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oliveirabruno01

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

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Let's examine this image for potential line intersections. The image has some tight areas where segments are too close. I should investigate those closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#0405feff b,#ea6760ff c,#9298f4ff d,#fc090aff e,#feb9b9ff f,#b0d6b0ff g,#4247f5ff ``` ```image fffffffffffffffffffffffffff fffffffffffffffffffffffffff fffffffffffffffffffffffffff c fffffffffffffffffffffffffff gaag fffffffffffffffffffffffffff caag fffffffffffffffffffffffffff caaac fffffffffffffffffffffffffff caaac fffffffffffffffffffffffffff gaag fffffffffffffffffffffffffff caag fffffffffffffffffffffffffff caaacffffffffffffffffffffffffff caaagfffffffffffffffffffffff fffgaagffffffffffffffffffff ffffffgaagfffffffffffffffff fffffffffcaaabfffffffffffff ffffffffffffdadddddddddddbbee fffffffffffdbcafffffffffbbbbddddddddddbbeee fffffffffbdfffacfffffffffff eebbdddddddddddbbee ffffffffbdfffffafffffffffff eebbdd fffffffddffffffgaffffffffff ffffffdbffffffffacfffffffff fffffdbffffffffffafffffffff fffbdffffffffffffggffffffff ffbdffffffffffffffaffffffff fddffffffffffffffffafffffff ddfffffffffffffffffggffffff dbfffffffffffffffffffaffffff edeffffffffffffffffffffcafffff bd fffffffffffffffffffffagffff dd ffffffffffffffffffffffaffff db ffffffffffffffffffffffcafff db ac ede a bd ca dd ac dd a db gg ede a bd a dd gg dd a db ca ede ac bd a bd ca e ac a ca ac a gg a a gg a ca ac a ca ac a ca ac a gg a a gg a ca ac a ca ac a ca ac a gg a a gg 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,#fe6263ff c,#8f8fffff d,#fd0809ff e,#fdb4b6ff f,#ccccffff g,#4d4dfeff ``` ```image agf aaaagc fgaaaaagcf fcgaaaaacf fcgaaaaagf cgaaaaagc fgaaaaagcf fcgaaaaacf fcgaaaaageee cgaaaadddddddbbbbbeeee bdaaaddddddddddddddddddddbbbb bddbaac eeeebbbbbddddddddddd ddde caaf eeeebb eddde gag eddd faac bddb caaf bddb gag ddde faac eddde caa eddd aag bddb faaf bddb gaa ddde aac eddde faaf eddd gag bddb aac bddb caaf bdde gag eddde faac eddde caaf bddb gag bddb faac dde caa de aag e faaf gaa aac faaf gag aac caaf ``` <!-- end of image --> Incredible, there's actually an intersection in area A! The image features two intersection points.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0505ffff b,#ff5656ff c,#8989ffff d,#fd0608ff e,#fdadafff f,#cdcdffff g,#4545ffff ``` ```image c gaag caagf caaaf faaac fgaag caagf caaaf faaac fgaag caagf caaaee daddddddddddbbeee deca eeebbddddddddddbbee ed ac eebbbddddddddddbbee bd a eebbdd dd ca db af de a ed gg bd af dd fa db gg de a ede fa bd ac dd a db ca de ac ede a bd ca dd af db a db gg ede af bd fa bd gg dd a db fa ede ac ed a bd ca e ac a ca af a gg af fa gg a fa ac a ca ac a ca af a gg af fa gg a fa ac a ca ac a ca af a gg af fa gg a ``` <!-- end of image -->

I'm approaching this image with caution. Intersections might be tricky to spot. Could these regions be concealing intersection points? Let's find out. <!-- image --> ```palette Key,Color ,#fefefeff a,#4b4ef8ff b,#fe0505ff c,#9ea2f7ff d,#f5544fff e,#aed5aeff f,#f7a6a2ff g,#0606feff ``` ```image c g gc g g cg g aa g aa g gc fdb g fbbbbffbbf gc fdbbbdf dbb eeeeeeeeeeeecgee dbbbbf fbbf eeeeeeeeeeeegeee fdbbbd dbb eeeeeeeeeeeageee dbbbdf fbbd eeeeeeeeeeegeeee fbbbbd dbb eeeeeeeeeeaaeeee fdbbbdf fbbd eeeeeeeeeegeeeee bbbf dbb eeeeeeeeegaeeeee fbbdeeeeeeeegeeeeee dbbeeeeegceeeeee eefbbdecgeeeeeee eeeeedbgeeeeeeee eeeeeeagbbdeeeee eeeeeegeeedbbfee eeeeeaaeeeeefbbd eeeeegeeeeeeeeedbbf eeeegaeeeeeeeeee fbbd eeeegeeeeeeeeeee d eeegceeeeeeeeeee eeegeeeeeeeeeeee eegeeeeeeeeeeeee ecgeeeeeeeeeeeee egeeeeeeeeeeeeee aa g g cg aa ag g aa gc ga g gc g g cg g g cg aa ag g ga aa gc g gc gc g g g gc cg cg ag g ga cg gc g gc aa g g cg gc cg g ag gc ga cg gc g g cg g g cg aa cg g ag gc ga g gc gc g g g g cg cg ag g aa aa ga g gc aa g g ggc cg ``` <!-- end of image --> Could this be where the intersection is hiding, in area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#4141feff b,#ff0404ff c,#c9c9ffff d,#f4434dff e,#8484ffff f,#fdabacff g,#0505feff ``` ```image cggc aga cggc age egg gge egg ggc ega cggc aga cggc age egg gge f egg bbdf gge bbbbdf ega fdbbbbdf cggc fbbbbdf aga fdbbbbdf cggc fbbbbdfage fdbbdggf fggdbdf eggdbbbbdf gge fdbbbdf ega fdbbbbdf cggc fdbbbdf aga fdbbbb cggc fdb aga f cggc age egg gge ega cggc aga cggc aga cggc age egg gge egg ``` <!-- end of image --> My investigation has led me to an intersection in area A! I have found one intersection!

<!-- image --> ```palette Key,Color ,#fefefeff a,#3535ffff b,#ff0505ff c,#bebeffff d,#ff6060ff e,#7777ffff f,#febbbcff g,#0404feff ``` ```image e g gc cg gc cg g ea g ae g ge fdb g dbbbbdfbbd gc fdbbbdf dbb cg dbbbbf fbbd g fdbbbdf dbb ea fdbbbdf fbbd g fbbbbd dbbf aa fdbbbdf fbbd g bbbd dbbf ae fbbd g dbbf gc fbbd cg dbgf egbbd g dbbf ea fbbd g dbbf ae fbbd g d gc cg gc cg g ea a g cg ae eg g aa gc ge cg gc gc g cg cg g cg ea eg g aa ae ge g gc ge g g cg gc eg cg ag g ga ea ge g gc aa g g cg ae eg g ag gc ga cg ge g gc eg g g cg ea eg g aa ae ge g gc gc gc cg g gc cg cg eg g aa ea ge g gc ae g g ggc cg ``` <!-- end of image -->

Alright, let's get to work and investigate this image for intersections. These zones indicate regions where lines appear to be in close proximity. <!-- image --> ```palette Key,Color ,#fefefeff a,#0606feff b,#fd0909ff c,#4549f8ff d,#ef6d69ff e,#dfccebff f,#8a8df7ff g,#aed5aeff ``` ```image e fae a ae ea ea ae ea ea fa af fa a ca cf ca a ac cc ac a af fa ae a ae ea a ae ea a ea af fa a ca cf ca a ac cc ac a af fa af a ae ea ae ae ea a ea af fa a fa cf ca a ca fc ac a ac fa af a ae ea ae ae a a ggaggggggggggggg af ggfagggggggggggg a gggfaggggggggggg cf ggggcagggggggggg a gggggcaggggggggg fc ggggggaagggggggg a gggggggacggggggg fa ggggggggacgggggg a gggggggggafggggg ea ggggggggggafgggg ae gggggggggggagggg a gggggggggbbggggg af gggggggdbdgggggg a ggggggbbgggggggg cf ggggbbgggggggggg a ggdbdggggggggggg fc gbbggggggggggggg a dbdgggggggggggggg fa ebbgggggggggggggggg a bbe gggggggggggggggg ea dbd gggggggggggggggg ae bb a dbe af ebd a bb cf dbd a bb fc bbe a ebd fa bb ggggggggagggggggg dbd ggggggggagggggggg ebb gggggggaggggggggg bbe gggggggaggggggggg dbd ggggggafggggggggg bb ggggggagggggggggg dbe gggggccgggggggggg ebd gggggaggggggggggg edddbbbbbbbb ggggccgggggggggdddbbbbbbbbbbbdddee gggdabbbbbbbbbbbddee gggdagggggggggggg gggaggggggggggggg ggggggggggggggggg ggggggggggggggggg ggggggggggggggggg ``` <!-- end of image --> I'm determined to find out if an intersection exists in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0907fdff b,#fe0606ff c,#6767ffff d,#ff5d5dff e,#bebeffff f,#9a2b8fff g,#feb7b8ff ``` ```image eaa aac eaa cac eaae cac aae cac aae caa aae eaa aac eaa cac eaae cac aae cac gggg aae ggggdddddbbbbbbbbb dfaabbbbbbbbbbbbbbbbbbbbdd gbaafbbbbbbdddddgggg faagg aac eaa cc ``` <!-- end of image --> Amazing! This area was hiding an intersection all along! Alright, let's concentrate on the next area. I wonder what we'll find inside area B? <!-- image --> ```palette Key,Color ,#fefefeff a,#0805fcff b,#fe090aff c,#4949ffff d,#ff6464ff e,#c0c0ffff f,#8782f9ff g,#fbb6baff ``` ```image aac eaac eaac eaaf eaaf faaf faae caae caae caae caa aac eaac eaac eaac eaaf faaf faae faae caae caag gaaa dbbaf gbbbd gdbbbg dbbbd gbbbd dbbbg gbbbd gbbbbg dbbbg gbbbd dbbbg dbbbd gbbbdg bbbg bd g ``` <!-- end of image --> Wow! I can see an intersection so clearly in area B! There's for sure two intersections on the image you sent me.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0606feff b,#fe0808ff c,#4949ffff d,#ff6464ff e,#ccccffff f,#8e8bfcff g,#febabaff ``` ```image e fae a ae ea ea ae ea a fa ae fa a ca cf ca a ac cc ac a af fa ae a ae ea a ae ea a ea af fa a ca cf ca a ac cc ac a af fa af a ae ea ae ae ea a ea af fa a fa cf ca a ca cc ac a ac fa af a ae ea ae ae a a ea af ea a fa cf ca a ca fc ac a ac fa af a af ea ae ae ga a bb af dbd a bb cf bbg a gbd fc bb a dbg fa gbb a bb ea gbd ae bb a dbg af gbd a bb cf dbd a bb fc bbg a gbd fa bb a dbg ea gbb ae bb a gbd af bb a dbg cc gbd a ggddbbbbbbbb fc ggdddbbbbbbbbbbdddgg dabbbbbbbbbbdddgg fag a ``` <!-- end of image -->

I'm curious to see if this image contains any intersection points. These zones are intriguing. I bet there's something interesting happening within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#e77469ff b,#343befff c,#fb0b0cff d,#0405feff e,#8c93f0ff f,#b2d7b2ff g,#a0caa0ff ``` ```image e bb de de d d ed bb de de d d ed bb db e de dd gggggdggggggggggggggggggggggggggggggggggggggg ede gffffgdfffffffffffffffffffffffffffffffffffffg dd gfffffedffffffffffffffffffffffffffffffffffffg ede gffffffbdfffffffffffffffffffffffffffffffffffg dd a gfffffffdbffffffffffffffffffffffffffffffffffg ede cccccaa gffffffffdefffffffffffffffffffffffffffffffffg dd acccccaafffffdgffffffffffffffffffffffffffffffffg ede gfgacccccaadffffffffffffffffffffffffffffffffg dd gfffffffgaccdccaafffffffffffffffffffffffffffg ede gfffffffffffbdgacccccaafffffffffffffffffffffg dd gffffffffffffdbfffffgacccccagfffffffffffffffg ede gfffffffffffffdeffffffffffgacgffffffffffffffg dd gffffffffffffffdgfffffffffffgcffffffffffffffg ede gffffffffffffffgdffffffffffffacfffffffffffffg db gfffffffffffffffedffffffffffffacffffffffffffg bde gffffffffffffffffbdffffffffffffcafffffffffffg db gfffffffffffffffffdbffffffffffffcaffffffffffbd gffffffffffffffffffdeffffffffffffcgfffffffgdb gfffffffffffffffffffdgfffffffffffgcffffffbdgg gfffffffffffffffffffgdffffffffffffacfffgdbffg gffffffffffffffffffffedffffffffffffccfbdgfffg gfffffffffffffffffffffbdffffffffffffcdbfffffg gffffffffffffffffffffffdbffffffffffbdcafffffg gfffffffffffffffffffffffdefffffffgdbffcfffffg gffffffffffffffffffffffffdgfffffbdffffgcffffg gffffffffffffffffffffffffgdfffedbffffffacfffg gfffffffffffffffffffffffffedfddfffffffffccffg gffffffffffffffffffffffffffbdbfffffffffffcafg gfffffffffffffffffffffffffffffffffffffffffcgg gffffffffffffffffffffffffffffffffffffffffffcg gggggggggggggggggggggggggggggggggggggggggggac ac cc ca c c fc ac ca ca c c ac ac ca cf c c ac cc ca cf c fc ac cc ca c c fc ac ca ca c ``` <!-- end of image --> This is a magnified view of the region A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe9899ff b,#4441fcff c,#fe0303ff d,#0505feff e,#8e8cfdff f,#f93e44ff g,#e6d6eeff ``` ```image bddg bddg ddb gddb gdde edde eddg bddg bdb gddb gdde edde ffaag eddg ccccccffaag bddg aaffccccccccffaag bdb gaaffccccccccffaaddb gaaffccccccfddbaag gaaffcfddfcccffaag gbddfccccccccffaag bddggaaffccccccccffaag bdb gaaffccccccccffaag gddb gaaffccccccccffag gdde gaaffcccccca edde gaafccg eddg fcf bddg gccf bdb gcca gddb acca gdde accg edde fccg eddg fcf bddg gccf bdb gcca gddb acca gb gdde accg edd edde fccg gbddb eddg fcf eddde bddg gccf gbddbg bdb acca eddde gddb acca gbddbg gdde fccg eddde edde fcc gbddbg eddg fcfeddde bddg gfdddbg bdb eddde gddb gbddbcca gdde eddde fccg edde gbddbg fcf eddg eddde gccf bddg gbddbg gcca bdb eddde acca gddb gdddb acca gdde eddde fccg edde gdddb fcf eddbdddg gccf bddde gcca bbg acca accg fccg fcf gccf ``` <!-- end of image --> I've cracked the case! This area contains the intersection. I've identified a total of two intersection points.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fd9697ff b,#5050ffff c,#fe0405ff d,#0707ffff e,#a3a3ffff f,#fb4144ff g,#f0dbeaff ``` ```image e bd db de d gd ed bd db de d gd ed bd db e de dd dg edb gd dd ed ede bd dd a db ede fccccfa de dd gafccccfa dg ede gafccccfad dd gaffdccfa ede bdgafccccfa dd db gafccccfg bde de gacg dd dg gc bde gd ac dd ed fc bde bd cf gdd db ca bdg de cg gdb dg gc bdg gd ac gdb ed fc bdg bd cdb db bdca de gdb c dg ddg gc gd edb ac ed dd ff bdb ca cg c gc ac ff ca cg gc ac fc cf ca cg gc ac fc cf ca cg gc ac ff ca cg c gc ac ff ca cg gc ac fc cf ca c ``` <!-- end of image -->

This is the image I'm working with. The goal is to count the intersections. My analysis shows there's absolutely no intersections in the image

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff3c3cff b,#3b3bffff c,#ff0c0cff d,#0404ffff e,#bfbfffff f,#ffa5a5ff g,#7c7cffff ``` ```image ff fffaaacccccccccccccca ffffaaacccccccccccccaaaffff accccaaafff ac ac ac ac ac ac ac ac ac ac ac ac ac ac ac ac ac ac ac ac ac ac ac ac ac ac ac ac ac ac ac ac ac ac ac f ddde edg eddbe bd eddb db gddg gde bddg dd bdde edg eddb bd gddb db gddg gde bdde dd ebdde edg eddb bd gddg edg gddg bd bdde db eddd gde e dd edg bd db gde dd edg bd db ``` <!-- 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,#fd0605ff b,#0a0bfbff c,#de998aff d,#b1d7b1ff e,#ea4943ff f,#95c69bff g,#6469deff ``` ```image ca aca ca ac a a a ea ac a a a ec ee a a ee a a ac ca a a ca ca ac a a a ca ac a a a ec ee a a ee daffffffffffffffffffff a dbg aeddddddddddddddddddd ca b bb daddddddddddddddddddd ffffffffffffffffffffffffffffa bg gbg dcadddddddddddddddddd dddddddddddddddddddddddddddca b bb ddacddddddddddddddddd dddddddddddddddddddddddddddaf b dbg dddaddddddddddddddddd dddddddddddddddddddddddddddad bg bb dddeadddddddddddddddd ddddddddddddddddddddddddddacd b bb ddddacddddddddddddddd ddddddddddddddddddddddddddadd b gbddddddaddddddddddddddd dddddddddddddddddddddddddeedd gb bbddddeedddddddddddddd dddddddddddddddddddddddddaddd b gbgdddadddddddddddddd ddddddddddddddddddddddddeeddd b ddbbddcaddddddddddddd ddddddddddddddddddddddddadddd gb dddgbgdaedddddddddddd dddddddddddddddddddddddcadddd b dddddbbdadddddddddddd dddddddddddddddddddddddaddddd bd ddddddgbgaddddddddddd ddddddddddddddddddddddcadddddgb ddddddddbbcdddddddddd ddddddddddddddddddddddacdddddb dddddddddfbbddddddddd ddddddddddddddddddddddadddddbg ddddddddddebbfddddddd dddddddddddddddddddddacddddgb dddddddddddacbbdddddd dddddddddddddddddddddadddddbf ddddddddddddadgbgdddd ddddddddddddddddddddeeddddbgd ddddddddddddeeddbbddd ddddddddddddddddddddaddddfbdd dddddddddddddadddgbgd dddddddddddddddddddeeddddbddd dddddddddddddcaddddbb dddddddddddddddddddaddddbgddd ddddddddddddddaeddddgbg ddddddddddddddddddcadddfbdddd dddddddddddddddaddddd bb ddddddddddddddddddaddddbfdddd dddddddddddddddcadddd bg dddddddddddddddddcadddgbddddd ddddddddddddddddacddd bb dddddddddddddddddacdddbdddddd dddddddddddddddddaddd bb dddddddddddddddddadddbfdddddd dddddddddddddddddeadd gbd ddddddddddddddddacddgbddddddd ddddddddddddddddddacd b ddddddddddddddddadddbdddddddd dddddddddddddddddddad dddddddddddddddeeddbgdddddddd dddddddddddddddddddee dddddddddddddddaddgbddddddddd ffffffffffffffffffffa ddddddddddddddeeddbdddddddddd a ddddddddddddddaddbgdddddddddd ee dddddddddddddcadgbddddddddddd a dddddddddddddaddbdddddddddddd ca ddddddddddddcadbgdddddddddddd ac ddddddddddddacfbddddddddddddd a ddddddddddddadbdddddddddddddd ca dddddddddddacbbdddddddddddddd ac dddddddddddafbddddddddddddddd a ddddddddddeebfddddddddddddddd ee ddddddddddagbdddddddddddddddd a dddddddddeebddddddddddddddddd a dddddddddabfddddddddddddddddd ee ddddddddcgbdddddddddddddddddd a ddddddddabddddddddddddddddddd ca dddddddcbgddddddddddddddddddd a dddddddebdddddddddddddddddddd dddddddbddddddddddddddddddddd ddddddbgddddddddddddddddddddd dddddgbdddddddddddddddddddddd dddddbedddddddddddddddddddddd ddddbgddddddddddddddddddddddd dddfbeddddddddddddddddddddddd dddbadddddddddddddddddddddddd dddcadddddddddddddddddddddddd dddaddddddddddddddddddddddddd ddddddddddddddddddddddddddddf ``` <!-- end of image --> I wonder what we'll find inside area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#fd080aff b,#0a08fdff c,#fd6365ff d,#b4b3feff e,#76048cff f,#feb8b8ff g,#645ffaff ``` ```image a fa ca faa cac faaf cac aaf caa aaf faa aaf faa cac faa cac aaf cac aaf caa aaf faa aac faa cac faa cac aaf aaf b caa gb aaf dbb faa bbg aac gbb faa dbbd cac bbg faa gbb cac dbbd aaf bbg cac gbb aaf dbbd caa gbg aaf dbb faa bbd aac gbg faa dbbd cac bbg faa gbb cac dbbd aaf bbg cac gbb aaf dbbd caa bbg aaf gbb faa dbbd aac bbg faa gbb cac dbbd faa gbg cac dbb aaf bbd cac gbg aaf dbbd caa bbg aaf gbb aa dbbd ac bbg fa gbb cc dbbd fa bbg ca gbb aa dbbd cac bbg aafgbb caa bbd aaf bg faa db aac bd faa gb cacdbb faafbbg cacgbb aadbbd cacbbg aagbb aabbg faebb aabbd fabbg cebb fabbd cebg ebb cbbd ebb gbbd bbg gbb dbbc bbe gbbc dbbaf bbec gbbaf dbbec bbeaf dbbaa deaf faa aac faa cc ``` <!-- end of image --> The close-up clearly shows an intersection point in area A. Time for a closer look at another area. I'm now examining the contents of area B in detail. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0405ff b,#0b08fcff c,#fe7a7bff d,#b6b5fdff e,#f9353bff f,#fec0c1ff g,#615dfaff ``` ```image ae aaf caa eac faaf cae aac faaf eae faac caa eae faaf caa eac faaf cae aac g faaf bbd eae bbbg aac gbbbd caa dbbbg eae gbbbd faaf dgbbgd caa dbbbg eac gbbbd faaf dbbbg cae gbbbdaac dbbbgaaf gbbbee dbbbbc gbbbd dbbbg febbbg cabbbbd eagbbbg faafgbbbd cae dbbbg aac gbbbd faaf dbbbg eae gbbbd aac dbbbg caa gbbbd eae dgbbg faaf dbb caa g eac faaf cae aac faaf eae aac caa eae faaf caa eac faaf cae aac faa ea a ``` <!-- end of image --> Wow! I can see an intersection so clearly in area B! The image features two intersection points.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fe0404ff b,#0706fdff c,#fe8384ff d,#aeaefeff e,#fb3b3eff f,#fec6c7ff g,#534af6ff ``` ```image f ca aca fa af af a a ce af af a a ec ee a a ce fa a ac ce a a ca fa ac af a a ca af af a a ec ee a a ce fa a dbd ec ce b bb a a bg dbg ca fa db bb ac af b dbg a a gg gb ca af b bg af a b gbd a ec gg bb ee a b gbd a ce bd bb fa a gb dbd ec ca b bb a a bd dbga fa db bbc af b dbg a bd cbbd ac db afbb a b a gbd ec bg ee bb a db af dbd ce b fa bb a gg ec dbg ca b a bb a b fa dbg fa gg ac gb af b a bg a bd ca gbd ac gb af b a b a ec bd ee a db af ce b fa a bd ee ca db a a b fa fa bg ac afdb a a b ca acgg af a b a ecbd ee agg af ceb fa abd ee cgb a ab fa fbd e eb b bg db bc bg dbe ba fa a ``` <!-- end of image -->

I have a feeling there might be some intersections in this image. I've examined the entire image, and there are zero intersections present.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0505ff b,#0404ffff c,#ff8181ff d,#b6b7ffff e,#ff3d3dff f,#ffc5c5ff g,#5f5fffff ``` ```image f ee a fa ec a fa ac a fa ac a fa ac a fa ac a ca fa ac ca a ea ca ae ac ac a faf ca ca ac ea a aa ca ae af ac a faf ca ca af ea a ae ca ac af faf a ca ce ea af aa a ae ee ac af faf a ca ee ea b af ae db a ac db ee faf db af ca db fa ea db ee aa db af ae db fa faf db ee faf db a ea db fa aa db eae db f db db db db db db db db db db dbb db dbbbd db gbbg db gbbg db gbbg db gbbg db gbbg db gbbg db gbbg db dbbbd db dbbbd db dbbbd db dbbbd db dbbbd dbbd ``` <!-- end of image -->

Based on a first glance, I suspect there could be intersection regions here. It's crucial to examine these regions more closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#0a09fbff b,#da6e5cff c,#5a64e9ff d,#b9b9feff e,#b0d7b1ff f,#97c39bff g,#fd0403ff ``` ```image d caa fffffffffffffffffffffffffffffffaacfcafffffffffffffe eeeeeeeeeeeeeeeeeeeeeeeeeeeeeaaceeeeaeeeeeeeeeeeeef eeeeeeeeeeeeeeeeeeeeeeeeeeeaaceeeeeecaeeeeeeeeeeeef eeeeeeeeeeeeeeeeeeeeeeeefaaceeeeeeeeeafeeeeeeeeeeef eeeeeeeeeeeeeeeeeeeeeefaafeeeeeeeeeeefaeeeeeeeeeeef eeeeeeeeeeeeeeeeeeeefaafeeeeeeeeeeeeeeaceeeeeeeeeef eeeeeeeeeeeeeeeeeecaafeeeeeeeeeeeeeeeeeaeeeeeeeeeef eeeeeeeeeeeeeeeecaaeeeeeeeeeeeeeeeeeeeeaceeeeeeeeef eeeeeeeeeeeeeecaaeeeeeeeeeeeeeeeeeeeeeeeaeeeeeeeeef eeeeeeeeeeeecaaeeeeeeeeeeeeeeeeeebggggggaaggggggggggggggggggggggggggggggggggggg eeeeeeeeeecaceeeeeeeeeeeeeeeebggggbeeeeeeaeeeeeeeef eeeeeeeeaaceeeeeeeeeeeeeebgggbfeeeeeeeeeecaeeeeeeef eeeeeeaaceeeeeeeeeeefbgggbeeeeeeeeeeeeeeeeaeeeeeeef eeeeaaceeeeeeeeebggggbeeeeeeeeeeeeeeeeeeeefaeeeeeef eeaaceeeeeeebggggbeeeeeeeeeeeeeeeeeeeeeeeeeafeeeeef daaceeeefbgggbfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeef afeebggggbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaceeeef bggggbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeef bfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecceeef a ca a da ad a ad a cc a ca a da ad da ad a ac a ca a da a da ad a ac a cc a da a da ad a ac a cc a ca a da ad a ad a cc a ca a da ad da ad a ac a cc a ``` <!-- end of image --> I'm analyzing this close-up of area A with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#0404feff b,#fd4b4dff c,#7a7affff d,#b9b8fdff e,#fea9a9ff f,#3835fcff g,#fe0404ff ``` ```image dfaaac caf dfaaac aad cfaaac caf caaaac aac caaaac daa caaafd fac caaafd daa dcaaafd faf dfaaafd daad dfaaafd caf dfaaafd aad dfaaacd caf dfaaac aac dfaaac caa caaaac fac caaaac daa caaafc fac caaafd eeeedaadeeeeeeeeeeeeeeee caaafd ebbgggggggggggfafgggggggggggggggg dcaaafd ebggggggggggggggggbaabbbbbbbbbbbbbbbb dfaaafd eebggggggbbe caf dfaaafd eebggggggbbe aad dfaaacd ebbggggggbee caa dfaaac eebgggggggbe fac dfaaac eebggggggbbe daa cfaaac ebbggggggbee fac caaaac ebgggggggbee daad caaaac eebggggggbbe faf caaafd eebggggggbbe daad caaafd ebbggggggbee caf dcaaafd eebgggggggbe aad aaafd eebggggggbbe caa afd ebbggggggbee fac ebgggggggbee daa ebggggggbbe fac ggggbbe daad bee faf ``` <!-- end of image --> I've cracked the case! This area contains the intersection. One intersection, that's it, but I found it.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0303ffff b,#ff4747ff c,#7b7bffff d,#c2c2ffff e,#ffa2a2ff f,#3631f9ff g,#ff0101ff ``` ```image d faa fac cf fac a aac ca daad ad daad da daad ad daa a caa fc caf a caf ebgggggffggggggggggggggggggggggggggggggggggggg faf egggbe a fac bgggbe ca fac ebgggb a aac ebggge da aac egggbe ad daad bgggb a ad ebggge fc egggbe a be ff a cf a da ad a ac a fc a cf a da ad da ad a fc a cf a ca ad da ad a fc a cf a ca a da ad a fc a ff a cf a da ad a ac a fc a cf a da ad da ad a fc a cf 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,#fd0706ff b,#4441f1ff c,#f3554fff d,#8e94f2ff e,#efa49dff f,#afd6afff g,#0405feff ``` ```image d bg gd gg dgd gb bg gd gg dgd gb bg dgd gg dg gb bg fffffffffffffffffffffff dgd fffffffffffffffffffffff gg ffffffffffffffffffffffc dg fffffffffffffffffffffea gb fffffffffffffffffffffaf bg ffffffffffffffffffffacf dgd fffffffffffffffffffcaff gg fffffffffffffffffffafff bg ffffffffffffffffffaefff gb fffffffffffffffffacffff bgb ffffffffffffffffeafffff dgggb ffffffffffffffffaffffff dgggd fffffffffffffffacffffff bgggd ffffffffffffffcafffffff bgggd ffffffffffffffaffffffff dbggbdffffffffffffaeffffffff dgggbffffffffacfffffffff fffbgggbfffeaffffffffff fffffffbgggbfffffffffff ffffffffffabgggdfffffff fffffffffcafffdbgggdfff fffffffffaffffffffdgggb ffffffffafffffffffffffd fffffffacffffffffffffff ffffffeafffffffffffffff ffffffaffffffffffffffff fffffacffffffffffffffff ffffcafffffffffffffffff ffffaffffffffffffffffff fffafffffffffffffffffff ffacfffffffffffffffffff feaffffffffffffffffffff fafffffffffffffffffffff aefffffffffffffffffffff caffffffffffffffffffffff afffffffffffffffffffffff a fffffffffffffffffffffff ac fffffffffffffffffffffff ea a ae ca a a ac ea a ae ca a a ac e ea caac a eaaae ae ecaac cc caaae ea eaaac a caace ac eaaae ea caac a eaaae ae ecaac cc caa ``` <!-- end of image --> Eureka! Let's inspect this close up of area A <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0606ff b,#5958fdff c,#f63941ff d,#ff7d7dff e,#fec3c3ff f,#acacffff g,#0606feff ``` ```image d ea aa caa eaae eaad cac daae eaae aad cac daae eaad cac daa eaae aad cac daae eaad cac daa eaae aad cac bf daae gggbff eaad bggggggbf cac ffbggggggbf daa ffbggggggbf eaae fbbgggggbbf aad fbgggggggcc fbggggggbff eacbggggggbf cac ffbggggggbf daa fbbggggggbf eaae fbbgggggbbf aad fbgggggg cac fbgg daae eaad cac daa eaae aad cac daae eaad cac daa eaae aad cac daae eaad aac daa eaae eaad cac daae eaae aac aa ae d ``` <!-- end of image --> Case closed! This is definitely an intersection point in area A. One intersection, that's it, but I found it.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fe0607ff b,#3b39fdff c,#fb5155ff d,#7f7fffff e,#ffacacff f,#c2c2ffff g,#0303feff ``` ```image d bg fgd gg dgf gb bg fgd gg dgf gb bg fgd gg dgf gb bg fgd gg c dgf ea gb a bg ae fgd ca gg a dgf ae gb cc bgbf ea dgggd a dgggd ae dgggd ca fbggbf a fbggbf ae dgggbf cc dgggd ea dgggc abgggd ca fbggbf a fbggb ae d ac ea a ae ca a a ac ea a ae ca a a ac ea a ae ca a a ac ea a ae ca ea a ac e ea caac a eaaae ae ecaac cc caaae ea eaaac a caace ac eaaae ea caac a eaaae ae ecaac cc caa ``` <!-- end of image -->

This image seems promising for intersection detection. There are 2 areas where the lines seem to converge. We should take a closer look at area A,, and B. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd0807ff b,#0303feff c,#f6a09cff d,#5f62f9ff e,#f45852ff f,#efeef0ff g,#afd6b0ff ``` ```image ffffffffffffffffff fffdffffffff fgggggggggggggggggg gggdbbggggggf fgggggggggggggggggg ggggggbbdgggf fgggggggggggggggggg ggggggggdbbgf fgggggggggggggggggg gggggggggggbbd fgggggggggggggggggg ggggggggggggfdbbf fgggggggggggggggggg ggggggggggggf fbbd fgggggggggggggggggg ggggggggggggf dbbf fgggggggggggggggggg ggggggggggggf fbbd fgggggggggggggggggg ggggggggggggf dbbg fgggggggggggggggggg ggggggggggggf fbbd fgggggggggggggggggg ggggggggggggf dbbg fgggggggggggggagggg ggggggggggggf fbbd fggggggggggggaegggg ggggggggggggf dbbd fgggggggggggcaggggg ggggggggggggf fbbdffffffffffffffffffffffffffffffgggggggggggagggggg gggeggggggggf dbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbgggg gggeegggggggf fggggggggggaggggggg ggggagggggggf fgggggggggagggggggg ggggeaggggggf fggggggggeagggggggg gggggaggggggf fggggggggaggggggggg gggggcagggggf fgggggggacggggggggg ggggggacggggf fggggggeagggggggggg gggggggaggggf fggggggaggggggggggg gggggggaegggf fgggggaeggggggggggg ggggggggagggf fggggcagggggggggggg ggggggggeeggf fggggaggggggggggggg gggggggggaggf fgggaeggggggggggggg gggggggggeagf fgggagggggggggggggg ggggggggggagf fggaggggggggggggggg gggggggggggaf fgeaggggggggggggggg gggggggggggac fgagggggggggggggggg gggggggggggga acffffffffffffffff ggggggggggggae ca a a ee ac a ca ca af af ee fa fa ac af a ea ee a a ac ca ca af a ca ac ac ca fa af ac ee a fa ee af a ea ca a af ac fa ca ac a a ae ee ca a af ea ee af fa ca af af ea fa a ac ac a ca ee a a ae ca fa af af ca ee ac fa fa af ae ea a a ee ac a ca ca a aae fa ``` <!-- end of image --> This close-up of area A is like examining a piece of evidence. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff0404ff b,#0606ffff c,#ff8585ff d,#5152ffff e,#ff4242ff f,#afafffff g,#ffcbcbff ``` ```image bbdf fdbbbbdf fbbbbdf fdbbbbdf fbbbbdf fdbbbbdf fbbbb fdb cc gaag eae gaag eae gaag cae aac caa eac gaag eae gaag cae aac caa aac caa eac gaag eae gaag cae aac caa eac gaag eae gaa ea ga c ``` <!-- end of image --> Area A is clear of intersections, but the search continues. Let's shift our focus to the next area. This close-up might reveal an intersection in area B. <!-- image --> ```palette Key,Color ,#fffefeff a,#fe0404ff b,#0303feff c,#ffa0a0ff d,#fd6769ff e,#fd3435ff f,#e6e5feff g,#ffdadaff ``` ```image g gad eae caag gaac dae caag aad fffffffffffffffffffffffdaeffff bbbbbbbbbbbbbbbbbbbbbbbbbbbbbb bbbbbbbbbbbbbbbbbbbbbbbbbbbbbb daa gaac eae caag gaac dae caag aad dae gaac ead daag gaac eae caag gaac dae caag ead dae gaac ead caag gaac eae caag gaac dae caag ead ``` <!-- end of image --> I am surprised, so clear, an intersection has appeared in area B. There's only one, but is an intersection after all.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fe0606ff b,#0404feff c,#ff8989ff d,#6868ffff e,#ff4747ff f,#dedefeff g,#ffcacaff ``` ```image d dbbf fbbd dbbf fbbd dbbf fbbd dbbf fbbd dbbf fbbd g dbbf a fbbd ac dbbd ga fbbbfffffffffffffffffffffffffffffffffffffffffaff c dbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb ee ga a ag ca ee a a ga ag ag ca a a ac ac a ga ee a a ee ca ga ag ag ga ee ag a a ag ec ca a a ce ac a ga ca a ag ee ga ga ac ag a ee ee a a ag ca ca a a ga ac ag ga a a ac ee a ga ee ag a ea ca a ag ac ga ca ac a a ac ee ga a a ce ee a a ga ag ag ca ga a ac ac a ca ee a a ac ca ga a a ga ee ag a a ag ac ca a a ee ac a ca ca a aac ga ``` <!-- end of image -->

I'm ready to tackle this image and find those intersections! These spots mark what I'd call 'danger zones' - areas where intersections are more likely. <!-- image --> ```palette Key,Color ,#fefefeff a,#0909fcff b,#fd0202ff c,#565eeeff d,#eb8b82ff e,#afd6afff f,#a5a9f7ff g,#f53a35ff ``` ```image f fa fa fa a c a ca a aa af ac af af af a ac a ac fa aa ca ca aa ca ac ca af fa a fa a fa fa a ca a ac af ac af af af a ac a ac fa ac ca eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaaeeeee ac eeeeeeeeeeeeeeeeeeeeeeeeeeeeeaaeeeeee ac eeeeeeeeeeeeeeeeeeeeeeeeeeeecaeeeeeee dgbbb af eeeeeeeeeeeeeeeeeeeeeeeeeeecaeeeeeeee dgbbbbgd a eeeeeeeeeeeeeeeeeeeeeeeeeecaeeeeeeeee dgbbbbgd aeeeeeeeeeeeeeeeeeeeeeeeeefaeeeeeedgbbbbgd faeeeeeeeeeeeeeeeeeeeeeeeeaedgbbbbgdee caeeeeeeeeeeeeeeeeeeedgbabbgdeeeeeeee eaaeeeeeeeeeeeedgbbbbgdaeeeeeeeeeeeee eeaceeeeeeeebbbgdeeeeeaeeeeeeeeeeeeee eeeafeeeeeebeeeeeeeeeafeeeeeeeeeeeeee eeeeaeeeeebdeeeeeeeeaceeeeeeeeeeeeeee eeeeeaeeebgeeeeeeeeaceeeeeeeeeeeeeeee eeeeecaegbeeeeeeeeaceeeeeeeeeeeeeeeee eeeeeecabeeeeeeeeaaeeeeeeeeeeeeeeeeee eeeeeeeaceeeeeeeaaeeeeeeeeeeeeeeeeeee eeeeeebeaceeeeecaeeeeeeeeeeeeeeeeeeee eeeeebdeeaeeeecaeeeeeeeeeeeeeeeeeeeee eeeebgeeeeaeecaeeeeeeeeeeeeeeeeeeeeee eeegbeeeeeeacaeeeeeeeeeeeeeeeeeeeeeee eedbeeeeeeecaeeeeeeeeeeeeeeeeeeeeeeee eebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee ebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee bdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee gg db db b b bd gg db db b b bd gg db b b b bd gg db b b bd bd gg db b b bd ``` <!-- end of image --> This is a magnified view of the region A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0907fcff b,#fe0405ff c,#9c9cffff d,#fe9b9bff e,#5454feff f,#e8d7eeff g,#fc4648ff ``` ```image faae faae faaaf eaaf eaaf eaaf eaaf eaac caac caac caac caae fd e caae fddggbbb ac faae fddggbbbbbbbbg aac faae fddggbbbbbbbbggddf eaaf faaagbbbbbbbbggddf eaaf fddggbaaabbbbggddf eaa fddggbbbbbbaaagddf faae fddggbbbbbbbbggdaaaf faae ddggbbbbbbbbggddf eaaf caac fbbbbbbbggddf eaaf caac gbbgddf eaac eaaf gbbf eaac eaaf dbbf caac eaa dbbd caac faae fbbd caac faae fbbg caae caac gbg caae caac gbbf faae eaafdbbd faae eaabbd faae aaag faaa fgaae aaaf gbgaae eaaf gbbfcaac eaaf dbbd caac eaaf dbbd eaaf eaac fbbg eaaf eaac fbbg aaa caac gbb faae caac gbbf faaecaac dbbd caaaae dbbd caae fbbg cc bbg gbb gbbf dbbd ``` <!-- end of image --> Gotcha! I've found the intersection hiding in area A! I've identified a total of two intersection points.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0404feff b,#fe0303ff c,#7d7dffff d,#fe9f9fff e,#3a3afeff f,#c3c3ffff g,#ff4444ff ``` ```image c ca fa fa fa c a ca af ee af ac af af ac af ac a ae fa ee ca ea ee ea ac ca af ca a fa fa fa fa fa ca a ee af ac af af ac a ac fa ae fa ae ea ee ee ea ac ea dgbbb af ca dgbbbbgd a ca dgbbbbgd fa fa dgbbbbgd ca fa dgbbbbgd ea dgbabbgd ae dgbbbbgdaf ac bbbgd af af b af a bd ac fa bg ac ca gb ae eab ae ae ee b ac ea bd af ca bg a ca gb fafa db ca b b bd bg gb db b b bd gg gb db b bd bd gg db db b bd bd gg db db b bd bg gg db b b bd ``` <!-- end of image -->

This image might have some surprises. Let's look for intersections carefully. These zones are intriguing. I bet there's something interesting happening within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#0606feff b,#fb0b09ff c,#5359f2ff d,#e87368ff e,#b6b6ffff f,#b1d7b1ff g,#9ac29aff ``` ```image ffffffffffffffffffffffffffffffffffffffffffffff ffffffffffffffffffffffffffffffffffffffffffffff ffffffffffffffffffffffffffffffffffffffffffffff fffffffffffffffffffffffffffffffffffffffffffffd fffffffffffffffffffffffffffffffffffffffffgbbbb fffffffffffffffffffffffffffffffffffffgbbbbdfff fffffffffffffffffffffffffffffffffgdbbbdfffffff ffffffffffffffffffffffffffffffdbbbdfffffffffff ffffffffffffffffffffffffffdbbbdfffffffffffffff ffffffffffffffffffffffdbbbdfffffffffffffffffff ffffffffffffffffffdbbbdgffffffffffffffffffffff ffffffffffffffdbbbbgffffffffffffffffffffffffff ffffffffffdbbbbgffffffffffffffffffffffffffffff ffffffdbbbbdffffffffffffffffffffffffffffffffff ffgbbbbdfffffffffffffffffffffffffffffffffffffg fddddbbbbbbbbbbbbbbdffffffffffffffffffffffffffffffffffffffcaaa ddddbbbbbbbbbbbbbbbddddf ffffffffffffffffffffffffffffffffffffffgaaacgff ddddf ffffffffffffffffffffffffffffffffffgcaaacffffff fffffffffffffffffffffffffffffffcaaacffffffffff fffffffffffffffffffffffffffcaaacgfffffffffffff fffffffffffffffffffffffgcaaagfffffffffffffffff ffffffffffffffffffffcaaacfffffffffffffffffffff ggggggggggggggggcaaacggggggggggggggggggggggggg ecaace caaae eaaac caace ac ea a cc a ae ca a ae ea a ac ea a cc a a cc a ae ca a ae ea a ac ea a cc a ae ca a ae ea a ac ea a ac ea a cc a ae ca a ae ea a ac ea a cc a ae ``` <!-- end of image --> Let's see what secrets area A holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#0707ffff b,#ff0404ff c,#ababffff d,#ff8989ff e,#ffc8c8ff f,#ff4747ff g,#5a5affff ``` ```image edfb edfbbbbb edfbbbbbbfd edfbbbbbbfde edfbbbbbbfde edfbbbbbbfde edfbbbbbbfde dfbbbbbbfde edfbbbbbfde edfbbbbbfde edfbbbbbfde edfbbbbbbfd edfbbbbbbfde edfbbbbbbfde edfbbbbbbfde edfbbbbbbfde edfbbbbbbfde dfbbbbbbfde edfbbbbbfde edfbbbbbfde edfbbbbbfde edfbbbbbbfd bbbbbbbbbbfde cga bbbbbbfde ccgaaaa eee cgaaaaaagc cgaaaaaagc ccgaaaaaggc cgaaaaaagc cgaaaaaagc cggaaaaaggc cgaaaaaagc cgaaaaaagc cggaaaaagcc ccgaaaaaagc cgaaaaaagc cgaaaaaagcc ``` <!-- end of image --> Area A does not contain any intersection points. My final answer is: no intersections found.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0404ffff b,#ff0505ff c,#8383ffff d,#ffa6a6ff e,#c6c6ffff f,#ff5252ff g,#4141ffff ``` ```image d dfbbb dfbbbd fbbbd fbbbd fbbbf dbbbf dbbbf dbbbfd dbbbfd dfbbfd dfbbbd dddfffbbbbbbbbbbbbbd caaa ddfffbbbbbbbbbbbbbbfffddd egaage ffdddd egaaae caaac eaaage egaage caaac caaag egaage caaac caaac gaage gg ea a gg a ae ca a ae ca a ac ea a gg ea ae gg a ae ca a ac ea a ac ea a gg a ae cg a ae ca a ac ea a gg ea ae gg a ae ca a ac ca a ac ea a gg a ae ``` <!-- end of image -->

This is the image I'm working with. The goal is to count the intersections. Let's take a closer look at what's happening inside these zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#0708fdff b,#fd0a09ff c,#5c5fedff d,#ed6d64ff e,#b2b3feff f,#b1d6b1ff g,#97c698ff ``` ```image e ae a ae ea a ea a cc a a cc ea a a ae ac a a ae ae ea ca a a ea ae a ea cc a a cc cc a a ae ae ca a a ae ae ea ea a a ea cc a a cc ae a ca cc a fggaggggggggggggf ac gffacfffffffffffg bbf ea gfffafffffffffffg dbf bd a gfffagffffffffffg dbd bb cc gfffgaffffffffffg bb db a gffffaffffffffffbbf db ae gffffcafffffffdbd bd gffffffffffffcag gfffffaffffffbbfg bd gffffffffffffaff gfffffccfffbbgffg bb gfffffffffffacff gffffffafdbdffffg dbgffffffffffgafff gffffffacbffffffg bgfffffffffaffff gfffffbbafffffffg gbdfffffffcaffff gfffdbdfacffffffg gfbbffffffafffff gffbbffffaffffffg gffdbffffacfffff gbbgfffffagfffffg gfffdbgfcaffffff dbdfffffffgafffffg gfffffbdafffffff bbgfffffffffafffffg gffffffacfffffff bb gfffffffffcaffffg gfffffgabbffffff dbd gffffffffffaffffg gfffffagfdbfffff bb gffffffffffccfffg gffffcafffgbdfff bb gfffffffffffafffg gffffaffffffbdff dbd gfffffffffffacffg gfffacfffffffbbf bb a gffcafffffffffdb ae gffafffffffffffdb a gfacffffffffffff bd a gfafffffffffffff bb ea gagfffffffffffff bb a cagggggggggggggg db ea a bf a ae bd cc ea bb a a db ac cc fb a a bd ae ae bb a ca bb a a db ea ac a ea ea a a cc cc a a ae ac ea a a aac a ``` <!-- end of image --> Let's see if area A yields any clues. <!-- image --> ```palette Key,Color ,#fefefeff a,#0403feff b,#fe0606ff c,#3c36f9ff d,#fa4b4fff e,#c2c2ffff f,#7d7dfeff g,#fda9aaff ``` ```image eaa caf faa aae fac aae fac eaae caf eaa caf eaa caf d fac gbb aae gdbbd fac dbbbg aae gbbbd fac gdbbdg eaae dbbbg caf gbbbd eaagdbbdg cacbbg gdaad gbbbaaf dbbbgfac gbbbd aae gbbbdg fac dbbbg aae gbbbd fac gbbbdg eaae dbbbg caf bbd eaa d caf eaa caf fac aae fac aae fac eaae caf eaa caf ``` <!-- end of image --> Aha! I've found an intersection inside area A! Let's inspect the next region. Let's see what secrets area B holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#0505feff b,#fd080aff c,#4441fbff d,#ff5656ff e,#c6c6ffff f,#8685fdff g,#feabacff ``` ```image eaae cac faa aaf cac eaae aaf faa d eaae bb cac bbbg faae dbbg aaf dbbd cac gbbd eaae gbbbg caf bbbg faa dbbd eaae dbbd cac gbbb faae gbbbg aaf dbbgcac dbbaae gaac faabbg eaafbbbg cac dbbd eaae dbbd aaf gbbb fac gbbbg eaae dbbg cac dbbd faa gbbd eaaf gbbbg cac bbbg eaae dbb aaf db faa g eaae cac faa aaf cac eaae aaf ``` <!-- end of image --> Eureka! There's definitely an intersection in area B! Two intersections have been found!

