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oliveirabruno01

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

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

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0909ff b,#0505ffff c,#7f7fffff d,#ff7171ff e,#ffd6d6ff f,#c3c3ffff g,#3d3dffff ``` ```image d daae eaaa daad daae eaaa daad daae eaaa daad daae eaaa daad daae eaae ead aa dae ead aa dae ead aa dae ead aa dae ead aa dae ead aa dae ead aa dae ead aa dae ead aa dae ead aa dae ead aa fg d gbgb fbc fbc bb bb cbc cbf bb fbc gbf bb fbg cbf bb bg cbc gb bb fbf cbf bg fbg gb gbf fbc fbg bb bb cbf cbc bg bb bb gbf cbf fbg bg gb gb fbc fbc bb bb bc gb fbc bb cbf bg gb fbf bg gb fb ``` <!-- end of image -->

Here's an image. My task is to find intersections or areas where lines come close together. I have a hunch that these areas might contain the intersections we're looking for. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd0908ff b,#090afcff c,#ef5d5bff d,#a8aafaff e,#feb6b5ff f,#add3adff g,#585ef2ff ``` ```image e ca acc g ac a gb a ea bg ae a b ea ea b a ae db ca a db bg a ac db bd ac a db b a cc db db ae a gb gb ea ea gb bg a a gb bd ca ea gb b a ae bb db cc a bb bg a ac bb bd ae a bg bfffffffffffafff cc bg fbfffffffffaffff a bg fgbfffffffcaffff ca bg ffbgffffffafffff ffafffffffffffff bd fffbfffffacfffff fffaffffffffffffbd ffffbffffaffffff fffafffffffffffbd ffffgbffacffffff ffffafffffffffbf fffffbbfafffffff ffffacfffffffbff ffffffbcffffffff fffffaffffffbfff ffffffcbffffffff fffffacffffbffff ffffffafbfffffff ffffffaffdbfffff fffffccfgbffffff ffffffcagbffffff fffffafffbgfffff fffffffcbfffffff ffffacffffbfffff ffffffgbafffffff ffffaffffffbffff fffffgbfafffffff fffafffffffgbfff ffffgbfffaffffff ffcaffffffffbbff fffbbffffacfffff ffaffffffffffbgf ffbbffffffafffff fccfffffffffffbf fbbfffffffacffff a db bbfffffffffaffff ae gb bbffffffffffcafff a bg bgffffffffffffafff ae bd bg ffffffffffffcaff ea b bg ae a db bd ea cc gb bd ae a bd bd a ae b bd ac a b b a ae gb cc ea a a ea cc a a ea ac ae a a ae ac ea a a cc cc a a ca ac a a ea ae ae a ae a cc a ca a ea ae ea ae a ac a cc a ``` <!-- end of image --> My goal is to determine if there's an intersection inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0505ff b,#0706fdff c,#fc8f91ff d,#9c9cfeff e,#eed5e6ff f,#fa4448ff g,#4b4bfeff ``` ```image bbd eaac dbbe faf gbb eaae bbg faf ebbd caae dbbd aac gbbe caa gbg eaac ebbg faf dbbd eaae dbbe faf gbb caae bbg aac ebbd caa dbbd eaac gbbe faf gbg eaae ebbgfaf dbbfae dbbc cbbb eaabbg fafebbd eaae dbbd faf gbbe caae gbg aac ebbg caa dbbd aac dbbe caf gbb eaae bbg faf ebbd caae dbbd fac gbbe caa gbg aac ebbg caf dbbd eaae dbb faf gb ``` <!-- end of image --> There's no doubt about it - this is an intersection in area A. Time to investigate another area. My goal is to determine if there's an intersection inside area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff0404ff b,#0808feff c,#ff8282ff d,#c2c2feff e,#ffc9c9ff f,#f43b46ff g,#4c48faff ``` ```image caa fac eaae faf eaae g faf gb eaae gbb caf gbbd aac bbbd caa dbbbd fac dbbb eaae dbbg faf dbbg eaae dbbg faf dbbg eaae dbbg caf dbbg aagbbg cfbbg gbbg gbbfa gbbdfac gbbd eaae gbbd faf gbbd eaae gbbd caf gbbd aac gbbd caa gbbd aac bbbd caa dbbbd fac dbbb eaae dbbg faf bbg eaae bg caf g aae caa aac ``` <!-- end of image --> Amazing! This area was hiding an intersection all along! The image features two intersection points.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0505ff b,#0808ffff c,#fe8282ff d,#b5b5feff e,#ffc9c9ff f,#f93c41ff g,#5555ffff ``` ```image e ca acf g fc a gb a ca bg ae ae bd ea ea b a ae db cf a db bg a fc db bd fc a db b a ff db db ae a gb gb ea ca gb bg a a gb bd cf ea gb b a ae bb db fc a bb gg a ac bb bd ae a bg b ea ff bg db a a bg gb ca ca bg bg a a bd bd ff ea bd b a ae bd db ac ea bd ggea ac bd bfe a db cb ff db adb a db ff gb cfdb a bg fb ac bd gba ea b gb ae ae db gb ea ca gg gb ac a bd bb a ff b bb fc a db bb a ac gb bg cf ea bg bg a ae bd bg ca ca b bg ae a db bd ea ff gb bd ae a bd bd a ac b bd fc ea db bd a ae gb ff ca a a ca ff a a ea ac ae a a ae ac ea a a ff cf a a ca fc a a ea ae ae ea ac a ff a cf a ea ae ea ac a fc a cf a ``` <!-- end of image -->

This image looks interesting. I wonder if there are any intersections hidden in there? It's crucial to examine these regions more closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#0607feff b,#fe0908ff c,#f7605dff d,#a9acfaff e,#feb7b6ff f,#5457f9ff g,#aed5aeff ``` ```image c cb cb cb bb bb bb bc bc bc bc be be be be eb eb eb eb eb cb cb cb cb bb bb bb bc bc bc bc be be be be gggggggggggggggg eb gggggggggggggggg eb gggggggggggggggg eb gggggggggggggggg eb gggggggggggggggg eb gggggggggggggggg cb gggggggggggggggg cb gggggggggggggggg ebb gggggggggggggggg cbb gggggggggggggggg bbc gggggggggggggggg ebbe gggggggggggggggg cbbe gggggggggggggggg cbc gggggggggggggggg ebbc gggggggggggggggg ebbe a gggggggggggggggg cbb fa ggggggggggggggggebbc aa ggggggggggggggcbbe fad ggggggggggggcbbg aa ggggggggggbbcggg dad ggggggggbbcggggg aa gggggcbbgggggggg daf gggbbbgggggggggg aa gggcgggggggggggg af gggggggggggggggg fa gggggggggggggggg af gggggggggggggggg fad gggggggggggggggg aa gggggggggggggggg dad gggggggggggggggg aa gggggggggggggggg dad gggggggggggggggg aa gggggggggggggggg daf gggggggggggggggg fa gggggggggggggggg af gggggggggggggggg fad gggggggggggggggg aa gggggggggggggggg dad gggaaaafdggggggg aa gggggggfaaaaafgg dad ggggggggggggdfaaaafd aa gggggggggggggggg dfaaaafd daf dfaaaafd fa dfaaaaaf af dfaaa ``` <!-- end of image --> This close-up of area A is like examining a piece of evidence. <!-- image --> ```palette Key,Color ,#fefefeff a,#0606ffff b,#ff0505ff c,#ff8a8aff d,#b4b4ffff e,#ffcbcbff f,#5f5fffff g,#ff4444ff ``` ```image cg cbbb egbbbbc egbbbgc cbbbbge ecbbbbce egbbbgc cgbbbge ecbbbbce egbbbbc egbbbge ebbge c aaffd daaaaaaaffdd dffaaaaaaaaaffdd ddffaaaaaaaaaffdd ddffaaaaaaaa ddffaa ``` <!-- end of image --> This isn't an intersection in area A, but I'm not discouraged. After a thorough analysis, I conclude that there are no intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0707ffff b,#ff0404ff c,#ff7b7bff d,#b9b9ffff e,#ffc1c1ff f,#5d5dffff g,#ff3939ff ``` ```image c cb gb gb gb bg bg bg bg bc bc bc be be be ebe eb eb eb cb cb cb gb gb gb bg bg bg bg bc bc bc be be be ebe eb eb eb cb cb cb ebb cbb gbg ebbc cbbe gbg ebbc cbbe a gbg fad bbc aa ebbe fad cbb aa gbg dad ebbc aa cbbe daf gbg aa e daf fa af fad aa dad aa daf aa daf fa af fad aa fad aaaafd aa dfaaaaafd dad dfaaaafd aa dfaaaafd daf dfaaaafd fa dfaaaaafd af dfaaad ``` <!-- end of image -->

Here's an image. My task is to find intersections or areas where lines come close together. I need to zoom in on these areas to get a better look. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0808ff b,#0707feff c,#f65858ff d,#a3a5fbff e,#fdaeadff f,#afd5aeff g,#4e4df6ff ``` ```image ca aca ae a ea ea a ae cc a a ae ae a ea cc a a ac ea ea a a ea ca ae a a ae ac ea a a cc cc a a ea ae ae ea a a ae ac a a cc a a ca ca a a ae ea ea ae a a cc ac a a ae cc ea a a ea ac a a ea ae ae ca a a cc ae a ea ca a a cc ea a g ae ae bgb a ea db dbd ae a db bb a cc db dbd cc a gb bg a ae gb gb ea ea bb dbd a a bg bb ea ac bg gbd ae ea bg bg a a bd gb ac ca bd dbd a c b bb ca db gb a db bg ffcafffffffffffff gb bb fffafffffffffffff gb dbd ffffaffffffffffff bb bb ffffacfffffffffff bb gb fffffafffffffffff bg bg fffffccffffffffff bg bb ffffffaffffffffff bd dbgfffffcafffffffff bd bbfffffafffffffff b fgbfffffaffffffff db fffbgfffaefffffff db ffffbbfffafffffff gb fffffdbdfacffffff gb fffffffbbfaffffff gb ffffffffgbcafffff bb ffffffffffbgfffff bg fffffffffffbbffff bg ffffffffffffcffff bd fffffffffffffffff fffffffffffffffff fffffffffffffffff fffffffffffffffff ``` <!-- end of image --> I'm focusing my attention on this specific region, area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff0404ff b,#0706fdff c,#f97a7fff d,#a1a0feff e,#fec2c2ff f,#f3343fff g,#4a3df1ff ``` ```image fac eaa fac eaae faf eaae caf aac caa fac eaae faf eaae caf aae bd caa bbg aac dbbbd eaa dbbbd fac gbbg eaae dbbbd faf gbbg eaae dbbbd caf dbbbd aac gbbg caa dbbbd fac gbbg eaae dbbbd faf dbbbdeaae gbbgcaf dbbbfae gbbgf dbbbc dbbbd gbg eff e ``` <!-- end of image --> Case closed! This is definitely an intersection point in area A. I've found a single intersection point in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0505ff b,#0808feff c,#fe7c7dff d,#a8a8ffff e,#ffbfbfff f,#fc3e40ff g,#5451fbff ``` ```image e fa acf ae a ea ea a ae ff a a ac ae a ca ff a a ac ca ea a a ea cf ae a a ac fc ea a a cf ff a a ea ae ae ca ea a ac fc a ea ff ae a ca ca a a ac ea ea ae a a ff ac a a ae ff ea a a ca fc ae a ea ae ae ca a a fc ac a ea cf a a ff ea a g ae ae bgb a ea db dbd ac a db bb a ff db gbd ff a gb bg a ae gb gb ca ca bb dbd a a bb bb ea ac bg gbd ae ea bg bg a a bd gb fc cf bd dbd a f b bb cf db gb a db bg ea gb bb ae gb dbd a bb bb ac bb gb a bg bg ff bg bb a bd dbd ca bd bb a b gb ea db bg ae db bb a gb dbd fc gb bb a bb gbcf bb bg bg bb bg f bd ``` <!-- end of image -->

