbbbbbcg cbbbbcg gcbbbbbcg gcbbbbc bbbbbcg cbbbbcg bbcg gbbbbbg g gcbbbbc cbbb gc ff eef deee feeeea aeafeed feef deef aea aea feef feed aea deef feef aee aed eed fee feef aed dee dee aea eed feed dee deef eed aea dee eed eed feef dea dee eef aea dea feed feef deef aea aea feef fee aea fe eef a ea ef d ``` <!-- end of image --> Based on this close-up, I can conclude that there's no intersection in area A. I'm extremely confident. No intersections at all.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff4343ff b,#0505ffff c,#6161ffff d,#ff8686ff e,#ff0505ff f,#ffcbcbff g,#b0b0ffff ``` ```image g cbbbbc cbbc cbb cbbc gbbg cbbc bbc cbbc cbbg cbbc gbbc cbbc cbb cbbc gbbg cbbc bbc cbbc cbbg cbbc f gbbc cbbc de cbb g efe gbbg aa aa bbc e ef cbbg ad e gbbc e de cbb ed ed gbbg e e b ed fe e aa ef ef fe fe ef ae fe ed e e de de e ed da e e fe aa aa e ef aa e e de ad ed e e ed fe e aa ef ef fe e ef de fe ed ef e fe fe e aa de ef e fe da ae e ed aa e e de ad ed e ef ed fe e aa ed ef e e ef de fe ed ef e fe fe e aa de ef e e da de e ed aa e e fe aa aa e ef ad fe e ae ed e e ef fe ef fe ef ``` <!-- end of image -->

I'm on the case! Let's uncover any intersections hidden in this image. It's crucial to examine these regions more closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#0909feff b,#fe0707ff c,#6264fbff d,#ffb3b3ff e,#afd5aeff f,#b9bafeff g,#f85956ff ``` ```image f aa affa faf af ca a aa ca aa a ac fa faf ac fa a ca fa aa af ac a ac ca faf a ca fa aa ac aa a ac fa af af fa a ca ca aa af ac fa ac ac faf a eeeeeeeecaeeee fa eeeeeeeaaeeeee af eeeeeeaaeeeeee a eeeeeaceeeeeee ca eeeeaceeeeeeee af eeeaeeeeeeeeee a eeeebeeeeeeeee ac eeeegbeeeeeeee a eeeeebgeeeeeee fa eeeeeebeeeeeee af eeeeeeebeeeeee a eeeeeeegbeeeee ca eeeeeeeebgeeee af eeeeeeeeebeeee a eeeeeeeeeebeee cc eeeeeeeeeegbee a eeeeeeeeeeebge fa eeeeeeeeeeeebe af eeeeeeeeeeeeeb a db ca gb af bd a b cc db a gb fa bg ac b a b ca gb af bg a bd cc b a db fa gg ac bd a b ca db af gb a bg cc b a b fa gb ac bg a bd ca b a db bg bd b db gb bgdd gbbbbbbbbbbbbbbbbbbbbbbbgggggddddd dddddgggggbbbbbbbbbbbb ``` <!-- end of image --> I'm analyzing this close-up of area A with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#0e0cfdff b,#fd0809ff c,#7070ffff d,#fcc7c9ff e,#ff9191ff f,#c9c8feff g,#ff5151ff ``` ```image faaaf faaaf caac caac aaac faaaf faaaf caaa caac caac faaaf faaaf daaf bbg dbbe ebbd gbb bbg dbbe ebbd gbb bbg dbbe ebbd gbbd gbg dbbg dbbe ebbd gbb bbg dbbe ebbd gbb bbg dbbe ebbd gbb ``` <!-- 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,#0505feff b,#ff0707ff c,#8a8affff d,#ffb3b3ff e,#4242ffff f,#cdccfeff g,#ff5959ff ``` ```image f aa acca faf af ca a ea ee ae af ac fa faf ac ca a ea ca aa af ae a ac ee faf af ca fa ea ec ae a ae ca faf ac caf a ea ee aa af ae fa ac ee faf a ca ca ea ac aa a ae ce fac af af fa db ee gb a bd fa b ac db a gb ca bg af bd fa b ee db a bg fa bd ac b a db ca gb af bd a b ee db a gb fa bg ac b a b ca gb af bg a bd ee b a db fa gg ac bd a b ca db af gb a bg ee b a b fa gb ac bg a bd ca b a db bg bd b db gb bgdd gbbbbbbbbbbbbbbbbbbbbbbbgggggddddd dddddgggggbbbbbbbbbbbb ``` <!-- end of image -->

Hmm, I'm not sure what to expect from this image. Let's see if any lines cross. My final answer is: no intersections found.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff5e5eff b,#2323ffff c,#ff0808ff d,#8f8fffff e,#ffa2a2ff f,#0101ffff g,#f1dae7ff ``` ```image egg acccccccccccaaeeg ggeaaacccccccccccaaeeg geeaaccccccca acce gcccg ecca acce gcccg ecca acce gcccg ecca acce gcccg ecca acce gcccg ecca acc g b bfd bfd bg bfd gffg bfd gff bfd dfb bfd dfb bfd dfb bfd dfd bfd bfd bfd bfd bfd bfd bfd ffg bfd gffg bfd gffg bfd dff bfd dfb bfd dfb bfd dfb bfd bfd bfd bfd bfd bfd ``` <!-- end of image -->

Let's examine this image for potential line intersections. There are 1 regions I'd like to highlight in the image. <!-- image --> ```palette Key,Color ,#fefefeff a,#0405fdff b,#fc0606ff c,#9399f3ff d,#de5853ff e,#4745efff f,#b1d7b1ff g,#98c498ff ``` ```image gfffffffffffffffffffffffffffffffffg gffffffffffffffffffffffffffffffffff gffffffffffffffffffffffffffffffffff gffcfffffffffffffffffffffffffffffff gffacffffffffffffffffffffffffffffff gfffaffffffffffffffffffffffffffffff gfffagfffffffffffffffffffffffffffff gffbgafffffffffffffffffffffffffffff gffgbafffffffffffffffffffffffffffff gfffddaffffffffffffffffffffffffffff gffffbaffffffffffffffffffffffffffff gfffffeefffffffffffffffffffffffffff gfffffdafffffffffffffffffffffffffff gffffffeeffffffffffffffffffffffffff gfffffffaffffffffffffffffffffffffff gfffffffadfffffffffffffffffffffffff gffffffffabffffffffffffffffffffffff gffffffffabdfffffffffffffffffffffff gffffffffgabfffffffffffffffffffffff gfffffffffadbffffffffffffffffffffff gfffffffffcabdfffffffffffffffffffff gffffffffffafbgffffffffffffffffffff gffffffffffeefbffffffffffffffffffff gfffffffffffafdbfffffffffffffffffff gfffffffffffeefbdffffffffffffffffff gffffffffffffaffbffffffffffffffffff gffffffffffffacfgbfffffffffffffffff gfffffffffffffaffbdffffffffffffffff gfffffffffffffagffbgfffffffffffffff gfffffffffffffgafffbfffffffffffffff gffffffffffffffafffdbffffffffffffff gffffffffffffffcafffbdfffffffffffff gfffffffffffffffaffffbfffffffffffff gfffffffffffffffeefffgbffffffffffff gffffffffffffffffaffffdbfffffffffff gffffffffffffffffeeffffbgffffffffff gfffffffffffffffffafffffbffffffffff gfffffffffffffffffacffffdbfffffffff gffffffffffffffffffafffffbdffffffff gffffffffffffffffffagfffffbffffffff gffffffffffffffffffgafffffgbfffffff gfffffffffffffffffffaffffffdbffffff gfffffffffffffffffffcaffffffbdfffff gffffffffffffffffffffafffffffbfffff gffffffffffffffffffffeeffffffdbffff gfffffffffffffffffffffafffffffbdfff gfffffffffffffffffffffeefffffffbgff gffffffffffffffffffffffaffffffffbff gffffffffffffffffffffffacfffffffdbf gfffffffffffffffffffffffaffffffffbd gfffffffffffffffffffffffagffffffffb fggggggggggggggggggggggggagggggggggb a dd ca b a b ee db a bdffff ec dddbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb a ac a a ca a ca a ee a ec a ac a a ca a cea ce caaaaec a ceaaaaec ee ceaaaaec a ceaaaac ec ceaaaaec a caaaaec ac ceaaaaec aaec ``` <!-- end of image --> I'm analyzing this close-up of area A with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#0806fdff b,#fe0505ff c,#aaa9fdff d,#f23744ff e,#5751f8ff f,#fec2c3ff g,#fd8183ff ``` ```image cc caa aac caa aac eae aac ffeae fbbcaa dbdeae fbbgaa gbbaac dbdaa bbaac fbdaa gbaac deae fbaac geae daa aae caaf aad caad aadg caabf aadb eaabd aadbg eaebbf caadbd eaebbg caafbbf aacgbb caa dbd aacfbbg caa gbbf aac dbd eae bbg aac fbbf eae gbb caa dbd eae fbbg caa gbbf aac dbd caa bbg aac fbbf cae gbb aac dbd eae fbbg aac gbbf eae dbb caa bbd eae fbbf caa gbbf aac dbd caa bbg aac fbbf cae gbb aac dbd eae fbbg aac gbbf eae dbd caa bbg eae fbbf caa gbb aac dbd caa fbbg aac gbbf cae dbd aac bbg eae fbbf aac gbb eae dbd caa fbbg eae gbbf caa dbb aac bbd caa fbbf aac gbbf cae dbd aac fbbg eae fbbf aa gbb eae dbd caa fbbg eae gbbf caa dbd aac bbg caa fbbf aac gbb eae dbd aac fbbg eae gbb aa db ``` <!-- end of image --> Aha! I've found an intersection inside area A! One intersection, that's it, but I found it.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0404feff b,#fe0505ff c,#8484ffff d,#f64b53ff e,#453df7ff f,#feb8b8ff g,#c3c3feff ``` ```image g ac a ag bga fba dda ba ee fa ee a ad ab abf gab afb cabd a bf ce b a db ec bf a b ac fb a dd ag bf ga b a db ca bd a b ce fb a dd ec bf a b ag fb a bd ag b ga fb a db ca bf a b ce fb a bd ec bf a b ag db a bf ag b ga fb a dd ca bf a b ce db a bdfffffff ec ddddbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb a ag a ag ga a ce a ee a ec a ag a ag ga a gea ce gcaaaaec a ceaaaacg ee gcaaaaec a ceaaaacg ec geaaaaeg a gceaaaecg ag geaaaaeg aaec ``` <!-- 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,#fd0808ff b,#0809fdff c,#f06059ff d,#b0d6b1ff e,#feb6b5ff f,#6369edff g,#9ac598ff ``` ```image e ea aca ea a a ea a ae ae a a ac cc a a ca cc a a ea ea ae a a ea ac ae a a cc ae a a ea cc ae a a cc ac a a bf ea cc bf a a bb ea ea fb ae ae bd dggggggggggggagg a bf gdddddddddddacdd ae bb gdddddddddddaddd a fb gddddddddddacddd cc dbgddddddddddadddd a bfddddddddccdddd cadddddddddddddg gbbdddddddaddddd dagddddddddddddg gdbbdddddcaddddd dgaddddddddddddg gddfbgdddadddddd ddacdddddddddddg gddddbfdgadddddd dddadddddddddddg fbb gdddddbbagdddddd dddccddddddddddg dbbf gddddddbbddddddd ddddaddddddddddg fbb gddddddafbdddddd ddddcadddddddddgfbbf gddddddadgbfdddd dddddagddddddfbbf gdddddacdddbfddd dddddgaddddbbbgg gdddddadddddbbdd ddddddacfbbfdddg gddddccddddddfbg dddddfbbfddddddg gddddaddddddddgbd dddbbbgccddddddg gdddcadddddddddgbf fbbfddddaddddddg gdddaddddddddddd bb fbbfdddddddcadddddg gddgaddddddddddd fb bbb dddddddddagddddg gddagddddddddddd db fbbd dddddddddgaddddg gddadddddddddddd bf fbbf ddddddddddacdddg dgacgggggggggggg bb bbb dddddddddddadddg a fb fbbd dddddddddddacddg cc fbf ddddddddddddaddg a ddddddddddddcadg cc gddddddddddddagg a ea ea ae a a ea cc ae a a ca ae a a ea cc ae a a cc ac a a ea ca a a ea ea ae ae a a ae ac a a cc ca a a cc ea a a ea a ``` <!-- end of image --> Time to investigate area A up close. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0405ff b,#0b0afdff c,#fe8787ff d,#bdbdffff e,#fdcacbff f,#6764fbff g,#ff4444ff ``` ```image cag aae cag aac caa gac eaa gac eaa d gag bd eaae bbf cag fbbf aae dbbbd cag dbbbd aac fbbf caa fbbf gac dbbbd eaa dbbbd gac bbbf eaae fbbf gag fbbbeaae dbbbag dbbbf cbbbf aafbbf caa dbbbd gac dbbbd eaa fbbf gac fbbf eaae dbbbd gag dbbbd eaae fbbf cag fbbf aae dbbb cag dbb aac b caa gac eaa gac eaae gag eaae cag aae ``` <!-- end of image --> I can confirm that an intersection exists in area A. Onward to the next region of interest. Time to investigate area B up close. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0505ff b,#0807fdff c,#fe8687ff d,#b7b7ffff e,#ffcccbff f,#6060ffff g,#f63a43ff ``` ```image aac caa gac eaae gag eaae cag aac caa gac eaae gag eaae cag aac caa gac eaae dfb gag dfbbbb eaae dbbbbbfd cag dfbbbbfd aacdfbbbbfd cgbbbbbfd dfbbbbfd dfbbbbbgae fbbbbbfd gag dfbbbbfd eaae dfbbbbfd cag bbbbbf aac bbfd caa d gac eaae gag eaae cag aac caa aac eaae gag eaae gag eaac caa aac caae ``` <!-- end of image --> I've cracked the case! This area contains the intersection. After a long analysis, I found two intersections.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0505ff b,#0808feff c,#fe7d7dff d,#b1b1ffff e,#ffc0c0ff f,#5c5afdff g,#ff3f3fff ``` ```image e ca acg ea a ae ea a ae ae a a gc gc a a cg cg a a ea cg ae a a ea ac ae a a cg ae a a ea gc ae a a cg ac a a bd ca gg bf a a bb ea ea fb ae ae dbd a a bf ae ac bb a a fb gc gg dbd a a bf cg ca bb a ae fb ca ea db a ac bd ea a fbb bfae gg dbbf bb a fbbd afb ca fbbd a dbd ae dbbf gc bf ea bbbd a bb acfbbd cg fb dbbf a dbd bbb gg ca bf fbbd a a bb dbbf ca ea fb bbb a ae dbd fbbd ea a bf dbbf ae ae bb dbbb a a fb fbbd gg gc dbf a a ca cg a a ea ea ae a a ea gc ae a a ca ac a a ea gc ae a a cg gc a a ea cg a a ea ea ae ae a a ac gc a a gc cg a a cg ea a a ea a ``` <!-- end of image -->

I have a feeling there might be some intersections in this image. These zones are intriguing. I bet there's something interesting happening within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#8894e7ff b,#fb0b0aff c,#3f46f0ff d,#0506fdff e,#e36e60ff f,#b1d7b1ff g,#9bc598ff ``` ```image fffffffffffffffffffffffffffffffffffffffffffffffffffffffg fffffffffffffffffffffffffffffffffffffffffffffffffffffffg fffffffffffffffffffffffffffffffffffffffffffffffffffffffg fffffffffffffffffffffffffffffffffffgfffffffffffffffffffg ffffffffffffffffffffffffffffffffebbbgffffffffffffffffffg ffffffffffffffffffffffffffffgbbbefffbgfffffffffffffffffg fffffffffffffffffffffffffgbbbefffffffbfffffffffffffffffg ffffffffffffffffffffffebbbeffffffffffgbffffffffffffffffg fffffffffffffffffffebbbgffffffffffffffebfffffffffffffffg ffffffffffffffffebbbgffffffffffffffffffebffffffffffffffg fffffffffffffebbefffffffffffffffffffffffebfffffffffffffg fffffffffgbbbefffffffffffffffffffffffffffbbffffffffffffg ffffffgbbbefffffffffffffffffffffffffffffffbbfffffffffffg fffebbbefffffffffffffffffffffffffffffffffffbeffffffffffg ebbbgfffffffffffffffffffffffffffffffffffffffbefffffffffg bbffffffffffffffffffffffffffffffffffffffffffffbeffffffffg fffffffffffffffffffffffffffffffffcddffffffffffbgfffffffg fffffffffffffffffffffffffffffffddcfadffffffffffbfffffffg fffffffffffffffffffffffffffffddaffffdafffffffffgbffffffg ffffffffffffffffffffffffffaddafffffffdffffffffffgbfffffg ffffffffffffffffffffffffaddgfffffffffcdffffffffffebffffg ffffffffffffffffffffffcddfffffffffffffdaffffffffffebfffg ffffffffffffffffffffcdcffffffffffffffffdfffffffffffebffg ffffffffffffffffffddcffffffffffffffffffcdfffffffffffbbfg fffffffffffffffgddafffffffffffffffffffffdafffffffffffbbg fffffffffffffaddaffffffffffffffffffffffffdffffffffffffbe fffffffffffaddgffffffffffffffffffffffffffccffffffffffffbe fffffffffcddffffffffffffffffffffffffffffffdgfffffffffffgbf fffffffcdcffffffffffffffffffffffffffffffffgdfffffffffffg b fffffddcfffffffffffffffffffffffffffffffffffccffffffffffg b ffgddaffffffffffffffffffffffffffffffffffffffdffffffffffg b addaffffffffffffffffffffffffffffffffffffffffgdfffffffffg fb ddggggggggggggggggggggggggggggggggggggggggggggdcggggggggf eb d eb ad eb da bb d be ad be da be d bf ad b da b d b ad fb da eb d eb ad bb da bb d be cc be d bf d b cc d d cc d d dc d ad da d ad da d ad da d ad da d cc d d cc d d cc d d cc d ``` <!-- end of image --> My goal is to determine if there's an intersection inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#ababffff b,#ff0505ff c,#5555ffff d,#0707ffff e,#ff4343ff f,#ffc5c5ff g,#ff8686ff ``` ```image ff fgbbbf febbbbbbbf gebbbbbef ebbf gebbbbbgf ebbf fgebbbbegf ebe fgebbbbegf bbe fgbbbbbeg fbbe febbbbbef fbbe gebbbbbgf fbbg fgebbbbbgf fbbg fgebbbbegf gbbg fgbbbbbegf gbbf febbbbbeg gbbf gebbbbbef ebbf gebbbbbgf ebbf fgebbbbegf ebb fgebbbbegf ebe fgbbbbbeg fbbe febbbbbeg fbbe gebbbbbef fbbe fgebbbbbgf fbbg fgebbbbegf gbbg bbbbbegf gbbg bbeg gbbf f cdd ebbf acddddc ebbf acdddcadda ebbf addddca add ebb addddc cdc bbe cdddda adda fbbe cdddda add fbbe acdddca ddc fbbe acdddca adda fbbg addddc cdd gbbg addddc ddc gbbg cdddda adda gbbf acdddda cdd ebbf acdddca ddc ebbf acdddca adda ebbf addddc cdd ebe addddc ddc bbe cdddda adda fbbe acdddca cdd fbbe acdddca dda fbb acdddca adda fb addddc cdc g cdddda dda cdddda add acdddca cdc acdddca dda addddca add addddc cdc cdddda dda cdddda add acdddca cdc acdddca adda addddc cdd ``` <!-- end of image --> I'll move on to the next area. The intersection must be somewhere. My final answer is: no intersections found.

<!-- image --> ```palette Key,Color ,#fefefeff a,#8383ffff b,#ff0707ff c,#3e3effff d,#0404ffff e,#ff5b5bff f,#ffb5b5ff g,#c9c9ffff ``` ```image f ebbbf ebbe b fbbbf b fbbbf fb fbbbf fb ebbe eb ebbe eb febbe eb fbbbf be fbbbf be ebbbf be be bf cdd bf cdc ad b dda da b gddg d fb addg ad fb add dg eb cdc d eb cda ac bb gdda dg be gddg d be addg cc bf adc dg bf cdc gd bf dda cc b gdda d fb gddg gd fb dd cc fb d eb gd eb da bb d be gd be da bf d bf ad b da b d fb ad fb dg eb d eb ad eb dg be d be cc be dg bf d b cc dg gd cc d gd ca d gd da d ad da d ad da d ad dg d ac dg d cc dg gd cc d gd cc d ``` <!-- end of image -->

I have a feeling there might be some intersections in this image. These spots mark what I'd call 'danger zones' - areas where intersections are more likely. <!-- image --> ```palette Key,Color ,#fefefeff a,#5d62efff b,#ea4f4cff c,#0909fdff d,#fd0908ff e,#f49793ff f,#b5b4ffff g,#add5aeff ``` ```image gggggggggggggggggg ggggggggggggggbggg gggggggggggggedggg gggggggggggggdgggg ggggggggggggdegggg gggggggggggdbggggg ggggggggggbdggaggg ggggggggggbcccaggg gggggggacccggggggg gggacccadbgggggggg fcccagggbdggggggggg acccagggggedgggggggggg facca ggggggdggggggggggg acccf gggggdeggggggggggg fccca ggggdbgggggggggggg acccf gggbdggggggggggggg fccca gggdgggggggggggggg acccf ggdggggggggggggggg fccca gdbggggggggggggggg acf bdgggggggggggggggg c ed ca d c de cf db fc ed c d aa d c de ca bd c ed cf d fc de c db aa ed c d cf d fc de c bd ac ed c d ca de c db cf ed fc d c d aa de c bd cf ed fc d c de ac db c ed ca d c d cf de fc bd c ed ac ed c edd ca edd c edd cf edb fc bdb c bdb ggggggggggggcaggggggg bdb ggggggggggggcgggggggg bdb gggggggggggcagggggggbdb gggggggggggcggggggbdb ggggggggggcgggggbdbgg gggggggggacgggddbgggg gggggggggcggddbgggggg ggggggggcaddbgggggggg ggggggggcdbgggggggggg ggggggdcbgggggggggggg ggggddacggggggggggggg gggdegcgggggggggggggg gggggacgggggggggggggg gggggcggggggggggggggg ggggcaggggggggggggggg ggggcgggggggggggggggg gggcggggggggggggggggg ggggggggggggggggggggg ``` <!-- end of image --> This close-up of area A is like examining a piece of evidence. <!-- image --> ```palette Key,Color ,#fefefeff a,#a3a0fbff b,#f52933ff c,#0806fcff d,#fe0404ff e,#fb7f82ff f,#ffb6b6ff g,#5450faff ``` ```image gcg acc ccg acc cca f gcg fbd acca fbddd gcg fbddde acc fbddde cca fbddde gcc fbddde cca fbddde gcg fbddde acc fbddde ccgfbddde accbddde ccbdde egccde ebbcce edddccg edddbacc fdddbe cca dbf acc f cca gcg acca gcg acc cca gcc cca gcg acc aa ``` <!-- end of image --> My analysis confirms the presence of an intersection in area A. Right then, let's explore the next spot. Let's take a closer look at area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#a0a0ffff b,#f5323cff c,#0605fdff d,#fe0404ff e,#fe7f7fff f,#fcbfc2ff g,#5149f6ff ``` ```image e edb fdde ddb bdb eddf fddf fdde bdb bdd eddf aga fddeaggcccg bbgcccccgaa agccccccga agcccccgaa agccccccgbf agcccccgafdde agccccccga bdb agcccccga bdd ccccga eddf ga fdde dde bdb eddf fddf fdde bdb bdd eddf fdde dde bdb eddf fddf fdde bdb ``` <!-- end of image --> An intersection is present within area B. I can confirm there's two intersections in there.

<!-- image --> ```palette Key,Color ,#fefefeff a,#7e7bfcff b,#fc4346ff c,#0404feff d,#fe0606ff e,#fd9496ff f,#c4c4ffff g,#3d3dfeff ``` ```image e ed d de bb ed g bccca fgccgf acccade fgccgf bd accca ed fgccgf d accca de fgccg db acccf ed fgcca d acccf d fccca de acf bd c ed ga d c de cf db fc ed c d ag d c de ca bd fc ed cf d ac de c db gg ed c d cf d fc de c bb ag ed c d ga de c db cf ed fc d c d gg de c bb ca ed fc d cf de ac db c ed ga d c d cf de fc bb c ed ag ed c edd ca edd fc edb cf edb ac bdb c bdb gg bdb c bdb cf bdb fc bdb c bdb ag bde c bde gabde cde dce ddac de c gg c ca fc cf ``` <!-- 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,#fe0505ff b,#0809fdff c,#f79996ff d,#b0d6b0ff e,#99c598ff f,#6a72efff g,#f44944ff ``` ```image ca agg gg a a ca gg a a a gg ac a a gg gc a a gc gg a a ac ca a a ac ca a ac ac a a ac ac a a gg ac a a ca a a a ca a ac ca a a ac ca a a gg ca a a cg ca a a ca ca a a a cg ac a a gg gg edddddddddddadde a dddddddddddggdde gg dddddddddddaddde a ddddddddddggddde ca ddddddddddadddde a bf dddddddddggdddde a fbbdddddddddaddddde ac fbbedddddagddddde a debbfdddadddddde gc ddddbbfagdddddde a ddddddfbbdddddde gg ddddddacfbbeddde a ddddddadddebbfde ca dddddacddddddbbf a dddddadddddddddfbb ca ddddacddddddddde fbb ac ddddadddddddddde bbf a dddaedddddddddde bbf ac ddeaddddddddddde fbb eaeeeeeeeeeeeeee ddaeddddddddddde fbb dggddddddddddddd deadddddddddddde bbf ddaddddddddddddd eaeeeeeeeeeeeeed bbbf ddgadddddddddddd ca fbbbf dddadddddddddddd a fbbbbd dddcaddddddddddd ca fbbbbf ddddaedddddddddd a dfbbbf dddddadddddddddd ca fbbbf dddddacddddddddd a fbbbf ddddddaddddddddd ca fbbbbfdddggdddddddd a dfbbbbfadddddddd cg dddddfbbbbfddddd a ddddddddaefbbbdd ddddddddcadddddd dddddddddaeddddd dddddddddeaddddd ddddddddddacdddd dddddddddddadddd dddddddddddggddd ddddddddddddaddd ddddddddddddggdd dddddddddddddadd eeeeeeeeeeeeeeee ``` <!-- end of image --> Could this be where the intersection is hiding, in area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0404ff b,#0505feff c,#ff8888ff d,#9a9affff e,#fccdd0ff f,#463cf5ff g,#fc484bff ``` ```image gag eaae gag eaae gag eaae gag eaae gag eaae gag eaae gac eaae fd gac bbbd eaa dbbbbf gac dfbbbfd caa dfbbbfd aac dbbbbd caa dbbbbfeaac dfbbbfg dfbbbfd cafbbbbd aac dbbbbfe caa dfbbbfd aac dfbbbfd cag dbbbbd aac dbbb cag df aae cag eaae cag eaae gag eaae gag eaae gag eaae gag eaae gag ``` <!-- end of image --> Gotcha! I've found the intersection hiding in area A! Let's shift our focus to the next area. I'm going to scrutinize area B for any signs of an intersection. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0404ff b,#0504feff c,#fd7879ff d,#a09dfbff e,#ffc1c1ff f,#5042f0ff g,#ff3b3bff ``` ```image gac eaae gag eaae cag aae cag aac caa gac eaae gag eaae cag aae cag aac caa gac fdd eaa bbbbfdd gac dfbbbbbbffd eaae dfbbbbbbbfdcag dffbbbbbbfd ddfbbbbbbfdd dffbbbbbbfdd caaddfbbbbbbf gac dfbbf eaa gac eaae gag eaae cag aae caa aac eaa gac eaae gag eaae cag aae cag ge ``` <!-- end of image --> Amazing! This area was hiding an intersection all along! The final answer is: two intersections found.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fe0505ff b,#0808ffff c,#ff8383ff d,#acacfeff e,#ffc5c5ff f,#5656feff g,#ff4141ff ``` ```image e ca acg cg a a ca gg ae a ea gg ae a a gc gc a a gc gg a a gc ca a a ac ea a ae ac a a ac ae a a gg ae a ea ca ae a ea ea ae ae ea a a ac ea a a gg ca a a cg ca a a ea cg ae a ea cg ac a a cg gc a a gg cg a a gg ca a ae bf gc ea fbb a ae dbbd gc a dbbd a gc bbfac a fbb gg acdbbd a a dbbd ca ae bbf a a fbb ea ae dbbd ae ea dbbd a ae bbf ac ea fbb a ae dbbd gg ea dbbd a ae bbbf ca ea fbbbfd a a dbbbfd ea ea dbbbbd ae a dfbbbd a ca dfbbbf ac a fbbbfd a ca dbbbfd gg a dbbbbda cg dfbbbd a adfbbb ea ae ea ac a gc a cg a ``` <!-- end of image -->

Let's examine this image for potential line intersections. These spots mark what I'd call 'danger zones' - areas where intersections are more likely. <!-- image --> ```palette Key,Color ,#fefefeff a,#0808feff b,#f55d58ff c,#a0a0fdff d,#ffb7b7ff e,#4b4ff8ff f,#acd3acff g,#fd0c0dff ``` ```image d ggb gb gg gb bg gb dgd gg gb gg gg gg bg gg dgd gg gb gg gg gg bg bg dgd bg gb a bg gg ac bg bg ca bg dgd a bg gb ac bg gg ca bg bg fffffffffffffaff bg dg ffffffffffffaeff bg gbffffffffffcafff bg ggfffffffffaffff bg fggfffffffaeffff dg ffbgffffffafffff dg ffffgbfffaffffff dg fffffggfaeffffff dg ffffffggafffffff dg fffffffagfffffff dg ffffffeefgbfffff dg ffffffafffgbffff dg fffffafffffggfff dg ffffeaffffffbgff dg ffffafffffffffgb dg fffafffffffffffgb dg ffeaffffffffffffgg dg ffafffffffffffff b g ac ca a ac ca a ac ca a ac ca a ae c ca aa a ca ee ac a ae a aa ee ca a ac a ae ee ea a ca ac ac ea aa a ea ac ca ea ac a aa ac ea ca cac a ae ac aa ca ea a cac ac ae ca aa a ea ae cac ca ae a aaae ea ``` <!-- end of image --> I'm focusing my attention on this specific region, area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0201feff b,#fe5353ff c,#6e6cfcff d,#ffb3b3ff e,#2924faff f,#bbbbffff g,#fd0809ff ``` ```image cae faaf eac d cae gd faaf ggb eac dggb cae dgggd faaf bggd eac bggb cae dggb faaf dgggd eac gggd cae bggb faaf dggb eac dgggdcaa gggaaf beae caagb aacgggd eae dgggd faaf bggb aac bggb cae dgggd faaf dgggd aac bggb cae bggb faaf dgggd eac dggg cae bg faaf b eac cae faaf eac ``` <!-- end of image --> Gotcha! I've found the intersection hiding in area A! The image features one single intersection point.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0404ffff b,#ff4b4bff c,#8181ffff d,#ffaaaaff e,#3939ffff f,#c4c4ffff g,#fe090aff ``` ```image ggb gb gg gb bg gb dgd gb gb gb gg gg bg gg dgd gg gb bg gg bg bg bg dgd f bg gb a bg gg ac bg bg ca bg dg a bg gd ac bg gb fa bg bg a bg dg ac bg gd fa dg gb a dg bg ec dg dg fa dg gd a dg gb ee dg gga dg ag dg ee gd dg a gb dg af gg dg ee bg dg a dgd dg af gb dg ce gg g a b g af ca a ac ca a ac ca a ac fa a ec f fa ea a ca ee fac fa ae a ea ee ca fa fac af ae ee ea a caf af ac ce ae a ea af caf ca ac a ae af ea ca faf a ac ac aa ca ea a faf ac ac fa aa a ea ac faf fa ae a aaec ca ``` <!-- end of image -->

I have a feeling there might be some intersections in this image. Could these regions be concealing intersection points? Let's find out. <!-- image --> ```palette Key,Color ,#fefefeff a,#0707feff b,#ec716cff c,#adadfeff d,#565bf3ff e,#fd0908ff f,#97c797ff g,#b1d7b1ff ``` ```image caa a cad ca aa a aa a dac ac aa a cad dd dac a aa dd cad a aa ca aa a dac ca aa a cad a dac ac aa a cad dd aac a aa dd dac a aa ca cad a fggggdadgggggggf ca fggggggaaggggggg ac fgggggggdadggggg a fgggggggggaagggg ac fggggggggggggggg a fggggggggggggggg dd fggggggggggggggg a fggggggggggggggg dd fgggggggggfbgggg a fggbbeeeeeebgggg ca bbeeeeeebbgggggggggg gfffffffffffffaffffff gbeeeeeebb fggggggggggggggg fggggggggggggfagggggg bbeeeeeebg fggggggggggggggg fggggggggggggafgggggg gbeeeeeebb fggggggggggggggg fggggggggggggaggggggg beeeeeebb fggggggggggggggg fgggggggggggadggggggg beee fggggggggggggggg fgggggggggggagggggggg eeeb fggggggggggggggg fggggggggggddggggggbeeeb fggggggggggggggg fggggggggggaggggbeeef fggggggggggggggg fgggggggggddfeeebgggg gfffffffffffffff fggggggggbaeebggggggg fgggggbeebagggggggggg fgfeeebggaggggggggggg beeebggggfaggggggggggg beebfgggggggafggggggggggg eeb fgggggggagggggggggggg fggggggadgggggggggggg fggggggaggggggggggggg fgggggddggggggggggggg fgggggagggggggggggggg gffffdaffffffffffffff a ca a ca ac a ac a dd a dd a ca a ca ac a ac a dd a dd a ca a ``` <!-- end of image --> I'm eager to see what's happening in this magnified view of area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0503fdff b,#f45762ff c,#c3c3ffff d,#706cfaff e,#fe0707ff f,#ffa9a9ff g,#3737ffff ``` ```image gad caa gad caa dad caac dag aac dag aac caa gad caa gad fb caa fbeeee dad fbeeeeebf caac fbeeeeebf dag fbeeeeeebf aabeeeeebf fdaaeeebf fbeeeaabbf fbeeeeebaa fbeeeeebf gad fbeeeeeebf caa fbeeeeebf gad eeeeebf caa eebf dad caac dag aac dag aac caa gad caa gad caac dad caac ``` <!-- end of image --> Aha! I've found an intersection inside area A! Alright, let's concentrate on the next area. This close-up of area B is like examining a piece of evidence. <!-- image --> ```palette Key,Color ,#fefefeff a,#0707ffff b,#ff4848ff c,#a0a0ffff d,#ffc6c6ff e,#ff0303ff f,#ff8d8dff g,#5252ffff ``` ```image caaag gaaac caaag caaac gaaac caaag gaaac cgaag cag ddff dffbbeeeeeb ddffbbeeeeeeeeeebbf fbbeeeeeeeeeeebbffd eeeeeebbffdd bffd ``` <!-- end of image --> No intersection in area B, but I'll keep looking. There's only one, but is an intersection after all.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0404feff b,#fb5a5eff c,#c5c5ffff d,#8080ffff e,#fe0707ff f,#ffa9a9ff g,#3b3bffff ``` ```image c daa a dad ca gac ac cag a dad ac aa a cag gd gac a aa dg dad a gac dg cag a dad ca aa ac cag a gac ac aa a dad gd gac a caa dg dad a aa dg cag a gac ca aa ac dad a ga ac a gd a dg f a fbeeeeeeb da fbeeeeeebf a fbbeeeeebf ca fbeeeeeebf ac fbbeeeeebff a feeeeeebf ac beebf a feeeb gd feeef a beeb dgfeeeb faeef beeba feeeb a feeef ca beeb ac eeb a ad a gd a dg a da a ca ac a ad a gd a dg a ca a ca ac a ad a gd a dg a ca a ``` <!-- end of image -->