<!-- image --> ```palette Key,Color ,#fefefeff a,#0505feff b,#fe0c0cff c,#433ef9ff d,#ff7272ff e,#c7c7ffff f,#8686ffff g,#ffc8c8ff ``` ```image e af a ae ea a fa a fc a a cf fa a a af cf a ea ae ae ea fc a a fa af a ea fc a a cc cf a a ae af fa a a ae af ea ea a a fa cc a a fc ae a fa cf a a af af bbg ea a bbg bd a ae gbd bb cc ea bb db a a bbg dbg ae fa dbd gbd fa a bb bb a fc bbg bb af a dbd db ea ccb gbg ae bba bd cc dbd ae bb a gbb a db ae bbg ae gbg fa dbd ea bda gbb a ac bbg fa eabb dbd a ae db gbb fc fc gbg bbg a a bd dbd cf af bb bb a ea db ae a gbg a cc bd ae a bb ea ae bb a fa db fc a gbg a af bd cc ea bb a a db cf cc gbg a a bd ae ae bb a fa bb ae a db ea af g a ea fc a a cc cc a a ae cf fa a a aaf ea ``` <!-- end of image -->

This image looks interesting. I wonder if there are any intersections hidden in there? I need to zoom in on these areas to get a better look. <!-- image --> ```palette Key,Color ,#fefefeff a,#fb0c0cff b,#0606fdff c,#959cf0ff d,#e87d72ff e,#b0d6b0ff f,#494ff2ff g,#97c797ff ``` ```image bb cbff b b b cb bc b ff b cb bc b b b bc bc b fb ff ae cb b a b cb a b b da bf cb ad fb bc ad cb b aggggggggggggggggb bc aeeeeeeeeeeeeeebc b daeeeeeeeeeeeebf ff gaaeeeeeeeeeefbe b geadeeeeeeeecbee cb geeaeeeeeeeebeee b geegaeeeeeebceee cb geeedaeeeebfeeee bc geeeeaaeefbeeeee b geeeeeadgbeeeeee bc geeeeeeabeeeeeee b geeeeeebaeeeeeee ff geeeeebfdaeeeeee b geeeefbeeaaeeeee cf geeeebeeeeadeeee b geeebeeeeeeaeeee cb geebfeeeeeegaeee b gefbeeeeeeeedaee b gcbeeeeeeeeeeaae bc gbeeeeeeeeeeeead b bgeeeeeeeeeeeeea ff bfeeeeeeeeeeeeeega b fb da ff cb aa b b ad cb b a b bf a cb fb da geebceeeeeeeeeeeeeg c aa geeebeeeeeeeeeeeeee ad geeebfeeeeeeeeeeeee a geeeebeeeeeeeeeeeee a geeeeffeeeeeeeeeeee da geeeeebeeeeeeeeeeee aa geeeeefbeeeeeeeeeee ad geeeeeebeeeeeeeeeee a geeeeeecbeeeeeeeeee a geeeeeeebceeeeeeeee da edddddaaaaaaabaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaadddddddgeeebfeeeeeeee geeeeeeeeebeeeeeeee geeeeeeeeeffeeeeeee geeeeeeeeeebeeeeeee geeeeeeeeeefbeeeeee geeeeeeeeeeebeeeeee geeeeeeeeeeecbeeeee geeeeeeeeeeeebceeee geeeeeeeeeeeeebeeee geeeeeeeeeeeeebceee eggggggggggggggbggg ff b cf b cb b b bc b ff b ff b ``` <!-- end of image --> This close-up of area A is like examining a piece of evidence. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff5f5fff b,#0505feff c,#7876fdff d,#feb9b9ff e,#fd0809ff f,#3c34f7ff g,#c6c6feff ``` ```image a c ea cb eed gbb aeed gbbc aee fbf eea cbbg deea cbbg deed gbbc aeed bbf aee fbf eea cbbg deea gbbg deed gbbc aeed bbf aee fbf eea cbbg deea gbbg deed gbbc aeedfbf aefbb fbbg gbbea gbbceed fbf aeed fbb aee cbbg eea gbbc deea gbbc deed fbf aeed cbbg aee cbbg eea gbbc deea bbc deed fbf aeed cbbg aee cbbg eea gbbc eea bbf deed fbf aee bbg ae bg e c ``` <!-- end of image --> I can confirm that an intersection exists in area A. Onward to the next region of interest. Let's zoom in on area B to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#f64851ff b,#0404feff c,#7f7efeff d,#fe9b9bff e,#fe0203ff f,#3a3afeff g,#c8c8ffff ``` ```image cbf gbbg cbf bbc cbb fbc gbbg fbc gbbg fbf gbbg cbf bbc cbb fbc gbb fbc gbbg fbf gbbg cbfdddddddddaaaaaaae daaaaaaaaeeeeeeeebbaeeeeeeeeeeeeeeee eeeeeeeeeeeeeeeeeabbaaaaaaaddddddddd addddddddd bbc cbb fbc gbbg fbf gbbg cbf bbg cbf bbc cbb fbc gbbg fbf gbbg cbf gbbg cbf bbc cbb ``` <!-- end of image --> Yes! I knew it! There's an intersection right here in area B! I can confirm there's two intersections in there.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fb373bff b,#0505ffff c,#8a8affff d,#ff9292ff e,#fe0202ff f,#3f3fffff g,#e1d5f2ff ``` ```image g fb cbcf gb b bg cb bc bg ff gb cb bc gb b bg fc bc b ff ff ed cb b e b cb ge bg bg de bc gb ea fb bg ed gb gb e b bc ge bg b de bf ff aa fb b ed gb cb e b b ge bc gb de bf bg aa cb gb edgb bc ebg b ba ff ffde b cb aa cf gb ed b bg e cb bc ge bg ff de gb cb aa bc gb ed b bg eg fc bc ge b ff de cf cb aa b b ed cb bg eg bg bc ge gb fb de bc c aa b ed fc eg b ge ff de b aa cb ed bg eg gb e bg gg de ggddddaaaaeeeebeeeeeeeeeeeee aeeeeeeeeeeeeeeeeeaaaadddddgg bc g b ff b cb b gb bg gb bc b ff b cf b cb bg gb bc b fc b cf b ``` <!-- end of image -->

This image seems promising for intersection detection. There are 2 areas where the lines seem to converge. We should take a closer look at area A,, and B. <!-- image --> ```palette Key,Color ,#fefefeff a,#0a0bfdff b,#fd0605ff c,#656ceeff d,#e95d55ff e,#97c599ff f,#b0d7b0ff g,#dfcaeaff ``` ```image c a ag ga ag ca a cc a ac a ag eeeeeeeeeeeeeeeecaeee ffffffffffffffffaffff fffffffffffffffcaffff fffffffffffffffafffff ffffffffffffffacfffff ffffffffffffffaffffff fffffffffffffacffffff ffffffffffffeafffffff ffffffffffffaefffffff fffffffffffcaffffffff fffffffffffafffffffff ffffffffffcafffffffff ggggdddddddbbbbbbabbbbbbbbbbbbb gbbbbbbbbbbbbbbbdddddddddeeeffacffffffffff bg fffffffffafffffffffff dd ffffffffaefffffffffff gb fffffffeaffffffffffff bg fffffffafffffffffffff dd ffffffcafffffffffffff b ffffffaffffffffffffff bg fffffacffffffffffffff db fffffafffffffffffffff c b ffffacfffffffffffffff ca bg fffeaffffffffffffffff ac db fffaeffffffffffffffff ac b eecaeeeeeeeeeeeeeeeee ag bg a ga db ca ca b a ca bg ac ac feeeeeeeeeeeeeedb a ageffffffffffffffb ag aefffffffffffffbd ga gaffffffffffffdbf ag cafffffffffffbff ca eaafffffffffbdff a efacfffffffdbfff cc effaeffffffbffff a efffafffffbdffff ac efffcafffdbfffff ga effffcaffbffffff ag efffffacbdffffff ga effffffadfffffff a effffffbafffffff ca efffffbdeaffffff a effffdbffcafffff ac effffbffffaaffff a efffbdfffffacfff ag effebfffffffaeff ga effbfffffffffaff ag efbdfffffffffeaf ca eebfffffffffffca a ebfffffffffffffaa cc bdffffffffffffffac a gbfffffffffffffff ag ac beeeeeeeeeeeeeeee a ga bd ga ag gb ca ga b ac a dd ag ca gb a a bg ga ac dd ca a gb aa ag bg acga dd aag b a bg ``` <!-- end of image --> I wonder what we'll find inside area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#0606feff b,#fe0404ff c,#aaaaffff d,#ff7777ff e,#4e45f6ff f,#fb3437ff g,#fec1c1ff ``` ```image d gb fb dbb gbbg e fbf ae dbb aac gbbg caac fbf eaa dbb eae gbbg aae fbf caac dbb caac gbbd eaac fbf eaa dbbg aae gbbd caae fbf caac dbbg caac bbd eaa fbf eae gbbg aae bbd caaebf caafg eaac fbeaa gbbgeae bbd aae dbf caac gbbg caac bbd eaa dbf eaa gbbg aae bbd caae dbf caac gbbg caac bbd eaa dbf eae gbbg aae fbd caac dbf caac gbbg eaa fbd ea dbb a gbbg fbd bb bg d ``` <!-- end of image --> Case closed! This is definitely an intersection point in area A. Now, let's scrutinize the next spot. Time to investigate area B up close. <!-- image --> ```palette Key,Color ,#fefefeff a,#0403feff b,#fc0508ff c,#8282ffff d,#ffa2a2ff e,#3d38f9ff f,#ff5c5cff g,#c7c5fcff ``` ```image eae gaag eac caa aac cae gaag eae gaag eac gaa eac caa aac cae gaag eae gaag eac caa aac cae gaag eae gaagdddddddddfffffffff fffffffffbbbbbbbbbbbeaebbbbbbbbbbbbbbbbbbb bbbbbbbbbbbbbbbbbbbbaabbbbfffffffffffddddd ffddddddddddd eac caa aac cae gaag eae gaag eac caa aac cae aag cae gaag eae gaag eac caa aac cae gaag eae gaag ``` <!-- end of image --> Wow! I can see an intersection so clearly in area B! There are precisely two intersections present in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0707feff b,#fe0404ff c,#9797ffff d,#ff9898ff e,#4e4effff f,#fc474aff g,#e7d7eeff ``` ```image c a ac ga ag ca a ee a ac ga ag ca a ca a ee a ac ga ag ca a ee gggdddddfffffbbbbbabbbbbbbbbbbbb gbbbbbbbbbbbbbbbfffffdddddggg ac bg a ff ac gb ga bg ag ff ca gb a bg ee ff a e b ac ea bg ga ae fb ag ac b ca ag bd a ga fb ee ca b a ea bd ac ae db a ac b ac a bd ga ga db ag ca b ca ee bd a ac db ee ag b a a bd ac ca db ga ea b ag aebd ca af a bag ee bdga a db ca ee b ea a bd ae ac db ag ga b a ag bf ga ca gb ea a b ae ee ff ac a gb ag ac b ga ga ff ca ag gb ea ca bg ae a ff ac ca gb ag a bg ga ee ff ca a gb ea ac bg acga ff aag gb a bg ``` <!-- end of image -->

I'm examining this image closely. My goal: find any and all intersections. These spots are like clues. Let's see what they reveal about potential intersections. <!-- image --> ```palette Key,Color ,#fefefeff a,#e87166ff b,#0708fdff c,#fc0908ff d,#9ba6e9ff e,#b1d7b1ff f,#4d56ecff g,#9bc595ff ``` ```image accc c eccc ac accc c accc ac accc c accc gggggggggggggggggggggggggggggggac acca eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecg acca eeeeeeeeeeeeeeeeeeeeeeeeeeeeeegcg acca eeeeeeeeeeeeeeeeeeeeeeeeeeeeeecgg acca eeeeeeeeeeeeeeeeeeeeeeeeeeeeegceg acca eeeeeeeeeeeeeeeeeeeeeeeeeeeeecgeg acca eeeeeeeeeeeeeeeeeeeeeeeeeeeegceeg acca eeeeeeeeeeeeeeeeeeeeeeeeeeeecgeeg acca eeeeeeeeeeeeeeeeeeeeeeeeeeeeceeeg acc eeeeeeeeeeeeeeeeeeeeeeeeeeecaeeeg f eeeeeeeeeeeeeeeeeeeeeeeeeeeceeeeg bbb eeeeeeeeeeeeeeeeeeeeeeeeeecaeeeeg b fb eeeeeeeeeeeeeeeeeeeeeeeeeeceeeeegbd db eeeeeeeeeeeeeeeeeeeeeeeeecaeeeeefb db eeeeeeeeeeeeeeeeeeeeeeeeeceeeeeeb bd eeeeeeeeeeeeeeeeeeeeeeeecaeeeeefb bd eeeeeeeeeeeeeeeeeeeeeeeeceeeeeebg bf eeeeeeeeeeeeeeeeeeeeeeecaeeeeebfg bf eeeeeeeeeeeeeeeeeeeeeeeceeeeeebeg bb eeeeeeeeeeeeeeeeeeeeeeaaeeeeebdeg fb eeeeeeeeeeeeeeeeeeeeeeceeeeedbeeg fb eeeeeeeeeeeeeeeeeeeeeaaeeeeebeeeg db eeeeeeeeeeeeeeeeeeeeeceeeeefbeeeg db eeeeeeeeeeeeeeeeeeeeaceeeeebeeeeg bd eeeeeeeeeeeeeeeeeeeeceeeeebfeeeeg bd eeeeeeeeeeeeeeeeeeeaceeeeebeeeeeg bf eeeeeeeeeeeeeeeeeeeceeeeebdeeeeeg bf eeeeeeeeeeeeeeeeeeaceeeedbeeeeeeg bb eeeeeeeeeeeeeeeeeeceeeeebeeeeeeeg fb eeeeeeeeeeeeeeeeeaceeeefbeeeeeeeg fb eeeeeeeeeeeeeeeeeceeeeebeeeeeeeeg db eeeeeeeeeeeeeeeeaceeeeffeeeeeeeeg db eeeeeeeeeeeeeeeeceeeeebeeeeeeeeeg bd eeeeeeeeeeeeeeegceeeebdeeeeeeeeeg bd eeeeeeeeeeeeeeecgeeedbeeeeeeeeeeg bf eeeeeeeeeeeeeegceeeebeeeeeeeeeeeg bf eeeeeeeeeeeeeecgeeefbeeeeeeeeeeeg bb eeeeeeeeeeeeegceeeebeeeeeeeeeeeeg fb eeeeeeeeeeeeecgeeeffeeeeeeeeeeeeg fb eeeeeeeeeeeeeceeeebeeeeeeeeeeeeeg db eeeeeeeeeeeecaeeebfeeeeeeeeeeeeeg db eeeeeeeeeeeeceeegbeeeeeeeeeeeeeeg bd eeeeeeeeeeecaeeebgeeeeeeeeeeeeeeg bd eeeeeeeeeeeceeefbeeeeeeeeeeeeeeeg bf eeeeeeeeeecaeeebeeeeeeeeeeeeeeeeg bf eeeeeeeeeeceeeffeeeeeeeeeeeeeeeeg bb eeeeeeeeecaeeebeeeeeeeeeeeeeeeeeg fb eeeeeeeeeceeebfeeeeeeeeeeeeeeeeeg fb eeeeeeeecaeeebeeeeeeeeeeeeeeeeeeg db eeeeeeeeceeebdeeeeeeeeeeeeeeeeeeg eeeeeeeaaeedbeeeeeeeeeeeeeeeeeeeg eeeeeeeceeebeeeeeeeeeeeeeeeeeeeeg eeeeeeaaeefbeeeeeeeeeeeeeeeeeeeeg eeeeeeceeebeeeeeeeeeeeeeeeeeeeeeg eeeeeaceebfeeeeeeeeeeeeeeeeeeeeeg eeeeeceeebeeeeeeeeeeeeeeeeeeeeeeg eeeeaceebdeeeeeeeeeeeeeeeeeeeeeeg eeeeceedbeeeeeeeeeeeeeeeeeeeeeeeg eeeaceebeeeeeeeeeeeeeeeeeeeeeeeeg eeeceefbeeeeeeeeeeeeeeeeeeeeeeeeg eeaceebeeeeeeeeeeeeeeeeeeeeeeeeeg eeceebfeeeeeeeeeeeeeeeeeeeeeeeeeg eaceebeeeeeeeeeeeeeeeeeeeeeeeeeeg eceebdeeeeeeeeeeeeeeeeeeeeeeeeeeg gcedbeeeeeeeeeeeeeeeeeeeeeeeeeeeg cgebeeeeeeeeeeeeeeeeeeeeeeeeeeeeg ecefbeeeeeeeeeeeeeeeeeeeeeeeeeeeeg cgebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg ff b bd b b ``` <!-- end of image --> I'm focusing my attention on this specific region, area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff8686ff b,#0707feff c,#fe0505ff d,#acacffff e,#ff4747ff f,#5b5bffff g,#ffc8c8ff ``` ```image e gc gcc eca ccg ce gcg gcg ec gcc ece gccg ccg ace ccg ce cg ca ac cc acc cca cca acc eca f cc b ca fb ea fbf gc bb ec bf gcc db ece bd ece dbb gccg fbf ece dbb ccg bbf ce dbb ae bb cg bd ac ff cc db ccg dbb ace bbd cca fbb acc bbd cca fbf ca bf ac db ca bd ac fb ec bb eca dbbd gcc fbf eca dbb cc bbf ca bb ee ff gcg dbd ec fb gcc dbb ece bbf ece bbd gccg fbb ace bbd ccg bf ce db ae db cg bb ac fbb cc bbd acc fbf acc bf cca db acc bd cca fb ca fbf gc dbbd ea fbf gc dbb ec bbd eca bd gccg ff ece dbd gccg fb ece dbb ce dbb gcg bbd ee fbf gcg bbd ac bf ace bf ccg db ace bb ccg fbb ace bbd acc dbb cca bbf cc bb ca bd ac fb ac fb ec dbb gcc bbf eca dbb gcc bbd gcc bbd eca fbf ccg bbd ce bf gcg db gcg fb ec bb ``` <!-- end of image --> No intersection in area A, but I'll keep looking. The image is completely devoid of intersections. Zero.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff9090ff b,#0707ffff c,#ff0404ff d,#aeaeffff e,#ff4a4aff f,#5454ffff g,#ffd1d1ff ``` ```image g acccg c acccg ac acceg c acceg ac acceg c acceg gc acceg cg acce gc acce cg acce gc acce cg acce gc acce cg ecce c ecc ca f c bbb ca b fb c bd db ca db db c b bd ea ff bd c b bf ee bf bf c b bb ee bd fb c db fb ee b db c fb db ae b bd c bf bd ae b bf c bd bf ac db bb c b fb ac fb fb c b db gc ff db cg b bd gc bd bd cg db bf gc b bf cg db bb gc b fb cg ff fb c b db ca bd db c b bd ca bd bd c db bf ca b bf c ff bb ea b fb c bd fb ee b db c bd ee db c b ee ff c b ae bf c b ae bd c db ac b c fb ac b c ff gc b cg bd gc db cg b gc db cg b ff b bd db 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,#e6675bff b,#0606fdff c,#fc0a0aff d,#919ce8ff e,#b2d7b1ff f,#a2cca1ff g,#494decff ``` ```image ffffffffffffffffffffffffffffff feeeeeeeeeeeeeeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeegef feeeeeeeeeeeeeeeeeeeeeeeeeebef feeeeeeeeeeeeeeeeeeeeeeeeebdef feeeeeeeeeeeeeeeeeeeeeeeefbeef feeeeeeeeeeeeeeeeeeeeeeeebfeef feeeeeeeeeeeeeeeeeeeeeeedbeaef feeeeeeeeeeeeeeeeeeeeeeebeccef feeeeeeeeeeeeeeeeeeeeeegbcceef feeeeeeeeeeeeeeeeeeeeeebcaeeef feeeeeeeeeeeeeeeeeeeeeggaeeeef feeeeeeeeeeeeeeeeeeeefbaeeeeef feeeeeeeeeeeeeeeeeeefbgeeeeeef feeeeeeeeeeeeeeeeeefcbeeeeeeef feeeeeeeeeeeeeeeeeacbdeeeeeeef feeeeeeeeeeeeeeeeacdbeeeeeeeef feeeeeeeeeeeeeeeccebeeeeeeeeef feeeeeeeeeeeeeeccegbeeeeeeeeef feeeeeeeeeeeeecceebeeeeeeeeeef feeeeeeeeeeeecaeeggeeeeeeeeeef feeeeeeeeeeecaeeebeeeeeeeeeeef feeeeeeeeefcaeeebgeeeeeeeeeeef feeeeeeeefcfeeefbeeeeeeeeeeeef feeeeeeeaceeeeebdeeeeeeeeeeeef feeeeeeaceeeeedbeeeeeeeeeeeeef feeeeeaceeeeeebfeeeeeeeeeeeeef feeeecceeeeeegbeeeeeeeeeeeeeef feeecceeeeeeebeeeeeeeeeeeeeeef feecaeeeeeeeggeeeeeeeeeeeeeeef fecaeeeeeeeebeeeeeeeeeeeeeeeef fcaeeeeeeeebgeeeeeeeeeeeeeeeef cffffffffffbffffffffffffffffff ec bd ac b ac b ac db cc b fffffffffffffffffffff cc gg feeeeeeeeeeeeeeeeeeef ca b feeeeeeeeeeeeeeeeeeef ca gg feeeeeeeeeeeeeeeeeeef ce b feeeeeeeeeeeeeeeeeeef c bd bfeeeeeeeeeeeeeeeeeeef ec b beeeeeeeeeeeeeeeeeeef ac b dbeeeeeeeeeeeeeeeeeef ac db fdbeeeeeeeeeeeeeeeeef cc b fedbeeeeeeeeeeeeeeeef accccc dg feegbeeeeeeeeeeeeeeef eaccccae b feeegbeeeeeeeeeeeefaccccca gg feeeegbeeeeeeacccccaf b feeeeebbaccccaaeeeeef bd ffaccccbbfeeeeeeeeeef b cccafeeeebgeeeeeeeeeef bd feeeeeeeebgeeeeeeeeef db feeeeeeeeebgeeeeeeeef b feeeeeeeeeebdeeeeeeef db feeeeeeeeeeebdeeeeeef b feeeeeeeeeeeebdeeeeef gg feeeeeeeeeeeeebfeeeef b feeeeeeeeeeeeefbfeeef bd feeeeeeeeeeeeeefbeeef b feeeeeeeeeeeeeeedbeef bd feeeeeeeeeeeeeeeedbef db feeeeeeeeeeeeeeeeedbf b feeeeeeeeeeeeeeeeeegb db ffffffffffffffffffffgb b gb gg gb b bg bd bg b bg bd bd b bd b bd db bd b b gg b b b gg b b dbbd db ``` <!-- end of image --> I'm determined to find out if an intersection exists in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff5757ff b,#0604fdff c,#fd0507ff d,#8181ffff e,#fda6a8ff f,#c1c1ffff g,#4241feff ``` ```image f bg bbg fbbg fbbg fbbg fbbg fbbd fbbd dbbd dbbd dbbf dbbf gbbf eeaa gbbf eeacccccc gbbf eeaaccccccccaae gbbf eeaaccccccccaaee gbbeacccccccccaae eeaacbbbccccaaee eeaaccccccccbbge eacccccccccaae fbbg cccccaaee fbbg aee fbbg fbbg fbbd fbbd dbbd dbbd dbbf dbbf gbbf gbbf gbbf gbbf gbb gbg bbg fbbg fbbg fbbg fbbg fbbd fbbd dbbd dbb db ``` <!-- end of image --> There is an intersection point visible in this close-up of area A. Let's move forward and inspect another region. Time to investigate area B up close. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd5657ff b,#0605feff c,#fd0809ff d,#a4a1fcff e,#feb3b4ff f,#740a94ff g,#4d4cfeff ``` ```image d dbb bbd dbb bbd gbg bbd gbg dbb gbg dbb ae bbd acc dbb ccce bbdeccce gbgeccc bbdcca gbgcca dbbcca gbfca dbbce bbfe fbbe cbbd ecfbb eccbbd eccfbg eccabbd accagbg accadbb acce gbg acce dbb ccce bbd eccce dbb eccc bbd ecca gbg ecca bbd ecca gbg acca dbb acce gbg acce dbb acce bbd ccce dbb eccce bbd eccc gbg ecca bbd ecca gbg acca dbb acca gbg acce dbb acce bbd ccce dbb eccce bbd eccc gbg ecca bbd ecca gbg ecca dbbd acca gbg acce dbb acce bbd acce dbb ``` <!-- end of image --> The evidence is clear: this is an intersection in area B. I've identified a total of two intersection points.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff5555ff b,#0505feff c,#fe0708ff d,#8685feff e,#ffaeaeff f,#c5c5feff g,#433ffbff ``` ```image d b bd fb bf fb a b cc dgcc bca gga be bd ecb ecbf acfb ac b cc db ca b ca gg ce b ce bd ec b ec bf ac fb ac b cc db cc b ca gg ca b ce gd ce b ec bf ec fb ac bf ac db cc b ca dg ca b ce gd ce b ec bd b ec fb fb ac bf fb ac fb fb cc b db eaccca dg db eaccccae b gb eaccccae gg gb eaccccae b gbaccccae bd eaccccbg b cccae bg bf bg fb bd b bd db bf b bf gg bf b b bd fb b fb bf fb fb db b db db gb b gb gg gb b bg gd bg b bg bf bd fb bd bf bf db bf b bf dg b b fb gd fb b fbbd db ``` <!-- end of image -->

Based on a first glance, I suspect there could be intersection regions here. These areas seem to enclose narrow spaces where lines might be close. <!-- image --> ```palette Key,Color ,#fefefeff a,#b1d7b1ff b,#0808fdff c,#f90c0cff d,#595feeff e,#db7f6eff f,#b7b7feff g,#97c699ff ``` ```image f fb bdd fb b b fb b bf bf fb b bf dd b b bd dd b b db fb b b fb fb bf bf fb b bf bf b b dd dd b b db dd b b fb fb bf b fb aggggggggggggggbgggggggggggggggggggggggbdggggggggggggggggggggga gaaaaaaaaaaaaabgaaaaaaaaaaaaaaaaaaaaaaaabaaaaaaaaaaaaaaaaaaaaag gaaaaaaaaaaaaabaaaaaaaaaaaeaaaaaaaaaaaaabdaaaaaaaaaaaaaaaaaaaag gaaaaaaaaaaaabdaaaaaaaaaccccaaaaaaaaaaaaabaaaaaaaaaaaaaaaaaaaag gaaaaaaaaaaaabaaaaaaaecceaaeccaaaaaaaaaaadbaaaaaaaaaaaaaaaaaaag gaaaaaaaaaaabdaaaaaeccaaaaaaaeceaaaaaaaaaabaaaaaaaaaaaaaaaaaaag gaaaaaaaaaaabaaaacccaaaaaaaaaaaccgaaaaaaaadbaaaaaaaaaaaaaaaaaag gaaaaaaaaaaddaacceaaaaaaaaaaaaaagccaaaaaaaabgaaaaaaaaaaaaaaaaag gaaaaaaaaaabecceaaaaaaaaaaaaaaaaaaeceaaaaaagbaaaaaaaaaaaaaaaaag gaaaaaaaaadbcgaaaaaaaaaaaaaaaaaaaaaacceaaaaabdaaaaaaaaaaaaaaaag gaaaaaaaccbaaaaaaaaaaaaaaaaaaaaaaaaaaaccaaaaabaaaaaaaaaaaaaaaag gaaaaaccegbaaaaaaaaaaaaaaaaaaaaaaaaaaaaeccaaabdaaaaaaaaaaaaaaag gaaecceaabgaaaaaaaaaaaaaaaaaaaaaaaaaaaaaacceaabaaaaaaaaaaaaaaag geccgaaaabaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaccadbaaaaaaaaaaaaaag eccaaaaaabdaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaeccbaaaaaaaaaaaaaag ccegaaaaaaabaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaecbaaaaaaaaaaaaag cce gaaaaaabdaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaabcgaaaaaaaaaaag ecc gaaaaaabaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaagbccaaaaaaaaaag ecc gaaaaaddaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaabdeceaaaaaaaag e gaaaaabaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaabaacceaaaaaag gaaaadbaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaabdaaaccaaaaag gaaaabaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaabaaaaeccaaag gaaagbaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaadbaaaaacceag gaaabgaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaabaaaaaaaccg gaaabaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaadbaaaaaaaecc gaabdaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaabgaaaaaaagece b fb cc dd bf cc b b ec dd dd b b fb db b b fb fb bf bf b b bf bf b b dd dd b b dd db b b fb fb b bf fb b bf bf b b bf dd b b dd db b b dd fb b bf fb b b d ``` <!-- end of image --> Let's take a closer look at area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#ffbebeff b,#0908fdff c,#fe0505ff d,#6260fcff e,#fd7d7eff f,#b0b0ffff g,#f53d46ff ``` ```image fbb bbf dbd fbb bbf bbd dbd fbb bbf aa dbd bbf eccccccc dbd fbb acccce gcce bbf bbf agccga accga dbb bb egccca ecccg bbf bd ecccce eccce fbb fb ecccce agccca bb dd agccga acccg fb bf egccga ecce dd db ecccce agcca fbf dbbgcccga eccce bbf bbgccga gccce dbb dbbcea agccg bbf aecbbge eccg fbb agccgbb ecce bbd acccgdbd gccca fbb eccceafbb acccga dbd aecccc dbd eccce fbbf agcccga bbf agccc dbd ecccea bbf ecce dbb eccce dbb gccce bbf cccge bbf agccgdbb cga fbb ecccbbd a bbf ecgbb bb agbba bd ebcga fb dbcce dd bgccca db bbf eccce bb fbb gcce dbb bbd agcga bbf fbb cccg fbb dbd eccce bbf fbbf agccca fbb dbd acccg dbd bbf ecce fbb dbb agcca bbf fbb eccc dbd bbd gc bbf fbb a dbb db bbf fbf ``` <!-- end of image --> I can confirm that an intersection exists in area A. My analysis indicates that there are two intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#febcbcff b,#0404feff c,#fd090bff d,#8584fdff e,#ff6868ff f,#cdcdffff g,#3b3bffff ``` ```image f db bdg fb b bf db fb bf bf fb b bd gd b b gd dg b b dg dg b b db fb bf bf fb b bd bf b b gd gd b b dg dg b b db dg bf b fb fb bd bf b b a gd bd cccc b b acca acc dg gd ecc ece b b ecc cca db dg cce acc bf bacca ece fb dbca cca bd ecb cc b ccefb ace gd acca bf eca b ecca b cc dg ecc bd accb cce b ecb acca gd bca acca b fbcc ecc dg bdece e b b cca db gd cc b b ace fb dg eca bf b cc b fb acc bd bf ece b fb cca gd bd acc b b ec dg gg b b db dg b b fb fb bf bf b fb bd bd b b gd gg b b dg dg b b db fb b bf fb fb bf bd b b bd gg b b gd dg b b dg fb b bf db fb b g ``` <!-- end of image -->

I'm analyzing this image to identify any points where lines intersect. I wonder what's going on inside those areas? Perhaps intersections are hiding there. <!-- image --> ```palette Key,Color ,#fefefeff a,#0808feff b,#f3554fff c,#5b5cf6ff d,#fd0807ff e,#f1a59eff f,#add5aeff g,#b5b5ffff ``` ```image g ga a a ga ga a ca a ac ag ag a a cc ga a ga cc ca a ac ga ag a a ga ga ag ca a aa ag ac a ag cc a a ga d cc ca d a ac bd ga ag de a ag d ga a ed ag ga bd a ca de ag ac d a ag ed cc a bb a a de cc ga d a ca ed ga ac fdbffffffffaffff ag ffdffffffffaffff a fffdffffffafffff ga fffbdfffffafffff ca ffffdbfffacfffff ca fffffdfffaffffff ac fffffedfacffffff ag ffffffbdafffffff a fffffffcafffffff ga fffffffadfffffff ca ffffffcaedffffff ac ffffffaffdbfffff ag ffffffafffdeffff ag fffffafffffdffff a fffffafffffbdfff ga ffffacffffffdbff ca ffffaffffffffdff ac fffacfffffffffdf ffffffffacffff a bd fffffffffaffff cc de ffffffffffffff a d ffffffffffffff ga ed ffffffffffffff a bb ffffffffffffff ga de ffffffffffffff ag d ffffffffebffff a ed ffffeddddbffff ag db bddddeffffffff a de bdddbeffffffffffff cc d ebdddb ffffffffffffff a ed ebddde ffffffffffffff cc db edddde ffffffffffffff a d bdddbe ffffffffffffff ga d bdddb ffffffffffffff a bd ebddde ffffffffffffff ga dbdddde ag be a ag a cc a cc a ga a ``` <!-- end of image --> Let's zoom in on area A to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#0807feff b,#fc373aff c,#a9a8feff d,#fe0404ff e,#ffc6c6ff f,#5750f7ff g,#ff8080ff ``` ```image bdb aac ddg caa edde faf gdde caa bdb faf eddg aac edde faf gdd aac bdb caf eddg aac gdde caa bdb aac bdb caa eddg faf gddecaa bdbfaf ddaac efaf aabe caadb aacddg caa edde aac gdd caa bdb faf eddg caa gdde faf bdb aac bdb faf eddg aac gdde caa bdb aac ddg caa edde aac gdde caa bdb ``` <!-- end of image --> Gotcha! I've found the intersection hiding in area A! Alright, let's examine the next area. Let's get to the bottom of what's happening inside area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#0404ffff b,#ff4646ff c,#6161ffff d,#ff0505ff e,#ffc1c1ff f,#ff8383ff g,#b7b7ffff ``` ```image gaac gaag caag caa cg efbf efbddddb efbddddddbfe efbdddddddbfe efbddddddbfe dddddbfe dbfe ``` <!-- end of image --> Hmm, it seems there's no intersection in area B after all. The image features one single intersection point.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0606ffff b,#ff4e4eff c,#8282ffff d,#fe0606ff e,#ffa9a9ff f,#443ffaff g,#c3c3ffff ``` ```image g cag aga ga ga ag fa a af ag ag a a fc ga a ca cf fa a ac ca ag a a ga ga ag ca a ff ag ac a ag fc a a ga d cf ca d a af bd ca ac de a ag d ga a ed ag ga bd a fa de ag af d a ag ed fc a bb a ga de cf ca d a fa ed ca af db a ag d ga a d ag ga bd a ca de ag ff d a ac ed fc ag bba a ff ga ad ca caed ff a bb ac ga de ag ag d a a ed ga ac db fa a d af fc d ac a bd a cf de a d ca ed a bb ga de ag d eb a ed ebddde ac db edddbe a de bdddbe fc d ebdddb a ed ebddde cf db edddbe a d bdddbe ga d ebdddb a bd ebddde ga dbdddde ag be a ac a fc a cf a ga a ``` <!-- end of image -->

I'm on the case! Let's uncover any intersections hidden in this image. There are 1 regions I'd like to highlight in the image. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd0606ff b,#5c60f5ff c,#f3a29dff d,#0809fdff e,#b3b3ffff f,#f0504dff g,#add5adff ``` ```image c ac a ac a acgggggggggggggggg gagggggggggggggggg gagggggggggggggggg gcaggggggggggggggg ggaggggggggggggggg ggcagggggggggggggg gggagggggggggggggg gggfaggggggggggggg ggggaggggggggggggg ggggfagggggggggggg gggggagggggggggggg degggggffggggggggggg ddgggggaggggggggggg gddgggffgggggggggg ggbddggagggggggggg ggggbdbffggggggggg ggggggddfggggggggg ggggggggddgggggggg gggggggggaddgggggg gggggggggacgddgggg ggggggggggaggbddgg ggggggggggacgggbdb gggggggggggagggggdde gggggggggggagggggg dde gggggggggggcaggggg dd ebdddd ggggggggggggaggggg edd ebdddddbe ggggggggggggcagggg bdb ebddddbe gggggggggggggagggg bdb ebdddddbe gggggggggggggcaggg dde ebdddddbe ggggggggggggggaggg dde ebdddddbe ggggggggggggggfagg ddebdddddbe gggggggggggggggagg edbe gggggggggggggggffg ggggggggggggggggag ggggggggggggggggff a ff a ac a ac a ac a ac a a ca a ca a ca a ff a ff a ff a fc a ac a ac a ac a a ca a caafcc ccffaaaaaaaaffcc ccfaaaaaaaaafcc ccffaaaaaaaaffcc ccfaaaaa ``` <!-- end of image --> Let's see if area A yields any clues. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0505ff b,#5a52f6ff c,#fe8485ff d,#0706fdff e,#b6b5feff f,#fc4447ff g,#ffc9c9ff ``` ```image af aag faf gaag faf gaag faf gaag fac gaa fac gaa fac caa aac caa aac caa aag caf aag caf aag caf e gaag db faf dddb gaag ebddde faf edddde gaag edddbe fac bdddbe gaa bdddb fac ebdddbaa ebdddfc edddde edddbe cbdddb aabdddb caaebdddb aac ebddde caf edddde aag edddbe caf bdddb aag bdd caf eb gaag faf gaag faf gaag fac gaa fac gaa fac gaa fac caa aac caa aac caf aag caf aag caf gaa fa ga ``` <!-- end of image --> Yes! I knew it! There's an intersection right here in area A! I have found one intersection!