I'm optimistic that I'll find some intersections in this image. Could these regions be concealing intersection points? Let's find out. <!-- image --> ```palette Key,Color ,#fefefeff a,#4946f2ff b,#fc1e1cff c,#0405feff d,#e26e67ff e,#9ea3f4ff f,#b0d6b0ff g,#eef5f1ff ``` ```image g ecc c eca ec ace cg gcc gc eca ce ace c gcc ae eca c ace aa gcc c eca ec ace c ccg ec eca cg ace gc ccg ce eca c ace ae ccg c eca aa ace c ccg ec eca cg ace ec ccg cg eca gc a ce c d ae bbb c bd bb aa bd bb c bd bb ec bd bb gggggggggggggggggggcgggggggggbd bb gffffffffffffffffffecffffffffbdg bb gffffffffffffffffffcffffffffbdfg bb gffffffffffffffffffcfffffffbdffg bb gfffffffffffffffffceffffffbdfffg bb gfffffffffffffffffcffffffbdffffg bb gffffffffffffffffaafffffbdfffffg bb gffffffffffffffffcfffffbdffffffg bb gfffffffffffffffaaffffbdfffffffg bb gfffffffffffffffcffffbdffffffffg bb gffffffffffffffecfffbdfffffffffg bb gffffffffffffffcfffbdffffffffffg bb gfffffffffffffecffbdfffffffffffg bb gfffffffffffffcffbbffffffffffffg bb gfffffffffffffcfbbfffffffffffffg bb gffffffffffffcebbffffffffffffffg bb gffffffffffffcbbfffffffffffffffg bb gfffffffffffaabffffffffffffffffg bb gfffffffffffcbfffffffffffffffffg bb gffffffffffaaffffffffffffffffffg bb gfffffffffbcfffffffffffffffffffg bb gffffffffbdcfffffffffffffffffffg bb gfffffffbbcffffffffffffffffffffg bb gffffffbbfcffffffffffffffffffffg bb gfffffbbfceffffffffffffffffffffg bb gffffbbffcfffffffffffffffffffffg bb gfffbbffcefffffffffffffffffffffg bb gffbbfffcffffffffffffffffffffffg bb gfbbfffaaffffffffffffffffffffffg bb gbbffffcfffffffffffffffffffffffg bb bbffffaafffffffffffffffffffffffg bb ffffffcffffffffffffffffffffffffg bb gffffecffffffffffffffffffffffffg bb gffffcfffffffffffffffffffffffffg bb gggecggggggggggggggggggggggggg bb ce bb gc bb ce bb c b aa c ea c ec cg ``` <!-- end of image --> I'm going to scrutinize area A for any signs of an intersection. <!-- image --> ```palette Key,Color ,#fefefeff a,#453bf4ff b,#fe0607ff c,#0404feff d,#ff9090ff e,#9594fdff f,#f83d44ff g,#f1d9e6ff ``` ```image ecc d ace db gccg dbb aca dbbd gccg dbbd eca dbbd cce dbbd eca dbbd cce dbbd ecc dbbd ace dbbd ecc dbbd ace dbbd gccg dbbd aca dbbd gccg dbbd eca dbbd cce dbbd eca dbbf cce dbbf ecc dbbf ace dbbf ecc dbbf ace dbbf gccg dbbf aca dbbf gccg dbbf eca dbbf cce gbbf eca gbbf ccegbbf eccgbbf acebbf eccbbf acabf gccbf acaf gccf gaca gbcce gbfca gbbcce gbbfcc gbbface gbbfecc gbbfgace gbbfggccg gbbfg aca gbbfg gccg gbbfg eca gbbfg cce gbbfg eca gbbfg cce gbbbg ecc gbbbg ace gfbbg ecc gfbbg ace gfbbg gccg gfbbg aca gfbbg gccg fbbg eca bbg cce dg eca cce ecc ace ``` <!-- end of image --> There's no doubt about it - this is an intersection in area A. I have found one intersection!

<!-- image --> ```palette Key,Color ,#fefefeff a,#5252ffff b,#ff1111ff c,#0505ffff d,#ff8484ff e,#b3b3ffff f,#ff3030ff g,#710f9cff ``` ```image e ecc c eca ec ace c cc c eca ce ace c cc aa eca c ace aa cc c eca ec ace c cc ec eca ce ace c cc ce eca c ace aa cc c eca aa ace c cc ec eca c ace ec cc ce eca c a ce c d aa bbf c bd bf aa bd bf c bd bf ec bd bf c bd bf ec bd bf ce bd bf c bd bf ce bd bf c bd bf aa bd bf c bd bf aa bd bf c bd bf ec bd bf c bd bf ec bf bf ce bf bf c bf bf cebf bf cbf bf agf bf cf bf gg bf bc ff bgc fb bfc fb bfec fb bf ce fb bf c fb bf ce fb ff c fb fb aa fb fb c fb fb aa fb d c fb ec fb c fb ec fb ce fb c fb ce fb c f aa c aa c ec c ``` <!-- 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,#0706fdff b,#ea685eff c,#878df1ff d,#fb0c0bff e,#dfccebff f,#aed5aeff g,#494df6ff ``` ```image e ca agg ea a ae ca ea ae d ae ea bd ed a ac bd ed ac a dd ed a ac db ede gc a ede de a gg bd de gg a dd de a ca db de ca ae ede de a ea bd de ea ae dd de ae a dd de ea ac db db ae a ede dbfffffffffffaffffffffffffffffffggffffffffffff bd dbfffffffffacfffffffffffffffffffaffffffffffffdd dbffffffffaffffffffffffffffffffgaffffffffffdb fdbffffffggfffffffffffffffffffffafffffffffdb ffdbfffffaffffffffffffffffffffffcaffffffbdff fffdbfffggfffffffffffffffffffffffacffffddfff ffffdbffafffffffffffffffffffffffffafffddffff fffffdbcafffffffffffffffffffffffffacfdbfffff ffffffdafffffffffffffffffffffffffffadfffffff ffffffcadfffffffffffffffffffffffffdagfffffff ffffffafddfffffffffffffffffffffffddfafffffff ffffffaffddfffffffffffffffffffffdbffgaffffff fffffacfffddffffffffffffffffffbdfffffaffffff fffffafffffddffffffffffffffffbdffffffcafffff ffffacffffffddffffffffffffffddffffffffafffff ffffaffffffffddffffffffffffdbffffffffffaffff fffggfffffffffddffffffffffdbfffffffffffacfff fffafffffffffffddfffffffbdffffffffffffffafff gg bd dd gg a bd dd a ca bd db gg a bde a ea ca ae ae ea ea ae ac a a ac ac a a gc gg a a gg ca a ae ca ea a ae ea a ae ac ea a ae gg a a ac ca a a gc ea a ae gg ea a ac ca a a gg ea a ae cg ea a ae ca a ae ac ea a ac gc a a gc gg a a gg a ``` <!-- end of image --> Here's a close-up of the area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0807fdff b,#fc3b3dff c,#a5a5ffff d,#fe0606ff e,#f7d6deff f,#fb8d90ff g,#5953f9ff ``` ```image f aac gag df caa eaac ddf aac gag fddf caa aac fddf aac caa b fddf caa aac ebd fddf gag caa eddd fddf caa aag fddbe fddf gag caae fddb fddb eaae gag bddf fddb gag eaac ebddf fddb aac gag fddde fddb gag aac fddbe fddb aac gaa bddf fddb caa aac ebddf eddbaac caaeddde edbaa aagdbe eaag faab caadb ebdaag gagddb edddfaae caa eddb fddbe gag gag eddb fddb eaac eaae eddbe bddf gaa gag eddbe ebddf aac aac eddbe eddde caa gag eddbe fddbe aac aac eddbe bddb caa caa ebdde ebddf gag aac ebdde eddde caae caa ebdde fddbe gag aac ebdde fddb eaac caa ebdde bddf gag gag ebdde ebddf aac caa bdde fddde caa gag bdde fddbe aac ``` <!-- end of image --> The evidence is clear: this is an intersection in area A. The image features two intersection points.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0504feff b,#ff4e4eff c,#8181ffff d,#ff0808ff e,#c5c5ffff f,#ffb3b3ff g,#3e3efeff ``` ```image e ca acg ea a a ca ea ae d ae ea fd fd a ae bd fd ac a dd d a gc db d gc a fdf d a gg bd df cg a dd df a ca db df cg a fdf df a ea fd df ea ae bd df a a db df ea ac df df ae a fdf df a gg bd df ac a dd db a ca db db gc a fdf db a ea bd db cg ae dd db a a db dbcg ac df da ad eab bag a db dd a ea db db cg ae dd fdf a a dd bd ea ac dd dd ae a dd db ea gc bd fdf ac a bd fd a cg bd bd gc a bd db a cg bd df cg a bdf a ea ca a ae ea ea ae ae a a ac gc a a gc gg a a cg ca a a cg ea a ae ea a a ac ea a ae gg a a ac ca a a gc ea a ae cg a a ac cg a a gg ea a a cg ea a ae ea a ae ac ea a ac gc a a gc cg a g cg a ``` <!-- end of image -->

I'm curious to see if this image contains any intersection points. Could these regions be concealing intersection points? Let's find out. <!-- image --> ```palette Key,Color ,#fefefeff a,#3942e6ff b,#d4745fff c,#fa0c0aff d,#7088ceff e,#b2d7b1ff f,#a2cca2ff g,#0505fcff ``` ```image ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff e feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef aafeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef dgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef gdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef fgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef fageeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef fegfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef fefgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef feeaaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef feeegeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef feeedgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef feeeegdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef feeeeegeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef feeeeedgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef feeeeeegdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef feeeeeefgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef feeeeeeeaaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef feeeeeeeegfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef feeeeeeeedgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef feeeeeeeeegdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef feeeeeeeeeegeeeeeeeeeeeeeeeeeeeebcceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef feeeeeeeeeedgeeeeeeeeeeeeeeeefcccfbceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef feeeeeeeeeeegdeeeeeeeeeeeeecccbeeeecbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef feeeeeeeeeeeegeeeeeeeeeebccbeeeeeeeeceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef feeeeeeeeeeeeaaeeeeeebccbeeeeeeeeeeefceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef feeeeeeeeeeeeegfeefcccfeeeeeeeeeeeeeebceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef feeeeeeeeeeeeefgbccbeeeeeeeeeeeeeeeeeecbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef feeeeeeeeeeeebcgaeeeeeeeeeeeeeeeeeeeeeeceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef feeeeeeeeebccceegeeeeeeeeeeeeeeeeeeeeeefceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef feeeeeefcccfeeeedgeeeeeeeeeeeeeeeeeeeeeecceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef feeeebccbeeeeeeeegdeeeeeeeeeeeeeeeeeeeeeecbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef febccbeeeeeeeeeeeegeeeeeeeeeeeeeeeeeeeeeeeceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef ecccfeeeeeeeeeeeeeeaaeeeeeeeeeeeeeeeeeeeeeebceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef ccbeeeeeeeeeeeeeeeeeegfeeeeeeeeeeeeeeeeeeeeeecceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeefgeeeeeeeeeeeeeeeeeeeeeeecbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeegaeeeeeeeeeeeeeeeeeeeeeeeceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeegeeeeeeeeeeeeeeeeeeeeeeebceeeeeeeeeeeeeeeeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeedgeeeeeeeeeeeeeeeeeeeeeeecceeeeeeeeeeeeeeeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeegdeeeeeeeeeeeeeeeeeeeeeeecbeeeeeeeeeeeeeeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeegeeeeeeeeeeeeeeeeeeeeeeeeceeeeeeeeeeeeeeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeageeeeeeeeeeeeeeeeeeeeeeebceeeeeeeeeeeeeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeegfeeeeeeeeeeeeeeeeeeeeeeecceeeeeeeeeeeeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeefgeeeeeeeeeeeeeeeeeeeeeeeecbeeeeeeeeeeeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeaaeeeeeeeeeeeeeeeeeeeeeeeeceeeeeeeeeeeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeegeeeeeeeeeeeeeeeeeeeeeeeebceeeeeeeeeeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeedgeeeeeeeeeeeeeeeeeeeeeeeecceeeeeeeeeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeegdeeeeeeeeeeeeeeeeeeeeeeeecbeeeeeeeeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeegeeeeeeeeeeeeeeeeeeeeeeeeeceeeeeeeeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeedgeeeeeeeeeeeeeeeeeeeeeeeebceeeeeeeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeegdeeeeeeeeeeeeeeeeeeeeeeeecceeeeeeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeefgeeeeeeeeeeeeeeeeeeeeeeeeecfeeeeeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeaaeeeeeeeeeeeeeeeeeeeeeeeeeceeeeeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeegfeeeeeeeeeeeeeeeeeeeeeeeebceeeeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeedgeeeeeeeeeeeeeeeeeeeeeeeeecbeeeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegdeeeeeeeeeeeeeeeeeeeeeeeeecfeeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegeeeeeeeeeeeeeeeeeeeeeeeeeeceeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedggggaaaaaddddffeeeeeeeeeeebceeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeffdddddaaaaagggggggggggggggggggggaaaadddddf feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecfeffdddddaaaagg feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefceeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebceeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecbeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecfeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefceeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebceeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecbeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecfeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefceeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebceeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecbeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecfeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefceeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebceeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecbeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecfef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefcef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebcf feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecb feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeec feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef ``` <!-- end of image --> I'm eager to see what's happening in this magnified view of area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#4f4fffff b,#ff4646ff c,#fe0505ff d,#9b9afdff e,#ff8f8fff f,#e9d5ebff g,#0605feff ``` ```image g g aa fgd ag ag g aa fgd ag fgd ga ag fgd g gd ga gg gd ga gg ga fgf gg aa fecce fg ecccbcf aa fecccf cc fgd ecccb fce gg feccbf c dgf feccce cb fgd fbccb cc ag ecccb cb fgdcccb fce feccgf bc ecccbgf cb feccbf fgd cf ecccb ag cb fbccb fgd cc ecccb ga bb ebccb gg fcb cce gd ecf b dgf bb gg cc ga bb fg fc gd ecf dgf cb gg ece dgf ecf fgd cc gg ec dgf c fgd ece gg cc fgd fce g cc gf bc fgd ecf gg cc fgd fce dg ec gg bb fgd cc dg bc gd fce dg cc gg cb ag fce dgf bc gg fc dggggggaaaaadddddffff cf fffddddddaaaaagggggggggggggggggggggggggggaaaaaadddddf fffddddddaaaaagggggggggggggggggggg bc cc ecf fc ce cb cc ecf cc fce cb cc ec ce ece bc fce cc bc ec bb fce bcf bb c b ``` <!-- end of image --> Wow! I can see an intersection so clearly in area A! There's for sure two intersections on the image you sent me.