I'm approaching this image with caution. Intersections might be tricky to spot. These regions highlight areas that look suspicious. Lines seem to converge within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#474feeff b,#fb0a0aff c,#ea6d63ff d,#969defff e,#0506fdff f,#b1d7b1ff g,#98c697ff ``` ```image c b b bc cb b b bc cb b b bc cb b gffffffffffffffffffg b gffffffffffffffffffg bc gffffffffffffffffffg cb gffffffffffffffffffg b e gffffffffffffffffffgb eded gffffffffffffffffffbc de ee gfffffffffffffffffcb e ae gfffffffffffffffffbg aa ea gffffffffffffffffbgg e ee gfffffffffffffffbcfg ed de gffffffffffffffcbffg de eaffffffffffffffbfffg e eeffffffffffffbgfffg aa gdedfffffffffbcffffg e gffeafffffffcbfffffg ed gfffeeffffffbffffffg e gffffdedfffbgffffffg e gffffffeefbcfffffffg de gfffffffaebffffffffg e gffffffffbeafffffffg aa gfffffffbgfeeffffffg e gffffffbcfffaefffffg ed gfffffcbfffffgeafffg de gfffffbffffffffeeffg e gffffbgfffffffffaegg aa gfffbbffffffffffffea e gffcbffffffffffffffee ed gffbfffffffffffffffgded e gfbgfffffffffffffffg ea e gbbffffffffffffffffg ae de cbfffffffffffffffffg ded e bffffffffffffffffffg ea aa bcffffffffffffffffffg ae e bbgffffffffffffffffffg ded ed fb gffffffffffffffffffg ee de b gffffffffffffffffffg ae e bf gffffffffffffffffffg e aa cb gffffffffffffffffffg e fb fggggggggggggggggggf gfffffffffffffffffeafffffg b gffffffffffffffffgefffffff bc gffffffffffffffffegfffffff cb gfffffffffffffffaeffffffff fb gfffffffffffffffefffffffff b gffffffffffffffaafffffffff bc gffffffffffffffeffffffffff bbc gfffffffffffffedffffffffff cbbc gffffffffffffdefffffffffff cbb gffffffffffffeffffffffffff fbbc gfffffffffffaaffffffffffff cbb gfffffffffffefffffffffffgbbc gffffffffffeafffffffffcbbg gfffffffffgefffffffgbbcfff gfffffffffegfffffcbbcfffff gffffffffaeffffbbbffffffff gffffffffeffcbbcffffffffff gfffffffeabbbfffffffffffff gffffffcebcfffffffffffffff gffffcbedfffffffffffffffff gffbbcdeffffffffffffffffff gfffffefffffffffffffffffff gffffaafffffffffffffffffff gffffeffffffffffffffffffff gfffeaffffffffffffffffffff gffgefffffffffffffffffffff gffegfffffffffffffffffffff gfffffffffffffffffffffffff gfffffffffffffffffffffffff gfffffffffffffffffffffffff ``` <!-- end of image --> Could this be where the intersection is hiding, in area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#4b46faff b,#fe0607ff c,#fea8a9ff d,#8989ffff e,#0706feff f,#fa5054ff g,#c6c5feff ``` ```image aea dee eed dee geeg aea geeg eed dee eed aea geeg aea dee eed dee geeg aea geeg eed dee eed aea geeg aea cfb dee cfbbb eed fbbbbfc dee cfbbbbc geeg fbbbbfc aea cfbbbbc geeg cbbbbfc eed cfbbbbf dee cbbbbfc eed cfbbbbfc aea cfbbbfc geeg cfbbbbfc aeacfbbbbc deebbbbfc ceefbbc fbaeefc cfbbbeeg cbbbbfaea cbbbbf geeg bfc eed dee eed aea geeg aea dee eed dee geeg aea geeg dd ``` <!-- end of image --> Incredible, there's actually an intersection in area A! Let's inspect the next region. This close-up of area B is like examining a piece of evidence. <!-- image --> ```palette Key,Color ,#fefefeff a,#5857feff b,#fe0708ff c,#ff8f8fff d,#b1b1feff e,#0907fdff f,#fe4949ff g,#ffc9c9ff ``` ```image c gb bb fbf cbbg gbbc bbf fbf cbbg gbbc a bbf eed fbf eeed cbbg aeea gbbc deeed bbf deeea fbb aeea cbbg deeed gbbc aeea bbf aeea fbb deeed cbbg aeea gbbc aeeed bbf deeedfbb aeeebg aeeed bbeeed fbb aeea cbbg deeed gbbc deeea bbf aeea fbb deeed cbbg aeea gbbc aeea bbf deeed fbb aeea cbbg aeeed gbbc deee fbf ae fbb d cbbg gbbc fbf fbb cbbg gbbc fbf fbb cbbg bbc bf bg g ``` <!-- end of image --> Incredible, there's actually an intersection in area B! My analysis indicates that there are two intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#4b4bfeff b,#fe0506ff c,#fe9191ff d,#9f9ffeff e,#0505feff f,#ff4444ff g,#efd9e9ff ``` ```image c gb b bc fb gb bg bc fb gb bg bc fb gb bg bc cb gb ge bg eded bc de ee cb e aeg gb aa gea bg e ee bf ed deg cb de gea gb e ee bg aa ded bf e ea cb ed ae gb ge ded bg eg ea bf de aeb e bed aa bg ee e bf aeg ed cb gea de b ee e bg deg aa ff gea e cb ee ed b ded ge bg ea eg ff ae de cb ded e b ea aa bc ae e ff ded ed cb ee de b aeg e bc ge aa ff e cb ed b ge bc eg ff de gb e b aa bc e fbf ed cbbc de fbbg e cbbc aa fbbg e gbbf ed cbbg ge gbbf eg cbbc de gfbf e cbbc aafbf cebc fbed bbcde g e aa e ed ge eg ``` <!-- 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,#0b0bfdff b,#fc0707ff c,#c5c5feff d,#f25d57ff e,#aed5afff f,#686ef2ff g,#f9a5a2ff ``` ```image c fa afa af a ca ca a ac fa ca a ac af a g ca af dbbb eeeeeeeeeeeeeeeaeeeeeeeeeeaeeeeeeeeeeee dbbbg eeeeeeeeeeeeeefaeeeeeeeeeefaeeeeeeeeeee dbbbd eeeeeeeeeeeeeeaeeeeeeeeeeeeaeeeeeeeeeee gbbbd eeeeeeeeeeeeeafeeeeeeeeeeeefaeeeeeeeeee gbbbdg eeeeeeeeeeeeeaeeeeeeeeeeeeeeaeeeeeeeeee gdbbbg eeeeeeeeeeeeaeeeeeeeeeeeeeeeeaeeeeeeeedbbbg eeeeeeeeeeefaeeeeeeeeeeeeeeeeafeeedbbbd eeeeeeeeeeeaeeeeeeeeeeeeeeeeeeabbbdeeee eeeeeeeeeeafeeeeeeeeeeeeeedbbbafeeeeeee eeeeeeeeeeaeeeeeeeeeeedbbbdeeeeaeeeeeee gggggggddddddbbbbbbbbbabbbbbbbbbbbbbgeeeeeeeffeeeeee bbbbdddddddggggdgeeeeeefaeeeeeeeeeeeeeeeeeeeeeeaeeeeee eeeeeeeeaeeeeeeeeeeeeeeeeeeeeeeefaeeeee eeeeeeeafeeeeeeeeeeeeeeeeeeeeeeeeaeeeee eeeeeeeaeeeeeeeeeeeeeeeeeeeeeeeeefaeeee eeeeeeaeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeee eeeeefaeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeee eeeeeaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeafee eeeeafeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaee ca af ac a fa fa a a af ca ca ac ac ca fa ac a a af af ca a ac fa fa a a ca af ac a ca ac ac fa a a af af a a ff ac a fa fa a a af ca a ac ac a fa af a a af ff a a ac fa a ca ac a af a ff a fa a ca ac ca ac a af a fa a ``` <!-- end of image --> I wonder what we'll find inside area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#0706feff b,#fe0405ff c,#ead6ebff d,#f7464eff e,#524ffbff f,#9e9efeff g,#ff9292ff ``` ```image eae faac faac eae aaf caac eaa eae caaf caaf eae eaa faac aaf aaf faa eaa aaf caaf faac eae eae faac caac cg aaf eae cgdbbb eaa caaf cgdbbbbbbd caaf eae cgdbbbbbbdgc eae caadbbbbbdgc faac cgdbdaabdgg aaf cgdbbbbbbaaf eaa cgdbbbbbbdgc faac caaf cgdbbbbbbdgc eae ccccceaeggggggggggggggdddddddbbbbbbdgc faac dddbbbbbbbbbbbbbbdaabbbbbbbbbbbbbbbbbbbbbbbbdgc eae bbbbbbbbbbbbbbbbbaaebddddddddddddgggggggggg caac ggcccccccc eaa eae caaf caaf eae faa faac aaf aaf faa eaa eae caaf faac eae eae faac caac aaf eae faa caaf caaf faa eae aaf faac faa ``` <!-- end of image --> The close-up clearly shows an intersection point in area A. The image features two intersection points.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0303feff b,#fe0909ff c,#d0cffeff d,#ff6262ff e,#2f2fffff f,#7b7afeff g,#ffb3b3ff ``` ```image c fa afe af a ca fa a ac fe ca a ac af a g ca ef dbbb ac a dbbbd fe fe dbbbd a a gbbbd af fa gbbbdg ca ac gbbbbg ac ca gdbbbg fe ac dbbbg a cabbbd af dbbbaf ca gbbbdg a gggggggdddddddbbbbbbbbbabbbbbbbbbbbbdg ee bbbbbdddddddggggggg fe a a fe ef a ca ca ac ac fe ca a af ef a ca ef ac a fe fe a a ef ca ca ac ac ca fe af a a ef ef ca a ac fe fa a a fa ef ac ca ca ac ac fa a a ef ef a ca fe ac a fa fa a ac ef ca a ac ac a fa ef a a ef ee a a ac fe a ca ac ca af a ef a fe a ca ac ca af a ef a fe a ``` <!-- end of image -->

I'm analyzing this image to identify any points where lines intersect. These regions highlight areas that look suspicious. Lines seem to converge within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#0b0cfdff b,#fc0d0bff c,#7176f1ff d,#f07971ff e,#e5d3ebff f,#b0d6b0ff g,#99c598ff ``` ```image e bbe bdeb ebe db db db db bd bb be bb b c bd eb a bd db ae ebe bb ca db bd a db be ac bb eb ea bb db ae bd db ca ebe bd a ebe be ac gfffffffffffffffgdb b ea ffcfffffffffffffbb eb ae ffacfffffffffffbb db ca fffaffffffffffbbg bb a fffcaffffffffbdfg bd ac ffffagfffffgbgffg be ea fffffaffffdbffffg ebgggggggggggggagf fffffacffdbfffffg dbfffffffffffcafg ffffffafbbffffffg bbffffffffffaffg ffffffcabfffffffg fbdffffffffacffg ffffffbagfffffffg ffbdffffffcafffg fffffbdfafffffffg fffbffffffaffffg fffgbgffacffffffg fffgbffffaaffffg ffdbfffffaffffffg ffffdbfffafffffg ffbffffffcafffffg fffffbbfacfffffg ffffffffffagffffg ffffffbcaffffffg fffffffffffaffffg fffffffagffffffg fffffffffffacfffg ffffffaabffffffg ffffffffffffafffg ffffffafdbfffffg gfffffffffffcaffg fffffagffbbffffg ae ffffcaffffbdfffg ea ffffaffffffbdffg ac fffacfffffffbffg a fffaffffffffgbfg ca ffagfffffffffdbg ae fcafffffffffffbb ea gagggggggggggggbd ac ac be a ea eb ca ae db ae ca db ea a bd ac ac be a ea b ca ae eb ae ca db ea a b ac ac a ea ca a ae ca ea a ac ac a ea ca a ae cc ea a ac ae a ca ca a ae ac ea a ac ae a ca ca a ae ac ea ea ac ae a ca ca a aac ea ``` <!-- end of image --> Let's see if area A yields any clues. <!-- image --> ```palette Key,Color ,#fefefeff a,#413dfbff b,#fd0809ff c,#8786fdff d,#ff5353ff e,#c1c1ffff f,#fea8a8ff g,#0503fdff ``` ```image ee egg agc fb egge fbb aga fbbd ggc dbbd cgg dbbf agc dbbf egge bbbf aga fbbb ggc fbbd cgg fbbd agc dbbd egge dbbf aga dbbf ggcbbbf cggbb fgga fbbgge dbbdaga dbbf ggc bbbf cgg fbbbf agc fbbb egge fbbd aga fbbd ggc df cgg agc egge aga ggc cgg agc egge aga ggc cgg ``` <!-- end of image --> An intersection is present within area A. Let's shift our focus to the next area. Could this be where the intersection is hiding, in area B? <!-- image --> ```palette Key,Color ,#fefefeff a,#4542fbff b,#fd0809ff c,#8c88fbff d,#ff5959ff e,#ccccffff f,#feb2b2ff g,#0504feff ``` ```image d cgg bd ggc bbf aga dbbf egge dbb aga bbd cgg fbbd eggc fbbf aga fbbf egge dbb agc dbb cgg bbd eggc fbbd aga fbbf egge dbbf ggc dbb cgg bbd egge bbd aga fbbcgge fbggc aggf eggbb agabbd cggefbbd ggc fbbf cga dbbf egge dbb aga bbd cgg bbd ggc fbbf aga fbbf egge dbb aga dbb cgg bbd ggc fbbd aga fbbf egge dbbf agc dbb cgg bb eggc b ``` <!-- end of image --> Area B contains an intersection. There are precisely two intersections present in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#2726feff b,#ff0707ff c,#7c7bfdff d,#ff5757ff e,#d3d3feff f,#ffb2b2ff g,#0101feff ``` ```image bb bf b fbf fb fb db db bd bb bf bb b c bd fb g bf db ge fbf bd cg fb bf g db b ac bb b eg bd fb ge bd db ca bf bd g fb bf ac db b eg e db fb ge ac bb db ca g bd bd g cg bd bf gc ge bf b eg eg fb b ge ac db fb ca g db db g cgb bd gc bge bf eg bfeg b g fbf ac fb aa fb g db g d ca bd ge ge bcg eg ge ac aab g g fb ca ge db ge cg bd eg g bf ac ac b g eg fb ca ge db ge ca bd eg g bf ac ac b g eg b ca ge fb ge ca db eg g bd ac ac bf g eg b ca ge fb ge ca db eg g d ac gc g eg ca g ge ca eg g ac gc g eg ca g ge aa eg g ac ge g cg ca g ge ac eg g ac ge g cg ca g ge ac eg eg ac ge g ca ca g gac eg ``` <!-- end of image -->

I have a feeling there might be some intersections in this image. I did not find anything, there's no intersections

<!-- image --> ```palette Key,Color ,#fefefeff a,#0404ffff b,#ff0808ff c,#ffaeaeff d,#7d7dffff e,#ff5959ff f,#c8c8ffff g,#3636ffff ``` ```image d ga ga ag ad ad faf fa da ga ag ga ga ag da ad faf ad ad faf ag fa ga da da ga faf ga ag ag aa ad ga ad faf faf ad fa ag da ga ga da ga faf ag ad ad aa ad ga faf daf fa fad da ag ga ga ga da ag faf ad ad ad be agfaf cbbbc ga cbbbe ebbe cbbbc cbbbe ebbe cbbbc cbbbe ebbe cbbbc cbbc bb ebc be eb cbe bb cbc bb ebc bb eb be bb cbe bb cbc bb ebc be eb cbe bb cbc bb ebc bb eb be bb cb ``` <!-- end of image -->

Hmm, I'm not sure what to expect from this image. Let's see if any lines cross. I've noticed 2 areas of interest. These could be potential intersection zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#0203feff b,#fc0909ff c,#383cf3ff d,#ed6c64ff e,#838deaff f,#97c699ff g,#b1d7b1ff ``` ```image fgggggggggggggggggggggf fgggggggggggggggggggggf fgggggggggggggggggggggf fgggggggggggggggggggegf fggggggggggggggggggfagf fggggggggggggggggggaggf fgggggggggggggggggacggf fggggggggggggggggeagggf fggggggggggggggggaggggf bbbddd fgggggggggggggggaeggggf bd dddbbbbbbbbbddg fggggggggggggggcagggggf a b gdddbbbbbbbbbdddgggggggfaggggggf a bd fgfdddbbbbbbbbadddfgggf cc b fggggggggggggacdddbbbgf a bd fgggggggggggeaggggggggf a b fgggggggggggagggggggggf cc bd fggggggggggaegggggggggf a b fgggggggggcaggggggggggf a dd fggggggggfagggggggggggf cc b fggggggggafgggggggggggf a dd fgggggggacggggggggggggf a b fggggggeagggggggggggggf cc dd fggggggaggggggggggggggf a fffffffffffffffgb fgggggaeggggggggggggggf a gggggggggggggggdd fggggcagggggggggggggggf cc gggggggggggggggb fggggaggggggggggggggggf a ggggggggggggggdb fgggafggggggggggggggggf a ggggggggggggggbf fggccgggggggggggggggggf ccgggggggggggggdbf fgeaggggggggggggggggggf afggggggggggggbgf fgagggggggggggggggggggf agggggggggggdbgf faegggggggggggggggggggf ccggggggggggbggf caffffffffffffffffffffg gafggggggggdbggf a gfaggggggggbgggf a ggccggggggdbgggf cc gggafgggggbggggf ea gggfaggggdbggggf a ggggccgggbgggggf ae gggggafgdbgggggf ea gggggfagbggggggf a ggggggccbggggggf a gggggggafggggggf cc ggggggfbaggggggf ga ggggggbfccgggggf a gggggfbggagggggf ae gggggbfggfaggggf ea gggggbggggccgggf a ggggbfgggggagggf ag ggggbggggggfaggf cc gggbdgggggggccgf a gggbgggggggggagf a ggbdgggggggggfaf ae ggbgggggggggggcc ea gbdgggggggggggga a fbgggggggggggggfa ae bdgggggggggggggfcc cc bggggggggggggggf a a bdggggggggggggggf a a bgggggggggggggggf cc ae bdgggggggggggggggf a ea b fffffffffffffffg a a dd cc ae b a cc dd a a b ca dd e b dd b dd b db b db b db b db b gb b gb b ``` <!-- end of image --> Could this be where the intersection is hiding, in area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#0403feff b,#fe0405ff c,#3f3efeff d,#ff8e8eff e,#9291feff f,#fb3437ff g,#eadaeeff ``` ```image g d gb db gbb dbf gbbd dbf e bbd ag dbf ac bbd aae dbf eaag bbd cac dbf gaae bbd eaag dbf cac bbd gaae dbb eaag fbd cac dbb gaae fbd eaag dbb cac fbd gaae dbb eaag fbd cac dbb gaae fbd eaag dbbg cac fbd gaae gbbg eaagfbd cacbbg gaafd eaag faac gbbaae fbfeaag gbbg cac fbf gaae gbbg eaag fbf cac gbbg gaae dbf eaag gbbg cac dbf gaae gbbg eaag dbf cac gbbd gaae dbf eaag gbbd cac dbf gaae bbd eaag dbf cac bbd gaae dbf eaa bbd ca dbf ga bbd e dbf bbd dbb fbd dbb fbd bb bd b d ``` <!-- end of image --> The evidence is clear: this is an intersection in area A. Okay, let's proceed to the next area. Let's see what secrets area B holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#0505feff b,#fc0507ff c,#423efaff d,#ffafafff e,#8787ffff f,#fd5758ff g,#cacaffff ``` ```image e eaa gaae cac eaa gaag aae cac eaag gaae cac eaag gaag aae cac dd eaag bbbbbbffffdddd gaae fbbbbbbbbbbbbbbbbbffffdddd cac ddddffffbbbbbbbbbbbbbbcaaffffddd dddffffbbbaabbbbbbbbbbbbf aacdddffffbbbbbf caa dd eaag gaae cac eaag gaae aac caa eaag gaae cac eaag gaae cac caa gaag gaae cac eaag gaae cac eaa gaag aae cac eaag gaae cac eaa gaag aae cac eaag gaae cac ``` <!-- end of image --> Eureka! There's definitely an intersection in area B! Two intersections have been found!

<!-- image --> ```palette Key,Color ,#fefefeff a,#0303feff b,#fe0707ff c,#403ffeff d,#ff9999ff e,#9090ffff f,#fe5051ff g,#dfd8f8ff ``` ```image e ga ag ae ea a bbbffdg ae bd gdffbbbbbbbbbfddg cc ag b ddffbbbbbbbbffddg ga ga bd gddffbbbbbbbaffdd cc b acddfbbb ag bd ea ga b a cc fd ae ag b ca ga ff ga cc b ag ag ff cc ga b ea cc ff a ag b ae ga ff ca cc b ga ag ff ag ga b cc cc df ea ag b a ga db ae cc b ea ag db ga ga b ag cc db cc ag b ga ga db a cc b ae ag db ea ga b a ccb ag ag cc gba ga bgcc a gb ag ae bg ga ea gb cc a bd ag ag b ga cc bd cc ga b ag ag bd ga ae b cc ea bd ag a b ga ag bd cc cc b ag ga bd ga ag b cc ae fd ag ea b ga a ff cc ae b ag cc ff gaga b cag ff e b ff b ff b df b db b db b db b db b db b ``` <!-- end of image -->

I have a feeling there might be some intersections in this image. I have a hunch that these areas might contain the intersections we're looking for. <!-- image --> ```palette Key,Color ,#fefefeff a,#0607fcff b,#fc0908ff c,#8594e1ff d,#e85d52ff e,#9cc495ff f,#4149eeff g,#b1d7b1ff ``` ```image eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbdeeeeeeeeeeeeee gggggggggggggggggggggggggggggggggbbgbbggggggggggggg ggggggggggggggggggggggggggggggggbbgggdbgggggggggggg gggggggggggggggggggggggggggggggbbgggggebegggggggggg ggggggggggggggggggggggggggggggdbggeaggggbdggggggggg gggggggggggggggggggggggggggggdbggcaacggggbbgggggggg ggggggggggggggggggggggggggggdbggcaggagggggdbggggggg gggggggggggggggggggggggggggdbggcagggafgggggebeggggg ggggggggggggggggggggggggggdbggcagggggagggggggbdgggg gggggggggggggggggggggggggdbggfaggggggfagggggggbbggg ggggggggggggggggggggggggebggfaggggggggaggggggggdbgg gggggggggggggggggggggggebggfagggggggggeaggggggggebe ggggggggggggggggggggggebggfagggggggggggacgggggggggbd ggggggggggggggggggggggbggaagggggggggggggaggggggggggbb gggggggggggggggggggggbegaaggggggggggggggffggggggggg db ggggggggggggggggggggbegaaggggggggggggggggaggggggggg bg gggggggggggggggggggbegafgggggggggggggggggcagggggggg bd ggggggggggggggggggbegafgggggggggggggggggggacggggggg bb gggggggggggggggggbdgafgggggggggggggggggggggaggggggg db ggggggggggggggggbdgafggggggggggggggggggggggffgggggg bg gggggggggggggggbdgacggggggggggggggggggggggggagggggg bd ggggggggggggggbdgacgggggggggggggggggggggggggcaggggg bb gggggggggggggbdgacgggggggggggggggggggggggggggacgggg db ggggggggggggbbgacgggggggggggggggggggggggggggggagggg bg gggggggggggbbgaeggggggggggggggggggggggggggggggafggg bd ggggggggggbbeagggggggggggggggggggggggggggggggggaggg bb gggggggggbbcaggggggggggggggggggggggggggggggggggfagg db ggggggggdbcaggggggggggggggggggggggggggggggggggggagg bg gggggggdbcagggggggggggggggggggggggggggggggggggggcag bd ggggggdbcagggggggggggggggggggggggggggggggggggggggac bb gggggdbfaggggggggggggggggggggggggggggggggggggggggga db ggggdbfaggggggggggggggggggggggggggggggggggggggggggff bg gggebfagggggggggggggggggggggggggggggggggggggggggggga bd ggebfagggggggggggggggggggggggggggggggggggggggggggggca bb gebaagggggggggggggggggggggggggggggggggggggggggggggg ac db ebaaggggggggggggggggggggggggggggggggggggggggggggggg a baagggggggggggggggggggggggggggggggggggggggggggggggg ff bafeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee a af ca a a ac a ff a ca ac a ff a ca a a fc a ca a a ac a ff a ca ac a ff a ca a a ac a ca a a ac a ff a ``` <!-- end of image --> Let's take a closer look at area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0808feff b,#fe0505ff c,#b3b3ffff d,#fb3b3fff e,#fe8182ff f,#5858feff g,#fec8c8ff ``` ```image gbbe gbbbbd gbbdebbdg gbbd gbbbg gbbd dbbe dbd ebbd dbbg ebbdg dbbg gbbbg dbbg dbbe dbbg caa ebbd dbbg caaaf ebbdg dbbg caaaaac gbbbg dbbg caaf faf dbbe ebbg caaf aac ebbd ebbg caaf caa ebbdg ebbe caaf aaf gbbbg ebbe caaf caac dbbe ebbe caaf faf ebbd ebbe faaf aac ebbdg gbbe faaf faa gbbbg gbbe faac aaf dbbe gbbd faac caa ebbd gbbd faac faf ebbdg gbbd faac caac gbbb gbbd faac faa db gbbd faac aac e gbbd faac caa bbd aaac faf dbd aaac caac dbbg aaa faf dbbg caaa aac dbbg caaa caa dbbg caaf aaf dbbg caaf caac dbbg caaf faf ebbg caaf aac ebbg caaf faa ebbe caaf aaf ebbe caaf caa ebbe faaf faf ebbe faaf caac ebbe faac faa gbbe faac aac gbbe faac caa gbbd faac aaf gbbd faac caac gbbd faac faf gbbd faac aac gbbd aaac faa gbbd aaac aaf dbd aaa caa dbbgcaaa faf dbbgcaaa caac dbbgcaaf faa dbbgcaaf aac dbbgcaaf caa dbbgcaaf faf dbbgcaaf caac ebbgcaaf faf ebbgcaaf aa ebbefaaf ca ebbefaaf a ebbefaac c ebbefaac gbbefaac gbbefaac gbbdfaac gbbdfaac gbbdfaac gbbdaaac gbbdaaac gbbdaaa gbbdaaa dbdaaa dbdaaf ``` <!-- end of image --> The lines within area A do not intersect. The image is completely devoid of intersections. Zero.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0606feff b,#ff0a0aff c,#8787ffff d,#ff5e5eff e,#c9c9ffff f,#4343feff g,#ffbebeff ``` ```image g bbd bb bb bb db bb gbg db ea bd db eaae bb db ea a db db ca fc gbg gb ca a bd gb ca ca bb gb fa ae db gb fa ea gbg gb fa ac bd b fa a bb b aa ff db bg af a gbg bg af ea bd bg af ae bb bg af a db bd ac ff gbg bd ac a bd bd ac ca bb bd ae ae db bd ae ea gbg bbeae ac bd bbeae a bb dbea ca db dbea a gbg dbca ea bd dbca ac bb dbca a db gbfa ff gbg gbfa a bd gbfa ea bb gbfa ae db gbaa a g baf ff baf a af ca ae ea ac a cf a ea ac a ff a ca ae a fc a ca ae ea ac a ff a ea ae a ff a ca ae ea ac a cf a ea ac a ff a ``` <!-- end of image -->

Let's examine this image for potential line intersections. These zones indicate regions where lines appear to be in close proximity. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd0606ff b,#0a0bfbff c,#eb948bff d,#676ee9ff e,#f04b44ff f,#f0eeeeff g,#afd6b0ff ``` ```image g bd bf b db bd bf fb db bd bf fb db bd bf fb db bd a bf aac fb fa af db af fa bd ca ea bf a ac fb ee af db a fa bdfffffffffffacffffffffeeffffffffffffffffff f gbggggggggggcaggggggggggacgggggggggggggggggf bb gdbgggggggggaggggggggggggagggggggggggggggggf bbd ggbbgggggggeaggggggggggggcaggggggggggggggggf dbd gggbdggggggaggggggggggggggeegggggggggggggggf dbd ggggbgggggaegggggggggggggggacggggggggggggggf dbd ggggdbggggagggggggggggggggggaggggggggggggggf dbb gggggbbggacgggggggggggggggggcagggggggggggggf gbb ggggggbgcagggggggggggggggggggaeggggggggggggf fbbf gggggggbagggggggggggggggggggggacgggggggggggffbbf gggggggdbggggggggggggggggggggggagggggggggggbbf gggggggabdgggggggggggggggggggggcaggggggggbbd ggggggaegbggggggggggggggggggggggaegggggbbdgf ggggggagggbggggggggggggggggggggggagggbbdgggf gggggacgggdbggggggggggggggggggggggadbdgggggf ggggcagggggbdggggggggggggggggggggdbbgggggggf ggggagggggggbggggggggggggggggggdbbgaeggggggf gggeeggggggggbgggggggggggggggdbbggggaggggggf gggagggggggggdbgggggggggggggbbgggggggagggggf ggacggggggggggbdggggggggggbbgggggggggeaggggf ggaggggggggggggbggggggggbbggggggggggggaegggf gaggggggggggggggbgggggbbdggggggggggggggagggf eaggggggggggggggdbggbbdgggggggggggggggggaggf aggggggggggggggggbbbdgggggggggggggggggggeagf eegggggggggggggggggdggggggggggggggggggggggaef a fffffffffffffffffffffffffffffffffffffffffaf ac fa fa ea af ac ca a a ca ee ee fa ac ac a ca ca af ee ce af a a ac ca fa ae af af ca fa a ca ee ae a af ac fa fa ca af ac ca af a fa ee ea a a ac fa af ``` <!-- end of image --> Could this be where the intersection is hiding, in area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0909ff b,#0404feff c,#feb6b6ff d,#7977fdff e,#fb5a5eff f,#bebefeff g,#3832f9ff ``` ```image dbbf eae aae gbg caac caac bbd aae eaac fbbf caa eaa dbbf aac aae gbg eaa caac bbd caac eaa fbbf eae eae dbb caac aae gbg aae caac fbbd caa eaa fbbf aac aae dbb eaa caae gbg caac caac fbbd eae eaa fbbf caa aae dbb aae caae gbgaa caac fbbec eaa dbbf aae cagbg caac d eaegbg caac dbb caa fbbd eaa fgbbg aae dbbf aae fgbbbd eaa gbg caac fgbbbd aac bbd eaac fgbbbd eae fbbf eaa fgbbbd caac dbbf aaedbbbdf eae gbg cgbbbgf caa bbd dbbbgf aae fbbf dbbbgeaa eaa dbbf dbbbgf aae aac gbg fgbbgf caac eae bbd fgbbbd eaa caac fbbf fgbbbd eae aae dbb fgbbbd aae caa gbg fgbbbd caac aac bbd dbbbdf eaa eaa fbbf dbbbgf aae caac dbb dbbbgf aae eae gbg dbbbgf caac caac fbbd dbbbgf eaa aae fbbf fgbbbf aae caa dbb fgbbbd caae aac gbg fgbbbd caac aa fbbgbbbd eaa ac fbbbd aae e ddf caa ``` <!-- end of image --> Gotcha! I've found the intersection hiding in area A! Two intersections have been found!

<!-- image --> ```palette Key,Color ,#fefefeff a,#fe0505ff b,#0b0afeff c,#ff8b8bff d,#6461fcff e,#ff4242ff f,#b7b7ffff g,#ffcdcdff ``` ```image f bd bf b fb bd bf b db bd bf b db bd b b db bd a b aac fb ga a db ag ga bf ca ea b a ac fb ee a db a ga bf ac ee b ga ac bb fb a a bbf db ce ga dbd bf a ee dbd b ec ag dbd fb a a fbb bd ag ca fbb bfga ee fbb ba ag bb db a bbf abd ca bbf ac bf ae bbf ga b ag dbd ag db adbd ca bd dbb a bf fbb ac ee b fbb ag a db fbb ga ac bd bbf ca ga b bbf ac ag fb bbf a ca db bbf ga a bbbd ea ee d ac a a ac ga ga ee ag ac ca a a ga ee ee a ag ag a ga ca a ee ce ag a a ec ca a ae ag ag ca a a ca ee ae a ag ac ga ga ca ag ac ca ag a ga ee ea a a ac ga ag ``` <!-- end of image -->

Here's an image. My task is to find intersections or areas where lines come close together. I'm extremely confident. No intersections at all.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0505ffff b,#ff0202ff c,#a9a9ffff d,#ff8282ff e,#ff3a3aff f,#5151ffff g,#ffc6c6ff ``` ```image d ebe dbbg gbbd ebe dbbg gbbd ebe dbbg gbbd ebe dbbg gbbd ebe dbbg gggdddeeebbbbbbb gbbd gggdddeeebbbbbbbbbbbbbbbeeeddddgg ebbbbbbeeedddggg f ca ca ac ac af aa fa fa ca ca ac ac af aa fa fa ca ca ac af f af faaac aa caaaf fa cfaafc fa faaac ca faaac cac caaaf ac cfaafc af faaac af caaaf aa caaaf fa cfaafc faac ``` <!-- 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,#9aa1f0ff b,#fd0404ff c,#0606feff d,#eb998fff e,#b0d6b0ff f,#4c50f5ff g,#ed4749ff ``` ```image eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee a eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee fccc eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee fccca dgbbbbbdeeeeeeeeeeeeeeeeeeeeeeeeee acccf dgbbbbgdeeeeebbgeeeeeeeeeeeeeeeeeeeeeeeafccfa dgbbbbd eeeeeeeebbgeeeeeeeeeeeeeeeeeefccca dgbbbbgd eeeeeeeeeegbbeeeeeeeeeeeefcccfeee dbbbbgd eeeeeeeeeeeedbbdeeeeeacccfeeeeeee dgbbbbgd eeeeeeeeeeeeeeebbgfcccaeeeeeeeeee bbbgd eeeeeeeeeeeeeefcccggeeeeeeeeeeeee eeeeeeeeeeacccfeeeegbbeeeeeeeeeee eeeeeeafccfaeeeeeeeeedbbdeeeeeeee eeeecccaeeeeeeeeeeeeeeeebbgeeeeee eeecfeeeeeeeeeeeeeeeeeeeeegbbeeee eeeceeeeeeeeeeeeeeeeeeeeeeeedbbde eecaeeeeeeeeeeeeeeeeeeeeeeeeeedbbd eeceeeeeeeeeeeeeeeeeeeeeeeeeeeeeegbg ecaeeeeeeeeeeeeeeeeeeeeeeeeeeeeee gbb aceeeeeeeeeeeeeeeeeeeeeeeeeeeeeee dbbd ceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee bbd ac gbg c dbb ac db c ff c ff c ca c ca c ca ac c ac c ac c ff c ff c ca c ca c ca ac c ac c ac c ff c ff c ca c ca c ca ac c ac c ac c ff c ff c ca c ca c ca ac c ``` <!-- end of image --> My goal is to determine if there's an intersection inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#817ffcff b,#fe0708ff c,#0303feff d,#ffb8b8ff e,#c3c3ffff f,#403cfaff g,#fb6063ff ``` ```image dggbbbg ggbbbbbbbbbbgd bbbbbggd dgbbbbd gdd dgbbbbg gbbbbgd eafc dbbbbgd eaccccc dgbbbbd eafcccccfae dgbbbbg eafcccccfae gbbbbgd eafccccccae dgbbbgd eafcccccfae dgbbbbd eafcccccfae gbbbbgafcccccfae afccccccfa eafcccccfgbgd eafcccccfae dgbbbbg eafccccccae gbbbbgd eafcccccfae dbbbbgd eafcccccfae dgbbbbd eafcccccfae dgbbbbg fcccccfa gbbbbgd accfae dgbbbgd cca dgbbbbd acc gbbbbg cca dbbbbgd acf dgbbbg cce dgbb acf g ecce fcf ecce fcf ecce fca ``` <!-- end of image --> I've cracked the case! This area contains the intersection. My investigation reveals that there is exactly one intersection in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#9494ffff b,#ff0404ff c,#0707feff d,#fd9d9eff e,#dbd3f7ff f,#4e4effff g,#f9464bff ``` ```image a efccc accca dgbbbbbd acccfe dgbbbbgd ebbd efccfe dgbbbbde gbg efccca dgbbbbgd gbb accca edbbbbgd dbbd acccfe dgbbbbgd bbdfccca bbbgd acccgg acccf dbbe efccfe dbbd ccca bbg ca gbb c dbbd ca ebbd ec gbg ce gbb ec dbbd ce bbd ac gbg c dbbe ac db c ff c ff c ca c ca ec ce ec ce ac c ac c ff c ff c ca c ca ec ce ec ce ac c ac c ff c ff c ca c ca ec ce ec ce ac c ac c ff c ff c ca c ca ec ce ec ce ``` <!-- end of image -->

This image looks interesting. I wonder if there are any intersections hidden in there? My analysis shows there's absolutely no intersections in the image

<!-- image --> ```palette Key,Color ,#fefefeff a,#5757ffff b,#ff0505ff c,#ffc2c2ff d,#b5b5ffff e,#0808ffff f,#ff4444ff g,#ff8282ff ``` ```image g fb cbg bb gbc bf bb gbc bf fb cbg bb fb cbg bb gbc bf fb cbc bf fb cbg bb gbc bf bb gbc bbf gbbg fbbc cbbf gbbg fbbc cbbbc cbbf gbbg fbbc cbbf gbbg fbbc de cbbf aeae gbbg ee ae fbbc ea de cb ed ded de ed ae ea ee ea ea ee ded ae ae ae ee de ea de ded ed ae ed ee ea ea ea ed ee de ae ae ae ee de ea ded ded ed ae ea ee ea ea ee ded ee ae ae ee de ea de ed ed ea ea ee ae ae de ded e ``` <!-- 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,#5b62ecff b,#e96b62ff c,#b2b3feff d,#fb0a08ff e,#0809fdff f,#a1cba2ff g,#b2d7b1ff ``` ```image c ec e ec ce e ce e aa e aa e ec e e ec ec ce ce e e ea ce ce e e aa ea e e aa e e ae ec e e ec ec ae ce e e ec ce ce e e aa ea e ce aa e e ea ec ce e e ec aa ce e d e ec gdd ce ae bdd effffffffffffffffffffffffffffffffffffffffffeffffffff bdd aaggggggggggggggggggggggggggggggggggggggggeagggggggfbdb fegggggggggggggggggggggggggggggggggggggggaegggggggddb feaggggggggggggggggggggggggggggggggggggggeggggggddbf fgegggggggggggggggggggggggggggggggggggggeagggfddbggf fgeagggggggggggggggggggggggggggggggggggaeggbddfggggf fgfegggggggggggggggggggggggggggggggggggegbddfggggggf fggefgggggggggggggggggggggggggggggggggeaddgggggggggf fggfeggggggggggggggggggggggggggggggggbedgggggggggggf fgggeggggggggggggggggggggggggggggggddefggggggggggggf fgggaegggggggggggggggggggggggggggddbeagggggggggggggf fggggeggggggggggggggggggggggggfddbgfeggggggggggggggf fggggaagggggggggggggggggggggfddfgggefggggggggggggggf fgggggegggggggggggggggggggbddfggggaegggggggggggggggf fgggggeaggggggggggggggggbddgggggggeggggggggggggggggf fggggggeggggggggggggggbddggggggggefggggggggggggggggf fggggggeagggggggggggddbgggggggggaegggggggggggggggggf bbbbbbbbbbbbbbbbbbbbbbbbbbebbbbbbbbbddbgggggggggggeggggggggggggggggggf bbbbbbbbbbbbbbbbbbbbbbbbbbebbbbbbbbbbggggggggggggeaggggggggggggggggggf fgggggggfeggggggggggggggggggggaegggggggggggggggggggf fggggggggeggggggggggggggggggggeggggggggggggggggggggf fggggggggaeggggggggggggggggggeaggggggggggggggggggggf fgggggggggegggggggggggggggggfegggggggggggggggggggggf fgggggggggaaggggggggggggggggeggggggggggggggggggggggf fggggggggggegggggggggggggggeaggggggggggggggggggggggf fggggggggggeagggggggggggggfegggggggggggggggggggggggf ffffffffffffefffffffffffffefffffffffffffffffffffffff ec ae e e e ec ce ae e e ce ec e ce aa e e ea ea ce e e eea e ``` <!-- end of image --> I'm now examining the contents of area A in detail. <!-- image --> ```palette Key,Color ,#fefefeff a,#3d36f7ff b,#fc6e71ff c,#7e7dfeff d,#fe0808ff e,#0403feff f,#c1c0feff g,#ffb3b3ff ``` ```image eef feef cea aec eef cee cea feef feef aea g aec cee gdd fee feec gdddd aec aea bddddb fee ceef bddddg aec eec gbddddg cea aea gbdddbg eef feef gbdddbg cea eec gddddbg eef cea gddddb cea feefbddddb feef aeaddddg aec ceedddg fee gbeedbg aec gbdeeag fee gdddaee aec gddddbeef cea bddddb aea eef bddddb cee cea bddddg eec eef gbddddg aea cea gbdddbg feef feef gddddbg eec aec gddddb aea fee bddddb feef aec bddddb eec fee bddddg cea aec gbddddg feef cea gbdddbg aec eef gddddbg cee cea gddddb feef bbbbbbbbbbbbbbbbeebbbbbbbbbbbbbbbbbbbddddb aea ddddddddddddddddaeaddddddddddddddddddddb cee bbbbbbbbbbbbbbbbbeebbbbbbbbbbbbbbbbbbg feec aec aea fee ceef aec eec fee aea aec feef cea eec eef cea cea feef eef aec cea cee feef feef aec aea fee cee aec feef fee aea ``` <!-- end of image --> Incredible, there's actually an intersection in area A! I can confirm there's two intersections in there.