<!-- image --> ```palette Key,Color ,#fefefeff a,#fe0304ff b,#5353ffff c,#ff7d7dff d,#0505feff e,#adadffff f,#fb3b3eff g,#ffbfbfff ``` ```image g ac a ag a ag ga ag ga a ga a ca a cf a de cf dd a edd fc edb a bdbfc bdf dde add agedd a edb ag bdb a bde ag dde ga dd ebdddd a edd ebdddddbe ga edb ebddddbe a bdb ebdddddbe ga dde ebdddddbe a dde ebddddbee cf ddeebddddbe a edbe cf a ff a fc a fc a ag a ag a ag ga a ga a ga a cf a cf a cf a fc a fc a ac a ag a ag ga ag ga a gaffcgg gccfaaaaaaaafccg ggcffaaaaaaaffcgg gccfaaaaaaaafccg ggcffaaaa ``` <!-- end of image -->

The hunt for intersections begins! Let's analyze this image closely. My next step is to analyze the details within each area. <!-- image --> ```palette Key,Color ,#fefefeff a,#fc0606ff b,#0707fbff c,#e09588ff d,#5c60daff e,#97c799ff f,#b1d7b1ff g,#ec4b42ff ``` ```image ca a a ca ca a ga a ag ac ac a a gc a feeeeeeeeeeeeeeeeeeeeeaeeeeeeeeecaeeeeeeeeeeeeeeeeeeeeeee effffffffffffffffffffggffffffffffgaffffffffffffffffffffff effffffffffffffffffffaffffffffffffgafffffffffffffffffffff efffffffffffffffffffcafffffffffffffagffffffffffffffffffff efffffffffffffffffffafffffffffffffffacfffffffffffffffffff effffffffffffffffffcaffffffffffffffffafffffffffffffffffff effffffffffffffffffaeffffffffffffffffeaffffffffffffffffff effffffffffffffffffafffffdbbdfffffffffcafffffffffffffffff efffffffffffffffffacffffdbfebbdffffffffgaffffffffffffffff efffffffffffffffffaffffebfffffdbbdffffffagfffffffffffffff effffffffffffffffggffffbffffffffebbdfffffacffffffffffffff effffffffffffffffaffffbefffffffffffdbbdfffaffffffffffffff efffffffffffffffggfffbdffffffffffffffebbdffafffffffffffff efffffffffffffffafffbdffffffffffffffffffdbbdaffffffffffff effffffffffffffcaffbbfffffffffffffffffffffebbbfffffffffff effffffffffffffaffdbfffffffffffffffffffffffffdbbdffffffff efffffffffffffcafdbfffffffffffffffffffffffffffacbbdffffff efffffffffffffaefbfffffffffffffffffffffffffffffaefdbbdfff efffffffffffffafbfffffffffffffffffffffffffffffffafffebbdf effffffffffffacbdfffffffffffffffffffffffffffffffcafffffdbbf effffffffffffabdfffffffffffffffffffffffffffffffffgaffffff bbd efffffffffffgbbfffffffffffffffffffffffffffffffffffagfffff dbbf efffffffffffdbfffffffffffffffffffffffffffffffffffffagffff bbd effffffffffdbfffffffffffffffffffffffffffffffffffffffacfff dbbf efffffffffebfffffffffffffffffffffffffffffffffffffffffafff bb efffffffffbafffffffffffffffffffffffffffffffffffffffffcaff effffffffbafffffffffffffffffffffffffffffffffffffffffffgaf efffffffbdaffffffffffffffffffffffffffffffffffffffffffffga effffffbdacfffffffffffffffffffffffffffffffffffffffffffffag efffffbbfafffffffffffffffffffffffffffffffffffffffffffffffac effffdbfacfffffffffffffffffffffffffffffffffffffffffffffff a efffebffaffffffffffffffffffffffffffffffffffffffffffffffff a efffbffggffffffffffffffffffffffffffffffffffffffffffffffff ca effbeffafffffffffffffffffffffffffffffffffffffffffffffffff ga efbdffggfffffffffffffffffffffffffffffffffffffffffffffffff ag ebdfffaffffffffffffffffffffffffffffffffffffffffffffffffff ac bbfffcaffffffffffffffffffffffffffffffffffffffffffffffffff a dbffffafffffffffffffffffffffffffffffffffffffffffffffffffff a fbefffcafffffffffffffffffffffffffffffffffffffffffffffffffff ca b efffacfffffffffffffffffffffffffffffffffffffffffffffffffff ga b efffaffffffffffffffffffffffffffffffffffffffffffffffffffff ag bf effacffffffffffffffffffffffffffffffffffffffffffffffffffff ac bd effafffffffffffffffffffffffffffffffffffffffffffffffffffff a bd efggfffffffffffffffffffffffffffffffffffffffffffffffffffff a db efaffffffffffffffffffffffffffffffffffffffffffffffffffffff db eggffffffffffffffffffffffffffffffffffffffffffffffffffffff b eafffffffffffffffffffffffffffffffffffffffffffffffffffffff b cafffffffffffffffffffffffffffffffffffffffffffffffffffffff b affffffffffffffffffffffffffffffffffffffffffffffffffffffff afffffffffffffffffffffffffffffffffffffffffffffffffffffffe af a ac a gc a cg a ca a a a a ac a gg a cg a ca a ``` <!-- end of image --> Eureka! Let's inspect this close up of area A <!-- image --> ```palette Key,Color ,#fefefeff a,#fd0607ff b,#0605feff c,#fe9999ff d,#4b3ff3ff e,#f1d7e4ff f,#9695fdff g,#fd4d4eff ``` ```image eaae eaag gag eaac eaae caac gag caae eaae gaae cag gaa aac eaag caa eaag aac caac caa caac gac gaae eaae gaae gag eaag eaae eaag gag dbfe caac eaae dbbbbdf caac cag dbbfdbbbbfe gaae aac fbbf efbbbbdf gaae caa fbbf fdbbbbfe aag aac ebbd efbbbbdf eaag caa ebbd fdbbbbfe eaac gac dbd efbbbbdf caa eaae dbbe fdbbbbfe gae gag dbbe efbbbbdf gae eaae fbbf fdbbbbfe ag eaae fbbf fdbbbbfeaac cag ebbd efbbbdfaac aac bbd fdbbbdae caa dbb fbbbbdf aac dbbe fdbbbbfe caa fbbe edbbbbdf gac fbbf eaadbbbbfe eaae fbbf caacfbbbbdf gag ebbd caac fdbbbbfe aae ebbd gaae efbbbbdf ag dbd gaae fdbbbbfe eae dbbe eaag efbbbbdf cg dbbe eaag fdbbbb acfbbf caac efbb cafbbf caac f aabbf gaae caabd gaae gabd aag eabb eaag gdbb eaac edbbf caac dbbf caae fbbd gaae ebbd gag ebbdc eaag dbba eaag dbbac caac dbbaa caae fbbgac gaae fbbfaae gaa ebbdgag eaa ebbdeaae ea dbd gag c dbbe aac dbbe cag fbbf aac fbbf caa fbbf aac ebbd caa bbd gac dbb eaae dbbe gag fbbe eaae fbbf gag fbbf aac ebbd cag ebbd aac dbd caa bbe caa bf gag f eaae gag eaae gag aac cag aac caa gac caa gag eaae gag eaae gag aac cag aac caa gac caa gag aae ``` <!-- end of image --> Case closed! This is definitely an intersection point in area A. The final answer is: two intersections found.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fe0505ff b,#0907fcff c,#fd8081ff d,#685ff5ff e,#ffc6c6ff f,#c2c2ffff g,#fe3c3dff ``` ```image e cae aea ea ea ae ca a gg ae ac a ae gc a a ea cg ca a gg cg ac a ae ea a ae ea a dbbf ca ae db fbbd ga a fb dbbf ag gc b fbbd ae a bf dbbf ae cg bf fbbd ea a bd dbbda ca bb fbbb a db dbbf ea fb acbbd ae b ae dbbf a b a fbbd aebf ea dbbf abd ca fbbd gbb gg dbbf bb ac fbbd db ae dbbf fb a fbb bg ea ba ca bda gg bdae ac db a ae db ae a fb a ea b gc ca bf a ga bf cg ag bd a ac bb ca ae db a a fb ea ea fb ae ga b a ag bf ac ac bd a ae bd gc a db a db cg fb a b ca bf a ea ae a ac a gc a cg a ea a ea ae a ac a gc a cg a ea a ``` <!-- end of image -->

Alright, let's get to work and investigate this image for intersections. My next step is to analyze the details within each area. <!-- image --> ```palette Key,Color ,#fefefeff a,#fc0d0cff b,#0809fcff c,#fe9595ff d,#6068e6ff e,#a0cba1ff f,#d36e5eff g,#b2d7b2ff ``` ```image c ac a ac a ac a ac a ac a ac a ac a ac a ac a ac a ac a ac a ac a ac a ac a ac a ac a ac a ac a ac a ac a ac a ac aeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee afgggggggggggggggggggggggggggggggggggggggggggggge eagggggggggggggggggggggggggggggggggggggggggggggge c eafggggggggggggggggggggggggggggggggggggggggggggge caa egaggggggggggggggggggggggggggggggggggggggggggggge aa egafgggggggggggggggggggggggggggggggggggggggggggge aac eggaggggggggggggggggggggggggggggggggggggggggggggeaac eggafggggggggggggggggggggggggggggggggggggggggggaac egggaggggggggggggggggggggggggggggggggggggggggfafe egggafgggggggggggggggggggggggggggggggggggggfaagge eggggagggggggggggggggggggggggggggggggggggfaagggge eggggafggggggggggggggggggggggggggggggggeaagggggge egggggagggggdbdgggggggggggggggggggggggaaeggggggge egggggafggebbebbbdggggggggggggggggggaafggggggggge eggggggagbbegggggdbbdgggggggggggggaafggggggggggge eggggggdbdggggggggggdbbbegggggggfafggggggggggggge eggggebbaggggggggggggggdbbbeggfaaggggggggggggggge egggbbegafggggggggggggggggdbbbfggggggggggggggggge egdbdggggaggggggggggggggggeaaebbbdgggggggggggggge dbbggggggafgggggggggggggeaaeggggedbbdggggggggggge bbgggggggggaggggggggggggaaeggggggggggdbbdeggggggge bbgegggggggggafgggggggggaafgggggggggggggggdbbbegggge dbd eggggggggggagggggggaafggggggggggggggggggggdbbbdge bb eggggggggggafggggfafgggggggggggggggggggggggggebbbd bb egggggggggggaggfaaggggggggggggggggggggggggggggggedbbd dbd egggggggggggafaagggggggggggggggggggggggggggggggge dbbd gbd eggggggggggggagggggggggggggggggggggggggggggggggge db bb eggggggggggggggggggggggggggggggggggggggggggggggge bbg eggggggggggggggggggggggggggggggggggggggggggggggge dbd eggggggggggggggggggggggggggggggggggggggggggggggge bb eggggggggggggggggggggggggggggggggggggggggggggggge bb eggggggggggggggggggggggggggggggggggggggggggggggge dbd eggggggggggggggggggggggggggggggggggggggggggggggge bb eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee ``` <!-- end of image --> I'm now examining the contents of area A in detail. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0909ff b,#0505feff c,#fe9394ff d,#9595feff e,#f8474dff f,#4b44f8ff g,#ead5e9ff ``` ```image a ac aa aac caa aac caa aac caa aac caa aac caa aac caa g aac gea caa geaaa aac geaaaeg caa caaaeg aac caaaeg caa caaaac aac ceaaac caa geaaac aac geaaac caa geaaaeg aac dbbfdg caaaeg caa gfbbbbbbfdg caaaeg aac gfbbbdgdfbbbbfdg caaaec caa dbbbfg gdfbbbbbfd caaaac aac dbbbfg dfbbbbbfd geaaac caefbbbd dfbbbbbfdg geaaac fbbbd gdbbbbbfdg geaaaeg dbbbfg gdfbbbbfdg geaaaeg gfbbbeac gdfbbbbbdg caaaeg gfbbbd caa dfbbbbbfdcaaaeg dbbbfg aac dfbbbbbfec dfbbfg caa cefbbbbbfdg gfbbbd aac geaaacgdfbbbbfdg dbbbd caa geaaac gdfbbbbbdg dbbbfg aac geaaaeg gdfbbbbbfd bbbd caa caaaeg dfbbbbbfd bd aac caaaeg dfbbbbbfdg g caa caaaec gdbbbbbfdg aac caaaac gdfbbbbfdg caa geaaac gdfbbbbbfd aac geaaac dfbbbbbfd caa geaaaeg dfbbbbbfd aac geaaaeg gdbbbb caa caaaeg gdf aac caaaeg caa caaaac aaeeaaac caaaac eac ``` <!-- end of image --> Aha! I've found an intersection inside area A! I can confirm there's two intersections in there.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fd2426ff b,#0404feff c,#ff8e8dff d,#8383ffff e,#fe0101ff f,#4540f9ff g,#d8caf0ff ``` ```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 e ac e ac e ac e c ac gee e ee ac eeg e aec ac aec e cea ac cea e cea ac gee e dbd eeg ac bbgfbbd aec e fbg fbbf aec fbd dbbfg aec gbbe dbbbg cea bbg ac gbbba fbd e geegfbbd dbf ac ee fbbd bb e eeg dbbf fbg ac aec dbbfg dbd e aec dbbbg gbb ac cec gbbbd bbg e cea gfbbd fbd acea fbbf gbf e db bb fbg dbd gbb bbg fbd bf ``` <!-- end of image -->

This is the image I'm working with. The goal is to count the intersections. I've spotted 1 narrow regions that might be worth examining further. Let's call them area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0605ff b,#0c0afbff c,#ee958dff d,#7278f3ff e,#b1d7b1ff f,#f5443fff g,#95c798ff ``` ```image d dbb bbd bbd bbd dbb bbd ggggggggggggggggggggggggggge bbd dbb eeeeeeeeeeeeeeeeeeeeeeeeeeeg dbbd dbb eeeeeeeeeeegaeeeeeeeeeeeeeeg bbb dbb eeeeeeeeeeeafaeeeeeeeeeeeeeg dbbd ebb eeeeeeeeeeeaeaceeeeeeeeeeeeg dbb bbd eeeeeeeeeeaceeaeeeeeeeeeeeeg ebbd bbd eeeeeeeeeeaeeecaeeeeeeeeeeeg dbb bbd eeeeeeeeeaceeeefaeeeeeeeeeeg bbd dbbeeeeeeeeeaeeeeeeaceeeeeeeedbbd dbbeeeeeeaceeeeeeeaeeeeeebbbg edbbeeeeaeeeeeeeecaeedbbdeeg eeedbbgaceeeeeeeeefbbbeeeeeg eeeeegbbdeeeeeeegbbbceeeeeeg eeeeeeacbbdeeedbbgeeaeeeeeeg eeeeeeaeeebbbbdeeeeecaeeeeeg eeeeeffeeeeegeeeeeeeeffeeeeg eeeeeaeeeeeeeeeeeeeeeeaceeeg eeeeffeeeeeeeeeeeeeeeeeaeeeg eeeeaeeeeeeeeeeeeeeeeeecaeeg eeeffeeeeeeeeeeeeeeeeeeeafeg eeeaeeeeeeeeeeeeeeeeeeeeeacg eeffeeeeeeeeeeeeeeeeeeeeeeag eeaeeeeeeeeeeeeeeeeeeeeeeeca effeeeeeeeeeeeeeeeeeeeeeeeeaf gagggggggggggggggggggggggggea cf a a ca cf af a a ca a a ca ca af a a ca a a ca ca ac a a ca a a fa a ac a a a a a fa a ac ac a a a ac fa a ac ac a a ca ac ff a ac fc a a ca fc ff a ac fc a a ca ff ff a ac ff a a ff a cf a cf a ca a ca a ca a ca a ``` <!-- end of image --> Let's see what secrets area A holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0404ff b,#0505feff c,#fd7778ff d,#a1a1feff e,#473df5ff f,#fb373aff g,#fec1c1ff ``` ```image gc gaac caaag gaafaf caf aaf aag gaac caf caag aag faf caf aac aag gaag caf caag aag faf caf aac ed aag gaag d bbed caf caag debb ebbbbd aag faf debbbe dbbbbd caf aac ebbbbed dbbbbd aag gaag debbbed debbbe caa caag dbbbbed debbbed aac ffebbbbd debbbefa dbbbbed ebbbed debbbbeag cebbbed debbbed caag facdbbbbd debbbbed faf gaa dbbbbd debbbed gaac fac debbbbbbbed gaag gaa debbbd caa fac dd faf gaa gaac fac gaag gaa caa fac faf gaa gaac fac gaag gaag caa fac faf gaag gaac fac gaag gaag caa faf fa gaag ga caf c gaag caf aag ``` <!-- end of image --> I observe an intersection inside area A. I've identified a total of two intersection points.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0404ff b,#0606feff c,#fe7d7eff d,#aaaaffff e,#514bf8ff f,#fe3a3aff g,#ffbcbcff ``` ```image d ebb bbd dbbe bbd ebbd ebe bbe ebe dbbd ebb ga ebe dbb aff dbbd dbbd a ac ebb bbd ag a dbbe bbd a ga ebbd ebe ag ff bbe ebe a ag dbbd ebb ag a ebe dbb a ga dbbd dbbdac febb dbbd dbbeg fcbbd ebbd a a bbbbe ga fc d ff a ag fc a a ga fc ff a ag ff a a ca cf ff a ag cf a a ca cf af a ag cf a a ca ca ac a ag ga a a ca ga ac a a ga ga a ca ga ac ag a ga ga ag ca a ac ag a a ga ag ff a ac ag a a ga ac ff a ag fc a a ga fc ff a ag fc a a ga fc ff a ag ff a a cf a cf a cf a cf a ca a ga a ga a ``` <!-- end of image -->

I'm approaching this image with caution. Intersections might be tricky to spot. These spots are like clues. Let's see what they reveal about potential intersections. <!-- image --> ```palette Key,Color ,#fefefeff a,#4b4bf6ff b,#f74845ff c,#0708feff d,#f69d99ff e,#fe0605ff f,#a3a5faff g,#add4adff ``` ```image f ac cc ca ca cf fc fc ac ac ca ca cf cf fc ac ac b cc deed ca be e cf eb deggggggggggggggg cf ed ebgggggggggggggg fc de geggggggggggggggfc be ggeggggggggggggac ee ggbbggggggggggcc eb gggedggggggggcag ed ggggegggggggcagg de ggggbegggggcfggg be gggggedgggcggggg eb ggggggegacgggggg ed ggggggdacggggggg de ggggggccbggggggg be gggggccgeggggggg ee ggggcagggegggggg eb gggcaggggbeggggg ded ggcgggggggedgggg be fcgggggggggegggg ee acggggggggggbeggg eb acggggggggggggebgg ed cc gggggggggggggegg de cc gggggggggggggdeg be ca ggggggggggggggeb eb ca e ed ca e de ca bb be ca ed ee cf e cf de cf ed cf e cf de cf bb cf e c e c be fc ed fc e fc de fc ed fc e fc de ac bb ac e ac e ac be ac ed ac e cc de cc ed ca e ca de ca bb ca e ca e be 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,#504bf9ff b,#fb373aff c,#0707feff d,#fdbec0ff e,#fe0404ff f,#a8a8feff g,#fe7b7bff ``` ```image deed beb eeg deed gee beb deeg geed a beb cc eeg fccc deed fcca beb fcca eeg acca deed accf gee accf beb cccf deeg fccc geed fcca beb fcca eegacca deaccf accf accbg fcccdeed fccc gee fcca beb fcca deeg acca geed accf beb accf eeg cccf deed fccc gee fcca beg fcca deed acca gee ccf beb cf deeg f geed beb eeg deed gee be ``` <!-- end of image --> I am surprised, so clear, an intersection has appeared in area A. After careful examination, I conclude that there is one intersection.

<!-- image --> ```palette Key,Color ,#fefefeff a,#4b48fcff b,#ff3b3bff c,#0707feff d,#ffc4c4ff e,#ff0404ff f,#a8a8ffff g,#ff7f7fff ``` ```image f ac cc ca ca cf fc fc ac ac ca ca cf cf fc ac ac db cc geeg ca be e cf eb de cf eg eg fc ded e fc be de ac ee bb cc eb ed ca ded e ca ge ge cf be eg fc eb e fc eg dac ded acg be ca e ee ca de eg cf bb ded cf ed ge fc e be ac ge eb ac eg deg cc e ge cc de be ca bb eb ca ed eg ca de ded ca bb be ca ed ee cf e d cf ge cf eg cf e cf de cf bb cf ed c de c bb fc ed fc e fc ge fc eg fc e fc de ac bb ac ed ac e ac gb ac ed ac e cc ge cc eg ca e ca de ca bb ca ed ca e ge ed e ge eg e ``` <!-- end of image -->

Alright, let's get to work and investigate this image for intersections. My analysis shows there's absolutely no intersections in the image

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff4545ff b,#0606ffff c,#a1a1ffff d,#ffcbcbff e,#ff0404ff f,#5151ffff g,#ff8a8aff ``` ```image c fbbbbfc cbbbbfc cfbbbbfc cbbbbbc cfbbbbfc cfbbbbc cfbbbf cbbbc cbbbc cbbbc fbbc fbbf fbbf cbbf cbbbc cbbbc cbbbc fbbf fbbf fbbf cb e ded de ge ge ae ae ee ea ea eg eg ed ded de ge ge ae ae ea ea ea eg ed ded ded ge ge ae ae ee ea ea eg eg ed ded de ge ge dgaeeeee dggaeeeeeeagd dgaeeeeeeagd dgaeeeeeeaagd eeeeagd ``` <!-- end of image -->

I have a feeling there might be some intersections in this image. I'm extremely confident. No intersections at all.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0808ffff b,#ff0404ff c,#ff8686ff d,#b0b0ffff e,#5858ffff f,#ffc2c2ff g,#ff4444ff ``` ```image d daa aa aad aad eae eae dae daa daa aa aad aad eae eae dae daa daa aad aad ead eae eae daa aa ead dae aa dae aa ead dae aa dae aa ead aa aa dae aa ead aa ead dae aa ead aa ffcccgggbbbc ffcccgggbbbbbbbbbbbbbbbgggccfff fgbbgf bbbbbgggcccff fbbbg cbbbc fgbbgf fbbbgf cbbbc fgbbbf fgbbgf cbbbc gbbbf fgbbgf cbb ``` <!-- end of image -->

I'm examining this image closely. My goal: find any and all intersections. These spots mark what I'd call 'danger zones' - areas where intersections are more likely. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd0607ff b,#0b0cfcff c,#efa098ff d,#6d77ebff e,#f04c48ff f,#b1d6b2ff g,#97c599ff ``` ```image f bb bf b fb bb bd b fb db bd b b db bd b b db bd b b db bd b ea b aca db ac ea db bd ca ae dbb bggggggggggggagggggagggggggggggggggggg dbb gbffffffffffaeffffffafffffffffffffffff fbb fdbffffffffgafffffffcaffffffffffffffff bb ffbbfffffffafffffffffeafffffffffffffff bb fffbdfffffeeffffffffffacffffffffffffff bbf ffffbfffffaffffffffffffaffffffffffffff bbf ffffdbfffacffffffffffffgafffffffffffff bbd fffffbbfeaffffffffffffffeaffffffffffff bbd ffffffbdaffffffffffffffffaefffffffffff dbd fffffffbefffffffffffffffffacfffffffffdbd ffffffcabffffffffffffffffffafffffffdbb ffffffafbbfffffffffffffffffcaffffdbbff fffffeeffbdfffffffffffffffffeafdbbffff fffffaffffbffffffffffffffffffebbffffff ffffagffffgbfffffffffffffffgbbafffffff fffeaffffffdbffffffffffffgbbfffaffffff fffaffffffffbdffffffffffbbgffffeafffff ffacfffffffffbffffffffbbgfffffffaeffff fcaffffffffffgbfffffbbdffffffffffacfff faffffffffffffdbffbbdfffffffffffffafff aefffffffffffffbbbdfffffffffffffffcaff cafffffffffffffffdffffffffffffffffffeaf agfffffffffffffffffffffffffffffffffffae eegggggggggggggggggggggggggggggggggggggac a a ac ca ca ee a ac ac a ca a a ea ee ae a ac a a ea ca a ea ac ac ca a a a ae ca a ae a ac ee a a ca ac ea ca ac a a ac a ca ca a ee ee ac a a a ``` <!-- end of image --> This close-up might reveal an intersection in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0405ff b,#0807feff c,#fe7879ff d,#ababfeff e,#fc3639ff f,#5957fcff g,#fec2c2ff ``` ```image dbbd cae caag fbb gaag eae bbf eac eae dbbd caa gaac dbbd gaag gaag fbb eae caag bbf caa eae bbf aac aac dbbd eae gaac fbb gaag caag fbf aac eaa bbf cae eae dbbd gaag gaac fbb eac gaag fbf caa caag bbf gaag eae dbbdeae aae fbbaag gaac fbbc caag f cbbf caa fbb gaebbd eae fbbbf eacfbbd gaac fbbbfd caa fbb gaag dbbbfd gaag bbf caag dbbbbd eae dbbd eae dbbbbd caa dbbd eaedbbbbd aac fbb gebbbbd eae bbf dfbbbf gaag dbbd dfbbbfaag aac dbbd dfbbbf eae cae fbb dfbbbf aac gaag bbf fbbbf gaac eac dbbd fbbbfd caag caa dbbd fbbbfd eaa gaag fbb fbbbfd eae eae bbf dbbbfd gaac gaag bbf dbbbbd gaag aac dbbd dbbbbd caag cae fbb dbbbbd eae gaag bbf dbbbbd aac eac bbbbbbd gaac caa dbbbf caag aag df caa ae eae a gaac c gaa ``` <!-- end of image --> There is an intersection point visible in this close-up of area A. After a long analysis, I found two intersections.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fe0404ff b,#0707ffff c,#fe8687ff d,#a5a5feff e,#fb393dff f,#4c4cffff g,#ffcdcdff ``` ```image d ff bd b db ff bd b db fb bd b db fb bd b b fb bf b b db bf bd ca b aga db ac ea db bf ca ac dbb bd a ag dbb b ec a dbb db ga ca bb ff ag ee bb bd ee ac bbd b a a bbd db ag ga bbd ff ca ca fbd bda ae fbf bc ag fbf geb a fbf a fb ga dbf ee bd ee dbb ga b ebb ag db dbbag ce fb bb ga a bd bb ca ac b bbd ee ca b bbd ag a fb bbd a ec bbbd ga ga d ea ag ac ee ag a a ag ca ca ee a ac ac a ga ga a ca ee ae ga ag ag a ce ga a ee ac ac ca ag a ga ec ca ga ee ag ag ee a a ga ag ea ca ac a ag ac a ga ca a ee ee ac ga a ag ``` <!-- end of image -->

I'm optimistic that I'll find some intersections in this image. My next step is to analyze the details within each area. <!-- image --> ```palette Key,Color ,#fefefeff a,#4f50edff b,#fe0605ff c,#ed5249ff d,#9fa4f6ff e,#faa9a7ff f,#0706fdff g,#afd6b0ff ``` ```image e cb cb eb eb eb f eb fa be af be df be df bc ggggggggggggggggggggggggggggggggfgggg bc gggggggggggggggggggggggggggggggfdgggg bc ggggggggggggggggggggggggggggggfaggggg bb gggggggggggggggggggggggggggggafgggggg cb ggggggggggggggggggggggggggggafggggggg cb ggggggggggggggggggggggggggggfgggggggg cb gggggggggggggggggggggggggggfggggggggg eb ggggggggggggggggggggggggggfdggggggggg eb gggggggggggggggggggggggggfagggggggggg eb ggggggggggggggggggggggggafggggggggcbb b gggggggggggggggggggggggafggggggcbbcgg be gggggggggggggggggggggggfggggcbbcggggg be ggggggggggggggggggggggfggcbbcgggggggg be gggggggggggggggggggggfabbcggggggggggg bc gggggggggggggggggggefabgggggggggggggg bc gggggggggggggggggbbffgggggggggggggggg bc ggggggggggggggbbbeafggggggggggggggggg bb gggggggggggcbbcgggfgggggggggggggggggg cb ggggggggcbbcgggggfggggggggggggggggggg cb gggggcbbcgggggggfdggggggggggggggggggg cb ggcbbcgggggggggfagggggggggggggggggggg eb ebbcgggggggggggafggggggggggggggggggggg eb ebbbgggggggggggggafgggggggggggggggggggggg ebebbbe gggggggggggggfggggggggggggggggggggggg be ggggggggggggfgggggggggggggggggggggggg gggggggggggfdgggggggggggggggggggggggg ggggggggggfaggggggggggggggggggggggggg gggggggggafgggggggggggggggggggggggggg ggggggggafggggggggggggggggggggggggggg ggggggggfgggggggggggggggggggggggggggg f fd fa af df f f fd fa af df f f fd fa af df df ff afd dfa ff afd dfa ff dfd ff afd dfa ff afd dfa ff afd ff ff dfa ff afd fa ``` <!-- end of image --> Let's take a closer look at area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#524ffbff b,#fe0404ff c,#fa4449ff d,#a2a0fdff e,#fe9090ff f,#0907fdff g,#ecd7e9ff ``` ```image gffa ffa affg affg dffd dffd gffa ffa affg affg dffd dffd gffa ffa affg affg dffd dffd gffa ffa gec affg ecbbb affg ecbbbbce dffd ecbbbbceg dffd gcbbbbbeg gffa gebbbbbeg ffa gebbbbbcg affg gecbbbbce affggecbbbbce dffdcbbbbce dffcbbbceg ecffabceg gcbbfffeg gebbbbfffg gebbbbbcaffg gecbbbbce dffd gecbbbbce dffd ecbbbbce gffa ecbbbbceg ffa ecbbbbceg affg gcbbbbbeg affg gebbbbbeg dffd gebbbbbcg dffd gecbbbbce gffa gecbbbbce ffa bbbbce affg bceg affg g dffd dffd gffa ffa affg affg dffd dffd gffa ffa affg affg dffd dffd gffa ``` <!-- end of image --> As I suspected, there's an intersection within area A. My investigation reveals that there is exactly one intersection in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#4c49fbff b,#ff0707ff c,#ff5656ff d,#9d9afcff e,#ffa7a7ff f,#0706fdff g,#e8ddf4ff ``` ```image e cb cb cb eb eb f gbg fa gbe af be df be gf bc fg bc fd bc fa bb af bb df cb gf cb fg eb fd eb fa g ebg af cbb gbg df cbbe gbe gf cbbc be fg ebbc be fdbbc bc efabg bc ebbff bb gbbbedf bb cbbe gf cb cbbe fg cb cbbc fd cb ebbc fa eb ebbc af eb ebbbg df ebebbbe gf gbe fg fd fa af df gf fg fd fa af df gf fg fd fa af df gf fg fd fa af df df gff afg dfa ff afd gfa ffg dfd gff afg dfa ff afd gfa ffg dfd gff afg dfa ff afd fa ``` <!-- end of image -->

I'm on the case! Let's uncover any intersections hidden in this image. My final answer is: no intersections found.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0303ff b,#5d5dffff c,#ff8383ff d,#0707ffff e,#ffc4c4ff f,#b5b5ffff g,#ff3d3dff ``` ```image c ga ca ca ea eae ae ac ac ag ag ga ga ca ca ea eae ae ac ac ag ag ga ga ca ca ecaaa ea egaaaace eae cgaaagc ae cgaaagc ac ecaaaage ag egaaaace ag egaaaac aa cgaaagc gaaage d fdb dd bdf dd bdf fdb dd fdb dd bdf dd bdf fdb dd fdb dd bdf dd bdf fdb dd fdb dd bdf dd bdf fdb fbddd fbddddbf fbddddbf fbdddddb fbdddddbf fbdddddbf dddbf ``` <!-- end of image -->

I'm optimistic that I'll find some intersections in this image. The image has some tight areas where segments are too close. I should investigate those closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#fc0c0bff b,#0a0bfbff c,#ea756bff d,#3b41f2ff e,#b2d7b1ff f,#99c795ff g,#a2a2ffff ``` ```image e ac a a ca ac a ca ac a afffffffffffffffffffffffffffffffffff a aaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee a faceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee a feaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee ea fecaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee ca feeaceeeeeeeeeeeeeeeeeeeeeeeeeeeeeee ca g feeeaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee ca db feeefaeeeeeeeeeeeeeeeeeeeeeeeeeeeeee ca db feeeeaaeeeeeeeeeeeeeeeeeeeeeeeeeeeee ca db feeeeeafeeeeeeeeeeeeeeeeeeeeeeeeeeee aa db feeeeeeaeeeeeeeeeeeeeeeeeeeeeeeeeeee aa db feeeeeecaeeeeeeeeeeeeeeeeeeeeeeeeeee aa dbfeeeeeeeaceeeeeeeeeeeeeeeeeeeeeeeeee ac dbeeeeeeeeaeeeeeeeeeeeeeeeeeeeeeeeeee ac bbeeeeeeecaeeeeeeeeeeeeeeeeeeeeeeeee ac fbbeeeeeeeaaeeeeeeeeeeeeeeeeeeeeeeee ac febbeeeeeeeafeeeeeeeeeeeeeeeeeeeeeee ae feebbeeeeeeeaeeeeeeeeeeeeeeeeeeeeeee ae feeebbeeeeeecaeeeeeeeeeeeeeeeeeeeeee a feeeebbeeeeeeaceeeeeeeeeeeeeeeeeeeee a feeeeebbeeeeeeaeeeeeeeeeeeeeeeeeeeee ea feeeeeebdeeeeecaeeeeeeeeeeeeeeeeeeee ca feeeeeeebdeeeeeaceeeeeeeeeeeeeeeeeee ca feeeeeeeebdeeeeeaeeeeeeeeeeeeeeeeeee ca feeeeeeeeebdeeeefaeeeeeeeeeeeeeeeeee ca feeeeeeeeeebdeeeecaeeeeeeeeeeeeeeeee aa feeeeeeeeeeebdeeeeaceeeeeeeeeeeeeeee aa feeeeeeeeeeeebdeeeeaeeeeeeeeeeeeeeee aa feeeeeeeeeeeeebdeeecaeeeeeeeeeeeeeee aa feeeeeeeeeeeeeebdeeeaceeeeeeeeeeeeee ac feeeeeeeeeeeeeeebdeeeaeeeeeeeeeeeeee ac feeeeeeeeeeeeeeeebdeefaeeeeeeeeeeeee ac feeeeeeeeeeeeeeeeebdeeaaeeeeeeeeeeee ac feeeeeeeeeeeeeeeeeebdeeafeeeeeeeeeee ae feeeeeeeeeeeeeeeeeeebdeeaeeeeeeeeeefa feeeeeeeeeeeeeeeeeeeebdecaeeeeeeeefa feeeeeeeeeeeeeeeeeeeeebdeaceeeeeefaf feeeeeeeeeeeeeeeeeeeeeebdeaeeeeecaee feeeeeeeeeeeeeeeeeeeeeeebdcaeeecaeee feeeeeeeeeeeeeeeeeeeeeeeebdaaecaeeee feeeeeeeeeeeeeeeeeeeeeeeeebdaaaeeeee effffffffffffffffffffffffffbdaffffff bg bb gbd dbg bb gbd dbg bb gbg bb bd dbg bb gbd dbg bb gbd dbg bb gbg bb bd dbg bb gbd dbg bb gb ``` <!-- end of image --> Here's a close-up of the area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff0505ff b,#0a0affff c,#fe8383ff d,#4d4dfeff e,#fec6c6ff f,#fe4040ff g,#c4c4ffff ``` ```image af aac caae faf aac eaae caa faf eaac caae faf aac eaae caa faf eaac caae faf eaac eaae faa aaf eaae caae faf g eaac bg caae bbg faf bbbg aac bbbg eaae bbbg caa bbb faf bbb eaac gbbb caae gbbb faf gbbb aac gbbb eaae gbbb caa gbbb faf gbbb eaac gbbd caae gbbd faf gbbd eaac gbbd eaae gbbd faa gbbd aaf gbbd eaae gbbd caae gbbd faf gbbd eaac gbbd caae gbbd faf gbbd aac gbbd eaae gbbd caa gbbd faf gbbd eaac gbbd caae gbbd faf gbbd aac gbbd eaae gbbd caa gbbd faf gbbd eaac gbbd caae gbbd faf gbbd eaac gbbd eaae gbbd faa gbbd aaf gbbd eaae ef gbbd caae eaa gbbd faf eaaf gbbd eaac eaaf gbbd caae eaaf gbbd faf eaaf gbbd aac caaf gbbd eaae caaf gbbd caa caac gbbd faf caac gbbdeaac caac gbbdcaafaac gbbdfaaae ``` <!-- end of image --> My analysis shows that the lines in area A do not cross. There's definitely not a single intersection on the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0505ff b,#0e0effff c,#ff8383ff d,#4f4ffeff e,#ffc6c6ff f,#ff4040ff g,#afafffff ``` ```image e ff ae a ca ac a ea af ae ea a ff ae ae eae a ea ca ea ac ca g a ca db ea fa db ff fa db ae fa db a aa bb ca af bb ac af bb a af bb ea ac bb ff ac bb ae ae bb a ae bb ca eae bb ac ea bb a ea bd ea ca bd af ca bd ae ca bd ea fa bd ff fa bd ae fa bd a af bd ca af bd ac af bd a ac bd ea ac bd ff ac bd ae ae bd a ae bd ca eae bd ac ea bd a ea bdea ca bdff ca bdafa bda bd bb gbd dbg bb gbd dbg bb gbd bb gbb dbg bb gbd dbg bb gbd dbg bb gbd bb gbb dbg bb gbd dbg bb gb ``` <!-- end of image -->

Alright, let's get to work and investigate this image for intersections. I need to zoom in on these areas to get a better look. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0909ff b,#0505feff c,#ffb3b3ff d,#a2a2ffff e,#5151ffff f,#f85d59ff g,#add4adff ``` ```image d ebb dbbd dbbd ebe ebb dbbd bbe ebb dbbd gggggggggggggggg bbd gggggggggggggggg ebe gggggggggggggggg ebb gggggggggggggggg dbbd gggggggggggggggg bbe dddeeebbbbbbbbbbbbgggg ebb dddeebbbbbbbbbbbbbeedddgggggggggggggggg dbbbbbbbbbbeeeddd gggggggggggagggg ggggggggggfagggg ggggggggggaggggg gggggggggagggggg ggggggggafgggggg ggggggggaggggggg gggggggagggggggg ggggggafgggggggg gggggfaggggggggg gggggagggggggggg ggggafgggggggggg gggfaggggggggggg gggagggggggggggg ggaggggggggggggg gfaggggggggggggg gagggggggggggggg aggggggggggggggg faggggggggggggggg cagggggggggggggggg a af ca a af ca a ac fa a ac fa a a af ca a af ca a ac fa a ac c fa aac a aa ac caa ff caa ca faf a faf af aac ca aac a aa af caa ca caf a faf ac fac fa aac a aa ac caa fa caa a faf a fafff aa ``` <!-- end of image --> This is a magnified view of the region A. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff0404ff b,#0506ffff c,#ff7b7bff d,#bbbbffff e,#5b5bffff f,#ff3838ff g,#ffbebeff ``` ```image dd ddddddeeeeeebbbbbbbe bbbbbbbbbbbbbbbbbbbbbbbe bbbbbbbeeeeeedddddd d g gaf aac faf caag gaac faf caa gaag faf caa gaag fac caf gaag aac faf gaag aac faf caag gaac faf caa gaag faf caa gaag aac caf gaag aac faf aag ac f ``` <!-- end of image --> It's a shame, but area A doesn't contain an intersection. I can confidently say that there are no intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0505ff b,#0505ffff c,#ff8b8bff d,#aaaaffff e,#5454ffff f,#ff4242ff g,#ffccccff ``` ```image d ebb dbbd dbbd ebe ebb dbbd bbe ebb dbbd dbbd ebe ebb dbbd d bbe dddeeebbbbbbbbbbbb ebb ddeeebbbbbbbbbbbbbeeeddd dbbbbbbbbbbeeeddd a ff ga ag ff ga a ac ca a ac ca a ag fa a ag ff ga a af ga a ac ca a ac ca a ag ff ga ag ff ga a ac ca a ac ca a ag g fa aag a aag ag gaa ff caf ga caf a fac ff fac ga aag a gaa ac gaa ca caf a faf ac fac ca aag a aag ag gaa ff caf ga caf ag facff fa ``` <!-- end of image -->

Time to put on my detective hat and find those intersection points! These zones indicate regions where lines appear to be in close proximity. <!-- image --> ```palette Key,Color ,#fefefeff a,#ec504bff b,#0a0bfdff c,#b5b6feff d,#fd0706ff e,#acd3adff f,#f3a19bff g,#5960f0ff ``` ```image c bg b cb bg c b cb cb cb bg b b bc cb bc bg bg b bb eeebeeeeeeeeeeeee gb eeebgeeeeeeeeeeee cb eeeebeeeeeeeeeeee cb eeeeebeeeeeeeeeee ff b eeeeebgeeeeeeeeee faddddd bc eeeeeebeeeeeeeeee fddddaf d bc eeeeeeebeeeeeeeaddddaf aa bg eeeeeeebgfaddddaf d bb eeeefaddbdaeeeeee d gb faddddaeeebeeeeeee aa cb ddddaaeeeeeeeebgeeeeee df cb f eeeeeeeeeebeeeeee d b eeeeeeeeeeebeeeee ad bc eeeeeeeeeeebgeeee df bc eeeeeeeeeeeebeeee d bg eeeeeeeeeeeeebeee fd bb eeeeeeeeeeeeebgee df gb b d cb cb eeadeeeeeeeeeebe bg eeedaeeeeeeeebee b eeeedeeeeeeebeee cb eeeefdeeeeebgeee bg eeeeedaeeebgeeee b eeeeeedeebbeeeee cb eeeeeefdgbeeeeee bg eeeeeeeabeeeeeee b eeeeeeebdeeeeeee cb eeeeeebeedeeeeee bg eeeeebeeeaaeeeee b eeeebgeeeedeeeee cb eeebgeeeeeedeeee bg eebbeeeeeeeadeee b egbeeeeeeeeedfee cb gbeeeeeeeeeeedee bg cb ad b b df cb bc d bg bc fd b bg df cb bb d bg gb fd bcb df cb d fd da d fd aa d d aa d d ad df d ad df d fd df d fd df d fd da d ``` <!-- end of image --> Let's zoom in on area A to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#f9353aff b,#0a0afeff c,#bcbcffff d,#ff0202ff e,#fa7b7fff f,#ffc0c0ff g,#6964f9ff ``` ```image cbbc gbb bbg cbbc gbb bbg cbbc gbb bbg cbbc gbb bbg cbbc ffea gbb feeaddddd bbg feeadddddddaee febbaddddddaeff feaadddgbbaaeff ffeadddddddaaebbg adddddddaeef cbbc dddaeef gbb ff bbg cbbc gbb bbg cbbc gbb bbg cbbc gbb bbg cbbc gbb ``` <!-- end of image --> I observe an intersection inside area A. 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 ,#fefdfeff a,#ff5151ff b,#0909feff c,#b8b8feff d,#fe0707ff e,#860b84ff f,#fea8a8ff g,#5b58fcff ``` ```image ada cbb ddf cbbg fdd cbbg ada bbg ddf bbb fddf gbb add gbbc dda gbbc fddf cbbc add cbbg dda cbbg fddf bbg add bbb dda gbb fddfgbbc adebbc ebbc cbbef cbbgdd bbg ada bbb ddf gbb fdd gbbc ada gbbc ddf cbbc fdd cbbg ada cbbg ddf bbg fddf bbb add gbb dda gbbc fddf gbbc add ``` <!-- end of image --> There is an intersection point visible in this close-up of area B. The image features two intersection points.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fb474aff b,#2626ffff c,#babaffff d,#fe0505ff e,#0101ffff f,#ffa2a2ff g,#6464ffff ``` ```image c bg e ce bg c e ce ce ce bg e e ec ce eg bg eg e bb ce ge bg ce e ce ce ff e bg fadddad ec e fadddaf d ec ce fddddaf aa eg bgfaddddaf d bb faddedf d ge fadddaf ce aa ce ddddaf bg df ce f e d e ce ad ec bg df ec e d eg ce fd bb bg df ge e d ce ce fd ce bg df e e d ec ce fd ec bg da eg e d bb ce fdge bg ae e ced ce e d bg ec aa e ec d ce eg d bg bb aa e ge df ce ce d bg ce ad e e df ce ec d bg ec fd e eg df ce bb d bg ge fd ege df ce d fd da d fd aa d d aa d d aa df d ad df d fd df d fd df d fd da d ``` <!-- end of image -->

Based on a first glance, I suspect there could be intersection regions here. These regions highlight areas that look suspicious. Lines seem to converge within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0606ff b,#6974e6ff c,#f6938fff d,#0c0dfcff e,#b0d6b0ff f,#ed443fff g,#f0f2eeff ``` ```image g ca aca ca ac ag a ga ca ac ac a a fc ca a ac ff a dg a ca gdd ca ac bdb a a dd ga ca bdb ag ac ddg ggggggggggggaggggggggggggggggagggggggggggggggg gdd geeeeeeeeeeeaceeeeeeeeeeeeeeeefaeeeeeeeeeeeeeeeg bdg geeeeeeeeeeeaeeeeeeeeeeeeeeeeeeaceeeeeeeeeeeeeeg gdd geeeeeeeeeeffeeeeeeeeeeeeeeeeeeeaeeeeeeeeeeeeeeg bdbgeeeeeeeeeeaeeeeeeeeeeeeeeeeeeeefaeeeeeeeeeeeeeg ddeeeeeeeeeffeeeeeeeeeeeeeeeeeeeeeaceeeeeeeeeeeeg eddeeeeeeeaeeeeeeeeeeeeeeeeeeeeeeeaeeeeeeeeeeeeg b geddeeeeecaeeeeeeeeeeeeeeeeeeeeeeefaeeeeeeeeeeeg bdddb geeeddeeeaeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeeeeeeeeg bdddbg geeeebdbcaeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeeeeeeeg eddddg geeeeeeddeeeeeeeeeeeeeeeeeeeeeeeeeeeffeeeeeeeeeedddde geeeeeeefdbeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeeeddddb geeeeeeaceddeeeeeeeeeeeeeeeeeeeeeeeeeeaebdddbeeg geeeeeeaeeeeddeeeeeeeeeeeeeeeeeeeeeebdddbeeeeeeg geeeeeffeeeeebdbeeeeeeeeeeeeeeeebdddbeeaeeeeeeeg geeeeeaeeeeeeeeddeeeeeeeeeeebdddbeeeeeeeaeeeeeeg geeeeffeeeeeeeeebdbeeeeebddddeeeeeeeeeeeffeeeeeg geeeeaeeeeeeeeeeeeddbddddbeeeeeeeeeeeeeeeaeeeeeg geeecaeeeeeeeeeeeeeedbeeeeeeeeeeeeeeeeeeeeaeeeeg geeeaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeffeeeg geecaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeg geeaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeg geeaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeafeg geaceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeg gaggggggggggggggggggggggggggggggggggggggggggca fc af a ag cf ca a ac ca a ag ca ga ac ag a ga ca ac ac a a fc ca a ac cf a a ca ca ac ag a ga ca ag ac ga a ac ca a ac fc a a ca cf ac a ga ca c ag ga ag ga ac a fc a cf a ca ag ``` <!-- end of image --> Time to investigate area A up close. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0303ff b,#534efaff c,#ff7c7cff d,#0606feff e,#a8a7fdff f,#fb3539ff g,#fec0c0ff ``` ```image aag fac caf gaag aag caa caf fac fac gaag gaa caf fac fac gaa gaag fac caf gaag aac b caf gaag dde aag caf dddb caf aac eddde aag gaag bddbe caf faf edddb fac aac bddde gaa gaag edddb fac faf bddde gaa aac ebddbfac gaag edddbg faf bddde aac ee afdddb gaag eebddd caf bddde faf ebddddddb aag ebddb aac ebddddddbee caf eddde ebddddddbee fac bddde ebbdddddbbe gaa edddb ebbdddddbbfac fac bddde eebddddddbe caag gaa edddb eebddddddbe faf fac eddde ebddddddbe gaac gaag bddbe ebddddddbee caa caf edddb ebddddddbee faf aag bddde ebddddddbee gaac caf edddbebbdddddbbe caa aag bdddddddbe faf caf ebdbe gaag fac caa gaa faf fac gaag gaa caa fac faf gaag gaag caf caa aag fac caf gaag ``` <!-- end of image --> Eureka! There's definitely an intersection in area A! I've identified a total of two intersection points.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0505ff b,#5454ffff c,#ff8383ff d,#0808feff e,#ababffff f,#fc3c3fff g,#fec1c1ff ``` ```image g ca aca ga ac ag a a ca ag ac a a fc ca a ac cf a d a ca dd cf ag bde a a dd ga ca edb ag ag dd a a edb ag ca bde a ag dd fc a ede a cf dd cf ag edb a a b bde ca ff edddb dd a ag edddbe bdega a edddbe ddg ff ebddde fdb ag ebddde ag bd a bddde a dd bdddb fc bde edddb ag a dd edddb ga cf edb edddbe ff a ddebddbe a ca ede ga a ff ga a ag ga a ff ag a a ga fc fc a a cf ga a ac ca a a ga ga ac ag a a ga ac ac a a fc ca a ac cf a a ca ca ac a a ga ca ag ag a a ac ca a ag fc a a ca cf ag a a ga g a ga ag a ac a fc a cf a ga a ``` <!-- end of image -->

This image seems promising for intersection detection. These zones are intriguing. I bet there's something interesting happening within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#5d60f8ff b,#fe0303ff c,#f5a9a5ff d,#0809fdff e,#acadfcff f,#f53639ff g,#add4aeff ``` ```image a d d aa d d aa ed d da ed d da ed d da ed d da ed d da ed d da ed d da ed d da ed d de ed d de ed d de ed d b de bc ad bb d fb de bc ad bb d fb de cbc ad bb d fb de cbc ad bf d fb de cbc ad bf d fb gggggggggggggggggdgg cbc ggggggggggggggggadgg bfggggggggggggggggdggg fbggggggggggggggdgggg gbcgggggggggggadgggg ggbfggggggggggdggggg gggfbggggggggdgggggg ggggcbcgggggadgggggg ggggggbfgggddggggggg gggggggffddagggggggg ggggggdddbcggggggggg gggaddagggbfgggggggg ccccccccc gddagggggggfbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbfffffff addegggggggggggggggggg edda gggggggggggggggggggg adde gggggggggggggggggggg edda gggggggggggggggggggg ddd gggggggggggggggggggg adde gggggggggggggggggggg dda gggggggggggggggggggg adde edda dde ``` <!-- end of image --> Eureka! Let's inspect this close up of area A <!-- image --> ```palette Key,Color ,#fefefeff a,#3230fcff b,#fe0404ff c,#ff9494ff d,#0303feff e,#bbbbffff f,#f84c53ff g,#6e6dfeff ``` ```image gda edde ddg gda edde ddg bc gda bbf edde cbbb ddg cbbbc gda fbbf edde cbbf ddg cbbbc gda fbbf edde cbbf ddg cbbbc ada fbbf edde cbbf eaddg cbbbc egddddg fbfadddag egddddge gadddafbbc eaddddge fbbf egddddae cbbf eaddddge cbbbcccccccccccccc egddddae fbbbbbbbbbbbbbbb adddag cffffffffffffff ddge g ``` <!-- end of image --> Area A contains an intersection. I have found one intersection!