<!-- image --> ```palette Key,Color ,#fefefeff a,#4745fdff b,#ff4c4cff c,#ff0505ff d,#8787ffff e,#ffaaaaff f,#c2c2ffff g,#0605feff ``` ```image f aa g fg gd g dg gf g aa g fg gd g dg gf g aa g fg gd g ecc dg eccb bc gf bcce ce g bcce c aa eccb ec g ccc bc fgbcce ce ecga c eccb g ec bcce dg bc bcce gf ce eccb g c eccb aa ec cce gf bb fg ce aa c g ec fg bb gd ce g c dg ec gf bb g ce aa c g ec fg bb gd ce g c dg ec gf bb g ce aa c g ec fg cb gd ce g c dggggaaaadddffff ec fffddddaaaagggggggggggggggggggggaaaddddfff ce fffddddaaaag c ec cb ce c ec cb c c bc cb c c bc cb c c bc ce c ``` <!-- end of image -->

This image looks interesting. I wonder if there are any intersections hidden in there? There are 1 regions I'd like to highlight in the image. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd0c0bff b,#0a0bfdff c,#ebc4d7ff d,#f66a66ff e,#7378f2ff f,#98c595ff g,#b1d7b1ff ``` ```image d da ca a ac ac ad ad aa da da ca ca a ac ac ad ad aa da da ca ca a ac ac ad ad aa da da ffffffffffffffffffgca ggggggggggggggggggfa ggggggggggggggggggac gggggggggggggggggaf ggggggggggggggggadf gggggggggggggggadgf ggggggggggggggaaggf gggggggggggggaagggf ggggggggggggdaggggf gebbbbeggggdagggggf ebbbeggfbbbgfaggggggf ebbecggggggggebbeggggggf cbbbe gggggggggafbbbggggf ebbbe ggggggggafgggebbegf ebbbc gggggggadgggggggbbb cbbbe ggggggadggggggggggebbe ebbbe gggggaagggggggggggf bbb ebbbc ggggaaggggggggggggf ebbe ebbe gggaagggggggggggggf ebbc cbbbe ggaaggggggggggggggf cbbe bc gadgggggggggggggggf ebbc cadggggggggggggggggf cbbe cafgggggggggggggggggf ebbc da ffffffffffffffffffg cbbe aa ebbe aa bbb ad eb cac da da aa ad ac cac da aa aa ad cac da da aa ad ac cac da aa aa ad ``` <!-- end of image --> I'm determined to find out if an intersection exists in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0505ff b,#0805fcff c,#fdc8c9ff d,#ff8b8bff e,#5554feff f,#a7a7feff g,#fb4245ff ``` ```image g ga daa daad caad caag caag caag gag gaac gaac daac ffeef daad febbbbbbbef daad febbbbbeffebbbbf caad bbbbef febbbbef caag eff febbbbeaag ebbbbbf gbbbbbe gaacebbbbef gaac febbbbef daac fbbbbef daad febbbbe daad fbbb caad fe caag caag gag gaa gaac gaac gaac cgaac caaac daag daag gaad gaad aac gc ``` <!-- 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,#ff0505ff b,#0707feff c,#fdc9caff d,#ff8686ff e,#5656ffff f,#ababfeff g,#ff3c3cff ``` ```image d da ca ca ac ac ad ag gg ga da da ca a ac ac ad ag gg ga da ca ca a ac ad ad ag gg ga da ca ca ac ac ad ad ag ga da fbbbbf da fbbbf fbbe ca ebbe ebbf fbbbe acbbe fbbbf ac fbbf ebbef ad bbe ebbe ag fbbf fbbbf gg ebb ebbbf ga fbbe ebbe ga ebb fbbbf aa fbbe bf ag ebbf ad fbbe cac ebbf da fbbe ga ebbf ag bbe ad fb cac da ga aa ag ad cac da ga ag ad cac da ga aa ag ad cac da ga ag ad ``` <!-- end of image -->

I'm curious to see if this image contains any intersection points. The image has some tight areas where segments are too close. I should investigate those closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#ee5653ff b,#1112faff c,#6c73efff d,#fba8a6ff e,#fe0707ff f,#97c499ff g,#b1d6b1ff ``` ```image d e ed e e de e ffffffffffffaefg ggggggggggggeggf gggggggggggaaggf gggggggggggegggf ggggggggggeagggf ggggggggggeggggf gggggggggefggggf ggggggggdegggggf ggggggggeggggggf gggggggaeggggggf ggggccccccccccccccbbbbbbbbbbbbbbb gcccbbbbbbbbbbbbbbbbbbbbbbbbbbcccccccccccccccccaaffffffgf fffffffffcccbbbbbbbbbbbbbbcccg ggggggeggggggggf gggbbbbbbbcccg gggggeaggggggggf ggggggggggggf gggggegggggggggf ggggggggggggf ggggefgggggggggf ggggggggggggf gggfeggggggggggf ggggggggggggf gggegggggggggggf ggggggggggggf ggaegggggggggggf ggggggggggggf ggeggggggggggggf ggggggggggggf gaaggggggggggggf gggaggggggggf fegggggggggggggf gggaegggggggf ea ggggefggggggf e gggggeggggggf ed gggggaegggggf de ggggggeaggggf e gggggggeggggf de gggggggdegggf e ggggggggeaggf aa gggggggggefgf e ggggggggggegf aa ggggggggggaef e gggggggggggea ed e e de e ea de e e de ae aa e ed aa e e ae ed ed e e ed de de ea e e de e e ae aa ed e e ed de e ea ed e de de e aa de ed e e aa ae e ed ea e e de ed ea de e e e de ae e ed aa e e de aa ed e eed de ``` <!-- end of image --> I'm focusing my attention on this specific region, area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff4343ff b,#0606ffff c,#a7a7ffff d,#ff8585ff e,#ff0606ff f,#ffc0c0ff g,#5656ffff ``` ```image ccccccgg gggbbbbbbbbbbbbbb bbbbbbbbbbbgggggc ccccc dd feef aea eed feef aee eea feef dee aea feed deef aea eed feef dee aea feed deef aea eed feef aee ee fe ``` <!-- end of image --> Area A does not contain any intersection points. Let's move forward and inspect another region. Time to investigate area B up close. <!-- image --> ```palette Key,Color ,#fefefeff a,#fb2e32ff b,#0806fcff c,#a8a8ffff d,#f86b72ff e,#ff0303ff f,#ffb7b7ff g,#4a4afeff ``` ```image eef dea eef dea feef aed fee aed fee eef dea eef dea feef aed fee aed fee eed dea eef gggggggggggggggbbbgbbbbbbbbbbbb bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb ccccccccccccccdadcccccccc feef aed fee aed dea eef dea feef dea feef aed fee aed dee eef dea eef dea feef ``` <!-- end of image --> An intersection is present within area B. There's one and only one intersection present in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fa3f43ff b,#0a09feff c,#a9a9ffff d,#ff8484ff e,#ff0505ff f,#ffc7c7ff g,#5757ffff ``` ```image d e ed fe ef fe e da e aa e ed fe ef fe e de cccccccccccccggggggggggggbbbbbbbbbb cccgggbbbbbbbbbbbbbbbbbbbbbbgggggggggggggcccccccaacccc cccggbbbbbbbbbbbbgggccc e bbbbbbggccc ed e ef fe e de e aa d e aa ad ef e e ef de fe ed ef e de fe e aa da ef e fe ad ae e ef ed e fe de ef ed fe e e fe da aa e ef aa e e de ed ed fe e ef fe fe aa e ef de fe e aa aa ef e e ed de e ed ef e fe fe e aa de ef e e aa de e ed ad e e fe ef ea fe ef ef fe de aa e ef da e e de ad ed e eed fe ``` <!-- end of image -->

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

<!-- image --> ```palette Key,Color ,#fefefeff a,#3939ffff b,#ff0404ff c,#ffaeaeff d,#8080ffff e,#ff5757ff f,#0404ffff g,#cacaffff ``` ```image g gdfffffg gdffffdg gf gaffffdg df dafffad aa gdffffag fd gdffffdg fg affffdg gf d df aa fd f gf df aa fd f gf df aa fd f gf df aa fd f gf df aa fg f gf df aa fg f gf df aa fg f gf df fa fg f gf df fa fg f gf df fa f ccceeebbbb ccceeebbbbbbbbbbbbeeeccc ccceeebbbbbbbbbbbbeeeccc cebbbeeeccc ebbbc ebbbe cbbbe cbbbec cebbec cebbbc ebbbc ebbbe bbe ``` <!-- end of image -->