<!-- image --> ```palette Key,Color ,#fefefeff a,#4846fdff b,#fd6061ff c,#8d8dffff d,#ff0808ff e,#0606ffff f,#d3ccf8ff g,#fe8889ff ``` ```image f ec e ef fe e ce e ca e ac e f ec e e ec ef ce fe e e ec ce fe e e ca aa e fe ac ef e aa ec e e ef ef ce fe e e ec ce ce e e ca ec e fe ac e e aa ec fe e ef ef aa fe e fd e ef gddf ce ae gdd e e bdd aa ef bdb e ce ddb ac e ddg e ec fddg ec ce gddf e e gdd ef eadd fe beb e dde ce ddgaa e ddg fe aa gddf ef e gdd aa ac gdd e e bdb ef ec bdb ce bbbbbbbbbbbbbbbbbbbbbbbbbbebbbbbbbbbddg e ggggggggggggggggggggggggggegggggggggg ec fe ce e e ce ec e fe aa e e aa ac fe e ef ef aa fe e ef ef fe ce e e ca ec e ce aa e e ec ac fe e e eea fe ``` <!-- end of image -->

I have an image in front of me. I need to determine if there are any intersection segments. My next step is to analyze the details within each area. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0606ff b,#0707feff c,#f7a29eff d,#4f52f8ff e,#f44e4cff f,#add5adff g,#a5a6fdff ``` ```image c a ac a a ca a b ee b a bd ee b a gb ac bg a b ac db ca b a b ca dd a b ee gb a bg ac b a db ac bg ca b a dd ca b a gb ee bg a b ac gb a bg ac b a dd a b ca gb a a bg ee a b a ca gb ee ea bg a ae b ac ac dd a a b a a gb ca db ca bd a dbd ea b ffffffffffffffea dbd ae gb ffffffffffffffaf bbd ac bg fffffffffffffeef bbg a b fffffffffffffaff bbg a dd ffffffffffffaeff bbg ca b ffffffffffffafff gbbg ea b fffffffffffacfff gbb ae bd ffffffffffcaffff gbb ac b ffffffffffafffff gbb a gb fffffffffeaffffdbd a bg fffffffffafffdbd ca b ffffffffeefdbdff ea db ffffffffabbdffff ae b fffffffbbdffffff ac b fffffbbeffffffff a bd fffbbgacffffffff ca b fbbffcafffffffff ca gb gbbffffaffffffffff ee bdbb ffffeaffffffffff ac b ffffafffffffffff ac fffeefffffffffff a fffaffffffffffff ca ffaeffffffffffff ea ffafffffffffffff ae facfffffffffffff ac faffffffffffffff a afffffffffffffff a cafffffffffffffff ca a ea ee ae a ac ee a a aac ca ``` <!-- end of image --> I wonder what we'll find inside area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0404ff b,#0604fcff c,#f77f87ff d,#5e5efeff e,#f83e44ff f,#fec9c9ff g,#cfcfffff ``` ```image c a ca faa eae faaf eae faaf eac caa aac cae faaf eae faaf eae faaf eac caa aac caa g aaf gdb cae gdbbb faaf gdbbbdg eae gdbbbdg faafgdbbbdg eacbbbbdg cebbbbd dbbbbd dbbbbd gdbbbbec gdbbbbcae gdbbbdgfaaf gdbbbdg eae gdbbbdg faaf dbbbdg eac bbdg faa dg aac caa aac cae faaf eae faaf eae faaf eac caa aac cae faaf eae faaf eae faaf eac ``` <!-- end of image --> Success! This area contains an intersection point! The final count is: one intersection.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fe0404ff b,#0908feff c,#ff7777ff d,#6161ffff e,#fc3538ff f,#ffbebeff g,#bdbdffff ``` ```image c a af fa af fa a bg ce gb a bd ec b a gb ac bg a b af db fa bg a b ce bd a b ee gb a bg ac b a db af bg fa b a dd ca b a gb ce bd a b ec db a bg af b fa dd af b fa gb a af bd ce a b a fa db ec ea bg a ae b af af dd fa a b af a gb fa db fa bd a dbd ea b ce dbd ac gb a bbd af bg ec bbd a b a bbg fa db ac gbbg ca b a gbbg ee gb af gbbg ac bd fa gbb af b a dbb a gb ce dbb fa bg a dbd ca b ee dbd ee db abbd ac bg bbd af gb bbe a bd gbbgaf fa b gbbg fa ca gb gbbg a ee bdbb ca ac b a af ce a a fa ec ca a ee af ac fa af af a fa fa a ca ce ee a ac ec af a aaf fa ``` <!-- end of image -->

The hunt for intersections begins! Let's analyze this image closely. I'm going to focus my attention on these specific areas. <!-- image --> ```palette Key,Color ,#fefefeff a,#5563dcff b,#fb0907ff c,#d66355ff d,#b1d7b2ff e,#090afbff f,#a4caa2ff g,#eef4f0ff ``` ```image a ge ed ge eg ae e eg aa ge e eg ea ge ge eg eg ge de eg e ge aa bcffeafffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffffg gbddfeddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddeadddddddfg gbcddeaddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddfeddddddddbg gfbddfeddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddefdddddddbcg gfccddeaddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddfedddddddfbfg gfdbdddeddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddefdddddddbdfg gfdcbddeaddddddddddddddddddddddddddddddddddddddddddddddddddddddddddaedddddddbcdfg gfddbfddeddddddddddddddddddddddddddddddddddddddddddddddddddddddddddedddddddcbddfg gfddfbddeaddddddddddddddddddddddddddddddddddddddddddddddddddddddddeadddddddbdddfg gfdddbfddeddddddddddddddddddddddddddddddddddddddddddddddddddddddddedddddddbcdddfg gfdddfbddeaddddddddddddddddddddddddddddddddddddddddddddddddddddddeaddddddcbddddfg gfddddbcddedddddddddddddddddddddddddddddddddddddddddddddddddddddfeddddddfbdddddfg gfdddddbddeaddddddddddddddddddddddddddddddddddddddddddddddddddddefddddddbfdddddfg gfdddddccddedddddddddddddddddddddddddddddddddddddddddddddddddddaeddddddbcddddddfg gfddddddbddeaddddddddddddddddddddddddddddddddddddddddddddddddddeddddddfbdddddddfg gfddddddcbddedddddddddddddddddddddddddddddddddddddddddddddddddaaddddddbddddddddfg gfdddddddbfdeaddddddddddddddddddddddddddddddddddddddddddddddddeddddddbcddddddddfg gfdddddddfbddedddddddddddddddddddddddddddddddddddddddddddddddeadddddcbdddddddddfg gfddddddddbfdeadddddddddddddddddddddddddddddddddddddddddddddfeddddddbddddddddddfg gfddddddddfbddedddddddddddddddddddddddddddddddddddddddddddddefdddddbcddddddddddfg gfdddddddddbcdeadddddddddddddddddddddddddddddddddddddddddddaedddddcbdddddddddddfg gfddddddddddbddedddddddddddddddddddddddddddddddddddddddddddedddddfbddddddddddddfg gfddddddddddccdeadddddddddddddddddddddddddddddddddddddddddaedddddbfddddddddddddfg gfdddddddddddbddedddddddddddddddddddddddddddddddddddddddddedddddbcdddddddddddddfg gfdddddddddddcbdeadddddddddddddddddddddddddddddddddddddddeaddddfbddddddddddddddfg gfddddddddddddbfdedddddddddddddddddddddddddddddddddddddddedddddbdddddddddddddddfg gfddddddddddddfbdeadddddddddddddddddddddddddddddddddddddefddddbcdddddddddddddddfg gfdddddddddddddbfdeddddddddddddddddddddddddddddddddddddfeddddcbddddddddddddddddfg gfdddddddddddddfbdeadddddddddddddddddddddddddddddddddddefddddbdddddddddddddddddfg gfddddddddddddddbcdeddddddddddddddddddddddddddddddddddaeddddbcdddddddddddddddddfg gfdddddddddddddddbdeadddddddddddddddddddddddddddddddddeddddcbddddddddddddddddddfg gfdddddddddddddddccdeddddddddddddddddddddddddddddddddeadddfbdddddddddddddddddddfg gfddddddddddddddddbdaadddddddddddddddddddddddddddddddeddddbfdddddddddddddddddddfg gfddddddddddddddddcbdeddddddddddddddddddddddddddddddeadddbcddddddddddddddddddddfg gfdddddddddddddddddbfaaddddddddddddddddddddddddddddfedddfbdddddddddddddddddddddfg gfdddddddddddddddddcbdeddddddddddddddddddddddddddddefdddbddddddddddddddddddddddfg gfddddddddddddddddddbfaaddddddddddddddddddddddddddaedddbcddddddddddddddddddddddfg gfddddddddddddddddddfbdeddddddddddddddddddddddddddedddcbdddddddddddddddddddddddfg gfdddddddddddddddddddbcaaddddddddddddddddddddddddaadddbddddddddddddddddddddddddfg gfddddddddddddddddddddbdeddddddddddddddddddddddddedddbcddddddddddddddddddddddddfg gfddddddddddddddddddddbcaaddddddddddddddddddddddeaddcbdddddddddddddddddddddddddfg gfdddddddddddddddddddddbdedddddddddddddddddddddfeddfbddddddddddddddddddddddddddfg gfdddddddddddddddddddddcbaaddddddddddddddddddddefddbfddddddddddddddddddddddddddfg gfddddddddddddddddddddddbdedddddddddddddddddddaeddbcdddddddddddddddddddddddddddfg gfddddddddddddddddddddddcbaaddddddddddddddddddeddfbddddddddddddddddddddddddddddfg gfdddddddddddddddddddddddbfedddddddddddddddddaeddbdddddddddddddddddddddddddddddfg gfdddddddddddddddddddddddfbaeddddddddddddddddeddbcdddddddddddddddddddddddddddddfg gfddddddddddddddddddddddddbcedddddddddddddddeadcbddddddddddddddddddddddddddddddfg gfdddddddddddddddddddddddddbaeddddddddddddddeddbdddddddddddddddddddddddddddddddfg gfdddddddddddddddddddddddddbcedddddddddddddeadbcdddddddddddddddddddddddddddddddfg gfddddddddddddddddddddddddddbaedddddddddddfedcbddddddddddddddddddddddddddddddddfg gfddddddddddddddddddddddddddcbedddddddddddeffbdddddddddddddddddddddddddddddddddfg gfdddddddddddddddddddddddddddbaedddddddddaedbfdddddddddddddddddddddddddddddddddfg gfdddddddddddddddddddddddddddcbedddddddddedbcddddddddddddddddddddddddddddddddddfg gfddddddddddddddddddddddddddddbaedddddddeafbdddddddddddddddddddddddddddddddddddfg gfddddddddddddddddddddddddddddfbedddddddedbfdddddddddddddddddddddddddddddddddddfg gfdddddddddddddddddddddddddddddbaedddddeabcddddddddddddddddddddddddddddddddddddfg gfddddddddddddddddddddddddddddddbeddddfecbdddddddddddddddddddddddddddddddddddddfg gfddddddddddddddddddddddddddddddbaedddefbddddddddddddddddddddddddddddddddddddddfg gfdddddddddddddddddddddddddddddddbeddaebcddddddddddddddddddddddddddddddddddddddfg gfdddddddddddddddddddddddddddddddccedecbdddddddddddddddddddddddddddddddddddddddfg gfddddddddddddddddddddddddddddddddbeaebddddddddddddddddddddddddddddddddddddddddfg gfddddddddddddddddddddddddddddddddccebfddddddddddddddddddddddddddddddddddddddddfg gfdddddddddddddddddddddddddddddddddbbbdddddddddddddddddddddddddddddddddddddddddfg gfffffffffffffffffffffffffffffffffffbfffffffffffffffffffffffffffffffffffffffffffg ggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggg ``` <!-- end of image --> Here's a close-up of the area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#5e5cfcff b,#fe0606ff c,#fe8283ff d,#afaffeff e,#0909feff f,#fc4547ff g,#fec0c0ff ``` ```image bg ed aa bc eed ee bb aea ee bbc ee ed c fb ed ded b gbg ae ae cb gbg ee eea bb bf ee ee fbb bb ae ed bbg bc ae ed ff gb ed ae cbg bbg ee ea bf fbf de de cb gbb ed ea gbg bc ed ee fbb cb ee aea bbg bb dee ea ff fb ee de cbg ff ed de bf gbg de ee cb bf ed ee gbg cb ee aa bb bc de ded gbg bc de dee fb bbg ed eed cbb fbf ee ee bbc cb dee aa cb bg ee ded gbg bc ea ee bb bb de ea gbg fb ea ae bc ff ee ae cbb gbg de ee bbc bbg de de cb cbb ea ea gbg bb ee de bb fc dee aee gbg gbg ae eed bc bb aa ded cbb fb de ea bbc bg ea de bf bc ae ee gbg bb de ed bb gbb de ded gbg fb ea ae bc ff ae eea bb bgde ee gbc bb aa ed ff cb ea ded gbb fc ee ae bbf bfdee ea gbg bb ae de bc fb ded ed fb cb ded ee gbc bc ea aea ff fbcae ea gbb gbbded de bbf fb aa ed bb ff ea ee bc bgeed ea fb bb ee aa gbc cb ae de ff bc ed ee cb bf ed ed bbf bbgea ae bb gbbae ae bc cb ed dee fb bcaa eea bb bcea ed ff bbeed ae cb gbgee ae bf ffae ee fb gbged ea gbg bbced ed fbf cbbee ae bbg gbae aea ff fced eedcb bfed de bf bbee ea fb cbee de gbg cbed eefbf bae dedbbg fbee dedff gbeed eecb faee deebb bfe eecb bbed edbg bbeefbf gbeebbg feebc bb ``` <!-- end of image --> No intersection in area A, but I'll keep looking. I've examined the entire image, and there are zero intersections present.

<!-- image --> ```palette Key,Color ,#fefefeff a,#5754fcff b,#ff0606ff c,#ff8484ff d,#a9a9ffff e,#0707ffff f,#f8434aff g,#ffc0c0ff ``` ```image d e ed de e de e ed aa e e ed ed e e ed ed e de ed e e aa bg ed e b e ea bc ed e b b e ed ff ff ed de gb b e e b cb ed ae bc b e e cb gb ed aa b bg e e bg b ed ed fb bc e de b b ed e bg ff e de ff b ed e gb cb e aa b b ed e bc gb e ed cb bg ed e b b e ed bg bc ed de fb b e e b ff ea aa bg b e e ff cb aa ea gb b e e b gb aa ed bc bg e de cb b aa e b bc e ae bg b aa e fb ff e aa b b aa e bg cb e ed ff b aa de gb gb e e b bgaa de bc b e e cb bcaa aa b b e e bg ffaa ed fb b e e b cfaa ed bg b e de ff gbaa e gb bge aa b gbaa e bc bce ea cb baa e b ffe ed bg baa de fb cfe e b baa de bg gbe e ff bae aagb gbe e b bae edbc be ecb fae e b be debg cfe efb beaab gfebg bff gb ``` <!-- end of image -->

I'm ready to tackle this image and find those intersections! There are 1 areas where the lines seem to converge. We should take a closer look at area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0707fdff b,#f3736dff c,#a2a6f6ff d,#fd0a09ff e,#97c897ff f,#b1d7b1ff g,#5159edff ``` ```image c a ac a a ca a ga a gg a ac a ac ca efffffffffffffffffffffa effffffffffffffffffffga effffffffffffffffffffae efffffffffffffffffffgge efffffffffffffffffffafe effffffffffffffffffagfe ddddddbb effffffffffffffffffaffe bbdddddddbf efffffffffffffffffacffe fbdddddddbb effffffffffffffffcafffe bbddddddbbf effffffffffffffffaffffe bbddddb efffffffffffffffgaffffe bdd efffffffffffffffafffffe bdd effffffffffffffggfffffe ddb effffffffffffffaffffffe ddb efffffffffffffagffffffe bddefffffffffffffafffffffe bddbffffffffffacfffffffe efddbfffffffeaffffffffe efffdddfffffafffffffffe efffffbddefgafffffffffe efffffffbddaffffffffffe efffffffffgadbffffffffe efffffffffaffbddffffffe effffffffagffffbddefffe effffffffafffffffeddbfe efffffffagffffffffffddd effffffeafffffffffffffbdd effffffaefffffffffffffe bddf efffffcaffffffffffffffe ddb efffffafffffffffffffffe dd effffgafffffffffffffffe effffaffffffffffffffffe efffggffffffffffffffffe efffafffffffffffffffffe effagfffffffffffffffffe effaffffffffffffffffffe efaeffffffffffffffffffe ecafffffffffffffffffffe eaffffffffffffffffffffe gaffffffffffffffffffffe afffffffffffffffffffffe ggfffffffffffffffffffffe afeeeeeeeeeeeeeeeeeeeeef ac a ac ca ag a gaa ca caa a caa gg caac a aac ag aac a aac ac aag ca gag a gag ca gaa a caa gg caa a caac gg aac a aacac aa ``` <!-- end of image --> This close-up might reveal an intersection in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0505feff b,#fc585bff c,#8585ffff d,#fe0607ff e,#c8c8feff f,#ffb3b3ff g,#4341fcff ``` ```image c a ca aa cag eaae gag eaae gac caa aac caa aac cag eaae gag eaae gac eaa aac caa aac cag eaae gag eaae gag eaae gac caa aac dbf cag dddbf eaae fbddddf gag bddddb eaae fddddbf gag fbdddbf eaae fbddddf gac bddddb caa fddddbf aac fbdddgaa fbdaabb gaadddbf eaaefbdddbf gag fbddddf eaae bddddb gac fddddbf caa fbdddbf aac fbddddf caa bddddb aac fdddd cag fbd eaae f gag eaae gac eaa aac caa aac cag eaae gag eaae gag eaae gac caa aac cag eaae gag eaae gag eaae gac caa aac caa aae ag ae g ``` <!-- end of image --> Success! This area contains an intersection point! It was tricky, but I finally found one single intersection in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0505feff b,#ff5959ff c,#8888ffff d,#ff0606ff e,#c8c8ffff f,#ffaeaeff g,#4141feff ``` ```image c a ac ea ae ea a cg a gg a ac ea ae ea a ca a gg a ac ddddddbff a ffbddddddbbf ae fbbddddddbff ea ffbddddddbbf a fbddddb ca bdd a fddf gg fddf a ddb gc bdd a fddf ae ddb ea bdb ae bdd ca fdda gadb a bdd gc fddf a fddf ac ddb ea bdd ae fddf ea ddb a bd cg a gg a ac ea ae ea a ca a gg a ac a ae ea ag a cag ca caa a caae gg eaae a eaae gc aac a aac ae gac ea gag ae gag ca cag a caa cg caae a eaae gc eaae a aacac aa ``` <!-- end of image -->

Let's examine this image for potential line intersections. It's crucial to examine these regions more closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd0e0eff b,#0808fdff c,#b2b2ffff d,#b2d7b1ff e,#f47570ff f,#5659f9ff g,#97c598ff ``` ```image c fbbbc cbbbfc cbbbf fbbbc cfbbfc cbbbf fbbbc cfbbbc cbbbf fbbb bc b ff b cb bf b cb bc b fb bc b ff dggggggbggggggggggggggggg gddddddgbdddddddddddddddd eaegdddddddbfddddddddddddddd ea eaagddddddbddddddddddddddd ea ggaaeddddfbdddddddddddddd ea gdddeaaeddbgddddddddddddd ea gdddddgaaadbddddddddddddd ea gddddddddeabbdddddddddddd ea gddddddddddgbaadddddddddd ea gdddddddddddgbeaaeddddddd ea gddddddddddddbfddaaaddddd aa gdddddddddddddbddddeaaedd aa gdddddddddddddfbddddddaaa aa gddddddddddddddbgdddddddeaae aa gdddddddddddddddbdddddddd aaa aa gdddddddddddddddfbddddddd eaae aa dggggggggggggggggbggggggg aaa aa cb eaae aa bf aaa aa b eaa ae cb ae bc ae b ae fb ae bc ae b ae ff ae b ae cb ae bc ae b ad fb ad bc ad b a ff a b a cb a bf b cb bc b ff b cb bf b cb bc b fb bc b ff b ``` <!-- end of image --> I'm going to scrutinize area A for any signs of an intersection. <!-- image --> ```palette Key,Color ,#fefefeff a,#fa4146ff b,#0b09fdff c,#b9b8fdff d,#ffc1c1ff e,#ff7f7fff f,#655af3ff g,#fe0506ff ``` ```image cbbc fbb bbf cbbc fbb bbc ae cbb gggad fbf eagggge cbbc deggggad fbb eagggge bbf deggggad cbbc eagggge fbb deggggad bbf daggggfbbc degggbbf dagbbaed dfbbggad bbfgggged cbbceggggad fbb dagggged bbf deggggad cbbc dagggged fbf eggggae bbc dagggged cbb egggg bbf dag cbbc fbb bbf cbbc fbb ``` <!-- 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,#ff4040ff b,#0707feff c,#9a9affff d,#e5d6efff e,#ff8c8cff f,#4e4efeff g,#fe0606ff ``` ```image c fbbbc cbbbfd cbbbc dfbbbc dfbbfd cbbbf fbbbc dfbbfc cbbbfd cbbb bc b ff bd db bf b cb bc b fb bd db ff b cb ega bc eg aggd b eg dgga cb eg egge bd eg dggadb ag egbf ag dbga ag dbegge ag bc dgga ag b egge ag cb dgga ag bc egge ag b aga gg ff egge ga bd aga ga db egge ga bf aggd ga b egg ga cb ga bc ga b ga fb ge bd ge db ge ff ge b ge cb ge bc ge b ge cb gd bd gd b gd ff gd bd dgd db gd bc b cb bc b ff bd db bf b cb bc b fb bd db ff 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,#0506fdff b,#f90a0aff c,#8c99e5ff d,#b1d7b1ff e,#454aebff f,#e17264ff g,#99c695ff ``` ```image c a ac a a ca a ce a ee a ac a a ca a ca a a ee ca a ac ac a a ee ac a ca ca a a ca a a ac ee a a ee ac a a ca ac f ac a fbgggggggagggggggggggggggggggggggggggggggggggggggggd a bbddddddeeddddddddddddddddddddddddddddddddddddddddg ca dbbddddddaddddddddddddddddddddddddddddddddddddddddg a ddbfdddddcadddddddddddddddddddddddddddddddddddddddg ee dddbfdddddacddddddddddddddddddddddddddddddddddddddg a ddddbfdddddaddddddddddddddddddddddddddddddddddddddg ee dddddbgddddaedddddddddddddddddddddddddddddddddddddg a ddddddbdddddadddddddddddddddddddddddddddddddddddddg ac dddddddbddddeaddddddddddddddddddddddddddddddddddddg a dddddddgbddddaddddddddddddddddddddddddddddddddddddg a ddddddddfbdddcadddddddddddddddddddddddddddddddddddg ca dddddddddfbdddacddddddddddddddddddddddddddddddddddg a ddddddddddfbdddaddddddddddddddddddddddddddddddddddg ce dddddddddddbbddeedddddddddddddddddddddddddddddddddg a ddddddddddddbbddadddddddddddddddddddddddddddddddddg ee dddddddddddddbbdcaddddddddddddddddddddddddddddddddg a ddddddddddddddbfdacdddddddddddddddddddddddddddddddgac dddddddddddddddbfdadddddddddddddddddddddddddddddddga ddddddddddddddddbfaedddddddddddddddddddddddddddddda dddddddddddddddddbgadddddddddddddddddddddddddddddca ddddddddddddddddddbeaddddddddddddddddddddddddddddag ddddddddddddddddddgbadddddddddddddddddddddddddddeag dddddddddddddddddddgbaddddddddddddddddddddddddddadg ddddddddddddddddddddfacddddddddddddddddddddddddeedg dddddddddddddddddddddfaddddddddddddddddddddddddaddg ddddddddddddddddddddddeeddddddddddddddddddddddaeddg dddddddddddddddddddddddabdddddddddddddddddddddadddg dddddddddddddddddddddddcabdddddddddddddddddddacdddg ddddddddddddddddddddddddabbdddddddddddddddddcaddddg dddddddddddddddddddddddddabfddddddddddddddddadddddg dddddddddddddddddddddddddaebfddddddddddddddcadddddg ddddddddddddddddddddddddddadbfdddddddddddddaddddddg ddddddddddddddddddddddddddeadbgdddddddddddeeddddddg dddddddddddddddddddddddddddaddbdddddddddddadddddddg dddddddddddddddddddddddddddcadgbdddddddddaedddddddg ddddddddddddddddddddddddddddacdgbddddddddaddddddddg dddddddddddddddddddddddddddddaddfbddddddacddddddddg dffffbbbbbbbbbbbb dddddddddddddddddddddddddddddeeddfbddddcaddggffffbbbbbbbbbbbbbbffffd ddddddddddddddddddddddddddddddadddfbbbbabbbbbbffffg ddddddddddddddddddddddddddddddcaddddddcaddddddddddg dddddddddddddddddddddddddddddddacdddddadddddddddddg ddddddddddddddddddddddddddddddddaddddeedddddddddddg ddddddddddddddddddddddddddddddddaedddaddddddddddddg dddddddddddddddddddddddddddddddddaddeeddddddddddddg dddddddddddddddddddddddddddddddddeadadddddddddddddg ddddddddddddddddddddddddddddddddddaacdddddddddddddg ddddddddddddddddddddddddddddddddddcaddddddddddddddg ddddddddddddddddddddddddddddddddddddddddddddddddddg ddddddddddddddddddddddddddddddddddddddddddddddddddg ddddddddddddddddddddddddddddddddddddddddddddddddddg ``` <!-- end of image --> My goal is to determine if there's an intersection inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0404feff b,#fd0708ff c,#7876fcff d,#feacadff e,#3832f8ff f,#f85157ff g,#bcbcfeff ``` ```image bbd caa fbbd eac fbb gaa bbb eae bbf gaag bbf cae dbbf aac dbbf caa dbbf eac dbbd gaag dbbd cae fbbd aag fbbd caa fbbd eac fbb gaag fbb eae bbb gaag bbf cae bbf aac dbbf gaa dbbf eac dbbf gaag dbbd cae dbbd aag fbbd caa fbbd eac fbbd gaag fbb eae fbb gaag bbb cae bbf aac bbf gaa dbbf eac dbbf gaag dbbf cae dbbd aag dbbd caa fbbd eac fbbdgaag fbbdeae g fbbgaag e fbbcae ga bbfaac aa bbfaa cae dbbeac aag dbbaag cae dbeae gaag dbaag eae dfaa gaag daac eac faad gaa eaed eac gaafd caa caab aag aafb cae gaabb gaag eaebf eae gaabbf gaag caebbf eac aacbbf gaa caadbbd eac eacdbbd caa gaagfbbd aag eae fbbd cae gaag fbbd aag cae fbbd cae aac fbb gaag gaa bbb eac eac bbf gaa gaag bbf eac cae dbbf caa aac dbbf aac caa dbbf cae eac dbbd aag gaag dbbd cae eae fbbd gaag ddddddffffff aag fbbdddddfffeaebbbbbbbbbbbbbbbbbb cae fbbbbbbbbbaabbbbbbbbbffffffdddd aac fbffffffeacddd gaa gaa eae aac gaag cae cae aag aac cae caa gaag eac eae gaag gaag eae eac aag gaa caa eac eaccaa gaaaag eaae gaag gg ``` <!-- end of image --> Area A contains an intersection. After a long analysis, I found two intersections.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0505feff b,#fc0609ff c,#8484feff d,#feacacff e,#3f3cfbff f,#ff5757ff g,#c3c3ffff ``` ```image c a ac ga ag ga a ce a ee a ac a ag ga a ca a a ee ga a ag ac a a ee ag a ga ca a ag ca ga a ac ee a a ce ec a a ga ag d ag ga fb a ag bb ee ca bf a a bf ca ce bd ag a bd a ec bd ac a b a ac b ce ga db a ag db ga ga db ac a fb a ce fb ee a bb a ee bf ca a bf ag ac bd a a bdec ag bda ga bce a ba ca dba a dac ee da a ee ac ab a cab ag abf ga abf a ecbd ca a bd a ca bd ee a b a ga b ec ac db a a db ag dddfffbbbbbbbbbbb ee fb ga dddfffbbbbbbbbbbbbbfffddd a fbbbbabbbbbfffddd ga ca ag a a ce ec a a ec ca a aac ga ``` <!-- end of image -->

I'm optimistic that I'll find some intersections in this image. I have a hunch that these areas might contain the intersections we're looking for. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd0707ff b,#0809fdff c,#f05c55ff d,#babafeff e,#585de9ff f,#aed4adff g,#febbbaff ``` ```image g ga aga ga ac ag a a ga ag ac a a cc ga a ac cc a a ga ga cc a a ga ga ag cc a ag ag a a cc cc ag a a cc ca a ag ga a a ca ga ag ag a a ca ag ag a a cc ca b a acfffffffffffffff be d cc afffffffffffffff dbd bb a caffffffffffffff eb eb ga facfffffffffffff bb eb ffffffffffffafff ffafffffffffffffbe db ffffffffffffafff ffcaffffffffffebd dbd fffffffffffaffff fffacffffffffebf bdfffffffffffaffff ffffafffffffbbff befffffffffacffff ffffcafffffbefff beffffffffafffff fffffacffebfffff fbbffffffccfffff ffffffafbbffffff ffbbfffffaffffff fffffffbbfffffff fffebfffccffffff ffffffbecfffffff ffffebffafffffff ffffebffafffffff fffffebcafffffff fffbbffffaffffff fffffffbffffffff ffbbfffffacfffff fffffffabfffffff fbefffffffafffff ffffffaffbefffff ebffffffffffaffff ffffffafffbeffff bbfffffffffffacfff fffffacffffbbfff be ffffffffffffafff fffffaffffffbbff dbd fffffffffffffaff ffffccfffffffebf eb fffffffffffffacf ffffafffffffffeb bb ffffffffffffffaf fffccffffffffffeb be fffffffffffffffa fffaffffffffffffdb dbd cc ffcaffffffffffff bd eb ag ffafffffffffffff bd bb a ffafffffffffffff be be ca ag be dbd ag a bb eb a ag eb bb ca a eb be ag cc db dbd a a dbeb ca cc b a a ga a ga ag a ag a cc a cc a ga a ``` <!-- end of image --> Here's a close-up of the area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0405ff b,#0705fdff c,#fe8888ff d,#aaaaffff e,#5050feff f,#fd4243ff g,#fdcbcdff ``` ```image fac gaa fac gaag faf gaag caf aag d caf bd aac bbe caa dbbe fac dbbe gaa dbbe fac dbbb gaag bbbd faf ebbd gaag ebbd caf ebbd aag ebbe caf dbbe aac dbbecaa dbbbac dbbbg fbbbd gaaebbd faf ebbd gaag ebbd caf ebbe aag dbbe caf dbbe aac dbbe caa dbbb fac bbbd gaa ebbd fac ebbd gaag ebb faf eb gaag d caf aag caf aac caa fac gaa fac ``` <!-- end of image --> The lines cross each other within area A, forming an intersection. Now, let's turn our attention to the next spot. I wonder what we'll find inside area B? <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0404ff b,#0606feff c,#fc898cff d,#aaaaffff e,#4b48fbff f,#f73d45ff g,#fececeff ``` ```image af aac caag faf gaac caag faf gaac caag faf gaac caag d faf eb gaac ebb caag dbbbd faf dbbbd aac ebbe caag ebbd faf dbbbd aac dbbb gaag ebbe faf ebbd aacbbbd gfbbe ebbe ebbfac dbbbdgaag dbbe caa ebbe aaf ebbd gaag dbbbd caa dbbe faf ebbe gaag ebbd caa dbbbd faf dbbe gaac bbe caa bd faf d gaac caag faf gaac caag faf gaa ca f ``` <!-- end of image --> My analysis confirms the presence of an intersection in area B. Two intersections have been found!

<!-- image --> ```palette Key,Color ,#fefefeff a,#fe0606ff b,#0707feff c,#fe8888ff d,#b2b2ffff e,#5353ffff f,#fb4346ff g,#fecdceff ``` ```image g ca aca ga ac ag a ga ga ag af a a fc ga a ff ff a a ga ca ff a ag ga ga ag ff a ag ac ga a ff fc ag a a cf ff a ag ca a a fa ga ag ag a a ca ac ag a a fc ca b a ac be d cf a dbd bb a ca eb eb ca ac bb eb a a be db ga ca dbd dbd ag ac eb bd a a bb bd ac ca be be a ac dbd be fc a eb bb a gbb eb cf bfc eb a db a dbca eb ga dbg be af gabd bd a ag bd db ga a be bb ff ac be be ag a bb dbd ga fc eb eb ff a eb bb ag cf db be ga a db dbd ff ca bd eb ag a bd bb ga ga be be ff ag be dbd ag a bb eb a ac eb bb fa a eb be ag fc db dbd a a dbeb ca cf b a a ca a ga ag a ac a fc a cf a ca a ``` <!-- end of image -->

This image seems promising for intersection detection. The image has some tight areas where segments are too close. I should investigate those closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff5d5dff b,#5556fbff c,#ffa9a9ff d,#aed5aeff e,#0707feff f,#aeaeffff g,#ff0909ff ``` ```image f bef ee feb eef ee bef ee feb bef ee feb eef ee bef ee feb bef ee feb bef ee bef ef ef e e fe fe be be eb eb ef ef e a e ag fe gg fe ga be gc be g eb g eb cg ef ag ef ga ef gc e gc fe g fe cg be ag be ag ee ga eb gc eb g ef g ef cg e ag e ga fe ga fe gc be g be cg eb cg eb ag ef ga ef gc e g dddddddeddddddd g ddddddddedddddd cg ddddddddbeddddd ag dddddddddbedddd gg ddddddddddbdddd ga ddddddddddddddd gc ddddddddddddddd g ddddddddddddddd g ddddddddddddddd cg ddddddddddddddd ag ddddddddddddddd ggaaaaaaaacccccccccccc ddddddddddddddd cccccaaaaaaaaaaaggggggggggggggggggggggggggggdddd ddddddddddddddd ddddddddddddddd ddddddddddddddd ``` <!-- end of image --> I'm eager to see what's happening in this magnified view of area A. <!-- image --> ```palette Key,Color ,#fefeffff a,#ff4343ff b,#5e5effff c,#ffa2a2ff d,#ff7373ff e,#0505ffff f,#b4b4ffff g,#ff0000ff ``` ```image eeb feeb feeb feeb feef beef beef bee bf aaaaaaaaaaaaaaddddddddc gggggggggggggggggggggga ccccccccccccccddddddddc ``` <!-- end of image --> Area A doesn't meet the criteria for an intersection. There's definitely not a single intersection on the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff5858ff b,#4949ffff c,#ff9f9fff d,#e1d5f3ff e,#0505ffff f,#9595ffff g,#ff0909ff ``` ```image f bef ee feb bed dee fef ee deb bef ee feb bed dee fef eed deb bef ee feb bed dee fef ef ed ed de de fe be be eb eb ef ed ed a de ag de gg fe ga fe gc be g eb dg eb cg ef ag ef ga ed gc e gd de g fe cg fe cg be ag be ga eb gc ef gd ef dg ed cg ed ag de ga fe gc fe gc be g be dg eb cg eb ag ef ga ed gc ed gd de g de cg fe ag be gg b ga gc g dg cg ag ggaaaaaaacccccccccccdddd ccccccaaaaaaaaaaaggggggggggggggggggggggggggg ``` <!-- end of image -->

The hunt for intersections begins! Let's analyze this image closely. After a thorough analysis, I conclude that there are no intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff3e3eff b,#0808ffff c,#5c5cffff d,#ff8585ff e,#ff0505ff f,#b4b4ffff g,#ffc7c7ff ``` ```image g geeg aeg e ea ge aeg de ea ae deg aa ee ed ded eg ee eg ged e ee ge ged de ae ae gea ea ae ed ea eg aeg e ea ge deg ge ee de deg ae ee ea ded ed ee eg ed e ge de de aa ea ed eg e ge de ae aa ed eg eg e ge de ae ea bc ed bb eg cb e fbf ge bc ge bb d cb fbf bc bb cb fbf bc bb fb bc bb cb fbf bc bb cb fbf bc bb cb fbf bc bbbccf fccbbbbbbccf fcbbbbbbbccf ffcbbbbbbbccf ffcbbbbbbbcff ffcbbbb ``` <!-- end of image -->

This image seems promising for intersection detection. After a thorough analysis, I conclude that there are no intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff4848ff b,#0606ffff c,#4d4dffff d,#ff0505ff e,#9595ffff f,#ffa0a0ff g,#e4d8f2ff ``` ```image f aa df dg d fd ad da df dg gd fd ad da df d g fd be ad b da cc df b dg eb gd bg fd gb ad be da b df cc d b gd eb fd bg aa gb df be dg b d fddd cc fd addaf b ad fdddf eb da gaddaf bg df fdddf gb d gaddag be gd fdddf b fd faddag cc aa fdddf b df fadda eb dg adddf bg d fddda gb fddf be b cc b eb bg gb be b cc b eb bg gb be b cc b eb ebb bg gcbbg gb cbbe be ebbc b gbbbg cc cbbe b ebbc eb gbbbg bg cbbe gb ebbc be gbbcg b cbbe cc ebbe b gbbc eb cbbg bgebbe gbc ``` <!-- end of image -->

This is the image I'm working with. The goal is to count the intersections. It's crucial to examine these regions more closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd0908ff b,#0404feff c,#f65f5bff d,#4f4df1ff e,#ffb6b5ff f,#aaaaffff g,#aed5adff ``` ```image aa aecc eae a ca ea aa a ac ea ac ae eae a ca ac aa a aa cc ac a eae ea ea a ca ea aa ae ac a ae ac ea a ca cc aa a ac ca ae a eae ea ca ae aa a ac ae ac a eae cc ca a c ca a ea ae ea ae a ac a cc a ea a ea ae a ac a cc a ea a eagggggggggggggggg agggggggggggggggg gaggggggggggggggg gacgggggggggggggg ggagggggggggggggg ggccggggggggggggg gggaggggggggggggg gggcagggggggggggg ggggagggggggggggg gggggaggggggggggg gggggaggggggggggg ggggggagggggggggg ggggggacggggggggg gggggggaggggggggg gggggggacgggdbbgg ggggggggdbbbdgggg ggggdbbbdaggggggg dbbbdggggaggggggg bbbd fbbbdggggggggcagggggg dbbbbd fdbbdf ggggggggggagggggg fdbbbbf fdbbbf gggggggggggaggggg fdbbbbf dbbbf gggggggggggacgggg fdbbbdf dbbbd ggggggggggggagggg fdbbbdf fbbbd ggggggggggggacggg fdbbbdf fbbbdf gggggggggggggaggg fdbbbbdf gggggggggggggcagg ggggggggggggggagg ggggggggggggggggg ggggggggggggggggg ggggggggggggggggg ``` <!-- end of image --> Let's get to the bottom of what's happening inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0607ff b,#0403feff c,#ff9393ff d,#463df6ff e,#f2cfdcff f,#8d8dffff g,#fb4c4fff ``` ```image ag aae gag eaae gag aac caa aac caa gag eaae gag eaae gag eaac caa aac caa gac eaae gag eaae gag eaac caa aac caa aac caae efdf gag efdbbbbd eaaeefdbbbbbbdfe gdbbbbbbdfe ffdbbbbbdfe ffdbbbbbddag efdbbbbbdff aac efdbbbbbbdf caa bbbbbdfe aac bdfe caae gag eaae gag eaae gag aac caa aac caa gag eaae gag eaae gag eaac caa ge ``` <!-- end of image --> An intersection is present within area A. I've found a single intersection point in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0303ff b,#0404ffff c,#ff7979ff d,#544ef8ff e,#ffc3c3ff f,#aaaaffff g,#fe3535ff ``` ```image e aa accg eae a ca ca ga ae ag ea ac ae eae a ca gc ga a ag cg ac a eae ca ca a ga ea ag ae ac a eae gc ea a ga gg aa a ag cg ac a eae ea ca ae ga a ag ac ac a eae gc ca a c cg a ea ae ea ae a gc a cg a ca ae ea ae a gc a cg a ca a ea ae a gc a gg a cg a ea ae a ac a gc fdbb dbbbf dbbbdg fbbbd a bbbd fbbbdf ea dbbbbd fdbbdf ae fdbbbbf fdbbbf ea fdbbbbf dbbbf ae fdbbbdf dbbbd a fdbbbdf fbbbd gc fdbbbdf fbbbdf a fbbbbbdf cg a ``` <!-- end of image -->