<!-- image --> ```palette Key,Color ,#fefefeff a,#3838feff b,#fe0303ff c,#ffb2b2ff d,#0404ffff e,#bdbdffff f,#fa383dff g,#7a7affff ``` ```image g d de aa ed d aa ed d aa ed d aa ed d ag ed d ag ed d dg ed d dg ed d dg ed d dg ed d dg gd d dg gd d dg gd d b de bc gd bb d fb de cbc gd bb d fb de cbc gd bb d fb de cbc gd bf d fb de cbc ga bf d fb de cbc ga bf d fb de cbc aa bf d fb de cbc aa bf ad ffddg adabc gdde bf cccccccccc edda fbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbfffffff gdde eddg adde eddg ada gddg edda gdde edda dde ``` <!-- end of image -->

I'm ready to tackle this image and find those intersections! It's crucial to examine these regions more closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#0708feff b,#fe0606ff c,#a7a8fdff d,#f4534eff e,#faa6a4ff f,#add5adff g,#5355f9ff ``` ```image c ca a ac ag ca a a ac ga ca a ac ag ga a a ac gg ca a ac ag ga ca a ac ag ca a a ac ga ca a ac ag ga a a ac ga ca a bb ac ebbe ag ebb ga dbd ca bbd a ebbe ac ebb ag dbd ca bbd a ebbe aaaggcc ffffffffafffffff ebb ccggaaaaaaaaaaggcc fffffffagfffffff dbd ccggaaaaaaaaagggcffffgaffffffff bbd ccgaaaaaafffffffff ebbe ffffffffffffffffdbb ffffffffffffffdbd ffffffffffffbbdf fffffffffebbefff fffffffdbbffffff fffffdbdffffffff fffbbdffffffffff fbbdffffffffffff bbdffffffffffffff bbeffffffffffffffff ebbe ffffffffffffffff ebb ffffffffffffffff ebb ffffffffffffffff dbb ffffffffffffffff dbd ffffffffffffffff dbd bbd bbe bbe ebbe ebb ebb bb ``` <!-- end of image --> Could this be where the intersection is hiding, in area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#0909feff b,#ff0303ff c,#5b5bffff d,#ff3535ff e,#ffc6c6ff f,#aeaeffff g,#ff8383ff ``` ```image aac caa caa faaf faac aac cffff caa aaaaaaaaaacccaaf cccaaaaaaaaaaaf ffffcf e edb gdbbb gbbbbge egbbbdg edbbbde gdbbbde gbbbbge egbbbdg edbbbde edbbbde edbbbge gdbbbge gdbbbg gbbbbg bbdg dg ``` <!-- end of image --> After careful examination, I've determined that there's no intersection in area A. Zero, Nada.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0404ffff b,#ff0505ff c,#7f7fffff d,#ff5959ff e,#ffb0b0ff f,#c1c1ffff g,#3e3effff ``` ```image c fa a af gg ca fa a ac gg fa a af ag ca fa a ac gg ca a af ac ga fa a af gg ca a af ac ga fa a af ag ca fa a ac gg fa a bb af ebbe ac dbb ca dbd fa bbd a ebbe af dbb gg dbd ca bbd a ebbe aaagccf af dbb ffcggaaaaaaaaggcff ac dbd fccgaaaaaaaaagccff ga bbd ffcggaaaaa ebbe dbb dbd bbd ebbe dbb dbd dbd bbd bbe ebbe ebbe ebb ebb dbb dbd dbd bbd bbe bbe ebbe ebbe ebb bb ``` <!-- end of image -->

This image looks interesting. I wonder if there are any intersections hidden in there? I've noticed 1 areas of interest. These could be potential intersection zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#fb3b39ff b,#090afcff c,#fe0404ff d,#f1c4d2ff e,#5c5efbff f,#f7827eff g,#aed5adff ``` ```image d af c af c aa c fa c fa c fc c dc c dc cd dc cd c cd c cf c af c af c aa c fa c fa c c dcd fc fc c ac dc ca cd cf dc dcd cd fc dc ac cd cc c ca cf cf c dcd af fc be c ac bb af ca bb c cf eb aa dcd eb c fc eb fa ac eb c cc db fa ca db c cf bd fc dcd bd c fc be dc ac e be cd ca ebe be dc cf ebe be gggcgggggggggggg dcd ebe bb ggggcgggggggggggfc ebe bb ggggcfgggggggggac ebe eb gggggcggggggggcc ebe eb gggggcfggggggcag ebe eb ggggggcgggggcfgg ebe eb ggggggcfggfcgggg ebe db gggggggcgacggggg ebe db gggggggaccgggggg ebe bd ggggggggaggggggg ebe bdgggggggggggggggg ebe beggggggggggggggg ebe begggggggggggggg ebe gbeggggggggggggg bbe ggbbgggggggggggg bbe gggbbggggggggggbbe ggggbbgggggggbbe gggggbbggggbbegg eb bbe ebe ``` <!-- end of image --> This is a magnified view of the region A. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff4646ff b,#0404ffff c,#ff0707ff d,#ffc7c7ff e,#a1a1ffff f,#ff8888ff g,#3636ffff ``` ```image aca dccd aca dccd aca dccd a fca dac ccd dccc fca fcca ccf fcca fcc accf ccf accf fcc dcccd ccf dcccd fcc fcca ccf fcca dccdaccf accccd dcccd fa e be bbe ebbg ebbg ebbg ebbg ebbg bbg eg gbb egbb gbbe egbbbe ``` <!-- end of image --> The evidence suggests that this is not an intersection point in area A. I can confidently say that there are no intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff3d3dff b,#0606ffff c,#ff0505ff d,#ffc5c5ff e,#8787ffff f,#ff8181ff g,#4949ffff ``` ```image d af c af c aa c fa c fa c fc c dc c dc cd dc cd c cd c cf c af c af c aa c fa c fc c c dcd fc fc c ac dc ca cd cf dc dcd cd fc dc ac cd cc c ca cf cf c dcd af fc bg c ac bg af ca bb c cf gb aa dcd gb c fc eb fa ac eb c cc eb fa ca b c cf b fc dcd be c fc be dc ac g be cd ca gbg bg dc cf gbg bg cd dcd gbg bb dc fc gbg bb cd ac gbg gb c cc gbg gb cd ca gbg eb c cf gbg eb cf dcd gbg eb c fc gbg b acc gbg b a gbe be gbe be gbe be gbe bg gbe bg gbe bb gbe gb gbe gb bbe gb bbe ebe ``` <!-- end of image -->

I'm curious to see if this image contains any intersection points. I have a hunch that these areas might contain the intersections we're looking for. <!-- image --> ```palette Key,Color ,#fefefeff a,#f56460ff b,#5b5df6ff c,#fd0a0aff d,#aeaefeff e,#ffb5b5ff f,#add4acff g,#0808feff ``` ```image d gb g bb g dg gd g gb c g ac bb c g ca dg ec gd c g ac gd c g ce bb ec g c dg aa g c g ce gd ec g c bb ca g c dg ce g ac dg c gd ca g ec c bb c c g ac ac bg c ca g ce c dg ec ec gd c ac g aa ce gb c c g ce ec bg ec ac g c ce dg ca c gd c ec g ce ac gb ac ce g c c bg ca ec g ec ca dg c ce gd ac c g c ec gb ce ca g ec ce bb c c g fffffffffffffcaf ec dg fffffffffffffcff ca gd ffffffffffffcfff ce g fffffffffffacfff c gd fffffffffffcffff ac g ffffffffffcaffff ca bb ffffffffffcfffff ce g fffffffffcffffff c dgbfffffffacffffff ac dgggbffffcfffffff ca fffbgggcafffffff c ffffffbgggbfffff c ffffffcfffgggbff ac fffffacffffffbggb ca fffffcffffffffffdgggd c ffffcaffffffffff dgggb ec fffacfffffffffff bggb ac fffcffffffffffff dgggd ce ffcaffffffffffff dgggb c ffcfffffffffffff bggb ec fcffffffffffffff bgggd ac acffffffffffffff dggg ce cfffffffffffffff cca ec ``` <!-- end of image --> I'm focusing my attention on this specific region, area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe494aff b,#4e49faff c,#fe0607ff d,#9a98fcff e,#ff9090ff f,#f4d1dcff g,#0404feff ``` ```image aca eccf cce aca fccf aca ecc fcce aca fccf cce ecc fcce aca eccf d cce gbd ecc ggggbdf fccf fdbgggggbd aca dbgggggbd eccf dbgggggbdcce fdbgggggbd dbgggggbd acadbgggggbdf ecc fdbgggggbd fcce dbggggg aca dbgg eccf f cce ecc fcce aca eccf cce acc fccf aca eccf fcce aca fccf cca ecc ``` <!-- end of image --> The lines cross each other within area A, forming an intersection. There's one and only one intersection present in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff4a49ff b,#4b4bffff c,#fe0707ff d,#9998fdff e,#ff9090ff f,#f0d4e2ff g,#0605feff ``` ```image d gd g bb g dg gf g gd c g ec bb c g ce dg fc gf cf fg ac gd c g ce bb fc g c dg aa gf c fg ce gd ec g c bb aa g fc dg cf gf ec fg c gd ce g fc cf bb cf fc g aa ac dg c ce g ce cf fg ec fc gd c ac g aa ce bb c c g cf fc dg ec ac g c ce dg aa c gd fc fc g cf aa bd ec ce g c c bb ce ec g fc aa dg cf cf gf aa c g c ec gd ce aa g ec cf bb c c g aa ec dg c ca gf cf cf fg ec c gd c ec g ce ca bb fc cf g cf fc dgd ec ec fbggb c ce bggbce cf dgggd fc c fbggb ac aa bggbf ce c dgggd cf ce fbggd fc ec bggbf ac c dgggd ce aa dgggd c fc bggb fc cf dgggd ac ec dggg ce c f cce fc ``` <!-- end of image -->

This image seems promising for intersection detection. These zones are intriguing. I bet there's something interesting happening within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd0606ff b,#0606feff c,#9fa2f8ff d,#f4a09bff e,#f64d4cff f,#aed5aeff g,#4b4ff5ff ``` ```image d eaae eaae daae daaad daaad daaad eaad eaae eaae daae daaad daa ea ad a da ae a a ea ad a da ee a a ea ad a da ffffffffffffffff ee ffffffffffffffff adffffffffffffffff b affffffffffffffff gbc dafffffffffffffff bb aeffffffffffffff gb faffffffffffffff cbg fdafffffffffffff bb ffeaffffffffffff cbc fffadfffffffffffbb ffffafffffffffgbc ffffeaffffffcbgf fffffaeffffbbfff ffffffaffgbgffff fffffffabbffffff ffffffgbefffffff ffffcbgfadffffff fffbbffffaffffff fgbgfffffdafffff bbffffffffaeffff gbcffffffffffaffff cbg ffffffffffffafff bb ffffffffffffeaff cbc fffffffffffffadf bb ffffffffffffffaf gbc ffffffffffffffda cbg fffffffffffffffae bb ffffffffffffffffa cbc ffffffffffffffff a bb ffffffffffffffff ea bbc ffffffffffffffff ad gbc a cbg da cbb ee bb ad bbc a gbc da gbg ad cbg a cbb da bb ee bbc ad gbc a cbg cbb bb bbc gbc gbg bg ``` <!-- end of image --> I'm going to scrutinize area A for any signs of an intersection. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0405ff b,#0908fdff c,#6560faff d,#ffb9b9ff e,#fc3436ff f,#bebeffff g,#ff6e6eff ``` ```image g ad aa eae aag daad gaa eag daad gaad eae aag daad gaa f eae fcb daad cbbb gaad fbbbc eae cbbbf aag fbbbc daad fcbbbf gaa cbbbc eae fbbbc daacbbbf cbbbc fcbbbe cbbbcaag fbbbcf daad cbbbf gaa fbbbc eae fcbbbf daag cbbbc daad fbbbcf gae cbbbf aag bbc daad bf gaa eae aag daad gae eag daad gaad eae aa da g ``` <!-- end of image --> The evidence is clear: this is an intersection in area A. One intersection, that's it, but I found it.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fe0606ff b,#0606ffff c,#8383ffff d,#ffa3a3ff e,#fd4d4fff f,#c4c4ffff g,#4444ffff ``` ```image d eaae eaae daae daaad daaad daaad eaad eaae eaae daae daaad daa ea ad a da ae a a ea ad a da ae a a ea ad a da ee ad b a cbc da bb ad gbf a fbg da bb ee cbc ad bb a gbf da fbg ae bb a cbc abb gbe fbg ad bb a cbc da bb ae gbf a fbg a bb ea cbc ad bb a gbf da fbg ae bb a cbc a bb ea bbf ad gbc a cbg da fbb ee fbb ad bbf a gbc da cbc ad cbg a fbb da bbf ee bbf ad gbc a cbg fbb bb bbf gbc cbg bg ``` <!-- end of image -->

I'm on the case! Let's uncover any intersections hidden in this image. These spots are like clues. Let's see what they reveal about potential intersections. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0909ff b,#0a0afdff c,#f66a65ff d,#5d61f6ff e,#ffb9b9ff f,#add4adff g,#b6b6fdff ``` ```image e ae a ae ea a ea a ca a cc b a bg cc bg a bd ae bd a bb ae db ea db a gb ea gb a b ca b a bg cc bg a bd ac bd a bd ae bb a db ae db ea gb a gb ea b a b ca bg a bg cc bd a bd ac bb a db ae db a gb ae gb ea gb a b ea bg a bg ca bg a bd cc bd a bb ffacffffffffffff db fffaffffffffffff db fffacfffffffffff gb ffffafffffffffff gb ffffafffffffffffgb fffffaffffffffffb fffffafffffffffbg fffffcaffffffbbf ffffffaffffdbdff ffffffcaffbbffff fffffffabbffffff ffffffdbbfffffff fffffbbfafffffff fffdbdffacffffff ffbbfffffaffffff eaa bbfffffffacfffff caace dbdfffffffffafffff eaaac gbb ffffffffffafffff caaae bb fffffffffffaffff caac dbd fffffffffffaffff eaaac bb fffffffffffcafff caaae bbg ffffffffffffafff ecaac gbd ffffffffffffcaff eaaac bb fffffffffffffaff caaae dbg cc eaaac gbd a eaaae bb accaace dbg ac bd ``` <!-- end of image --> I'm eager to see what's happening in this magnified view of area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff0505ff b,#0606feff c,#ff7979ff d,#4c44f7ff e,#feb6b6ff f,#f9363bff g,#a5a5ffff ``` ```image fac eaa fac eaa aae caf aae caf aae caf eaae fac eaa fac eaa d fac gbb eaa gdbbd aae dbbbg caf gbbbd aae gdbbdg caf dbbbg aae gbbbd cafdbbbg edbbbg gbbbd dbbbfa gbbbg fac gbbbd eaa dbbbg fac gbbbd eaa gdbbdg aae dbbbg caf gbbbd aae bbdg caf bg aae caf eaae fac eaa fac eaa fac eaa aae caf aae caf ``` <!-- 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,#ff0404ff b,#0808ffff c,#ff7c7cff d,#5755fdff e,#ffbebeff f,#ff3d3dff g,#b2b2ffff ``` ```image e ac a ae ea a ea a cf a cf b a bg fc bg a bd ae bd a bb ae db ea db a gb ea gb a b cf b a bg cf bg a bg fc bd a bd ae db a db ae db ea gb a gb ea b a b cf bg a bg ff bd a bd fc bb a db ae db a gb ae gb ea gb a b ea bg a bg cf bg a bd fc bd a bb fc db a db ae gb a gb ae b ea b a bg ea bbg a gbd cf bb adbg gbd bb a dbg fc gbd a caa bb ae caafe dbg a efaac gbb ae caaae bb ea faaf dbd a eaaac bb ca caaae bbg a efaaf gbd cf eaaac bb a caafe dbg fc efaac gbd a caaac bb fccaafe dbg ac bd ``` <!-- end of image -->

I'm curious to see if this image contains any intersection points. These spots mark what I'd call 'danger zones' - areas where intersections are more likely. <!-- image --> ```palette Key,Color ,#fefefeff a,#0505fdff b,#fc0908ff c,#818aecff d,#e7887dff e,#ebd2e5ff f,#add4adff g,#4143f4ff ``` ```image e ac a gc a gc a gc a gg a gg a gg a cg a cg a ca a ca a ca a ca a ea ae ea ae a ea eae ae eae ea ca ffacffffffffffff ca fffaffffffffffff ca fffacfffffffffff ga ffffafffffffffff ebb ga ffffacffffffffff ebbeeb aa fffffafffffffffdbbe ebe ag fffffacffffffdbbe ebe ag ffffffaffffdbbff ebe ac ffffffacfdbbffff be ac fffffffabbffffff be ae fffffdbacfffffff be eae fffdbbffafffffff beffffffffffffffffeae fdbbffffacffffff bdffffffffffffffca dbbfffffffaffffff bdffffffffffffca dbbfffffffffggfffff fbdffffffffffgaf dbb ffffffffffafffff ffbdffffffffgaff dbb ffffffffffggffff fffbdffffffaafff dbb fffffffffffaffff ffffbdffffaaffff dbb fffffffffffggfff fffffbbffagfffff dbb ffffffffffffafff ffffffbbagffffff dbb gg fffffffagfffffff d a ffffffacbbffffff gg fffffacffbbfffff a ffffafffffbbffff cg ffcafffffffbbfff a fcafffffffffbbff cg gafffffffffffbbf a gafffffffffffffbb cg gafffffffffffffffbb a ga ffffffffffffffffdb ca ag ffffffffffffffff db a ag db ca ag db a ac db ca ac db aeae db cae db eb eb eb ebe ebe ebe ebe be b ``` <!-- end of image --> Let's zoom in on area A to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#0403feff b,#fe0404ff c,#7776fdff d,#f7555cff e,#b6b6ffff f,#ffc4c4ff g,#3232feff ``` ```image eaae cag aae cag aae cag aae cag aae cag aae cag fd aae fdbb cag fdbbbd aae fdbbbdf cag fdbbbdf aae fdbbbdf cag fdbbbdf gadbbbdf fdaabd fdbbaac fdbbbdcaa fdbbbd gac fdbbbd eaa fdbbbd gac fbbbbd eaa bbbbd gac bbd eaa d gac eaa gac eaa gac eaa gac eaa gac eaae gac ``` <!-- end of image --> My investigation has led me to an intersection in area A! Alright, let's concentrate on the next area. Let's take a closer look at area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#0707feff b,#fe0404ff c,#524df9ff d,#ff8484ff e,#a9a9feff f,#ffd1d1ff g,#f42f39ff ``` ```image f bd bbd e dbbd ea dbbd caa dbbd caae dbbd caae dbbd caae dbbd caae dbbd aaae dbbd aaa dbbd eaaa dbbd eaac dbbg eaac fbbg eaac fbbgeaac fbgaac caac caagbg caaefbbg caae fbbg caae fbbg aaae fbbgf aaa fbbgf eaaa fgbgf eaac fgbgf eaac fgbbf eaac fgbbf eaac gbbf eaac gbbf caae gbb aae gb ae g e ``` <!-- end of image --> Incredible, there's actually an intersection in area B! There's for sure two intersections on the image you sent me.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0404feff b,#ff0808ff c,#7373feff d,#ff7a7aff e,#bcbcffff f,#ffcbcbff g,#3a37fcff ``` ```image e gc a gc a gc a gc a gc a cg a cg a cg a cg a cg a ca a ea a ea a ea a ea ae a ea ae ae ea ea ea ae ca a ca ae ga a fbb ga ae fbbffb ag a fbbf fbf ag ae fbbf fbf ag a fbbf fbf ac ae fbbf bf ae abbf bf ae fbac bf eae fbb a bf ea fbb gc bf ea fbb a bd ca fbb gc bd ca dbb a bd ga dbb gc bd ga dbb a bd ag dbb gc bd ag dbb a bdac dbb gg ag d a aebb cg ae bb a eae bb cg ea bb a ea bb cg ca bb a ca bb cg ga db a ga db ca ag db a ag db ea ac db a ac db ea ae db aeae db eae fb fb fb fb fb fbf fbf bf bf b ``` <!-- end of image -->

I'm examining this image closely. My goal: find any and all intersections. Could these regions be concealing intersection points? Let's find out. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd0807ff b,#0809fcff c,#5861dbff d,#e39d8fff e,#b1d7b1ff f,#98c39dff g,#e8554aff ``` ```image eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefeeeeeeeeeef eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegaeeeeeeeeeef eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeadaeeeeeeeeef eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeageadeeeeeeeef eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeaeeeeeeeef eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeadecccccccccccceeee eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefaecbccccccccccbcbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeafebeeeeaeeeeeef eeeeeeeeeeeeeeeeeeeeeeeeeeeeeedaecbeeeeggeeeeef eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeebeeeeeeaeeeeef eeeeeeeeeeeeeeeeeeeeeeeeeeeeegaecbeeeeeedaeeeef eeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeebeeeeeeeeageeef eeeeeeeeeeeeeeeeeeeeeeeeeeeeagecbeeeeeeeeeaeeef eeeeeeeeeeeeeeeeeeeeeeeeeeeeaeebeeeeeeeeeedaeef eeeeeeeeeeeeeeeeeeeeeeeeeeeadecbeeeeeeeeeeeagef eeeeeeeeeeeeeeeeeeeeeeeeeedaeebeeeeeeeeeeeeeaef eeeeeeeeeeeeeeeeeeeeeeeeeeafefbeeeeeeeeeeeeegaf eeeeeeeeeeeeeeeeeeeeeeeeegaeebfeeeeeeeeeeeeeead eeeeeeeeeeeeeeeeeeeeeeeeeaeefbeeeeeeeeeeeeeeeea eeeeeeeeeeeeeeeeeeeeeeeeggeebfeeeeeeeeeeeeeeeega eeeeeeeeeeeeeeeeeeeeeeeeaeefbeeeeeeeeeeeeeeeeefa eeeeeeeeeeeeeeeeeeeeeeeageebfeeeeeeeeeeeeeeeeef a eeeeeeeeeeeeeeeeeeeeeeeaeefbeeeeeeeeeeeeeeeeeef gg eeeeeeeeeeeeeeeeeeeeeeadeebfeeeeeeeeeeeeeeeeeef a eeeeeeeeeeeeeeeeeeeeedaeeebeeeeeeeeeeeeeeeeeeef da eeeeeeeeeeeeeeeeeeeeeaeeebceeeeeeeeeeeeeeeeeeef ad eeeeeeeeeeeeeeeeeeeegaeeebeeeeeeeeeeeeeeeeeeeef a eeeeeeeeeeeeeeeeeeeeaeeebceeeeeeeeeeeeeeeeeeeef da eeeeeeeeeeeeeeeeeeeggeeebeeeeeeeeeeeeeeeeeeeeef ad eeeeeeeeeeeeeeeeeeeaeeebceeeeeeeeeeeeeeeeeeeeef a eeeeeeeeeeeeeeeeeeageeebeeeeeeeeeeeeeeeeeeeeeef ga eeeeeeeeeeeeeeeeeeaeeebceeeeeeeeeeeeeeeeeeeeeef ad eeeeeeeeeeeeeeeeeadeeebeeeeeeeeeeeeeeeeeeeeeeef a eeeeeeeeeeeeeeeedaeeecceeeeeeeeeeeeeeeeeeeeeeef gg eeeeeeeeeeeeeeeeaeeeebeeeeeeeeeeeeeeeeeeeeeeeef a eeeeeeeeeeeeeeegaeeecceeeeeeeeeeeeeeeeeeeeeeeef a eeeeeeeeeeeeeeeaeeeebeeeeeeeeeeeeeeeeeeeeeeeeef ag eeeeeeeeeeeeeeggeeecceeeeeeeeeeeeeeeeeeeeeeeeef a eeeeeeeeeeeeeeaeeeebeeeeeeeeeeeeeeeeeeeeeeeeeef da eeeeeeeeeeeeeageeecbeeeeeeeeeeeeeeeeeeeeeeeeeef ad eeeeeeeeeeeeeaeeeebeeeeeeeeeeeeeeeeeeeeeeeeeeef a eeeeeeeeeeeeadeeecbeeeeeeeeeeeeeeeeeeeeeeeeeeef da eeeeeeeeeeedaeeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeef ad eeeeeeeeeeeaeeeecbeeeeeeeeeeeeeeeeeeeeeeeeeeeef a eeeeeeeeeegaeeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeef ga eeeeeeeeeeaeeeecbeeeeeeeeeeeeeeeeeeeeeeeeeeeeef a eeeeeeeeeageeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef a eeeeeeeeeaeeeefbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef gg eeeeeeeeadeeeebfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef a eeeeeeefaeeeefbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef da eeeeeeeafeeeebfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef ad eeeeeedaeeeefbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef a eeeeeeaeeeeebfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef da eeeeegaeeeefbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef ad eeeeeaeeeeebfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef a eeeeageeeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef ga eeeeaeeeeebceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef ad eeeadeeeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef a eedaeeeeebceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef gg eeafeeeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef a edaeeeeebceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef a eaeeeeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef ag ggeeeeebceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef a aeeeeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef da ageeeeebceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef ad d b a cc da b ad cc a b d cc b cb b cb b eb b eb b ``` <!-- end of image --> I'm going to scrutinize area A for any signs of an intersection. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0505ff b,#0707feff c,#5b55f8ff d,#ff8686ff e,#a6a6ffff f,#ffc8c8ff g,#ff4141ff ``` ```image aa daa faaad gagdaf ad aad da daa ad gag da faaf aa ecccccceeeeeeeeeee faaf cbccccccccccccccccc gag bbe gg faaf cbc ad gad bbe aaf ad be faad da cb daa af be ga ga eb faf faa bb da faaf bbe aaf gad ebb dag aa bbe aad ad ebb faaf faf bb aa ga be daf faa eb gg gag cc fad faaf eb aa daa ebb fa aad cbc d ag ebb faf cbc faf bc ga b faa cc aad be daa cb ag cbc faf bbe gg cbc faf bbe daa bbe aad bb daa be aad eb ag be gg bb faf ebb ga bbe daa ebb daa bb aad bc dag eb aaf cc faf cb gd ebb da cbc aa ebb daa cbc gag bc aaf be ag cc faf be da bb aa cbc dag bbe faaf cbc gag bbe gag bbe aaf bb ad be da eb da eb faa bb gag ebb faaf bbe gag ebb ad bb da bc ad eb da cc gag cb faaf ebb gad cbc daa bb aad cbc ad cbc dg bbe faf bc ga be gad be daa cb aad bb aa ebb af bbe faf bbe ga bb faa be gad eb aad eb dag bb aaf ebb ag cbc faf ebb faf ebb ga cbc ``` <!-- end of image --> Eureka! There's definitely an intersection in area A! I've found a single intersection point in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0404ff b,#0707ffff c,#5850f7ff d,#ff7c7cff e,#a9a9ffff f,#ffc2c2ff g,#ff3939ff ``` ```image f da ada gd af a a af cccceeeeeeeeeeeeeee fa cccccccccccccccbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb af b a da cc gg a b a dg eb fa a b gd gd eb a a b fa af eb ad fa b a af eb da da b af a eb a gg b dg a b af gd be fa a b gg af be a fa b fa a be ad da b a a be da gg b af a be a ad b da a cc af af b a fa cc gg a b a dg cc fa a b gd gg cc a a b fa ad cc ad a b a af eb da fa b af a eb a dg b dg a eb af gd b fa a eb gg ad b a fa eb fa af b ad fa eb a a be da dg b af a be a gd b da a be af af b a fa be gg af b a da be fa a b gd dg cc a a b fa gd cc ad f b a cc da b af cc a b f cc b eb b eb b eb b eb b ``` <!-- end of image -->

Let's examine this image for potential line intersections. There are 1 areas where the lines seem to converge. We should take a closer look at area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#f35d5aff b,#0909fcff c,#ffb4b4ff d,#fe0706ff e,#b5b5ffff f,#add4adff g,#6063f1ff ``` ```image c cdddac d addda cd addda d cadddc d cadddc dc cdddac d cddda ffffffffffffdaff addda ffffffffffffdfff adddc fffffffffffaafff cadddc fffffffffffdffff cdddac ffffffffffadffff cdd ffffffffffdfffff ffffffffffdfffff fffffffffdffffff fffffffffdffffff bbbbbbbgggeeee ffffffffdaffffff eeeggggbbbbbbbbbbbbbbbbbggggfff fffffffaggggbbbbbbg fffffffdffffffff gbbg ffffffaaffffffff gbbg ffffffdfffffffff gbbg fffffadfffffffff gbbg fffffdffffffffff gbbg fffffdffffffffff gbbg ffffdfffffffffff ebbb ffffdfffffffffff ebbbe fffdafffffffffff ebbbe fffdffffffffffff ebbbe ffdaffffffffffff ebbbe d ebbbe aa ebbbe d ebb cd d cd dc d dc d aa d aa d cd d cd dc d dc d aa d aa d cd d cd dc d dc d aa d aa d cd d cd dc d dc d aa d aa d cd d ``` <!-- end of image --> I'm determined to find out if an intersection exists in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#f8343bff b,#0a07fcff c,#ffc2c2ff d,#ff0303ff e,#c0c0feff f,#ff7d7dff g,#6c67f9ff ``` ```image adf cdd adf cdd adf cddc fda ddc fda ddc fda adf cdd adf cdd adf cddc fda ddc fda ddc ggeeeeee fda bbbbbbbbbbbbbbbbbggggggeeeeee ggggbbbbbbbbbbbbbbbbbbbbbbbbbbb eeeaagggggggggbbbbbb cdd adf cddc fda ddc fda ddc fda adf cdd adf cdd adf cddc fda ddc fda ddc fda adf cdd ``` <!-- end of image --> As I suspected, there's an intersection within area A. One intersection, that's it, but I found it.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fc3f42ff b,#0908fdff c,#ffbdbdff d,#ff0505ff e,#b5b5ffff f,#ff7c7cff g,#6562fbff ``` ```image c fdddac d fdddf cd fdddf dc cadddc d caddac dc cdddac d fdddf af fdddf d adddf fa caddac d caddac fa fdd d cd dc d bbbbbbbgggeeee dc eeeggggbbbbbbbbbbbbbbbbbggeee eagggggbbbbbg d gbbg fa gbbg d gbbg fd gbbg d gbbg cd gbbg dc ebbb d ebbbe dc ebbbe d ebbbe af ebbbe d ebbbe fa ebbbe d ebb fd d cd dc d dc d af d fa d cd d cd dc d dc d af d fa d cd d cd dc d dc d af d fa d cd d cd dc d df d af d fa d cd d ``` <!-- end of image -->

I have an image in front of me. I need to determine if there are any intersection segments. There's definitely not a single intersection on the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff4242ff b,#0505ffff c,#a4a4ffff d,#ff0202ff e,#ff8d8dff f,#4f4fffff g,#f3dde9ff ``` ```image c ccfbbbbbf gcfbbbbbbfcg gcfbbbbbbfcg cffbbbbbfcc ccfbbbbbffc cbbbbbfcg bb fbc gbb fbg cbf bb cbc bb fbc gbf bbg cbf bb fbc gbf bbg cbf bb fbc gbb fbg cbf f gd gddg ddg ade ade ada eda eda gdd gddg ddg dde ade ade eda eda edd gddg gddg ddg ade ade ada gada gadde gadde gadde gadde gadde gadde gadde gadde gadde gadde gadde dde ``` <!-- end of image -->

This image might have some surprises. Let's look for intersections carefully. I have a hunch that these areas might contain the intersections we're looking for. <!-- image --> ```palette Key,Color ,#fefefeff a,#f35752ff b,#0706feff c,#fe0605ff d,#b5b5ffff e,#ffaaaaff f,#5659f5ff g,#add4adff ``` ```image e gcaggggggggggggg ggcggggggggggggg ggcggggggggggggg gggcgggggggggggg gggcgggggggggggg gggacggggggggggg ggggcggggggggggg ggggaagggggggggg gggggcgggggggggg gggggaaggggggggg gbbgggcggggggggg gggbbgcagggggggg ggggfbfcgggggggg ggggggfbfggggggg ggggggggbbgggggg ggggggggcgbbgggg ggggggggacggbbgg gggggggggcgggfbf gggggggggaaggggfbd ggggggggggcggggg bbd ggggggggggaagggg bb gggggggggggcgggg dbb gggggggggggcaggg fbf ggggggggggggcggg fbd ggggggggggggcggg bbd gggggggggggggcgg dbb gggggggggggggcgg dbf gggggggggggggacg fbf ggggggggggggggcg bbd aa bbd c dbbbbfd aa fbbbbfd c dfbbbbfd ce dfbbbbfd c dbbbbbd ce dfbbbbfd ec dfbbbbfd c dfbbbbf ec dfb c aa c aa c ce c c ec c ec c aa c aa c a ce aca c eca c ecc ec cc c cce ec ace c aca aa eca c ecc ae cc c cce ce ace c aca c eca ec ecc c cc ec cce c ace aa aca c eca ae ecc c cc cecce ce ``` <!-- end of image --> Here's a close-up of the area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fb3e42ff b,#0807fdff c,#fe0506ff d,#b8b8ffff e,#fecacaff f,#5b51f4ff g,#ff8a8aff ``` ```image ecc ccg gca cce gca ecce aca ecce acg ecc acg gcc ccg gca cce gca ecce aca ecce acg bfd ecc dbbbf acg fbbbf gcc dfbbbd ccg dbbbbdgca dbbbfcce fbbbfa dfbbbf dbbbbd eabbbfd acfbbbfd eccefbbbf acg dfbbbd gcc dbbbbd ccg dbbbfd gca fbbbf cce fbb gca df ecce aca ecce acg ecc acg gcc ccg gca cce gca ecce aca ecce acg ecc acg gcc ccg ``` <!-- end of image --> My investigation has led me to an intersection in area A! It was tricky, but I finally found one single intersection in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff4545ff b,#0707feff c,#ff0606ff d,#b5b5ffff e,#fec8c8ff f,#5d5bfdff g,#ff8888ff ``` ```image e cg c ce ec c gc c ga c ag bb c dbb cg dbfc fbf ebbd c bb gc dbb c fbf ga fbd c bbd ag bb c dbb cg fbf c fbd ce bbd ec dbb c dbf gc fbf c bbd ga bbd c dbbbbfd ag fbbbbfd c dfbbbbfd cg dfbbbbfd c dbbbbbd ce dfbbbbfd ec dfbbbbfd c dfbbbbf gc dfb c ga c ag c ce c ce ec c gc c aa c ag c a ce acg c gca ce ecc ec ecc c cce gc acg c acg aa gca c ecc ag ecc c cce ce acg c acg ce gca ec ecc c ecc ga cce c acg aa acg c gca ag ecc c ecc cecce ecg ``` <!-- 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,#fd0707ff b,#0606fdff c,#f2a59fff d,#b0b1fcff e,#4e53f4ff f,#afd6afff g,#f45956ff ``` ```image cag a aa gg ga a ca gg ac a ag gg aa a ga gg ca a ac gg ag a aa gg ga a cac gg ag a aa gg ga a ca gg ac a ag gg aa a ga ffffffffffffff ag ca ffffffffffffff a ac ffffffffffffff ac ag ffffffffffffff a aa ffffffffffffff ac ga ffffffffffffff a caffffffffffffff ac agffffffffffff a faafffffffffff ac ffaaffffffffff a fffgafffffffff ac ffffcacfffffff a ffffffagffffff ac fffffffaafffff a ffffffffgaffff ac fffffffffgffff a ffffffffffffff ac ffffffffffffff a ffffffffffffff ac ffffffffffffff a ffffffffffffff ac ffffffffffffff a ffffffffffffff ac fffffffffbffff a ffffffffbeffff a ffffffebffffff ca fffffbbfffffff a ffffbbffffffff ca dbd a eb ffffffffffffcaff bb ffffffffffffafff be fffffffffffcafff dbd fffffffffffaffff eb ffffffffffcaffff be ffffffffffafffff dbd fffffffffcafffff eb fffffffffaffffff bb ffffffffcaffffff be ffffffffafffffff dbd fffffffgafffffff eb fffffffaffffffff be fffeffgaffffffff dbd fffebbafffffffff eb fffffgbbefffffff bb fffffaffebbfffff be ffffgaffffdbbeff dbd ffffaffffffffebbd eb fffgaffffffffffebbd be fffaffffffffffff ebb dbd ffffffffffffffff dbbd eb ffffffffffffffff bbe bb ffffffffffffffff dbbd be ffffffffffffffff bbe dbd ffffffffffffffff ebbd eb ffffffffffffffff bbe be ffffffffffffffff ebbddbd ffffffffffffffff dbb ``` <!-- end of image --> Let's see what secrets area A holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff0303ff b,#0404feff c,#fc9597ff d,#c7c7ffff e,#4134f1ff f,#8181ffff g,#fc2426ff ``` ```image caa gac caa gac caa gac caa gac caa gac caa gac caa gac caa gac caa gac cag gac cag gac cag gac fd cag dbbef gac dfbbbbegg febbbef cebbbbfd gacfebbbef cag debbbbfd aac fbbbbed cag debbbbfd aac dfbbbbed cag debbb aac dfb cag aac cag ``` <!-- end of image --> I am surprised, so clear, an intersection has appeared in area A. Let's continue our search in the next region. Could this be where the intersection is hiding, in area B? <!-- image --> ```palette Key,Color ,#fefefeff a,#ff0606ff b,#0606ffff c,#ff9696ff d,#9292ffff e,#4b4bffff f,#f8d5dbff g,#ff4747ff ``` ```image f af aac gaac gaag caagf faaaf fgaac gaac caag caagf faaaf fgaac gaag caag caaaf faaac fgaac gag cf dbd dbbe ebbe fbbbd dbbbf ebbe ebbd ``` <!-- end of image --> Area B is clear of intersections, but the search continues. The final count is: one intersection.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fe0506ff b,#0505feff c,#fd8586ff d,#b2b2ffff e,#5151ffff f,#ffcacaff g,#ff4242ff ``` ```image f cag a aa cg ga a caf cg fac a ag cg aa a ga gg faf a ac gg ag a ga gg ca a faf gg ac a ag gc ga a ca gc faf a ag gc aa a ga gc caf a fac gc ag a aa ac ga a faf ac ac a ag ac ga a ca ac faf a ac af aa a ga af c a af fa af fa af fa af b fa be af dbd fa eb af be fa dbd af eb fa bb af be fa dbd a eb fa be a dbd fa eb a bb ca be a dbd ca eb a be e ca dbd ebba eb cbbe bb a ebbd be cg dbbe dbd a ebb eb cg dbbd be a ebb dbd dbbd eb bbe bb dbbd be bbe dbd ebbd eb bbe be ebbddbd dbb ``` <!-- end of image -->

This image seems promising for intersection detection. I need to zoom in on these areas to get a better look. <!-- image --> ```palette Key,Color ,#fefefeff a,#5055f5ff b,#fe0707ff c,#ffbfbfff d,#9a9ff5ff e,#0706fcff f,#f26c66ff g,#add5adff ``` ```image d e ed e e de e ae e aa e ed e ed de e de e aa e ed e ed de e de e aa e ed e ed e bc e cbbf de fbbc e cbbf aa fbbc e cbbf aa fbbc e cbbf ed fbbc e cbbf e fbbc ggggggggggggggde cbbf ggggggggggggggeg fbbc gggggggggggggaeg cbbf gggggggggggggegg fbbc ggggggggggggaagg cbb ggggggggggggeggg fbc gggggggggggeaggg bbgggggggggggegggg fbgggggggggedgggg gbbggggggdeggggg ggfbfggggegggggg ggggbbggaegggggg gggggfbfeggggggg gggggggeeggggggg gggggggefbfggggg ggggggeaggbbgggg ggggggeggggfbfgg gggggedggggggbbg ggggdeggggggggfbf ggggegggggggggggbb gggaeggggggggggg cbf gggegggggggggggg bb ggaagggggggggggg cbf ggeggggggggggggg bb geaggggggggggggg cbf eed gegggggggggggggg bb deeed edgggggggggggggg cbf aeea eggggggggggggggg bb aeea e cbf deeed de bb deeed e cbf aeea aa bb aeea e cbf deeed aa bb deeed e c aeea ed dee ``` <!-- end of image --> Let's see what secrets area A holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#342ef9ff b,#fd0a0bff c,#ffbbbbff d,#7877feff e,#0404feff f,#ff6767ff g,#b8b8ffff ``` ```image ae gee aed dee eeg dea eeg dea geeg aed gee aed dee eed dea c eeg bf dea bbbc geeg cbbbf aed fbbbc gee cbbbf aed fbbbc gee cbbbf eed fbbbc dea cbbbf eeg fbbbcdea cbbbeeg faeac geebbf aedfbbbc gee cbbbf aed fbbbc dea cbbbf eeg fbbbc dea cbbbf geeg fbbbc aea cbbbf geeg fbb aed cf gee aed dee eeg dea eeg dea geeg aed gee aed dee eed dea eeg ``` <!-- end of image --> Case closed! This is definitely an intersection point in area A. One intersection, that's it, but I found it.