This image seems promising for intersection detection. Could these regions be concealing intersection points? Let's find out. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd0505ff b,#626ae6ff c,#eb9b91ff d,#b1d7b1ff e,#090afcff f,#97c698ff g,#f34843ff ``` ```image c fffffffffffffffffffffffffffffffffffffffffaa dddddddddddddddddddddddddddddddddddddddaafd dddddddddddddddddddddddddddddddddddddgacddd dddddddddddddddddddddddddddddddddddgagddddd dddddddddddddddddddddddddddddddddcaaddddddd ddddddddddddddddddddddddddddddddaaddddddddd ddddddddddddddddddddddddddddddaacdddddddddd ddddddddddddddddddddddddddddgagdddddddddddd ddddddddddddddddddddddddddcagdddddddddddddd ddddddddddddddddddddddddfaaddddddddddfbbeee dddddddddddddddddddddddaafdbbbeeeeeeeebbfdd eeebbbd ddddddddddddddddfbbeeeeeeeeebbfdddddddddddd dbbbbeeeeeeeeeeeeebbbd ddddddfbbeeeeeeeeebbagddddddddddddddddddddd dbbbeeeeeeeeeeeeeeeeeeeeebbbdddddddcaaddddddddddddddddddddddd dfdddddddddddddddaaddddddddddddddddddddddddd ddddddddddddddaacdddddddddddddddddddddddddd ddddddddddddgagdddddddddddddddddddddddddddd ddddddddddcagdddddddddddddddddddddddddddddd ddddddddfaadddddddddddddddddddddddddddddddd dddddddaafddddddddddddddddddddddddddddddddd dddddgacddddddddddddddddddddddddddddddddddd dddgagddddddddddddddddddddddddddddddddddddd dcaaddddddddddddddddddddddddddddddddddddddd aaddddddddddddddddddddddddddddddddddddddddd cacffffffffffffffffffffffffffffffffffffffffff a gg a a gg a a gg a a gg a a gg a ac ga a ac ca a ac ca a ac ca a ac ca a ac ca a ac ca a ac ca a ag ca a gg a a gg a a gg a a gg a a ``` <!-- end of image --> Let's take a closer look at area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0505ff b,#4d48f9ff c,#ff9393ff d,#9b98fbff e,#0404feff f,#efd5e5ff g,#fa4348ff ``` ```image fg fgaa caaag caaagf cgaagc fgaaac fgaaac caaagf caaagf fgaaac fgaaac caaagf caaagf cgaagc fgaaac fgaaac caaagf caaagf fgaaac f fgaaac fdddbbbeeee caaagf fdddbbbeeeeeeeeeeeeee caaagf ffdddbbbeeeeeeeeeeeeeebbbddddf fdggbbbbeeeeeeeeeeeeeebbbdddff fddddbbbeeeeeeeeeeeeeebbbdddff fdddbbbeeeeeeeeeeeeeeebbbdddf ffdddbbbeeeeeeeeeeeeeeebbbddgaagf ffdddbbbeeeeeeeeeeeeeebbbdddff caaagf beeeeeeeeeeeeeebbbdddff fgaaac eeeeebbbdddff fgaaac df caaagf caaagf cgaagc fgaaac fgaaac caaagf caaagf fgaaac fgaaac caaagf caaagf cgaagc fgaaac fgaaac caaagf caaagf fgaaac fgaaac caaagf ``` <!-- 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,#fe0505ff b,#5757ffff c,#fa888cff d,#afafffff e,#0505ffff f,#ffccccff g,#fe4343ff ``` ```image c faa aaf gac cag faa aa gaf gac cag faa ddbeee aaf dbbeeeeeeeebdd eebbbddd dbbeeeeeeebbdd dddbbbeeeeeeeeeeeebbbddd ddbbeeeeeeebbcag dddbbbeeeeeeeeeeeeeeeeeeeebbd faa dd aa gaf gac cag faa aaf gac cag faa aa faf a gg fa a gg fa af gg fa af gg a af gg a af gg a af ca a af ca a ac ca a ac ca a ac ca a ac fa a ac fa a ac fa a gg fa a gg fa af gg fa af gg a af ``` <!-- 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,#e77165ff b,#0708fdff c,#4d56edff d,#fb0a09ff e,#b1d7b1ff f,#99c399ff g,#b1b1ffff ``` ```image a ad d d de da da ad ad ed feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefdf eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedff eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedaef eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedaeef eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeddeeef c eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeadeeeef bb eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeadeeeeef bb eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefdeeeeeef bc eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedfeeeeeef bc eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedaeeeeeeef bg eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedaeeeeeeeefbg eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeddeeeeeeeefbg eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeadeeeeeeeefbf eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeadeeeeeeeecbef eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefdeeeeeeeecbeef eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedeeeeeeeecbeeef eeeeeeeeeeeeeeeeeeeeeeeeeeeeeedfeeeeeeebbeeeef eeeeeeeeeeeeeeeeeeeeeeeeeeeeedaeeeeeeebbeeeeef eeeeeeeeeeeeeeeeeeeeeeeeeeeeddeeeeeeebceeeeeef eeeeeeeeeeeeeeeeeeeeeeeeeeeddeeeeeeebceeeeeeef eeeeeeeeeeeeeeeeeeeeeeeeeeadeeeeeeebceeeeeeeef eeeeeeeeeeeeeeeeeeeeeeeeefdeeeeeeebfeeeeeeeeef eeeeeeeeeeeeeeeeeeeeeeeeedeeeeeefbfeeeeeeeeeef eeeeeeeeeeeeeeeeeeeeeeeedfeeeeefbeeeeeeeeeeeef eeeeeeeeeeeeeeeeeeeeeeedaeeeeecbeeeeeeeeeeeeef eeeeeeeeeeeeeeeeeeeeeedaeeeeecbeeeeeeeeeeeeeef eeeeeeeeeeeeeeeeeeeeeddeeeeecbeeeeeeeeeeeeeeef eeeeeeeeeeeeeeeeeeeeadeeeeebbeeeeeeeeeeeeeeeef eeeeeeeeeeeeeeeeeeeadeeeeebbeeeeeeeeeeeeeeeeef eeeeeeeeeeeeeeeeeefdeeeeebceeeeeeeeeeeeeeeeeef eeeeeeeeeeeeeeeeeedeeeeebceeeeeeeeeeeeeeeeeeef eeeeeeeeeeeeeeeeedaeeeebceeeeeeeeeeeeeeeeeeeef eeeeeeeeeeeeeeeedaeeeebfeeeeeeeeeeeeeeeeeeeeef eeeeeeeeeeeeeeeddeeefbfeeeeeeeeeeeeeeeeeeeeeef eeeeeeeeeeeeeeadeeefbeeeeeeeeeeeeeeeeeeeeeeeef eeeeeeeeeeeeeadeeecbeeeeeeeeeeeeeeeeeeeeeeeeef eeeeeeeeeeeefdeeecbeeeeeeeeeeeeeeeeeeeeeeeeeef eeeeeeeeeeeedeeecbeeeeeeeeeeeeeeeeeeeeeeeeeeef ddddddddaaae eeeeeeeeeeedfeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeef aaadddddddddaaae eeeeeeeeeedaeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeef aaaddddddddddaafdaeebceeeeeeeeeeeeeeeeeeeeeeeeeeeeeef fffffaadddffbcfffffffffffffffffffffffffffffffe bg bg gbg bb bc cb bc cbg bb gbg bb gbc cb bc cbg bb gbg bb gbc cb bc cbg bb gbg bb gbg bb bc ``` <!-- end of image --> I'm focusing my attention on this specific region, area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff4444ff b,#0808ffff c,#5858ffff d,#ff0606ff e,#ff8888ff f,#ffc7c7ff g,#b8b8ffff ``` ```image f fd ad add addf eddf edde fdde fdda dda add addf eddf edde fdde fdda fdda ada addf addf eddf fdde fdde fdda dda g add gb addf gbb eddf gbbc edde gbbc fdde cbbc fdda cbbc dda cbbg ada cbbg addf cbbg eddf bbbg eddf gbbbg fdde gbbb fdda gbbc fdda gbbc ada gbbc addf cbbc addf cbbc eddf cbbg edde cbbg fdde cbbg fdda bbbg dda gbbbg add gbbb addf gbbc eddf gbbc edde gbbc fdde cbbc fdda cbbc dda cbbg ada cbbg addf cbbg eddf bbbg eddf gbbbg fdde gbbb fdde gbbc fdda gbbc ada gbbc add cbbc addf cbbc eddf cbbg edde cbbg fdde cbbg fdda bbbg dda gbbbg add gbbb addf gbbc eddf gbbc edde gbbc fdde cbbc fdda cbbc fdda cbbg ada cbbg addf cbbg addf bbbg eddf gbbbg fdde gbbb aaeeefff fdde gbbc dddddddddddaaaeeefffdda gbbc ``` <!-- end of image --> Unfortunately, there's no intersection inside area A. I've examined the entire image, and there are zero intersections present.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff3f3fff b,#0909ffff c,#5858ffff d,#ff0404ff e,#ff8888ff f,#ffc9c9ff g,#b6b6ffff ``` ```image e ed fd d df de da ad ed fd d df de da aa c ed bb fd bb fd bc df bc df bg de bg aa gbg ad gb ed gb fd cb d cb df bb de bb da bc ad bc ed bg fd bg d gbg df gb de gb da cb aa cb ed bb fd bb fd bc d bc df bg de bg da gbg ad gb ed gb fd cb d cb ddddddddaeef df bb feeaaddddddddaeef de bb feeaaddddddddaeefda bc feeada bc bg bg gbg bb gbc cb bb cbg bb gbg bb gbc cb bc cbg bb gbg bb gbc cb bc cbg bb gbg bb gbc bb bc ``` <!-- end of image -->

Time to put on my detective hat and find those intersection points! There are 1 areas where the lines seem to converge. We should take a closer look at area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0505fdff b,#fb0908ff c,#373bebff d,#df605aff e,#b1d7b1ff f,#9ec09cff g,#7883e8ff ``` ```image e ag a a a a gc a a ga cg a a gc ag a a cg a a ga ag a a cg a a a ag a a ga a a ga gc a a cg cg a d a feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeageeeeeeeedb ag feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefaeeeeeeeefbe a feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeafeeeeeeeebfe a feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegaeeeeeeeebdee a feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeeeeedbeee a feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecceeeeeeefbeeee ga feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeeeeebeeeee a feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeageeeeeeebdeeeee gc feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefaeeeeeeebbeeeeee a feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeafeeeeeedbeeeeeee cg feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegaeeeeeeebeeeeeeee a feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeeeebfeeeeeeee ag feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecceeeeeebdeeeeeeeee a feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeeedbeeeeeeeeee a feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeageeeeefbeeeeeeeeeee a feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefaeeeeeebeeeeeeeeeeee a feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeafeeeeebdeeeeeeeeeeee ga feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegaeeeeebbeeeeeeeeeeeee a feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeedbeeeeeeeeeeeeee gc feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecceeeeebeeeeeeeeeeeeeee a feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeebfeeeeeeeeeeeeeee cg feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeageeeebdeeeeeeeeeeeeeeee a feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefaeeeedbeeeeeeeeeeeeeeeee ag feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeafeeefbeeeeeeeeeeeeeeeeee a feeeeeeeeeeeeeeeeeeeeeeeeeeeeeegaeeeebeeeeeeeeeeeeeeeeeee a feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeebdeeeeeeeeeeeeeeeeeee eafeeeeeeeeeeeeeeeeeeeeeeeeeeeeecceeebbeeeeeeeeeeeeeeeeeeee afeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeedbeeeeeeeeeeeeeeeeeeeee gaeeeeeeeeeeeeeeeeeeeeeeeeeeeeageeebeeeeeeeeeeeeeeeeeeeeee aeeeeeeeeeeeeeeeeeeeeeeeeeeefaeeebfeeeeeeeeeeeeeeeeeeeeee cceeeeeeeeeeeeeeeeeeeeeeeeeeafeebdeeeeeeeeeeeeeeeeeeeeeee faeeeeeeeeeeeeeeeeeeeeeeeeegaeedbeeeeeeeeeeeeeeeeeeeeeeee fcgeeeeeeeeeeeeeeeeeeeeeeeeaeefbeeeeeeeeeeeeeeeeeeeeeeeee feaeeeeeeeeeeeeeeeeeeeeeeecceebfeeeeeeeeeeeeeeeeeeeeeeeee feageeeeeeeeeeeeeeeeeeeeeeaeebdeeeeeeeeeeeeeeeeeeeeeeeeee feeaeeeeeeeeeeeeeeeeeeeeeagedbeeeeeeeeeeeeeeeeeeeeeeeeeee feeafeeeeeeeeeeeeeeeeeeefaefbeeeeeeeeeeeeeeeeeeeeeeeeeeee feegaeeeeeeeeeeeeeeeeeeeafebeeeeeeeeeeeeeeeeeeeeeeeeeeeee feeeaeeeeeeeeeeeeeeeeeegaebfeeeeeeeeeeeeeeeeeeeeeeeeeeeee feeegaeeeeeeeeeeeeeeeeeaebdeeeeeeeeeeeeeeeeeeeeeeeeeeeeee feeeeaeeeeeeeeeeeeeeeeccdbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee feeeecceeeeeeeeeeeeeeeafbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee feeeeeaeeeeeeeeeeeeeeagbfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee feeeeecgeeeeeeeeeeeefabdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee feeeeeeaeeeeeeeeeeeeadbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee bd feeeeeeageeeeeeeeeegabeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee dbbd feeeeeefaeeeeeeeeeeabeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee dbbbd feeeeeeeafeeeeeeeeccdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee dbbbe feeeeeeegaeeeeeeeeabeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee ebbbd feeeeeeeeaeeeeeeeadeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee dbbbe feeeeeeeegceeeeefaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee ebbbdfeeeeeeeeeaeeeeeafeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee dbbbdeeeeeecceeedaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee fefbbbdfeeeaeedaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee feeeeedbbbdcgfcceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee feeeeeeeefdbabaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee feeeeeeeeeeeaageeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee feeeeeeeeeeefaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee ``` <!-- end of image --> This close-up of area A is like examining a piece of evidence. <!-- image --> ```palette Key,Color ,#fefefeff a,#0706fdff b,#fe0606ff c,#4e47f8ff d,#fe8f8fff e,#e8d9f0ff f,#f43b46ff g,#9999feff ``` ```image ga f eag db eaa ebf cac ff aae dbe ga bbd eag bf ca fbe cac ebb gaae ebbf aag fbf aa bbe cc ebd eae fb ca fbb aag ebd aa bf eag fb cc dbb ca bbd gaa bf aag fbe aag ebb ac bbf eae bb gae dbd aa ebb gaa fbf aag dbbe eae ebd cc ff gae fb gaa bbd eaag ebf cac ff aae dbe gae ebbd ag fbf ga bbe cac ebd aae ebb ac fbf ag dbd g ga ebd a eaa fb ag cac fbb aa ac bbd ca gae ebf eae ag ff eae eaa dbb ag cac bbd aa eaae bf aag cac fbe aa ag ebb ga ga bbf eae eag bb eae eaa dbd ac cac ebb aae aae fbf gaa ga bbd aag eag ebd gaa ca bf aa eaa fb eae gaaebbd cc aagebf eae aaeff aae ccdbb cag eagbbd gaa cafbf aa gaabbe ag aabd gc eafb eae cabf aae cabd cac gaad gaae aac gaa aafe aa aad ga eaf ag cc bfe eae daa bbbbfe ac faa edbbbbfdd aae aag dfbbbbdd gaa dbag dfbbbbfeca ebcc dbbbbfaebfae edbbafbaa aaag aac aag ``` <!-- end of image --> Oh my, look at that! It's an intersection in area A! I can confirm there's two intersections in there.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0706fdff b,#fe0506ff c,#4b4bfeff d,#ff9999ff e,#e1d3f1ff f,#f6464eff g,#9292ffff ``` ```image e ag a ae a ea ga a a ga cc a a gc ag a ea cg ae a ga ag a a cc ae a ea ag a ea ga ae a ga gc a a cc cg a f a ag db ag ea b a ae be ae ga bd ea a fb a cc eb ga a b a ag bd cc ea ff a ae db cg ga b a a be ag cc bf a a fb ae ag eb ea ea b a ae bd ga ga ff a a db cc cc b a a be cg ag bf a ea fb ag ae eb ea ga b ae a bd ea cc ff a a db ga ag b a ea bd cc ae bf a ga db cg a eb a cc be ag a bd ea ag fb ae ea db ea ae b a ga bd ga a bf a ccdb cc aeb a agbe cg eabd a afb bd ag gab efbbfe ea ab dbbbd ae cad fbbbd ea af dbbbf a af fbbbd ga ea dfbbf a ae dbbbd cc fa efbbfe a fa dbbbdcgeac efbaba aag ea ``` <!-- end of image -->