Based on a first glance, I suspect there could be intersection regions here. My next step is to analyze the details within each area. <!-- image --> ```palette Key,Color ,#fefefeff a,#4849f4ff b,#f0504dff c,#0808fdff d,#f5a49fff e,#fd0506ff f,#9ea4f2ff g,#b0d6b0ff ``` ```image f ac ac cc ca gggggggggggggggggggggggggggggg ca gggggggggggggggggggggggggggggg ca gggggggggggggggggggggggggggggg ca gggggggggggggggggggggggggggggg ca gggggggggggggggggggggggggggggg ca gggggggggggggggggggggggggegggg cf ggggggggggggggggggggggggecgggg cf gggggggggggggggggggggggccggggg cf gggggggggggggggggggggfcagggggg cf ggggggggggggggggggggcceggggggg cf ggggggggggggggggggacbegggggggg cf gggggggggggggggggcceeggggggggg c gggggggggggggggacfbegggggggggg c gggggggggggggfcagbeggggggggggg c ggggggggggggccggbegggggggggggg c ggggggggggacaggbeggggggggggggg c gggggggggccgggbegggggggggggggg fc gggggggacfgggbeggggggggggggggg fc ggggggcaggggbegggggggggggggggg fc ggggccgggggbeggggggggggggggggg fc ggfcagggggbegggggggggggggggggg fc gccggggggbeggggggggggggggggggg fc acfggggggdegggggggggggggggggggg ac ccgggggggdeggggggggggggggggggggg ac ac ggggggdegggggggggggggggggggggg ac fca gggggdeggggggggggggggggggggggg ac cc ggggdegggggggggggggggggggggggg ac fcf ggggeggggggggggggggggggggggggg ac cc gggegggggggggggggggggggggggggg cc acf ggeggggggggggggggggggggggggggg ca fca gegggggggggggggggggggggggggggg ca cc eggggggggggggggggggggggggggggg ca fca e ccc e f ed ed ed ed ed ed ed ed ed eb eb eb eb eb eb eb eb ded ee ded be eb ded ee ded be eb bed ee ded be eb be ee ded ee eb be ee ded ee eb ``` <!-- end of image --> This is a magnified view of the region A. <!-- image --> ```palette Key,Color ,#fefefeff a,#504ffeff b,#fd5759ff c,#0805fcff d,#8f0d7cff e,#fe0809ff f,#aaa9fdff g,#feb7b7ff ``` ```image geb gedb gecca gdcccf fccca acccf fcccd acccd fcccde facccee acccdee fcccabeeg acccfbeeg fccca beeg accaf beeg fcccf beeg fccca beeg acccf beeg fccca beeg acccf beeg fcccf beeg facca beeg acccf beeg fccca beeg acccf beeg fccca beeg faccaf beeg acccf beeg fccca beeg acccf geeg fccca geeb accaf geeb fcccf geeb facca geeb cccf geeb ca geeb f geeb geeb geeb geeb geeb geeb geeb geeb geeb geeb geeb geee eee eee eee eee eee ``` <!-- end of image --> The lines cross each other within area A, forming an intersection. My investigation reveals that there is exactly one intersection in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#4c49fcff b,#f83c42ff c,#0808feff d,#ff8181ff e,#ff0404ff f,#adadffff g,#ffc3c3ff ``` ```image f ac ac cc ca ca ca ca ca ca e cf bc cf cc cf fca cf ccb cf acbe cf ccbe cf acfbe c fca be c cc be c fcf be fc cc de fc acf de fc fca de fc cc de fc fca de fc cc de fc acf ge ac cc ge ac acf ge ac fca ge ac cc ge ac fcf ge ac cc ge cc acf ge ca fca e ca cc eg ca fca eg ccc eg f eg eg eg eg eg ed ed ed ed ed ed eb eb eb eb eb eb deg ee ged be eb deg ee ged be eb deg ee ged be eb deg ee ged be eb deg ee ged be eb ``` <!-- end of image -->

I'm ready to tackle this image and find those intersections! These areas seem to enclose narrow spaces where lines might be close. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0706ff b,#090afdff c,#faa6a4ff d,#6265f7ff e,#acd3abff f,#b9b9ffff g,#f6514dff ``` ```image f fbb fbb bbf bbf bbf bbf dbd dbd dbd dbd fbb fbb fbb fbb bbf bbf bbf bbd dbd dbd eeeeeeeeeeedbbee eeeeeeeeedbbeeee eeeeeddbbbeeeeee fdbbbbbbbdeeeeeeeee fddbbbbbbdfeeeeeeeeeeeeeeee fdbbbbbbdff eeeeeeeeeeeeeeee fdbbbbbbddf eeeeeeegaceeeeee bbbdf eeeeeeeaeaeeeeee eeeeeeaeeeaeeeee eeeeeageeeeaeeee eeeeeaeeeeecaeee eeeeaeeeeeeegaee eeeageeeeeeeegae eecaeeeeeeeeeega eeaeeeeeeeeeeeeaa eageeeeeeeeeeeeeag gaeeeeeeeeeeeeee ag aeeeeeeeeeeeeeee ac ac ac ca ac a a ac a ca a a ca ac ca ga ga a ga ac ga ga ag a ag ac ac gg ac a ac a a gg a a ca a ca gg ca ca ga a ga ag ga ca ag a ag ag ac ca ac a ac ac a ca a a ca ac ca ca ca a ga ac ga ga g a ac ga a ac ``` <!-- end of image --> Let's zoom in on area A to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0404ff b,#0606feff c,#ff7675ff d,#4e4effff e,#ffbebeff f,#a3a3ffff g,#ff3535ff ``` ```image dbbbdf fbbbdf fbbbdf fbbbbf fffddbbbbbf ffdddbbbbbbbbbbf bbbbbbbbbbddfff bbdddff e aae gaaae caagaae eaac gaae gag gag caa gag eaae aag gag eaag caa eaac eaae eaac gag eaac caa caac eaae caae gac caae caa caae eaae gaa gac ga cag g eaae aac cag eaae ``` <!-- end of image --> No intersection found in area A, but I won't give up. Zero, Nada.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0505ff b,#0808ffff c,#ff8484ff d,#5e5effff e,#ffc5c5ff f,#b0b0ffff g,#ff4343ff ``` ```image f fbb fbb bbf bbf bbf bbf dbd dbd dbd dbd fbb fbb fbb bb bbf bbf bbf bbf dbd dbd dbd fbb fdbbb fddbbbbbddf ffdbbbbbbdf fdbbbbbbdf e fdbbbbbbddf gae bbbdf ea ae ae a gg ea ea ea a ca gg ca ea ga a ga ac ag ea ag a ac ac ac ca ae a ae ac a ca ea a ea ae ca ca ca a ga ae ga ga ag a ag ae ac gg ae a ae ae ae gg a ea ea a ea gg ca ea ca a ga ag ga ea ag a ag ac ac ea ae a ae ac ae ca a a ea ac ea ca ca a ca ae ga ca g a ae gg a ae ``` <!-- end of image -->

Time to put on my detective hat and find those intersection points! It's crucial to examine these regions more closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#0909fdff b,#fe0909ff c,#6165f7ff d,#feb3b3ff e,#bebeffff f,#f5605dff g,#add4adff ``` ```image e aa acea ac ca ae ae ae a eae ea ea ac ea ae ca a b ca ca bb ggggggggggggggggca ac fbd gggggggggggggggaa a bb ggggggggggggggaa ea fbdgggggggggggggaag ca bbgggggggggggacgg ae fbfggggggggacggg a ggbbggggggacgggg ea gggfbfgggacggggg ac gggggbbgaggggggg ae gggggggafggggggg a ggggggagbbgggggg ca ggggcaggggbbgggg ac gggcaggggggfbggg a ggcagggggggggbbg ea gcagggggggggggfbd ca aaggggggggggggggbb ae aaggggggggggggggg fbd a aagggggggggggggggg bb ea ac gggggggggggggggg dbf ac ac bb ae ac dbf a ae bb ca ae dbf ac ae bf a bf ea bf ca bd ae bd a bd ea bd ac b ae b a db ca db ac db a db ea fb ca fb ae fb a fb ea bb ac bb ae bf a bf ca bf ac bf a bd ea bd ca bd ae bd a b b db db db db fb fb fb fb bb bb bf bf bf bd bd bd b ``` <!-- end of image --> I'm analyzing this close-up of area A with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#0604fdff b,#fd0607ff c,#9f9fffff d,#fda0a2ff e,#efdcebff f,#fd4d4fff g,#4444ffff ``` ```image e eg eaa eaag d caage bfe caag bbbd caag efbbfe caag dbbbd caag efbbfe caac dbbbd gaac efbbbe gaac dbbbf gaac efbbbd gaac dbbbfegaac fbbaaae daaafe eaaabbbd caageefbbfe caag dbbbd caag efbbfe caag dbbbd caag efbbfe caac dbbbf gaac efbbbd gaac dbbb gaac fb gaac d egaac egaae aaae age ge ``` <!-- end of image --> Aha! I've found an intersection inside area A! The image features one single intersection point.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0404ffff b,#ff0707ff c,#7a7affff d,#fdaaacff e,#bebeffff f,#fd5354ff g,#3d3dffff ``` ```image e aa acea ac gg ae ae ae a eae ea ea ag ea ae ca a b ca ca bf ga ac fbd ga a bb aa ea fbd ag gg bb ag ae dbd ac a bb ac ea dbf ae gg bb ae ae daf a ea fb ca ea bf ac ca fbd a ca bb ea ga fbd gg ga bb ae aa dbd a ag bb ea ag dbf gg ac bb ae ac dbf a ae bb ca ae dbf ac ae bf a bf ea bf gg bd ae bd a bd ea bd gg b ae b a b ca db ac db a db ea db gg fb ae fb a fb ea fb gg bb ae bf a bf ca bf ac bd a bd ea bd ga bd ac b a b b db db db db fb fb fb fb bb bf bf bf bf bd bd bd b ``` <!-- end of image -->

Hmm, I'm not sure what to expect from this image. Let's see if any lines cross. Let's take a closer look at what's happening inside these zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#0707fcff b,#ec5852ff c,#8d9be3ff d,#b1d7b1ff e,#9ac596ff f,#4b4de8ff g,#fb0907ff ``` ```image c a ac ca ac a a af ac a a a ac ca a a ff ac a a ff a gbeeeaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee fa geddffdddddddddddddddddddddddddddddddddddddddddddd a egdddadddddddddddddddddddddddddddddddddddddddddddd ac degddfaddddddddddddddddddddddddddddddddddddddddddd ca ddbgddaddddddddddddddddddddddddddddddddddddddddddd a dddgbdcadddddddddddddddddddddddddddddddddddddddddd ff ddddgedadddddddddddddddddddddddddddddddddddddddddd a dddddgdcaddddddddddddddddddddddddddddddddddddddddd ac dddddegdaddddddddddddddddddddddddddddddddddddddddd ca ddddddbgcadddddddddddddddddddddddddddddddddddddddd a dddddddgbacddddddddddddddddddddddddddddddddddddddd ff ddddddddgeaddddddddddddddddddddddddddddddddddddddd a dddddddddgacdddddddddddddddddddddddddddddddddddddd ac dddddddddbgadddddddddddddddddddddddddddddddddddddd ca ddddddddddbacddddddddddddddddddddddddddddddddddddd a dddddddddddgaddddddddddddddddddddddddddddddddddddd ff ddddddddddddafdddddddddddddddddddddddddddddddddddd a dddddddddddddadddddddddddddddddddddddddddddddddddd a dddddddddddddafddddddddddddddddddddddddddddddddddd ca ddddddddddddddagdddddddddddddddddddddddddddddddddd a ddddddddddddddffbddddddddddddddddddddddddddddddddd ac dddddddddddddddagedddddddddddddddddddddddddddddddd a dddddddddddddddffgdddddddddddddddddddddddddddddddd a ddddddddddddddddabgddddddddddddddddddddddddddddddd fa ddddddddddddddddfaggdddddddddddddddddddddddddddddd a dddddddddddddddddadgbddddddddddddddddddddddddddddd ac dddddddddddddddddfadgddddddddddddddddddddddddddddd ca ddddddddddddddddddadegdddddddddddddddddddddddddddd a ddddddddddddddddddcadbgddddddddddddddddddddddddddd ff dddddddddddddddddddaddgbdddddddddddddddddddddddddd a dddddddddddddddddddcaddgbddddddddddddddddddddddddd ac ddddddddddddddddddddaeddgddddddddddddddddddddddddd ca ddddddddddddddddddddcaddegdddddddddddddddddddddddd a dddddddddddddddddddddacddbgdddddddddddddddddddddddff ddddddddddddddddddddddadddgbdddddddddddddddddddddea ddddddddddddddddddddddacdddgeddddddddddddddddddddac dddddddddddddddddddddddaddddgdddddddddddddddddddca dddddddddddddddddddddddacdddegddddddddddddddddddad ddddddddddddddddddddddddaddddbgddddddddddddddddafd ddddddddddddddddddddddddafddddgbdddddddddddddddadd dddddddddddddddddddddddddadddddgedddddddddddddacdd dddddddddddddddddddddddddffdddddgddddddddddddfaddd ddddddddddddddddddddddddddadddddegdddddddddddadddd ddddddddddddddddddddddddddffdddddbgdddddddddafdddd dddddddddddddddddddddddddddaddddddgbdddddddeaddddd dddddddddddddddddddddddddddffddddddggbdddddaeddddd ddddddddddddddddddddddddddddaddddddddggbddfadddddd ddddddddddddddddddddddddddddfadddddddddggbaddddddd dddddddddddddddddddddddddddddadddddddddddabbdddddd dddddddddddddddddddddddddddddcadddddddddcadggbdddd ddddddddddddddddddddddddddddddadddddddddaddddggbdd ddddddddddddddddddddddddddddddcadddddddfaddddddggb dddddddddddddddddddddddddddddddadddddddadddddddddggb dddddddddddddddddddddddddddddddcadddddacdddddddddd bgb ddddddddddddddddddddddddddddddddacdddcaddddddddddd bgb ddddddddddddddddddddddddddddddddeadddadddddddddddd bgb dddddddddddddddddddddddddddddddddacdffdddddddddddd bgb eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeaeeeeeeeeeeeee bgb aac bgb a bgb bgb bgb bgb bgb bgb bgb bg ``` <!-- end of image --> I wonder what we'll find inside area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#0505feff b,#f63d46ff c,#8987fdff d,#fe9d9dff e,#c9c8feff f,#4941f7ff g,#fe0606ff ``` ```image gb eaae ggb faf dggd eaae dggd caf bgg aae bgb caf ggb aac dggd caa dggd aac bgg caa bgb aa ggb ca dggd ac dggd ca bgg ac bgb aa ggb fac dggdeaae dgg faf bb faf gbeaae ggdfaf dggeaae bggfaf bgbaae ggfaf dggaae dgfaf bgaac gbaa gaac dbaa daac baa aaf caad fafd eaag fafb eaagb fafgd eaaggd fafgg eaabgb fafggb eaacggd cafdggd aaebgg caf bgb aac ggb caa dggd aac dggd caa bgg aac bgb caa ggb aac dggd fac bgg eaa bgb fac ggd eaae dgg faf dg eaae bg faf gb eaae ggd faf dggd eaae dgg faf bgb eaae ggb caf dggd aae dggd e caf bgg f aac bgb ca caa ggb aa aa dggd caf ca dggd eaae ac bgg faf ca bgb caa ac ggb aac aa dggd faf fac dggd eaae eaa bgg fac fac bgb caa eaae ggb eaac faf dggd faf eaae dggd eaae faf bgg aac eaae bgb caa faf ggb eaae eaae dgggd faf caf dggggd eaae aae dggggd aac caf dggggd caa aac dggggd eaae aac dbbaae caa aabgd aac aabgggd caa eae dbgggd aac ff dbgggd caa ca dbgggd fac aa dbgggd eaa faf dbggg fac eaae dbg eaae faf d faf caa eaae aac faf faf eaae eaae faf aac eaae caa faf eaac eaae faf caf eaae ``` <!-- end of image --> I've cracked the case! This area contains the intersection. My analysis indicates that there are two intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0404feff b,#fc5153ff c,#8180feff d,#fe9f9fff e,#c6c5fdff f,#3e37f8ff g,#fe0707ff ``` ```image c a ae ca ae a a fc ac ea a ae fc ca a a fc ac a ea ff ae gb a cf gd cf a g a ac dg cf ea bg a a gb ca ff gd a a g ea ae dg ae ea bgea a gbae ff gea a gae ae dga ca bac a ga fc ac a a ae ff ca ag a ffd ac ag ea cfg ae adg cf cfbb a a gd ac ca g ea a g a ea dg ff a gb a ea gd ac ae g ea ea g a ae bg ff ea gb a ae gd ae a g ca ac dg a a bg ff fc gb a a gd ae fc g ca a dg a ff bg fc a gb ea cf ggd ae a ggd cf cf ggda a abd ca ea ggd a a bgd ea cf bgb ae a bgb ea ac bgb ae ea bgb ea a bgb ae ff bgb a a bgb aae bgb a bgb bgb bgb bgb bgb bgb bgb bg ``` <!-- end of image -->

This image seems promising for intersection detection. The image has some tight areas where segments are too close. I should investigate those closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#0607fdff b,#eb4f46ff c,#969defff d,#e99a92ff e,#afd6afff f,#fc0908ff g,#474defff ``` ```image c ac a gc a gg a gg a gg a gg a cg a ca a a ca ag a ga ca ca a a ca ac a ag ca ga a ca a a a ac a ag ac ga a ca ac a a a ac ac a gg ac ca a a ac a a ac gc ag a ca eggeeeeeeeeeeeeeebeeeeeeeeeeeeeeeeeeeeee a eeaeeeeeeeeeeeeefffeeeeeeeeeeeeeeeeeeeeea eeggeeeeeeeeeeefbebfeeeeeeeeeeeeeeeeeeeac eeeaeeeeeeeeeefbeeedfdeeeeeeeeeeeeeeeeag eeeggeeeeeeeefbeeeeeefbeeeeeeeeeeeeeegae eeeeaeeeeeeeffeeeeeeeeffeeeeeeeeeeeecaee eeeeggeeeeebfeeeeeeeeeebfeeeeeeeeeeeaeee eeeeeaeeeebfeeeeeeeeeeeedfeeeeeeeeeaceee eeeeegaeedfeeeeeeeeeeeeeeefbeeeeeeageeee eeeeeeaedfeeeeeeeeeeeeeeeeeffeeeegaeeeee eeeeeegafeeeeeeeeeeeeeeeeeeeffeecaeeeeee eeeeeeeaeeeeeeeeeeeeeeeeeeeeebfeaeeeeeee eeeeeefgaeeeeeeeeeeeeeeeeeeeeeeadeeeeeee eeeeefdeaeeeeeeeeeeeeeeeeeeeeeagfbeeeeee eeeefdeecaeeeeeeeeeeeeeeeeeeegaeeffeeeee eeefbeeeeaeeeeeeeeeeeeeeeeeecaeeeebfeeee eefbeeeeecaeeeeeeeeeeeeeeeeeaeeeeeedfdee effeeeeeeeaeeeeeeeeeeeeeeeeaeeeeeeeeefbe bfeeeeeeeecaeeeeeeeeeeeeeeageeeeeeeeeeff bfeeeeeeeeeeaeeeeeeeeeeeeeaaeeeeeeeeeeeebf dfeeeeeeeeeeecaeeeeeeeeeeegaeeeeeeeeeeeeeedf df eeeeeeeeeeeeaceeeeeeeeeeaeeeeeeeeeeeeeee fd df eeeeeeeeeeeeeaeeeeeeeeeaeeeeeeeeeeeeeeee ff f eeeeeeeeeeeeeaceeeeeeeaceeeeeeeeeeeeeeee bf f eeeeeeeeeeeeeeaeeeeeeageeeeeeeeeeeeeeeee df f ac ca fd fd a a fb fd ac a ff fb a ac df fb aag fd ff a fb bf ff bf bf df df df fd f ff f b f fd fd ``` <!-- end of image --> Let's zoom in on area A to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#0706feff b,#f8393fff c,#5553fdff d,#fec5c5ff e,#b3b3feff f,#fe0505ff g,#fe7e7fff ``` ```image eaa cac gg eaa gffbd cac gfffffd eaa gffg bffg cac dffg gffb e eaae dffg gffbd ea cac dffb dfffd aa eaae dffb dbffg caa cac dffb bffg caa aae bfb gffb eaae cac bff dfffd eaae aae bffd dbffd aac cac bffd bffg cac aae gffd gffb caa cac gffd dffbd eaae aae gffg dfffd eaae cac gffg bffg aac aae dffg gffb aac caa dffg gffbd caa aaedffb dfffd caae eaaffb bffg eaae aabb bffg eaac baa gffbdaac bfaae dffaaa bffeaa dcaag bffd aae eaabfg gffd eaa eaacgffb gffd aae aac dffbd gffg eaa caa dfffd gffg aac caae bffg dffg eaa eaae gffb dffg cac eaac gffbd dffb eaa aac dfffd dffb cac caa bffg ffb eaa caa gffg bfb cac eaae gffb bffd eaa eaae dff bffd cac aac db ffd eaae cac fd cac caa d eaae eaae cac eaae eaae aac cac aac aae caa cac caae aae eaae ``` <!-- end of image --> An intersection is present within area A. There are precisely two intersections present in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0404ffff b,#ff5a5aff c,#7877feff d,#fdb2b3ff e,#bfbfffff f,#ff0909ff g,#3939feff ``` ```image e gc a gc a gc a gc a gg a cg a cg a cg a a ca ag a ca ea ea a a ea ae a ac ea ga ae ea ea a ae ae ea ac ae gg a ea ae a a ae ae ac a gg ac ca a ea gc a a ac gc gg a ca gc b ea a fff a gc fb bf ae a fb dfd ag cg fb fb ca a ff ff ea cg bf bf a a bf dfd ae cg df fb ac a df ff ga cgf bf ea a df a fca ad fd a acfb fd ea gg ff fb a ea bf fb ea a dfd ff a ae fb bf ea ac ff bf ae gg bf bf ea ca dfd df ae ea fb df ea a ff f ae ae bf f a gg df fd ae ca fd fd a ea fb fd ae a ff fb a ae bf fb aag dfd ff a fb bf ff bf bf df dfd df fb df ff f b f fd fd ``` <!-- end of image -->

Based on a first glance, I suspect there could be intersection regions here. I wonder what's going on inside those areas? Perhaps intersections are hiding there. <!-- image --> ```palette Key,Color ,#fefefeff a,#fa0b0aff b,#0707fcff c,#5760e9ff d,#e36156ff e,#f0f3efff f,#a3cca2ff g,#b2d7b2ff ``` ```image g cb bb bc bc bc bc bc bg be ebe ebe eb eb aaffffffffffcbffffffffffffffffffffffffffffffffffffffffffffffe edadgggggggggcbggggggggggggggggggggggggggggggggggggggggggggfe efgdadggggggggcbgggggggggggggggggggggggggggggggggggggggggggfe efgggaadgggggggcbggggggggggggggggggggggggggggggggggggggggggfe efgggggaafggggggcbgggggggggggggggggggggggggggggggggggggggggfe efggggggfaafgggggbbggggggggggggggggggggggggggggggggggggggggfe efggggggggfaagggggbbgggggggggggggggggggggggggggggggggggggggfe efggggggggggdaaggggbcggggggggggggggggggggggggggggggggggggggfe efggggggggggggdadgggbcgggggggggggggggggggggggggggggggggggggfe efggggggggggggggdadggbcggggggggggggggggggggggggggggggggggggfe efggggggggggggggggaadgbcgggggggggggggggggggggggggggggggggggfe efggggggggggggggggggaafbcggggggggggggggggggggggggggggggggggfe efgggggggggggggggggggfaabfgggggggggggggggggggggggggggggggggfe efgggggggggggggggggggggfabfggggggggggggggggggggggggggggggggfe efgggggggggggggggggggggggdbagggggggggggggggggggggggggggggggfe efggggggggggggggggggggggggfbadgggggggggggggggggggggggggggggfe efgggggggggggggggggggggggggfbdadgggggggggggggggggggggggggggfe efggggggggggggggggggggggggggfbgaadgggggggggggggggggggggggggfe efgggggggggggggggggggggggggggcbggaafgggggggggggggggggggggggfe efggggggggggggggggggggggggggggcbggfaaggggggggggggggggggggggfe efgggggggggggggggggggggggggggggcbgggdagggggggggggggggggggggfe efggggggggggggggggggggggggggggggcbgggaaggggggggggggggggggggfe efgggggggggggggggggggggggggggggggbbgggaagggggggggggggggggggfe efggggggggggggggggggggggggggggggggbbgggaaggggggggggggggggggfe efgggggggggggggggggggggggggggggggggbbfggadgggggggggggggggggfe efggggggggggggggggggggggggggggggggggcbbcfadggggggggggggggggfe efgggggggggggggggggggggggggggggggggggggcbbbdgggggggggggggggfe efggggggggggggggggggggggggggggggggggggggggcbbcgggggggggggggfe efggggggggggggggggggggggggggggggggggggggggggacbbcggggggggggfe efgggggggggggggggggggggggggggggggggggggggggggafgcbbcgggggggfe efggggggggggggggggggggggggggggggggggggggggggggafgggcbbcggggfe efggggggggggggggggggggggggggggggggggggggggggggfafgggggcbbcgfe efgggggggggggggggggggggggggggggggggggggggggggggfaggggggggcbbc efggggggggggggggggggggggggggggggggggggggggggggggfagggggggggfcbbc efgggggggggggggggggggggggggggggggggggggggggggggggdaggggggggfe cbbc efggggggggggggggggggggggggggggggggggggggggggggggggdagggggggfe cbbc efgggggggggggggggggggggggggggggggggggggggggggggggggdaggggggfe cbbc efggggggggggggggggggggggggggggggggggggggggggggggggggdagggggfe cbbc efgggggggggggggggggggggggggggggggggggggggggggggggggggdaggggfe cbbc efggggggggggggggggggggggggggggggggggggggggggggggggggggaagggfe cb efgggggggggggggggggggggggggggggggggggggggggggggggggggggaaggfe efggggggggggggggggggggggggggggggggggggggggggggggggggggggaagfe efgggggggggggggggggggggggggggggggggggggggggggggggggggggggadfe efggggggggggggggggggggggggggggggggggggggggggggggggggggggggade effffffffffffffffffffffffffffffffffffffffffffffffffffffffffad eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeag ae ae eae eae ea ea ga da da da da aa aa ad ad ad ad ag ae a ``` <!-- end of image --> I'm focusing my attention on this specific region, area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0506ff b,#0c09fbff c,#6b69fcff d,#fc8183ff e,#fec3c4ff f,#fa4145ff g,#babaffff ``` ```image aaae gbc daaafe bbc daaafe gbbc daaae cbbg efaad cbbg eaaad cbbg efaaad cbbg efaaae cbbg daaafe bbbg daaafe bbb efaaad bbb efaaa bbb efaad gbbb eaaae gbbc daaafe gbbc daaafe gbb daaafe gbc efaaad gbc efaaad bbc efaaad cbbc eaaaa cbbg daafecbbg daafcbbg daaabbbg efaabbbg efbbbd ebbbfe bbbafe bbbaaf gbbbaafe gbbcfaad gbbcfaaad gbb efaaad gbc eaaaae gbc daaafe bbc daaafe cbbg daaae cbbg efaae cbbg faae cbbg faa cbbg fae cbbg fa bbb aaf bbb eaaf bbb eaaf gbbbg eaaf gbbbbc eaaf cbbbbcg eaad cbbbbccaad gcbbbbbbfd gcbbbbbbg gcbbbbbcg dfbbbbbg faacbbbbcg faaegbbbbbcg faae gcbbbbbcg faa gcbbbbbcg fae gcbbbbbcg af gcbbbbcg aaf cbbbbbcg eaaf gcbbbb eaaf gcb eaaf eaaf eaad daad daad daad daad daae faae faae faae faa fae af aaf eaaf eaaf eaaf eaaf eaad daa ``` <!-- end of image --> I am surprised, so clear, an intersection has appeared in area A. After a thorough search, I conclude that there are two intersections.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fe0505ff b,#0807feff c,#605ffeff d,#fe7879ff e,#fec1c2ff f,#fe3738ff g,#abaafeff ``` ```image g cb bb bc bc bc bc bg bg bg b b b gb af gb daf gb dad cb fad cb aae cb aae bb eaa bb eaf bc daf bc dad bc fad bg aaebg aabg eabg ebf baf gbdad gb fad gb aae gb aa cb fa cb fa cb ff bb af bb af gbbc ad gbbbd cbbc acbbc ae cbbc ae cbbc a cbbc ea cbbc ea cbbc ea cbbc da cbbc da cbbc da cbbc fa cbbc fa cb ff af af ad ad ae ae ae ae a ea ea ea da da da fa fa ff af af ad ad ae ae 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,#fd0908ff b,#505ae3ff c,#ef5f5bff d,#0d0dfcff e,#a5a9f6ff f,#acd4acff g,#ffb8b8ff ``` ```image g gag a a ga ga ag ca a aa ag ac a ag cc a a ga cc ga a ca ga ac a ag ga ag ag a a ga ag ca a aa bd cc ac bdb a acffffffffffffff edd cc faffffffffffffff dd a ffafffffffffffff dde ga ffcaffffffffffff bde a fffcaffffffffffbdb ga ffffacffffffffdd ag fffffacfffffddff a ffffffafffbdbfff ag fffffffabdbfffff a fffffffddfffffff cc fffffddfcaffffff a fffddefffaafffff cc fbdbffffffacffff a eddfffffffffaffff fffffffffffcafff ddffffffffffffafff fffffffffffaffff dde fffffffffffffaff fffffffffffaffff bde fffffffffffffcaf ffffffffffafffff edb ffffffffffffffca ffffffffffafffff dd fffffffffffffffac fffffffffacfffff dd ag fffffffffaffffff bde ag ffffffffacffffff edb a eeebeeebbbbcbbbbbbbbbbbbdddddddd ga dddddddddddddbbbbbbbbbbbbeeeeeeeeee ca fffffffaffffffff aa ffffffcaffffffff ac ffffffafffffffff ag ffffffafffffffff a fffffaffffffffff ga fffffaffffffffff ga ffffacffffffffff ca ffffafffffffffff ac fffacfffffffffff a a cc a ga a ga ag a ag a cc a cc a ga a ga ag a ag a cc a cc a ga a ``` <!-- end of image --> I'm focusing my attention on this specific region, area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0a0aff b,#6060ffff c,#ffa7a7ff d,#0404ffff e,#9e9effff f,#ff5a5aff g,#721aa6ff ``` ```image aac caa aac caa faf caa faf aac faf aac caa aac caa aac caa faf caa eeeeeeeeeeeeeeegggebbbbbbbbbbbb ddddddddddddddddddddddddddddddd dddbbbbbbbbbbbgggbbbbbbbbbbeeee aac caa aac caa aac caa faf caa faf aac faf aac caa aac caa aac ``` <!-- end of image --> There's no doubt about it - this is an intersection in area A. Let's move forward and inspect another region. Let's take a closer look at area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0505ff b,#5a54f9ff c,#ff7d7dff d,#0706fdff e,#b0b0feff f,#fb3a3eff g,#fec4c4ff ``` ```image aag faag faf aaf gaac gaac caag caag faa e faf ebd gaaf bddd gaac bdddb gaac edddbe caag edddde faag ebddde faf bdddb aafedddb gfdddbe ebdddb bdddbaag bdddb caag edddbe faa ebddde faf bddde gaaf bdddb gaac edddbe gaac ddde caag de faag faf aaf gaac gaac caag caag faa fa ``` <!-- end of image --> The lines cross each other within area B, forming an intersection. The final answer is: two intersections found.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0505ff b,#5b58fcff c,#ff8585ff d,#0c0cfeff e,#aeaefeff f,#fb3c40ff g,#ffcacaff ``` ```image g cag aga ga ga ag ca a ff ag ac a ag fc a a ga cf ca a fa cf af a ac ga ag ag a a ga ag ca a ff bd fc ac bdb a ag edd cf a dd a ga dde ca ca bdb a fa edb ga af dd ag ac dde a ag bde ac aedb a edd fc dd ca a dde ff cf bdb ac a edd ag ca dd a a dde ga ga bdb ca ag edb fa a dd af ac dde ac a bde ag fc edb a eeeeeeeeeeefbbbbbbbbbbbbbddddddd ga dddddddddddbbbbbbbbbbbbeeeeeeeeeeeee ca a ff ca ac a ag ga a ag ga a ca ac fa a af fc a a cf a ca a ga ag a ac a fc a cf a ca a ga ag a ac a fc a cf a ca a ``` <!-- end of image -->

Alright, let's get to work and investigate this image for intersections. There's definitely not a single intersection on the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff5d5dff b,#0404ffff c,#ff0707ff d,#7c7cffff e,#ffb3b3ff f,#3d3dffff g,#c3c3ffff ``` ```image eee accccccccccccccccccccccaaaaaeeee aca eeeeeaaaacccccccccccccccc aca ecc ecc ecc ecc ecc ecc cce cce cce cce cce cce cca aca aca ca d db db db gb gb gb gb b bg bg bg bg bd bd bd bf bf bf ff fb fb db db db gb gb gb gb b bg bg bg bg bd bd bd bf bf bf ff fb fb fb fdddggg db dddfffbbbbbbbbbbbbbbbfffdddggg db gggdddffbbbbbbbbb ``` <!-- end of image -->

This image seems promising for intersection detection. I'm extremely confident. No intersections at all.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff3636ff b,#0808ffff c,#5050ffff d,#ff8484ff e,#ff0404ff f,#b0b0ffff g,#ffcfcfff ``` ```image g ee gedge deg ad ae e ea ge ed aa geg eg de ge ee aa ea eg ged e deg de ae ed ea e ed de geg ed de e ae ge ea ad ged e deg ge ae aa ea eg ed ge geg aa de eg ae e ea de ged ed eg e de ed e ge ad e ge b aa fbcb eg fb cb ge fb cb aa fb fb eg fb fb e cb fb de cb fb ed cb bf e cb bf de bb bf ed bb bf e bc bc ge bc bc ed bc bc e bc bb ge bf bb aa bf cb eg bf cb ge bf cb aa bf fb eg fb fb e fb fb de fb fb ed fb bf e fb bf de cb bf e cb bf cb bc cb bc bb bc bb bb bc bb bc cb bc cb cb fb fb fb fb bf b ``` <!-- end of image -->

I'm ready to tackle this image and find those intersections! I need to zoom in on these areas to get a better look. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd0606ff b,#0a0bfbff c,#de9787ff d,#636ee6ff e,#e94b48ff f,#95c898ff g,#b1d7b1ff ``` ```image gfffffffffffffffffffffffffffffffffaafffffffffffffg fggggggggggggggggggggggggggggggggcaeeggggggggggggf fggggggggggggggggggggggggggggggggaggaggggggggggggf db fgggggggggggggggggggggggggggggggacggcagggggggggggf dbbbdg fggggggggggggggggggggggggggggggaeggggagggggggggggf dbbbbd fgggggggggggggggggggggggggggggeagggggcaggggggggggf dbbbdg fgggggggggggggggggggggggggggggagggggggacgggggggggf dbbbbd fggggggggggggggggggggggggggggagggggggggagggggggggf dbbbbg fgggggggggggggggggggggggggggaegggggggggaeggggggggfgbbbbd fggggggggggggggggggggggggggeagggggggggggagggggdbbbbd fgggggggggggggggggggggggggcaggggggggggggeebbbbdfgf fgggggggggggggggggggggggggaggggggggggdbbbbdggggggf fggggggggggggggggggggggggacgggggggdbbdfggcaggggggf fgggggggggggggggggggggggeaggggggfbbgggggggaggggggf fggggggggggggggggggggggcaggggggbbfggggggggcagggggf fggggggggggggggggggggggagggggdbdgggggggggggacggggf fgggggggggggggggggggggacggggbbggggggggggggggaggggf fggggggggggggggggggggaegggdbdgggggggggggggggaegggf fgggggggggggggggggggcagggbbggggggggggggggggggagggf fgggggggggggggggggggaggdbdgggggggggggggggggggeeggf fggggggggggggggggggacgbbggggggggggggggggggggggaggf fgggggggggggggggggaebbfgggggggggggggggggggggggeagf fggggggggggggggggeebdggggggggggggggggggggggggggagf fggggggggggggggggbbggggggggggggggggggggggggggggcaf fggggggggggggggdbdggggggggggggggggggggggggggggggac fgggggggggggggbbegggggggggggggggggggggggggggggggga fgggggggggggdbeagggggggggggggggggggggggggggggggggac fggggggggggbbcaggggggggggggggggggggggggggggggggggfa fggggggggbbfgagggggggggggggggggggggggggggggggggggfee fggggggfbbggacgggggggggggggggggggggggggggggggggggf a fgggggbbgggeaggggggggggggggggggggggggggggggggggggf ce fgggdbdgggcagggggggggggggggggggggggggggggggggggggf a fggbbgggggaggggggggggggggggggggggggggggggggggggggf ca fdbdgggggacggggggggggggggggggggggggggggggggggggggf a bbggggggaegggggggggggggggggggggggggggggggggggggggf a bfggggggcaggggggggggggggggggggggggggggggggggggggggf ac fggggggagggggggggggggggggggggggggggggggggggggggggf a fgggggacgggggggggggggggggggggggggggggggggggggggggf ee fggggaeggggggggggggggggggggggggggggggggggggggggggf a fgggeagggggggggggggggggggggggggggggggggggggggggggf ee fgggaggggggggggggggggggggggggggggggggggggggggggggf a fggagggggggggggggggggggggggggggggggggggggggggggggf ca fgaegggggggggggggggggggggggggggggggggggggggggggggf a feaggggggggggggggggggggggggggggggggggggggggggggggf a cagggggggggggggggggggggggggggggggggggggggggggggggf ac afgggggggggggggggggggggggggggggggggggggggggggggggf a ac ac a ee a ca a ga ac a ac a ee a ca a ca a a ac a ee a ce a ca a a ac a ee a ee a ``` <!-- end of image --> Eureka! Let's inspect this close up of area A <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0505ff b,#0706fdff c,#fd8284ff d,#5752faff e,#fa3d41ff f,#fec4c4ff g,#adadfeff ``` ```image eaae caaaaf caafcae faac aaf eae caa eaa aac caaf caa faac eac aae faaf eae eae caaf faaf faaf eae aac aaf eae cae caaf aac faaf caa faac eac eae faaf gg eaa eae gddbbb caaf faaf ggdbbbbbbbd faac eaeddbbbbbbbdgg eae gdbbbbbbbddg eaa ggdbbbbbbbdgg caaf gddbbbbbbddg aac faac dbbbbbdgg caa aae gbbbdg eac eae dbbdg faa caaf gbbbg eac faaf gdbbd faaf faac dbbbg eae eae gbbbd faaf caaf dbbbg cae faaf gbbbd aac faac dbbbg caa eae gbbbg aac eaa gdbbd caa caaf dbbbg eac faac gbbbd faaf aae dbbbg eae eaa gbbbd faaf caaf dbbbg cae faac gbbbd aaf aaegdbbdg caa eaedbbbg aac caebbbd caa fadbbbg eac febbbd faa dbbbg ea gbbbd fa dbbbf e gbbbec gbbbbae dbbbcaa gbbbdcaaf dbbbgfaac gbbbd aae dbbdg eae gbbbg caaf gdbbd faac dbbbg aae gbbbd eae dbbbg caaf gbbbd faaf dbbbg faac gbbbg eae gdbbd caa dbbbg caaf gbbbd faac bbbg eae bd eaa g caaf faac aae eae caaf faac aac eae caaf faaf faac eae caa caaf faac eae eaa caaf faac aae ``` <!-- end of image --> The close-up clearly shows an intersection point in area A. The final answer is: two intersections found.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0505ff b,#0807fdff c,#fc8284ff d,#5f5efeff e,#fb3e42ff f,#ffc9c9ff g,#b2b2feff ``` ```image f ea cace a a gb af ca gdbbbdg ae af gbbbbd ca fa gdbbbdg fa af gbbbbd af a dbbbdg ac ec gdbbbd ea a dbbbbg fa eedbbbdg a dbbbbg ac dbbdg ca ee bb a fa bb fa a gbd af af bb a ee gbd ac ca bb a a dbg ee af bb a aedbg ca cebd a fbb fa gbd af bbc fa dbca ac bbfa a dbg a ee gbd ac a bb ee ce gbd fa a bb a fa dbg af af bb ee fa bg ca ac a a af ec ac a ca ce fa a af ca ac af ea fa fa af a a ac ec a ee a ca a fa af a ac a ee a ca a fa af fa ac a ee a ce a fa af fa ac a ec a ce a ``` <!-- end of image -->