<!-- image --> ```palette Key,Color ,#fefefeff a,#423df9ff b,#ff0808ff c,#ffbbbbff d,#8383ffff e,#0505ffff f,#ff6868ff g,#c4c4ffff ``` ```image d e ed ge eg ge e da e aa e ed e eg ge e de e aa e ed e eg ge e de e aa e ad e eg ge bc eg cbbf de fbbc e cbbf da fbbc e cbbf ad fbbc e cbbf ed fbbc ge cbbf eg fbbc ge cbbf e fbbc da cbbf e fbbc aa cbb e fbc ed bb e fbc eg bb ge fbc e bb de fbce aa efbc ed bb e fbc eg bb ge fbc e bb de cbf e bb aa cbf e bb ad cbf eeg e bb geeed eg cbf gaeed ge bb deeag eg cbf deeeg de bb geeed e cbf aeea da bb deeag e cbf deeeg ad bb gaeed e c aeea ed dee ``` <!-- end of image -->

Here's an image. My task is to find intersections or areas where lines come close together. There are 1 regions I'd like to highlight in the image. <!-- image --> ```palette Key,Color ,#fffefeff a,#5b61d3ff b,#f80c0cff c,#090af9ff d,#d4685eff e,#b2d7b2ff f,#a7cea7ff g,#eff6f0ff ``` ```image d b ggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggbe gffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffbg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebfg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedbfg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedbefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebdeefe gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebeeefc gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebdeeece gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefbeeeacg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebfeeecfg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedbeeecafg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebfeeacefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedbeeeceefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebeeecaeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeddeeaceeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebeeeceeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebdeecaeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefbeeaceeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebfeeceeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefbeecaeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebfeaceeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedbeeceeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebeecaeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedbefceeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebeecfeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebdecaeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefbefceeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebdecfeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefbecaeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebffceeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedbecfeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebecceeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedbfceeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebecfeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebdaceeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebfceeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebdcfeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefbaceeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebfceeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedbcfeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebaceeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedbceeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebcaeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebaceeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebceeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebcaeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefdceeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebceeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedcaeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedceeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedceeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecaeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedceeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeceeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecaeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaceeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg bb gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg dbdfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg dbdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefcfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfbbdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeebbfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeefbbfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefcbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeefbbfeeeeeeeeeeeeeeeeeeeeeeeeeeeecbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeedbbeeeeeeeeeeeeeeeeeeeeeeeeeeccdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeedbbeeeeeeeeeeeeeeeeeeeeeeefcbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg ag gfeeeeeeeeeeedbdeeeeeeeeeeeeeeeeeeeeecbdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg acccccafeeeeeeeeeebbdeeeeeeeeeeeeeeeeeeacbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gffacccccafeeeeeebbdeeeeeeeeeeeeeeefcbfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeaaccccaaeeebbfeeeeeeeeeeeeecdbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeefacccccabbfeeeeeeeeeeacbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeefacccccafeeeeefcdbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeedbacccccacfbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeedbbeeaacbdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeedbdeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeebbdbdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg gfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffg ``` <!-- end of image --> I'm focusing my attention on this specific region, area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#5e5dfdff b,#fd0809ff c,#0807fdff d,#fb5a5dff e,#fdacadff f,#b5b3fdff g,#700e9dff ``` ```image b b dd eb bb be db db ebb bb bd eb db c bb c ebe ca dd ac bb ca bb ac db cc be acc db ccf dbd fc bb cf eb cc be cf bb fcf bb cc be ca ebe ca db ac bd cca eb cc db ca bb ac bbe ca bd ac eb fcf eb cc bb fcf be ac dd fcc db cc bb fcf bd aa be cc db ca dbd cf bbeac eb cf bd aa bb cc bbacc beccf beac dbfcf bdcc ebfcf ebac bbcc dbbca bdcf ebcc ebccf bbca bcf dcc dbcf bga gc bca egcf gc cc egc gcf ecc ccf cg fce cc fcd cge bbd cc ebbe cg ebbbe acb ebbd ccb bbde acce dbbd cgb ebbb fcbd ebbe acbd ebbb ccb bbde cge dbbd fcbb f dbb ccbd accccccaf ebbe fcdd faacccccaaf ebbbe cab faaccccccaff ebbd fccbb faaccccccaf bbde ccabe facccccccggf fcfbe faaccccccaff cadb fagccccccaf acebb ebbbfaccccccabb bbde faaa bd dbbd be bbb eb ebbbb ebbe e ``` <!-- end of image --> As I suspected, there's an intersection within area A. There are precisely two intersections present in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#5b5bfeff b,#fc080aff c,#0807feff d,#fe5f5fff e,#fcafb2ff f,#b4b4feff g,#75139cff ``` ```image d b be b be eb b db b dd f b c be cf b ac be c eb cf b ac db c b cf dd fc b c bd cf b fc be c eb ca b fc eb c b ca dd fc b c bd ca b fc be c eb ca b fc eb c b aa dd c b cf bdaa b c becf bac bec ebcf bac dbc bcf dgc bc bcf gc bc ecf gc dc ca gc c cg fc bd ce dbd cg dbd fc bbe cb bbe cg bb fcd ebb cb ebb agd dbd cb af dbd cbe acccccaf dbd acb faccccaf bbe cb faccccaf bbe ceb faccccabb acb facccccaf cdd ebgccccafcfb dbd faabd dbd b dbdbe bb ``` <!-- end of image -->

I'm on the case! Let's uncover any intersections hidden in this image. My analysis shows there's absolutely no intersections in the image

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0303ff b,#0404ffff c,#ff9393ff d,#9d9dffff e,#4d4dffff f,#ff4444ff g,#f3d6e2ff ``` ```image gggc gggccccffffaaaaaaaaaaaaaaaaaff aaaaaaaaaaaaaaaaffffccccggg gag gag gag ga ca ca ca ca fa fa fa fa fa aa af af af af af ac ac ac ac ag gag gag gag gag ga ca ca ca ca fa c d ebbeg dbbbd gebbeg dbbbd gebbed dbbbe ebbbd dbbbe ebbbd debbeg dbbbbbbbbbeeddg gddeebbbbbbbbbeeddg gddeebbbbbbbbbeeddg gddeebbbbb ``` <!-- end of image -->

Hmm, I'm not sure what to expect from this image. Let's see if any lines cross. I've spotted 1 narrow regions that might be worth examining further. Let's call them area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0809fdff b,#fd0606ff c,#b4b4feff d,#f29791ff e,#5d62f4ff f,#f04847ff g,#aed5aeff ``` ```image cc eaaaaaaaaaaaaaaeeeccc ccceeeaaaaaaaaaaaaaaeeec cccea ea a ca ac a ae a ea a ca ac a ae a ee a ca ac a ac a ee a ca a ca ac a ee a ea a ca ac a ae a ea a ca ac a ae dd ggggggagggggggggggggggggg ddfbbbbbbbbffbb ggggggeaggggggggggggggggg ddffbbbbbbbbfdd dbbf gggggggaggggggggggggggggg ddffbbbbbbbbfdd dbbd gggggggeagggggggggggggggg bbfdd fbbd ggggggggagggggggggggggggg dbbf gggggggggaggggggggggggggg dbbd gggggggggaegggggggggggggg fbbdgggggggggagggggggggggggg bbbgggggggeeggggggggggggg ggdbbfgggggaggggggggggggg gggggfbbdggeagggggggggggg ggggggggbbbgagggggggggggg ggggggggggdbbaggggggggggg gggggggggggggafbfgggggggg ggggggggggggggagfbbdggggg ggggggggggggggaeggdbbfggg gggggggggggggggagggggfbbf gggggggggggggggeagggggggf ggggggggggggggggagggggggg gggggggggggggggggaggggggg gggggggggggggggggaegggggg ggggggggggggggggggagggggg ggggggggggggggggggaeggggg gggggggggggggggggggaggggg gggggggggggggggggggeagggg ggggggggggggggggggggagggg ca ac a ae a ee a ``` <!-- end of image --> Here's a close-up of the area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0504feff b,#fd080aff c,#c4c4ffff d,#fbb2b6ff e,#8484ffff f,#fe6262ff g,#423efaff ``` ```image caa gag caac gag aac eaa aae eaa gae caac gag caac eag aae eaa fd gae bbbfd caac fbbbbbf gag dfbbbbfd caac dfbbbbfd eag fbbbbbf aae dfbbbbfd eaa dfbbbbfd gae fbbbbbfdcaac dfbbbbbgag dfbbbaad dbgaabfd daabbbbf eaafbbbbfd aae dfbbbbfd caa dfbbbbbf gag dfbbbbfd caac dfbbbbfd gag fbbbbb aac dfbb eaa d aae eaa gae caac gag caac eag aae eaa gae caac gag caac eag aae eaa ``` <!-- end of image --> Gotcha! I've found the intersection hiding in area A! The final count is: one intersection.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0202feff b,#fc0609ff c,#babaffff d,#ffb5b5ff e,#7575ffff f,#ff5b5bff g,#3333ffff ``` ```image cc ggaaaaaaaaaaaaggeeccc ccceeggaaaaaaaaaaaaggeec cceea eg a ca ac a ge a eg a ca ac a ge a eg a ca ac a ae a gg a ea ac ca ac a ge a eg a ca ac a ge a eg a ca ac a ge ddd a ddffbbbbbbbbfbbbd eg ddffbbbbbbbbffdd dbbf a ddffbbbbbbbbffdd fbbf ca bbffdd fbbd ac dbbf a dbbf ae fbbd a dbbb gg dbbf a fbbd ea bbbda dbba abbd a fbbd ge dbbf a fbbf eg f a ca ac a ge a eg a ca ac a ge a eg a ``` <!-- end of image -->

Here's an image. My task is to find intersections or areas where lines come close together. I'm going to focus my attention on these specific areas. <!-- image --> ```palette Key,Color ,#fefefeff a,#4948f6ff b,#fe0505ff c,#fa4745ff d,#0606fdff e,#9a9ff5ff f,#add5adff g,#f19c95ff ``` ```image e ad dd da da de de ed ed ad ad da da de de ed ed ad ad dd da de ffffffffffffffff de ffffffffffffffff ed ffffffffffffffff ed ggffffffffffffffad gcbbbbbgffffffffffffdd gcbbbcg ffbfffffffffffdd gbbbbcg ffgbfffffffffdaf cbbbbcg fffcbfffffffdaff gcbbbbg ffffbcfffffdefff gcbbbbg fffffbgffedfffff cbbbcg ffffffbfedffffff g fffffffadfffffff ffffffadbfffffff fffffddfbcffffff ffffdafffbgfffff fffdafffffbfffff ffdefffffffbffff eddfffffffffgbfff eadddaefffffffffffcbff eadddae fffffffffffffbcf adddde ffffffffffffffbf edddda fffffffffffffffb eadddae fffffffffffffffgb eadddae ffffffffffffffffcb adddde ffffffffffffffff bc de bg b gb cb bc bg b b gb cc bg b b gb cc bg b b gb cb bc bg b gb cb bc bg b b gb cc bg b ``` <!-- end of image --> Let's see what secrets area A holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#3b35f9ff b,#fe0606ff c,#fb4548ff d,#0404feff e,#817efbff f,#c9c9feff g,#ffababff ``` ```image ggg bbbbg bbcbbg cbb fa cbc fdd bbc fdda gbbg edda gbbg edde cbb edde cbc adde bbc addf gbbg faddf gbbg fddaf cbbg fdda cbb edda bbcedde gbadde adde addcbg faddfcbb fdddf cbc fdda bbc edda gbbg edda gbbg edde cbb adde cbc addf bbc faddf gbbg aadddf gbbg dddaf cbb ef cbc bbc gbbg gbbg cbb cb b g ``` <!-- end of image --> There's no doubt about it - this is an intersection in area A. The image features one single intersection point.

<!-- image --> ```palette Key,Color ,#fefefeff a,#433ffbff b,#ff0707ff c,#ff5454ff d,#0505feff e,#8d8dffff f,#cdcdffff g,#ffb2b2ff ``` ```image e ad ad da da de fdf fdf ed ad ad da da de fdf fdf ed ad ad da da de fdf fdf ed gg ad gcbbbbbg ad gcbbbcg b dd cbbbbcg gb da gcbbbbcg cb de gcbbbbcg bc df gcbbbbg bg fdf cbbbcg b ed g gad adb dd bc da bg de b de b eddf gb eadddaf cb fadddae bc fedddde bg eddddef b eadddaf gb fadddae cb fadddae bc def bg b gb cb bc bg b gb cb bc bg b b gb cb bc bg b gb cb bc bg b gb cb bc bg b gb cb bc bg b ``` <!-- end of image -->

I'm optimistic that I'll find some intersections in this image. There's definitely not a single intersection on the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0404ff b,#0b0bffff c,#6767ffff d,#ff6c6cff e,#bcbcffff f,#ffb7b7ff g,#ff3535ff ``` ```image f gg af a fa da ad af a fa gg af a fa da ad da af aa a fad fa ga gg ag af faf a ga fa ag da daf ad aa af fad a ga fa ag gg faf c af ga cb a ag eb fa daf b da aa be ad fad be af da bc a ag bb fa faf cb gg ga eb af ag b a daf be fa aa be da ad bc ad da bb af aa cb a faf eb fa ga b gag be f be bc bb cb eb b be be bc bb cb eb b be be bc bb cb eb b b be bc bb cb bbce eb ecbbbbce b cbbbbce b cbbbbce be ecbbbbc bc ecbbbbce bb ecbbbbce cb cbbb ``` <!-- end of image -->

This image might have some surprises. Let's look for intersections carefully. 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,#0808fdff b,#fc0807ff c,#aab0f2ff d,#e69a8eff e,#555bebff f,#eb4d44ff g,#b0d6b0ff ``` ```image d fb bf bf bd bd b b b db db db fb fb bf bf bd bd b b b db db fb fb bbggggggggggggggggggggggggggggggggggggggggggggg bfgggggggggggggggggggggggggggggggggggggggggggg gbfggggggggggggggggggggggggggggggggggggggggggg ggbdgggggggggggggggggggggggggggggggggggggggggg gggbdggggggggggggggggggggggggggggggggggggggggg ggggbgggggggcagggggggggggggggggggggggggggggggg gggggbgggggeaaaggggggggggggggggggggggggggggggg gggggdbgggaaggaegggggggggggggggggggggggggggggg ggggggdbgaeggggaeggggggggggggggggggggggggggggg gggggggeagggggggacgggggggggggggggggggggggggggg ggggggaafbgggggggagggggggggggggggggggggggggggg gggggaeggbbgggggggaggggggggggggggggggggggggggg gggeagggggbfggggggcagggggggggggggggggggggggggg ggaagggggggbfggggggeaggggggggggggggggggggggggg gaegggggggggbfggggggeagggggggggggggggggggggggg caggggggggggggbbfgggggaaggggggggggggggggggggggg aagggggggggggggggfbbggggaegggggggggggggggggggggg ae gggggggggggggggggdbbdggaeggggggggggggggggggggg cac ggggggggggggggggggggbbfgacgggggggggggggggggggg ea ggggggggggggggggggggggfbfagggggggggggggggggggg ae ggggggggggggggggggggggggfbadgggggggggggggggggg cac ggggggggggggggggggggggggggeabfgggggggggggggggg ea gggggggggggggggggggggggggggeafbfgggggggggggggg aa ggggggggggggggggggggggggggggeagfbbgggggggggggg cac gggggggggggggggggggggggggggggaaggdbbdggggggggg ea ggggggggggggggggggggggggggggggaeggggbbfggggggg aa gggggggggggggggggggggggggggggggaegggggfbbggggg ae ggggggggggggggggggggggggggggggggacggggggdbbdgg ea gggggggggggggggggggggggggggggggggagggggggggbbf aa ggggggggggggggggggggggggggggggggggaggggggggggfbb ae ggggggggggggggggggggggggggggggggggeagggggggggg dbbd cac ea bbf aa ea fbb c ae dbb ae ac ac a ca ca ea ea ae ae ac ac a ca ca ea ea ae ae ac a ``` <!-- end of image --> I wonder what we'll find inside area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#0707feff b,#fe0405ff c,#acaafdff d,#ff8080ff e,#4e4afaff f,#f43741ff g,#fec4c4ff ``` ```image f bf bbf gbbd gbbd dbbd dbbg dbbg fbbg fbbg fbbg caac fbf caaaa bbf eaaeaae gbbf caaac aae gbbf caaac caae gbbd eaae caae gbbdcaaac caac dbfaaac caac eaae eaac eaafbg eaac caaacfbbg eaa eaae fbbg aae eaae fbb aae caaac fbf caae caae gbbf caae eaae gbbf caac caaac gbbd caac caae gbbd eaac eaae dbbd eaa aaac dbbbd eaa aac dbbbbdg aae e dfbbbfg aae gfbbbfd caae gdbbbbdg caae dfbbbfg caac gfbbbfd caac gdbbbbdg eaac dfbbbfgeaa gfbbbfeaa gdbbbaae dbbaaeg gfaaefg caafbbd caafbbbdg caacfbbbfg eaacgfbbbbd eaa dbbbbdg eaa dfbbbfg aae gfbbbfd aae gdbbbbdg caae dfbbbfg caac gfbbbfd caac gdbbbbdg eaac dbbbbfg eaac gfbbbfd eaa gdbbbbd eaa dbbbb aae gfb aae g caae caac ``` <!-- end of image --> There's no doubt about it - this is an intersection in area A. Two intersections have been found!

<!-- image --> ```palette Key,Color ,#fefefeff a,#0808feff b,#fe0708ff c,#908ffdff d,#ff9999ff e,#4a48fcff f,#fe4a4bff g,#e3d3efff ``` ```image d fb bf bf bd bd bg bg gb gb db db fb fb bf bf bd bd bg b gb db db fb fb bf bf bd bd bg bg ga gb eaae gb aa ae dbgac ac ea ag aafb ag gac fb ga cag bf ga aa bf ca ae bd ea cag bbf ae aa fbb ae ae dbbd ac cag gbbd ag ea fbfag ae dbag gac cabd ea cafbf aa ea dbbg gac ae dbbd eag ae bbf aa ac fbbg gac ag dbbd cag ag bbf aa ga fbb ae ca dbbd cag ca gbbf aa ea fbb g ae dbb ae g ac ag a ga ca ca ea ae ac ac ag a ga ca ea ea ae ac ac 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,#eb534fff b,#0101feff c,#8189edff d,#f8a29fff e,#aed5aeff f,#2f2ef3ff g,#fe0707ff ``` ```image d g gd dg g gd dg g aa g gd dg g ga g g ag g gd dg g aa g gd dg g gd dg g aa g gd dg g ga g g ag g gd dg g aa g gd dg g gd dg d g agd aa gg g dga gd agd dg gg g gg eeeeeeeeeeeeeeeeeeeeeeeeeeeeegaee dga eeeeeeeeeeeeeeeeeeeeeeeeeeeeegeee ggd eeeeeeeeeeeeeeeeeeeeeeeeeeeegeeee ggeeeeeeeeeeeeeeeeeeeeeeeeeeeageeee dgaeeeeeeeeeeeeeeeeeeeeeeeeegeeeee eagdeeeeeeeeeeeeeeeeeeeeeegaeeeee eeeggeeeeeeeeeeeeeeeeeeeedgeeeeee eeeedgaeeeeeeeeeecbbbbceegeeeeeee eeeeeeagaeeeeecbbfeeeefbfaeeeeeee eeeeeeeeggefbbfeeeeeeeeeabbceeeee eeeeeeeefbbfeeeeeeeeeeegdeefbfeee eeeeefbbceeagaeeeeeeeeageeeeecbbc ecbbbceeeeeeeggeeeeeeegeeeeeeeeefbf cbbbceeeeeeeeeeeeggeeeegaeeeeeeeeee cbbc cbbf eeeeeeeeeeeeeeeeagaeegeeeeeeeeeee fbf cbbf eeeeeeeeeeeeeeeeeegggeeeeeeeeeeee cbbc fbbc eeeeeeeeeeeeeeeeeeeeaeeeeeeeeeeee fbf fbbc eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee cbbc bbc eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee fbf eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee cbbc fbf cbbc fbf cbbc fb ``` <!-- end of image --> Could this be where the intersection is hiding, in area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#f6343cff b,#0706fdff c,#acabfdff d,#fd787aff e,#ffc1c1ff f,#5652faff g,#fe0404ff ``` ```image dga egge agd dgg egge aga egge ggd d dga gae egge ggga aga dgggd dgg eaggae ggd egggae dga dgggd egge eaggge cfbbfc agd eaggae cfbbbbbbbfc dgg dgggd cfbbbbbfccfbbbbfcegge agggd cfbbbbbfc cbbbbbaa eaggae cfbbbbbfc cfbbbbfc dgggd cfbbbbbfc aabbbbfc dafbbbbbfc dga cfbbbbfc cfbbbbbfc egge cbbbbfc cfbbbbbfdgggae agd cfbbbbfc ccfbbbbfcc dgggd dgg cbbbbf cfbbbbbfc eaggae egge cfbb cfbbbbbfc egggae aga c cfbbbbbfc dgggd egge bbbbfc eaggge ggd bfc eaggae dga dgggd egge dgggd aga eaggggg dgggd dd ``` <!-- end of image --> There's no doubt about it - this is an intersection in area A. My analysis indicates that there are two intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fa393eff b,#0101ffff c,#9494ffff d,#ff8181ff e,#ffc8c8ff f,#3530faff g,#ff0505ff ``` ```image d g ge dg g gd eg g aa g ge dg g ad eg ge da g gd eg g aa g ge dg g gd eg g aa g ge dg g ad eg ge da g gd eg g aa g ge dg g gd eg d g agd aa gg g ega ge dgd dg gge g egg ad dgd eg age ge gg da dga g age gd gg eg ega cbbbbc g agd cbbf fbfa gg cbbf abbc fbbf ge fbf fbbc dgd dg cbbc cbbbc gge g fbf cbbbc egg gd cbbc cbbf dgd eg fbf fbbf agg cbbc fbbc d fbf cfbbc cbbc bbc fbf cbbc fbf cbbc fbf cbbc fb ``` <!-- end of image -->

This is the image I'm working with. The goal is to count the intersections. Let's take a closer look at what's happening inside these zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#fc0908ff b,#0303fdff c,#f5aba6ff d,#393ae6ff e,#afd6afff f,#7b80f5ff g,#ec5a51ff ``` ```image c ag a ga a ca ac a gg a ca a a ac a gg g a ga ca ga ac ca a ca ag ca a a ga a a ac ca ac ac ac a ag gg ag a ag ca ga a ga a ga ac ca a ca gg ca a a ca a ac ac aeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeac ageeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeac eaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeag egaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeage eeaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaaee eecaeeeeeeeeeeeeeeeeeeeeeeeeeeeaaeee eeeaceeeeeeeebbbbdeeeeeeeeeeeegaeeee eeeeaeeeeeeebdeeedbbbfeeeeeeegaeeeee eeeeageeeeebdeeeeeeefdbbdeeegaeeeeee eeeeeaeeeebdeeeeeeeeeeeefbbbdeeeeeee eeeeegaeebdeeeeeeeeeeeeeeecadbbbfeee eeeeeeaebdeeeeeeeeeeeeeeeeaeeeefdbbde eeeeeeebdeeeeeeeeeeeeeeeeaeeeeeeeeefbbbf eeeeeebdgeeeeeeeeeeeeeeeaeeeeeeeeeee fbbbf eeeeebdeaeeeeeeeeeeeeeeaceeeeeeeeeee edbbd eeeebdeeggeeeeeeeeeeeeageeeeeeeeeeee fbbbf eeebdeeeeaeeeeeeeeeeeageeeeeeeeeeeee fbbbf eebdeeeeegaeeeeeeeeeageeeeeeeeeeeeee dbbd ebdeeeeeeeaceeeeeeeaaeeeeeeeeeeeeeee f bdeeeeeeeeeaeeeeeeaaeeeeeeeeeeeeeeee bdeeeeeeeeeeageeeegaeeeeeeeeeeeeeeeee bdeeeeeeeeeeeeaeeegaeeeeeeeeeeeeeeeeee bf eeeeeeeeeeeegaegaeeeeeeeeeeeeeeeeeee bf eeeeeeeeeeeeeagaeeeeeeeeeeeeeeeeeeee bf ca bf bf bf bf bf bf bf bf bf bf bf bf bf bf bf bf bf ``` <!-- end of image --> I'm going to scrutinize area A for any signs of an intersection. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0607ff b,#0504fdff c,#fd8b8dff d,#4f4bfbff e,#fecdcdff f,#b8b8feff g,#fc4447ff ``` ```image ae ag aac caa aac c eaae ca gag eaa eaae eaag cag eaag aac eaag caa eaag gac aag eaae f gaae gag fbbbdf gaae eaae fbbbbbbbddf gaae caa fbbd fddbbbbbdff gaae aac fbbd fdbbbbbbdf gaae caae fbbd ffdbbbbbddf caac gag fbbd fddbbbbbdff caac eaae fbbd fdbbbbbbdf caac gag fbbd ffdbbbbbbdc aac fbbd fddbbbbbdff caa fbbd eaagdbbbbbbdf aac fbbd eaag ffdbbbbbddf eaaefbbd eaag fddbbbbb gagbbd aag fdbb eabbd gaae f fbbd gaae fbbbac gaae fbbdcaa gaae fbbd gac gaae fbbd eaae caac fbbd gag caac fbbd eaae caac fbbd caa caac fbbd aac eaag fbbd caae eaag fbbd gag eaag fbbd eaae eaag fbbd gag eaag fbbd eaac gaae bbd caa gaae bd aac gaae d eaae gaae gag gaae eaae caac cag caac ``` <!-- end of image --> Amazing! This area was hiding an intersection all along! My analysis indicates that there are two intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fe0405ff b,#0504fdff c,#ff8080ff d,#5350fbff e,#ffc4c4ff f,#9898ffff g,#ff3d3dff ``` ```image e gc a cg a ea ae a gg a ca ae ea ac a gg g a ga ea ca ae ca a ea gc ea a a cg ae a ae ea ae ae ac a ac gg ag a ag ca ga ae ga ea ca ac ca a ea gg ea a ea ea a ae ae a ae gc ac a ac cg ag a ag ea ga ae bbbbf ga a bd dbbbf ca gg bd fdbbd ca a bd fbbbd ca bd eadbbbf aebd ea fdbbd ebd a fbbbd bbc ae dbbbf bd a ae fdbbdf bd gg ac fbbbd bd a ac dbbbf bd ea ag fdbbd bd ae ag f bd a gg bd gc ga bd a ca bd cg ca bd aca bd ea bd bd bd bd bd bf bf bf bf bf bf bf bf bf bf bf bf ``` <!-- 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,#fe0808ff b,#6468f7ff c,#f95956ff d,#0909fdff e,#b9b9ffff f,#acd3acff g,#fda9a8ff ``` ```image g ag a cc a cc a cc a ca a ga a ga a ga ag a ag a ag a ag a ac a cc a cc a ca a ga bdd a ebddddbe ga ebddddbe a ebddddb fffaffffffffffff bddddbe fffaffffffffffff ebddddbe ffffafffffffffff ebddddbe ffffafffffffffff ebddddb fffffaffffffffff eddddde fffffagfffffffffbddde ffffffaffffffdddb ffffffacfbdddbff ffffffbdddffffff ffbdddbacfffffff bdddfffffafffffff edddbffffffffacffffff bddde fffffffffaffffff edddb fffffffffccfffff bddde ffffffffffafffff dbe ffffffffffcaffff fffffffffffaffff ca a ga a ga a ga ag a ag a ag a ag a cc aaacg gaaaag gcaaag gcaaac caaac caaacg gaaacg gaaaag gcaaag gcaaac caa ``` <!-- end of image --> Let's get to the bottom of what's happening inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0202ff b,#544ffaff c,#ff6f6fff d,#0404feff e,#a7a7feff f,#fa373cff g,#ffc8c8ff ``` ```image gaag fac gaag fac gaag caf gaag caf gaag caf aag caf eb aag eebddd caf ebdddddbb aac ebdddddbe cafbddddddbe ebdddddbe ebbdddddbe ebdddddbeefac eebdddddbe gaa bdddddbbe fac dddbe gaag be fac gaag fac gaag caf gaag caf gaag caf aag caf ``` <!-- end of image --> Wow! I can see an intersection so clearly in area A! I have found one intersection!

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0303ff b,#5555feff c,#ff7c7cff d,#0505ffff e,#aaabffff f,#fe3838ff g,#ffc0c0ff ``` ```image g fc a fc a ff a cf a cf a ca a ga a ga ag ga ag a ag a ac a fc a fc a cf a cf a ca edd a ebddddbe ga ebddddbe a ebdddde ga eddddbe ag bddddbe ga ebddddbe ag ebddddb a ebdddbe ag bddde a ebddb ac eddde bddb edddefc bddbe a edddb fc bddde a ebddb ff eddde a db cf a cf a ca a ga ag ga ag ga ag a ac a fc a fc aaafg cfaafg gfaaac gfaaac gcaaacg caaafg caaafg gfaafc gfaaac gfaaac caa ``` <!-- end of image -->

I'm optimistic that I'll find some intersections in this image. I'm extremely confident. No intersections at all.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff3c3cff b,#0707ffff c,#ff0404ff d,#ffbcbcff e,#bdbdffff f,#5e5effff g,#ff7d7dff ``` ```image e ebbbbe fbbbe be ebbbf be fbbbe be ebbbf be efbbfe b fbbbf b efbbfe eb fbbbe eb ebbbf eb be eb eb eb eb fb fb fb fb fb fb fb bb bb bb bf bf bf bf bf bf bf be be be d be ca be ca be ca be ac b ac b ac eb ac eb ac eb ac eb ac eb gc e gc gc gc gc dc dc dc dc dc dc dc c cd cd cd cd cd cd cd cg cg cg cg cad gccccgd dgccccgd gccccad gccccad gacccad gacccad gacccad dacccad dacc ``` <!-- end of image -->

I'm examining this image closely. My goal: find any and all intersections. These regions highlight areas that look suspicious. Lines seem to converge within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#565af7ff b,#fe0707ff c,#f8a7a4ff d,#0707feff e,#b5b5ffff f,#f65450ff g,#add4aeff ``` ```image c fbc bb e cbb dd fbf ade bbc dd bb ade cbf eda fbc dd bb eda cbb dd cbf ade fbc dd bb ade cbf eda fbc dd bb eda bb gggggggggggggggg dd cbf gggggggggggggggg ade fbc gggggggggggggggg dd bbggggggggggggggggade cbbgggggggggggggda gfbggggggggggddg ggcbfggggggadagg ggggbbggggddgggg gggggfbgadaggggg gggggggddggggggg gggggadgbbgggggg ggggdagggfbcgggg ggddgggggggbbggg gdagggggggggfbgg dggggggggggggcbf daggggggggggggggbb edggggggggggggggggfb d gggggggggggggggg bf de gggggggggggggggg bb ad gggggggggggggggg cbc ed bf d fb da cbc ad bb d fb de bf da bb ed cbc d bf de fb ad cbc ed bb d fb da bf ad bb d cbc de b da ed d de aa ed d de ad d d da ed d de aa ed d de ad ed d da ad d de ``` <!-- end of image --> This close-up of area A is like examining a piece of evidence. <!-- image --> ```palette Key,Color ,#fefefeff a,#5149f7ff b,#fe0506ff c,#ff8787ff d,#0606feff e,#adacfeff f,#fb3b3fff g,#fdc9caff ``` ```image c bbc fbbfg ea cbbbc add fbbf eddda cbbbg addde gbbbc eddda fbbf addae cbbbg eddde gfbbc eadda cbbfg addde gbbfddda gaddde edddabfg addaegbbbc eddde fbbf eadda cbbbg addde gfbbc eddda cbbfg addde gbbbc ddda gfbbf adde cbbfg edde gbbb dde fb da c d e ``` <!-- end of image --> Bingo! This close-up reveals an intersection in area A! There's one and only one intersection present in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#5a5affff b,#ff0606ff c,#ff8585ff d,#0807feff e,#b6b6ffff f,#ff4343ff g,#feccccff ``` ```image c fbc bbg e gbb dd cbc ade fbg dd bb ade cbf eda fbc dd bbg eda gbb dd cbc ade fbg dd bb ade gbf eda fbc dd bbg eda gbb dd cbf ade fbg dd bb ade gbf eda fb dd gbc eda bb dd cbgade gdd adebb eda cbg dd bf da fb de gbc da bb ed cbg d gbf de bb ad cbg ed bf d fb da gbc ad bb d fbg de gbc da bb ed cbg d bf de fb ad gbc ed bb d fbg da gbc ad bb d cbg de b da ed d de aa ed d de ad d d da ed d de aa ed d de ad ed d da ad d de ``` <!-- end of image -->

I'm curious to see if this image contains any intersection points. I'd describe these as 'hotspots' for potential intersections. <!-- image --> ```palette Key,Color ,#fefefeff a,#f38883ff b,#0909feff c,#fe0807ff d,#585bf7ff e,#95c897ff f,#b1d7b1ff g,#aaabfcff ``` ```image g db bb bd bd bg gb gb db bb bd bd bg gb gb db bb bd bd bg feeeeeeeeeeeeeee gb efffffffffffffff gb efffffffffffffff db efbbffffffffffff bb efcdbbgfffffffff bb efacffbbdfffffff bd effcafffdbbfffff bg efffcfffffdbbeff gbg efffacffffffebbd gb effffcaffffffffbbd db efffffcfffffffff dbb bb efffffacffffffff gbbg bb effffffcafffffff bbd bd efffffffcfffffff dbb bg efffffffacffffff gbbg gbg effffffffcafffff gbbg gb efffffffffcfffff bbd db efffffffffacffff dbb bb effffffffffcafff gbbbb efffffffffffcfff d efffffffffffacff effffffffffffcaf efffffffffffffcf efffffffffffffac effffffffffffffca feeeeeeeeeeeeeeec ac ca c ac ca c ac ca c ac ca c ac ca c ac ca c ac ca c ac ca c ac ca c ac ca c ac ca cccccccccccccccccccccccaaaaaaaa faaaaaaaaccccccccccccccc ``` <!-- end of image --> This close-up might reveal an intersection in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe3f3fff b,#0707feff c,#ff0404ff d,#a2a1feff e,#ff9393ff f,#5454ffff g,#f8dbe2ff ``` ```image fd dbbbd dbbbbfg gcadfbbbfd gcce dfbbbbd eccg gfbbbbfg aca dbbbbfd gcce dfbbbfd eccg gfbbbbd aca dbbbbfg gcce dfbbbfd eccg dfbbbbd aca gfbbb gcce db eccg aca gcce eccg aca gcce eccg aca gcce eccg aca gcce eccg aca gcce eccg aca gcce eccg aca gcce eccg aca gcce eccg aca gcce ecc ac gc e ``` <!-- end of image --> I'll move on to the next area. The intersection must be somewhere. The image is completely devoid of intersections. Zero.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff6868ff b,#0404ffff c,#ff0707ff d,#8080feff e,#ff9c9cff f,#3b3bffff g,#c2c2ffff ``` ```image d fb bb bf bd bg gbg db fb bb bf bd bg gbg db fb fb bf bd bg gbg db fb bb fb cdbbg bf ec gbbd bd ce fbf bg c dbbg gbg ec gbbd db ce fbf fb c dbb fb ec gbbg bf ce bbd bd c fbf bd ec dbbg gbg ce gbbd db c fbf fb ec dbb fb ce gbbbf c d ec ce c ec ce c ec ce c ec ce c ec ce c ec ce c ec ce c ac ce c ac ce c ac ce c ac ce c ac ce c ac ce ccccccccccccccccccccccaaaaaeeeee eeeeeaaaaacccccccccccccc ``` <!-- end of image -->

Time to put on my detective hat and find those intersection points! There are 2 areas where the lines seem to converge. We should take a closer look at area A,, and B. <!-- image --> ```palette Key,Color ,#fefefeff a,#656af3ff b,#fc0c0cff c,#ef6f67ff d,#98c598ff e,#0909fdff f,#b0d7b0ff g,#e1c8e5ff ``` ```image g aee e aea ge eeg eg gee ge aea eg ee e gea ea aeg e ee aa gea e eeg aa ee e aea dfffffffffffffffd ae eeg dfffffffffffffffd e gee dfffffffffffffffd ge aea dffffffffffffcffd eg ee dfffffffffffdbffd b ge geadfffffffffffbfffd cb eg aedfffffffffbcfffd bg e deefffffffcbffffd gb ea dfaeafffffbfffffd bc e dfffeedffbcfffffd b aa dfffffeecbffffffd cb e dffffffaeaffffffd b aa dffffffbdeefffffd gb e dfffffbbffdeefffd bg ae dffffdbfffffaeffd b e dffffbffffffffffd bc ge dfffbcffffffffffd b eg dffdbfffffffffffd cb ge dffbffffffffffffd bg eg dfbcffffffffffffd dbdddddddddddedd dcbfffffffffffffd dbcfffffffffeaff dbffffffffffffffd dfbfffffffffefff bcffffffffffffffd dfcbfffffffaafff cbdddddddddddddddf dffbfffffffeffff b dffdbfffffaeffff bg dfffbcffffefffff cb dffffbfffaefffff gb dffffbbffeffffff b dfffffbfdeffffff bc dfffffcbedffffff gb dffffffbefffffff b dffffffebfffffff bc dffffffebcffffff cb dfffffeafbffffff b dfffffeffcbfffff bg dffffaafffbdffff cb dffffeffffdbffff b dfffaefffffbcfff bg dfffefffffffbfff cb dffaefffffffcbff gb dffefffffffffbff b dfdefffffffffcbf bc dfedffffffffffbc gb ge gb b eg bc bc e b cb ea cb b e bg bg aa gb cb e bc b ae b bg e cb bc ge b gb e gb b ge bc bc eg b gb e cc b eg b bc e cb cb ea bg b e b bg aa bc cb e b b ae cb bg e bbc gb ``` <!-- end of image --> Here's a close-up of the area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#4741f8ff b,#fd0607ff c,#ff4949ff d,#9494feff e,#0504feff f,#ff9a9aff g,#e9d6ebff ``` ```image cbc dea gbbf eed fbb dee bbf aed fbbg dee cbc aed gbbf geeg cbc aea bbf geeg fbbg aea cbc geeg gbbg dea cbc eed gbbf dea fbb eed bbf dee fbbg aed cbc dee gbbf aed fbb geeg bbf aea fbbgeeg cbaea gbeeg aea eebf deebb eedcbc dee fbbg aed cbc dee gbbf aed fbb geeg bbf aea fbbg geeg cbc aea gbbf geeg cbc dea bbf eed fbbg dea cbc eed gbbg dee cbc aed gbbf dee fbb aed bbf geeg fbbg aea cbc geeg gbbf ``` <!-- end of image --> As I suspected, there's an intersection within area A. Let's continue our search in the next region. Could this be where the intersection is hiding, in area B? <!-- image --> ```palette Key,Color ,#fefefeff a,#7373feff b,#fd0506ff c,#ff4747ff d,#babaffff e,#0e0cfcff f,#fe8889ff g,#fec7c7ff ``` ```image cg fbb gbbg bbc cbb a gbbg eed bbf eeea cbc aeeea fbbg deeeed gbbf deeea cbc aeeed fbbg deeeed gbbf aeeea cbc aeeedfbb deeeebg aeeea cbeeeed gbbgdeeea bbf aeeea cbc deeeed fbbg aeeea gbbf aeee cbc dea fbbg gbbf cbc fbb gbbg bbc cbb gbbg bbf cbc fbbg gbbf cbc fbbg bbf bc ``` <!-- end of image --> I can confirm that an intersection exists in area B. There are precisely two intersections present in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#5252ffff b,#fe0809ff c,#fe5353ff d,#9999feff e,#0707feff f,#ff9a9aff g,#ecd7e9ff ``` ```image g dee e dea de eeg eg gee ge aed eg ee e gea ed aed e ee aa dea e aeg aa gee e ded de eeg e gee de aed c eg ee gb b ge dea b fb ed aed bc bg e ee fb gb ed dea b bf e eeg bf b aa geecb cc e ded b aa bgeeg fb e cb gea bf de gb ae b e bg cc de bc b eg fb fb ge b bg ed bf gb e fb bf ed b b e bf cb aa cb bg e b gb aa bg bf e cc b de gb cc e bg b ge bc fbeg fb be b eb bf ebc fb ed b b e fb bf aa bg cb e gb gb da bf bg e b cc de cc gb e b bg ge fb bc eg bf fb ge b b ed cc bf e b fb ed fb b e bg bf aa gb cb e bf gb da b bg e cb cc de bg gb e gb bg ge bf bc eg b fb ge cc b ed b bf e fb fb ad bg b e gb bf aa bc cb e b gb da fb bg e bbc gb ``` <!-- 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,#9399f3ff b,#fd0a09ff c,#0505feff d,#f2736dff e,#494ef4ff f,#aed6afff g,#efeaecff ``` ```image a acccccea c gaecccceag ac aecccccag cg aecccccea gc gaeccccea ca gaecccceag c aeccccca ea ae c ee c ac c ac cg gc ca c ea c ee c ac c fffffffffffffffacff gfffffffffffffffcfffg g gfffffffffffffffcfffg dbb gffffffffffffffcafffg gbbd gffffffffffffffcffffg dbbg gfffffffffffffeeffffg gbbd gfffffffffffffcfffffg dbbg gffffffffffffeefffffg dbbd gffffffffffffcffffffg gbbbg gfffffffffffacffffffg dbbd gfffffffffffcfffffffg gbbbg g gffffffffffacfffffffg dbbd bbbbdg gffffffffffcffffffffg gbbd gdbbbbddffffffffcffffffffg dbbg gdbbbbbdffcaffffffffg gbbd gfffffdbbbcbdfffffffg dbbg gffffffffeedbbbbbdffg dbbd gffffffffcffffffddbbbbdg gbbbg gfffffffeeffffffffffggdbbbbddbbd gfffffffcfffffffffffg gdd gffffffacfffffffffffg gffffffcffffffffffffg gfffffacffffffffffffg gfffffcfffffffffffffg gfffffcfffffffffffffg gffffcafffffffffffffg gffffcffffffffffffffg gfffeeffffffffffffffg gfffcfffffffffffffffg gffeefffffffffffffffg gffcffffffffffffffffg fecffffffffffffffff cg gc cg gc ca c ee c ae c ac cg gc cg c ca c ee c ae c ac cg ``` <!-- end of image --> This close-up might reveal an intersection in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#8785fdff b,#fe0506ff c,#0404feff d,#ffababff e,#4444ffff f,#ccccffff g,#f7525aff ``` ```image fcc ece fccf ace ccf ace cca acc eca fcc eca fcc ece fccf ace ccf ace cca acc eca fcc eca fccf ece fccf ace bgdd ccf bbbbbbggd ace ddgbbbbbbbbggd cca ddggbbbbbbbggacc ddggbbbbccgggdd ddgccbbbbbbggdd eca dggbbbbbbbbgdd fccf dggbbbbbbbb ece ddgbbb fccf d ace ccf ace cca acc eca fcc eca fccf ece fccf ace ccf ace cca acc eca fcc eca fccf ece fccf ace ccf ace ``` <!-- end of image --> Gotcha! I've found the intersection hiding in area A! It was tricky, but I finally found one single intersection in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#7b7bfeff b,#fe0606ff c,#0404ffff d,#ffa2a2ff e,#3f3fffff f,#bbbbffff g,#ff5353ff ``` ```image f acccccef c aeccccea fc fecccceaf cf facccccaf c faeccccef cf aecccceaf c feccccea ea fa c ae c ae c fc cf c cf c ea c ae c ac c fc cf c dbb cf bbg c gbbd ea dbbg c gbbd ae dbbg c gbb ac dbbd c bbg fc gbbd bbbbgd cf dbbg dbbbbgd c gbbd dbbbbgd cf dbbg dgbbcgd gbb eadgbbbbd dbbd c dgbbbbd bbb ae dgbbbbgdbbd c gg fc c fc cf c cf c ea c ae c fc c fc cf c cf c ea c ae c fc c fc cf c ca c ea c ae c fc c ``` <!-- end of image -->

Here's an image. My task is to find intersections or areas where lines come close together. These spots mark what I'd call 'danger zones' - areas where intersections are more likely. <!-- image --> ```palette Key,Color ,#fefefeff a,#f55c58ff b,#7779fbff c,#ffb6b6ff d,#fe0807ff e,#98c697ff f,#090afeff g,#b1d7b1ff ``` ```image c add cdd cd cdd da dd d ddc cd ddc da ada d ada cd cda aa cdd d dd d ddc aa ddc dc ada d ada ad cda dc cdd d dd ad ddc dc dc d ad dc d cd dc d cd da d cd da d cd da d cd aa d d aa dc d ad dc geeeeeeeeeeeee d eggggggggggggg ad eggggggggggggg dc eggggggggggggg d eggggggggggggg adeggggggggggggg daggggggggggggg dggggggggggggg adgggggggggggg edaggggggggggg egdggggggggggg egadgggggggggg eggdaggggggggg egggdggggggggg egggedgggggggg ffffb eggggdaggggggg bbfffffbb egggggdggggggg bffffffb egggggedgggggg bbfffffbb eggggggdaggggg bffffffb egggggggdggggg bbfffffb egggggggedgggg bffb eggggggggagggg bffb eggggggggggggg bffb eggggggggggggg bffb eggggggggggggg bffb eggggggggggggg bffb eggggggggggggg bffb eggggggggggggg bffb eggggggggggggg fffb eggggggggggggg fffb eggggggggggggg fffbeggggggggggggg fffbggggggggggg eefffbgggggggg egggefffbggggg eggggggeffgggg eggggggggggggg ``` <!-- end of image --> Let's take a closer look at area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff4848ff b,#6565ffff c,#ff8c8cff d,#ff0707ff e,#b6b6ffff f,#0909ffff g,#ffceceff ``` ```image c dg da ddc cddg ada gddc cddg ada gddc cddg ada ddc gddg add ddc gddg add dda gddg cdd dda gddc cdd ada gddc cddg ada gddc cdd cg be fffbe bfffffbe ebfffffbe ebfffffbe ebfffffbe ebfffffbe ebffff ebe ``` <!-- end of image --> No intersection found in area A, but I won't give up. My final answer is: no intersections found.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff5151ff b,#4c4cffff c,#ff9a9aff d,#ff0707ff e,#9393ffff f,#0303ffff g,#f3d6e1ff ``` ```image g add cda cd gdd da gddg d ddg gd ddc da adc dg ada gd cda aa gdd dg gddg gd ddg aa ddc dg adc gd ada ad cda dg cdd d gddg ad ddg dc dc d cd dc d cd dc d cd dc d cd da d gd da dg gd aa dg gd aa dg gd ad dg d ad dc d cd dc d cd dc d cd dc d cd fffbeg da ebfffffbe d gebffffbeg gd ebfffffbe aa gebffffbeg dg ebfffffb gd gbffb a bffb bffe bffe bffe bffe bffe bffe bffe gbffe gbffe gbffe gbffe gfffe gff ``` <!-- end of image -->

I'm ready to tackle this image and find those intersections! There are 2 areas where the lines seem to converge. We should take a closer look at area A,, and B. <!-- image --> ```palette Key,Color ,#fefefeff a,#0606fdff b,#fe0505ff c,#9a9ff5ff d,#eb9f95ff e,#f73d39ff f,#aed5aeff g,#494bf4ff ``` ```image ffffffffffffffff ffffffffffffffff ffffffffffffffff fffdddddddddddddddddddddddddddddddddddd fffeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeb ffffffffffffffff b ffffffffffffffff db fffgffffffffffff eb fffggfffffffffff be ffffafffffffffff bd ffffggffffffffff b fffffaffffffffff b fffffagfffffffff db ffffffafffffffff eb ffffffacffffffff be fffffffaffffffff bd fffffffacfffffff b a b ac db a ee a be ca bd a b ca b a db ca ee a bd cg bd a a b gg gg db ca a db ffffffffffffffff a gg eeffffffffffffffffa a beffffffffffffffag gc bdffffffffffffga a fbfffffffffffcaf ac fdbffffffffffaff a ffebffffffffacff ac fffbeffffffagfff a ffffbdffffgaffff ac fffffbfffcafffff a ffffffbffaffffff a ffffffdbacffffff ca fffffffagfffffff a ffffffgabeffffff ca ffffffaffbdfffff a fffffaffffbfffff ca ffffacfffffbffff a fffagffffffdbfff cg ffgaffffffffebff a ffaffffffffffbef gg faffffffffffffbd a agfffffffffffffb gg gafffffffffffffffb a caffffffffffffffffdb gc a ffffffffffffffff eb a a be ac ag b a ga ac ca a a ac ac a ag a ga ca ca a a ca ac a ag ca ca a a cg a a ac gg gg a ca gg a a a gc ac a ga ac ca a a ac a a ag aga a ``` <!-- end of image --> I'm now examining the contents of area A in detail. <!-- image --> ```palette Key,Color ,#fefefeff a,#0606ffff b,#ff0000ff c,#cdcdffff d,#ffacadff e,#ff3c3cff f,#8e8dffff g,#4545ffff ``` ```image dddddddddddddddddddddddd bbbbbbbbbbbbbbbbbbbbbbbb eeeeeeeeeeeeeeeeeeeeeeee cgg caac gag caac gag caac gaf caa gaf caa gaf faa aaf faa aaf faa aaf fag ``` <!-- end of image --> After careful examination, I've determined that there's no intersection in area A. Let's inspect the next region. I'm determined to find out if an intersection exists in area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#0605feff b,#fd0506ff c,#ebd6eaff d,#ff9595ff e,#ff4242ff f,#9b99fcff g,#4845fcff ``` ```image f d ca bd aa bbc gaa ebbc faac ebe faaf cbbe caag dbbd gag dbbd gaac ebbc faac ebb faaf bbe caag cbbe gag dbbd gaac dbbd faaf ebbc caaf ebe caag cbbe gag cbbd gaac dbbfaaf dbaaf caagc gaabe faacbbe faaf cbbd caaf dbbd aag dbbc gaa ebbc faac ebe faaf cbbe caag cbbd gag dbbd gaac dbbc faac ebbc faaf ebe caag cbbe gag cbbd gaac dbbd faaf dbb aaf eb ag e g c c ``` <!-- end of image --> The close-up clearly shows an intersection point in area B. I have found one intersection!