I'm examining this image closely. My goal: find any and all intersections. I've spotted 1 narrow regions that might be worth examining further. Let's call them area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd0807ff b,#6d78e7ff c,#feb6b5ff d,#b1d7b1ff e,#e85c53ff f,#9cc396ff g,#0b0cfcff ``` ```image c ac a ac ca g a bg ca g a gb ee bg a g ee gb a bg ac g a gb ac bg ca g a gd ca bg a g ee gd e a bg ca ee g a a g ac ac bg ea a g ca ac g a ca gg ae a g ea ca g a a gb ac ee g ae a g ca ee fffffffffffffffffffffffffffffffffffffggffffffffa a ddddddddddddddddddddddddddddddddddddfgddddddddae ac ddddddddddddddddddddddddddddddddddddgddddddddead a dddddddddddddddddddddddddddddddddddgbdddddddfadd ac ddddddddddddddddddddddddddddddddddbgddddddddaddd ca ddddddddddddddddddddddddddddddddddgddddddddaeddd a dddddddddddddddddddddddddddddddddgbdddddddeadddd ca ddddddddddddddddddddddddddddddddbgddddddddaddddd a ddddddddddddddddddddddddddddddddgddddddddafddddd ee dddddddddddddddddddddddddddddddgbdddddddaedddddd a ddddddddddddddddddddddddddddddbgdddddddeaddddddd ee ddddddddddddddddddddddddddddddgddddddddadddddddd a dddddddddddddddddddddddddddddgbdddddddafdddddddd ac ddddddddddddddddddddddddddddbgdddddddeaddddddddd a ddddddddddddddddddddddddddddgdddddddfadddddddddd acdddddddddddddddddddddddddddgbdddddddaddddddddddd caddddddddddddddddddddddddddbgdddddddaeddddddddddd afdddddddddddddddddddddddddgdddddddeadddddddddddd caddddddddddddddddddddddddgbdddddddaddddddddddddd adddddddddddddddddddddddbgdddddddafddddddddddddd eeddddddddddddddddddddddgdddddddaedddddddddddddd dadddddddddddddddddddddgbddddddeaddddddddddddddd ggb daedddddddddddddddddddbgdddddddadddddddddddddddd ggg ddadddddddddddddddddddgdddddddafdddddddddddddddd bggd ddaedddddddddddddddddgbddddddeaddddddddddddddddd ggb dddaddddddddddddddddbgddddddfadddddddddddddddddd bgg dddafdddddddddddddddgdddddddaddddddddddddddddddd dggb dddfaddddddddddddddgfddddddaeddddddddddddddddddd bgg ddddadddddddddddddbgddddddeadddddddddddddddddddd bggb ddddeaddddddddddddgdddddddaddddddddddddddddddddd ggg dddddadddddddddddgfddddddafddddddddddddddddddddd bggbdddeedddddddddggddddddaedddddddddddddddddddddd fggbddadddddddddgddddddeaddddddddddddddddddddddd dddbggeedddddddgdddddddadddddddddddddddddddddddd dddddbggbdddddggddddddafdddddddddddddddddddddddd dddddddagggddfgddddddeaddddddddddddddddddddddddd ddddddddadbgggddddddfadddddddddddddddddddddddddd ddddddddafdddbddddddaddddddddddddddddddddddddddd ddddddddfadddddddddaeddddddddddddddddddddddddddd dddddddddaddddddddeadddddddddddddddddddddddddddd dddddddddeadddddddaddddddddddddddddddddddddddddd ddddddddddaddddddafddddddddddddddddddddddddddddd ddddddddddeeddddaedddddddddddddddddddddddddddddd dddddddddddadddeaddddddddddddddddddddddddddddddd dddddddddddaeddadddddddddddddddddddddddddddddddd ffffffffffffafafffffffffffffffffffffffffffffffff aae a ``` <!-- end of image --> Let's zoom in on area A to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0606ff b,#5756fdff c,#ff8484ff d,#aeaeffff e,#fc4245ff f,#ffc6c6ff g,#0807feff ``` ```image dggd fa ggb ea bgg caa dggd faaf ggb aac bgg eae dggd caaf ggb faac bgg aae dggd eaa ggb caaf bgg faac dggd eae ggb caa bgg faaf dggd aac ggb eae bgg caaf dggd faac ggb aae bgb eaa dggd caaf ggd faac bgb eae dggd caa ggd faaf bgb aac dgg eae ggd caaf bgb faac dgg aae f ggd eaa c bgb caaf a dgg faac ac dggd eae aa bgb caa aac bgg faaf caa dggd aac aaf ggb eae cae bgg caaf aaf dggd faac cae ggb aae faaf bgg eaa eac dggd caaf faa ggb faac eac bgg eae faa dggd caa aac ggb faaf caa bgg aac aaf dggd eae cae ggb caaf aaf bgg faac eae dggd aae faaf ggb eaa eac bgg caaf faa dggd faac eac ggb eae faa bgg caa aac dggd faaf caa ggb aac aaf bgb eae cae dggd caaf gb aaf ggd faac gggbd eae bgb aae dbggggd faaf dgg eaa bggggbd eac ggd caaf dbggggd faa bgb faac dbggggbeac dgg eae dggggge ggd caa dbggggb bgb faaf bggggbd dgg aac aebggggd dggd eae cae bggggbd bgb caaf aaf dbgggggg faac eae dbgggd aae faaf dd eaa eac caaf faa faac eac eae caa caa aac faaf cae aac aaf eae cae caaf aaf faac eae aae faaf eaa eac caaf faa faac eac eae ``` <!-- end of image --> My analysis confirms the presence of an intersection in area A. The image features one single intersection point.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fe0606ff b,#4746feff c,#ff8f8fff d,#9999ffff e,#fd4445ff f,#f1d4e2ff g,#0505feff ``` ```image f ac a af fa g a dg ca g a gd ce dg a g ec gd a dg ac g a gd af dg fa g a gd ca bg a g ce gf e a bb ca ec g a a gf ac ac bb ee a fg fa af gf a fa bb ac a fg ca ca gf fa a bb af ce fg ae a g ca ec bb a a fg ac ac g ee fa gb fa af dg a fa g ac a gd ca ca dg fa a g af ee gd ae a dg ca ec g a a gd ac ac dg ee fa g fa af gd a fa dg ac a g ca ca gd fa a dg af ee g ae a gd ca ggd ec bg a bgb a g ac dggd ac gd ee fggb fa bg fa bggf af g a dggd fa gf ac bgg a bb ca dggd ca fg fa bgb a gf af dggd ee bb ae fggb a fg ca bggec gf a dggd bb ac abgg fg ee fa dgggf fa af d a fa ac a ca ce fa a af ee ae a ca ec a a af aae fa ``` <!-- end of image -->

This is the image I'm working with. The goal is to count the intersections. I'm going to focus my attention on these specific areas. <!-- image --> ```palette Key,Color ,#fefefeff a,#0304feff b,#ee5451ff c,#8f95f2ff d,#f8a4a1ff e,#fd0707ff f,#add5adff g,#4347f7ff ``` ```image c gc a gg a ca a a ac a gc a gg a ca a a ac a gc a gg a ca a a ac a gg a cg a ca a a ac a gg a cg a ffcaffffffffffffb fffafffffffffffebee ffffafffffffffeb deed ffffacfffffffebf eed fffffaffffffebff beb fffffggffffebfff bee ffffffafffeeffff deed ffffffgafeefffff eeb fffffffabeffffff bee fffffffbafffffff deed ffffffbeacffffff deed fffffbeffaffffff eeb fffffffffffff ffffdefffacfffff bee fffffffffffff fffdefffffafffff deed fffffffffffff fffeffffffggffff eeb fffffffffffff ffeffffffffaffff bebfffffffffffff fefffffffffgafff deefffffffffff efffffffffffafff fdeebffffffff effffffffffffcaff ffffeebffffff ed ac ffffffbeeffff ed a ffffffffbffff ed ac fffffffffffff eb a fffffffffffff eb ggc fffffffffffff eb ggaaaaaaggc fffffffffffff ee ccgaaaaaaagcc fffffffffffff be cggaaaaaaggc fffffffffffff be ccgaaaaaaaggcffffffff be ffcggaaaaffff de de de de e e e ed ed ed ``` <!-- end of image --> This is a magnified view of the region A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0908fdff b,#fe3637ff c,#5c57f9ff d,#fdcfd0ff e,#fe0505ff f,#aeaeffff g,#f98085ff ``` ```image faa cac g faaf ge cac gee aaf geeg caa geeg aaf deeg faa deeg aac deeb faa deeb cac deeb faaf deeb cac dbeb aaf bebd caa beed aaf beed faabeed aaced gaad geaac geegaaf geeg cac geeg aaf geeg caa geeg aaf deeg faa deeb aac deeb faa deeb cac deeb faaf deeb cac dbeb aaf bebd caa beed aaf eed faa ed aac ``` <!-- end of image --> Success! This area contains an intersection point! Next up, a closer look at another region. This close-up might reveal an intersection in area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#0808ffff b,#ff4242ff c,#6667ffff d,#ffbfbfff e,#ff0606ff f,#bbbbffff g,#ff8686ff ``` ```image d eeg eeeegd gbeeebd dbeeebg dgeeeeg geeeebd dbeeebd dbeeeeg geeb gd ff aaaaaccccff aaaaaaaaaaaaaaacccf ``` <!-- end of image --> Unfortunately, there's no intersection inside area B. The final count is: one intersection.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0303feff b,#fb585cff c,#7575ffff d,#ffaeaeff e,#ff0808ff f,#bcbcffff g,#3838ffff ``` ```image f gc a cg a ca a fa af a gc a cg a fa af fa af a gc a cg a fa af fa af a gc a cg a fa af fa af a gc a cg a fa b af ebee a ed deed ac eb eeb a eb beb gc eb bee a ee deed cg ee eeb abe bee ba deed beaf deed de a eeb de ac bee de a deed de gg eeb e a beb e cg bee ed a deed ed fa eeb ed af bee ed a d eb ac eb a eb ggf eb cgaaaaaagccf ee fcgaaaaaaagcf be ffcgaaaaaagccf be fcgaaaaaaagcf be ffcgaaaa be de de de e e e ed ed ed ``` <!-- 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,#484af9ff b,#fe0202ff c,#ef9e97ff d,#0505fdff e,#cbccfeff f,#f83936ff g,#aed5aeff ``` ```image bbbc cbc bbc fb bbc bf bbc cbc fbc fb fbc bf fbf cbc fbf fb fbf bf cbf cbc cbf ggggggggggggggggg fb cbb ggggggggggggggggg bf cbb ggggggggggggggggg cbc cbb ggggggggggggggggg fb cbbggggggggggggggggg bf cbbcgggggggggggggg cbc ggbbcgggggggdgggg gggggggggggggggfb ggggbbcggggadgggg ggggggggggggggbf ggggggbbcggdggggg ggggggggggggcbcg ggggggggbbdgggggg gggggggggggfbggg gggggggggadbfgggg ggggggggggbfgggg gggggggggdggfgggg ggggggggcbcggggg ggggggggdgggggggg gggggggfbggggggg gggggggdagggggggg gggaggbfgggggggg gggggggdggggggggg gggadbcggggggggg ggggggdgggggggggg gggfdggggggggggg gggggdagggggggggg gggcgdgggggggggg ggggadggggggggggg gggggadggggggggg ggggdgggggggggggg ggggggdggggggggg gggdggggggggggggg gggggggdgggggggg aa gggggggadggggggg ed ggggggggdggggggg d gggggggggdgggggg da gggggggggadggggg ed ggggggggggdggggg d ed de aa ad de d ed de aa aa de ed ed d aa da de ed ed d aa de de ad ed ed aa de de aa ed ed aa d de da ed ad aa d de de ed aa aa ed de de ed da aa ed de d ed de aa ad d d ed de aa aa d ed ed d aa da d ed ed d aa de d ad ed d aa de daa ed ``` <!-- end of image --> This is a magnified view of the region A. <!-- image --> ```palette Key,Color ,#fefefeff a,#4439f3ff b,#fe0505ff c,#ff9999ff d,#0404feff e,#eadcf0ff f,#f93a40ff g,#9191ffff ``` ```image c cb efbb cbbbc cbbfe efbbc cbbbc cbbfe efbbc cbbbc cbbfe efbbf cbbbc gg cbbfe gddeefbbf adabbbc eddafe effdde cbbada ceeddg gdde ada eddg gdde ada eddg gdde ada eddg gdde ada eddg gdde ada eddg gdde ``` <!-- end of image --> Incredible, there's actually an intersection in area A! Next up, a closer look at another region. Let's put area B under the microscope. <!-- image --> ```palette Key,Color ,#fefefeff a,#4d46f8ff b,#fe0708ff c,#ff9595ff d,#0806fdff e,#e5d3ecff f,#f94d52ff g,#9090ffff ``` ```image fe bbfe fbbbfe efbbbfe efbbbfe edg efbbbfc ada efbbbfc gdde efbbbfc eddg cbbbbc dda cbbbbc add cbbbfdde cbddac addbbbc gddecbbbb eddg cbc ada gdde eddg dda add gdde eddg ada gdde eddg ada gdde eddg dda add ``` <!-- end of image --> My investigation has led me to an intersection in area B! After a long analysis, I found two intersections.