Let's examine this image for potential line intersections. It's crucial to examine these regions more closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#0304feff b,#f45753ff c,#9fa3f7ff d,#afd5aeff e,#3e42f5ff f,#fec9c9ff g,#fe0807ff ``` ```image c aaaaaec ee ceaaaec ea ceaaaec ea ceaaaec ca ceaaaec ca ceaaaec a ceaaaec a ceaaaec a ceaaa ac ac ae ae ea ea ca ca ca ddddddddddddddddd a ddddddddddddddddd a dddddddddddddddddac ddddddddddddddddac dddddddddddddddae ddddddddddddddaed dddddddddddddaedd ddddddddddddeaddd bddddddddddeadddd bgddddddddeaddddd ddggdddddcadddddd dddbgbddcaddddddd dddddggdadddddddd dddddddabdddddddd ddddddacggddddddd dddddacdddggddddd ddddaedddddbgbddd dddaeddddddddggdd ddaeddddddddddbgb deadddddddddddddggf eadddddddddddddddfgb edddddddddddddddd bgf ddddddddddddddddd gg ddddddddddddddddd fgb ddddddddddddddddd gg ddddddddddddddddd fgb ddddddddddddddddd bgf gg bgb gg fgb bgf fgb bgf fgb bgf fgb bgf fgb bg fgb bg fgb gg fgb gg fgb gg fgb gg fgb gg fgb gg fgb gg fgb gg fgb gg fg ``` <!-- end of image --> Let's take a closer look at area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0907fdff b,#fd4142ff c,#b6b6ffff d,#ff8a8aff e,#5959ffff f,#fecacbff g,#fd0405ff ``` ```image e ca caa caae caae caae aae aaa eaa eaac df eaac fggd eaac fbggbf eaac dgggd caac bgggf caae fbggbf caae dgggd caae fbggbf caae dgggd aae bggaaa faaab eaagggd eaacfbggbf eaac dgggd eaac fbggbf caac fgggb caae dgggd caae fbggbf caae dgggd caae fbggbf aae dggg aaa bg eaa f eaac eaac caac ec ``` <!-- end of image --> Case closed! This is definitely an intersection point in area A. There's one and only one intersection present in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0404ffff b,#ff3333ff c,#a2a2ffff d,#fd6d6eff e,#4040ffff f,#fec9c9ff g,#ff0202ff ``` ```image c aaaaaec ee ceaaaec ea ceaaaec ea ceaaaec ca ceaaaec ca ceaaaec a ceaaaec a ceaaaec a ceaaa ac ac ae ae ea ea ca ca ca a a ac ac ac ae ae ea d ea bgf ca gg ca dgd ca gg a fad acbgf ac fgb ac dgf ae gg ae fgd ea bgf ea fgb c dgf gg dgd bg fgb bgf gg dgd gg fgd bgf fgb bgf fgb bgf fgb bgf fgb bg fgb bg fgd bg fgd bg fgd bg fgd bg fgd bg fgd bg fgd bg fgd bg fgd gg fg ``` <!-- end of image -->

This image might have some surprises. Let's look for intersections carefully. I'd describe these as 'hotspots' for potential intersections. <!-- image --> ```palette Key,Color ,#fefefeff a,#fb0c0aff b,#090afbff c,#de665fff d,#5b69e1ff e,#eff5efff f,#a4cca2ff g,#b2d7b2ff ``` ```image c ga ea ae ac ca ca ea ae ac ac ca ea ae ag ac ca ga ea ae ac aa ca effffffffffffffffffffffffffffffffffffffffffffffffffffffffffffae efggggggggggggggggggggggggggggggggggggggggggggggggggggggggggafe efgggggggggggggggggggggggggggggggggggggggggggggggggggggggggacfe efggggggggggggggggggggggggggggggggggggggggggggggggggggggggaagfe efgggggggggggggggggggggggggggggggggggggggggggggggggggggggcaggfe efggggggggggggggggggggggggggggggggggggggggggggggggggggggfagggfe efggggggggggggggggggggggggggggggggggggggggggggggggggggggaggggfe efgggggggggggggggggggggggggggggggggggggggggggggggggggggafggggfe gb efggggggggggggggggggggggggggggggggggggggggggggggggggggacgggggfe dbbe efgggggggggggggggggggggggggggggggggggggggggggggggggggcaggggggfe ebbd efggggggggggggggggggggggggggggggggggggggggggggggggggcagggggggfe dbbe efgggggggggggggggggggggggggggggggggggggggggggggggggfaggggggggfe ebbd efgggggggggggggggggggggggggggggggggggggggggggggggggafggggggggfe dbbg efggggggggggggggggggggggggggggggggggggggggggggggggacgggggggggfeebbd efgggggggggggggggggggggggggggggggggggggggggggggggaaggggggggggdbbd efggggggggggggggggggggggggggggggggggggggggggggggcagggggggggbbbe efgggggggggggggggggggggggggggggggggggggggggggggfagggggggdbbdgfe efgggggggggggggggggggggggggggggggggggggggggggggafgggggdbbfgggfe efggggggggggggggggggggggggggggggggggggggggggggacgggfbbdggggggfe efgggggggggggggggggggggggggggggggggggggggggggacggdbbfggggggggfe efggggggggggggggggggggggggggggggggggggggggggcafbbdgggggggggggfe efgggggggggggggggggggggggggggggggggggggggggfcbbdgggggggggggggfe efggggggggggggggggggggggggggggggggggggggggbbbggggggggggggggggfe efgggggggggggggggggggggggggggggggggggggdbbcfgggggggggggggggggfe efgggggggggggggggggggggggggggggggggggbbbfacggggggggggggggggggfe efgggggggggggggggggggggggggggggggggbbdggaagggggggggggggggggggfe efgggggggggggggggggggggggggggggggbbdgggcaggggggggggggggggggggfe efgggggggggggggggggggggggggggggbbdggggfagggggggggggggggggggggfe efgggggggggggggggggggggggggggbbdggggggafgggggggggggggggggggggfe efgggggggggggggggggggggggggdbdgggggggacggggggggggggggggggggggfe efgggggggggggggggggggggggdbdggggggggaagggggggggggggggggggggggfe efgggggggggggggggggggggdbbgggggggggaaggggggggggggggggggggggggfe efgggggggggggggggggggdbbgggggggggfacgggggggggggggggggggggggggfe efgggggggggggggggggdbbggggggggggcafggggggggggggggggggggggggggfe efgggggggggggggggfbbgggggggggggaaggggggggggggggggggggggggggggfe efgggggggggggggfbbfggggggggggcafgggggggggggggggggggggggggggggfe efgggggggggggfbbfgggggggggggaagggggggggggggggggggggggggggggggfe efgggggggggfbbfgggggggggggfacggggggggggggggggggggggggggggggggfe efggggggggbbdggggggggggggaaggggggggggggggggggggggggggggggggggfe efggggggbbdggggggggggggfaagggggggggggggggggggggggggggggggggggfe efggggbbdgggggggggggggcafggggggggggggggggggggggggggggggggggggfe efggbbdggggggggggggggaaggggggggggggggggggggggggggggggggggggggfe efdbdggggggggggggggcacgggggggggggggggggggggggggggggggggggggggfe dbdgggggggggggggggaagggggggggggggggggggggggggggggggggggggggggfe dfggggggggggggggfacggggggggggggggggggggggggggggggggggggggggggfe efgggggggggggggcafgggggggggggggggggggggggggggggggggggggggggggfe efggggggggggggaagggggggggggggggggggggggggggggggggggggggggggggfe efggggggggggcacggggggggggggggggggggggggggggggggggggggggggggggfe efgggggggggaaggggggggggggggggggggggggggggggggggggggggggggggggfe efgggggggfacgggggggggggggggggggggggggggggggggggggggggggggggggfe efggggggaafggggggggggggggggggggggggggggggggggggggggggggggggggfe efggggfaaggggggggggggggggggggggggggggggggggggggggggggggggggggfe efgggcafgggggggggggggggggggggggggggggggggggggggggggggggggggggfe efggaagggggggggggggggggggggggggggggggggggggggggggggggggggggggfe efcacggggggggggggggggggggggggggggggggggggggggggggggggggggggggfe eaaggggggggggggggggggggggggggggggggggggggggggggggggggggggggggfe acffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee ``` <!-- end of image --> Eureka! Let's inspect this close up of area A <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0707ff b,#0908fdff c,#ff8c8cff d,#6464ffff e,#ffccccff f,#fd4749ff g,#b8b6fcff ``` ```image e ea fa faa caae caac aaf aa cae cae eaa eaaf faf faae caae eaac eaaf faa caae caac aac af fa fae caa eaac eaaf faf faae gdb eaac bbbbdg eaaf gdbbbd aaf dbbbbg faa gdbbbbd caae gbbbbdg aac gbbbbdg eac gbbbbg af gdbbbbg fa gdbbbbd faa dbbbbdg caagbbbbd gbbbbbg gbbbbbg gdbbbbbg gbbbbfae gdbbbdgaac gdbbbb eaac dbbbbdg aaf dbbbbd faa bbbbg aae gbbbg cac gbbbg eac gbbbbd eaa gdbbbd faae gdbbbd caae gbbbd eaac dbbdg eaaf dbbbg faf dbbbdg faae dbbbdg eaaae dbbbbg caaae bbbbg eaaf gbbbg caae gbbbg faae gbbbbd eaaac gdbbbd eaaac dbbbd caaae gdbbd efaaf dbbdg caaac dbbbd aafe dbbbdg eaac dbbbdg caae dbbbbg efaaf gbbbg caaac gbbbg faafe gbbbb eaaac gbbbbd faac gdbbbd caae gbbbd efaf gdbbd caaa gdbbb faafe dbbbdg eaaac bbdg caaae dg efaaf caaac aafe eaac caae caaae efaaf caaac faafe aaac caae efaf caaa faafe eaaac caaae caaae aaf eaac faae eaaac caaae ``` <!-- end of image --> My investigation has led me to an intersection in area A! I've found a single intersection point in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0505ff b,#0808feff c,#ff8181ff d,#5d5dfeff e,#ffc6c6ff f,#f73840ff g,#aeaeffff ``` ```image c ea a ae ac ff ca ea ae ac ff ca ea a ae af fa ea a ae ac ff ca ea a ac af ca ea a ae gb ac dbb fa gbbd ea dbbg a bbd ae dbbg ac bbd ff gbbg ca dbb ea gbbd a dbb ae gbbd af dbbg ca bbd efbbg bbd gbbfe dbb ac bbd fa bbg ca bbg a dbd ae dbd ac dbd ff dbd aa gbb eac gbb fa gbb af gbb cae bb aa bbg eac bbg fa bbg af bbg cae dbd aa dbd eac dbd aa d eaf fae af cae aa eac fa af cae aa eac fa af ``` <!-- end of image -->

I have an image in front of me. I need to determine if there are any intersection segments. I have a hunch that these areas might contain the intersections we're looking for. <!-- image --> ```palette Key,Color ,#fefefeff a,#f24b4aff b,#474bf7ff c,#fe0605ff d,#0505feff e,#f49a95ff f,#9b9df9ff g,#aed5aeff ``` ```image e c ce ec c aa c ce ec c aa c ce ec c aa c ce c c ac c bdd ce fdddf df gggggggggggggggg c fdddb db ggggggggggggggggc fbddbf bd gggggggggggggggac bdddf fd gggggggggggggggc fdddf df ggggggggggggggca fdddb dd ggggggggggggggcg fbddbf bd gggggggggggggcgg bdddf fdf ggggggggggggacgg fdddf dbggggggggggggcggg b ddggggggggggcaggg bdgggggggggcgggg ggdfggggggcegggg gggdbggggecggggg ggggddgggcgggggg gggggbdgaagggggg gggggggdaggggggg gggggggcddgggggg ggggggecgbdggggg ggggggcgggfdfggg gggggaagggggdbgg gggggcgggggggddg ggggceggggggggbd gggecgggggggggggdf gggcgggggggggggg db ggaagggggggggggg bd ggcggggggggggggg fd gceggggggggggggg df ecgggggggggggggg dd cggggggggggggggg bd acggggggggggggggg fdf cgggggggggggggggg db cegggggggggggggggg dd c bd c fd ac c ce c c ec c ce c c ec c aa c ce ec ec eaccccae eacccccae eaccccae eacccccae eaccccaee cccae ``` <!-- end of image --> This is a magnified view of the region A. <!-- image --> ```palette Key,Color ,#fefefeff a,#f73840ff b,#5350fcff c,#fe0404ff d,#0707feff e,#ffc5c5ff f,#aeaeffff g,#fc7f82ff ``` ```image g ec ac ecc acg gcc ecce aca ecce acg gcc ccg aca ecce df acg ddf gcc bddb ccg fdddf gca fdddf ecce bddb acg bddb gcc fdddf ccg dddf gca bddb ecce fddb aca fdddgcc bddag bddb ecadddf acafdddf ecce bddb ccg bddb gca fdddf ecce dddf aca bddb ecce fddb ccg fdddf gcc bddf ecce bdd aca fd ecce f acg gcc ecce aca ecce acg gcc ccg aca ecce acg cc cg a e ``` <!-- end of image --> Eureka! There's definitely an intersection in area A! It was tricky, but I finally found one single intersection in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fa3f44ff b,#5b5bffff c,#ff0505ff d,#0606feff e,#ffc4c4ff f,#b1b1ffff g,#ff8383ff ``` ```image g c ce ec c aa c ce ec c aa c cg ec c aa c cg ec c ga c bdd cg bdddb fdf ec fdddb db ce fbddbf dd gc bdddf fd c bdddb db cg fdddb dd ec fbddbf bd ce bdddf fdf gc bdddb db c b dd ag bd c fdf ce db gc dd c fd aa da cdd ec bd c fdf aa db c dd ce bd ec fdf c db aa dd c fd cg db ec dd c bd aa fdf c db cg dd ec bd c fd ga c cg ec ce gc c cg ec ce gc c ag c ce gc gc egaccccae eacccccge egaccccage egcccccae gaccccage cccag ``` <!-- end of image -->

The hunt for intersections begins! Let's analyze this image closely. There are 1 regions I'd like to highlight in the image. <!-- image --> ```palette Key,Color ,#fefefeff a,#f5625dff b,#0404feff c,#fe0707ff d,#d5d5feff e,#ffb2b2ff f,#6468f7ff g,#add3adff ``` ```image e ac ac ac ac ec ec ec ec c ce ce ce ce ca ca ca ca cc cc cc ac ac ac ac gggggggggggggggg ec gggggggggggggggg ec gggggggggggggggg ec gggggggggggggggg ecgggggggggggggggg eacc cggggggggggggggg eacccccaae gcgggggggggggggg eaccccccae ggcggggggggggggg eaacccccae gggcaggggggggggg eacccccae ggggcaggggggaacccccae gggggcaccccccagg ggggggaggggggggg ggggfbbggggggggg ggfbbggbgggggggg fbbgggggbggggggg fbbggggggggbgggggg fbf ggggggggggbggggg bbf dbd bbf dbd dbbd dbd dbbd dbd dbbd dbd fbbd dbd fbb dbd fbb dbd fbf dbd fbf dbd bbf dbd bbf dbd bd dbd dbd bd bd bd bd bd bd bd bd bd bd bd bd bd bd bd bd bd bd bd bd bd bd bd bd b ``` <!-- end of image --> Let's zoom in on area A to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff4747ff b,#0001ffff c,#ff0505ff d,#edddefff e,#2424ffff f,#9090ffff g,#ff9a9aff ``` ```image d ad cad cccd dcccd daccd daccd accg accg accg accg d accg dggaacc accg dggaaccccccccc gccaaccccccccccaaggd gccccccaaggd gggdd feed febbbed febbefebed dfebbef debed dfbbbef debed dfbbbef debed bbbef debed bed debed d debed debed ``` <!-- end of image --> This close-up reveals that there are no intersections in area A. After a thorough analysis, I conclude that there are no intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff4a4aff b,#0303ffff c,#ff0404ff d,#d8d8ffff e,#ffccccff f,#6a6affff g,#ff9292ff ``` ```image g ac ac ac gc gc gc ec ec ece ce ce cg cg cg ca ca ca ca cc ac ac ac ac gc gc gc ec ec gacc ece eacccccage ce egaccccage ce egacccccae cg egacccccag cg gacccccage cacccccage ge fbbd fbb dbd fbb dbd fbf dbd fbf dbd bbf dbd bbf dbd dbbd dbd dbbd dbd dbbd dbd fbbd dbd fbb dbd fbb dbd fbf dbd fbf dbd bbf dbd bbf dbd bd dbd dbd dbd dbd bd bd bd bd bd bd bd bd bd bd bd bd bd bd bd bd bd bd bd bd bd bd b ``` <!-- 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,#0908fdff b,#fe0808ff c,#f76c68ff d,#b3b3ffff e,#5b60f5ff f,#95c799ff g,#b1d6b1ff ``` ```image d ea dad ae aa ea ae aa ea dad ae aa dad ae aa ea dad aa ea dad ae aa ea dad aa ea dad ae aa ea ea da da ad ad ae ae ae aa aa ea ea da da dad ad ad ae ae aa aa ea fgggggggggggggggggf eafgggggggggggggggggf dagggggggggggggggggf eaggggggggggggggggf ffafggggggggggggggf fggafgggggggggggggf fgggaeggggggggggggf fggggaegggggggggggf fgggggaeggggggggggf fggggggaaggggggcbgf fgggggggaagggbbcggf fggggggggaabbcggggf fgggggggcbaaggggggf fgggggbbbggeagggggf fgggbbcgggggeaggggf fcbbcggggggggfagggf bg cbbggggggggggggfafgf bbbc bbcfgggggggggggggggagf bbbc bbc fgggggggggggggggggf bbbc cbb fgggggggggggggggggf cbbc cbb fgggggggggggggggggf cbbc bbc fgggggggggggggggggf cbbc gbbg fgggggggggggggggggf cbbc cbb fgggggggggggggggggf cbbc bbc gfffffffffffffffffg cbbc bbc cbbc cbb cbbc cbb cbbc ``` <!-- end of image --> Let's put area A under the microscope. <!-- image --> ```palette Key,Color ,#fefefeff a,#0403feff b,#fe0606ff c,#fea0a1ff d,#7474ffff e,#322cf9ff f,#c7c7ffff g,#f74951ff ``` ```image d ad aae faae faae faaef feaaf eaaf eaaf eaaf daad daad daad daad faae cc faae cgbbg faaef cgbbbgc feaef cbbbbgc feaaf gbbbbc eaagbbbbc ceaaggc cbbbeaad gbbbbc daad cgbbbgc daad cbbbbgc daad gbbbbg faae cgbbbbc faae cgbbbgc faae cbbbbg feaef bbbc feaaf gc eaaf eae df ``` <!-- end of image --> The evidence is clear: this is an intersection in area A. It was tricky, but I finally found one single intersection in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0505feff b,#ff0404ff c,#ff8d8dff d,#9090ffff e,#4340fbff f,#d9cff5ff g,#ff4c4cff ``` ```image d ea faf ae aa daf fad aa ea fad ae ea daf ad aa ea fad ae ea daf ae aa daf fad ae ea daf ae aa ea da da faf faf ad ad ae ae aa ea ea da da fa faf af ad ad ae ae ea ea ea da da faf faf ad ad ae ae gb aa bbg eabbc cbea gbg da bbc da cbbc faf bc gbb faf fbbbc bbg a fgbbc fbbc fgbbc cbbf gbbc gbg gbbc bbc gbbc cbbc gbbg gbb gbbg gbg cbbg fbbc cbbg cbbf cbbg gbg cbbg ``` <!-- end of image -->

Here's an image. My task is to find intersections or areas where lines come close together. Could these regions be concealing intersection points? Let's find out. <!-- image --> ```palette Key,Color ,#fefefeff a,#fc0b0aff b,#4c52f2ff c,#eb7168ff d,#9da3f2ff e,#b1d6b0ff f,#0807fcff g,#f0f0edff ``` ```image geeeeeeeeeeeeeeeeeeeeeeeeeeeeg geeeeeeeeeeeeeeeeeeeeeeeeeeeeg geeeeeeeeeeeeeeeeeeeeeeeeeeeeg geceeeeeeeeeeeeeeeeeeeeeeeeeeg geaceeeeeeeeeeeeeeeeeeeeeeeeeg geeaeeeeeeeeeeeeeeeeeeeeeeeeeg geeaeeeeeeeeeeeeeeeeeeeeeeeeeg geeeaeeeeeeeeeeeeeeeeeeeeeeeeg geeeaeeeeeeeeeeeeeeeeeeeeeeeeg gf geeecaeeeeeeeeeeeeeeeeeeeeeeeg gfg gefeeaeeeeeeeeeeeeeeeeeeeeeeeg dfg geefecaeeeeeeeeeeeeeeeeeeeeeeg df geeefeaeeeeeeeeeeeeeeeeeeeeeeg df geeedfaceeeeeeeeeeeeeeeeeeeeeg bf geeeedfaeeeeeeeeeeeeeeeeeeeeeg bf geeeeebfceeeeeeeeeeeeeeeeeeeeg ff geeeeeebfeeeeeeeeeeeeeeeeeeeeg ff geeeeeeeffeeeeeeeeeeeeeeeeeeeg fb geeeeeeeeffeeeeeeeeeeeeeeeeeeg fb geeeeeeeeaffeeeeeeeeeeeeeeeeeg fd geeeeeeeecafbeeeeeeeeeeeeeeeeg fd geeeeeeeeeaefbeeeeeeeeeeeeeeeg gfd geeeeeeeeecaefbeeeeeeeeeeeeeeg gfg geeeeeeeeeeaeefdeeeeeeeeeeeeeg dfg geeeeeeeeeeaceefdeeeeeeeeeeeeg df geeeeeeeeeeeaeeefeeeeeeeeeeeeg df geeeeeeeeeeeaceeefeeeeeeeeeeeg bf geeeeeeeeeeeeaeeeefeeeeeeeeeeg bf geeeeeeeeeeeeaeeeedfeeeeeeeeeg bf geeeeeeeeeeeeeaeeeedfeeeeeeeeg ff geeeeeeeeeeeeeaeeeeebfeeeeeeeg fb geeeeeeeeeeeeecaeeeeebfeeeeeeg fb geeeeeeeeeeeeeeaeeeeeebfeeeeeg fb geeeeeeeeeeeeeecaeeeeeeffeeeeg fd geeeeeeeeeeeeeeeaeeeeeeeffeeeg gfd geeeeeeeeeeeeeeeaceeeeeeefbeeg gfg geeeeeeeeeeeeeeeeaeeeeeeeefbeg gfg geeeeeeeeeeeeeeeeaceeeeeeeefbg dfg geeeeeeeeeeeeeeeeeaeeeeeeeeefd df geeeeeeeeeeeeeeeeeaeeeeeeeeeefd bf geeeeeeeeeeeeeeeeeeaeeeeeeeeegfg bf geeeeeeeeeeeeeeeeeeaeeeeeeeeeggfg bf geeeeeeeeeeeeeeeeeecaeeeeeeeeg gf ff geeeeeeeeeeeeeeeeeeeaeeeeeeeeg df fb geeeeeeeeeeeeeeeeeeecaeeeeeeeg df fb geeeeeeeeeeeeeeeeeeeeaeeeeeeeg df fb geeeeeeeeeeeeeeeeeeeeaceeeeeeg bf fd geeeeeeeeeeeeeeeeeeeeeaeeeeeeg bf fd geeeeeeeeeeeeeeeeeeeeeaceeeeeg bfd geeeeeeeeeeeeeeeeeeeeeeaeeeeeg geeeeeeeeeeeeeeeeeeeeeeaeeeeeg geeeeeeeeeeeeeeeeeeeeeeeaeeeeg geeeeeeeeeeeeeeeeeeeeeeeaeeeeg geeeeeeeeeeeeeeeeeeeeeeecaeeeg geeeeeeeeeeeeeeeeeeeeeeeeaeeeg geeeeeeeeeeeeeeeeeeeeeeeecceeg geeeeeeeeeeeeeeeeeeeeeeeeeaeeg geeeeeeeeeeeeeeeeeeeeeeeeeaceg geeeeeeeeeeeeeeeeeeeeeeeeeeaeg geeeeeeeeeeeeeeeeeeeeeeeeeeacg geeeeeeeeeeeeeeeeeeeeeeeeeeeag geeeeeeeeeeeeeeeeeeeeeeeeeeeag gggggggggggggggggggggggggggea a ca a cc a ac a ae ga ag ga gca a gcaaaacg ca gcaaaacg a gcaaaacg cc gcaaaacg a gcaaaacg ac gcaaaacg a gcaaaacg aggcaaaacg gaacg ``` <!-- end of image --> This is a magnified view of the region A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0405ff b,#5150fdff c,#fe8283ff d,#afadfdff e,#f93c42ff f,#0806fdff g,#fec4c4ff ``` ```image gg aa aac cae cae aag eae gaa ea ec ca dd ac ff ae bff aag ffb aag ff eae dfbgaag dfbeac ffbaa dffe dffc bfe bfd ffd efff gafff eafff gaaff eacfb aacffb caedffb aa dffb ca dff gag dfd ga ffd ac bffd aa bffd eac bff caa bf cae fb aag ffb cae dffb gaa dffb ea dffb ga dff ga dfd ac ffd aa bffd aag bffd cae bff cae bf gaag ff eae ffb gaa ffb ea dffb ec dfb ca dfb ag ffd ae dff aag bf gaag eac gaa eac gaa caa aa ca ag ce ac aa eac gaa eac aag cae aa ca gag ga ac aa aac caa cae aag cae gaa ea ec ga ac ae aag aa ca ga ``` <!-- end of image --> I am surprised, so clear, an intersection has appeared in area A. I have found one intersection!

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0707ff b,#4e4dfeff c,#ff8787ff d,#a7a7ffff e,#fe4e4eff f,#0706fdff g,#ffc3c3ff ``` ```image g ac a ag ga a f ca f f a df f ce df f a df dfec bf dfa bf dfc ff bf ff ff fb gff fb afb fd cafb fd a fb fd ce fd f a fd df ec fd df a f df ac f bf a f bf ag df bf ga df ff a df fb ca bf fb a bf fb ce bf fd a fb fd ec fb fd a fb df ag fd df a fd df ag fd bf ga f bf a f bf ca f ff a df fb ee df fb a df fb ec bf fd a bf fd ag bfd a ag ga a ca a ee a ec a ag a ag ga a ca a ee a ec a ag a ag ga gca a caaaaeg ca caaaaeg a caaaaeg ee caaaaeg a caaaaeg ec caaaaeg a caaaaeg ag caaaaeg aaeg ``` <!-- end of image -->

I'm optimistic that I'll find some intersections in this image. I have a hunch that these areas might contain the intersections we're looking for. <!-- image --> ```palette Key,Color ,#fefefeff a,#acacfeff b,#fd0908ff c,#0808fdff d,#e5605bff e,#95c39bff f,#b1d6b0ff g,#5258f2ff ``` ```image a ca c ca ac c ac c gg c gg c ca c ca ac c ac c gg c gg c ca c ca ac c ac c gg c gg c ca c ca ac c ac c gg c gg c ca ac efecfffffffffffe gc effcefffffffffff cc effecfffffffffff ca efffcfffffffffff bbb ac efffgcfffffffffdb db cc effffcffffffffbb bb cg effffggfffffdbdf db eeeeeeeeeeeeeeeef aca efffffcffffbbfff bd ffffffffffffffffe gc efffffcgfebdffff db ffffffffffffffffe cc effffffcbbffffff bd ffffffffffffffffecg effffffcdfffffff bb fffffffffffffffeca effffdbecfffffff bdfffffffffffffgce efffbbffceffffff bbfffffffffffccfe efdbdfffecffffff febdffffffffcgffe ebbffffffcffffff fffbbfffffgcefffe bdfffffffgcfffff ffffdbdffccfffffe dbefffffffffcfffff ffffffbbccffffffe bb efffffffffggffff ffffffecddffffffe dbf effffffffffcffff fffffgcffbbfffffe bb effffffffffcgfff ffffccffffdbdfffe fbd efffffffffffcfff fffcgfffffffbbffe bb feeeeeeeeeeeceee fecefffffffffdbde bd c gcfffffffffffffbb db c ccfffffffffffffffdbf bb ac cgffffffffffffffffe bb dbf c aca ffffffffffffffffe db bb ac gc ffffffffffffffffe bb bd c cc efffffffffffffffe db b gg ca bd c ac db ca cc bd c cg db caca b c ``` <!-- end of image --> Here's a close-up of the area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#7c7bfeff b,#fe0808ff c,#0403feff d,#fa565aff e,#c3c3ffff f,#fdb5b6ff g,#3d37f9ff ``` ```image acg cce acg ecce gca ecc gca ecc gca acg cce fb acg dbb cce fdbbd acg fbbbf ecce dbbd gca fbbbf ecc dbbbf gca fbbbd ecc dbbbf gcadbbd accbbf dccd fbbgcg dbbbfcce fbbbd acg fbbbf ecce dbbd gca fbbbf ecc dbbdf gca fbbbd ecc dbbbf gca dbbd acg bbf cce d acg cce acg ecce gca ecc gca ecc cca ``` <!-- end of image --> Gotcha! I've found the intersection hiding in area A! Let's shift our focus to the next area. Let's get to the bottom of what's happening inside area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#7670f9ff b,#fe0808ff c,#0303feff d,#f9555bff e,#bcbbfeff f,#ffb2b2ff g,#3531faff ``` ```image e f ac bd gcc bbbf egcce fbbbd eccge dbbbf accg fbbbd gcca dbbbf egcce fbbbd eccge dbbbf accg fbbbd gcca dbbbf eccce fbbbaccg dgcca egccdbf ecccedbbd accg fbbbf gcca dbbd egcce fbbbf eccge dbbd accg fbbbf gcca fdbbd eccce dbbbf accge fbbb acca db gcca f cce g ``` <!-- end of image --> Incredible, there's actually an intersection in area B! My analysis indicates that there are two intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#8989ffff b,#fe0707ff c,#0504feff d,#f95157ff e,#cdcdffff f,#feb9baff g,#3e3effff ``` ```image e ca c ce ec c ac c ag c ga c ca c ce ec c ac c ag c ga c ca c ce ec c ac c ag c ga c ca c ce ec c ac c ag c ga c ca ac c gc ce cg ec f eca c bbb ace ag dbf dbf gc c bb bd cg ag fbf dbf eca c bb bd ac ga fbd db cc cdb fbd cg cd db ece dbfc fbd gc bb ce bb cc fbf ec fbd ca bb c bb ace fbd ag fbd gc db c bbcg bb gg ecdf fbf c ac bb bb ga cc fbf fbd c cg bb db ce ece dbf bd ec gc bb dbf ce cc dbf bb ec ca bb fbf c ace dbf bb ag gc bb fbd c cg dbf b gg eca bd c ace db ga gc bd c cg db caca fb ec ``` <!-- end of image -->

Here's an image. My task is to find intersections or areas where lines come close together. There are 2 regions I'd like to highlight in the image. <!-- image --> ```palette Key,Color ,#fefefeff a,#090afdff b,#fc0c0bff c,#6168f1ff d,#e0c4e3ff e,#f06e6aff f,#96c59aff g,#b0d7b0ff ``` ```image fggggggggggggggcgf fggggggggggggggagf fgggggggggggggacgf fggggggggggggfaggf ed fggggggggggggafggf bebbbbed fgggggggggggcagggf db ebbbbed fgggggggggggaggggf b debbbbed fggggggggggcaggggf ee debbbbe fggggggggggagggggf b debbbbe fgggggggggacgggggf bd debbbbegggggggaggggggf eb febbbbbegacggggggf b fgggggebbabbeggggf be fgggggggafgebbbbgf db fggggggfaggggggggf b fggggggagggggggggf be fgggggcagggggggggf db fgggggaggggggggggf bd fggggccggggggggggf eb fggggagggggggggggf b fgggacgggggggggggf bd fgggaggggggggggggf eb fggafggggggggggggf b fgfagggggggggggggf be fgaggggggggggggggf db gcaffffffffffffffg b a ee cc b a bd ac eb a b ad be da db ad b ca be a db ca bd a eb ac b a bd ad eb da b ad be da db a b ca be a db cc gggggggggggbfgf a ggggggggggebggg ac ggggggggggbgggg a gggggggggbegggg ad ggggggggebggggg da ggggggggbgggggg a gggggggbegggggg ca ggggggfbggggggg a ggggggbgggggggg cc gggggbbgggggggg a gggggbggggggggg ac gggabfggggggggg a gggeaaggggggggg ad gggbgcacggggggg da gggggggcacggggg a gggggggggaafggg ca gggggggggggaagg a ggggggggggggfaa cc ggggggggggggggcac a ggggggggggggggg cac ac ggggggggggggggg aad a ggggggggggggggg aad ad ggggggggggggggg daa da ggggggggggggggg daa ad ggggggggggggggf cac ca cac a aad ca aa a daa ac cac a cacad aa ``` <!-- end of image --> I'm analyzing this close-up of area A with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#0b0afdff b,#fe0505ff c,#6b61f4ff d,#bbbbffff e,#ff3f3fff f,#f98187ff g,#ffcacaff ``` ```image gbbf ebe gbbg bbf fbe gbbg ebe fbb gbbf ebe fbbg bbf ebe gbbg bbf fbb gbbg ebe fbb gbbf ebe gbbg bbf fbe acbbg daaac faaaad gbbcaaaad gee caaacd caaac dcaaac daaaad daaaad caaacd caaac dcaaac dcaaa daa d ``` <!-- end of image --> I've cracked the case! This area contains the intersection. Let's continue our search in the next region. I'm determined to find out if an intersection exists in area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#0807feff b,#fe0304ff c,#9b9bffff d,#e6d8f0ff e,#fa4246ff f,#534ffbff g,#ff9292ff ``` ```image cd caa aac caa daac faf daac faf daad faf caad aac caa aac faa daac faf daad faf gd caad bbbeegd aac ebbbbbbbeegd caa dggebbbbbbbeggd aac dggebbbbbbbfaad dggebbaaebbeggd faaebbbbbbbeggd daad dgeebbbbbbe faf dgeebe caad d aaf caa aac caa daac faf daad faf caad faf caad aac caa daac faf daac faf daad faf caad ``` <!-- end of image --> There's no doubt about it - this is an intersection in area B. The final answer is: two intersections found.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0505ffff b,#fe0808ff c,#8585ffff d,#c4c4ffff e,#fc5a5cff f,#4242ffff g,#ffb3b3ff ``` ```image c a ac da eg ad bebbbbeg da gb ebbbbeg a b ebbbbe cf ee gebbbbe a b gebbbbg ff bg gebbbbg a eb gebbbeg ac b gebabeg bg ad gbbbb gb da b a be ca b a b ff eb a b ac bg a gb ad b da be a gb ca b a ee ff b a bg fc eb a b ad bg da gb ad b ca be a gb cf b a ee fc b a bg ac gb da b ad be da gb a b cf ee a b ff bg a eb ac b a bg ad gb da b a be ca gb a b ff ee a b ac fbg a eaa ad b caf da fac a aad ca aa a daa ff caf a fac fc fac a aad ad daa da daf ad caf ca fac a aad cf aa a daa fc caf a facac fa ``` <!-- end of image -->

This image seems promising for intersection detection. These regions highlight areas that look suspicious. Lines seem to converge within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd0606ff b,#0b0afbff c,#ec968dff d,#6b73eeff e,#f04847ff f,#98c698ff g,#b0d6b1ff ``` ```image c a fgggggggggggggggac gggggggggggggggfaf gggggggggggggggaff ggggggggggggggcagf ggggggggggggggaggf gggggggggggggeaggf gggggggggggggagggf ggggggggggggeegggf ggggggggggggaggggb gggggggggggacggdbf gggggggggggaggbbgf ggggggggggacdbdggf gggggggggcabbggggf gggggggggebdgggggf ggggggggbbgggggggf ggggggfbbggggggggf gggggbbeeggggggggf ggggbbgagggggggggf ggdbfgaegggggggggf fbbgggaggggggggggf c dbfgggacggggggggggf ee bbggggcagggggggggggf a dbd ggggaggggggggggggf faffffffffffffff bb gggcaggggggggggggf faeggggggggggggg gbd gggagggggggggggggf fgaggggggggggggg bb ggeegggggggggggggf fgcagggggggggggg bd ggaggggggggggggggf fggacggggggggggg db gaeggggggggggggggf fgggaggggggggggg bb fagggggggggggggggf fgggeagggggggggg db acgggggggggggggggf fggggafggggggggg bb gaggggggggggggggggf fggggfaggggggggg dbd afggggggggggggggggf bbbbdfgaegggggggg bb ca fgddbbbbbdgggggg gbd a fggggggcebbbbbdd bb ee fgggggggacggggdbbbbbdg bd a fggggggggagggggg dbbbbbd db ee fggggggggeaggggg gdbbbbbd bb a fgggggggggacgggg ddbbb ac fggggggggggagggg a fggggggggggeeggg a fgggggggggggaggg ca fgggggggggggcagg a fggggggggggggaeg ce gfffffffffffffaf a ca ee ac a a ac ee a a a a ca ac a a ca ca a ac ee a a ee ac a a a ac ee ca a a ca ca ac a a ee ca a a ac a a ee ac a a ca a ac ca a a ca ee ac a a ee ee a aac a ``` <!-- end of image --> This is a magnified view of the region A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd0405ff b,#0606feff c,#ff7676ff d,#5f5cfcff e,#f73239ff f,#febbbbff g,#acacffff ``` ```image faaf caa eac faaf cae aac faa eae faaf caa eac faaf cae aac faaf eae aaf ddgg caa bbbbbbddg eac gddbbbbbbbbbddeaf ggddbbbbbbbbddgg gddbbbbbbbbbddgg faeddbbbbbbbbbdd eae ggddbbbbb aac ggd caa eae faaf caa eac faaf cae aac faa eae faaf caa eac faaf cae aac faaf ``` <!-- end of image --> Oh my, look at that! It's an intersection in area A! Now, let's scrutinize the next spot. Time to investigate area B up close. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd0607ff b,#0d09faff c,#fd898bff d,#6b6afdff e,#fb4549ff f,#ffcacaff g,#bcbcffff ``` ```image c a ca faa eae faaf eae caa aac caa aac cae faaf eae faaf eae faaf aac caa gb aac dbb caa gbbbd faaf dbbbg eae gbbbd faaf dbbbg eaegbbbd faadbbbg eabbbd cebbbd bbbbg gbbbd dbbbc gbbbbe dbbbaaf gbbbdeae dbbbgfaaf dbbd eac gbbbg caa dbbbg aac gbbbd caa dbbbg aac gbbbd cae dbbbg faaf bbd eae bg faaf eae caa aac caa aac cae faaf eae faaf eae faaf aac caa aac caa faaf eae faaf eae ``` <!-- end of image --> Yes! I knew it! There's an intersection right here in area B! After a thorough search, I conclude that there are two intersections.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fe0505ff b,#0707feff c,#ff8484ff d,#5a56faff e,#f93e43ff f,#fec8c8ff g,#b6b6ffff ``` ```image c a ac fa af fa a ce a ee a b ac dbg fa bb afdbg fabb ebg bb gbd dbee bd a dbg ac bb a c dbg af ee bb fa af gbg a fa bb ca ac gbd a a bb ee ca bd a ac db ec a bb a ce dbg af af bb fa fa gbg af bbbbdg ee bb ca gdbbbbdg gbd a fedbbbbdg bb ce ac gdbbbbdg gbd a a gdbbbbbdg db ec ca gdbbbbdg bd a af gdbbbg ac a fa ee af a fa fa a ac ce a a ca ee af a a ac ee fa a af fa fa ac a a ca ca a af ee a a ee ac af a fa af ee fa a a fa ca ac a a ee ca a af ec a a ee af a fa fa af ac ca a a ca ce af a a ec ee a aac fa ``` <!-- end of image -->

I'm curious to see if this image contains any intersection points. My final answer is: no intersections found.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0707ffff b,#ff0505ff c,#aaaaffff d,#ff8181ff e,#ffc4c4ff f,#5151ffff g,#ff4141ff ``` ```image e bbbd dbe bbd bb gbg ebd dbb gb dbbe bg ebbe dbe bbd bb gbg ebd gbg gb dbb bg ebbe dbe ebbd bb bbd ebd gbg gb dbb bb dbbe ebe ebbe gb bbd bg gbg dbe gbg bb d ebd gb bg dbe bb e c ca ca fa fa fa fa aa aa af af af af ac ac ac ac a ca ca ca ca ca fa fa fa fa aa aa af af af af ac ac ac ac afcc ac cfaaaaaafc a ccfaaaaafcc ca cfaaaaaafc ca ccfaaaaaffc ca cfaaaa ``` <!-- end of image -->

Alright, let's get to work and investigate this image for intersections. Could these regions be concealing intersection points? Let's find out. <!-- image --> ```palette Key,Color ,#fefefeff a,#5b60f3ff b,#fe0505ff c,#add5aeff d,#faaba9ff e,#0809fdff f,#e85248ff g,#b6b7fdff ``` ```image g eg e eg ge e ge e aa e aa e eg e eg ge e ge e aa e aa e eg e eg ge e cccccccccccccccc ge cccccccccccccccc e cccccccccccccccc aa cccccccccccccccc e cccccccccccccccc aa cccccccccccccccc e cccccccccccccfbc eg cccccccccccfbfcc e cccccccccfbfcccc eg cccccccfbfcccccc ge cccccfbfcccccccc e cccbbfcccccccccc ge cbbfccccccccccac e bbfccccccccccceec aa bbdcccccccccccceecc e bbd ccccccccccceeccc aa bbd cccccccccceacccc e bbd ccccccccceaccccc eg bbd cccccccceacccccc e bbd cccccccecccccccc eg dbbd geg cccecccccccccccc dbbd ge cccecccccccccccc dbb ae cccaeccccccccccc dbb ae cccceccccccccccc dbb ee ccccaacccccccccc dbb ee cccccecccccccccc dbb ea ccccceacccccccccfbb ea cccccceccccccfbbf eg cccccceacdbbbfcc eg ccccccfebbdccccc ge cccfbbfecccccccc ge fbbfcccceccccccc ae fbbfccccccceccccccc ae dbbbd ccccccccaecccccc ee dbbbd cccccccccecccccc ee dbbf cccccccccaaccccc ea fbbf cccccccccceccccc ea fbbf cccccccccceacccc eg d cccccccccccecccc eg ccccccccccceaccc ge ge ge e ae ge ae e ee ge ee e ea aa ea e eg ea eg e geg eae e ``` <!-- end of image --> Let's see what secrets area A holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#3831f7ff b,#fd0607ff c,#7f7fffff d,#fba7aaff e,#0303feff f,#ff5959ff g,#c0c0ffff ``` ```image geeg aec gee aec gee aec cea eeg cea eeg cea geeg aec gee aec gee d aec dfbb cea dfbbbbbf eeg dfbbbbbfd ceadfbbbbbfd deebbbbfd dfbbaeafd dfbbbbbfdeeg dfbbbbbfd aec dfbbbbbfd gee bbbbbfd aec bbfd gee aec cea eeg cea eeg cea geeg aec gee aec gee aec cea eeg ``` <!-- end of image --> The close-up clearly shows an intersection point in area A. Let's shift our focus to the next area. This close-up might reveal an intersection in area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#5c5cffff b,#ff0404ff c,#ff8c8cff d,#ffccccff e,#0b0bffff f,#ff4f4fff g,#bfbfffff ``` ```image dfc dfbbb dfbbbfd dfbbbfd dfbbbfd dfbbbfd dfbbbfd dfbbbfd dfbbbfd dfbbbfd dfbbbfd dfbbbc cfbbbc cbbbbc ag cbbbbc aee bbbc aeeg bc eeeg geeeg geeeg geee geea geea aeea aeea aeeg aeeg eeeg geeeg ``` <!-- end of image --> My analysis shows that the lines in area B do not cross. The image features one single intersection point.