<!-- image --> ```palette Key,Color ,#fefefeff a,#0404feff b,#ff0606ff c,#c4c4ffff d,#ffababff e,#ff4242ff f,#7b7bffff g,#3836fdff ``` ```image dddddddddddddddddddddddddddddddddddd eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeb b db g eb fg be a bd gf b a b gf db a eb af be a bd ac b a b ac db ca eb ac be ca bd a b ca db a db fg ee a be fg bd a a b gg fg db fa a eb a gf ee ac a bd af gf bd gg a b ca af db a a eb ac ac be af a bd fa ac b ca ca b a ac dbac ca ag a fabe ca ca bd a a b fg af b a gg db fg fa eb a ca be fg ac bd a af b gf gg b a ca db gf a eb a ac be gf af b a ga ac ca a a ac ac ca af ac fa ca ca a a ca ac a gg fa fa a ca fg a a af fg gg a fa gf a a ac gf af a gg gf ca a a ac ac a af aga ca ``` <!-- end of image -->

I'm ready to tackle this image and find those intersections! It's crucial to examine these regions more closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd0505ff b,#0909fbff c,#e5413dff d,#636fe7ff e,#e18e80ff f,#f1f0ecff g,#b0d6b0ff ``` ```image f ae fa af fa af ea a ec a ce a ae fa af fa af ea a ec a ce a ae fa af fa af ea a ec a ce a ae fa affffffffffffffffffffffffffffffffffffffffffffffff fagggggggggggggggggggggggggggggggggggggggggggggggg a fagggggggggggggggggggggggggggggggggggggggggggggggg af feaggggggggggggggggggggggggggggggggggggggggggggggg faf fgaggggggggggggggggggggggggggggggggggggggggggggggg faf fgccgggggggggggggggggggggggggggggggggggggggggggggg faf fggagggggggggggggggggggggggggggggggggggggggggggggg faf fggccggggggggggggggggggggggggggggggggggggggggggggg faf fgggaggggggggggggggggggggggggggggggggggggggggggggg faf fgggaegggggggggggggggggggggggggggggggggggggggggggg fa fggggagggggggggggggggggggggggggggggggggggggggggggg ea fggggagggggggggggggggggggggggggggggggggggggggggggg ea bbdf fggggeaggggggggggggggggggggggggggggggggggggggggggg ea fdbbbdg fgggggagggggggggggggggggggggggggggggggggggggggggggea dbbbbdf fgggggeagggggggggggggggggggggggggggggggggggggggggca fdbbbdgggggggaggggggggggggggggggggggggggggggggggggggggca dbbbbdggccggggggggggggggggggggggggggggggggggggggcag fgggdbbbbdggggggggggggggggggggggggggggggggggggcagg fgggggggcbbbbdgggggggggggggggggggggggggggggggcaggg fggggggggagggdbbbbdgggggggggggggggggggggggggcagggg fggggggggaeggggggdbbbdgggggggggggggggggggggaaggggg fgggggggggaggggggggggdbbdgggggggggggggggggaagggggg fgggggggggagggggggggggggbbbggggggggggggggaaggggggg fgggggggggeaggggggggggggggdbbdggggggggggacgggggggg fggggggggggagggggggggggggggggbbbgggggggacggggggggg fggggggggggeaggggggggggggggggggdbbdgggacgggggggggg fgggggggggggagggggggggggggggggggggdbbccggggggggggg fgggggggggggccggggggggggggggggggggggabbbgggggggggg fggggggggggggagggggggggggggggggggggacggdbbdggggggg fggggggggggggcegggggggggggggggggggaeggggggbbbggggg fgggggggggggggaggggggggggggggggggaegggggggggdbbdgg fgggggggggggggaeggggggggggggggggaegggggggggggggdbbg fggggggggggggggagggggggggggggggaegggggggggggggggggbbbf fggggggggggggggaggggggggggggggaegggggggggggggggggg dbbd fggggggggggggggeaggggggggggggaeggggggggggggggggggg dbbf fgggggggggggggggagggggggggggaegggggggggggggggggggg fbbd fgggggggggggggggeagggggggggagggggggggggggggggggggg dbbd fggggggggggggggggaggggggggaggggggggggggggggggggggg fb fggggggggggggggggccgggggeagggggggggggggggggggggggg fgggggggggggggggggaggggeaggggggggggggggggggggggggg fgggggggggggggggggceggeagggggggggggggggggggggggggg fggggggggggggggggggageaggggggggggggggggggggggggggg fggggggggggggggggggacagggggggggggggggggggggggggggg fffffffffffffffffffaffffffffffffffffffffffffffff ``` <!-- end of image --> Eureka! Let's inspect this close up of area A <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0404ff b,#0806fdff c,#fc3739ff d,#b0affeff e,#ff7c7cff f,#ffc3c3ff g,#5c58fbff ``` ```image af ae aa cae faa cae eac aaf eac aaf eac faaf cae faa cae faa cae eac aaf eac aaf eac faaf cae faa cae faa cae eac aaf eac e bbgdd aaf ea bbbbbbggd eac caa dggbbbbbbbgddaaf caaf ddgbbbbbbbbgd caaf dggbbbbbbbgdd caaf dcbbbbbbbbggd caaf faa dggbbbbbbbgdd caaf cae ddgbbbbbbbggd caaf eac dggbbbbbbbgd caaf aaf ddgbbbbbbgd caaf eac dgbbbbbd caaf aaf dgbbbbgd fcacf eac dgbbbbg faac faaf dgbbbbgd faac cae dgbbbbgd faac faa gbbbbbd faac cae dgbbbbgd faac faa dgbbbbg faac cae dgbbbbgd faac eac dgbbbbgd faac aaf dbbbbbd faac eac dgbbbbgcac aaf dgbbbbgd eac eagbbbbgd faaf eaae dgbbbbgd cae eaae dbbbbbd faa eaae dgbbbbgd cae eaae dgbbbbgd faa eaae gbbbbgd aae eaae dgbbbbgd eac eaae dbbbbb aaf eaaf dgbb eac caaf d aaf caaf eac caaf faaf caaf cae caaf faa caaf cae caaf faa caaf aae caaf eac caaf aaf fcacf eac faac aaf faac eac faac faaf faac cae faac faa faac cae faac faa faac aae faac eac faac aaeaae ``` <!-- end of image --> Oh my, look at that! It's an intersection in area A! The final answer is: two intersections found.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fd0607ff b,#0705fdff c,#fc5255ff d,#9a9affff e,#ff9f9fff f,#f6d5deff g,#5151ffff ``` ```image f ae a af fa a ea a cc a cc a ae a af fa a ea a cc a cc a ae a af fa a ea a cc a cc a ae fa af fa a a ae ea af a faf cc faf a faf ce faf a fa ae ea fa ea af ea bbd fa ea fgbbbgd a ea dbbbbd ea ca fgbbbgd a ca dbbbbd cc ca fgbbbbd ca cbbbbd ca a fgbbbgd ca ae dbbbg aa fa gbbd aa af fbbg aa fa dbbd ac a gbbf ac ea dbbg ac a gbbac cc abbg a ac dbbd ce ae gbbf a ae dbbg ae ae gbbd fa ae fbbg af ae dbbd ea af gbbf a faf dbbg ea faf gbbd a faf fb cc faf a fa ce ea a ea aca fa ``` <!-- 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,#ef554eff b,#4b51f2ff c,#979df2ff d,#0505feff e,#fba7a5ff f,#fe0707ff g,#aed5aeff ``` ```image e c fa cddddddddddbbcc gggggggggggggg f d ccbbdddddddddbbcc gggggggggggggg aa cd ccbbdddddddddbbbcgggggggg f d ggcbbbddddgggg ef d gggggggggggggg fe dc gggggggggggggg f d gggggggggggggg fe bc gggggggggggggg f d gggggggggggggg aa bb gggggggggggggg f d gggggggggfgggg ef cd ggggggggfagggg fe d gggggggafggggg f cd ggggggefgggggg fe d ggggggfggggggg f d gggggfgggggggg aa dc ggggfagggggggg f d gggfaggggggggg ef bc ggafgggggggggg fe d gefggggggggggg f bb gfgggggggggggg fe d fggggggggggggg fgggggggggggbdgg faggggggggggggg aaggggggggggdggg fagggggggggggggg gfgggggggggcdggg af gggggggggggggg gafggggggggdgggg ef gggggggggggggg ggfggggggggdgggg f gggggggggggggg gggfggggggdcgggg f gggfagggggdggggg fe ggggfggggbbggggg fa ggggaagggdgggggg af gggggfggbbgggggg ef gggggafgdggggggg f ggggggfbdggggggg f gggggggdgggggggg fe ggggggcdaggggggg fa ggggggdgfggggggg af ggggggdgaagggggg ef gggggdcggfgggggg f gggggdgggafggggg f ggggbbggggfggggg fe ggggdggggggfgggg fa gggbbggggggfaggg af gggdggggggggfggg ef ggcdggggggggaagg f ggdggggggggggfgg f gcdggggggggggafg fe gdggggggggggggfg fa gdgggggggggggggf af dc fe ef d f ef bb aa f d f fe bb ef fa d f af cd ef ef d fe ef d f f dc aa fe d f fa dc ef af d faf bb ef d cb d cd d d dc d dc d bb d cb d cd d ``` <!-- end of image --> I'm going to scrutinize area A for any signs of an intersection. <!-- image --> ```palette Key,Color ,#fefefeff a,#fc383bff b,#544ef9ff c,#a8a7feff d,#0606feff e,#ff8383ff f,#fe0404ff g,#ffc8c8ff ``` ```image ffe cdb eff ddc afe cdd gffg ddc afa cdd gffg bdb efa cdd ffe bdb eff dd afe bdb gffg ddc afa cdb gffg ddc efa cdd ffe ddc eff cdd afe bdb gffg cdd afa bdb gffg dd efa bdb ffe ddc eff cdb afe ddc gffcdd afddc gadd bdb cddfe bdbff ddcafe bdb gffg ddc afa cdb gffg ddc efa cdd ffe ddc eff cdd afe bdb gffg cdd afa bdb gffg ddc efa bdb ffe ddc eff cdb afe ddc gffg cdd afa ddc gffg cdd efa bdb ffe cdd eff bdb af ddc gf ``` <!-- end of image --> An intersection is present within area A. Moving on to the next area. Eureka! Let's inspect this close up of area B <!-- image --> ```palette Key,Color ,#fefefeff a,#ff3232ff b,#5b5bffff c,#babaffff d,#0606ffff e,#ff7777ff f,#ff0303ff g,#ffc5c5ff ``` ```image cc ddddddbbbbbcccc dddddddddddddddddddbbb ccccbbbbbddddddddb ccccc g gfa gffe afa afa effg effg gffe gffe afa afa effg effg gffe gffe afa afa effg effg gffe gffe afa afa effg effg ffe fe a ``` <!-- end of image --> I don't observe any intersections inside area B. The final count is: one intersection.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff4c4cff b,#4f4fffff c,#9797feff d,#0505feff e,#ff9999ff f,#ff0707ff g,#ebd5e9ff ``` ```image e cg fe cddddddddddbbccg f d gccbbdddddddddbbccg aa gd gccbbdddddddddbbccg f dg gccbbdddd ef gd fg dc gf d fe bc f d aa bb f d f ef cd fa fg d af gf gd ef fe dg f f gd fg aa dc fe f d fa ef bc af fg d ef gf bb gf fe d fg f cd fe aa d fa f gd af ef dg ef fg d gf gf dc fg fe d fe f bc fa aa d af f bb ef ef d gf fcd fg gd fe gde fa dgf af d aa ef dc f gf d ef fg bc fg fe d gf fa bb fe af d f ef cd aa gf d f fg gd ef fe dg fg fa d gf af dc fe ef d f gf bb aa f d f fe bb ef fa d fg af cd gf ef d fe gf gd f f dg aa fg d f fe dc ef aa d faf bb gf d cb d cd d gd dg d dc d bb d cb d cd d ``` <!-- end of image -->

Hmm, I'm not sure what to expect from this image. Let's see if any lines cross. I need to zoom in on these areas to get a better look. <!-- image --> ```palette Key,Color ,#fefefeff a,#0706fdff b,#fd0706ff c,#b4b4ffff d,#f49f9aff e,#afd6afff f,#595cf2ff g,#ee4847ff ``` ```image c caac a aac ca aac a aac a aaf ac aaf a faf ff faf a faf ff faf a faf ca faa a faa ca caa ac caa a caa ac caa a caac ff caac a caac ff aac a a ca a ca ac a ac a ff a b ff bdbd a bd bb ca bd dbg a bg gb ca bg bg ac gb gbd a gb bb ac db dbd a db bb ff b dbd eeeeeeeeeeeeeeeeaeeeeeeeeb bb eeeeeeeeeeeeeeeffeeeeeeebd dbg eeeeeeeeeeeeeeeaeeeeeeebde gb eeeeeeeeeeeeeefaeeeeeebgee bg eeeeeeeeeeeeeeaeeeeeebgeee gbd eeeeeeeeeeeeeeaeeeeegbeeee bb eeeeeeeeeeeeeaeeeeegbeeeee dbd eeeeeeeeeeeeeaeeeegbeeeeee bb eeeeeeeeeeeeafeeedbeeeeeee dbg eeeeeeeeeeeeaeeeebeeeeeeee bb eeeeeeeeeeeffeeebeeeeeeeee dbg eeeeeeeeeeeaeeebdeeeeeeeee gb eeeeeeeeeeffeebdeeeeeeeeee bb eeeeeeeeeeaeebgeeeeeeeeeee gbd eeeeeeeeefaebgeeeeeeeeeeee bb eeeeeeeeeaebbeeeeeeeeeeeee dbd eeeeeeeeeagbeeeeeeeeeeeeee bb eeeeeeeeagbeeeeeeeeeeeeeee db eeeeeeeeabeeeeeeeeeeeeeeee eeeeeeeageeeeeeeeeeeeeeeee eeeeeeeaeeeeeeeeeeeeeeeeee eeeeeeafeeeeeeeeeeeeeeeeee eeeeebaeeeeeeeeeeeeeeeeeee eeeebfaeeeeeeeeeeeeeeeeeee eeebgaeeeeeeeeeeeeeeeeeeee eebbfaeeeeeeeeeeeeeeeeeeee egbeaeeeeeeeeeeeeeeeeeeeee gbeeaeeeeeeeeeeeeeeeeeeeee dbeeaeeeeeeeeeeeeeeeeeeeeee geeeaeeeeeeeeeeeeeeeeeeeeee eeafeeeeeeeeeeeeeeeeeeeeee eeaeeeeeeeeeeeeeeeeeeeeeee ff a ff a ca a ``` <!-- end of image --> This close-up of area A is like examining a piece of evidence. <!-- image --> ```palette Key,Color ,#fefefeff a,#0907fdff b,#fe0506ff c,#9e9dfeff d,#fd989aff e,#eed8e9ff f,#5950f6ff g,#f9464cff ``` ```image faf g eaae gb faf gbb aac dbbd caa dbbd aac dbbd caa dbbg aac ebbg caa ebbg faf ebbg eaae gbbe faf gbbe eaae gbbe faf dbbd aac dbbd caa dbbd aac dbbg caa ebbg aac ebbg caa ebbg faf gbbe eaae gbbe faf gbbe eaae gbbd faf dbbd aac dbbd caa dbbd aac ebbg caa ebbg aac ebbg caa gbbe faf gbbe eaaegbbe fafgbbd eaadbbd fafbbd aagbd caabg aagg caag aafe gaae gaaf gbaae dbfaf dbbaae dbbfaf ebbgaac ebbgcaa ebbg aac gbgecaa gbbe fac gbbe caa gbbe faf dbbd eaae dbbd faf dbbd eaae bbg faf gg aac caa aac caa fac ``` <!-- end of image --> Amazing! This area was hiding an intersection all along! The image features one single intersection point.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0706feff b,#ff0606ff c,#9898ffff d,#fd999bff e,#e2d6f2ff f,#5351fcff g,#fb4347ff ``` ```image e caac a eaac ea aac ae aac ea aac ac aac a faf fc faf a faf ff faf a faf ca faf a caa ea caa ae caa ea caae ac caae a eaae fc eaae a eaae ff eaac a ea ca a ea ae ea ac a fc a eb ff bdbd a bd bb ca bd dbg a bg gbe ea bg ebg ae gb gbd a gb bb ac db dbd a db bb ff eb dbd a be bb ff be ebg a bd gbe ca bg ebg a bg gbd ea gb bb ae gb dbd a db bb ac db dbg a eb bb ff b ebg a be gbe ff bd ebg a bd gbd ca bg bb a gb dbd eagb bb adb db ab ag a af ba bff bga ggca gb ae db ea db ae g a ac a ff a cf a ca ae ``` <!-- end of image -->

This image might have some surprises. Let's look for intersections carefully. These areas seem to enclose narrow spaces where lines might be close. <!-- image --> ```palette Key,Color ,#fefefeff a,#f65a56ff b,#0a0afdff c,#6467f8ff d,#fe0808ff e,#fbaeacff f,#bcbcffff g,#add4aeff ``` ```image e aa de d ed ad da de d ed ad de d ggggggggggggggggggg d ggggggggggggggggggg ad ggggggggggggggggggg da ggggggggggggggggggg de gggggggggggggggggga d gggggggggggggggggdd ed gggggggggggggggadeb ad ggggggggggggggddgbb da ggggggggggggadaggbg d gggggggggggddgggbgg d gggggggggedagggbcgg ed ggggggggddggggcbggg da gggggggdagggggbgggg de gggggddggggggbggggg d ggggdaggggggbbggggg ed ggadggggggggbgggggg ad gddggggggggbggggggg da adgggggggggbcggggggg de ddgggggggggcbgggggggg d ade gggggggggbggggggggg ed dd ggggggggbcggggggggg ad ede gggggggcbgggggggggg de dd gggggggbggggggggggg d ede b d dd bc ad eda fb da dd b de eda bf d ad cb ed da fb ad ade b da dd bc d ade fb d dd b ede bf cb b b bc fb b bf cb b bf bc fb b bf cb b bf bc fb b bc cb b bf bc fb bbbcf b cbbbbbcf bc fcbbbbbcf cb fcbbbbbcf b fcbbbbbcf bf fcbbbbbcf cc fcbbb ``` <!-- end of image --> Eureka! Let's inspect this close up of area A <!-- image --> ```palette Key,Color ,#fefefeff a,#ff4040ff b,#0808ffff c,#5959ffff d,#ff0505ff e,#ffc8c8ff f,#b0b0ffff g,#ff8585ff ``` ```image ed gdd eaddg gdddef eadda b gddde cb eadda cbb gdddg fbbf addae bbc gdddg cbb addae fbbf edddg bbc addae cbc edddg fbb gddde fbbf eaddg bbc gddde cbb eadda fbbf gddde bbc eadda cbc gdddg fbb eaddae fbbf gdddg bbc addae cbb edddg fbbf ddae bbc dg cbb e fbbf fbbf bbc cbb fbbf bbc cbb fbbf ``` <!-- end of image --> The evidence suggests that this is not an intersection point in area A. I've examined the entire image, and there are zero intersections present.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff5a5aff b,#0404ffff c,#7574ffff d,#ff0808ff e,#ffb1b1ff f,#c3c3ffff g,#3434ffff ``` ```image e aa de d ed ad da de d ed ad de d d ad da de a d dd ed adeb ad dd gg da ede fb de dd b d eda bc ed dd cb da eda b de dd bf d da gg ed ad fb ad da b da ade bc de dd cb d ade b ed dd bf ad ede gg de dd fb d ede b d dd bc ad eda cb da dd b de eda bf d ad gg ed da fb ad ade b da dd bc d ade fb d dd b ede bf cg fb bf gc fb b bf cb b bf gg fb b bc cb b bf gg fb b bc cb b bf gg fb bbbcf b fcgbbbbcf bc fcgbbbbcf cb fcgbbbbcf b fcbbbbgcf bf fcbbbbgcf gg fcbbb ``` <!-- end of image -->

Time to put on my detective hat and find those intersection points! I'm extremely confident. No intersections at all.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff4b4bff b,#0606ffff c,#ff0606ff d,#9c9cffff e,#ff9f9fff f,#4949ffff g,#ebdaeeff ``` ```image g fbg gbgb bg fb bf bf db bg b gb bd db db bf b bd bd b ff db gb ff bg bd ff b db gb b fb bd bd db bg b gb bd db fb bf gb bg bg b ff db gb ff bg bd bf b db db b fb bd bd db bg b a gb bd ccc fb ff ca ac bf gb ec ac bg bg c ac gb ff cg ec db db ca ec bf b ec ec bd bd gc ec b db cg gcg db b ca gcg ff bd ac gcg bd fb gc gcg b gb cg ce gb bg ce ce fb ff ac ce bd gb ec ce bg bg c ca gb bf ce ca db db aa ca bf b ec ca bg c cc b ce cc db aa ac ff ec ac bd c ac b cg ac ca ec ec ec gc ec cg ec ca gcg ac gcg gc gcg cg ce ce ce ac ce gc ce c ca ce ca aa ca ec ca c c ce aa ec c ce ``` <!-- end of image -->

Based on a first glance, I suspect there could be intersection regions here. Zero, Nada.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff4f4fff b,#0101ffff c,#ff0707ff d,#7575ffff e,#ff9e9eff f,#3d3dffff g,#f5d6dfff ``` ```image g cce ac ca ec ca gc ca cg cc ce ac ca ac ac ac ec ec gc ec cg gcg ce gcg ca ce ac ce ec ca gc ca c ca cg cc ce ac ca ac ac ac ec ec gc ec cg gcg ce gcg ca ce ac ce ec ca gc ca cg ca ce cc ca ac ac ac ec ac gc ec c ec cg gcg ce gcg ca ce ac ce ec c gc cg df dbbfdbf gfbbd dbf dbbbd dbf dbbfg dbf fbbf dbf gfbbd dbf dbbbd dbf dbbfg dbf gfbbd dbf dbbbd dbf bbfg dbf dbf dbf dbf dbf dbf dbf dbf dbf dbf dbf db ``` <!-- end of image -->

Time to put on my detective hat and find those intersection points! I wonder what's going on inside those areas? Perhaps intersections are hiding there. <!-- image --> ```palette Key,Color ,#fefefeff a,#fb504eff b,#4246f6ff c,#fe0606ff d,#a7a7feff e,#fba5a4ff f,#0606feff g,#aed5aeff ``` ```image e ec c ce ca ac ec c ce ca ac ec c ce ca ec c c ce aa ec c c ce aa ec c c ce ac ec c ce ca ac ec c ce ca ac ec c ce ca ac ec c ce ca ac c b c bfb ce ffd ca dffd ec dff ac bfb ecce bfb acc ffd gggggggggggggg ecce dffd gggggggggggggg cca dff gggggggggggggg ecce bff gggggggggggggg cca bfb gggggggggggggg acce ffd gggggggggggggg ecca dffd gggggggggggggg acce dff ggggggggggggecca bff ggggggggggaccg bfb gggggggeccaggg ffd gggggaccgggggg dffd gggccagggggggg dffd gggggggggggggg dbff gggggggggggggg dbffbd gggggggggggggg dfffbd gggggggggggggg dfffbd gggggggggggggg dfffbd gggggggggggggg dfffbd gggggggggggggbfffbd gggggggggbfffbd gggggbfffbgggg gggffbgggggggg ``` <!-- end of image --> I wonder what we'll find inside area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#ff5f60ff b,#4a4affff c,#ff0606ff d,#8c8cffff e,#ffbabaff f,#0404ffff g,#ccccffff ``` ```image eac acccc eaccccae accccae eaccccae eaccccae eacccca eaccccae ecccca cae gd gdbfff gdbffffffb gdbffffffbdg gdbffffffbdg ``` <!-- end of image --> No luck this time. Area A doesn't have an intersection. I did not find anything, there's no intersections

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff3f3fff b,#4040ffff c,#ff0505ff d,#a7a7ffff e,#ffbfbfff f,#0505ffff g,#ff7e7eff ``` ```image g ec c ce ca gc ec c ce ca gc ec c ce aa gc ec c cg aa gc c c cg aa gc c ce cg aa ec c ce cg ac ec c ce cg ac ec c ce ca gc ec c ce ca gc ec b c bfb ce ffd aa dffd gc dff ac bfb gccg bfb aca ffd gccg dffd cca dff gcce bfb ecca bfb gcce ffd ecca dffd acce dff eccg bff acce bfb eccg ffd acce dffd ccg dffd dbff dbffbd dbffbd dfffbd dfffbd dfffbd dfffbd dfffbd dfffbd ffbd ``` <!-- 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,#5055f5ff b,#fe0606ff c,#0607feff d,#fbadacff e,#add5aeff f,#f4534dff g,#abacfbff ``` ```image d dbb dbb dbb bb bbd bbd eeeeeeeeeeeeeeeee bbd eeeeeeeeeeeeeeeee bbd eeeeeeeeeeeeeeeee bbd eeeeeeeeeeeeeeeee bbd eeeeeeeeeeeeeeeee fbd acccceeeeeeeeeeeeee fbf gacccageeaceeeeeeeeeeeee fbf gacccag eeecgeeeeeeeeeeee fbf accccg eeeeceeeeeeeeeeefbf gacccag eeeeaceeeeeeeefbf gacccag eeeeeceeeeeefbfee accccg eeeeeeceeefbbeeee acccag eeeeeecafbbeeeeee g eeeeeefcbeeeeeeee eeeedbbeceeeeeeee eedbbeeecaeeeeeee efbeeeeeeceeeeeee ebeeeeeeeaceeeeee beeeeeeeeecaeeeee bfeeeeeeeeeeceeeee fbeeeeeeeeeeeaceeee db eeeeeeeeeeeecgeee b eeeeeeeeeeeeeceee bd eeeeeeeeeeeeeacee ff eeeeeeeeeeeeeecee db eeeeeeeeeeeeeeece b eeeeeeeeeeeeeeeaa bd eeeeeeeeeeeeeeeec bf gc db ca b c bd gc bf cg fb c b gc b cg bd c fb ac db cg b c bd aa ff c db gc b ca bd c bf gc db cg b c b gc bf cg fb c db ac b cg bd c fb aa db c b gc bd ca ff c db gc b cg bd c bf gc cg c ac cg c aa c c aa c ``` <!-- end of image --> Time to investigate area A up close. <!-- image --> ```palette Key,Color ,#fefefeff a,#3b36faff b,#fe0404ff c,#0404feff d,#ff9292ff e,#7878feff f,#f82f35ff g,#bebefeff ``` ```image ggeacc cccccca caeggccg ecc ace gccg eca cce gccg db aca dbbb cce dbbbfd gccg dbbbfd aca dbbbfd cce dbbbfd ecc dbbbfd aca dbbbfd gccfbbfd daccfd dfbbcce dfbbbdgccg dfbbbd eca dfbbbd cce fbbbd gccg dbbd eca dbbd cce bbd gccg fbf aca dbb cce bbd ecc bd aca f gccg ecc ace gccg eca ace gccg eca cce gccg aca cce ecc ac gc ``` <!-- end of image --> My investigation has led me to an intersection in area A! After careful examination, I conclude that there is one intersection.

<!-- image --> ```palette Key,Color ,#fefefeff a,#3b3bffff b,#fe0606ff c,#0404ffff d,#ffababff e,#7777ffff f,#ff5050ff g,#bdbdfeff ``` ```image d dbb dbb dbb bb bbd bbd bbd bbd bbd bbd fbd ecccc fbf gaccceg ec fbf gacccag cg fbf ecccce c fbf gaccceg aa fbf gacccag cg fbf ecccce c dbf accceg aadbb g dcb dbbgc dbb ce fb c b gc b ce bd c fb ec db cg b c bd ea ff cg db c b aa bd c bf gc db ae b c bd gc bf ce fb c b ec b cg bd c fb ea db cg b c bd aa ff c db gc b ae bd c bf gc db ce b c b ec bf cg fb c db ea b cg bd c fb aa db c b gc bd ae ff c db gc b ce bd c bf ec cg c ec cg c aa c gc aa c ``` <!-- end of image -->

I'm examining this image closely. My goal: find any and all intersections. I did not find anything, there's no intersections

<!-- image --> ```palette Key,Color ,#fefefeff a,#8585ffff b,#ff4f4fff c,#0505ffff d,#ffa5a5ff e,#ff0505ff f,#c2c2ffff g,#4242ffff ``` ```image a ac fc fc fc c cf cf cf ca ca cg cg gg gc gc ac f ac cc fc gc fc fcf fc ca c cg cf gc cf ac cf fcf ca cg ca cc cg gc cg fcf gc ca gc cg gc gc ac ac ac fcf fc cg fc cc c gc c fcf cf ca cf cg ca gc ca ac cg fcf cg ee cg cg dee cc gc deb gcgc beb fc bed eed ee dee deb beb bed eed ee ee dee deb beb bed eed eed beed deeb deeb beed eee deeb beed beed deee deeb beed beed deeb deeb beed be ``` <!-- 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,#3e41f2ff b,#fc0b0aff c,#e7695dff d,#0405feff e,#8d97e9ff f,#b1d7b1ff g,#98c796ff ``` ```image e adgggggggggggggggggggggggggggggggggggggggggggggf edefffffffffffffffffffffffffffffffffffffffffffg ffdaffffffffffffffffffffffffffffffffffffffffffg fffadfffffffffffffffffffffffffffffffffffffffffg ffffedefffffffffffffffffffffffffffffffffffffffg ffffffdaffffffffffffffffffffffffffffffffffffffg fffffffadfffffffffffffffffffffffffffffffffffffg ffffffffedefffffffffffffffffffffffffffffffffffg ffffffffffdaffffffffffffffffffffffffffffffffffg fffffffffffadfffffffffffffffffffffffffffffffffg ffffffffffffedefffffffffffffffffffffffffffffffg ffffffffffffffdaffffffffffffffffffffffffffffffg fffffffffffffffddfffffffffffffffffffffffffffffg ccccccggfffffffffedefffffffffffffffffffffffffffg fccccbbbbbbbbbbbbbbdabbbbccccccggffffffffffffffg fffffffffffffffffffddggccccccbbbbbbbcfffffffffg ffffffffffffffffffffedefffffffffffffbbffffffffg ffffffffffffffffffffffdafffffffffffffcbgffffffg fffffffffffffffffffffffddffffffffffffffbbfffffg ffffffffffffffffffffffffedgfffffffffffffcbgfffg ffffffffffffffffffffffffffdaffffffffffffffbbffg fffffffffffffffffffffffffffddffffffffffffffbbfg ffffffffffffffffffffffffffffadgfffffffffffffgbc ffffffffffffffffffffffffffffffdaffffffffffffffbb fffffffffffffffffffffffffffffffddfffffffffffffgfbc ffffffffffffffffffffffffffffffffadffffffffffffg bb ffffffffffffffffffffffffffffffffffdaffffffffffg cbc fffffffffffffffffffffffffffffffffffdefffffffffg bb ffffffffffffffffffffffffffffffffffffdfffffffffg cbf gggggggggggggggggggggggggggggggggggggdggggggggf bb ed cb ad bc da cb de bc d bb d fbc ed bb ad cbc aa bb de cbf d bb d cb ed bb ed cb aa bc de b de d d ed ad da de d d ed ad da de d d ed ed aa de de d d ed aa da de d d ed ad da de d ``` <!-- end of image --> I'm going to scrutinize area A for any signs of an intersection. <!-- image --> ```palette Key,Color ,#fefefeff a,#3934faff b,#fe0505ff c,#fea0a1ff d,#0404feff e,#babaffff f,#fd4f51ff g,#7675feff ``` ```image dde addg gddae eddde addg gddae eddde addg gdda eddde addg gdda eddde addg gdda eddde addg gdda eddde eaddg gdda eddde eaddg gdda eddde eaddg gdda ffffffcccccccc eddde bbbbbbbbbbbbbbbbbbbbbbbffffffffcccccaddg cccccffffffffbbbbbbbbbbbbbbbbbbbbbbbbaddabbbbbbbfffffffccccccccc cccccccccfffffffbfdddbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbf eaddg ccccccccffffffffbbbbbbbbbbbbc adda ccfbbf gddae cbbbc eaddg fbbf addg cbbbc gddae cbbbf eddde fbbbc addg cbbbc gddae fbbf eddde cbbbc addg fbbf gddae cbbbc eddde fbbf addg cbbb gddae fb eddde c addg gdda eddde addg gdda eddde addg gddg gdde gdde add ``` <!-- end of image --> Aha! I've found an intersection inside area A! The final count is: one intersection.

<!-- image --> ```palette Key,Color ,#fefefeff a,#4846fcff b,#fe0707ff c,#ff9999ff d,#0505feff e,#9e9effff f,#ff4c4cff g,#e9daefff ``` ```image e ad ede da ad ede da ad ede da ad ede da ad fffccccgg edg cccffffbbbbbbbbbbbbdabbbffffcccgg ddggccccfffbbbbbbc edg bb gda cbc dd bb edg fbg gda gbf dd fbg edg gbf gda bb dd cbc adg bb gde cbc de bb dg cbc gd bb ed fbg ad gbf da fbg de gbf dg bb gd cbc ed bb ad cbc da bb de cbc dg bb d fbg gd gbf ed fbg aa gbf da f de dg gd ed ad da de dg gd ed ad da de dg gd ed ad aa de dg d gd ed ad da de dg gd ed ad da de d ``` <!-- end of image -->

I'm examining this image closely. My goal: find any and all intersections. My final answer is: no intersections found.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0505ffff b,#ff0606ff c,#ffb8b8ff d,#a7a7ffff e,#ff7e7eff f,#4e4dffff g,#ff4243ff ``` ```image e gb bb bg be bc cb eb gb bb bg be bc cb eb gb bb bg be bc cb eb gb bb bg be bc cb eb gb bb bg be bbbbgec bc cgbbbbbec cb cebbbbbgc eb cegbbbbgc gb egbbbbge bb cgbbbbgbg cc ddfaaaa ddfaaaaafd ddfaaaaafd ddfaaaaafd ddfaaaaafd ddfaaaaafd faaafd daf aa fad aa aa daf aa fad daf aa dad aa fad daf aa fad af aa daf aa fad af ``` <!-- end of image -->

I'm optimistic that I'll find some intersections in this image. The image has some tight areas where segments are too close. I should investigate those closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#fc0c0bff b,#0304feff c,#b1d7b1ff d,#d9caefff e,#99c4a0ff f,#5655edff g,#ec7871ff ``` ```image d ag ad a ga ag a da ga ag a ga ag ad a ga ag a da aa ad a ga ag a da ga ag a ceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee daeccccccccccccccccccccccccccccccccc aaccccccccccccccccccccccccccccccccc aa aecccccccccccccccccccccccccccccccc daag eacccccccccccccccccccccccccccccccc gaad egaccccccccccccccccccccccccccccccc gaa ecagcccccccccccccccccccccccccccccc gaa eccacccccccccccccccccccccccccccccc aag ecceaccccccccbbccccccccccccccccccc aag ecccaaccccccbbebcccccccccccccccccc daad eccccagccccbfccebccccccccccccccccc gaad ecccccaccebeccccebcccccccccccccccc gaa ecccccgaebeccccccebeccccccccccccccgaa eccccccfbcccccccccebecccccccccccaag ecccccbbaecccccccccebeccccccceaagc eccccbbccaccccccccccebeccccgaagccc ecccbfcccgaccccccccccebecgaaeccccc ecebfcccccagccccccccccebaacccccccc eebecccccccacccccccccaagbecccccccc fbcccccccccgaccccccaagccebeccccccc fbcccccccccccaacceaagcccccebecccccc bbeccccccccccccagaaeccccccccebeccccc bf ecccccccccccccaccccccccccccebecccc bd ecccccccccccccccccccccccccccebeccc dbd eccccccccccccccccccccccccccccebecc fb ecccccccccccccccccccccccccccccebec fb eccccccccccccccccccccccccccccccebe bb ecccccccccccccccccccccccccccccccebd bf eccccccccccccccccccccccccccccccccebd bd ecccccccccccccccccccccccccccccccccdbd dbd eccccccccccccccccccccccccccccccccc bd fb ceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee bd fb bd bb bd bf bd bd bd dbd bd fb bd fb bd d bd bd bd bd bd bd bd bd bd bd bd bd b ``` <!-- end of image --> I wonder what we'll find inside area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#f9484eff b,#0100feff c,#fe0606ff d,#fe9a9bff e,#e7def5ff f,#2624fdff g,#8b87fbff ``` ```image e a cd cce acc cca dccd dcce aca eccd dccd acc cca gfe eccd efbbfe dcce efbffbfe aca gbbfeefbfe ecca gbbf efbfe dccd gbbg efbfe acce fbbg efbfe aca efbbg efbfe eccd efbfe efbfe dccegbbfe efbfe acabbf efbfe da efbbg efbfe dccc fbbad efbfe dccccd efbbgcce efbfe eaccccd efbfe aca efbfe eacccad gbbfe eccd efbfe dacccad gbbf dccd efbfe dacccae gbbg acce efbfe dccccae fbbg aca efbfedccccd efbbg eccd efbfcccd efbfe dcce eacbbfd gbbfe acc dacccafbfe gbbfe cca dacccae efbfe gbbg dccd dccccae efbfe bbg dcce edccccd efbfe bg aca eaccccd efbfe e eccd eacccad efbfe dccdacccad efbfe accccae efbfe acde efbfe efbfe efbfe efbfe efbfe efbfe efbfe efbfe efbfe efbf efb ef e ``` <!-- end of image --> Wow! I can see an intersection so clearly in area A! I can confirm there's two intersections in there.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fd3c3dff b,#0303ffff c,#fe0404ff d,#ffc4c4ff e,#d6d6ffff f,#544ef9ff g,#ff8484ff ``` ```image d aa cd c gc cg c dc aa cd c gc aa cd c gc cg c dc aa cd c gc cg c dc ac cg c dc aa cc cd dccd c dccd gc gcc cg aca c aca dc bb ccg aa bfebe dccd cd bf ebe gccd c ebe ebe gcc gcebe ebe aca fb ebe acg fbcd ebe dccg bf c ebe dccd bf gc ebe gccd ebe cg ebca ebe c acabe fb dc ccg ebe fb aa dccg ebe bb cgccd ebe bf c ebe ebe ebe ebe ebe fb ebe fb ebe bb ebe bf ebe ebe ebe ebe ebe fb ebe fb ebe bb ebe bf ebe be be ebe be fb be fb be e be be be be be be be be be be be be b ``` <!-- end of image -->

I'm analyzing this image to identify any points where lines intersect. These areas seem to enclose narrow spaces where lines might be close. <!-- image --> ```palette Key,Color ,#fefefeff a,#0909fcff b,#fb0b09ff c,#eb7c73ff d,#6168efff e,#fdd2d2ff f,#b7b7ffff g,#acd4adff ``` ```image f af a af a af fa a fa a fa a fa a dd a dd a dd a ad a d af fa a a af af a ad af da fa fa a a fa af a ad fa eb da a bcb fa da bc cb a a cb cb af dd eb eb ad a be eb da dd bc eb fa a cb eb a ggadggggggggggbg ebe a gggagggggggggbgg ebe ad gggadgggggggbcgg ebe ggggggggggggggaa ggggaggggggcbggg begggggggggggggdag ggggadgggggbgggg bcggggggggggggagg gggggaggggbggggg bcggggggggggaggg gggggagggbbggggg gbcggggggggadggg ggggggagcbgggggg ggbcggggggaagggg ggggggagbggggggg gggbcggggdaggggg gggggggacggggggg ggggbcgggagggggg ggggggbagggggggg gggggbcgaggggggg gggggcbdaggggggg ggggggbadggggggg gggggbggaggggggg ggggggaabggggggg ggggbcggdagggggg gggggdagbbgggggg gggbbggggagggggg gggggagggbbggggg ggcbgggggdaggggg ggggagggggbbgggg ggbgggggggaggggg gggadggggggbbggg gbcgggggggddgggg ggaaggggggggbbgg bbgggggggggagggg gdaggggggggggbbg ebggggggggggadggg gaggggggggggggbb be a aggggggggggggggbb bc ad adgggggggggggggggcb cb a adgggggggggggggggg cb eb af da cb b a fa cb bc af a cb cb a af cb eb af ad eb be fa da eb bc a fa eb cb fa a ebe eb a af ebe be fa ad ebe bc a da be cb da fa b b a a be daf bc f cb b be ``` <!-- end of image --> Let's take a closer look at area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0807feff b,#fe0405ff c,#ff7f7fff d,#a8a8ffff e,#ffc4c4ff f,#fb363aff g,#5651f9ff ``` ```image daa eb gag bb daa fbf aad cbbe daa ebbe aad bbc daa fbf aad cbbe daa ebbc aad bbf gag fbf aad cbbe gag ebbc aad fbf gag fbf aad cbbe gag ebbc daa fbf gagbb daabe eaag ffaa cbbgad ebbedaa ebbc aad fbf daa cbb aad ebbe daa ebbc aad fbf daa cbbe aad ebbe gag bbc aad fbf gag cbbe aad ebbe gag bbc aa fbf gag cbbe daa ebbc gag ``` <!-- end of image --> Oh my, look at that! It's an intersection in area A! Okay, on to the next area of interest. Here's a close-up of the area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#0706fdff b,#fd0607ff c,#fc999cff d,#9494feff e,#e8d6ecff f,#ff4848ff g,#4845fcff ``` ```image e g ga e daa be eaad bbc eaag fbbc gag fbbc gaae fbbc daae fbbc daad fbbc eaag fbbc gag fbbc gaae cbbc daae cbbc daad cbbc eaag cbbf gag cbbf gaae cbbfdaae cbbaad caag gaabf gaacbbf daae cbbf daad ebbf eaag ebbf aag ebbf gaae ebbfe daae ebbbe daad ebbbe eaad ebbbe aag efbbe gaae efbbe daae fbb daad fb eaad f aag gaa daae aad ``` <!-- end of image --> I observe an intersection inside area B. The image features two intersection points.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0303feff b,#ff0909ff c,#ff7272ff d,#8585ffff e,#ffc8c8ff f,#c6c5feff g,#3a38fdff ``` ```image f gd a af a af fa af fa a fa a dg a dg a gg a gd a gd a d ad fa a a af af fa ad af gg fa fa a a fa af a ad da eb gg a bcb da dg bc cb a a cb cb af dg eb eb ad a be eb gg gd bc eb da a cb eb a gd b eb af a be ebe ad gd bc be gg a cb be da af b be fa a be be af af bc be ad fa cb bc gg afb bc da fae bc fa ba bc a ebfa bad b a ggc be dg da bc bb a fa bb eb dg a bb b a ad bb be gg gg bb cb a da bb eb gd fa bb b a a cb bc gd af cb cb a ag cb eb ad da cb b a fa cb bc af a cb cb a af eb eb af ag eb b fa da eb bc a fa eb cb fa a eb eb a af ebe be da ag ebe bc a ga be cb dg fa b b a a be daf bc d cb b be ``` <!-- end of image -->