<!-- image --> ```palette Key,Color ,#fefefeff a,#403ffeff b,#ff0202ff c,#ffababff d,#0303feff e,#d8d8feff f,#ff3d3dff g,#8989ffff ``` ```image c bbbc cbc bbc fb bbc bf bbc cbc fbc fb fbf bf fbf cbc fbf fb fbf bf fbf cbc cbf fb cbb bf cbb cbc cbb fb cbb bf cbbc cbc cbbc d fb bbc gd bf bbc d cbc bbde fb adbc bf ed f cbc de fb da g bf gd aabc d fde dg ced gd aa d de de ed aa aa ed de de ed dg aa gd de d ed dg aa gd de ed ed de aa aa de ed ed d aa dg de gd ed d aa dg de aa ed ed aa de de aa ed ed aa d de dg ed gd aa d de de ed aa aa ed de de ed aa aa gd de d ed dg aa gd de d ed de aa aa de ed ed de aa dg de gd ed d aa dg d gd ed ed aa de daa ed ``` <!-- end of image -->

The hunt for intersections begins! Let's analyze this image closely. I have a hunch that these areas might contain the intersections we're looking for. <!-- image --> ```palette Key,Color ,#fefefeff a,#0607feff b,#fd0606ff c,#ed968eff d,#a2a6f6ff e,#f64745ff f,#acd3acff g,#4a4deeff ``` ```image da a a da da a da da ga a ag da ad a ad da a a a da da c a ga ec da ag b a ag ee da ad b a a ce da a b a da cb da ga b a ga cb da ag b a ad b da a bc a a b da da bc a da b da ga ee a ag b da ad ee a ad b da a c ffebffffffffafff daffffffffffffffcb fffbfffffffdafff gafffffffffffffb fffcbffffffaffff fgafffffffffffbf ffffbfffffdaffff ffagfffffffffbff ffffcbffffafffff fffagfffffffbcff fffffbcffdafffff ffffadfffffbcfff ffffffbffaffffff fffffaffffbeffff ffffffbcfaffffff ffffffaffbefffff fffffffbafffffff ffffffdabbffffff fffffffeafffffff fffffffgafffffff fffffffabfffffff ffffffebaaffffff fffffffaeeffffff fffffcbffagfffff ffffffaffbffffff ffffcbffffadffff ffffffaffebfffff ffffbffffffaffff fffffaffffbfffff fffbffffffffafff fffffaffffcbffff ffbfffffffffdaff ffffaffffffbffff fbcffffffffffgaf ffffaffffffcbfff bcffffffffffffga fffaffffffffbfff beffffffffffffffag fffafffffffffbff beffffffffffffffffa ad bc ee a b eb ad bc cb a b cb ad ee cb a b b ad ee b a b b ad cb bc a b bc ad cb be a b be ad b eb a bc eb ad b cb a bc cb ad b cb a ec b ad b b a ee b ad b bc ce bc b be cb be b eb cb eb beb b ``` <!-- end of image --> This is a magnified view of the region A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0000feff b,#fe0607ff c,#fc9193ff d,#d2d2ffff e,#fc4d4fff f,#ffd0d0ff g,#544ff9ff ``` ```image bbc gag cbb daad bbc gag cbb daad bbc gag cbb daad ebe gag fbbf daad ebe gag fbbf daad ebe gag fbbf daad ebe gag fbbc daad cbb gag bbc daad cbb gag bbcaad cbgag eaad gagf daabe gagbbf daadebe gag fbbf daad ebe gag fbbf daad cbe gag bbc daad cbb gag bbc daad cbb gag bbc daad cbb gag ebe daad fbbf gag ebe daad fbbf gag ebe ``` <!-- end of image --> Eureka! There's definitely an intersection in area A! Alright, let's concentrate on the next area. This is a magnified view of the region B. <!-- image --> ```palette Key,Color ,#fefefeff a,#0505feff b,#fd090aff c,#feb4b5ff d,#8c8bfeff e,#ff5d5dff f,#ceccfdff g,#433ef9ff ``` ```image g ag c aad cb daad cbb daaf bbe gaaf bbb gaa bbb aag ebb faag ebbc faad ebbc daad ebbc daaf cbbc gaaf cbbe gaaf cbbe gag cbbe faag cbbe faad bbe daadbbb daabb gaaf ebgaaf ebbcgag ebbc faag cbbc faag cbbe faad cbbe daad cbbe daaf cbbe gaaf bbe gag bbb aag ebb faag ebbc faad ebbc daad ebbc daaf ebbc gaaf bbc gaa be ga e fa ``` <!-- end of image --> My analysis confirms the presence of an intersection in area B. There's for sure two intersections on the image you sent me.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0606feff b,#fe0707ff c,#ffa5a5ff d,#a1a1ffff e,#fd5152ff f,#e5d9f3ff g,#4743fbff ``` ```image f daf afa dg fa a da da ga a ag da ad a af da af a fa da da c a ga ee da ag b a ag ee da ad b a af ee da fa b a da cb da ga bf a gg cb da ag bf a ad fb da af bc af fa b da fa bc af da b da ga ee af ag b da ad ee af af b da a c cb af fa cb b da da fb cb af ga fb bf fa ag bf fb af ad bc bc fa ad bc fb af af be bcfa fa be baf dabb ea ga ab ebgg faee cb ag af b cb ad fa ee fb af af b b fa fa cb bf da af b bc da fa cb bc ga af bf be ag fa fb be a af bc bb fa b eb af bc eb fa b cb ad ee cb fa b fb ad ee b fa b bf ad cb bc fa b bc ad cb be fa bf be ad fb eb fa bc eb ad fb eb a bc cb ad b cb a be fb ad b bf a ee bf ad b bc f ee bc b be cb be b eb cb eb beb fb ``` <!-- end of image -->

Based on a first glance, I suspect there could be intersection regions here. I'm going to focus my attention on these specific areas. <!-- image --> ```palette Key,Color ,#fefefeff a,#0b0afbff b,#ea746aff c,#a4a7f9ff d,#afd5aeff e,#fc0b0aff f,#5c65ebff g,#eef0f0ff ``` ```image g ca afa ca a a ca g ca ag ee ag ga eb ca ac eb ag ga eb ca af eg ag a geg ga ff ge ag a ge ga ca be ac ag be ga ca be ac ac ee gdddddddddddddadd ga eb gddddddddddddafdd ac ebgddddddddddddaddd a ebdddddddddddafddd ff edddddddddddadddd a gedddddddddafdddd fa gdeddddddddaddddd ag gdbeddddddafddddd ca gddbedddddadddddd ac gdddbedddafdddddd ga gddddeeddaddddddd ac gdddddeeffddddddd a gddddddeadddddddd ff gddddddfabddddddd a gddddddadebdddddd fa gdddddfaddedddddd ag gdddddaddddeddddd ca gddddfadddddedddd ag gddddaddddddbeddd ga gdddfadddddddbedd ac gdddadddddddddbed a gddfaddddddddddee af gddaddddddddddddee a gdfadddddddddddddeb fa gdadddddddddddddd eb a gfadddddddddddddd eg ca aggggggggggggggg eg ag ca geg ga ag geeg gggggacgggggggggggggggggg ga beeb gddddddaddddddddddddddddddg ac geeeg gddddddafdddddddddddddddddg ga beeb gdddddddadddddddddddddddddg ac geeb gdddddddfaddddddddddddddddg ga beeg gddddddddaddddddddddddddddg ac geeb gddddddddfadddddddddddddddg ga beedddddddddadddddddddddddddg ac deebddddddcaddddddddddddddg a gddeeedddddacdddddddddddddg ac gddddbeebdddadddddddddddddg a gdddddddeeedafddddddddddddg af gdddddddddbeeaddddddddddddg a gddddddddddddaaeddddddddddg ff gdddddddddddddabeebdddddddg a gdddddddddddddfaddeebdddddg ff gddddddddddddddaddddbeedddg a gddddddddddddddcaddddddeebg ff gdddddddddddddddaddddddddbg a gddddddddddddddddaddddddddg ff gddddddddddddddddafdddddddg a gdddddddddddddddddadddddddg fa gdddddddddddddddddafddddddg a gddddddddddddddddddaddddddg ca gddddddddddddddddddfadddddg a gdddddddddddddddddddadddddg ca gggggggggggggggggggcagggg a ag ca ga ag ac a af a fa a ``` <!-- end of image --> Let's get to the bottom of what's happening inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#322cf8ff b,#fb4e52ff c,#adadffff d,#fbabaeff e,#ff0707ff f,#7b7bffff g,#0404feff ``` ```image ggc fga ggc fga ggc fga d agc ed cgg eed agf bee cgg bee agf eeb cgg eeb agf deeb cgg deeb agf deed cgg deed agf beed cgg beed agf beed cgg bee agf bee cgg eeb agf eebggc deaga dggb fgaed ggdeed fga beed ggc beed fga beed ggc bee fga eee ggc eeb fga eeb ggc deeb fga deeb ggc deed fga deed ggc beed cga bee agf be cgg b agf cgg agf cgg agf cgg agf ``` <!-- end of image --> Area A contains an intersection. Okay, let's direct our attention to the next zone. My goal is to determine if there's an intersection inside area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#342cf7ff b,#fd595aff c,#c2c2feff d,#ffaaaaff e,#fd0708ff f,#7c7bfdff g,#0404feff ``` ```image ggc fga ggf fgg agf cgg agf cggc fga cggc fga ggf fgg agf ebd cgg eeebd agf dbeeeeb cggc deeeebd aga dbeeeeb cggc beeeebd fga dbeeeed ggc beeeebd fga dbeeeed agf dbeeeebfgg deeeeagf dbeeggb dagaebd cggeeeeb fgabeeeebd ggc dbeeeed fga beeeebd ggf dbeeeed fgg dbeeeebd agf deeeebd cggc dbeeee agf dee cggc d fga ggc fga ggf fgg agf cgg agf cggc fga cggc fga ggf fgg ``` <!-- end of image --> Aha! I've found an intersection inside area B! The image features two intersection points.

<!-- image --> ```palette Key,Color ,#fefefeff a,#342ff9ff b,#fe5353ff c,#bebeffff d,#ffb1b1ff e,#fe0707ff f,#7878ffff g,#0303ffff ``` ```image c fg gfa fa g g cg d cg gc ee g cg eb cg gc eb g g ed cg af ed gc g e cg fa e gc g de cg fg de gc g be g cg be gc gc eb g g eb gc af eb g g ed af aa ed g g e af fa e g g de af cg de g gc be af g be g gf ebaf g eg af fad g g ed fa fa ed g g e cg fa de gc g de cg fa de gc g be g cg be af g eb g cg eb fa g ed g cg ed cg g ed gc cg e cg gc dee gc cg deed g gc beb af g deed g gc eeb fa g beed g gc deeb fg g beed g gc deeb cg g bee gc af deed g g bee af af deeg g aab af gbeed g fa eeb af g beed g cg deeb fa gc b g g fa gf g g fa af g g fa fa g g fa cg g gc cg cg g gc g af g fa g ``` <!-- end of image -->

I have an image in front of me. I need to determine if there are any intersection segments. I've noticed 2 areas of interest. These could be potential intersection zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#f45954ff b,#0807fdff c,#adaefdff d,#fe0908ff e,#ed9e96ff f,#5759edff g,#aed5aeff ``` ```image c fbbc b bb bc cbb cb cbb d b cbb ed ff cbb d b cbb da bc cbb d cb cbb ggggggggggggdegg b cbb gggggggggggedggg ff fbf gggggggggggdgggg b fbf ggggggggggadgggg bc fbf ggggggggggdggggg cb fbfgggggggggdaggggg b fbfgggggggdgggggg ff gfbfggggdegggggg b gggbbfgedggggggg bc gggggbbfgggggggg cb ggggggabbfgggggg b ggggggdggbbfgggg bf gggggdeggggbbfgg b ggggedgggggggbbf bc ggggdggggggggggb cb gggadggggggggggg b gggdgggggggggggg bf ggdagggggggggggg b ggdggggggggggggg b gdeggggggggggggg fb edgggggggggggggg b d bf ad cb d b de fb d b d bc ed cb d b aa ff d b de bc d cb d b ed ff d b aa bc d cb de b ed ff d gggggggggbgggggg ad ggggggggbcgggggg d gggggggfbggggggg de gggggggbgggggggg d ggggggbfgggggggg de ggggggbggggggggg ed gggggbgggggggggg d ggggfbgggggggggg aa ggggbggggggggggg d gggbfggggggggggg de gggfddgggggggggg d gggggadagggggggg d gggggggadagggggg ed gggggggggddegggg d gggggggggggddggg aa ggggggggggggeddg d ggggggggggggggada de ggggggggggggggggada ed gggggggggggggggg dde d gggggggggggggggg dd ad dd d edd da ada d ade de dde ed dd d edd aa eda d adade dd ``` <!-- end of image --> Let's get to the bottom of what's happening inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#f73e46ff b,#0a08fdff c,#b2abf8ff d,#fe0606ff e,#ffc2c2ff f,#6060feff g,#ff8383ff ``` ```image cbb bbf fbb cbbc fbf cbb bbf fbb cbbc fbf cbb bbc fbb cbbc bbf cbb bbc fbb cbbc bbf cbbdg caddde gdddae gdddae gdddg eadddg eadddg edddae gdddae gddda eadddg eaddd ead g ``` <!-- end of image --> My investigation has led me to an intersection in area A! Let's continue our search in the next region. I'm eager to see what's happening in this magnified view of area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#f42c36ff b,#0908feff c,#a2a2ffff d,#ff0303ff e,#febbbbff f,#5555ffff g,#ff7373ff ``` ```image gda edde ada edde adg gdd dde gda edde adg edd f adg bbf gda fbbbf dde cfbbbf gda cfbbbf edde cfbbbf adg cfbbbf edd cfbbbf ddg cfbbbaa cbbbbc aabbbbc eddecbbbbc adg cbbbbc gdd cbbbbc dde cbbbbc gda cbbbbc edde cbbb adg cb edd adg gda dde gda edde adg edd ddg gda edde ``` <!-- end of image --> The evidence is clear: this is an intersection in area B. I can confirm there's two intersections in there.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fa3b40ff b,#0706feff c,#acabfdff d,#ff0505ff e,#ffc0c0ff f,#5454feff g,#ff7e7eff ``` ```image c fbbc b bb bc cbb cb cbb d b cbb gd ff cbb d b cbb ag bc cbb d cb cbb de b cbb ed ff fbf d b fbf ga bc fbf d cb fbf dg b fbf d ff fbf de b fbf gd bc fba cb abbc b d bbc bf dg bbc b ed bbc bc d b cb gd b d bf ag b d b de fb ed b d bf ga cb d b dg fb d b de bc gd cb d b aa ff d b dg bc ed cb de b gd ff d b ag bc d cb de b ed ff d b ga bc d cb dg b d ff de b ed bc d cb aa b d bf dg cda ed gda de adg gd dde d dd aa edd d gda de gdg ed ade d dde ga edd d eda ag gda d adg de dde ed dd d edd aa gda d adgdg ad ``` <!-- end of image -->