<!-- image --> ```palette Key,Color ,#fefefeff a,#3c3cffff b,#ff0505ff c,#8383ffff d,#feadaeff e,#0404ffff f,#ff5757ff g,#c9c9ffff ``` ```image g ec e eg ge e ce e ca e ac e ec e eg ge e ce e ca e ac e ec e eg ge e ce e ca e ac e fb ec fbf e fbf eg fbf ge fbf e fbf ce bbf c e bbd ae ca bbd ae e bbd ea ac bbd ea e bbd ec eg bbd eg e bbd geg eg dbbd ge ge dbbd ce e dbb ce ca dbb ae e dbb ae ca dbb ea e dbb ea ac fbb ec e fbbf ec eg dbbbd geg debbd geg fbbfeg ce fbbf ge ce fbbf e ae dbbbd ca ae dbbbd e ea fbbfd ca ea fbbf e ec fbbf ac ec d e eg eg geg e ge eg ce ge ae e ae ca ea e ea aa ec e ec ac eg e geg ece ge ``` <!-- end of image -->

Let's examine this image for potential line intersections. It's crucial to examine these regions more closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#0707feff b,#fd0707ff c,#595bf9ff d,#feb2b2ff e,#b8b9feff f,#add4aeff g,#f2605eff ``` ```image e aa cacc ca a ea ea a a a ea ae ae ac a ac ac ca a ca cc ea a a ea a a ae ea ac ae ac a ca ac ca a ea cc a a a ca ae a ac ea ac ae ca a ca ae ea a a cc a a ae ca ac a ac ea ca ae ca ea ea ae a a a cc ae a ac cc ac a e ea a ea ae a fffacfffffffffff ffffafffffffffff ffffccffffffffff fffffaffffffffff fffffcafffffffff g ffffffafffffffffdgbbbg fffffffaffffgbbbbd fffffffagbbbbgff ffffgbbbafffffff dbbbbgfffacffffff dbbbbgffffffffaffffff gbbbgd fffffffffccfffff dgbbbgd ffffffffffafffff dgbbbg ffffffffffcaffff dbbbbd fffffffffffaffff dggbbbbbgd ffffffffffffafff dgbbbbbbgd ffffffffffffafff dgbbbbbbgdd ea dggbbbbbggd ae bbbbbbgd a d cc a ca a ea ae ea ae a ac a cc a ``` <!-- end of image --> This close-up of area A is like examining a piece of evidence. <!-- image --> ```palette Key,Color ,#fefefeff a,#0706fdff b,#fe0203ff c,#9491fbff d,#fb9094ff e,#e5d3ecff f,#4c46f9ff g,#ff4646ff ``` ```image aac caa aac caae faf eaae faf eaac caf aac caa aac caae faf ddg eaae edggbbbb faf edgbbbbbbggd eaadgbbbbbbgdd ddgfaabbbgde edggbbbbbaace edgbbbbbbggdecaa dgbbbbbbgdd aac bbbbgde caa gde faf eaae faf eaae faf eaac caa aac caa fac caae faf ``` <!-- end of image --> The evidence is clear: this is an intersection in area A. I've found a single intersection point in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0606feff b,#fe0606ff c,#8080ffff d,#ffb2b2ff e,#cacaffff f,#4141ffff g,#fc5b5dff ``` ```image e aa facf ca a ea ca ea ae ae ea ae ae ac a af fc fa a ca ff ea a ea ca ae a ae ea ac ae af a fa ac ca a ea ff ea a ae ca ae a ac ea af ae fa ea ca ac ea a ea ff ae a ae cf ac a af ea fa ae ca ea ea ac ea a ae fc ae a ac cf af a e ca ae ea ae a fc a ff a ca g a dgbbbg ea dbbbbd agbbbgd gbbbad dgbbbg ac dbbbbd a gbbbgd ff dgbbbgd a dgbbbg ca dbbbbd a dggbbbbbgd ea dgbbbbbbgd ae dgbbbbbbgdd ea dggbbbbbggd ac bbbbbbgd a d ff a cf a ea ae ea ac a fc a cf a ``` <!-- end of image -->

I'm ready to tackle this image and find those intersections! Could these regions be concealing intersection points? Let's find out. <!-- image --> ```palette Key,Color ,#fefefeff a,#5e65efff b,#fc0c0aff c,#0809fdff d,#b5b5ffff e,#e9998fff f,#95c798ff g,#b1d7b0ff ``` ```image d cd c cd dc c dc c aa c aa c cd c c ac cd c dc cd c ac dc c c cd aa dc c c gfffcafffffffffffffg ca fggggcgggggggggggggf dc fggggcaggggggggggggf c fgggggcggggggggggggf ca fgggggcfgggggggggggf dc fgggggfcgggggggggggf c fggggggcgggggggggggf aa fggggggacggggggggggf c ee fgggggggcggggggggggf cd ebbbbbbbbegggaagggggggggf ac fgeebbbbbcbbeegggggf c fggggggggcaebbbbbbbbee cd fgggggggggcggggggggeebbbbbbbbee ac fgggggggggcagggggggf eebbb c fggggggggggcgggggggf ebb fggggggggggggcaf fggggggggggcfggggggf ebb ggggggggggggacgf fggggggggggfcggggggf ebb ggggggggggggcggf fgggggggggggcggggggf ebb gggggggggggcaggf fgggggggggggacgggggf ebb ggggggggggacgggf fggggggggggggcgggggf ebb ggggggggggcggggf fggggggggggggaaggggf ebbggggggggcaggggf gfffffffffffffcffffg ebbgggggfcgggggf aa ggebbgggcggggggf c ggggebbcaggggggf cd ggggggecbggggggf c ggggggcfebbggggf cd gggggacgggebbggf dc gggggcggggggebbf c ggggcfggggggggebb dc gggacggggggggggfebb c gggcgggggggggggf ebb aa ggcagggggggggggf ebb c gacggggggggggggf ebb ca gcgggggggggggggf ebb c cagggggggggggggf ebb cd dc e c c cd ca dc dc c c dc ca c dc aa c c aa ca c c cd cd ac c c c cd dc ac c c dc cd c dc aa c c ca ca dc c c cca c ``` <!-- end of image --> I wonder what we'll find inside area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#3d34f5ff b,#fe0506ff c,#0404feff d,#bbbafeff e,#fda3a4ff f,#fc5254ff g,#7d7cfeff ``` ```image dcc acg dcc acg dcc ccd gca ccd gca ccd acg dcc acg dcc acg gcc ccd gca eee ccd bbbbbbffeee gca ffbbbbbbbbbbbbfffeccd eeeffbbbbbbbbacabbffeee eeefffccbbbbbbbbbbfffee acgeeeffbbbbbbbbbbb dcc eeefffbb acg gcc ccd gca ccd gca dccd acg dcc acg dcc acg gcc ccd gca ccd gca ``` <!-- end of image --> Amazing! This area was hiding an intersection all along! Next up, a closer look at another region. Let's get to the bottom of what's happening inside area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#403ffdff b,#fe0404ff c,#0505feff d,#cbcafeff e,#fd9496ff f,#f12936ff g,#8787ffff ``` ```image gcc dccg aca gccd dccg aca gccd ccg aca dccd ccg gca be dccd bbbe acg efbbbe gcc efbbbe dccd efbbbe aca efbbbe gcc efbbbe dccg efbbbeaca efbfccd eccfbe acafbbbe gccd efbbbe ccg efbbbe aca efbbbe dccd efbbbe ccg efbbb aca efb dccd e ccg gcc dccd aca gcc dccd aca gcc dccg aca gccd dccg ``` <!-- end of image --> My investigation has led me to an intersection in area B! I've identified a total of two intersection points.

<!-- image --> ```palette Key,Color ,#fefefeff a,#4a4afeff b,#ff0707ff c,#0606ffff d,#c6c6ffff e,#feafb0ff f,#ff6262ff g,#8a8afeff ``` ```image d cg c cd dc c gc c ga c ag c cg c c ac cd c dc cd c gc gc c c cg ga gc c c ag cg c dc cg c c aa cd dc dc c c aa gc c fe c cd fbbbbbbbfe ga aa effbbbbcbffe c agefbbbbbbbfe cd c effbbbbbbfee gc cg eefbbb c c ebb cg cd ebb gc dc ebb c c ebb cg gc ebb dc c ebb c aa ebb ca c ebb dc ag ebb c c ebbaa cd ecb c cdebb cd aa ebb dc c ebb c cd ebb gc gc ebb c c ebb aa cd ebb c gc ebb ag c ebb c cg ebb cd gc e c c cd cg dc dc c c gc aa c dc aa cd c aa ag c c cd cd ac c c cd cd dc gc c c gc cg c gc aa c c cg ag dc c c cca dc ``` <!-- 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,#0809feff b,#fd0c0bff c,#aaabfcff d,#f06d69ff e,#ffb9b9ff f,#aed5adff g,#565af6ff ``` ```image e bbb eb ebb b dbd bd bbe db bb b ebb be dbd bd bbe eb bb b ebb be dbd db bbe b bb b ebb bd dbd eb bbe b bb be ebb db dbd eb bbe b bb bd ebb db dbd b bbe fffffffffffffffbe bb ffffffffffffffbb e ffffffffffffffbf fffffffffffffbff ffffffffffffbdff ac fffffffffffdbfff aafffffffffffbffff caaffffffffbfffff fgacfffffbbfffff fffaafffdbffffff ffffgagfbfffffff ffffffaadfffffff ffffffdbaaffffff ffffffbffgagffff fffffbfffffaafff ffffbdfffffffaaf fffdbfffffffffgac fffbffffffffffffaa ffbdffffffffffff cag fdbfffffffffffff gac fbffffffffffffff aa bfffffffffffffff cag bdfffffffffffffff gac dbffffffffffffffff aa b cag be aac aa gac aa cag gac aa gac aa cag gac aa gac aa cag gac aa gac aa cag aa aa gac aa cag aa aa gac aa ca ``` <!-- end of image --> I wonder what we'll find inside area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#0807fdff b,#f93136ff c,#bfbfffff d,#fc7072ff e,#ffbcbcff f,#fe0404ff g,#6360fcff ``` ```image e f bf dff effe bfd dfb effe effd bfb dff effe g ffd aac bfb aaagc effe gaaag effd gaaac bfb caaagc dff gaaag effe cgaaac ffd caaag bfb gaaagffe cgaaad baaag dfbgaaac effe caaagc ffd gaaag bfb gaaac dffe caaagc effe gaaag bfd cgaaac dfb caaa effe ga effd c bfb dff effe ffd dfb effe effd bfb dff ffe fd b e ``` <!-- end of image --> There's no doubt about it - this is an intersection in area A. After careful examination, I conclude that there is one intersection.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0707ffff b,#fe2d2eff c,#ababffff d,#fc7073ff e,#ffbcbcff f,#ff0202ff g,#5555ffff ``` ```image e bff ef efb f dfd fd bfe df ff f efb fe dfd bb bfe ef ff f efb fe dfd db bfe f ff fe efb bd dfd ef bfe f ff fe efb bb dfd ef bfe f ff fd efb df dfd f bfe fe ff bb e ef f fd ac df aa f cag fe gac bb aa ef cag f gad dbaa f cag fe aa bd aa ef gac f aa fe cag db gac ef aa f cag fd gac df aa f cag fe aac aa gac aa cag gac aa gac aa cag gac aa gac aa cag gac aa gac aa cag ga aa gac aa cag aa aa gac aa ca ``` <!-- end of image -->

Hmm, I'm not sure what to expect from this image. Let's see if any lines cross. Let's take a closer look at what's happening inside these zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#4345f1ff b,#fb0c0bff c,#e57669ff d,#0606fdff e,#8e94f0ff f,#9ecb9dff g,#b2d7b1ff ``` ```image c cb cb bg bc fffffffffffffffff bbfgggggggggggggggf edd bbgggggggggggggggf addede cbggggggggggggggf edde d ffbfggggggggggggf edda aa fggbcgggggggggggfadd d fgggbbggggggggadde ed fggggbbggggeddagf de fgggggcbfdddfgggf d fgggggaddeggggggf aa fggeddaggbcgggggf d fdddggggggbbggggf ed addegggggggggbbgggf d edde fgggggggggggcbggf d dda fggggggggggggcbff de fgggggggggggggfbc d fgggggggggggggggbc aa fgggggggggggggggfbb d fgggggggggggggggf cb ed fffffffffffffffff cb de bg d bc aa bb d bb ed cb d b d bc de bb d bb ea cbc d bbg ed bbffffffffdefffffffffffffffffff cbbgggggggdggggggggggggggggggf fbbcgggggaagggggggggggggggggf fggbbgggggdgggggggggggggggggf fgggcbbgggedggggggggggggggggf fgggggcbcggdegggggggggggggggf fgggggggbbfgdgggggggggggggggf fggggggggfbbdaggggggggggggggf fggggggggggcbdggggggggggggggf fggggggggggggadfggggggggggggf fgggggggggggggdbbgggggggggggf fgggggggggggggfdcbbgggggggggf fggggggggggggggdegbbcgggggggf fgggggggggggggggdgggbbggggggf fgggggggggggggggaagggcbbggggf fggggggggggggggggdgggggcbcggf fggggggggggggggggedggggggbbff fgggggggggggggggggdeggggggfbb fggggggggggggggggggdggggggggcbc fffffffffffffffffffaaffffffff bbg d bb ed cb d d de d aa d ed de d aa d ed d d de d ed d d de d aa d ``` <!-- end of image --> I'm now examining the contents of area A in detail. <!-- image --> ```palette Key,Color ,#fefefeff a,#6362fdff b,#ff0505ff c,#fe8788ff d,#0a07fcff e,#b1affdff f,#ffcdcdff g,#f93d43ff ``` ```image f bf bbc gbbc cbbg cbbgf fbbbf fgbbc gbbc cbbg ea cbbg eaddd fbbbf addddda fgbbf eaddddae gbbc eaddddae cbbg addddda cgdddddae eaddddde adddddagbbf eaddddae gbbc eaddddae gbbc eaddddde cbbg dddddae fbbgf ddae fbbbf e fgbbc gbbc cbbg cbbgf fbbbf fgbb gb c ``` <!-- end of image --> Wow! I can see an intersection so clearly in area A! Let's move forward and inspect another region. I'm now examining the contents of area B in detail. <!-- image --> ```palette Key,Color ,#fefefeff a,#574af1ff b,#fe0404ff c,#ff7979ff d,#0706feff e,#adaafcff f,#febebeff g,#fc373aff ``` ```image edde ada bc dde bbgf edd fbbbgf dda cbbbc edd fgbbbf ada fgbbgf dde cbbbc add gbbbc dde fgbbgf edd cbbbc ada cbbbc edde fgbbgf ada fbbbgf dde cbbbc edd fgbbbfdda fgbbgdde cbbada gbdde faddgf ddabc eddbbbc adagbbgf eddefbbbgf add cbbbc dde fgbbbf edd fgbbgf ada cbbbc edde gbbbc ada fgbbgf dde cbbbc edd cbbbc dda fgbbgf edd fbbbgf ada cbbbc dde fgbb add fg dde ``` <!-- end of image --> Yes! I knew it! There's an intersection right here in area B! Two intersections have been found!

<!-- image --> ```palette Key,Color ,#fefefeff a,#4c49fbff b,#fe0505ff c,#ff8989ff d,#0606feff e,#9796feff f,#e8d0e7ff g,#ff3f3fff ``` ```image c gb cb fbf bc bg fdd gb addfde cb edde d fbf edda aa bc addf d bg adde ed gb edda de cbfdddf d adde aa edda bc d fddaf bg ed adde bb df edde gb fd dda cbf de f fbc d bg aa bb d gb ed cb de fbf d bc aa bg d gb ed cb df fbf fd bc de bbf d fbb ed cbc df gbf fd bb de cbg d gbc aa bb d fbg ed gbc df bbf d fbbaa cbd adf dbb fdcbg de gbc d bb aa fbg d gbc ed bbf de fbb d cbc aa gbf d bb ed cb df fd de d aa d fd de d aa d ed df fd de d ed df fd de d aa d ``` <!-- end of image -->

I'm optimistic that I'll find some intersections in this image. Let's take a closer look at what's happening inside these zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#f9aaa7ff b,#0707feff c,#fe0807ff d,#9ea2f6ff e,#f65652ff f,#4d50f8ff g,#afd5afff ``` ```image d fb bb gggggbbgggggg ggggbfggggggg gggbfgggggggg ggbdggggggggg gbggggggggggg dbgggggggggggg dbggggggggggggg fb ggggggggggggg bb ggggggggggggg bf ggggggggcgggg bf gggggggcegggg bd gggggggcggggg bd ggggggcgggggg db gggggeegggggg db gggggcggggggg fb ggggcgggggggg fb gggecgggggggg bb gggcggggggggg bf ggcaggggggggg bf gecgggggggggg bd gcggggggggggg bd ceggggggggggg db ac db c fb ce fb ac bb c bf ce bf c bd c bd ee db c db ca fb ec fb c bb ca bf ac fbbd c dbbf ca dbbf ac dbbf c dbbbd ce fbbd ac fbbd c fbbd ee gggggggggggggfbbf c ggggggggggfbbfg c gggggggdbbbgggg ee ggggdbbbggggggg c gggbbdggggggggg ca ggggggggggggggg ec ggggggggggggggg c ggggggggggggggg ca gggcggggggggggg ac ggggccggggggggg c gggggecaggggggg ca gggggggccgggggg ac ggggggggecegggg c ggggggggggccggg ce gggggggggggaceg ac gggggggggggggcc c gggggggggggggggce ee ggggggggggggggg eca c ggggggggggggggg cc c ggggggggggggggg eca ee ggggggggggggggg cc c ggggggggggggggg ace ca cc ec ace c eca ca cc ac eca c cc ca ace ac cc c acece ec ``` <!-- end of image --> I'm analyzing this close-up of area A with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff8888ff b,#0808ffff c,#ff0606ff d,#b8b8ffff e,#ff4444ff f,#6566ffff g,#ffcacaff ``` ```image d dfbb fbbbbb dfbbbbfd dfbbbbfd dfbbbbbf dfbbbbbfd dfbbbbbfd fbbbbbfd dbbbfd fd g ceg gccca gecceg accca ecccg gccce accca gecceg accca gecceg accca ecccg gccce accca gecc ac g ``` <!-- end of image --> Darn it! This close-up doesn't show any intersections in area A. Moving on to the next area. Time to investigate area B up close. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff8484ff b,#0909ffff c,#ff0505ff d,#b8b8ffff e,#ff4242ff f,#5858ffff g,#ffc3c3ff ``` ```image dbbb dbbf dbbf fbbf fbbf fbbd fbbd bbbd dbbbd dbbb bbf bf f eg acc gccg ece acc gccg ece acc gcca ece accg cca ece gccg cca ece gccg cca acc gccg ece acc gccg ece acc gcca ``` <!-- end of image --> Area B is clear of intersections, but the search continues. I can confidently say that there are no intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff8383ff b,#0606ffff c,#ff0505ff d,#a6a6ffff e,#ff3f3fff f,#4a4affff g,#ffc8c8ff ``` ```image d fb fb bf bf bd bd db db db fb bb bf c bf ea bd gc bd c db ee db c fb cg fb ee bb c bf cg bf ac bd c bd ca db ac db c fb ca fb gc bb c bf ee bf gc bd cg bd ee db c db cg fb ae fb c bb cg bf ac fbbd c dbbf ca dbbf ac dbbf c dbbbd ca fbbd gc fbbd c fbbd ee dbbf gc dbbf cg dbbf ee dbbbd c bbd cg ac c cg cg ac gce c ecg ca cc gc aca c cc ca gce gc ecg c gce ee ecg gc cc cg aca ee cc c gca cg ec ac gce c ecg ca cc ac aca c cc ca aca gc cc c gceea ec ``` <!-- end of image -->

I have an image in front of me. I need to determine if there are any intersection segments. These zones are intriguing. I bet there's something interesting happening within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0504ff b,#4143f8ff c,#f79895ff d,#9296f5ff e,#0506feff f,#acd5acff g,#f64441ff ``` ```image d bee deed bee deed bee a deed gg bee ca deed a beb a deed ac beb gg deed ca beb a deed a ee ac bb gg e ca e a bb a e ac e ag bb ca ed a e a be ac ed ag e ca de a ed a e ac fbeffffffffffagf ffedffffffffgaff fffefffffffcafff fffdeffffffaffff ffffedffffacffff fffffefffagfffff fffffdefgaffffff ffffffebafffffff fffffffeffffffff ffffffadefffffff fffffagfebffffff ffffgafffeffffff fffcaffffdefffff fffaffffffebffff ffacfffffffeffff fagffffffffdefff gaffffffffffebff ca e a e a bb ac e ga e ca bb a e a e aaggcc ac bb ccggaaaaaaaaggcc ga ed ccggaaaaaaaaggcc ca e ccggaaaaaaa be ed e de ed e de ed e de ed e de ed e de ed e de eb e ``` <!-- end of image --> Let's zoom in on area A to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd0406ff b,#4440fbff c,#ffa4a4ff d,#8884faff e,#0605fdff f,#c9c9ffff g,#ff4848ff ``` ```image feed caac dee aag beb gag feed gaa deef caac beb caac feed aag deef gag beb gaa feed caac deef caac beb aag feed gag deef gaa beb caac eedaac feeag bee gaeed caadeef caac beb aag eed gag feef gaa bee caac eed caac feef aag dee gag eeb gaa feef caac dee caac beb aag feef gag dee gaa beb ``` <!-- end of image --> Oh my, look at that! It's an intersection in area A! There's one and only one intersection present in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0808ff b,#3636ffff c,#ffb4b4ff d,#8885fcff e,#0404ffff f,#c6c6ffff g,#ff5b5bff ``` ```image d beef feed beef feed bee a deed ag beb ca deed a beb a deed ac beb ag deed ga beb a deed a be ac bb ag ef ga fe ca bb a ef ac e ag bb ga ef ca e a db ac ef ag e ga de ca ef a e ac de ag ed ga e ca de a ed ac e ag de ga eda e ade ag ed ga e ca fe a bd ac e ag fe ga bb ca e a fe ac bb ag ef ga fe ca bb a ef ac e aaggcc ag bb ccggaaaaaaaaaggcc ga ef ccggaaaaaaaaaggcc ca e ccggaaaaaaaa db ef e de ef e de ed e de ed e de ed e fe ed e fe bd e ``` <!-- end of image -->

I'm approaching this image with caution. Intersections might be tricky to spot. There's definitely not a single intersection on the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff3b3bff b,#0505ffff c,#5959ffff d,#ff8181ff e,#ff0404ff f,#afafffff g,#ffc8c8ff ``` ```image d ge e eg ed aa de ge eg ed aa de ge e eg ea ae ge e eg ed aa de ge eg ed aa de ge e eg ea ae ge e eg ed aa de ed ge aeeg e geed ed aea aa deeg de geea ge deeg e geed eg aea ed deed ae aea ge deeg e geed eg aeeg ed geedaa ae f fcbbbbc fcbbbbbcf fcbbbbbcf fcbbbbbcf fcbbbbbcf fcbbbbbcf fccbbbbbcf ffcbbbbbbbccff ffccbbbbbbbcff fccbbbbbbbccf bbbbccff ``` <!-- end of image -->

I have an image in front of me. I need to determine if there are any intersection segments. Let's take a closer look at what's happening inside these zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#5051fbff b,#fe0605ff c,#f69f9aff d,#0707feff e,#a8a8ffff f,#add4adff g,#f84441ff ``` ```image e ad dd da da da de de de de d d d ed ed ed ad ad ad ad da da da da de de de d d d addd ed eaddda ed adddae ed edddda ed eadddae ad edddde ad eadddae ad edddde fffffddffffadddae ffffffdddddaffff ffffffffffffffff ffffffffffffffff ffffffffffffffff ffffffffffffffff ffffffffffffffff ffffffbbcfffffff fffffbgfbgffffff ffffbgfffbbfffff fffbcfffffgbffff ffbffffffffcbcff cbfffffffffffbgf gbfffffffffffffbb gbfffffffffffffffgb bb ffffffffffffffffcb bg ffffffffffffffff bc bc bg bc gb cb cb cb bc gb bg gb bb bg gb bg cbc bc bc bc bb cb gb cb cb gb bc bb bg bg gb bg cb bc cbc bc bg cb bb cb gb gb cb bb bc c bg gb cb b ``` <!-- end of image --> I wonder what we'll find inside area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#7676ffff b,#ff0505ff c,#ff8484ff d,#0e0effff e,#d5d5ffff f,#ffc7c7ff g,#ff3f3fff ``` ```image ddde eaadd eddde eaadddddd eddd eaaddddddddaee edddddddddaae eddddaee ee fgbf fbbbbc fbbggbbc cbbg cbbg cbbg fbbgf cbbc fbbbf gbbc gbbc gbbf cbbg fgbbf cbbgf fbbbf fbbbf fbbg fgbbc cbbg gbbc cbbg cbb cbbc fb bbc f bf f ``` <!-- end of image --> There is no intersection present within area A. Zero, Nada.

<!-- image --> ```palette Key,Color ,#fefefeff a,#5151ffff b,#ff0505ff c,#ff8585ff d,#0707ffff e,#a9a9ffff f,#ffc7c7ff g,#ff3f3fff ``` ```image e ad dd da da da de de de de d d d ed ed ed ad ad ad ad da da da da de de de d d d addd ed eaddda ed adddae ed edddda ed eadddae ad edddde ad eadddae ad edddde dd eadddae ddddde e bbc bg bg bc bb bf cb fbf fbf cb bc cb bb gb gb bb cbf bg bc bc bg bf gb fbf cb cb fbf gb bg gb bb bg gb bg fbf bc bc fbf bg fb gb cb cbf gb fbc gb bg bg gb bg cb bc fbf fbf bg fb bb cb gb gb fbf bb bc f bg gb cb fb ``` <!-- end of image -->

I'm on the case! Let's uncover any intersections hidden in this image. These regions highlight areas that look suspicious. Lines seem to converge within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#ed635aff b,#0a0afcff c,#fd0909ff d,#6e77ecff e,#b0d6b1ff f,#feb7b7ff g,#9ac597ff ``` ```image f fcc c ac fc fca cf cc c fcf cf cc c acf ca cc gggggggggggggggggge c ac eeeeeeeeeeeeeeeeeeg b aa fca eeeeeeeeeeeeeeeeeeg db c cc eeeeeeeeeeeeeeeeeeg bb fc fcf eeeeeeeeeeeeeeeeeegdbd c cceeeeeeeeeeeeeeeeeebb fc acgeeeeeeeeeeeeeegbd cf gcceeeeeeeeeeeebbeg c eecceeeeeeeeeebbeeg cf eeegcaeeeeeedbgeeeg c eeeeecceeeebbeeeeeg aa eeeeeeacadbdeeeeeeg c eeeeeeeebbeeeeeeeeg aa eeeeeegbdacgeeeeeeg c eeeeebbeeeecceeeeeg ggggggggggggacge eeeebbeeeeeecceeeeg eeeeeeeeeeeeceeg eedbgeeeeeeeegcaeeg eeeeeeeeeeegceeg ebbeeeeeeeeeeeecceg eeeeeeeeeeecgeeg dbdeeeeeeeeeeeeeeaca eeeeeeeeeeeceeeg bbeeeeeeeeeeeeeeeeeecc eeeeeeeeeecaeeeg bd eeeeeeeeeeeeeeeeeegacf bb eeeeeeeeeeceeeeg db eeeeeeeeeeeeeeeeeeg ca dbbbd eeeeeeeeecaeeeeg bb eeeeeeeeeeeeeeeeeeg cc dbbd eeeeeeeeeceeeeeg dbe eeeeeeeeeeeeeeeeeeg fc dbbbdeeeeeeeeaaeeeeeg bb geeeeeeeeeeeeeeeeeg bbbdeeeeeceeeeeeg ebd eedbbbdaceeeeeeg bb eeeeedbbbdeeeeeg bd eeeeeegcedbbbdeg db eeeeeecgeeeedbbbd bb eeeeeeceeeeeeeegdbbb dbe eeeeecaeeeeeeeeg dbbbbb eeeeeceeeeeeeeeg d eeeecaeeeeeeeeeg eeeeceeeeeeeeeeg eeeaaeeeeeeeeeeg eeeceeeeeeeeeeeg eeaceeeeeeeeeeeg eeceeeeeeeeeeeeg ggceeeeeeeeeeeeg cf c cf c aa c aa c fc c fc cf c cf c aa c aa c fc c fc cf c cf c aa c aa c fc c ``` <!-- end of image --> I'm focusing my attention on this specific region, area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd888aff b,#0907fdff c,#fe0505ff d,#b3b3ffff e,#6161ffff f,#ffcacaff g,#f53d47ff ``` ```image acc gca fcc gca fcc gcg fccf acg ccf acg cca acc gca fcc gca fcc gcg fccf acg bbed ccf bbbbbed acg debbbbbeed cca debbbbbbed acc debbbbbbga debbbbbbed ggbbbbbbed fccf debbbbbbed gcg deebbbbbed fccf debbbb acg dee ccf acg cca acc gca fcc gca fccf gcg fccf acg ccf acg cca acc gca fcc gca ``` <!-- end of image --> The close-up clearly shows an intersection point in area A. Alright, let's examine the next area. Let's see what secrets area B holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#fc9c9fff b,#0706feff c,#fd0809ff d,#a3a3ffff e,#524ffbff f,#efddedff g,#ff5353ff ``` ```image f ca d ccg eb gcccf fbbb accca dbbbd fgccgf febbef accca dbbbd fgccgf febbef accca dbbbd fcccg ebbbf gcccf fbbbe accca dbbbd fgccgf febbef accca dbbbd fgccebbef abbbe ebbbccg febbefgcccf dbbbd accca febbef fgccgf dbbbd accca ebbef fgccgf dbbbd accca ebbbd fcccg febbe gcccf dbbbd accca febbef fgccgf dbbbd accc bbef fgc be a d ``` <!-- end of image --> There's no doubt about it - this is an intersection in area B. The final answer is: two intersections found.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff7979ff b,#0606feff c,#ff0505ff d,#aeaeffff e,#5656ffff f,#ffbebeff g,#ff3c3cff ``` ```image f acg c gc fc fca cf gc c fca cf cc c acf ga cg c gc b ag fca ebd c cc bb ag fca dbd c cc bb fc acf dbe cf cg eb c gc be cf fca ebd c cc bb ga fcfdbd c bb ag dbeacf c eb cg ag be gc c ebd fca fc bb cc cf dbd acf c bb cc cf be acf bed c eb cg dbbbd ga be gc ebbe c ebd fc dbbbd ag bb debbe c dbd ebbbdac bb dbbbe be fc ebbbd eb cf dbbbe bb c ebbed dbd cf dbbbbb c d ga c ag c fc c fc cf c cf c ga c ag c fc c fc cf c cf c ga c ag c fc c fc cf c ca c ga c ag c fc c ``` <!-- end of image -->

Here's an image. My task is to find intersections or areas where lines come close together. After a thorough analysis, I conclude that there are no intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff5454ff b,#0505ffff c,#ff0505ff d,#8787ffff e,#ffb1b1ff f,#4242ffff g,#c9c9ffff ``` ```image e ac ac ac ac ac ac ac ec ec cc ec ace ec cc ec ace ec cc ec ace ec ca ec ace c eca c ac ce eca ce cc ce eca ce cc ce eca ce cc ce ece ce cc ce ece ca cc ca ace ca cc ca ace ca cc ca ace ca ca ca ace cca g gbbbg bb gbb gbd gbb bb dbf dbd dbf bb fbf dbd fbd bb fbd dbd bbg bb bbg dbd gbb bb gbb dbg dbf bb dbf dbg fbd bb fbd fbg bbd bf bbg fbg gbbg gbf gbb fbg gbb gbf dbf fbg dbf bf f ``` <!-- end of image -->

I'm optimistic that I'll find some intersections in this image. I'm going to focus my attention on these specific areas. <!-- image --> ```palette Key,Color ,#fefefeff a,#f74945ff b,#0607fdff c,#fd0a0aff d,#9ca1f1ff e,#eb9087ff f,#b0d6b0ff g,#4c51f1ff ``` ```image e ec ac ac ac ac ac ac ac ac ac ac ac ac ac cc cc cc cc cc ca ca ca ca ca ca ca ca ca ca ca ca ca ce ce ce ce ce ce ce ce ffffffffffffffffffffffffffff ce ffffffffffffffffffffffffffff ce ffffffffffffffffffffffffffff ce ffffffffffffffffffffffffffff ce ffffffffffffffffffffffffffff ec ffffffffffffffffffffffffffff ec ffffffffffffffffffffffffffff ac ffffffffffffffffffffffffffff cc ffffffffffffffffffffffffffffca fffffffffffffffffffffffffffce fffffffffffffffffffffffffece ffffffffffffffffffffffffecff fffffffffffffffffffffffacfff ffffffffffffffffffffffccffff fffffffffffffffffffffcafffff gffffffffffffffffffffcaffffff dbgfffffffffffffffffcefffffff fbbffffffffffffffecfffffffff ffdbgfffffffffffacffffffffff ffffgbdffffffffacfffffffffff ffffffbbffffffccffffffffffff fffffffgbgfffcafffffffffffff fffffffffbbfceffffffffffffff ffffffffffdbgfffffffffffffff fffffffffecfbbffffffffffffff ffffffffacffffbbffffffffffff dbb fffffffccffffffgbdffffffffff gbbg ffffffccfffffffffbbfffffffff dgbbg fffffcafffffffffffgbgfffffff dbbbd ffffceffffffffffffffbbffffff gbbg ffecfffffffffffffffffdbgffff gbbg facffffffffffffffffffffbbfff dbbbd acfffffffffffffffffffffffbbf gbbgd ccfffffffffffffffffffffffffgbd gbbg fffffffffffffffffffffffffffffbb dbbbd ffffffffffffffffffffffffffff dbd dbbbd ffffffffffffffffffffffffffff bb gbbg ffffffffffffffffffffffffffff dbg dbbbd ffffffffffffffffffffffffffff gbbd ffffffffffffffffffffffffffff ffffffffffffffffffffffffffff ffffffffffffffffffffffffffff ``` <!-- end of image --> I'm eager to see what's happening in this magnified view of area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff5656ff b,#0505feff c,#fe0809ff d,#8b8afdff e,#ffafafff f,#cacaffff g,#4441fbff ``` ```image a cc eccc eccc ecca acca acce acce ccce eccc ecca ecca gd acca bbgf acce dbbbd ccce gbbbf eccce fbbbg eccc dbbbd ecca fgbbgf acca dbbbd acca fgbbgf acce dbbbd ccce gbbbf eccce fgbbgf ecca dbbbd ecca fgbbgf acca dbbbd acce fgbbbcce dbbbg eccgbbbd ecca fgbbgf acca dbbbd acca fgbbgf acce dbbbd ccce gbbbf eccce fbbbg ecca dbbbd ecca fgbbgf acca dbbbd acce fgbbgf acce dbbbd eccce gbbbf eccc fbbbg ecca dbbbd acca fgbbgf acca dbbbd acce fgbbgf ccce dbbb ccce gb cc f e ``` <!-- 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,#ff4f4fff b,#0404ffff c,#ff0b0bff d,#8a88fdff e,#ffa2a2ff f,#cbcbffff g,#4342feff ``` ```image e ac ac ac ac ac ac ac ac ac ac ac ac ac cc cc cc cc cc cc cc ca ca ca ca ca ca ca ca ca ca ca ca ca ca ce ce ce ce ce ce ce ce ce ce ec ac ac cc ca ce ece ec ac cc ca g ca dbd ce bb ec fbg ac gbf ac bb cc dbd ca bb ce dbg ec gbf ac fbg dbb cc gbf gbbgf ca bb fgbbd ca dbd dbbbd ce bb dbbgf ec fbg fgbbd ec gbf dbbbd ac fbg dbbgf cc gbf fgbbg e bb dbbbd dbd dbbgf bb fgbbg fbg fbbbd gbbf ``` <!-- end of image -->

I have an image in front of me. I need to determine if there are any intersection segments. I'm extremely confident. No intersections at all.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0505ff b,#4848ffff c,#ff7d7dff d,#9e9effff e,#0505ffff f,#ff4343ff g,#ffbfbfff ``` ```image d bee deed deeb beed deed eeb beed deeb bee deed deeb beed deed eeb beed deeb bee eed deed dee beb beb eed deed dee beb eeb deed dee bee beb eed eed f fa fa fa fa ca ca ca ca ga ga ga ga ga ga ga a a ag ag ag ag ag ag ac ac ac ac ac af af af af fg af gaaag af gaaag fa gaaag fa gfaac fa gfaac fa faac fa faac fa faac ca caaf ca caaf ca caaf ca caa ``` <!-- end of image -->