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

<!-- image --> ```palette Key,Color ,#fefefeff a,#5656ffff b,#ff0808ff c,#ffa0a0ff d,#0808ffff e,#a1a1ffff f,#ff5252ff g,#f1dbe8ff ``` ```image e e adg gdd gdd gddg ade dde dd dde ade ada dd ada ede edd dd edd ede gddg dd ddg eda dde dd ade eda ada ddg eda gda edd adg gdd gda ddg adg dde b gdd ade cb ade ada bc dd eda b ade edd ff ddgdd b edg cb bc b b ff bg b bf cb fb bg cb gb gb bf b b bc cb bf bg fb gb cb bf gb b bg cb bc bg bf gb fb bc cb b gb fb bg bg bc gb bf bc fb b cb ff gb b bg cb bc bc bf b fb ff cb b gb cb bg bc bc b bf ff fb b cb cb gb bc bg gb bc ff bf b fb cb cb bg gb gb bg bf bc b bf cb fb bg cb gb gb bc bg b bc fb bf bfb gb ``` <!-- end of image -->

This image looks interesting. I wonder if there are any intersections hidden in there? These spots are like clues. Let's see what they reveal about potential intersections. <!-- image --> ```palette Key,Color ,#fefefeff a,#f44a45ff b,#0708fcff c,#fd0605ff d,#6669f0ff e,#f19790ff f,#98c597ff g,#b1d6b1ff ``` ```image ggggggggggggggggf ggggggggggggggggf ggggggggggggggggf gggeggggggggggggf gggcegggggggggggf dd ggggcgggggggggggf dbbbddbg ggggcfggggggggggf dbbbd bb ggggfcggggggggggf dbbbd dbd gggggcggggggggggf dbbbd dbg gggggecgggggggggfgdbbbd bb ggggggcggggggdbbbbd gbd fffffffffffffffg ggggggaagdbbbbdgf dbg gggggggggggggggf gggggdbbbbdgggggf bb gggggggggggggggf gggbbbfaagggggggf gbd gggggggggggggggc ggggggggcgggggggf dbd ggggggggggggggaa ggggggggceggggggf bb ggggggggggggggcf gggggggggcggggggf gbd gggggggggggggcff gggggggggcfgggggf dbd ggggggggggggacgf gggggggggfcgggggf bb ggggggggggggcggf ggggggggggcgggggf gbb gggggggggggceggf ggggggggggecggggf dbdggggggggggecgggf gggggggggggcggggf bbgggggggggcggggf gggggggggggaagggf fbbggggggaaggggf ggggggggggggcgggf ggdbdggggcgggggf ggggggggggggaaggf ggggbbggcfgggggf gggggggggggggcggf gggggfbbcggggggf gggggggggggggcegf gggggggdbdgggggf ggggggggggggggcgf ggggggcegbbggggf ffffffffffffffcfg gggggecgggfbbggf c gggggcggggggdbdf c ggggcaggggggggbb ec gggfcggggggggggf c gggcfggggggggggf aa ggacgggggggggggf c ggcggggggggggggf ae gceggggggggggggf c ecgggggggggggggf ce cggggggggggggggf c caggggggggggggggf c cgggggggggggggggf ec c gggggggggggggggf c aa fggggggggggggggf ec c c ce aa ec c c ae ce c c ce c c aa c c ec ce c ec ec c c ce aa ec c c ae aa c c ce c c ec c c ec ce c ec ec c c aa aa c c c ae ac c c ce ce c ec c c ec aa c c ea c c aa aa c c ce ae ec c c cce c ``` <!-- end of image --> Let's see what secrets area A holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#f93439ff b,#0706fdff c,#fe0505ff d,#a7a6fdff e,#ff7474ff f,#ffb3b3ff g,#5951f6ff ``` ```image ff fcc ccf eca ccf eca ccf ece fcc ace fcc ace fcc ccf dd eca dggbbb ccf dggbbbbbbg eca dgbbbbbbbgd cagbbbbbbbgd dgbbbbbbggd dgbbbbbbbgd dbbbbgdd ace gdd fcc ace fcc ccf eca ccf eca ccf ece fcc ace fcc ace fcc ccf eca ccf eca ccf ece fcc ace fcc ace fcc ccf eca ccf eca ``` <!-- end of image --> Amazing! This area was hiding an intersection all along! Now, let's turn our attention to the next spot. Could this be where the intersection is hiding, in area B? <!-- image --> ```palette Key,Color ,#fefefeff a,#fe4142ff b,#0808feff c,#fe0606ff d,#b0b0feff e,#ff8787ff f,#ffc9c9ff g,#5a54f8ff ``` ```image e fc ac ecc cce aca fccf cce ecc fccf aca eccf cce aca fccf bd cce bbg ecc gbbbd fccf dgbbbd aca dbbbg ecc gbbbd fcce dgbbbd aca dbbbg fccf gbbbd cce dgbbbcc dbbbg agbbbd eccdgbbbd fcce dbbbg aca gbbbg eccf dgbbbd cce dbbbg eca gbbbg fccf dgbbb aca dbb ecc g fcce aca eccf cce aca fccf ace ecc fccf aca eccf cce aca ccf ce c f ``` <!-- end of image --> Area B contains an intersection. There are precisely two intersections present in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff4545ff b,#0505feff c,#ff0606ff d,#a7a7ffff e,#ff8b8bff f,#ffcdcdff g,#504cfaff ``` ```image f ce dg c dbbbggbd cf gbbbgd bb fc gbbbg dbg c gbbbg gbd ec dgbbbd bb c dgbbbd dbg ea dbbbbd gbd dbbbgd bb bbgdae dbg c c gbd aa ce bb c c dbg cf cf gbd ec fc bb c c dbg ce ec gbd fc c bb c ea dbg aa c gbd fc ae bb cf c dbbc ce gbd c ce bb cf ec bb fc c gbd c aa bb ec fc c cf ea aa c c ae ce c ec ce c c ce cf fc fc cf c aa ec c c cf ea ec c c ae ce c fc ce c c aa cf c fc cf c ec ec c c ce aa fc c c ae aa c c cf cf c ec cf c fc ce c fc ec c c aa aa fc c cf ae ec c c cf ce fc ec cf c fc aa c fc ea cf c aa aa c c ce ae ec c c cce fc ``` <!-- end of image -->

This image might have some surprises. Let's look for intersections carefully. These zones are intriguing. I bet there's something interesting happening within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0808ff b,#0708fdff c,#feb1b1ff d,#989ceeff e,#b0d5afff f,#575af7ff g,#f2635dff ``` ```image c ac a ac a ac ca a ca a ca a gg a gg a ag a ac a ac a a ca a ca a ga a gg a gg a ac a ac a ac ca a ca a ca a gg a gg a gg a ac a ac a d ac bb ca bb a fbd ca dbf a bb ca bbd a fbf gg dbb a bb gg fbd a dbf ag bb a bb ac fbd a dbf f aeeeeeeeeeeeeeeeeeeebbe fbbbf eaeeeeeeeeeeeeeeeebbeee fbbbf eaeeeeeeeeeeeeeefbfeeee fbbbd eeaeeeeeeeeeeedbbeeeeee fbbbd eeaeeeeeeeeeebbeeeeeeee fbbbd eegaeeeeeeebbdeeeeeeeee dfbbbd eeeaeeeeefbfeeeeeeeeeee dfbbbd eeegaggdbbeeeeeeeeeeeee dfbbbdeeeggbbaaaaaaaaaaaaaggccc dbbbbbbdeeeeeeeeeeeeeggggaaaaaaaaaaaaagggcc eeedfeeeeeeeeeeeeeeeeee ccgggaaaaaaa eeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeeeeeeeeee ``` <!-- end of image --> Let's zoom in on area A to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0607ff b,#0303feff c,#ffa7a7ff d,#b4b1fcff e,#3a2ff4ff f,#7272ffff g,#fa565aff ``` ```image aac db gag debb aac ebbbf gag fbbbf aac dbbbed gag debbed caa fbbbf gag fbbbf caa debbed gag debbbd caa fbbbf aac fbbbf caa debbed aac debbbd caa fbbbf aac dbbbe caaggcccdebbed aaaaaaebbbgaaaaagggggcccccc fd cccgebbbeaaaaaaaaaaaaaaaaaaaaaaaagggg bbbefd dbbbed ccccccgggggaaaaaaaaaaaa febbbbbefebbed cccccg dfebbbbbf dff ``` <!-- end of image --> There is an intersection point visible in this close-up of area A. There's only one, but is an intersection after all.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fe0606ff b,#0707feff c,#fe8889ff d,#aeacfcff e,#ffc8c8ff f,#5c5cffff g,#ff4949ff ``` ```image e ac a ae ea ae ea a ea a ca a cg a gg a gc a ac a ae ea ae ea a ca a cg a gg a gc a ac a ae a ae ea a ea a ca a cg a gg a gc a ac a ae ea d ae bb ea bbd a fbd ea dbf a bb ca bbd a fbf cg dbb a bb gg fbd a fbf gc dbb a bb ac fbd a dbf f ae bb fbbbf ea bbd fbbbf ae fbd fbbbf ea dbf fbbbd a bb dfbbbd ca bbd dfbbbd a fbf dfbbbd caccdbb dfbbbd ccbbaaaaaaaaaaaaggccee dbbbbfbd eeccggaaaaaaaaaaaaggccee df eeccgggaaaaaa ``` <!-- end of image -->

I'm analyzing this image to identify any points where lines intersect. I'd describe these as 'hotspots' for potential intersections. <!-- image --> ```palette Key,Color ,#fefefeff a,#f93e3bff b,#474bf5ff c,#e59184ff d,#999bfaff e,#fe0606ff f,#0405feff g,#afd5afff ``` ```image c ae ae ae ae ae aa ea ea ea ea ea ea ea ea ea ea ea ec ec ec ec ec ec ec ec ecggggggggggggggggggggggggggggggg gecgggggggggggggggggggggggggggggg d ggecggggggggggggggggggggggggggggg bffb gggecgggggggggggggggggggggggggggg dfffd ggggecggggggggggggggggggggggggggg bffb gggggecgggggggggggggggggggggggggg dfffd ggggggecggggggggggggggggggggggggg bffb gggggggecgggggggggggggggggggggggg dfffd ggggggggegggggggggggggggggggggggg bffbgggggggggeggggggggggggggggggggggg dfffbggggggegggggggggggggggggggggg gggbffbggggeegggggggggggggggggggg ggggggbfffbgceecggggggggggggggggg ggggggggggbfgggeeaggggggggggggggg ggggggggggggfdgggaeaggggggggggggg gggggggggggggfdggggceeggggggggggg ggggggggggggggfbgggggceecgggggggg gggggggggggggggfbgggggggeeagggggg ggggggggggggggggfbggggggggaeagggg gggggggggggggggggffgggggggggaeegg ggggggggggggggggggffggggggggggceec bf eec bf aea df cee df ceec df eec f aea fd aee fd cee fd eec fb ae fb ff bf bf bf df df df f fd fd fd fb fb ff bf bf bf df df df f f ``` <!-- end of image --> Let's zoom in on area A to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff3b3bff b,#5353ffff c,#ffbebeff d,#afafffff e,#ff0404ff f,#0707ffff g,#ff7373ff ``` ```image eec geec geec geec geec geec geec aeec aeec aeec aeec aeec aeec aeec aeec aeec aeec aeec aeec dd aeec fffbd aeec bfffffbdd aeec dbffffffbd aeeg dbfffffbdd aeeegc dbffffffbd caeeeac dbfffffbdd caeeeac dbfffffb cgeeeeg dbfffd geeeegc fffd caeeeac bffd caeeeac bffd cgeeeeg bffd geeeegc bffd caeeeac bffb caeeeac dffb cgeeeag dffb geeeeg dffb gaeeegc dffb caeeeac dffb cgeeeag dfff geeeeg fffd gaeeeg fffd caee ``` <!-- end of image --> The lines within area A do not intersect. After a thorough analysis, I conclude that there are no intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff4545ff b,#4545ffff c,#ff9d9dff d,#9090ffff e,#ff0707ff f,#0404ffff g,#e1d4f2ff ``` ```image c ae ae ae ae ae ee ea ea ea ea ea ea ea ea ea ea ea ea ea ec ec ec ec ec ec ec ec d ec bffbg ec dfffd ec gbffbg ec dfffd eg gbffbg eg dfffd eg gbffbg eg dfffd eg gbffbg eeg dfffd ceec gbfg eea gfg aea fd ceeg fd ceec fb eec fb aea fb cee bf ceec bf geec bf aea df aee df ceec gfg geec gfg aea fg aee fd ceeg fd geec fb ee fb ff bf bf bf df df gfg gfg fg fd fd fb fb ff bf bf bf df df gfg gfg f ``` <!-- end of image -->

I'm curious to see if this image contains any intersection points. These spots are like clues. Let's see what they reveal about potential intersections. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0605ff b,#0607fdff c,#f79a97ff d,#4a4ff2ff e,#9099ebff f,#add4adff g,#f44944ff ``` ```image c a ac a a ca a a ca ca a a cg cg a a gg gg a a ac gc a a ac ac ca a a ac ca a a a gg ca a a ac ca a a ac cg ca a a gg ca a a gc gg a a ac gc a a ac ac a a a a ca ca a a ca gg a a cg ffffffffffffagff a d ffffffffffffafff ffggffffffffffff dbebb fffffffffffacfff fffaffffffffffff bb ebbe fffffffffffaffff fffggfffffffffffebe dbd ffffffffffafffff ffffaffffffffffbb ebbfffffffffcafffff ffffagfffffffebd ebbeffffffaffffff fffffaffffffbbff ffbbdfffgaffffff fffffacffffbdfff ffffdbbfafffffff ffffffaffdbfffff ffffffebbeffffff ffffffafbbffffff fffffffafbbdffff ffffffdbefffffff ffffffacfffdbbff fffffbbaffffffff ffffffaffffffebbe fffebefcafffffff fffffacfffffffffbbd ffbbffffafffffff ffffcaffffffffff dbb ebdfffffcaffffff ffffafffffffffff ebbe dbffffffffaffffff fffgafffffffffff bbd bdfffffffffggfffff fffaffffffffffff dbb db ffffffffffafffff ffggffffffffffff ebbe bb ffffffffffggffff a bbd ebe fffffffffffaffff ac db bb gc a ebe a ac bb ac ca bd a a db ac ca bd a a a gg ca a a gc ca a a ac cg a a a gg ca a a gc gg a a ac gg a a aac a ``` <!-- end of image --> Let's take a closer look at area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd0708ff b,#0505feff c,#fe5c5cff d,#413cfaff e,#c3c3ffff f,#feb2b3ff g,#8480faff ``` ```image aaf cac aaf cac faa cac faa cac faa d aaf ebb faa gbbd aaf edbbg faa gbbbe aaf edbbd cac gbbbe aaf dbbd cac ebbbg aafdbbde cabbbg gbbbe edbbdc gbbbgaa edbbd cac gbbbg faa dbbde aac ebbbg faa gbbde aaf edbbg faa gbbbe aaf dbbd caa bbe aaf d cac aaf cac faaf cac faa cac ``` <!-- end of image --> An intersection is present within area A. Let's inspect the next region. Here's a close-up of the area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0404ff b,#0b08fbff c,#ff7b7bff d,#5c5cfeff e,#a8a8ffff f,#febebeff g,#fb3538ff ``` ```image faaf gac faa gac caa aaf cag faaf gag faaf gac d faa bbde gac dbbbbe caa dbbbbd aac ebbbbde cag edbbbbe aaf dbbbbd cag ebbbbbgf edbbbbe fabbbbbd gac ebbbbde caa edbbbbe aac edbbbbd cag ebbbbd aaf edbb cag ed faaf gag faaf gac faa aac cag aaf cag faaf gag ``` <!-- end of image --> The lines cross each other within area B, forming an intersection. There are precisely two intersections present in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0505ff b,#0707ffff c,#ff8585ff d,#5756feff e,#a7a7ffff f,#fec6c6ff g,#ff4242ff ``` ```image c a ac af fa fa af a fa ca a a cg cg a a gg gg a a ac gc a a af ac fa a a af ca fa a af gg fa a a ac ca a a af cg fa a a gg ca a a gc gg a a ac gc a a af af a fa af af fa ca a a fa cg a a cg gc a d a cg dbdbbe ac a bb ebbe fa gc ebe bbd af a bb dbb fa gc ebe ebbe a a bb bbd cg af bd dbb a a db ebbe afbd a bbd dbe ac dbb bba a ebbe ebe fa af bbd bb a fa dbb ebd ca a ebbe db a ca bbd bd cg a dbb db a gg ebbe bb gg a bbd ebe a ac db bb gc a ebe a af bb ac fa bd a a db af ca bd fa a af gg fa a a gc ca a a af cg fa a af gg ca a a gc cg a a ac gc a a aac fa ``` <!-- end of image -->

Time to put on my detective hat and find those intersection points! There are 1 regions I'd like to highlight in the image. <!-- image --> ```palette Key,Color ,#fefefeff a,#f55f5aff b,#0506feff c,#acd4adff d,#6b70f4ff e,#fd0808ff f,#bcbcfeff g,#ffb3b3ff ``` ```image g eg f e dbd eg b bf ge bd bf e b bf ge bf bf e fb bf aa bf bf e fb bf aa b bf e db bf eg b bf e bd bf eg b bf ge bf bf e fb bf ge bf bf e fb bf aa b b e db b aa b b e dd b eg b fb e bd fb eg b fb ge bf fb e fb fb cccaecccccccbccc fb cccceccccccdbccc fb ccccaacccccbcccc fb ccccceccccddcccc fb ccccceacccbccccc fb cccccceccbdccccc fb cccccceacbcccccc fb cccccccebdcccccc fb cccccccebccccccc fb cccccccbeccccccc fb ccccccdbeccccccc fb ccccccbcaecccccc db cccccdbccecccccc db cccccbcccaaccccc db ccccbdcccceccccc db ccccbccccceacccc db cccbdccccccecccc db cccbccccccceaccc db ccbccccccccceccc d fb eg b ge db e b ge bd e b aa bf e fb aa bf e fb eg b e db e b ge dd e b ge bd e b aa bf e fb ea b e eg e e ge e ge e aa e ea e ggg eg gggggaaaaaeeeeeeeeeeeeeeeeeeeeeeea eeeeeeeeeeeeaaaaaggggg ``` <!-- end of image --> I'm going to scrutinize area A for any signs of an intersection. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff4c4cff b,#0404feff c,#fd9c9dff d,#7b7bffff e,#fd0709ff f,#bdbdffff g,#3e32f2ff ``` ```image cee fbbf eec gbd cee fbb eec bbd cea dbb eec bbf aea dbg ee fbbf aea gbg cee fbbf aec gbd cee fbb eec gbd cee dbb eec bbf cea dbg eecbbf aegbg ebbf gbg fbbe gbgec dbbcee bbd eec dbg cee bbf eec dbg cea fbbf eec gbd aea fbb ee gbd aea dbb cee bbd aec dbg cee bbf eec dbg cee fbbf eec gbg cea ``` <!-- end of image --> Area A contains an intersection. The image features one single intersection point.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff4141ff b,#0505feff c,#ff8686ff d,#7171ffff e,#fe0405ff f,#bebeffff g,#ffc6c6ff ``` ```image g ec f e dbd eg b bd ge bd bf e b bf ce bf bf e fb bf ca bf bf e fb bf ac b bf e db bf ec b bf e bd bf eg b bf ge bf bf e fb bf ce bf bf e fb bf ca b bf e db b ac b b e dd b ec b fb e bd fb eg b fb ge bf fb e fb fb ce b fb e db fb ca b fb e dd fb ac b fb e bd fb ec b fb ebf fb eb fb be fb dbe fb b ce db dd e db b ca db bd e db b ac db bf e db fb eg db bf e d fb eg b ge db e b ce bd e b ca bf e fb ac bf e fb eg b e db eg b ge dd e b ca bd e b aa bf e fb ac b e eg e eg ge e ca e aa e ac e gggg eg ggggccccaaaaeeeeeeeeeeeeeeeeeeeeeaa geeeeeeeeeeeaaaaccccgggg ``` <!-- 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,#5a5bf4ff b,#fe0706ff c,#f44f4aff d,#0808fdff e,#b3b3ffff f,#f39e98ff g,#add4adff ``` ```image eee addddddddddddddddddddaaaaeeee eeeeaaaadddddddddd de d aa d ad d ed de d da d aa d ed de d de d ggggggdagggggggggggggggg gggggggdgggggggggggggggg b gggggggadggggggggggggggg fbfbbfggggggggdggggggggggggggg fb bbcgggggggdgggggggggggggg cb gcbbfggggdgggggggggggggg cb gggfbbcgggdggggggggggggg bb ggggggcbbgdagggggggggggg bc ggggggggfbbdgggggggggggg bf gggggggggggadcgggggggggg bf ggggggggggggdcbbgggggggg b ggggggggggggadgfbbcggggg fb gggggggggggggdggggcbbggg cb ggggggggggggggdgggggcbbf cb ggggggggggggggdagggggggbbc bb gggggggggggggggdgggggggg cbb bc gggggggggggggggaaggggggg fbbf bc ggggggggggggggggdggggggg cbc bf ggggggggggggggggadgggggg fbbf b d bbc fb ed cbb fb de f cb d bb da bc d bc aa bf d bf ed fb de fb d cb de bb d bc aa bc d bf ad d ed de d da d aa d ed de d de d aa d ad d ed de d da d aa d ``` <!-- end of image --> Let's zoom in on area A to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#5d59fbff b,#fe0405ff c,#fb3f43ff d,#0807fdff e,#b4b2fdff f,#ffc5c5ff g,#fc7e81ff ``` ```image ada edde ada dde add dda edd bgf ada bbbcf edde fcbbbbg ada fgbbbbcf dde gcbbbcg add fcbbbbgf dde gbbbbcf edd fcbbbbg dda fgbbbbgedd gcbbbdda fcbbddgf gaddbcf ddcbbcg addgbbbbgf dda gcbbbcf edd fcbbbbg ada gbbbbcf edde fcbbbcg ada fgbbbbgf dde gcbbbcf add fcbbb dde fgb edd dda edd ada edde ada dde ``` <!-- end of image --> I can confirm that an intersection exists in area A. The final count is: one intersection.

<!-- image --> ```palette Key,Color ,#fefefeff a,#4441fcff b,#fe0808ff c,#fe5a5bff d,#0504feff e,#c9c9ffff f,#ffb2b2ff g,#8b8bffff ``` ```image geee aaddddddddddddddddddaaaggggeee eeeggggaaaddddddddd dg d aa d gd d ed de d ag d aa d gd de ed dg d aa d b gd fbfbbf d fb bbc ed cb cbbf de cb fbbc d bb cbb ag bc fbbd bc adc bf dcbbf fbf gd fbbc fb de cbb cb ed fbbf cb dg bbc bb d cbb bc aa fbbf bc d bbc bf gd cbbf fbf d fbbc fb ed cbb cb de f cb d bb ag bc d bc aa bf d bf gd fb de cb ed cb dg bb d bb aa bc d bf gd d ed de d ag d aa d gd de ed dg d aa d gd d ed de d ag d aa d ``` <!-- end of image -->

I have a feeling there might be some intersections in this image. It's crucial to examine these regions more closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#0808fdff b,#fc0d0cff c,#575feaff d,#ef7b73ff e,#b7b7feff f,#96c698ff g,#b1d6b0ff ``` ```image fgggggggggggggggggf fgggggggggggggggggf fgggggggggggggggggf fggggggggggggggcggf fggggggggggggggaggf fgggggggggggggacggf fggggggggggggfagggf fggggggggggggafgggf fgggggggggggcaggggf fgggggggggggagggggf bbbbbdddg fggggggggggcagggggf bd ddddbbbbbbbbbbbbbdddd fggggggggggaggggggf a b gdddbbbbbbbbbbbbbbacddfgggf ea b fgggggggfdadbbbbggf a b fggggggggacgggggggf ea b fggggggggaggggggggf a db fgggggggafggggggggf ea b fggggggfagggggggggf a db fggggggaggggggggggf ea b fgggggcaggggggggggf a db fgggggagggggggggggf ea b fggggccgggggggggggf ae dd fggggaggggggggggggf ea b fgggacggggggggggggf ae bd fgggagggggggggggggf ea b fggafgggggggggggggf ae bd gffaffffffffffffffg a b a ae bd ea a b a ae bg cc a b a ae b ac fagggggggggggdbf a gacggggggggggbgf ae ggagggggggggdbgf ea ggacggggggggbggf a gggagggggggdbggf ea gggacggggggbgggf a ggggagggggdbgggf cc ggggacggggbggggf a gggggagggbdggggf ac gggggacggbgggggf a ggggggagbdgggggf ae ggggggacbggggggf ea gggggggadggggggf ae gggggggacggggggf ea ggggggbdaggggggf a gggggfbgccgggggf ca gggggbfggagggggf a ggggdbgggccggggf cc ggggbgggggaggggf a gggdbgggggccgggf ae gggbgggggggagggf a ggdbgggggggccggf ae ggbgggggggggaggf ea gdbgggggggggcagf a gbgggggggggggagf ca bdgggggggggggcaf a b a cc bd ca a b a ac bd ca a b a ae bg ea ea b a a b ea ea gb a a b ea cc db a a b ea ac db a a b ea ae db a ea b ea a dd a ea b ea a bd ae cc d ea a ae ac ea a aae a ``` <!-- end of image --> Let's get to the bottom of what's happening inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0605feff b,#fe0607ff c,#9393feff d,#fc5053ff e,#e7d4ecff f,#4d49fbff g,#fc9b9dff ``` ```image caf dbd aac gbbe caf dbd aac gbb caa bbg aac gbb caa bbg aac gbb caa bbg aac gbb caa ebbg aac dbd caa ebbg aac dbd caa ebbe aac dbd caa ebbe aac dbd caa gbbe fac dbd caa gbb fac bbg caa gbb facbbg caabb fafg gaae ebaaf dbdaae ebbgfaf dbd eaae ebbe faf dbd eaae ebbe faf dbd eaae gbbe faf dbd eaae gbb faf bbg eaae gbb faf bbg eaae gbb faf bbg eaae gbb faf bbg eaae dbd faf ebbg eaae dbd faf ebbe eaae dbd faf ebbe eaac dbd caf ``` <!-- end of image --> Amazing! This area was hiding an intersection all along! Hmm, interesting. Let's check out another area. Here's a close-up of the area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#0606feff b,#fc0508ff c,#8b8bffff d,#fe4f4fff e,#cbcbffff f,#4740f8ff g,#feababff ``` ```image c caa aac caa aac caf eaae faf eaae faf caa aac caa aac caf eaae faf bdddddgggggg eaae bbbbbbbbbbbbbbbbbbddfafgggggg gggggdddddbbbbbbbbbbaabbbbbbbbbd gggaafdddddbbbbd caa aac caf eaae faf eaae faf eaae fac caa aac caa aac faf eaae faf eaae fac caa aac caa aac caf eaae ``` <!-- end of image --> An intersection is present within area B. The final answer is: two intersections found.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0505feff b,#ff0808ff c,#8585feff d,#ff6060ff e,#c8c8ffff f,#413efcff g,#feb7b8ff ``` ```image c a ac ea ae ea a bbbbdddggg cf bg ggdddbbbbbbbbbbbbbdddgg a a b gggdddbbbbbbbbbbbbdffggg ca bg ggaddbbb a gb ac ea b ea a gb ae ea b ea a gb a ea b ca ae db a ea b ff ae dd a ea b ac ae dd a ea b ae ae bd ea ea b a ae bg ca ea b a ae bg ff a gb a ae bg fc a gb a ac b ae a gb ea ac b ae a db ca ac b a a dd cf ac b a a dd fc fc b a a bd ac fcb ea ag ae ac ea bga a gb fc cf bg a a gb ff ff b a a gb ff ac b a ea db ff ae b a ea dd cf a b a ca dd cf a b a ff bd cf a b a ac bg cf a b a ae bg ca ea gb a a bg ca ca gb a a b ca ff gb a a b ea fc db a a b ea ae dd a ea b ea ae dd ae ca b ea a bd ae cf g ea a ae fc ea a aac ea ``` <!-- end of image -->

I have an image in front of me. I need to determine if there are any intersection segments. I'm going to focus my attention on these specific areas. <!-- image --> ```palette Key,Color ,#fefefeff a,#f2554fff b,#0909feff c,#6369f2ff d,#f5a4a0ff e,#fd0807ff f,#b6b6ffff g,#aed5aeff ``` ```image c cb cbe c gggggggggggggggggcbae cb ggggggggggggggggcbgeg bb ggggggggggggggggbgeag bc gggggggggggggggbggegg bf ggggggggggggggbggedgg b gggggggggggggbggdeggg fb ggggggggggggbgggegggg fb gggggggggggbgggaegggg cb ggggggggggbggggeggggg bc gggggggggbggggaaggggg bf ggggggggbcggggegggggg bf gggggggbcggggeagggggg b ggggggbcgggggeggggggg fb gggggbcgggggegggggggg cb ggggbcgggggdegggggggg bb gggbcggggggeggggggggg bc ggbcggggggaeggggggggg bf gbcgggggggegggggggggg b bbgggggggeagggggggggg fb bbggggggggeggggggggggg fb bbggggggggedggggggggggg cb bb gggggggdegggggggggggg bc cb gggggggeggggggggggggg bf cb ggggggaeggggggggggggg bf cb ggggggegggggggggggggg b cb gggggaagggggggggggggg fb cb gggggeggggggggggggggg cb cb ggggeaggggggggggggggg bb fb ggggegggggggggggggggg bc fb gggeggggggggggggggggg bf fb ggdeggggggggggggggggg b fb ggegggggggggggggggggg fb fb gaegggggggggggggggggg fb b geggggggggggggggggggg cb b eaggggggggggggggggggg bc b egggggggggggggggggggg e bf bf ed e bf bf de e b bf e de fb bf de ae cb bf e ae bb bf aa ea bbc e ea f ed ed e ed e e de e e de aa de e ae ea ea e ea ed ed de ed e e de e e de aa de e ae ed ee e ea e ed de ed e e aa e e de ea de e ae ed ae de ea e ea de ed e e aa e e deed de ``` <!-- end of image --> I'm now examining the contents of area A in detail. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff4141ff b,#0707feff c,#b1b1ffff d,#fec6c6ff e,#ff0505ff f,#fe8383ff g,#5553fcff ``` ```image cbbg cbbge cbbgfe cbbgdee cbbg aea cbbg deed cbbg aef cbbg fee cbbg eef cbbg fea cbbg deed bbg aea bbb deed bbb aea bbb dee bbb eef gbb fee gbbc eef gbbc fea gbbc deed gbbc aea gbbc deed gbbc aef gbbc fee gbbc eef gbbc fea gbbc deed cbbc aea cbbc deed cbbg aea cbbg dee cbbg eef cbbg fee cbbg eef cbbg fea cbbg deed cbbg aea cbbg deed bbg aef bg fee g eef fea deed aea deed aea dee eef fee eef fea deed aea deed aef fee eef fea deed aea deed aea dee eef fee eef fea deed aea deed aef ee ``` <!-- end of image --> There is no intersection present within area A. My analysis shows there's absolutely no intersections in the image

<!-- image --> ```palette Key,Color ,#fefefeff a,#fe5252ff b,#0404ffff c,#8585ffff d,#ffacacff e,#ff0707ff f,#c7c7ffff g,#3b3bffff ``` ```image c cb cbe c cbaa cb fb e gg fb aa bc fb e bf fb ed b fb de fb b e cb bf de gb bf e bg bf aa bc bf e bf bf ed b bc e fb bc ed cb bc de gg bc e bc bg aa bf bg e b bg ea fb bg e cb gg ed gb gb de bg gb e bc gb de bf gb e b cb aa fb cb e cb cb ed gg cb e bc fb ed bf fb de b fb e fb fb aa cb fb e gb b ea bg bf e ed bc bf ed e bf bf de de b bf e de fb bf de ae cb bc e ae gg bc aa ea bbc e ea c ed ed e ed ed e de e e de aa de e ae ea ea e ea ed ed de ed e e de e e de aa de e ae ed ee e ea ed ed de ed e e aa e e de ea de e ae ed ae de ea e ea de ed e ed aa e e deed de ``` <!-- end of image -->

This image looks interesting. I wonder if there are any intersections hidden in there? I'm extremely confident. No intersections at all.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff4343ff b,#0505ffff c,#a3a3ffff d,#ff0505ff e,#ff8e8eff f,#4c4cffff g,#f1d3e1ff ``` ```image e ad ed gdg de da ad ed gdg de da dd ad edg gde da dd ad ed gdg de da ad ed gdg de da dd ad edg gde ddg gdd eda ade ade bg ddg b gdd cb eda fb eda bf ade bc ddg bg gdd b eda cb eda fb ade bf ddg bc gdd bg gdd gb eda cb ade fb ddg bf gddg bc gdd b eda gb a cb fb bf bc b gb cb ff bf bc b cb c fb cbbbf ff cfbbfc bc gfbbbc bg cbbbc b cbbbfg cb cfbbfc fb gfbbbc bf fbbbc bc cbbbf bg cbbbfg b gfbbfc cbbc ``` <!-- end of image -->

I'm optimistic that I'll find some intersections in this image. I've noticed 1 areas of interest. These could be potential intersection zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#4145edff b,#fc0c0bff c,#e77167ff d,#0506fdff e,#b1d7b1ff f,#8896e2ff g,#97c895ff ``` ```image c bb cbe bb bb cbc bb cbe eggggggggggggggggggggggggggggggggggggggggge ebc geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg bb geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg cbc geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg bb geeeeeeeeeeeeeeeeeeeeeeeefdeeeeeeeeeeeeeeeg bb geeeeeeeeeeeeeeeeeeeeeeeaddfeeeeeeeeeeeeeeg ebc c geeeeeeeeeeeeeeeeeeeeeeadeedeeeeeeeeeeeeeeg bb cbbc geeeeeeeeeeeeeeeeeeeeeddeeeadeeeeeeeeeeeeeg cbc cbbc geeeeeeeeeeeeeeeeeeeedaeeeeedfeeeeeeeeeeeeg bb bbbegeeeeeeeeeeeeeeeeeeedfeeeeeeedeeeeeeeeeeeebb ebbbeeeeeeeeeeeeeeeefdfeeeeeeeeadeeeeeeeeecbc gcbbceeeeeeeeeeeefdeeeeeeeeeeedfeeeeeeebbeg geeecbbceeeeeeeeadeeeeeeeeeeeeedeeeeecbceeg geeeeeebbbgeeeeddeeeeeeeeeeeeeeaaeegbbeeeeg geeeeeeeecbbbedaeeeeeeeeeeeeeeeedebbeeeeeeg geeeeeeeeeeecdaceeeeeeeeeeeeeeeecdceeeeeeeg geeeeeeeeeeedfebbbceeeeeeeeeeeebbaaeeeeeeeg geeeeeeeeefdeeeeegbbbeeeeeeeebbceedeeeeeeeg geeeeeeeeadeeeeeeeeecbbceeegbbeeeefdeeeeeeg geeeeeeeddeeeeeeeeeeeeecbbbbeeeeeeedaeeeeeg geeeeeeddeeeeeeeeeeeeeeeeeceeeeeeeeedeeeeeg geeeeedaeeeeeeeeeeeeeeeeeeeeeeeeeeeefdeeeeg geeeedfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedfeeeg geefdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedeeeg geadeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefdeeg gadeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedfeg ddeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedeg daeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeadg dfgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedf d geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeed fd geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaa ad d dd d da aa df d df d da d fd df d fd df d fd df d aa d d aa d d aa d fd df d fd df d fd df d aa d d aa d d aa d ``` <!-- end of image --> Let's put area A under the microscope. <!-- image --> ```palette Key,Color ,#fefefeff a,#413bf8ff b,#fe0707ff c,#f95359ff d,#0505feff e,#fea9aaff f,#8181ffff g,#c6c6ffff ``` ```image gddg fddda fddaddf addf fddg addf ada gaddg gddf gdddg fdd gdda ada fdda gddg fddf fdd addf adf c gaddg gddg c bbce gdddg fdd ebb cbbbbce gddag ddf cbbb ecbbbbce fdda gddg cbbbe ecbbbbbe fddf ada ebbbc ecbbbbce addf ddf cbbbe ecbbbbce addg gddg ebbbc ebbbbbce gdddg ada ecbbce ecbbbbce gddag ddf cbbbe ecbbbbce fdda fddgebbbc ecbbbadda adabbbe caddabc eddcc addcbbbbce ecbcdd gaddg ecbbbbce cbbbeada gdddg ebbbbbce ebbbc gddg gdda ecbbbbbe cbbbe fdd fdda ecbbbbce ebbbc adf fddf ecbbbbce ebbbc gddg addf ebbbbbc cbbbe fdd gaddg ecbbbbcbbbc ddf gdddg ecbbbbe gddg gddag ee ada fdda ddf fddf gddg addf ada addg ddf gdddg fddg gddag ada fdda gddf fdda fdd addf ada addf gddg gaddg fdd dddg ada da gddg a fdd dd gd f ``` <!-- end of image --> I am surprised, so clear, an intersection has appeared in area A. I've identified a total of two intersection points.

<!-- image --> ```palette Key,Color ,#fefefeff a,#423efaff b,#ff0707ff c,#fe5656ff d,#0606ffff e,#fdadaeff f,#8181ffff g,#c4c4ffff ``` ```image e bb cbe ebc bb ebc bb cbe ebc bb cbe bb gd cbe fddf ebc c ad d bb ebbc dd fd cbe cbbe da dg bb cbbe df d bb ebbc gdg fd ebc ebbc fd dg bb cbbe ad d cbe bbbe dd aa ebc ebbc da dgbb cdac edc gdg cbbe bbaa gd ebbb cbe d fd ebbc ebc gd ad cbbbb df da e d df gd dg df gdg d fd fd ad dg dd d da fd df dg gdg d fd aa ad dg dd gd da aa df d dg gd df d gd df d fd df d fd dg d aa dg d aa d gd af d gd df d fd df d fd dg d aa dg d aa d gd aa d ``` <!-- end of image -->

I'm approaching this image with caution. Intersections might be tricky to spot. I have a hunch that these areas might contain the intersections we're looking for. <!-- image --> ```palette Key,Color ,#fefefeff a,#3b3ff5ff b,#fe0c0bff c,#f6726eff d,#0505feff e,#888cf6ff f,#eecedeff g,#acd3acff ``` ```image f bb bc b fb cb bc bf b fb cb bc a bf dde fb fdde cb eddf bc edd bf ada b dde fb fdde cb eddf bc edd bf ada fb dde cb fdde bb eddf bf edd b ada fb dde cb fdde bc eddf bgggggggggggggadd gbgggggggggggdag gcbgggggggggdggg ggbbgggggggdeggg gggbcgggggaagggg ggggbggggedggggg gggggbgggdgggggg gggggcbgdggggggg ggggggbdaggggggg ggggggadgggggggg gggggedgbggggggg gggggdggcbgggggg ggggdegggbbggggg gggdagggggbcgggg ggadgggggggbgggg ggdgggggggggbggg gdggggggggggcbgg degggggggggggcbg aaggggggggggggggbc ed bb fd cbf d fbc de bb aa cbf ed fbc d bb df cb de fbc ad bb ed cb d fbc df bb da bb ed fbf fd bb d bb de cbf aa bc ed bb fd cbf d bc de bb aa cbf ed fbc d bb df cbf de fbc bb cb fb ``` <!-- end of image --> I'm determined to find out if an intersection exists in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#3e3dfdff b,#fe0708ff c,#feb0b1ff d,#0504fdff e,#8484feff f,#ccccffff g,#fd5759ff ``` ```image bbg cbbc gbbc e gbb fedd bbg fddda cbbg adaf cbbc addf gbb eddf gbg fdde bbg fdda cbbc ada cbbc eddf gbb eddf bbg fdde cbbg dda cbbc ada gbb eddf gbbeddf bbdde cdda addbc eddgbb fdde bbg fdde bbg ada cbbc addf gbbc eddf gbb fdde bbg fdda cbbc ada cbbc eddf gbb eddf gbg fdde bbg dda cbbc ada gbbc eddf gbbg eddf cbb fdde cb ``` <!-- end of image --> Success! This area contains an intersection point! I've found a single intersection point in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#4747ffff b,#ff0505ff c,#ff8c8cff d,#0605feff e,#9191ffff f,#ecd4e7ff g,#ff4040ff ``` ```image c gg bc b fb cb bg bf b cb gg bc a bf dde fb fdde cb eddf bg edd bf ada b dde fb fdde gb eddf bc edd bf ada fb dda cb fdde gg eddf bc edd b ada fb dda gb fdde bc eddf bf eddf b fda cb df gg de bc aa bf ed fb d cb df bde adf ed b d cb df gg da bc ad bf fd fb d cb de cbf da bg ed bb fd cbf df fbc de bb aa cbf ed fbc d bb df gb de fbc ad bg ed gb d fbc df bg da gb ad cbc fd bg d gb de cbf da bg ed gb fd cbf df bg de bb aa cbf ed fbc fd bb df cbf de fbc bb gb fb ``` <!-- end of image -->

I have a feeling there might be some intersections in this image. There are 1 areas where the lines seem to converge. We should take a closer look at area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#4748f6ff b,#fd0808ff c,#f4605dff d,#969bf4ff e,#0606feff f,#ffb8b8ff g,#add4adff ``` ```image f bc b cb b fb bf b cc b fb bf b cc b fb bf b aea bc de ee b e ae cb ed de b ea ed fb de ea bf e ae b e de cbggggggggggggged ed gbggggggggggggae ea gcbgggggggggggeg ee ggbggggggggggegg de gggbggggggggedgg ed gggbcggggggaeggg ea ggggbgggggdegggg ee ggggcbggggeggggg ae gggggbgggedggggg ded ggggggbgeagggggg ea ggggggbaeggggggg ee gggggggegggggggg ae ggggggecbggggggg de gggggeagbggggggg ed ggggaegggbgggggg ee ggggeggggbcggggg ae gggeggggggbggggg de ggedggggggccgggg ed gaeggggggggbgggg ea degggggggggcbggg ae egggggggggggbggg de edggggggggggggbgg ed aagggggggggggggbcg ea de ggggggggggggggbg ee e cb ae e bf ded ea fb ea ae bc e e b e cb ed b ae fb de bf e b ed cc aa b de fbf e fbbc e cbb fbbc cbb fbbf bbc cbbf fbbc cbbf fbbc cbb fbbf bbc cbbf fbbc cbbf fbbc cb ``` <!-- end of image --> My goal is to determine if there's an intersection inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#403efcff b,#fe0809ff c,#fd5a5bff d,#807dfbff e,#0505feff f,#ffb2b2ff g,#c4c4ffff ``` ```image bbc fbbf cbc g bbf a cbb ae bbc dee fbb geed cbc eea fbbf aee cbb deeg bbf geed fbb eea cbc aea fbbf deeg cbc geeg bbf geed fbb aea bbc dee fbbf deeg cbc geed bbf aea cbb aee bbdeeg fbeed eea aeebf deecbb geeg bbf geed fbb aea cbc dee fbbf geeg cbc geed bbf aea fbb aee bbc deeg fbbf geed cbc eea bbf aea cbb deeg bbc geeg fbb geed cbc aea fbbf deeg cbb eeg bbf ed fbb a bbc fbbf ``` <!-- end of image --> Area A contains an intersection. My investigation reveals that there is exactly one intersection in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#3636ffff b,#ff0808ff c,#fd5c5dff d,#7d7afcff e,#0303ffff f,#ffb7b7ff g,#c2c2ffff ``` ```image f bc b cb b fb bf b cc b fb bf b cc b fb bf b aed bc ge ea b e ae cb eg geg b aa ed fb de ea bf e ae b eg de cc ed ged b de ea fb ge ae bf e de b ed geg cc aa ea b ge ee fb e de bf eg geg b aa ed bde ee e ae ecb geg ed b ed de fb ea ge bf ae e b deg ed cc ed aa b ea ge fb ae e bf de eg b geg aa bc ea de b ae e cb de eg bf geg ed fb ed de bc e ge b e cb ed b aa fb ge bf e b eg cc aa b de fbf e fbbc eg cbb fbbc cbb fbbf bbc cbbf fbbc cbbf fbbc cbb fbbf bbc cbbf fbbc cbbf fbbc cb ``` <!-- end of image -->