I have an image in front of me. I need to determine if there are any intersection segments. These regions highlight areas that look suspicious. Lines seem to converge within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#0908fcff b,#fe0404ff c,#f9a29fff d,#6368f6ff e,#add4aeff f,#f34c46ff g,#b4b4feff ``` ```image c fbbfc cbbbf cbbbc eeeeeeeeeeeeeeeeeeee fbbfc eeeeeeeeeeeeeeeeeeee cbbbf eeeeeeeeeeeeeeeeeeee cbbbc eeeeeeeeeeeeeeeeeeee fbbfc eeeeeeeeeeeeeeeeeeee cbbbfeeeeeeeeeeeeeeeeeee fbbbfeeeeeeeeeeeeeee eeeefbbaeeeeeeeeeeee eeeeeeaaaaaeeeeeeeee eeeeeeaebbdaaadeeeee eeeeeadeefbeeeaaadee eeeeeaeeeefbeeeeeaaad eeeeadeeeeefbeeeeeeedaad eeeeaeeeeeeefbeeeeee daad eeeadeeeeeeeefbeeeee daad eeeaeeeeeeeeeefbeeee daad eeaeeeeeeeeeeeecbeee daad eeaeeeeeeeeeeeeecbee gaaag eaeeeeeeeeeeeeeeecbe gaaag eaeeeeeeeeeeeeeeeeeb gaaag ag b gaaag ga bc gaaa a bc ga bc a bc ga bc a bf da bf a bf dd bf a bf dd bb a fb dd fb a fb ad fb a fb ad cb a cb ag cb a cb ag cb a b ag b a bc ag bc ga bc a bc ga bc a b ga a ga a da a da a dd a dd a dd a ad a ag a ag a ag a ag ga ag ga a ``` <!-- end of image --> Let's take a closer look at area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0505feff b,#fe0606ff c,#feafafff d,#7777feff e,#3f31f1ff f,#f95359ff g,#bfbfffff ``` ```image c bbfc bbbbbbfc cffbbbbbfcc cfbbbbbbfc cfbbbbeedg cffaaaaedg eaeeaaaaadg gaa bbfeaaaaadg ead bbbcgdaaaaadg gaa fbbc gdaaaaaeg aad fbbc gdaaaaaeg daa fbbc gdeaaaaed aad fbbc gdeaaaa daa fbbc gdea aag fbbc dae fbbc aag fbbc dae fbbc aag fbbf dae cbbf aag cbbf dae cbbf gaag cbbf dae cbbf gaag cbbf eae cbbf gaag cbbf ead cbbb gaag cbb ``` <!-- end of image --> Incredible, there's actually an intersection in area A! I've identified a total of two intersection points.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0505feff b,#fe0404ff c,#ffa1a1ff d,#8a8affff e,#413efcff f,#ff4848ff g,#cacaffff ``` ```image c fbbfc cbbbf cbbbc fbbfc cbbbf cbbbc fbbfc cbbbf cbbbc fbbag eeaaag a fbgaaag ad fb gaaad a fb geaad ad fb geaad a fb eaad ag cb eaae ga cb daae ag cb daaeg ga cb daaeg ag cb daaag ga b gaaag ag b gaaad ga bc geaa a bc g da bc a bc da bc a bf de bf a bf de bf a bf ee bb a fb ee fb a fb ed fb a fb ed cb a cb ad cb a cb ad cb a b ag b ga bc ag bc ga bc ag bc ga bc a b da a da a de a de a ee a ee a ed a ed a ad a ad a ag ga ag ga ag ga ag ``` <!-- end of image -->

I'm examining this image closely. My goal: find any and all intersections. Let's take a closer look at what's happening inside these zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#0909feff b,#fe0706ff c,#5e62f7ff d,#f35852ff e,#f9a3a0ff f,#adadffff g,#acd4acff ``` ```image c a a cc a af ca a af ca a af ca a af ca a af ca a af ca a af ca a af ca a af ca a af fa a af fa a af fa a af fa a ac fa a f ac cac fa aaf a aaf ac aaf fa aaf a aaf ac aa fa faa a faa ac faa fa faa a faa ac cac fa cac a cacggggggggacgggg gcacggggggaggggg gggaacgggagggggg gggggaacacgggggg gggggggaaggggggg gggggggggggggggg gggggggggggggggg gggggggggggggggg gggggedbbbdggggg gdbbbbdgggdbbbbd ebbbbdggggggggggggedbbbbe edbbbde gggggggggggggggg edbbbde dbbbbe gggggggggggggggg edbbbde ebbbbd gggggggggggggggg ebbbbde edbbbde gggggggggggggggg ebbbbd dbbbbe gggggggggggggggg dbbbbe bd gggggggggggggggg edbbbbe gggggggggggggggg edbb gggggggggggggggg ``` <!-- end of image --> I'm eager to see what's happening in this magnified view of area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0909ffff b,#ff0404ff c,#6161ffff d,#ff4d4dff e,#ff9898ff f,#b2b2ffff g,#ffcfcfff ``` ```image caaac aac fcaaac caa fcaaac faaf fcaaac aac fcaaac caa faaaac faaf faaaaf aac faaaaaa faaaf ff geeg gedbbbbbbddeg gedbbbbbbbddbbbbbbbdeeg geddbbbbbbbdeg geddbbbbbbb dbbbbbbbdeg geddbb bbbddeg g eg ``` <!-- end of image --> My analysis shows that the lines in area A do not cross. I can confidently say that there are no intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#2e2effff b,#ff0707ff c,#7575ffff d,#ff5e5eff e,#ffacacff f,#b8b8ffff g,#0303ffff ``` ```image c g gf aa g gf aa g gf ca g gf ca g gf ca g gf ca g gf ca g gf cg g gf cg g gf cg g gf cg g gf cg g gc fg g gc fg g gc fg g f gc agc fg agc g agf gc ggf fg ggf g ggf ac fggf fg fgg g fgg ac fgg fg fga g cga ac cga fg cga g cgc ac agc fg agc g agcac ag edbbbd dbbbbe edbbbbd ebbbbd edbbbbe edbbbde edbbbde dbbbbe edbbbde ebbbbd ebbbbde edbbbde dbbbbd dbbbbe edbbbbd bd edbbbbe edbb ``` <!-- end of image -->

The hunt for intersections begins! Let's analyze this image closely. The image has some tight areas where segments are too close. I should investigate those closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#e0665bff b,#0405fcff c,#fb0a0aff d,#8594d8ff e,#4042e4ff f,#b1d7b1ff g,#99c795ff ``` ```image a fggggggggggggggggggggggggggggggggggggggggggggggggggggggc gfffffffffffffffffffffffffffffffffffffffffffffffffffffcg gffffffffffffffffffffffffffffffffffffffffffffffffffffcaf gfffffffffffffffffffffffffffffffffffffffffffffffffffcaff gffffffffffffffffffffffffffffffffffffffffffffffffffacfff gfffffffffffffffffffffffffffffffffffffffffffffffffgcffff gfffffffffffffffffffffffffffffffffffffffffffffffffcfffff gffffffffffffffffffffffffffffffffffffffffffffffffcafffff gfffffffffffffffffffffffffffffffffffffffffffffffccfffffb gffffffffffffffffffffffffffffffffffffffffffffffacfffffbd gffffffffffffffffffffffffffffffffffffffffffffffcffffdbff gfffffffffffffffffffffffffffffffffffffffffffffcgfffebfff gffffffffffffffffffffffffffffffffffffffffffffcafffebffff gfffffffffffffffffffffffffffffffffffffffffffacfffbbfffff gffffffffffffffffffffffffffffffffffffffffffgcfffbeffffff gffffffffffffffffffffffffffffffffffffffffffcfffbefffffff gfffffffffffffffffffffffffffffffffffffffffcaffbdffffffff gffffffffffffffffffffffffffffffffffffffffccfgbdfffffffff gfffffffffffffffffffffffffffffffffffffffacfdbfffffffffff gfffffffffffffffffffffffffffffffffffffffcfebffffffffffff gffffffffffffffffffffffffffffffffffffffcgebfffffffffffff gfffffffffffffffffffffffffffffffffffffcabbffffffffffffff gffffffffffffffffffffffffffffffffffffacbefffffffffffffff gfffffffffffffffffffffffffffffffffffgcbeffffffffffffffff gfffffffffffffffffffffffffffffffffffcbdfffffffffffffffff gffffffffffffffffffffffffffffffffffcbdffffffffffffffffff gfffffffffffffffffffffffffffffffffabffffffffffffffffffff gffffffffffffffffffffffffffffffffebfffffffffffffffffffff gfffffffffffffffffffffffffffffffebffffffffffffffffffffff gffffffffffffffffffffffffffffffbbfffffffffffffffffffffff gfffffffffffffffffffffffffffffbeafffffffffffffffffffffff gffffffffffffffffffffffffffffbecffffffffffffffffffffffff gfffffffffffffffffffffffffffbdcfffffffffffffffffffffffff gfffffffffffffffffffffffffdbdcffffffffffffffffffffffffff gffffffffffffffffffffffffdbfcgffffffffffffffffffffffffff gfffffffffffffffffffffffebfcafffffffffffffffffffffffffff gffffffffffffffffffffffebfacffffffffffffffffffffffffffff gfffffffffffffffffffffbbfgcfffffffffffffffffffffffffffff gffffffffffffffffffffbeffcffffffffffffffffffffffffffffff gfffffffffffffffffffbeffcaffffffffffffffffffffffffffffff gffffffffffffffffffbdffccfffffffffffffffffffffffffffffff gffffffffffffffffdbgffacffffffffffffffffffffffffffffffff gfffffffffffffffdbffffcfffffffffffffffffffffffffffffffff gffffffffffffffebffffcgfffffffffffffffffffffffffffffffff gfffffffffffffebffffcaffffffffffffffffffffffffffffffffff gffffffffffffbbffffacfffffffffffffffffffffffffffffffffff gfffffffffddbeffffgcffffffffffffffffffffffffffffffffffff deebbbbbbbbbedfffffcfffffffffffffffffffffffffffffffffffff ddeebbbbbbbbeeddffffffffffffffcgfffffffffffffffffffffffffffffffffffff ddebbbbbbbbeedd gfffffffffffffffcaffffffffffffffffffffffffffffffffffffff edd gffffffffffffffacfffffffffffffffffffffffffffffffffffffff gfffffffffffffgcffffffffffffffffffffffffffffffffffffffff gfffffffffffffcfffffffffffffffffffffffffffffffffffffffff gffffffffffffcafffffffffffffffffffffffffffffffffffffffff gfffffffffffccffffffffffffffffffffffffffffffffffffffffff gffffffffffccfffffffffffffffffffffffffffffffffffffffffff gffffffffgcaffffffffffffffffffffffffffffffffffffffffffff gfffffffccffffffffffffffffffffffffffffffffffffffffffffff gfffffacafffffffffffffffffffffffffffffffffffffffffffffff gffffccfffffffffffffffffffffffffffffffffffffffffffffffff gffacaffffffffffffffffffffffffffffffffffffffffffffffffff gfccffffffffffffffffffffffffffffffffffffffffffffffffffff acafffffffffffffffffffffffffffffffffffffffffffffffffffff ccggggggggggggggggggggggggggggggggggggggggggggggggggggggg ac cc cc ca cc fca cc aca cc acf cc acf cc ac ca ``` <!-- end of image --> Time to investigate area A up close. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd7a7cff b,#0706fdff c,#fe0405ff d,#b5b3fdff e,#5b54f7ff f,#fa373cff g,#ffbfbfff ``` ```image a gc cc fcf ccg gca ff fc acc gccg gcca acc accg cca cf ff e acg eb gcc bbb gcca bbbd fcc dbe accg ebb gcca ebbe cca ebbd fcf ebbd ccg bbbd gcg dbbd fc dbb fcf ebbe accg ebbe gccg ebbd gcca ebbd fcf bbbd acc dbb ccg dbe cf ebbe fc ebbe acc ebbd gccgebbd gccadbbd fcfdbb fccdbb gccebbe ccebbe cbbbd abbbd gcbbd gfbb fbb ebbe ebbe ebba bbf dbbf dbbcg dbbba dbbec ebbeccg ebbdccg bbdcca dbbdfcf dbb fcc dbbeaccg dbbe cca ebbd ff ebbd acg bbd gcc dbbd gcca dbb fcf dbbe fcf ebbe accg ebbe gccg bbd fcf bbd cc dbbd acg dbbe gca dbbe cc ebbe fcf ebbe accg bbd gcca dbbd fcf dbb fcc dbbe ccg dddebbe gca dddeeebbbbbbbbbe ca deeebbbbbbbbbbbbbbbeeed fc bbbbbbbbbeeedddd acc gcca ccf fcf accg gccg cca cf acg gcc ccf fcf accg gfccg cccg gfcf gccca fccfg gccca ccfg acca gfccg accca cccg gfcf accg ccca ``` <!-- end of image --> I am surprised, so clear, an intersection has appeared in area A. One intersection, that's it, but I found it.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff8585ff b,#0705fdff c,#fe0506ff d,#aeacfcff e,#544ff9ff f,#fb3f42ff g,#ffc9c9ff ``` ```image a gc c cg cf ac gc cg ca ff b gc bd c db cg db cf eb ac bb gc be c be ca bd ff bd ac db c eb cgeb cabb fcbe gcbe cbd cbd fb eb eb bbg bba bef bdc dbdc db cg eb cf eb ac bb gc be c be ca bd ff db ac db c eb cg eb ca bb fc ddbe gc ddeebbbbbbbbbed c ddeebbbbbbbbeedd cg deebbbbbbbbeedd cf eedd ac gc c ca ff fc gcf cc aca cc aca cc acg cc fcg gcf fcg gcf cc gca cc aca cc aca cc fcg gcf fcg cf ``` <!-- end of image -->