I'm analyzing this image to identify any points where lines intersect. There's definitely not a single intersection on the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff3434ff b,#0808ffff c,#6262ffff d,#ffbabaff e,#ff0404ff f,#ff6d6dff g,#b3b3ffff ``` ```image g gcbbbb cbbbbc gcbbbcg gcbbbbg cbbbbc gbbbbcg cgg gcbbbcg ccbbbbbbbbbbbbccggg cbbbbc ggcccbbbbbbbbbbbcccgg gbbbbcg ggcccbbbbcg d eea ded ae ae ded ea ef ded ee fe fe ee def ef ea ded ae ae ded ea ea ded ae fe fed ee ef ef ee ded fe ae ded ea ea ded ae fe ded ee ef ef ee ded fe ae ef ea ea ded ae fe ded ee ea d ae ded ef ee fe de ``` <!-- end of image -->

This image seems promising for intersection detection. I'm going to focus my attention on these specific areas. <!-- image --> ```palette Key,Color ,#fefefeff a,#0708feff b,#f64c4cff c,#a6a7fcff d,#faa3a1ff e,#fe0707ff f,#5257f5ff g,#add4adff ``` ```image c a ac a a ee ca bed a ee fa deb a bed ff ee a deb ac bed a ee ac deb ca bed a ee ca deb a bed ff ee a ded ac ee a ee ac bed ca ee a deb ca bed a eb ff ee a be af be a de ac ed ggggggggggggggag ed gggggggggggggagg eb ggggggggggggfagg ee ggggggggggggaggg begggggggggggfaggg deggggggggggagggg geggggggggafgggg ggedggggggaggggg gggebggggafggggg ggggeegggagggggg gggggeegaggggggg ggggggbbaggggggg gggggggaeggggggg ggggggfagegggggg ggggggagggebgggg gggggffggggebggg gggggaggggggeegg ggggafgggggggbeg ggggagggggggggbe gggagggggggggggde aa ggcagggggggggggg ed fa ggaggggggggggggg eb cac gfaggggggggggggg eb af gagggggggggggggg ee fa ffgggggggggggggg be cac a de af ac de aa a ed ca ac eb af ca eb aa a be fa ca be ac a de aa ff fa a cac af af a fa ac cac ca af a aa ca cac a af ff aa a fa ff af a aaac fa ``` <!-- end of image --> Let's get to the bottom of what's happening inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0504feff b,#fe5353ff c,#8381fdff d,#feb0b0ff e,#fd080aff f,#4441fbff g,#c9c9ffff ``` ```image gaa faf gaag faf gaag fac caa aac caa aag d caf eb gaag eeb faf deeb gaag deeed fac eeed caa beed aac beed caa beeb aac deeb caf deee gaag deeed faf eeed gaag beedfac beeaa baaf caaeb aaceee caf deeed gaag beed faf beed gaag beeb faf deeb gaag deeb fac deeed caa eeed aac beed caf bee gaag be faf d gaag faf gaag fac caa aac caa aag caf gaag ``` <!-- 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,#0505feff b,#ff5656ff c,#8585ffff d,#ffaeaeff e,#fd080aff f,#4141ffff g,#c8c8ffff ``` ```image c a ac ga ag ee ga bed a ee cf deb a bed ff ee a deb ac bed ga ee ag deb ga bed a ee ca deb a eed ff ee a deb ac ee a ee ag bed ga ee a deb ca bed a eb ff ee a be fc be a de ag ed ga eb ag eb ca ee a be cf de a ded fc ed a eb ac ee ga ee ag bea ae cfded a ed ff eb a ee ac be ga be ag de af ga ed fa a eb gag ca eb af a ee fa ff be cag a de af ac ded aa a ed cag ag eb ac ga ee aa a ee ca ca be gac a de aa ff fa a gac fc af a fa ag gag ga af ag fa ca cag a af cf aa a cag fc gac a aaac fa ``` <!-- end of image -->

I'm on the case! Let's uncover any intersections hidden in this image. I've noticed 1 areas of interest. These could be potential intersection zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#db6e5dff b,#0b0cfaff c,#fb0b09ff d,#6472ddff e,#b2d7b2ff f,#eff5f0ff g,#a3cba3ff ``` ```image d fbb fbbf fbbf bbe bbd bbd dbd fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff dbd fgggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggdbb fgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedbb fgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegbbg fgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegbbgeg fgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegbbgeeeg fgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegccageeeeeeeeeeeeebbdeeeeeg fgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecggaccccaeeeeeeebbdeeeeeeeg fgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaceeeeeeaccccagbbdeeeeeeeeeg fgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeceeeeeeeeeeegdbbcageeeeeeeeg fgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecaeeeeeeeeeedbbeeeaccccaeeeeg fgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegceeeeeeeeedbbeeeeeeeeeaccccag fgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecgeeeeeeedbbeeeeeeeeeeeeeeegacccae fgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaceeeeeegbbgeeeeeeeeeeeeeeeeeeg acccca fgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeceeeeegbbgeeeeeeeeeeeeeeeeeeeeg facccaf fgeeeeeeeeeeeeeeeeeeeeeeeeeeeeaceeeebbgeeeeeeeeeeeeeeeeeeeeeeg facccce fgeeeeeeeeeeeeeeeeeeeeeeeeeeeeceeeebdeeeeeeeeeeeeeeeeeeeeeeeeg ecc fgeeeeeeeeeeeeeeeeeeeeeeeeeeecaeeegbeeeeeeeeeeeeeeeeeeeeeeeeeg fgeeeeeeeeeeeeeeeeeeeeeeeeeegceeeebgeeeeeeeeeeeeeeeeeeeeeeeeeg fgeeeeeeeeeeeeeeeeeeeeeeeeeecgeeebbeeeeeeeeeeeeeeeeeeeeeeeeeeg fgeeeeeeeeeeeeeeeeeeeeeeeeeaceeegbeeeeeeeeeeeeeeeeeeeeeeeeeeeg fgeeeeeeeeeeeeeeeeeeeeeeeeeceeeebgeeeeeeeeeeeeeeeeeeeeeeeeeeeg fgeeeeeeeeeeeeeeeeeeeeeeeecaeeedbeeeeeeeeeeeeeeeeeeeeeeeeeeeeg fgeeeeeeeeeeeeeeeeeeeeeeeeceeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg fgeeeeeeeeeeeeeeeeeeeeeeecaeeebdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg fgeeeeeeeeeeeeeeeeeeeeeeaceeedbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg fgeeeeeeeeeeeeeeeeeeeeeeceeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg fgeeeeeeeeeeeeeeeeeeeeeaceeebdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg fgeeeeeeeeeeeeeeeeeeeeeceeedbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg fgeeeeeeeeeeeeeeeeeeeecaeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg fgeeeeeeeeeeeeeeeeeeegceeebdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg fgeeeeeeeeeeeeeeeeeeecgeegbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg fgeeeeeeeeeeeeeeeeeeaceeebgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg fgeeeeeeeeeeeeeeeeeeceeedbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg fgeeeeeeeeeeeeeeeeecaeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg fgeeeeeeeeeeeeeeeeeceeebdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg fgeeeeeeeeeeeeeeeecaeedbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg fgeeeeeeeeeeeeeeegceeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg fgeeeeeeeeeeeeeeecgeebdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg fgeeeeeeeeeeeeeeaceedbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg fgeeeeeeeeeeeeeeceeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg fgeeeeeeeeeeeeecaeebdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg fgeeeeeeeeeeeegceegbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg fgeeeeeeeeeeeecgeebgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg fgeeeeeeeeeeeaceebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg fgeeeeeeeeeeeceegbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg fgeeeeeeeeeecaeebgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg fgeeeeeeeeeeceedbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg fgeeeeeeeeecaeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg fgeeeeeeeegceebdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg fgeeeeeeeecgedbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg fgeeeeeeeaceebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg fgeeeeeeeceebdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg fgeeeeeecaedbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg fgeeeeegceebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg fgeeeeecgebdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg fgeeeeacegbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg fgeeeeceebgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg fgeeeacedbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg fgeeecegbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg fgeecaebgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg fgegcedbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg fgecgebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg fgacebdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg fgcedbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg fcaebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg fcebdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg cagbgggggggggggggggggggggggggggggggggggggggggggggggggggggggggg fbfffffffffffffffffffffffffffffffffffffffffffffffffffffffffff bd fb bf ``` <!-- end of image --> I'm eager to see what's happening in this magnified view of area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff7b7bff b,#0a09feff c,#fe0404ff d,#6260fdff e,#fec0c0ff f,#b6b6ffff g,#ff3f3fff ``` ```image f fbb fbbb fdbbd dbbb dbbdf eae dbbbf eccccaae bbbbf gcggcccccge fbbbf cc agcccccgae fbbbf ac eagcccccae fdbbd ece eagccccbbbd gc edbbbbccgae ecc dbbdeacccccgae gca dbbdf eagcccccgae cca fbbbf egcccccga acg fbbbf eagccc cce fbbbb ea cg fbbbd ec fdbbd ac bbbd cc dbbdf gcg fbbbf ecce fbbbf gca bbd cca fbf cg bd ece db gg bb ece dbd acc bbd cce dbb gcg bbf ecce bd gca db ca bb ag dbb ece fbbf gc dbd ecc fbb acc bd cce fbf acg bd cce db ca fbb ca dbb ac fbbf ecc bbd gcg bb ecce bf acc fb cca bb cg dbb ece fbbf gg bbd ec dbb acc bd ecce db gcg fbf ecce db gca fbb ca dbd ag fbbf ece bbd gc bb ecc fbf acc db cce fbb gcg bbd cce dbb ca fbbf ca bb ac bf ecc db gcg fbf ecce bb acc fbbf cce bbd cg dbb ece bbf ga bd cc bf acg db ecce fbb gcg bbd ecce dbb cc bbd ce bb ag fbf ece bd gc db cca dbd acg fbb ecce bbf gcg dbd cce bbf ac db ca fbf ac bb ecc dbb gcg fbbf cca fbb acc bbf cce bd cg fbf ece bd ac fbb cc bbd acg dbb ``` <!-- end of image --> I am surprised, so clear, an intersection has appeared in area A. There's only one, but is an intersection after all.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff6666ff b,#0404ffff c,#ff0a0aff d,#8585ffff e,#ffb8b8ff f,#c9c9ffff g,#3f39f9ff ``` ```image d fbb fbb bbf bbf gbd gbd gbd dbg dbg fbb fbb fbbf bbf eccae bbf c acccce gbd ac ecccca gbd c egbgcae ca dbg acccce c dbg eaccca ce fbb acccae ec fbb ecccca c fbbf eacccae aa bbf acccce c gd ecc ce fb ec b c gg ac b c bf ca dg c b ce bf ec db c b ac bd c fb ca b ec gg ce fb ac bf c gg aa b c bf ce db ec b c bd ac db c b ca bd c fb ce b ec gg c b aa bf c dg ce b ec bf c db ac b c bd ca fb c b ce gg ec fb c bf aa gg c b ce bf ec db c b ac bd c db ca b c bd cefb b gg fb bf ``` <!-- end of image -->

Alright, let's get to work and investigate this image for intersections. Let's take a closer look at what's happening inside these zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#78118dff b,#f50a0fff c,#0a06f8ff d,#606cdbff e,#d66b5dff f,#b1d7b1ff g,#97c698ff ``` ```image d c fgggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggca gffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffgce gffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffcbf gfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffdcef gfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffcbff gffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffdcgff gffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffcbfff gfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffcaffff gfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffcbffff gffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffcafffff gffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffcefffff gfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffcbffffff gffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffdceffffff gffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffcbfffffff gfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffdcffffffff gfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffcbffffffff gffffffffffffffffffffffffffffffffffffffffffffffffffffffffffdafffffffff gffffffffffffffffffffffffffffffffffffffffffffffffffffffffffcefffffffff gfffffffffffffffffffffffffffffffffffffffffffffffffffffffffcaffffffffff gfffffffffffffffffffffffffffffffffffffffffffffffffffffffffceffffffffff gffffffffffffffffffffffffffffffffffffffffffffffffffffffffcbfffffffffff gfffffffffffffffffffffffffffffffffffffffffffffffffffffffgcgfffffffffff gfffffffffffffffffffffffffffffffffffffffffffffffffffffffcbffffffffffff gffffffffffffffffffffffffffffffffffffffffffffffffffffffdcfffffffffffff gffffffffffffffffffffffffffffffffffffffffffffffffffffffcbfffffffffffff gfffffffffffffffffffffffffffffffffffffffffffffffffffffdaffffffffffffff gfffffffffffffffffffffffffffffffffffffffffffffffffffffceffffffffffffff gffffffffffffffffffffffffffffffffffffffffffffffffffffcafffffffffffffff gffffffffffffffffffffffffffffffffffffffffffffffffffffcefffffffffffffff gfffffffffffffffffffffffffffffffffffffffffffffffffffcaffffffffffffffff gffffffffffffffffffffffffffffffffffffffffffffffffffgcfffffffffffffffff cd gffffffffffffffffffffffffffffffffffffffffffffffffffcbfffffffffffffffff c gfffffffffffffffffffffffffffffffffffffffffffffffffdcffffffffffffffffff c gfffffffffffffffffffffffffffffffffffffffffffffffffceffffffffffffffffff dc gffffffffffffffffffffffffffffffffffffffffffffffffdcfffffffffffffffffff cd gffffffffffffffffffffffffffffffffffffffffffffffffcefffffffffffffffffff c gfffffffffffffffffffffffffffffffffffffffffffffffcaffffffffffffffffffff c gfffffffffffffffffffffffffffffffffffffffffffffffcgffffffffffffffffffff dc gffffffffffffffffffffffffffffffffffffffffffffffcafffffffffffffffffffff cd gfffffffffffffffffffffffffffffffffffffffffffffgcffffffffffffffffffffff cf gfffffffffffffffffffffffffffffffffffffffffffffcbffffffffffffffffffffff c gffffffffffffffffffffffffffffffffffffffffffffdcfffffffffffffffffffffff fcgffffffffffffffffffffffffffffffffffffffffffffcefffffffffffffffffffffff dcfffffffffffffffffffffffffffffffffffffffffffdcffffffffffffffffffffffff cdffffffffffffffffffffffffffffffffffffffffffceffffffffffffffffffffffff gcfffffffffffffffffffffffffffffffffffffffffcafffffffffffffffffffffffff ggcffffffffffffffffffffffffffffffffffffffffcgfffffffffffffffffffffffff gfdcffffffffffffffffffffffffffffffffffffffcaffffffffffffffffffffffffff gffcdfffffffffffffffffffffffffffffffffffffcfffffffffffffffffffffffffff gfffcgfffffffffffffffffffffffffffffffffffcefffffffffffffffffffffffffff gffffcffffffffffffffffffffffffffffffffffdcffffffffffffffffffffffffffff gffffdcfffffffffffffffffffffffffffffffffceffffffffffffffffffffffffffff gfffffccfffffffffffffffffffffffffffffffdcfffffffffffffffffffffffffffff be gffffffcdffffffffffffffffffffffffffffffcgfffffffffffffffffffffffffffff bb gfffffffcfffffffffffffffffffffffffffffcaffffffffffffffffffffffffffffff be gfffffffgcffffffffffffffffffffffffffffcfffffffffffffffffffffffffffffff bb gffffffffdcffffffffffffffffffffffffffcafffffffffffffffffffffffffffffff fbe gfffffffffcdfffffffffffffffffffffffffcffffffffffffffffffffffffffffffff bb gffffffffffcgfffffffffffffffffffffffcaffffffffffffffffffffffffffffffff fbefffffffffffcffffffffffffffffffffffgcfffffffffffffffffffffffffffffffff bbffffffffffdcfffffffffffffffffffffcefffffffffffffffffffffffffffffffff gebefffffffffcdfffffffffffffffffffdcffffffffffffffffffffffffffffffffff gffbbfffffffffcgffffffffffffffffffcgffffffffffffffffffffffffffffffffff gfffebeffffffffcfffffffffffffffffdafffffffffffffffffffffffffffffffffff gfffffbbfffffffdcffffffffffffffffcffffffffffffffffffffffffffffffffffff gffffffebeffffffccffffffffffffffcaffffffffffffffffffffffffffffffffffff gffffffffbbffffffcdfffffffffffffcfffffffffffffffffffffffffffffffffffff gfffffffffebefffffcffffffffffffcafffffffffffffffffffffffffffffffffffff gfffffffffffbbffffgcffffffffffgcffffffffffffffffffffffffffffffffffffff gffffffffffffebefffdcfffffffffcgffffffffffffffffffffffffffffffffffffff gffffffffffffffbbfffcdfffffffdcfffffffffffffffffffffffffffffffffffffff gfffffffffffffffebgffcgffffffcffffffffffffffffffffffffffffffffffffffff gfffffffffffffffffbbffcfffffacffffffffffffffffffffffffffffffffffffffff gffffffffffffffffffebgdcffffcfffffffffffffffffffffffffffffffffffffffff gffffffffffffffffffffbbccffcafffffffffffffffffffffffffffffffffffffffff gfffffffffffffffffffffebcdfcffffffffffffffffffffffffffffffffffffffffff gfffffffffffffffffffffffbccaffffffffffffffffffffffffffffffffffffffffff gffffffffffffffffffffffffacfffffffffffffffffffffffffffffffffffffffffff gfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff gfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff gfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff ``` <!-- end of image --> This is a magnified view of the region A. <!-- image --> ```palette Key,Color ,#fefefeff a,#850d85ff b,#f70810ff c,#0903f8ff d,#5048f7ff e,#f8555cff f,#f9b4b9ff g,#a7a1f8ff ``` ```image c cb cb da ccb ccf dcb cae ccf gcb cae ce gc dcb ca gcb gcbf cce ca cbf ce da gcb cc dcb cbf ccf ca cae cf dc dce ccf gcb gcb ccf ca dce ce da gce cc ca cb cc ca caf ce dc dcf cc gce caf g cc c ca cg dcf c cf dd gc cc gce dd cc cd ca gcg gce dc dcf cg ca cc ca dc cf gcg dc cc ce cd cc cg gcf dc ca cc cc gcg cc cd da bf gcg c bb gc gc fbb cd gcf ebbf gcg cc ebe dc ca ebe cd cf bbf cc c bbf dd ca eb c gcf fbb gcg cc fbb cc dc ebb gcg gcf ebb cc cc bbe dc ca bbe gc ca bbe dc c bbf cd dc bbfgcg dc fbb dc cc fbbcc gcf fbacdc ebccc acg g ``` <!-- end of image --> The close-up clearly shows an intersection point in area A. I can confirm there's two intersections in there.

<!-- image --> ```palette Key,Color ,#fefefeff a,#79088dff b,#f80c12ff c,#0a06faff d,#6b64f7ff e,#f46670ff f,#fcb3b6ff g,#bebdfeff ``` ```image d c ca gce cb gcf cb dcf cb da cb ca ce cb gcf cb dc cb da ce ca cf cb gcf cb dc cb da ce ca cf ca gc cd cb c gc gc ce dc dc cd ce cg ca c cf gc ca cd gc cg cb c gc gc ce dc dc cd cf c ca gc c dc ca cd c cg ce c gc gc ce cc dc be cg cf bb c da fbe gc c bb dc ca fbe cd c bb cg ce fbe c gc bb dc cf fbe cd dc bb cg cf fbe c da bb gc c fbf dc ca bb cg c ebf c ce bb gc gc ebf dc cf bb cd dc ebf cg c bb c dc ebfdc c bbcd ca ebcg c bccd ac ``` <!-- end of image -->

Time to put on my detective hat and find those intersection points! Zero, Nada.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0000ff b,#0404ffff c,#6363ffff d,#ff6767ff e,#ffb2b2ff f,#b0b0ffff g,#ff2222ff ``` ```image f fcbbbbbbb fcbbbbbbccf ffcbbbbbbccf fccbbbbbbcff fccbbbbbbcf cbbbbcf cbbc cbbc cbbc cbbc cbbc cbbc cbbc cbbc cbbc cbbc cbbc bc ag dag eaae aad e gad daag dag egaad eaae daage eaae egaad gad daage dag egaad eaae daage eaae egaad gad daage dag egaad daa daage eaae egaad gage ``` <!-- end of image -->

I have a feeling there might be some intersections in this image. These regions highlight areas that look suspicious. Lines seem to converge within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#3439f4ff b,#fe0707ff c,#8486fbff d,#e89b90ff e,#0304feff f,#f64743ff g,#b0d6b0ff ``` ```image c ac e ac e ac e ac e ac e ac e ac e ac e ac e ac e ac e ac e ac e ac e ac e ac e ac e ac e ac e ac e ac d e c fb ac ee fb e cec fb ac ee fb e cec bb ac ee bf e cec bf ac ee bf e cec bf ac ee bf e cec bf ac ee bf e cec bf ac ee bd e cec bd ac ee bd e cec bd ac ee bd e cec bd ggggggaagggggggggggggggggggeegggg bd gggggggegggggggggggggggggceaggggg b bd gggggggaagggggggggggggggeeggggggg dbbd bd ggggggggegggggggggggggceagggggggg dbbf bdggggggggaagggggggggggeegggggggggg fbbd bdggggggggegggggggggceaggggggggggg dbbd bggggggggaagggggggeeggggggggggggg bbb gbggggggggeggggggeagggggggggggggg dbbd ggbgggggggaagggaegggggggggggggggg dbbf gggbgggggggeggeaggggggggggggggggg fbbd ggggbggggggaeegggggggggggggggggdbbd ggggdbggggggaggggggggggggggggbbbg gggggdbgggggggggggggggggggfbbdggg ggggggdbgggggggggggggggdbbfgggggg gggggggdbggggggggggggfbbdgggggggg ggggggggdbggggggggdbbfggggggggggg gggggggggdbgggggbbbgggggggggggggg ggggggggggdbgfbbdgggggggggggggggg gggggggggggdbfggggggggggggggggggg ggggggggggggggggggggggggggggggggg ggggggggggggggggggggggggggggggggg ggggggggggggggggggggggggggggggggg ``` <!-- end of image --> This close-up might reveal an intersection in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0707ffff b,#fe0505ff c,#5f5fffff d,#ff9494ff e,#ffd6d6ff f,#ff3f3fff g,#c6c6ffff ``` ```image cac gaaac gaag caaag cac gaaac gaag caaag cac gaaac gaag caaag cac gaaac gaag caaag cac gaaac gaag caaag e cac gaaac be gaag caaag bbe cac gaaac fbbe gaag caaag fbbe cac gaaac fbbe gaag caaag efbbe cac gaaac efbbe gaag caaag efbfe cac gaaac ebbfe gaag caaag ebbfe cac gaaac ebbf gaagcaaag e ebbf caaaac dfb ebbf gaaag efbbbb ebbf cc edfbbbfde ebbf dfbbbbfe ebbf edbbbbfd ebbf dfbbbbde ebbf efbbbbfd ebbf edfbbbfde ebbf dfbbbbfe ebbf edbbbbfd dbbf dfbbbbde dbbf efbbbbfd dbbf edfbbbfde dbbd dfbbbbfe dbbd edbbbbfd dbbfbbbbde dbbbfd dde ``` <!-- end of image --> After careful examination, I've determined that there's no intersection in area A. I did not find anything, there's no intersections

<!-- image --> ```palette Key,Color ,#fefefeff a,#3131ffff b,#ff0909ff c,#7777ffff d,#ffb0b0ff e,#0202ffff f,#ff5959ff g,#b0b0ffff ``` ```image g ac e ac e ac e ac e ac e ac e ac e ac e ac e ac e ac e ac e ac e ac e ac e ac e ac e ac e ac e ac e ac d e c fb ac ee fb e ceg fb ac ee bb e gec bb ac ee bb e gec bb ac ee bf e gec bf ac ee bf e gec bf ac ee bf e gec bf ac ee bf e gec bf ac ee bd e gec bd ac ae bd e gec bd ac ae bd e gec b bd ac ae fbbd bd e gec dbbf bd ac ae fbbd bd e gec dbbf b ac ae bbb b e gec fbbd b ac ae dbbf b e gec fbbd b aee dbbf db c bbb db fbbd db dbbf db fbbd db dbbf db bbb db fbbd dbf ``` <!-- end of image -->

I'm optimistic that I'll find some intersections in this image. These zones indicate regions where lines appear to be in close proximity. <!-- image --> ```palette Key,Color ,#fefefeff a,#0606feff b,#fd0707ff c,#acadfdff d,#eb5652ff e,#5055f5ff f,#aed5aeff g,#f7aba7ff ``` ```image c ac a ac ca a ca a ee a ee a ac a ac ca gbbbg a bb bbg ca dbg bbd a gbd dbb fffeefffffffffff gbb gbb ffffafffffffffff bb gbbg ffffeeffffffffff dbg bbd fffffaffffffffff gbd dbd fffffaefffffffffbb dbb ffffffafffffffbbg gbbg fffffffffffffff ffffffafffffdbdf gbbg fffffffffffffff fffffffaffgbbfff bbd fffffffffffffff fffffffafbbfffff dbd fffffffffffffff fffffffdagffffff dbb fffffffffffffff fffffdbdafffffff gbbfffffffffffffff ffffbbffeeffffff bbdffffffffffff ffbbfffffaffffff ffbbdffffffffff dbdffffffeefffff ffffdbbffffffff gbdfffffffffafffff ffffffdbbffffff bb ffffffffffaeffff ffffffffgbbffff bbg fffffffffffaffff fffffffffffffff g fffffffffffaffff fffffffffffffff ffffffffffffafff fffffffffffffff ffffffffffffafff fffffffffffffff ca fffffffffcaffff a ffffffffeafffff ee fffffffeaffffff a ffffffeafffffff ee fffffaaffffffff a aa ac ae a ae a ae ca ac a ac ca ac a ca ee ca a ca ee ea a ea ac ea a aa a ae ca ae a ae ca ac a ac ee ac a ca ec ca a ca ac ea a ea a ea ca aa a ae ca ae a ae ee ac a ac ec ac a ca aea a ``` <!-- end of image --> I'm now examining the contents of area A in detail. <!-- image --> ```palette Key,Color ,#fefefeff a,#0403feff b,#fe0809ff c,#8484feff d,#f55862ff e,#4343feff f,#cdcdffff g,#ffb7b7ff ``` ```image cae aaf cae faaf eae faaf eac faa eac caa aac cae db aaf gbbb cae gdbbbg faaf dbbbd eae gbbbd faaf gbbbbg eac gdbbbg faa dbbbd eadbbdg gdaabg dbbaac dbbbdcae gbbbdg aaf gdbbbg cae dbbbd faaf gbbbd eae gbbbbg faaf dbbbg eac bbd faa dg eac caa aac cae aaf cae faaf eae faaf eac ``` <!-- end of image --> I observe an intersection inside area A. Let's shift our focus to the next area. I'm now examining the contents of area B in detail. <!-- image --> ```palette Key,Color ,#fefefeff a,#0202ffff b,#ff0606ff c,#9f9fffff d,#ff4f4fff e,#5858ffff f,#ffd7d7ff g,#ff9494ff ``` ```image df bbdg dbbbbg fgbbbbgf gbbbbdf gdbbbdf fdbbbdg fdbbbbg fgbbbbgf gbbbbdf gdbbbd fdbd ff cae caae caae caae caae eaac eaac eaac eaac ``` <!-- end of image --> No intersection found in area B, but I won't give up. I have found one intersection!

<!-- image --> ```palette Key,Color ,#fefefeff a,#0505feff b,#ff0808ff c,#8181ffff d,#fb5e62ff e,#4040ffff f,#c8c8ffff g,#ffb4b4ff ``` ```image f ac a af fa a ca a ce a ec a ac a af fa gbbbg a bb bbd ca bbg bbd a dbd dbb ce gbb gbb a bb gbbg ec dbg bbd a gbd dbd ac bb dbb a bbg gbbg af dbd gbbg fa gbb bbd a bb dbd dag dbb dbda gbbg gbb ce gbbg bb a bbd dbg ec dbb gbd a dbb bb af gbb bbg a g af fa a f ca fa a ca ce ca a ea ec ea a aa af ae a ae af ac fa ac a af ca faf a faf ce fa a ca ec ca a ea af ea a aa af ae fa ae a ac ce ac a af ce faf a faf ec fa a ca af ca a ea af ea fa aa a ae ce ae a ac ee ac a af ec faf a fa aca fa ``` <!-- end of image -->

The hunt for intersections begins! Let's analyze this image closely. I've examined the entire image, and there are zero intersections present.

<!-- image --> ```palette Key,Color ,#fefefeff a,#3535ffff b,#ff0909ff c,#ffababff d,#7575ffff e,#ff5252ff f,#0303ffff g,#bebeffff ``` ```image d df gf gf gf f fg fg fg fd fd fa aa aa af df df gf gf gf f fg e fg eb fg eb fd bb fd bb fa bb fa be aa be af be df be df be gf be gf be gf be f bc fg bc fg bc fg bc ffd fd bc gdfffag fd bc gafffd fa bc gdfffag fa bc gafffd aa b gdfffag af b gafffdg df b dfffag df cb gaff cb cb cb cb cb cb cb eb eb eb eb eb eb eb eb bb bb ebe bbe cbbc ebb bbe cbbc ebb bbe cbbc ebb bbe cbbc ebb bbe cbbc bb ``` <!-- 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,#0c0bfbff b,#fe0404ff c,#ee968eff d,#6d74f1ff e,#f14041ff f,#b0d6b1ff g,#98c699ff ``` ```image c ee b b ee b b eb bc b cb bc b cb bc b cb ee b b ee b b ee bc b cb bc b cb bc b cb be b aaa ggbfffffffffdafdad ffeefffffffgaffg aaf fffbgffffffafffg aa fffgbfffffadfffg dad ffffeefffaaffffg aaf fffffbcfdafffffg aa ffffffbfaffffffg dad ffffffeagffffffg aa ffffffaacffffffg aa fffffdafbffffffg dad ffffgaffcbfffffg aa ffffaffffbcffffg aa fffadfffffbffffg dad ffaaffffffcbfffg aa fdaffffffffbeffg aa gaffffffffffbgfg dad af cb ggggggaagggggggggggggggggg ad eec fffffffgaaffffffffffffffff da cbbbbbec fffffffffdadffffffffffffff fa cebbbbbec fffffffffffaafffffffffffff a cebbbbbecffffffffffffgaafffffffffff af cebbbbeecfffffffdadfffffffff ad ffffcebbbbbecgffaaffffffff da fffffffffffcebbbbeaaffffff a fffffffffffffffffgcaaeffff a fffffffffffffffffffffaffff ad ffffffffffffffffffffffffff aa ffffffffffffffffffffffffff da ffffffffffffffffffffffffff a ffffffffffffffffffffffffff a ffffffffffffffffffffffffff ad ffffffffffffffffffffffffff da gggggggggggggggggggggggggg a a ad ad da a a ad da fa a af ``` <!-- end of image --> Let's put area A under the microscope. <!-- image --> ```palette Key,Color ,#fefefeff a,#5248f5ff b,#fe0404ff c,#fe8e8fff d,#a7a7feff e,#f93d42ff f,#0707feff g,#efd9e8ff ``` ```image ebe affd gbbc dffg cbbg dffd ebe gffa gbbc afa cbbg affg ebe dffd gbbc dffd cbbg gffa ebe aff gbbc affg cbbg dffd ebe gffa bbc ffa gbbaffg ceffd dffa gffabc afacbbg affg ebe dffd gbbc gffd cbbg ffa ebe aff gbbc dffg cbbg dffd ebe gffa gbbc afa cbbg affg ebe dffd gbbc dffd cbbg gffa ebb ``` <!-- end of image --> There's no doubt about it - this is an intersection in area A. I'm ready to analyze the next area. This close-up of area B is like examining a piece of evidence. <!-- image --> ```palette Key,Color ,#fefefeff a,#5655feff b,#fd0608ff c,#fea9a9ff d,#a7a5fcff e,#fe5758ff f,#0907fdff g,#7c0688ff ``` ```image afffd dfffa afffd afffd dfffa afffd afffd dfffa afffd c afffd bbbbeecc dfffa ebbbbbbbbbbeecc afffd cceebbbbbbbbbbeeccc dafffd cceebbbbbbbbbbeecc dfffa ccceebbbbbbbbbbeeccafffd cceebbbbbbbbbbffffd cceebbbbgfffgbee ccegfffge dafff dfa ``` <!-- end of image --> My investigation has led me to an intersection in area B! I can confirm there's two intersections in there.

<!-- image --> ```palette Key,Color ,#fefefeff a,#352ff8ff b,#fe0506ff c,#ffa0a0ff d,#8585ffff e,#fb4a4dff f,#0303ffff g,#e0d4f2ff ``` ```image c ee bg gb ee bg b eb bc b cb bc b cb bc b cb be b gb ee bg b eb bc b eb bc b cb bc b cb be g b aff gb df dfa ee gf afg bg fg ff gb fd dfa ee aa afg bc df ff b f dfd efg afg fac gff df b dfd gf cb afg f bc gff fd b dfd aa cb afg df be gfa gf b dfd fg cb afg fd eec gfa aa ebbbbbecg dfd gf cebbbbbec ffg f gcebbbbbec gfa fg gcebbbbecc dfd aa cebbbbbecg ffg df cebbbbbfa gf gcafe fg f fd aa df f fg fd df gf f fd aa df gf fg fd aa gf f fg ``` <!-- end of image -->

I'm optimistic that I'll find some intersections in this image. I'm going to focus my attention on these specific areas. <!-- image --> ```palette Key,Color ,#fefefeff a,#e96a64ff b,#0607fdff c,#fc0a0aff d,#939beeff e,#b2d7b1ff f,#474cf3ff g,#97c896ff ``` ```image ac cac c c aa ac c c c c ca ce b c c bf c ca fb ca c db c aa b c c b ca ac bd ec c bf c ec fb ca ce db ec c egggggggggggggge b c ca geeeeeeeeeeeeeeg b ca c geeeeeeeeeeeeeeg bd ec aageeeeeeeeeeeeeeg bf c cgeeeeeeeeeeeeeeg fb ca aceeeeeeeeeeeeeeg db ec ceeeeeeeeeeeeeeg b egggggggggggggggge c aceeeeeeeeeeeeeg b geeeeeeeeeeeeeeeeg ca gcgeeeeeeeeeeeegbd geeeeeeeeeeeeeeeegac geceeeeeeeeeeeebf geeeeeeeeeeeeeeeegc gecaeeeeeeeeeefb geeeeeeeeeeeeeeeeca geeceeeeeeeeedbg geeeeeeeeeeeeeeeac geecaeeeeeeeebeg geeeeeeeeeeeeeeecg geeeceeeeeeebgeg geeeeeeeeeeeeeecag geeeaceeeeebdeeg geeeeeeeeeeeeeaceg geeeeceeeebfeeeg geeeeeeeeeeeeeceeg geeeeaceefbeeeeg geeeeeeeeeeeecaeeg geeeeecgdbeeeeeg geeeeeeeeeeeaceeeg geeeeegcbeeeeeeg geeeeeeeeeeeceeeeg geeeeeebaeeeeeeg geeeeeeeeeecaeeeeg geeeeebdceeeeeeg beeeeeeeeeaceeeeeg geeeebfecaeeeeeg gbbeeeeeeeceeeeeeg geeefbeeeceeeeeg gefbfeeeecaeeeeeeg geedbeeeeaceeeeg geeebbgeaceeeeeeeg geebeeeeeeceeeeg geeeeebbceeeeeeeeg gebeeeeeeeaceeeg geeeeeeabfeeeeeeeg gbdeeeeeeeeceeeg geeeeeacefbdeeeeeg bfeeeeeeeeegceeg geeeeeceeeebbeeeeg fbeeeeeeeeeeecaeg geeeecgeeeeedbfeeg dbgeeeeeeeeeeeeceg geeeaceeeeeeeefbfg b geeeeeeeeeeeecag geeeceeeeeeeeeeebb b geeeeeeeeeeeeecg geecgeeeeeeeeeeeegbb bd geeeeeeeeeeeeeac geaceeeeeeeeeeeeeg dbf bf geeeeeeeeeeeeeec geceeeeeeeeeeeeeeg fbd fb geeeeeeeeeeeeeeac gcgeeeeeeeeeeeeeeg bb db geeeeeeeeeeeeeegc cceeeeeeeeeeeeeeeg dbf b geeeeeeeeeeeeeegec aeeeeeeeeeeeeeeeeg fbd b geeeeeeeeeeeeeeg ce geeeeeeeeeeeeeeeeg bb bd egggggggggggggge c geeeeeeeeeeeeeeeeg bb bf ca geeeeeeeeeeeeeeeeg dbf fb c geeeeeeeeeeeeeeeeg fbddb aa geeeeeeeeeeeeeeeeg bb c geeeeeeeeeeeeeeeeg ac geeeeeeeeeeeeeeeeg c egggggggggggggggge ec c c ca c aa c ac c ec c c ca c ca c ac c ``` <!-- end of image --> I'm eager to see what's happening in this magnified view of area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe7f80ff b,#0807fdff c,#fe0506ff d,#abaafeff e,#fec3c4ff f,#5656ffff g,#f63d45ff ``` ```image a ec gc acc ecca gcg acce ecca gcg acce ecca gcg acc ecca gcg acc ecce gcg bf acc bbbd ecce dbbbfd gcg dbbbf acc fbbbd ecce dfbbbd gcg dbbbf acc fbbbf ecce fbbbgcg dbbbbd egbbbf ccafbbbd acc dfbbbd ecce dbbbf cca fbbbf acc fbbbd ecce dbbbfd cca dbbbf acc fbbbd ecce dfbb cca db gcg ecce cca gcg ecce cca gcg ecce cca gcg cce aa ``` <!-- end of image --> My analysis confirms the presence of an intersection in area A. Right then, let's explore the next spot. Here's a close-up of the area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd8384ff b,#0807fdff c,#fd0506ff d,#a9a9feff e,#ffc8c8ff f,#5150feff g,#ff4242ff ``` ```image e g ce cc cca acc gca ecce gcg ecce gcg ecce acg f cca fb acc dbb gca dbbd ecce dbbf gcg bbf ecce fbb gcg fbb ecce dbbd acg dbbd cca dbbf acc bbf cca fbb ecc fbb gca dbbd ecce dbbd gcgdbbf eccbbf abbb fbba dbbcc dbbdcca dbbf acc bbf gca fbb ecce fbb gcg dbbd ecce dbbd acg dbbf cce bbf acc fbb cca fbb acc dbbd gca dbbd ecce dbbf gcg bbf ecce fbb gcg bb ecce bd acg d cca acc gca ecce gcg ecc gc ec a ``` <!-- end of image --> Bingo! This close-up reveals an intersection in area B! I can confirm there's two intersections in there.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fd7f80ff b,#0707feff c,#fe0505ff d,#a2a2feff e,#ffc4c4ff f,#4c4cffff g,#fb3e41ff ``` ```image e gc ecag ce c gg ac ec ce ce ec gg ce b ec c bf c ga fb gg c db ec gg b c c b gg ac bd ec c bf c ec fb ca ce db ec c b c ca b ca c bd ec gg bf c c fb ca ac db ec c b c ec b ca ce bd ec c bf c ca fb ca c db ac gg b c c b ca ag bd ac c bf c ec fb ca cedb ac ecb c ba ce bdc f ac bf ga dbf c fb c fbd ce db ag bb ac b c bbc b ac gbf bd ce ac fbd bf ec c bb fb ce ce dbf db c ag fbd b ga c bb b c ce bb bd gg gg dbf bf c c fbd fb ac ce bb db c gg dbf b ec a fbd b ce bb bd c bb bf ca dbf fb c fbddb gg bb c ac c ec ce c ca c gg c ag c ec ce ec ce c ga c ag c ``` <!-- end of image -->