I'm optimistic that I'll find some intersections in this image. There are 1 regions I'd like to highlight in the image. <!-- image --> ```palette Key,Color ,#fefefeff a,#5355fbff b,#fe0808ff c,#f45d5bff d,#0808feff e,#ffb7b7ff f,#adaefcff g,#add5aeff ``` ```image fddddd adddf adf fddda da faddaf ad adddf da fddda ad faddaf fda adddf dd fddda fda adddf dd f fda dd fdf dd fdf dd adf dd adf ggggggggggggggggg dd ggggggggggggggggg adggggggggggggggggg ddggggggggggggggg gadgggggggggggggg gggdagggggggggggg ggggddggggggbgggg ggggggdagggbggggg gggggggddcbgggggg ggggggggcdagggggg gggggggcbgddggggg ggggggcbgggfdgggg gggggbbgggggggggg ggggbbggggggggggg gggbbgggggggggggg ggbcggggggggggggg gbcgggggggggggggg bcggggggggggggggg bcgggggggggggggggg be be eb eb eb cb cb cb bb bb bb bc bc bc be be be eb eb eb cb cb cb bb bb bc bc bc cbbe ebbc cbbe cbbc ebbc cbbe ebbc bbb cbbe ebbc cbbe cbbe ebbc bbe ``` <!-- end of image --> I'm eager to see what's happening in this magnified view of area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#4b48fbff b,#fe0505ff c,#fa8e92ff d,#0705fdff e,#efd4e4ff f,#9c9cffff g,#fb3e42ff ``` ```image ae ddf addae fdddf eaddae fdddf eaddae fdddf ebc eaddae ebbg fdddf ebbge eadda ebbg fdddf cbbg eaddacbbg fdddgg cddda cbbadddf gbbc fddda gbbc addde gbbc fddd gbbe af egbbe egbbe ebbbe ebbge ebbge ebbg cbbg cbbg cbbg cbbc cbbc bbc ``` <!-- 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,#5555feff b,#ff0303ff c,#fc7073ff d,#0707ffff e,#feb8b9ff f,#b1b1ffff g,#ff3434ff ``` ```image fddddd adddf adf fddda da faddaf ad adddf da fddda ad faddaf fda adddf dd fddda fda adddf dd f fda dd fdf dd fdf dd adf dd adf dd adf da ad da ad eb fda eb ddeb cda cb dd gb fd gb gg bg bg bc bc be be be eb eb eb cb cb gb gb gg bg bg bc bc be be be eb eb eb cb cb gb gb bg bg bg bc cbbe ebbg gbbe cbbc ebbg cbbe ebbc gbg cbbe ebbc gbbe cbbc ebbg bbe ``` <!-- end of image -->

Time to put on my detective hat and find those intersection points! These zones indicate regions where lines appear to be in close proximity. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0909ff b,#0303feff c,#d3ccf8ff d,#f87976ff e,#b0d7b0ff f,#6969ffff g,#96bba7ff ``` ```image c cfbbbbb cfbbbbbfc cfbbbbbfc ffbbbbfc cfbbbbfc cfbbbbff cfbbbbbfc cbbbfc bc cb bc cb bc cb bc cb ggggggggggggggggbg eeeeeeeeeeeeeeegbe eeeeeeeeeeeeeeebge eeeeeeeeeeeeeegbee eeeeeeeeeeeeeebgee ad eeeeeeeeeeeeegbeee daa eeeeeeeeeeeeebgeee caa daa eeeeeeeeeeeegbeeee daac daa eeeeeeeeeeeebgeeee daad daa eeeeeeeeeeegbeeeee aaa daa eeeeeeeeeeebgeeeee daad daaceeeeeeeeeegbeeeeee daad caaeeeeeeeeebgeeeeee aaa gaageeeeegbeeeeeee daad eegaageeebgeeeeeee caad eeeeeaadgbeeeeeeee daac eeeeeeeabgeeeeeeee daad eeeeeeegbaadeeeeee aaa eeeeeeebgeeaadeeee daad eeeeeegbeeeeeaadee daad eeeeeebgeeeeeeeaad aaa eeeeegbeeeeeeeeeeaad daad eeeeebgeeeeeeeeeee daaad eeeegbeeeeeeeeeeee c eeeebgeeeeeeeeeeee eeegbeeeeeeeeeeeee eeebgeeeeeeeeeeeee eegbeeeeeeeeeeeeee eebgeeeeeeeeeeeeee egbeeeeeeeeeeeeeee ebgeeeeeeeeeeeeeee gbeeeeeeeeeeeeeeee bgeeeeeeeeeeeeeeee cbggggggggggggggggg bc cb bc cb bc cb bc cb bc cb bc cb bc cb bc cb bc cb bc cb bc cb bc cb bc cb bc cb bc ``` <!-- end of image --> Let's zoom in on area A to get a clearer view. <!-- image --> ```palette Key,Color ,#fffefeff a,#ff4e4eff b,#0100feff c,#d2d2ffff d,#f88d93ff e,#fe0607ff f,#5553fdff g,#ffccccff ``` ```image fb cbb fbf cbbc fbf cbbc fbf cbbc fbf cbbc fbf cbbc fbf cbbc fbf cbbc fbf cbbc fbf cbbc fbf cbbc fbf g cbbc eag fbf eeeag cbbc gaeeeag fbf gaeeeag cbbc gaeeeag fbf gaeeeag cbbc gaeeeag fbf gaeeeag cbbc gaeeeafbf deebbd fbbeed cbbdeeeed fbf deeeed cbbc deeeed fbf deeeed cbbc deeeed fbf deeeed cbbc daeee fbf gae cbbc g fbf cbbc fbf cbbc fbf cbbc fbf cbbc fbf cbbc fbf cbbc fbf cbbc fbf cbbc fbf cbbc fbf cbbc fbf cbbc ``` <!-- end of image --> Incredible, there's actually an intersection in area A! There's one and only one intersection present in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff3838ff b,#0303feff c,#cfcfffff d,#ff7c7cff e,#ff0404ff f,#6969ffff g,#fcc0c2ff ``` ```image c cfbbbbb cfbbbbbfc cfbbbbbfc ffbbbbfc cfbbbbfc cfbbbbff cfbbbbbfc cbbbfc bc cb bc cb bc cb bc cb bc cb bc cb bc ea cb dea bc gee dea cb aeeg dee bc deed dee cb geea gee bc deeg gee cb geed geeg bc aeeg geeg cb deed geeg bc geea geegcb aeeg ebg deed cbeed geea bc eed deeg cb aed geed bc aed aeeg cb aed deed bc aeeea cb g bc cb bc cb bc cb bc cb bc cb bc cb bc cb bc cb bc cb bc cb bc cb bc cb bc cb bc cb bc cb bc cb bc cb bc cb bc cb bc ``` <!-- end of image -->

I'm examining this image closely. My goal: find any and all intersections. These spots mark what I'd call 'danger zones' - areas where intersections are more likely. <!-- image --> ```palette Key,Color ,#fefefeff a,#f2a8a1ff b,#0606feff c,#fd0706ff d,#b6b6ffff e,#aed5aeff f,#5c61f4ff g,#f04c49ff ``` ```image eeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeeeee eeeeeeeeeeeeegeeee eeeeeeeeeeeeaceeee eeeeeeeeeeeeceeeee eeeeeeeeeeecaeeeee dddddd eeeeeeeeeecgeeeeee dbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbeeee b eeeeeeeeeceeeeeeee db eeeeeeeecaeeeeeeee b eeeeeeecgeeeeeeeee db eeeeeegceeeeeeeeee b eeeeeeceeeeeeeeeee db eeeeeceeeeeeeeeeee bd eeeecgeeeeeeeeeeee b eeegceeeeeeeeeeeee bd eeaceeeeeeeeeeeeee c b eeceeeeeeeeeeeeeee c bd ca ac b gg gc bd ac cg b c ca bf ca ca b cg c ff gc ac b c ac ff c gc b ca cg ff gc ca b ac ca fb c ceeeeeeeeeeebeeee ca aceeeeeeeeefbeeee gg gceeeeeeeebeeeee ac egceeeeeeebeeeee c eecgeeeeebeeeeee ca eeecaeeeebeeeeee cg eeeeceeebeeeeeee gc eeeeeceebeeeeeee c eeeeeacbeeeeeeee c eeeeeegbeeeeeeee ca eeeeeebgceeeeeee gc eeeeeebecgeeeeee ac eeeeebfeecaeeeee c eeeeebeeeeceeeee ca eeeebfeeeeeceeee gg eeeebeeeeeeaceee ac eeeffeeeeeeegcee c eeebeeeeeeeeecce ca eeffeeeeeeeeeecg cg eebeeeeeeeeeeeeca gc ff c c b c c fb ac ca b gc gc db cg ac b ca c db ca ca b cgg db ac bd b bd b bd b bd b bf b ff b ff b ff b fb b db b db b ``` <!-- end of image --> Let's zoom in on area A to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd9899ff b,#0706feff c,#fe0707ff d,#9593fdff e,#ebd4e7ff f,#504af9ff g,#fa494dff ``` ```image e dbb ce bbd cg dbb ccg bbd ecca dbb acca bbd acca dbb gcce fbd gcce dbb ccg fbd eccg ebbe ecca fbf acca ebbe acce fbf gcce ebbe gcc fbf eccg ebbe eccg fbf accabbe acfbf gbbd dbbce bbgcc dbbeccg bbd eccg dbb acca bbd acca dbb gcce bbd gcce dbb gcg fbd eccg dbb eccg fbd acca ebbe acca fbf gcce ebbe gcce fbf ccg ebbe ecc fbf ec ebbe a ``` <!-- end of image --> I am surprised, so clear, an intersection has appeared in area A. Hmm, interesting. Let's check out another area. Let's get to the bottom of what's happening inside area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#f98489ff b,#0000ffff c,#ff0505ff d,#8483feff e,#fbcaceff f,#473df4ff g,#f53942ff ``` ```image a acc ecca ccg gcg acce ecca ecca gcg dddddddddddddddddddaggddddde bbbbbbbbbbbbbbbbbbbbbbbbbbbf ddddddddddfffffffffffffffffd gcg gcc acce ecca ccg gcg acce ecca ecca gcg acce acce ecca gcg gcc acce ecca ccg ``` <!-- end of image --> An intersection is present within area B. My analysis indicates that there are two intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fe8889ff b,#0606ffff c,#ff0606ff d,#babaffff e,#ffc7c7ff f,#6363ffff g,#fc4345ff ``` ```image a ec c ca ddddddd gg fbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb b c db ce b cg db ac b ec db ce bd ca b gc bd ec c b c ec bd ce ac b gg gc bd ac cg b c ca bf ce ce b cg c ff ac ec b ec ac ff c gc b ca cg ff gc ca b ec ce fb c c b ce ec db gg ac b ac gc db c cg b ce ca db cg ce bd ac c b ec ecbd c ab ca bgg gc b cg ec bd ce c b ce ce bf ec gg b ec ac ff gc c b gg ce ff ca cg b ce ac ff c ec b ec c fb ac ca b gc gc db cg ec b ca c db ce ce b cgg db ec bd db bd b bd b bd b bf b ff b ff b ff b fb b db b db b ``` <!-- end of image -->

The hunt for intersections begins! Let's analyze this image closely. These spots mark what I'd call 'danger zones' - areas where intersections are more likely. <!-- image --> ```palette Key,Color ,#fefefeff a,#494aeeff b,#fc0b0aff c,#0606fdff d,#e6877bff e,#959cf0ff f,#b2d7b1ff g,#a0cda1ff ``` ```image cc acaa ac c ec ec ec c c c c ce c c ce ce ce c ca aa ca c ac ec ac c ec ec gggggggggggggggec ce gfffffffffffffgc c gfffffffffffffcg ce bb gffffffffffffcgg c dbb gfffffffffffcefg aa dbbgffffffffffcaffg c dbbffffffffcafffg ec gdbbfffffcaffffg c gffdbbffacfffffg ec gffffdbacffffffg ce gfffffacbbfffffg c gffffecffdbbfffg ce gfffgcfffffdbbfg c gfffcffffffffdbb aa gffcgffffffffffdbb c gfcefffffffffffg dbb ea gcaffffffffffffg dbb c cafffffffffffffg dbb ec ccffffffffffffffg dbb c acgffffffffffffffg dbb c ac gggggggggggggggg dbb ce ec dbd c ec bb aa c dbd c c bb aa db c bd ec bb c dbd c bb ce dbf c bb ce bb c bdgggggggaagggggggggggggggg gbbfffffffcfffffffffffffffg gfdbdfffffacffffffffffffffg gfffbbfffffcgfffffffffffffg gffffdbgfffecfffffffffffffg gfffffgbbfffceffffffffffffg gfffffffbbfffcffffffffffffg gffffffffdbdfcafffffffffffg gffffffffffbbfcfffffffffffg gfffffffffffdbaaffffffffffg gfffffffffffffbcffffffffffg gffffffffffffffacgffffffffg gfffffffffffffffcbdfffffffg gfffffffffffffffecbbffffffg gffffffffffffffffcedbdffffg gffffffffffffffffgcffbbfffg gfffffffffffffffffceffdbgfg gffffffffffffffffffcfffgbbg gffffffffffffffffffaaffffbb gfffffffffffffffffffcfffffd gfffffffffffffffffffacffffg gggggggggggggggggggggcggggg ec c c ce c aa c aa c ``` <!-- end of image --> This close-up might reveal an intersection in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#3030ffff b,#fe0d0dff c,#0303feff d,#ff9595ff e,#c9c9ffff f,#890f84ff g,#7979ffff ``` ```image e ec ecc eaca aca acae acce gcce gcce gcce bd gccg bbbd eccg dbbbbd eccg dbbbbd ecca dbbbbd eaca dbbbbd aca dbbbbd acae dbbbbd acce dbbbfcce dfccfd gccfbbbd eccg dbbbbd eccg dbbbbd eccg dbbbbd ecca dbbbbd eaca dbbbbd aca dbbbb acae dbb acce d gcce gcce gccg eccg eccg eccg ecca aca ca ce ``` <!-- end of image --> There's no doubt about it - this is 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,#574cf4ff b,#fd0506ff c,#0706fdff d,#fdc4c5ff e,#aca9fbff f,#fa3a3eff g,#ff7f7fff ``` ```image bbg aca gbbfd cce dbbbg acc fbbfd cce gbbbd ecc dfbbf cce gbbbd ecc dfbbg aca gbbfd ecce dbbbg aca fbbf cce gbbbd aca dfbbg cce gbbfd ecc dbbbg cce fbbfd ecc gbbbd aca dfbbfecc gbbbaca dfbbcce gbaca dbcce accf ccfbd eccbbg ccabbfd eccdbbbg aca fbbfd ecce dbbbg aca dfbbf cce gbbbd acc dfbbg cce gbbfd ecc dbbbg cca fbbf ecc gbbb aca dfb ecce g aca cce acc cce ``` <!-- end of image --> Incredible, there's actually an intersection in area B! I've identified a total of two intersection points.

<!-- image --> ```palette Key,Color ,#fefefeff a,#4a44f9ff b,#fe0809ff c,#0606feff d,#ffa3a3ff e,#c5c5ffff f,#ff5757ff g,#8888ffff ``` ```image e cc acaa ac c gc gc ec ce ec ec c ce ce c ce cg cg c ca aa ca c ac gc ac c gc ec ec ce ec c c cg bb ce c dbb ce aa dbb cg c dbb ca gc dbb ca c dbb ac ec dbac ce gcbb c ec dbb cg ec dbb c c dbb aa ce dbb c ce dbb ga cg dbb c ca dbb ec ca dbb ce ac dbb ec ac dbb cg gc dbf c ec bb ag ec dbd c c bb aa fb c bf gc bb ce dbd ec bb ce fbd c bf cg fb c dbf aa bb c dbd gc bb c fb ec bf ce bb c dbd cg bb c dbaa bc ac cbf ecbb cedbd c bb cg fb c bf aa fb c d ga c ec ce ec cg c ag c aa c ``` <!-- end of image -->

I have an image in front of me. I need to determine if there are any intersection segments. These areas seem to enclose narrow spaces where lines might be close. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0808ff b,#4446faff c,#f86360ff d,#888ef3ff e,#0505feff f,#ffb5b5ff g,#add4acff ``` ```image f af a af fa a fa a cc a cc a af a af fa a fa a cc a cc a af a af fa a fa a cc a cc a af a af fa a ee fa bed a bed cc beb a deb cc deb a dee af dee a ee af ee fa ee a eed fa eed a bed cc bed a beb ac deb ggggaggggggggggg deb ggggacgggggggggg dee gggggagggggggggg dee gggggagggggggggg ee ggggggaggggggggg ee ggggggagggggggdee ggggggcaggggbeed gggggggagbeedggg ggggggdeebgggggg gggdeebgaggggggg geeeggggacgggggg beedgggggggagggggg deed gggggggggacggggg deeb ggggggggggaggggg fc eee ggggggggggaggggg faaaaf beed gggggggggggagggg faaaaf deed gggggggggggagggg faaaaf deeb gggggggggggcaggg faaacf eeb a caaacf cc caaacf a caaacf ac caaac a caaac affcaaac aac ``` <!-- end of image --> Let's zoom in on area A to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0708ff b,#5655ffff c,#ff9d9dff d,#a7a7ffff e,#0606feff f,#7c0082ff g,#ff4b4bff ``` ```image gac caa aac caa aac cag aac gag aa gag caa gac caa dbe aac beeee caa dbeeeebd aac dbeeeebd cag dbeeeebd afeeeeeb deeeeebd dbeeeeff dbeeeebd gag dbeeeeed caa deeeeebd gac beeeebd caa eebd aac d caa aac cag aac gag aa gag caa gac caa aac ``` <!-- end of image --> The close-up clearly shows an intersection point in area A. My investigation reveals that there is exactly one intersection in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0404ff b,#5353ffff c,#ff8080ff d,#ababffff e,#0606ffff f,#ffc0c0ff g,#ff3e3eff ``` ```image f ac a af fa a fa a cg a gc a ac a af fa a ca a cg a gc a af a af fa a ca a cg a gc a af a af fa a ee ca bed a beb cg beb a beb gc deb a dee af dee a dee af ee fa eed a eed cg eed a bed cg beb a beb gc beb a deb af dee a dee af dee fa ee a deed cg beed a beed deeb deeb a eeed gc beed a beeb af deeb a fg deee af fgaaac beed fa fgaagf beed a caaagf deeb cg caaagf eeb a caaagf d gg caaagf a caaagf gc caaacf a caaac affgaaac aac ``` <!-- end of image -->

This image seems promising for intersection detection. There are 2 areas where the lines seem to converge. We should take a closer look at area A,, and B. <!-- image --> ```palette Key,Color ,#fefefeff a,#eb8980ff b,#0707fdff c,#fe0302ff d,#9ba4ecff e,#f8322fff f,#4e53f5ff g,#aed5aeff ``` ```image gggggggggggggggg gggggggggggggggg d gggggggggggggggg db gggggggggggggggg db gggggggggggggggg db caggggggggggggggg b ccgggggggggggggg b gacegggggggggggg bd gggecagggggggggg bd gggggccggggggggg bd gggggggccggggggg bf bdgggggggaceggggg bf bgggggggggecaggg bb gbggggggggggccgg fb ggbggggggggggacc fb gggbgggggggggggaca db gggdbggggggggggg eca db ggggdbgggggggggg cc db gggggdbggggggggg ace b ggggggfbgggggggg aca b gggggggfbggggggg ec b fb cc bd fb ace bd fb eca bf bb cc bf bf cc bf bf ac fb bf ac fb bf eegggggggggggggggfb bd cagggggggggggggfb bd gcggggggggggggdb bd ggcgggggggggggbg bd ggacgggggggggbgg b gggeegggggggbggg b ggggcagggggbdggg b gggggcggggbdgggg b ggggggcggbfggggg db ggggggacbfgggggg db gggggggbbggggggg db ggggggbbcagggggg db gggggfbggcgggggg fb ggggfbggggcggggg fb gggfbgggggacgggg fb ggdbgggggggeeggg fb gdbgggggggggcagg bb gbgggggggggggcgg bf bgggggggggggggcg bf bdgggggggggggggac bbdgggggggggggggggee d ca c c ac ee ca c c ac ee ca c c ac ee ca c c ac ee ca c c ac ee ca c c ac ee ca c ``` <!-- end of image --> Let's see if area A yields any clues. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff9b9bff b,#0505ffff c,#fe0707ff d,#9696ffff e,#ff4f4fff f,#3d3dffff g,#eed7e8ff ``` ```image g ceg ccceg geccca geccca accceg accce geccca aeccca accceg eccce geccca dd accceg bbg accceg fbbg geccca fbbg geccca fbbg accceg fbbg accceg gfbfg geccca gbbf gecc gbbf ac gbbf gbbf gbbf dbbf dbbf dbbd dbbd dbbd dbbd dbbd dbbd ``` <!-- end of image --> Area A does not contain any intersection points. Now, let's scrutinize the next spot. Let's take a closer look at area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff9a9aff b,#0a08fdff c,#fe0405ff d,#a3a1fcff e,#ff4848ff f,#4d4dffff g,#ecd7eaff ``` ```image cg ce cce gcca acca d eccg db ece gbb gcce gbbf gcca gbbf acca gbbb eccg fbbg ece fbbg gcce fbbg gcca fbbd acca fbbd eccg dbbd ece dbbd gcce dbbd gcca dbbf accdbbf ecbbf gbbbg gbbbce bbbgcca fbbg acca fbbg eccg fbbg ece fbbd gcce dbbd gcca dbbd acca dbbd eccg dbbf ece dbbf gcce gbbf gcca gbbf acca gbbf eccg gbbbg ece fbbg gcce bbg gcc bg ac d e ``` <!-- end of image --> Eureka! There's definitely an intersection in area B! One intersection, that's it, but I found it.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff9090ff b,#0807feff c,#ff0202ff d,#a6a6ffff e,#ff3535ff f,#5050ffff g,#efddedff ``` ```image d db db gb cg gb gcc bg ace bg eca bd ccg bd gcc bf bd ace bf bg eca bb gbg ccg fb gbg gce fb gb aca db db eca db db cc db db ace gb db aca gbg fb ecg bg fb gcc bd fb ace bd fb eca bf bb ccg bf bf gcc bf bf ac fb bf ac fb bf ee fb bd ca db bd cg db bd gc gb bd ac gbg bg ee bg gbg ca bd gbg cg bd gb gc bd db acbf db bb db bbca db fb cg fb fb gc fb db ac fb db ee fb gb ca bb gb cg bf bg gc bf bg ac bbd ee d ca cg gc ac ee ca cg gc ac ee ca cg gc ac ee ca cg gc ac ee ca cg gc ac ee ca cg gc ac ee ca c ``` <!-- end of image -->

Let's examine this image for potential line intersections. I wonder what's going on inside those areas? Perhaps intersections are hiding there. <!-- image --> ```palette Key,Color ,#fefefeff a,#f0423bff b,#090afcff c,#fd0504ff d,#6470e6ff e,#e48a7dff f,#b2d7b2ff g,#a3cba2ff ``` ```image f bd b db a b c db c b ec b c bd ae b c dd c b ec db c b aa c fb c ecggggggbdggggggggggggggggggggggggggggggggggggggggg cf cgffffffbffffffffffffffffffffffffffffffffffffffffg ec gcffffffbdfffffffffffffffffffffffffffffffffffffffg c gceffffffbfffffffffffffffffffffffffffffffffffffffg aa gfcffffffdbffffffffffffffffffffffffffffffffffffffg c gfaaffffffbffffffffffffffffffffffffffffffffffffffg ce gffcffffffdbfffffffffffffffffffffffffffffffffffffg ec gffecffffffbgffffffffffffffffffffffffffffffffffffg c gfffcgfffffgbffffffffffffffffffffffffffffffffffffg aa gfffgcffffffbdfffffffffffffffffffffffffffffffffffg c gffffceffffffbfffffffffffffffffffffffffffffffffffg ce gfffffcffffffbdffffffffffffffffffffffffffffffffffg c gfffffaaffffffbffffffffffffffffffffffffffffffffffg c gffffffcffffffdbfffffffffffffffffffffffffffffffffg ea gffffffecffffffbgffffffffffffffffffffffffffffffffg c gfffffffcgfffffgbffffffffffffffffffffffffffffffffg ce gfffffffgcffffffbdfffffffffffffffffffffffffffffffg c gffffffffceffffffbfffffffffffffffffffffffffffffffg c gfffffffffcffffffbdffffffffffffffffffffffffffffffg ec gfffffffffaaffffffbffffffffffffffffffffffffffffffg c gffffffffffcffffffdbfffffffffffffffffffffffffffffg ae gffffffffffecffffffbfffffffffffffffffffffffffffffg c gfffffffffffcgfffffdbffffffffffffffffffffffffffffg c gfffffffffffgcffffffbgfffffffffffffffffffffffffffg ec gffffffffffffcefffffgbfffffffffffffffffffffffffffg c gfffffffffffffcffffffbdffffffffffffffffffffffffffg aa gfffffffffffffaaffffffbffffffffffffffffffffffffffg c gffffffffffffffcffffffddfffffffffffffffffffffffffg cf gffffffffffffffecffffffbfffffffffffffffffffffffffg ec gfffffffffffffffcgfffffdbffffffffffffffffffffffffg c gfffffffffffffffgcffffffbgfffffffffffffffffffffffg aa gffffffffffffffffcefffffgbfffffffffffffffffffffffg c gfffffffffffffffffcffffffbdffffffffffffffffffffffg ce gfffffffffffffffffaaffffffbffffffffffffffffffffffg ec gffffffffffffffffffcffffffbdfffffffffffffffffffffg c gffffffffffffffffffecffffffbfffffffffffffffffffffgaa gfffffffffffffffffffcgfffffdbffffffffffffffffffffgc gfffffffffffffffffffgcffffffbffffffffffffffffffffce gffffffffffffffffffffcefffffdbffffffffffffffffffec gfffffffffffffffffffffcffffffbgfffffffffffffffffcg gfffffffffffffffffffffaafffffgbffffffffffffffffaag gffffffffffffffffffffffcffffffbdfffffffffffffffcfg gffffffffffffffffffffffecffffffbffffffffffffffcefg gfffffffffffffffffffffffcgfffffddffffffffffffgcffg gfffffffffffffffffffffffgcffffffbffffffffffffcgffg gffffffffffffffffffffffffcefffffdbffffffffffacfffg gfffffffffffffffffffffffffcffffffbgfffffffffcffffg gfffffffffffffffffffffffffaafffffgbffffffffcaffffg gffffffffffffffffffffffffffcffffffbdffffffgcfffffg gffffffffffffffffffffffffffecffffffbbdffffcgfffffg gfffffffffffffffffffffffffffcgffffffgbbbdecffffffg gfffffffffffffffffffffffffffgcfffffffffgbbbgfffffg gffffffffffffffffffffffffffffcefffffffffaadbbbgffg gfffffffffffffffffffffffffffffcffffffffgcffffdbbdg gfffffffffffffffffffffffffffffaafffffffcefffffffdbbd gffffffffffffffffffffffffffffffcffffffecfffffffffg dbbd gffffffffffffffffffffffffffffffecfffffcffffffffffg dbbd gfffffffffffffffffffffffffffffffcgfffaaffffffffffg bbbf gfffffffffffffffffffffffffffffffgcfffcfffffffffffg fbbb gggggggggggggggggggggggggggggggggcegcegggggggggggg fbbb cec dbbd ac dbbd e dbbd dbbd bb ``` <!-- end of image --> I'm focusing my attention on this specific region, area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff4040ff b,#0707feff c,#fe0505ff d,#afaffeff e,#fe8585ff f,#fec8c8ff g,#5a57fcff ``` ```image cc dbbd cce gbg ecc bbd aca gbb fccf bbd aca dbb fccf bbg cce gb ecc dbd ac gg fcf bd aa bb fcf bbg cc dbb cce gbg ecc dbbd aca gbg fccf bbd aca gbb fccf bbd ecc dbb ecc dbb ace gbg fccf dbbd aca gbg fccf bbd ecc dbb cce bbg ecc dbb ace gbg fccf dbb aca gb fcc bd ec gb ce bd ce bbg ccf dbb aca gbg fccf dbbd eca gbg cce bbd ecc dbb ace bbg fccf dbb aca gbg fccf dbbd eca gbg cce bbd ecc gbb fccf dbb aca bbg fccf dbb eca gbg cce dbb ecc gb ac bd fcf db aa bg fcf bb ca gbg cce dbbd ecc gbg ace bbd aca bbd fccf dbb eca bbg cce dbb ecc gbg ace bbd fccf gbb aca bbd fccf dbb eca bbg a cce dbb fc ecc gbg ac ace dbbd ecc fccf gbg cce fcc gbb fccf ec bb aca ce db ecc ec bg cce ce dbd eca ccf bg ccf aca bbd ca fccf gbb fcf eca bbd ce cce dbb ec ecc bbg fcc ace dbb aca fccf gbg fccf aca dbbd cce eca bbd fccf cce gbbd aca ecc bbbbgd fccf ace dgbbbbd ace fccf dgbbbgd ecc aca dbbbbbgce fccf dgbbbbbgd eca fcgbbbbbg cce ace dgbbbbd ecc ecc dgbbbgd cce cce gbbbbgd fcc eca dbbbb ac fccf dgb fcf aca ce ce cc ea cce fcf fccf ac aca ecc fccf cce aca ecc ``` <!-- end of image --> Amazing! This area was hiding an intersection all along! There's only one, but is an intersection after all.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff4a4aff b,#0505feff c,#ff0606ff d,#9999ffff e,#ff9797ff f,#efd7e7ff g,#4b4bffff ``` ```image d bd b gg a b fc db cf bf ec fb c bd ca b fc gg cf b ec db c bf aa c fb c ec bd ce cf b ec fc gd c ce b aa c gg c aa b ce c db ec ec bf c cf fb aa fc bd c ce b ce c gg fc aa b cf c db aa ec bf c cf fb ce fc bd fc ce b cf c gg ec aa b c c gg ce ec b fc cf db cf fc bf ec ce fb c c bd aa aa b fc c gg cf ec b ec cf db c fc bf aa ce fb c c bd ce aa b ec c gg c ec b aa cf gg c fc b ce ce db fc c bf cf aa fb aa c bd c ec b ce cf gg fc fc b cf ce db ec c bf c aa fb ce c bd fc ec bbd cf cf fgbbdec fc fbbbf ce aadbbgf c fc dbbg aa cf dbbg c ec gbbd ec c gbbd cf aa fgbbd fc c fbbbf ce ce dbbgf cec dbbg ac dbbg e gbbd gbbd fbb ``` <!-- end of image -->

I have an image in front of me. I need to determine if there are any intersection segments. It's crucial to examine these regions more closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0a09ff b,#0506feff c,#aeaefeff d,#f95f5cff e,#5151f5ff f,#ffb5b5ff g,#acd3acff ``` ```image c cebbbe cebbbec cbbbbec ebbbbec cebbbbec cebbbbec cebbbbe cebbbbc bbec bc cb b be b bc cb b ee b bc ad cb a b da ee af b a bc ad cb a b fa ee af b a bc dd cb a b fa ee af b a a bc aa dd cb aa gggaggggggggbggg da ggggaggggggebggg da ggggadgggggbgggg da gggggaggggbegggg da gggggdagggbggggg da ggggggaggbgggggg da gggggggaebgggggg da gggggggabggggggg fa gggggggbeggggggg fa gggggggbdagggggg fa ggggggbggagggggg fa gggggebgggaggggg fa gggggbggggadgggg fa ggggbegggggagggg fa ggggbggggggdaggg a gggbggggggggadgg a ggebgggggggggagg a b dd af ee a af b fa af bc af af cb a af b da af ee a af b fa ad bc ad ad cb a ad b da ad ee af ad b a ad bc ad ad cb a aa b fa aa af aa a da dd da a da fa da af da a da da da ada fa ``` <!-- end of image --> Let's take a closer look at area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0505ff b,#0404feff c,#c2c0fcff d,#fca4a7ff e,#3c31f4ff f,#7d7dffff g,#fd4648ff ``` ```image aad ebe daa cbb gag bbf daad fbe gag cbbc aad ebe daa cbbc gag bbf daad fbe gaa cbbc aad ebe daa cbbc gag ebf aadfbb dagbbc aebe dbbc ebeg fbbaad bbfdaa fbe gag cbbc daad ebf gag fbb aad bbf daa fbe gag cbbc daad ebf gag fbb aad bbf daa fbe gag cbbc aad ``` <!-- end of image --> As I suspected, there's an intersection within area A. I've found a single intersection point in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0505ff b,#0505ffff c,#a8a8ffff d,#ff7f7fff e,#4c49fbff f,#ffc5c5ff g,#ff3b3bff ``` ```image c cebbbe cebbbec cbbbbec cbbbbec ebbbbec cebbbbec cebbbbc cebbbbc bbec b cb b ee b bc cb b ee b bc ad cb a b da ee af b fa bc gd cb a b da ee af b a bc gg cb a b fa ee af b a a bc gg gg cb ga a b ga fa eb ga ad b ga a bc ga dg b da af b da facb da gb da ee da bda fa bc af fa cb a fa b gg fa ee a fa b fa fa bc af a cb a af b gg af ee a af b fa af bc ad af cb a af b dg ad ee af ad b fa ad bc ad ad cb a ad b da ag ee af ag b a ag bc gd ag cb a ag b da gg af ga a ga gg ga a ga fa ga ad da a da dg da ada fa ``` <!-- end of image -->

I have an image in front of me. I need to determine if there are any intersection segments. It's crucial to examine these regions more closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#0707fdff b,#fd0807ff c,#abacfeff d,#b1d7b1ff e,#ec6259ff f,#545af1ff g,#99c398ff ``` ```image c ca ca ca a a ac ac ac af af aa fa fa ca ca ca a a ac ac ac af af aa fa fa fa ca gddddddddddddddddddddddddddddddddddddgaddddg gdddddddddddddddddddddddddddddddddddgadddddg gdddddddddddddddddddddddddddddddddddaddddddg gddddddddddddddddddddddddddddddddddagddddddg gdddddddddddddddddddddddddddddddddagdddddddg gddddddddddddddddddddddddddddddddafddddddddg deebbbbb gdddddddddddddddddddddddddddddddafdddddddddg deebbbbbbbbeee gddddddddddddddddddddddddddddddafddgeebbbbbbbbbeed gdddddddddddddddddddddddgeeebbaabbbbeeegdddg gdddddddddddddddddddebbbbbeegaaddddddddddddg gddddddddddddddddddbbdddddddfadddddddddddddg gdddddddddddddddddbedddddddfaddddddddddddddg gdddddddddddddddgbgdddddddfadddddddddddddddg gddddddddddddddebddddddddgaddddddddddddddddg gdddddddddddddbbddddddddgadddddddddddddddddg gddddddddddddbedddddddddaddddddddddddddddddg gddddddddddgbgdddddddddagddddddddddddddddddg gdddddddddebddddddddddagdddddddddddddddddddg gddddddddbbddddddddddafddddddddddddddddddddg gdddddddbeddddddddddafdddddddddddddddddddddg gdddddgbgdddddddddgagddddddddddddddddddddddg gddddebddddddddddgaddddddddddddddddddddddddg gdddbbddddddddddfadddddddddddddddddddddddddg gddbeddddddddddfaddddddddddddddddddddddddddg ggbgddddddddddaadddddddddddddddddddddddddddg ebdddddddddddaaddddddddddddddddddddddddddddg bbgggggggggggafgggggggggggggggggggggggggggggd be ac db ac eb ca bb fa be fa db aa eb af bb af be ac db cac eb ca e fa fa aa af af ac ca ca fa fa aa af ac ``` <!-- end of image --> I'm determined to find out if an intersection exists in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0807fdff b,#fe0405ff c,#afafffff d,#fdc6c7ff e,#fe4748ff f,#5353feff g,#ff8787ff ``` ```image caac caaf caaf caaf aaf aaf aaa faa faac faac faac faac caac caac caaf caaf dddgg caaf ddgggeebbbbbbbb ddaafeeebbbbbbbbbbbbbbbeeg dddggeeebbbbaaabbbbbbbbeeeggddd dgeebbbbbbbbbbbbbbaaaegggdd gbbbbbbbbbeegggdddfaa ebbegddd faa dbbbd faac gbbed faac gbbe faac ebbg caac dbbbd caac gbbed caaf ebbe caaf ebbg caaf dbbbd caaf gbbed aaf ebbe aaa ebbg faa dbbbd faa gbbed faac ebbe faac debbg faac dbbbd faac gbbed faac ebbe faac debbg faac dbbbd aaac gbbed caaac ebbe caaa debbg caaf dbbbd caaf gbbed faaf ebbe faac debbg faac dbbbd aaac gbbe caaa ebbe caaf ``` <!-- end of image --> The lines cross each other within area A, forming an intersection. The image features one single intersection point.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0504fdff b,#ff0707ff c,#8888ffff d,#ffb6b6ff e,#ff5d5dff f,#4141feff g,#c9c9ffff ``` ```image c ca ga ga ga ag ag ag ac af af ff fa fa ca ga ga ga a ag ag ac ac af af fa fa ca ca ga ga a ag ag ac deebbbbb ac ddebbbbbbbbeedd af ddeebbbbbbbbeed deebbaabbbbeedd ebbbbeeddfa bb fa be ca dbd ca eb ga bb ga be a dbd ag eb ag bb ac be ac dbd gag eb gag bb ca be fa dbd fa eb af bb af be ac dbd gag eb ga bb ca be fa dbd aa eb af bb ac be ac dbd gag eb ca d ca fa aa af ac ag gag ca fa fa af af ac ``` <!-- end of image -->

Time to put on my detective hat and find those intersection points! I've noticed 1 areas of interest. These could be potential intersection zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#5554f0ff b,#fe0404ff c,#0708feff d,#fca1a0ff e,#9ea1f9ff f,#add4adff g,#f84a47ff ``` ```image e acc ecce cca acc ecce cca acc ecce cca acc ecce cca acc ecce cca ac ac ce c ec ce c ec ca c ec ca bd c bg c gb aa db c bd c bg ac bb ce gb c dbd ec bg ce bb c gb ec db ce bd c bg ec gb ca db c bd ec bg aa bb c gb c dbd fffacfffffffffffffffff bg ffffceffffffffffffffff bb fffffcffffffffffffffff gb fffffacfffffffffffffff db ffffffceffffffffffffff bd fffffffcffffffffffffff bg fffffffacfffffffffffff gb ffffffffcaffffffffffff dbbbbbbbgggddd fffffffffcffffffffffff dddgggbbbbbbbbbbbbgggacfffffffffff ffffffdgggcabbbbbbbbbbbbg fffffffffffcffffffffff dd fffffffffffecfffffffff ffffffffffffcaffffffff fffffffffffffcffffffff ffffffffffffffcfffffff ffffffffffffffaaffffff fffffffffffffffcffffff ffffffffffffffffcfffff ffffffffffffffffacffff ce c ac ce c ec ce c ec ca c ``` <!-- end of image --> Let's see what secrets area A holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#3a31f6ff b,#fe0606ff c,#0404feff d,#fdb4b6ff e,#c1c1ffff f,#7a77fbff g,#fe6061ff ``` ```image aca ccf ecce fca ccf ecce fcc acf ecce fcc aca ecce fcc aca eccf fcce aca ggddddd ccf bbbbbbbbbbbbbggggggfccddd ggggbbbbbbbbbbbbbbbbaccbbbbbbbbggggggddddd ddddddgggggccabbbbbbbbbbbbbbbbbb ecce ddddddggggggbb fca acf ecce fcc acf ecce fcc aca eccf fcce aca eccf fcce aca ccf ecce fca ``` <!-- end of image --> There is an intersection point visible in this close-up of area A. The final count is: one intersection.

<!-- image --> ```palette Key,Color ,#fefefeff a,#5753fbff b,#ff0404ff c,#0808feff d,#ff8e8eff e,#9f9dfcff f,#eed8e8ff g,#ff4141ff ``` ```image e acc ecce fcca acc ecce fcca accf ecce fcca accf ecce cca accf ecce cca ac ac ce c ec ce c ec ca c fc ca bd cf bg fc gb aa dbf cf fbd fc bg ac bb ce gb c fbf ec bd ce bb c gb ec dbf ce fbd c bg ec gb ca dbf c fbd fc bg aa bb cf gb fc fbf aa bd cf bb c gb ac dbf ce fbd c bg ec gb ce dbbbbbbbggdddff c fdddgggbbbbbbbbbbbbggdecff ffdddgcabbbbbbbbbbbgg c ffd ec ca cf fc aa cf fc ac ce c ac ce c ec ce c ec ca c ``` <!-- end of image -->

I'm examining this image closely. My goal: find any and all intersections. There's definitely not a single intersection on the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#3a3affff b,#ff0606ff c,#ff5b5bff d,#8080ffff e,#c7c7ffff f,#ffafafff g,#0404ffff ``` ```image e gge egd g dge eg ag dg gg ag ga ga ege gd dg ge ag g ga eg gd dg ege ag dg aa ag gd ga ge gd g ege eg dg eg ag dg ga aa gd gd ege ge dg ge ag g ga eg gd dg ege aa ag ga gg gd ga ge g eg dg ag ga gd ge g eg dg ag aa gd ge g eg eg dg aa gd g fb fbbbf fbbbf fbbbf bbbf cbbf cbbf cbbf cbbc cbbc cbbc bbbbccf cbbc ffcbbbbbbbcff cbbc ffcbbbbbbbcff fbbc ffcbbbbbbbcff fbbc fccbbbbc ``` <!-- end of image -->

Alright, let's get to work and investigate this image for intersections. The image has some tight areas where segments are too close. I should investigate those closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#4b4ff1ff b,#f14640ff c,#fd0403ff d,#9ca3efff e,#0708fdff f,#e5877bff g,#b0d6b0ff ``` ```image f bc bc fc fcggggggggggggggggggggggggggggggggggggggg fcgggggggggggggggggggggggggggggggggggggg gfcggggggggggggggggggggggggggggggggggggg gggcgggggggggggggggggggggggggggggggggggg ggggcfgggggggggggggggggggggggggggggggggg gggggcfggggggggggggggggggggggggggggggggg d ggggggcfgggggggggggggggggggggggggggggggg ae gggggggcbggggggggggggggggggggggggggggggg deaggggggggcbgggggggggggggggggggggggggggggg eeggggggggcbggggggggggggggggggggggggggggg deagggggggccgggggggggggggggggggggggggggg ggeegggggggccggggggggggggggggggggggggggg gggdeaggggggbcgggggggggggggggggggggggggg gggggeeggggggbcggggggggggggggggggggggggg ggggggdeagggggbcgggggggggggggggggggggggg ggggggggeegggggfcggggggggggggggggggggggg f gggggggggaedggggfcgggggggggggggggggggggg fccb gggggggggggeeggggfcggggggggggggggggggggg fccb ggggggggggggaedggggcgggggggggggggggggggg fccb ggggggggggggggeeggggcfgggggggggggggggggg fccb gggggggggggggggaedgggcfggggggggggggggggg fccb gggggggggggggggggeegggcfgggggggggggggggg fccb ggggggggggggggggggaedggcbggggggggggggggg fccb ggggggggggggggggggggeeggcbgggggggggggggg fccb gggggggggggggggggggggaeggcbggggggggggggg fccb gggggggggggggggggggggggeagccgggggggggggg fccb ggggggggggggggggggggggggaegccggggggggggg fccb ggggggggggggggggggggggggggeabcgggggggggfccb gggggggggggggggggggggggggggeebcgggggfccb ggggggggggggggggggggggggggggdeacgfccbggg ggggggggggggggggggggggggggggggeecbgggggg de e e e de de de de de de de de de de ae ae ae ae ae ae ae ae ae ee ee ee ea ea ea ea ea ea ea ea ea ed ed ed ed ed ed ed ed ed e ``` <!-- end of image --> This close-up might reveal an intersection in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#504ffdff b,#fe4040ff c,#fe0405ff d,#9f9ffeff e,#0707feff f,#fd9294ff g,#f2d7e4ff ``` ```image ccf fccb fccb fccb gccb gccbg gccbg gcccg gbccg gbccg bccf bccf bccf bccf fccf fccf fccb a fccb eed fccb eeea gccb aeeed gccbg deeea gccbg aeeed gcccg deeea gbccg aeeeg gbccg deeed bccf aeeag bccf deeed bccf gaeeag bccf deeed fccf gaeeag fccf deeed fccb gaeeag fccb deeed fccb gaeea gccb deeed gccbg gaeea gccbg deeed gcccg geeea gbccg aeeed gbccg deeea bccf aeeed bccf deeea bccf aeeeg bccf deeed fccf aeeag fccf deeed fccb aeeag fccb deeed fccb gaeeag gccb deeed gccbg gaeeag gccbg deeed gcccg gaeeaggbccg deeedgbccg gaeeagbccf g deeedbccf gfbc gaeeabccf gfbcccc deeefccf gfbccccbfg geeeaccf gfbccccbfg aeeeccbccccbfg ``` <!-- end of image --> Area A is clear of intersections, but the search continues. I'm extremely confident. No intersections at all.

<!-- image --> ```palette Key,Color ,#fefefeff a,#3432fcff b,#fe4344ff c,#fe0202ff d,#b9b9ffff e,#0404ffff f,#ff8d8dff g,#7272ffff ``` ```image f bc bc fc fc fc c c cf cf d cf ae cf deg cb ae cb deg cb ee bc deg bc ee bc deg fc ee fc f ged fc fccb ee c fccb ged c fccb ea cf fccb ged cf fccb ea cf fccb ged cf fccb ea cb fccb aed cb fccb ea cb fccb ae bc fccb degbc fccb aebc fccb deac fccb aecb de e de de de de de de de de de ge ge ge ge ge ge ge ae ae ae ae ae aa aa aa ea ea ea ea ea eg eg eg eg eg eg eg ed ed ed ed ed ed e ``` <!-- end of image -->