Based on a first glance, I suspect there could be intersection regions here. I'd describe these as 'hotspots' for potential intersections. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0707ff b,#0607feff c,#f25953ff d,#5458f6ff e,#fea8a8ff f,#a3a6f9ff g,#acd3acff ``` ```image e a ae ea a cc a ae ea a ca a ae a a ea a ac a ae ea a cc a ae ea a cc a ae ea a ca a ac a ae ea a cc a ae ea a cc a ae ea a bd ca dbd a dbb ac fbb a fbbf ae bbf ea bbd a dbd cc dbb a fbb ae fbbf ggggggggggggcaggg fbbf ggggggggggggagggg bbf gggggggggggccgggg dbd gggggggggggaggggg dbdggggggggggacggggg dbbggggggggagggggg gdbbgggggaggggggg ggggbbbfcaggggggg ggggggfbbbdgggggg gggggggacgdbbdggg gggggggagggggdbbb ggggggagggggggggdbbbf gggggcagggggggggg fbbbf gggggaggggggggggg dbbd ggggacggggggggggg dbbd ccaaagggggggggggg fbbbf ecaaaaaaccggggggggggggggg fbbbf ecaaaaaacee ggggggggggggggggg dbbd ecaaaaaacee dbbd ecaaaaaacee fbbbf cee fbb ``` <!-- end of image --> This close-up of area A is like examining a piece of evidence. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0404ff b,#0a09fdff c,#f4333dff d,#6363ffff e,#febdbeff f,#b3b3ffff g,#ff7979ff ``` ```image eaae cac eaa aag gac eaae cac eaae cag gaa f aae bbf gac bbbbd eaae fbbbbd cag fbbbbdf gaa fdbbbbdf aag fdbbbbbdf gac fdbbbbbbce fdbbbbbddf eacbbbbbbdf aag fdbbbbbdf gac fdbbbbbdf eaae fdbbbb cac fdb eaae cag gaa aae cac eaae cag egaa eeggcaaaaag aaaaaaaacg ccggee ``` <!-- end of image --> There is an intersection point visible in this close-up of area A. It was tricky, but I finally found one single intersection in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0606ff b,#0606feff c,#ff4d4dff d,#5454ffff e,#ffceceff f,#a9a9ffff g,#ff8f8fff ``` ```image g a ae ga a cc a ag ea a ca a ag ea ae ga a cc a ae ga a cc a ag ea a cc a ag ea ae ga a ag ea ae ga a cc a ae ea a cc a ag ea ae bd ga dbd a dbb ag fbb ea fbbf ae bbf ga bbd a dbd cc dbb a fbb ae fbbf ga fbbf a bbf cc dbd a dbd ag dbb ea fbbf a fbbbfcc fbbbf ag dbbd ea dbbd ae fbbbf ga fbbbf a dbbd cc dbbd egcaaa fbbbf egcaaaaaacge fbbbf egcaaaaaacge dbbd egcaaaaaacge dbbd gcaaaaaacge fbbbf cge fbb ``` <!-- end of image -->

I'm optimistic that I'll find some intersections in this image. Let's take a closer look at what's happening inside these zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0605ff b,#0b0cfbff c,#e8887eff d,#6772e6ff e,#ee4038ff f,#f1efecff g,#b0d6b0ff ``` ```image f ca aca fa af af fa fa ac ac a a ca ec af fffffffffffaffffffffaffffffffffffffffffffffff fggggggggggeeggggggggacgggggggggggggggggggggggg fggggggggggaggggggggggagggggggggggggggggggggggg fgggggggggcaggggggggggeaggggggggggggggggggggggg fgggggggggaggggggggggggaggggggggggggggggggggggg bbbbdf fggggggggcagggggggggggggagggggggggggggggggggggg ddbbbbbddf fggggggggaggggggggggggggacggggggggggggggggggggg fddbbbbbdf fggggggggagggggggggggggggaggggggggggggggggggggg fdbbbbbbdgggacgggggggggggggggeegggggggggggggggggggg fggddbbbbbddggggggggggggggagggggggggggggggggggg fggggggecgdbbbbbbgggggggggcaggggggggggggggggggg fggggggaggggggggbbgggggggggacgggggggggggggggggg fgggggeeggggggggggbdggggggggagggggggggggggggggg fgggggaggggggggggggbbgggggggeeggggggggggggggggg fggggcagggggggggggggdbgggggggaggggggggggggggggg fggggaggggggggggggggggbbgggggcagggggggggggggggg fgggcagggggggggggggggggbbgggggacggggggggggggggg fgggagggggggggggggggggggdbdggggaggggggggggggggg fgggagggggggggggggggggggggbbgggeegggggggggggggg fggacggggggggggggggggggggggdbgggagggggggggggggg fggagggggggggggggggggggggggggbdgcaggggggggggggg fgeeggggggggggggggggggggggggggbbgacgggggggggggg fgaggggggggggggggggggggggggggggdbdagggggggggggg feeggggggggggggggggggggggggggggggbbeggggggggggg faggggggggggggggggggggggggggggggggdbggggggggggg cagggggggggggggggggggggggggggggggggcbdggggggggg agggggggggggggggggggggggggggggggggggabbgggggggg faggggggggggggggggggggggggggggggggggggadbdgggggg afggggggggggggggggggggggggggggggggggggeegbbggggg fafgggggggggggggggggggggggggggggggggggggaggbbgggg acfgggggggggggggggggggggggggggggggggggggcagggbdgg a fggggggggggggggggggggggggggggggggggggggacgggbbg ec fgggggggggggggggggggggggggggggggggggggggaggggdbf a fgggggggggggggggggggggggggggggggggggggggeegggggbb ce fggggggggggggggggggggggggggggggggggggggggaggggg bb a fggggggggggggggggggggggggggggggggggggggggcagggg fbd ca fgggggggggggggggggggggggggggggggggggggggggacggg bb af fggggggggggggggggggggggggggggggggggggggggggaggg dbf fa fggggggggggggggggggggggggggggggggggggggggggeegg fbd af fgggggggggggggggggggggggggggggggggggggggggggagg bb fa fgggggggggggggggggggggggggggggggggggggggggggcag gbd ac fggggggggggggggggggggggggggggggggggggggggggggac bb a fggggggggggggggggggggggggggggggggggggggggggggga d ec fffffffffffffffffffffffffffffffffffffffffffffec a a ce ca a af ca fa af ec fa a af ca fa af ac fa a ac ec a a ca ce af a fa ca ac af a fa ce af af fa fa ac ac a a ec f a ce a ca af ``` <!-- end of image --> Let's see what secrets area A holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0303ff b,#0705fdff c,#fe7979ff d,#a6a6feff e,#f93439ff f,#fec1c1ff g,#524dfaff ``` ```image eac faaf faaf cae cae aac aaf faa cae eae aaf faaf cae cae eac aac faa faa eac eae faa faaf eac cae faaf aac cae caa aaf eac gddd cae faaf bbbbbbggdd aaf cae dggbbbbbbbbbbgggee aac dddggbbbbbbbbbggddd caa ddgbbbbbbbbbbbggdd eac eac ddggbbbbbbbbbg faaf faa dddggbbbbd cae eac gbbg aac faaf dbbbd caa cae dbbbd eac aaf gbbg faaf cae dbbbd cae aaf gbbg aac cae dbbbd caa eac dbbbd eac faa gbbg faaf eac dbbbd cae faa gbbg aaf eac gbbbd caa faaf dbbbd eac cae gbbg faaf aaf dbbbd eae cae gbbg aaf aaf gbbg caa cae dbbbd eac eac gbbg faaf faa dbbbd eae eac dbbbg faaf faa gbbg caa eac dbbbdeac faaf gbbgaaf cae dbbbee aaf dbbbef cae gbbb aaf dbbbd cae fbbbg eac egbbbd aa faebbbd ac caegbbg a aacdbbbd c faaf gbbg f eae gbbg faaf dbbbd cae gbbg aac dbbbd faaf dbbbg eae gbbg faaf dbbbd cae gbb aac db faa d eae faaf cae aac faa eac faaf cae aac caa eac faaf cae aac caa eac faa ca ``` <!-- end of image --> An intersection is present within area A. There's for sure two intersections on the image you sent me.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0606ff b,#0605feff c,#fe8a8bff d,#9f9ffeff e,#ff4545ff f,#f7d3dbff g,#4e4effff ``` ```image f ca aca fa af af fa fa ac ac a a ca ec af a fa ee ac a a ca ce a af bbbgdf fa fa dgbbbbbgd af ac fdgbbbbbgd fa a dgbbbbbgdf ac ee dgbbbbbgd af ecfdgbbbbg fa a gb ac ee fbd a a bb ee ca dbd a a bg fa fa gb ac af dbd a fa bb ee ac gbf a a bg fa ec bb ac a dbda ce bbe a gbf ca cbg a abb fa adbd af ee bg a a gb ac ca fbd a af bb ec a dbd a ee bg ce a gb a ca dbd ca af bb a a gbf fa ee bg af a bb a ca dbd ac af bb a fa g ec ee a a ce ca a af ca fa a ec fa a af ca a af ac fa a ac ec a a ca ce af a fa ca ac a a fa ca af af a fa ac ac a a ec f a ce a ca af ``` <!-- end of image -->

Let's examine this image for potential line intersections. These spots mark what I'd call 'danger zones' - areas where intersections are more likely. <!-- image --> ```palette Key,Color ,#fefefeff a,#5c63efff b,#fd0a0aff c,#0809fdff d,#ec645dff e,#add4acff f,#b1b1feff g,#ffbebeff ``` ```image f cf c cf fc c fc c aa c aa c cf c cf fc g c bb fc bbgb c db db aa db bg c gb b aa gb db c b bd cf bg b c bg gb cf bd db fc bd bg c bb b fc db gb eeeeceeeeeeeeedb bd eeeeaaeeeeeeeebe b eeeeeceeeeeeebee gb eeeeecaeeeeebeee db eeeeeeceeeebeeee bg eeeeeecaeebdeeee b eeeeeeecebdeeeee gb eeeeeeecbbeeeeee bd eeeeeeedceeeeeee bg eeeeeedbceeeeeee b eeeeedbeaceeeeee db eeeeebeeeceeeeee bg eeeebeeeeaaeeeee b eeebeeeeeeceeeee gb eebeeeeeeecaeeee bd ebdeeeeeeeeceeee bg bdeeeeeeeeecaeee b bbeeeeeeeeeeeceee db db cf bd db fc b gb c gb gb fc bd b c bg bg aa b bg c db bd aa bd bd c b cf gb c db c ebeeeeeeeeeeeeee fc eebeeeeeeeeeeeee c eedbeeeeeeeeeeee fc eeebdeeeeeeeeeee c eeeebeeeeeeeeeee aa eeeeebeeeeeeeeae c eeeeedbeeeeeccce ca eeeeeebdecccaeee c eeeeeeaccaeeeeee cf eeeaccadbeeeeeee c accaeeeebdeeeeee c fccceeeeeeeebeeeeee fc cccf eeeeeeeeeebeeeee c accf eeeeeeeeeedbeeee fc acca eeeeeeeeeeebdeee c fcca eeeeeeeeeeeebeee aa fccc eeeeeeeeeeeedbee c cccf eeeeeeeeeeeeebde ca accf b c acca cffcca ca ``` <!-- end of image --> Let's see what secrets area A holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#4f49f8ff b,#ff0404ff c,#0806fdff d,#ff7c7cff e,#f93b41ff f,#9e9cfdff g,#fdbfc0ff ``` ```image fcc d ccf db fca dbb ccf gbbd aca gbbd cc gbbe aca bbe fcc ebe acf ebb fcc ebbg ccf dbbg fcc dbbg ccf dbbd fca gbbd ccf gbbd acagbbe ccebe acae eccg ebccf dbbfcc dbbg ccf dbbd fcc gbbd ccf gbbd fca gbbe ccf bbe aca ebe cc ebbg aca ebbg fcc dbbg acf dbbg fcc gbbd ccf gbbd fcc bbe ccf ``` <!-- end of image --> Yes! I knew it! There's an intersection right here in area A! Onward to the next region of interest. Eureka! Let's inspect this close up of area B <!-- image --> ```palette Key,Color ,#fefefeff a,#5b5bfeff b,#fe0505ff c,#0706feff d,#fd797bff e,#f23440ff f,#b1b1ffff g,#ffbebeff ``` ```image bbd gbbg dbb ebe gbbd dbbg ebe bbd gbbg dbb ebe gbbd ff dbbg facca ebe faccccca bbd acccccaf gbbg faccccaf dbeaccccaf faccccaf faccccced facccccafdbbg fcccccaf ebe faccccaf bbd accccaf gbbg ccca dbb af ebe gbbd gbbg ebe bbd gbbg dbbg ebe bbd gbbg dbb ``` <!-- end of image --> Case closed! This is definitely an intersection point in area B. After a long analysis, I found two intersections.

<!-- image --> ```palette Key,Color ,#fefefeff a,#5a5afeff b,#ff0404ff c,#0707feff d,#fe8787ff e,#fc3b3eff f,#adadffff g,#ffcdcdff ``` ```image f cf c cf fc c fc c aa c aa c cf c cf fc g c bb fc eegb c eb ee aa db bg c gb b aa gb db c b bd cf bg b c bd gb cf bd ee fc be bg c eb b fc eb db c db bd aa gb bg c gb gb aa bg ee c bg bd cf bd b c bd db cee ee ec bg dbc gb db fc db gb c bd gb aa b bg c gb bg aa ee bd c bg be cf b ee c db eb c bd db fc b db c gb gb fc ee b c bg bg aa b bg c db bd aa bd be c b g cf gb c ee c bg fc b c db fc bd c b aa gb f c ee fccc aa bg accf c accf cf accadb c fcca bd c fccc bg fc cccf gb c accf ee fc acca bd c fcca b aa fcca db c cccf ee cf accf b c acca cffcca ca ``` <!-- end of image -->

I'm curious to see if this image contains any intersection points. These regions highlight areas that look suspicious. Lines seem to converge within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0404ff b,#0405fdff c,#8a8df8ff d,#f68581ff e,#f93837ff f,#ead2e6ff g,#acd4acff ``` ```image c cb cb cb cb cb cb cb cb cb cb cb cb fb fb fb fb fb fb e fb a de fb da af fb fa fa fbf af ad fbf ee a fbf da de bf a af bf ad fa bf ee ad bf fa a bf a de bf ad a bf da fa bf a ad bf af a bc ee ee bc da a bc a fa bc ad ad bc ee a bc fa ee bc af gagggggggggggggg bc ad gdaggggggggggggg bc da ggadgggggggggggg bc a gggagggggggggggg bc af gggeeggggggggggg cbbc ee ggggaggggggggggg cbbc fa ggggdaggggggggggbbbf a gggggadggggggcbbc ad ggggggagggcbbbgg ee ggggggeebbbggggg fa gggggcbbcggggggg af ggcbbbgdaggggggg ad fbbbgggggadgggggg da cbbcggggggggagggggg a cbbc gggggggggeeggggg af fbbbf ggggggggggaggggg ee cbbc ggggggggggdagggg fa bc gggggggggggagggg a ggggggggggggaggg ad ggggggggggggeegg da gggggggggggggagg fa da af af ad fa da ed a a af da ee af fa fa a ed ad a da da fa af af fa ad ad da a a de af aee fa ``` <!-- end of image --> Time to investigate area A up close. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0404ff b,#0907fcff c,#5c5bfeff d,#ff7d7dff e,#fb383bff f,#ffc3c3ff g,#acaafdff ``` ```image daa ead faaf eae faaf daa aad faaf eae faaf dae aad faaf eae gc faaf gcbbb dae gbbbbbc aad gcbbbbcg faa gcbbbbcg eaegbbbbbcg gbbbbbcg gcbbbbbg gbbbbbcead gcbbbbcg daa gcbbbbcg eae gbbbbbc faaf bbbbcg dae bcg aad daa ead faaf dae aad daa ead faaf dae aad daa ead ``` <!-- end of image --> As I suspected, there's an intersection within area A. The image features one single intersection point.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0505ff b,#0303ffff c,#8281feff d,#ff7d7dff e,#fe393aff f,#ffc5c5ff g,#c5c5ffff ``` ```image c cb cb cb cb cb cb cb cb gb gb gb gb gb gb gb gb gb gb e gb a de gb da af gb a fa gb af ad b ee a bg fa de bg a a bg af fa bg ee ad bg fa a bg a de bg ad a bg da fa bg a ad bg af a bg ee ee bg fa a bg a fa bg af af bc ee a bc fa ee bc a a bc ad fa bc da af bc a a bc af ee cbbc ee a gbbc fa fa bbbg a af cbbc ad a gbbc ea eebbbg fa cbbc a gbbc da ad bbbg af da cbbc a a gbbc ed af bbbg a ee cbbc da fa bc af a a ad ed da a fa da af af ad a da ed a a af da ee af fa fa a ed ad a da da fa af af fa ad ad da a a de af aee fa ``` <!-- end of image -->

I have a feeling there might be some intersections in this image. These spots mark what I'd call 'danger zones' - areas where intersections are more likely. <!-- image --> ```palette Key,Color ,#fefefeff a,#0808feff b,#fe0606ff c,#5d60f8ff d,#f7524eff e,#b5b5ffff f,#f8a7a3ff g,#abd3abff ``` ```image f dbbf fbbd dbbf bbd fbbf dbbf fbbd dbbf bbd fbbf ggggggggggggggggg dbb ggggggggggggggggg fbbdggggggggggggggggg dbbfgggggggggggggg ggbbdgggggggggggg ggggdbggggggggggg gggggfbdggggggggg gggggggbbgggggggg ggggggggdbfgggggg ggggggggggbbggggg gggaaggggggdbgggg ggacgagggggggbdgg gacggcagggggggbbg eagggggacgggggggdbf eagggggggagggggggggbb ca gggggggcagggggggg db ca ggggggggacggggggg bd aa ae bb aa a fbf ac ca bb ae ac dbf ae a bd ea ea db ea ca fbf ca ae bb ca a fbf aa ea bd ac ac db ac ae fbd ae a bb ae ca fbf ea ac bb ea a db ca ea bd aa ca bb aa ae fb ac a ac ea ae cc eae ae ea a ca ea c ac a a ca ae a ea ca ae a ea ac ae a ca ac a ea ca ae a ea ac ae a ca ac a ``` <!-- end of image --> Let's see what secrets area A holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#0909ffff b,#ff0404ff c,#6262ffff d,#ff3c3cff e,#babaffff f,#ffc4c4ff g,#ff8080ff ``` ```image dg bbbdf gdbbbbgf fgbbbbdf fdbbbf fdbbd gbbbf fdbbg gbbdf fbbbg dbbd gbbbf fdbbg e gbbdf eaae fbbbg eaaaa dbbd caacaac gbbbf caac eaae fdbbg caae caae gbbdf caae caa fbbb aaae aac db aae eaae g a caa aac eaac eaae caa ``` <!-- end of image --> Hmm, it seems there's no intersection in area A after all. The image is completely devoid of intersections. Zero.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0505ffff b,#ff0707ff c,#7f7fffff d,#ff5858ff e,#c3c3ffff f,#ffb1b1ff g,#3e3effff ``` ```image f dbbf fbbd dbbf bbb fbbd dbbf fbbd dbbf bbd fbbf dbbf fbbd dbbf fbbd db fbd bb fbf e bb aa db acea fbd ae gg bb eae ae fbf ea a bb ca ea db ga gg bd ga ae bb ag a fbf ag ca bb ac ac dbf ae a bd eae ea db ca gg fbd ca ae bb ga a dbf aa ea bd ag gg db ac ae fbd ac a bb eae ca fbf ea ac bb ca a db ga ea bd ga ga bb aa ac fb ag a ac ea ae gg eae ae ea a ca ca g ac ae ea ca ac a ea gg ae a ca ag ae a ca ac a ea gg ae a ea gg ae a ca ac a ``` <!-- end of image -->

I have a feeling there might be some intersections in this image. I have a hunch that these areas might contain the intersections we're looking for. <!-- image --> ```palette Key,Color ,#fefefeff a,#0707fdff b,#fc0e0dff c,#b5b5ffff d,#ef7c75ff e,#575bf0ff f,#98c49aff g,#b1d6b0ff ``` ```image c ca aca ca ee a ac a a ac ca a ae ee a a ca ee ea a ac ca a a ca ca ae ac a a a ac ea b a ac db ee a bb a ca bd ee ae b a ac b ca a db a ea bb ca ac bd ac a b a ca b ac ee db a ac bd ee a bdggggggggggaggf ea fbgggggggggeeggg ae ffbggggggggagggg a fgdbggggggeagggg ca fggbdgggggaggggg ea fgggbfgggfaggggg afgggggggggggggf fggggbgggafggggg fagggggggggggggf fggggdbggagggggg geaggggggggggggf fgggggbbaegggggg ggaegggggggggggf d fggggggbaggggggg gggagggggggggggfgbb fggggggeefgggggg gggfaggggggggggbb fggggggagbgggggg ggggeagggggggbbf fgggggeegdbggggg gggggaeggggbbdgf fgggggagggbbgggg ggggggaggdbdgggf fggggeaggggbdggg ggggggeabbgggggf fggggaggggggbggg gggggfbaeggggggf fgggfaggggggfbgg ggggbbggafgggggf fgggafgggggggdbg ggbbdggggagggggf fgggagggggggggbb bbdggggggeaggggf fggaeggggggggggbd dbbgggggggggaegggf gffaffffffffffffb dbb gggggggggggagggf ee b bb gggggggggggfaggf a db bb ggggggggggggaegf ee bd bbd gggggggggggggaff a bg dbd ggggggggggggggaf ca b dbb ffffffffffffffea a gb gbb ae ca db bb a ac bd bbg ca a b bbd ea ac b dbd a a db dbb ee bbb a ee a ca a ca ac a ac a ee a ee 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,#0504feff b,#fe0606ff c,#9e9bfbff d,#f9464bff e,#504bfaff f,#fe9a9bff g,#eed6e7ff ``` ```image bf gaag bbf eae dbbg gaag dbd eae gbbd aac gbbf cae fbbg aac dbbg caa dbd aac gbbd caa fbbf eac fbbg gaag dbbg eae bbd gaag gbbf eae fbbf aac fbbg cae dbbgaac bbdaa gbaac caaf eaebg gaadbd eaegbbd gaag gbbf eae fbbf aac dbbg cae dbd aac gbbd caa fbbf eac fbbg caa dbbg eae dbd gaag gbbd eae fbbf gaag fbbg eae dbb aac bbd cae gbb aac fb ``` <!-- end of image --> There is an intersection point visible in this close-up of area A. Time to investigate another area. Here's a close-up of the area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#0504feff b,#fe0607ff c,#7878ffff d,#fc575aff e,#3834fbff f,#ffb7b7ff g,#c0bffeff ``` ```image aac gaag caa eae gaac caag eae aac gaag caa eae gaac d gaag dbb cae fbbbd eac fbbbbf gaag fdbbbf caag fdbbbd eae dbbbd aac dbbbdf gaadbbdf feaabf fdbbaae dbbbdgaac dbbbd caag fbbbdf eae fbbbbf aac fdbbbf gaag fdbbbd caa bbbd eae bdf gaac f caag eae aac gaag caa eae gaac gaag cae eac ``` <!-- end of image --> There is an intersection point visible in this close-up of area B. After a thorough search, I conclude that there are two intersections.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0605feff b,#fe0808ff c,#8888ffff d,#ff5353ff e,#4541fbff f,#ffadadff g,#c8c8ffff ``` ```image g ca aga ga ee ag ag a a ag ca a ac ec a a ga ee ee a ag ca a a ca ga ae ag ag a ga ag ea b a ac fb ec a db a ga bf ce ee b a ag b ca a fb a ca bd ga ac bf ag a b a ga fb ac ee db a ag bd ec a bf a ca b ce ac fb a a db ca ga bd a ee bf ga ag b ag a fb a ca dbac ae f ba ag fbb ee ga bb a b ea bbf ce fb ac dbf a dd a dbd ca bf gabd a b fbae ga b bb ag ag db bbf a a bd dbf ca ac bf dbd ac a b fbb a ec fb bb ga a db bbf ee ce bd bbf ag a bf dbd a ca b fbd ca a fb fbb ac ga db bb a ag bd bbf ga a bf dbf ee ac b dbd a a fb fbd ec dbb a ce a ca a ga ag a ac a ec a ce a ca a ``` <!-- end of image -->

I have an image in front of me. I need to determine if there are any intersection segments. I have a hunch that these areas might contain the intersections we're looking for. <!-- image --> ```palette Key,Color ,#fefefeff a,#0909feff b,#fe0505ff c,#5f64f5ff d,#f4a29dff e,#bbbbfeff f,#f04847ff g,#aed5afff ``` ```image d ff b b ff bd b fb bd b db bd b db bd b db bf b db a ff ea b ae b a ff ca bd a b ea fb ac bd c a b ea ca db ea a bd a ea b ae ac db ac a bd ca ca b ca ae db ea ea ff a ac b ae a b ac ca ff aa ae b ca a b ea ac ff a a bd ae ca b ggggggggggggggggggacgg ae db gggggggggggggggggacggg a bd ggggggggggggggggcagggg ac b gggggggggggggggcaggggg a db gggggggggggggggagggggg ea bd ggggggggggggggaggggggg ae b gggggggggggggacggggggg a db ggggggggggggacgggggggg cc bfddd gggggggggggaaggggggggg a fffbbbbbbbbbbbbbbbbbbfabffffffdddd ea ggggggggggagdddffffffbbbbbbbbbbbb ae gggggggggagggggggggggg a ggggggggaggggggggggggg cc gggggggacggggggggggggg a ggggggaagggggggggggggg ea gggggcaggggggggggggggg ae ggggcagggggggggggggggg a ggggaggggggggggggggggg cc gggagggggggggggggggggg a ggacgggggggggggggggggg ea ac ae ca a ea cc ea a a ea ae ae ac a ca ca ca a ea ea a ae ae a ac ca ac aca ea ``` <!-- end of image --> This close-up might reveal an intersection in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0606feff b,#fe0202ff c,#ababfeff d,#ff9f9eff e,#a00563ff f,#ff5252ff g,#4e4dfeff ``` ```image caac caac caag aag gag gaa gaac caac caac aag aag gaa gaac caac caac caag aag gaa ffffffdddddddddd gaa bbbbbbbbbbbbbbbbbbbbbeaaebfffffffffdddddddd dddddfffffffffbbbbbbeaaebbbbbbbbbbbbbbbbbbb caag ddddddddddfffffffff aag gag gaa gaac caac caac aag aag gaa gaac caac caac caag aag gaa gaa caac caac ``` <!-- end of image --> Yes! I knew it! There's an intersection right here in area A! One intersection, that's it, but I found it.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0404feff b,#ff0606ff c,#7f7fffff d,#ffa5a5ff e,#c6c6feff f,#fa4b4fff g,#3838ffff ``` ```image d ff b b ff bd b fb bd b db bd b db bd b db bf b db a ff ea b ac b a ff cg bd a b ea fb ac bd c a b ca cg db ea ae bd a ea b ae ac db ac a bf gg cg b ca ae db ea ea bf a gc b ae a b ac ca ff gg ae b ca ea b ea gc fb a a bd ae ca b ac ae fb ag a bd ga gc b ca a db ea ca bd a ae b ae a db ac gg bfddd gg a fffbbbbbbbbbbbbbbbbbbfabffffddddd ca ea dddddffffbbbbbbbbbbbb ae a a ae gg ac a gg ea ca ae ea a a gg ae a ac ea ag ae ga a ca gg ea a a ea ae ac ac a gg cg ca a ea ea a ac ae a ac cg gg aga ea ``` <!-- end of image -->

Based on a first glance, I suspect there could be intersection regions here. Could these regions be concealing intersection points? Let's find out. <!-- image --> ```palette Key,Color ,#fefefeff a,#0404feff b,#f64544ff c,#a1a4f7ff d,#ff9393ff e,#3f41f9ff f,#fc0706ff g,#add5adff ``` ```image d bffffbd dbffffbd dbffffbd dbffffbd dbffffbd dbffffbd dfd c fd aa fd eac fd cae fd aa fb eac fb gggggggggggggggg cae fb gggggggggggggggg aa fbgggggggggggggggg eac fbggggggggggggggg cae fbgggggggggggggg aa gfbggggggggggggeac ggfbgggggggggcae gggfbgggggggaagg ggggfbggggeacggg gggggfbgcaeggggg ggggggfaaggggggg gggggeabfggggggg gggcaeggffgggggg ggaagggggffggggg eacgggggggffgggg caeggggggggggffggg aa ggggggggggggffgg eac gggggggggggggbfg cae ggggggggggggggbf aa gggggggggggggggbf eac ggggggggggggggggbf ee gggggggggggggggg bf ca bf a bf a bf ac bf ee bf ca bf a df ac df ae df ea df ca df a df ac df ee df ca df a d a ac ea ca a ac ae ca a a ac ee ca a ac ae ea ca a ac ee ca a a ac ea ca a ac ``` <!-- end of image --> I'm going to scrutinize area A for any signs of an intersection. <!-- image --> ```palette Key,Color ,#fefefeff a,#0404feff b,#fc3032ff c,#8787ffff d,#ffd4d4ff e,#3e34f5ff f,#ff0606ff g,#cfcdfcff ``` ```image b fb ffb dffb dffb dffb dffb dffb c dffb caa dffb geaae dffb caaac dffb caaaeg dffb geaaeg dffb caaac dffb caaaeg dffbgeaaeg dbeaaac caaaeg geaaebfbd caaac dbfbd caaaeg dbfbd geaaeg dbfbd caaac dbfbd caaaeg dbfbd geaaeg dbfbd caaac dbfbd aaeg dbffd eg dbffd bffd bffd bff bf b ``` <!-- end of image --> There is an intersection point visible in this close-up of area A. I've found a single intersection point in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0404feff b,#fd4647ff c,#8e8effff d,#ff9393ff e,#4444ffff f,#fe0606ff g,#bbbbffff ``` ```image d bffffbd dbffffbd dbffffbd dbffffbd dbffffbd dbffffbd dfd g fd aa fd eag fd gae fd aa fb eag fb gae fb aa fb eag fb gae fb aa fb eag fb cae fb aa fb eag fb cae faa eabb cae ff aa ff eag ff cae bf aa bf eag bf cae bf aa bf eag bf ee bf ca bf a bf a bf ac bf ea bf ga bf a df ag df ae df ca df ga df a df ac df ee df ca df a d ag ac ea ga a ag ae ca ga a ac ee ga a ag ae ea ga a ag ee ca a ag ac ea ga a ag ``` <!-- end of image -->

The hunt for intersections begins! Let's analyze this image closely. These regions highlight areas that look suspicious. Lines seem to converge within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#4547faff b,#f93836ff c,#0404feff d,#ef9f98ff e,#a2a6f6ff f,#afd6afff g,#fe0202ff ``` ```image ace c ce ce ce ec ce c ca aa ca c ca ce ca ec ca c ca aa ca c ca ce ca ec cc c cc aa ac c ac ce ac ec ac c ac aa ac c dg ac ce gbb ac ec gd gd ec c bb g ec aa dg dg ec c g bb ec ce gd gd ec ec bb g ec c dg g ec aa g bg ec c gd gd ec ce bb g c ec dg g c c g dg c aa gd gb c c bb g ce ce dg g ce ec g dg ce fffffffffffcfffffffffgd bb ce ffffffffffaaffffffffbb gd ce ffffffffffcffffffffdgf g ce fffffffffceffffffffgff dg c ffffffffecffffffffgdff bb ffffffffcffffffffbbfff gd fffffffaafffffffdgffff g fffffffcffffffffgfffff dg ffffffcefffffffgdfffff bb fffffecfffffffbbffffff gd fffffcfffffffdgfffffff g ffffaafffffffgffffffff dg ffffcfffffffgdffffffff bb fffceffffffbbfffffffff gd ffecffffffdgffffffffff g ffcfffffffgfffffffffff g faaffffffgdfffffffffff bg fcffffffbbffffffffffff gd cefffffdgfffffffffffff g ecffffffgffffffffffffff g cffffffgdffffffffffffff dg fffffbbfffffffffffffff gb ffffdgffffffffffffffff g ffffgfffffffffffffffff g fffgdfffffffffffffffff dg ffbbffffffffffffffffff bb fdgfffffffffffffffffff gd fgffffffffffffffffffff g gdffffffffffffffffffff dg bbfffffffffffffffffffff bb d gd g dg bb gd g dg bg gd g ``` <!-- end of image --> Eureka! Let's inspect this close up of area A <!-- image --> ```palette Key,Color ,#fefefeff a,#6161ffff b,#ff3737ff c,#0808feff d,#ffbcbdff e,#c4c4ffff f,#ff7171ff g,#ff0505ff ``` ```image acc dg ecce gg aca bgb ecce fggd cca dggd acc ggf ecce bgb aca fggd ecce dggd cca ggf acc bgb ecce fggd aca dggd ecce ggf cca bgb acc fggd ecce dggd aca ggf ecce bgb cca fggd acc dggd ecce ggf aca bgb ecce fggd cca dggd acc ggf ecce bgb aca fggd ecce dggd cca ggf acc bgb ecce fggd aca dggd ecce ggf cca bgb acc fggd ecce dggd aca ggf ecce bgb cca fggd cc dggd ee ggf bgb fggd dggd ggf bgb fggd dggd ggf bgb fggd dggd ggf bgb fggd dggd ggf bgb ``` <!-- end of image --> Unfortunately, there's no intersection inside area A. I'm extremely confident. No intersections at all.

<!-- image --> ```palette Key,Color ,#fefefeff a,#4b4bffff b,#ff3b3bff c,#0404ffff d,#ffc7c7ff e,#adadffff f,#ff9696ff g,#ff0202ff ``` ```image ace c ce ce ce ec ce c ca aa ca c ca ce ca ec ca c ca aa ca c ca ce ca ec cc c cc aa ac c ac ce ac ec ac c ac aa ac c dg ac ce gbb ac ec gf gf ac c bb g ec aa dg dg ec c g bb ec ce gf gf ec ec bb g ec c dg dg ec aa g bg ec c gf gf ec ce bb gd ec ec dg dg c c g fg c aa gf gb c c bb gd ce ce dg g ce ec g fg ce c gf bb ce aa bb gd ce c dg g ce ce g fg c ec gf bb c bb gd aa dg g c g dg ce gf bb ec bb gf c dg g aa g dg c gf bb ce bb gf ec dg g c g dg aa gf bg c bb gf ce dg gd ec g dg c gf fg bb gb dg gd g g gf fg bb bb dg gd g g gf fg bb bb f gf g dg bb gf g dg bg gf g ``` <!-- end of image -->

This image seems promising for intersection detection. Let's take a closer look at what's happening inside these zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0302ff b,#6e73f5ff c,#0b0bfbff d,#ea8c83ff e,#b1d6b2ff f,#f33633ff g,#96c798ff ``` ```image b cc eggggggggggggggggggggggggggccg geeeeeeeeeeeeeeeeeeeeeeeegcbee geeeeeeeeeeeeeeeeeeeeeeebceeee geeeeeeeeeeeeeeeeeeeeeecceeeee geeeeeeeeeeeeeeeeeeeeecceeeeee geeeeeeeeeeeeeeeeeeegcbeeeeeee geeeeeeeeeeeeeeeeeebceeeedfaaa geeeeeeeeeeeeeeeeeccdfaaaadeee geeeeeeeeeeeeeedfccafdeeeeeeee geeeeeeeeedfaaafcbeeeeeeeeeeee geeeedfaaafdeebceeeeeeeeeeeeee dfaaafdeeeeeecceeeeeeeeeeeeeee dfaaafdeeeeeeeeeecceeeeeeeeeeeeeeee dfaaafd geeeeeeeeegcbeeeeeeeeeeeeeeeee aaaafd geeeeeeeebceeeeeeeeeeeeeeeeeee fd geeeeeeecceeeeeeeeeeeeeeeeeeee a geeeeeecbeeeeeeeeeeeeeeeeeeeee ad egggggcbgggggggggggggggggggggg da bc a cc df cb a ece fd bc a cc ad cb ggggggggggggagge ece eeeeeeeeeeeaeeeg bc eeeeeeeeeedaeeeg cc eeeeeeeeeeaeeeeg cb eeeeeeeeeffeeeeg bc eeeeeeeeeaeeeeeg bc eeeeeeeeadeeeeeg cc eeeeeeegaeeeeeeg cb bbbbbbbbbbbbbcccccccccccccccccccccccc bbbbbbbbbbbbbbeeeeggggeedaeeeeeeeg eeeeeeaeeeeeeeeg eeeeeffeeeeeeeeg eeeeeaeeeeeeeeeg eeeeadeeeeeeeeeg eeegaeeeeeeeeeeg eeeageeeeeeeeeeg eedaeeeeeeeeeeeg ggagggggggggggge ff a ad a a da a df a fd a ae da a df a fd a ad da a df a fd a ad a a df a ff a ad a a ``` <!-- end of image --> Let's see if area A yields any clues. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0303ff b,#0606ffff c,#fd5a5cff d,#fd9394ff e,#d8d8ffff f,#fe2a2bff g,#ffcacaff ``` ```image caf gaag fac daa fad daf aad caf gaag fac daag fad daf aad caf gaag caceeeeeeeeeeeee bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb eeeeeeeeeeeeedaf aad caf gaag cac gaag fac daa aad caf gaag cac gaag fac daa aad ``` <!-- end of image --> I observe an intersection inside area A. Onward to the next region of interest. Time to investigate area B up close. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0405ff b,#4438f2ff c,#0605feff d,#ff9d9dff e,#918ffdff f,#fb5053ff g,#e6d6efff ``` ```image gccc eccbg bccb gbcce ecccg eccbg bcce gbcce ecccg eccbg bcce gbcce ecccg gdf eccbg ddfaaaaa bcce ddfaaaaaaaafd gccceddfaaaaaaaafddg ecccfaaaaaaafdd gddfbccbaaaafdd gddfaaaabccbfdd gdffaaaaaaafccce gdffaaaaaaaffdgecccg gdffaaaaaaaffdg eccb gdffaaaaaaaffdg gbcce dffaaaaaaaffdg gccce aaaaaffdg eccbg fddg eccb gbcce gccce eccbg eccb gbcce gccce eccbg bccb gbcce ``` <!-- end of image --> Oh my, look at that! It's an intersection in area B! The final answer is: two intersections found.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fe0404ff b,#6464ffff c,#0a09fdff d,#fe8081ff e,#b4b3feff f,#fd3f40ff g,#ffb8b8ff ``` ```image e cc cc ce bc cc cb ece bc gfaaa ccgfaaaad gfccafd gfaaafce gfaaafd bc dfaaafg cc dfaaafg cb daaaafg ece aaaafg bc fd cc a cb ag ece ga bc a cc df cb a ece fd bc a cc ag cb ga ece a bc da cc a cb ff ece a bc ag cc ga cb ebbbbbbbbbbbbbbcccccccccccccccccccccce bbbbbbbbbeeeeeeeeeeee da a ff a ad ga ag da a ff a ad a ag ga a ff a ad a ag ga a df a fd a ag ga a df a fd a ag ga a da a ff a ag ga a ``` <!-- end of image -->

This image seems promising for intersection detection. After a thorough analysis, I conclude that there are no intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0808ffff b,#ff0606ff c,#7979ffff d,#ffadadff e,#ff5858ff f,#3d3dffff g,#c1c1ffff ``` ```image c ca ca ca ca fa fa fa fa fa fa fa fa fa fa fa fa fa aa af af af af af af af af af af af af af af ac ac ac ac g ac faaaafc ac cfaaaafc ac gfaaaafcg ac gcaaaaacg ac gcaaaaacg ac gcfaaaaac gg bbbd debbbd dbbbed dbbbed deeb dbbbed debbbbbbed dbbbe deebbbbbedd ebbbe debbbbbbed ebbbe deebbbbbedd ebbbd debbbbbbed debbbbedd ``` <!-- end of image -->