I'm ready to tackle this image and find those intersections! I've noticed 1 areas of interest. These could be potential intersection zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#ee433eff b,#3940eaff c,#b0d7b0ff d,#fd0605ff e,#0606fdff f,#7983ebff g,#de9282ff ``` ```image f fee fee fee fee fee fee fee feb gd feb daa feb d d feb cccccccccccccccccccccccccccccccdaccgdcccccccccccc feb ccccccccccccccccccccccccccccccadccccdgccccccccccc feb cccccccccccccccccccccccccccccgdccccccdcccccccccccfeb cccccccccccccccccccccccccccccdcccccccadccccccccbeb ccccccccccccccccccccccccccccdgccccccccdgcccccbebc cccccccccccccccccccccccccccadccccccccccdcccbebccc ccccccccccccccccccccccccccgdcccccccccccaabebccccc ccccccccccccccccccccccccccdccccccccccccbebccccccc cccccccccccccccccccccccccdgccccccccccbebgdccccccc ccccccccccccccccccccccccaacccccccccbebcccdgcccccc cccccccccccccccccccccccgdccccccccbebccccccdcccccc cccccccccccccccccccccccdcccccccceeccccccccaaccccc ccccccccccccccccccccccdgccccccfefccccccccccdccccc cccccccccccccccccccccdacccccceeccccccccccccgdcccc ccccccccccccccccccccgdcccccfefccccccccccccccdaccc ccccccccccccccccccccdccccceecccccccccccccccccdccc cccccccccccccccccccdgccccebccccccccccccccccccgdcc ccccccccccccccccccdacccbecccccccccccccccccccccdgc cccccccccccccccccgdcccebcccccccccccccccccccccccdc cccccccccccccccccdccbecccccccccccccccccccccccccaa ccccccccccccccccdcceecccccccccccccccccccccccccccd cccccccccccccccdafefccccccccccccccccccccccccccccgd ccccccccccccccadeecccccccccccccccccccccccccccccccdg ccccccccccccccaefcccccccccccccccccccccccccccccccc d ccccccccccccceecccccccccccccccccccccccccccccccccc aa ccccccccccccebccccccccccccccccccccccccccccccccccc d ccccccccccbedcccccccccccccccccccccccccccccccccccc d cccccccccebdccccccccccccccccccccccccccccccccccccc dg cccccccbecdcccccccccccccccccccccccccccccccccccccc d cccccceecdgcccccccccccccccccccccccccccccccccccccc gd ccccfefcadccccccccccccccccccccccccccccccccccccccc dg ccceeccgdcccccccccccccccccccccccccccccccccccccccc d cfefcccdccccccccccccccccccccccccccccccccccccccccc aa eeccccdgccccccccccccccccccccccccccccccccccccccccc d cebccccaacccccccccccccccccccccccccccccccccccccccccc gd b ccccgdccccccccccccccccccccccccccccccccccccccccccc dg ccccdcccccccccccccccccccccccccccccccccccccccccccc d cccdgcccccccccccccccccccccccccccccccccccccccccccc gd ccdaccccccccccccccccccccccccccccccccccccccccccccc d cgdcccccccccccccccccccccccccccccccccccccccccccccc d cdccccccccccccccccccccccccccccccccccccccccccccccc aa dgccccccccccccccccccccccccccccccccccccccccccccccc d dacccccccccccccccccccccccccccccccccccccccccccccccc gd gd dg a d aa d d dg d gd d d aa d gd dg d aa d d dg d gd d d aa d ``` <!-- end of image --> Let's take a closer look at area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fb393dff b,#5854faff c,#ffc6c6ff d,#fe0405ff e,#0605fdff f,#c0bffeff g,#fe8182ff ``` ```image gdd gdd cddc adg cddg cddc ada gda add ddg gddc gddc cddg ada ada cddc f add gdd fbe gddc adg fbeee cddg cddc fbeeebf dda ada fbeeebf ada ddg fbeeebf gddc gdd fbeeebf cddg adafbeeebf ddg cdeeeebf ada fbeeebf gddc fbeeebdg cddc fbeeebfcddc cddg fbeeebf ada ada fbeeebf cddc gddc fbeeeb gdd cddc beeeb adg cddg feeeb cddc ada beeef ada gdd fbeeb ddg gddc feeef gdd cddg beeb ada ada feeef cddc add beebf gda gddc feeeb ddg cddg beeef cddc ada feeeb ada add beeef cddg gddc fbeeb gdd cddg feeef adg dda beeb cddc ada feeef gda gddc beebf ddg cddg feeeb gdd ddg beeef ad ada feeeb cd gddc beeef g cddc feeeb cddg beeef adafbeeb gddfeeef cddbeebf cdaeeef abeebf geeeb beeef feeeb beeea fbeeea feeeadc beebddg feeefada beebfada feeeb gddc beeef cddg feeeb dda beeef ada fbeeb gddc feeef cddg beeb ddg feeef ada beebf gddc feeeb cddc eeef cddg eb ada f gddc cddc cddg ada gdd gddc cddg ada add gddc cddg dda ada gddc ddg ``` <!-- end of image --> Amazing! This area was hiding an intersection all along! The final answer is: two intersections found.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fc3f41ff b,#514ffcff c,#ffc2c2ff d,#fe0505ff e,#0808feff f,#9494ffff g,#ff8282ff ``` ```image f fee fee fee fee fee fee fee fee gd fee cdaa feb d d beb dg cd beb ad dg beb cd d beb d gd beb dg dc beb aa d beb cd aabeb d beb dc bebcd aa beb dc cd beb d d ee aa dc fef d aa ee cd gd fef dg d ee d dc eb gd da be dc gd eb d d be aa dc ee d dgfef cd gdee dg caef d ee ga eb dc bed cd ebd dg be d d ee dg gd fef aa dc ee cd d fef d aa ee dc d fef aa cd e cd dg d d dc gd aa dc gd cd d ag dc d da gd gd dc a d aa d cd dg d gd dc d aa d cd dc d aa d cd dg d gd dc d aa d ``` <!-- end of image -->

I'm curious to see if this image contains any intersection points. My next step is to analyze the details within each area. <!-- image --> ```palette Key,Color ,#fefefeff a,#0808fdff b,#fc0908ff c,#5a61f1ff d,#e67064ff e,#b2b2ffff f,#98c599ff g,#b2d7b1ff ``` ```image e ae a ae ea a ea a e cc a a ae cc ea a a ae ac a a ae ae ea ea a a ea ac a a cc ae a ca cc a a ac ae ea a a ae ca ea a a ae ea ea a a cc cc a a cc ae a ea ae a a cc ae a ea ae a d ea ea bbb a ffafffffffffffffffbdfdbdfffffffffffffffffffacg ggccgggggggggggggbdggggbbggggggggggggggggggagf gggaggggggggggggbfggggggdbggggggggggggggggafgf gggacggggggggggbfggggggggfbdgggggggggggggcaggf ggggaggggggggfbfgggggggggggbbggggggggggggagggf ggggacggggggfbggggggggggggggdbdgggggggggacgggf gggggagggggfbgggggggggggggggggbbgggggggfaggggf gggggafgggdbgggggggggggggggggggdbggggggafggggf gggggfaggdbgggggggggggggggggggggfbdgggcagggggf ggggggagdbggggggggggggggggggggggggbbggaggggggf ggggggcabggggggggggggggggggggggggggdbacggggggf ggggggdaggggggggggggggggggggggggggggfabggggggf gggggdbccgggggggggggggggggggggggggggagdbfggggf ggggbbggaggggggggggggggggggggggggggcagggbdgggf gggbbgggacgggggggggggggggggggggggggagggggbbggf ggbbgggggaggggggggggggggggggggggggacggggggdbdf gbbggggggacggggggggggggggggggggggfagggggggggbb bbggggggggaggggggggggggggggggggggagggggggggggdb bbgggggggggafggggggggggggggggggggcagggggggggggf bd bdggggggggggfaggggggggggggggggggggaggggggggggggf bb bd gggggggggggagggggggggggggggggggacggggggggggggf gbd bd gggggggggggcagggggggggggggggggfagggggggggggggf bb bd ffffffffffffafffffffffffffffffaffffffffffffffg db bg cc cc bd bg a a bb b ac ae gbd b a ea bb b ae a dbg gb a cc bb gb a a db db ea ae db a ea db ea a d a ac cc a a ae ac ca a a aac a ``` <!-- end of image --> I'm now examining the contents of area A in detail. <!-- image --> ```palette Key,Color ,#fefefeff a,#0606feff b,#fe0606ff c,#a3a3feff d,#fc3c3fff e,#ff8a8aff f,#4f4af9ff g,#fecdceff ``` ```image caf dbbe ebbbg faf aac dbbe gdbbe caa faf dbbg ebbdg aac aa dbbg gbbbe faf faf dbbg dbbdg caac caa dbbg ebbbg faf fac gdbbg gdbbe caa caa gdbbg ebbdg aac aac gbbbg gbbbe faf caa gbbdg dbbdg caac aac gbbd ebbbe aaf caf gbbd gdbbd caa aac gbbd ebbdg aac faf gbbd gbbbe faf aa gbbd dbbdg caa faf ebbd ebbbe aaf caa ebbd gdbbd caa fac ebbe ebbbg aac caa ebbe gbbbe faf aacebbe dbbdgcaa caabbe ebbbaac aade gdfaa dfaf gaadbg dbbaac fafdbbe dbbgfaf caa dbbdg dbbg aa aac ebbbe dbbg faf faa gdbbd dbbg caa caac ebbbg dbbg fac faf gdbbe gdbbg caa caa ebbdg gbbbg aac aac gbbbe gbbdg caa faf gdbbd gbbd aac caac ebb gbbd caf faf gd gbbd aac caa gbbd faf aac bbd aa faf bd faf caac d caa aaf fac caa caa aac aac faf caa caa ``` <!-- end of image --> Wow! I can see an intersection so clearly in area A! The image features two intersection points.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0505feff b,#ff0707ff c,#8686ffff d,#ff5c5cff e,#cac9feff f,#4040ffff g,#ffb7b7ff ``` ```image e ac a ae ea a ca a c cf a a ae fc ca a a ac ff a a ae ae ea ca a a ca fc a ea cf ae a ca fc a a ac ac ea a ae ae cf ea a a ac ca ea a a cf ff a a fc ac a ea ac a a ff ae a ea ae a d ca ca bbb a a bg gbg ff cf bg bb a a bg db ae fc bg gbd ca a gb bb a ae gb gbg fc a gb bb ea ae gb db ae ea gb bd ca a db bb a cab gbac da eab dbcf aedbg db a cf bd bb fc a bb bb a ac gbg bb ae ea bb bd a a dbg bd ae ff bd bd ea a bb bd a ac gbg bd cf ea bb bg a a dbg bg ff ff bd bg a a db bg fc ae gbd bg a ca bb gb ae a dbg gb a ff bd gb ae a db gb ea ae g gb a ca db cf a d a fc ff ea a ae fc ca a a aac ea ``` <!-- end of image -->

Here's an image. My task is to find intersections or areas where lines come close together. The image is completely devoid of intersections. Zero.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0505ffff b,#ff3b3bff c,#a7a7ffff d,#ff8a8aff e,#5454ffff f,#ff0404ff g,#ffd0d0ff ``` ```image g bffg df gffg gf gffg fg gffg fd gffg bb gffg df gffg f gff fg gff fd dff bf dff gf dff f dff fg dfb fb dfb df dfb gf dfb f dfb fd dfb bb dfb df dfb gf bfb fg b fd bb df f fg fd bf gf f fg fb df gf f fd bb df gf fg fd bb df b aaeecc cceeaaaaaaaaaeecc cceeaaaaaaaaaeecc cceeaaaaaaae ceaaaac ceaaaec ceaaaec ceaaaec caaaaec eaaaae ceaaaac ceaaaac ceaa ``` <!-- end of image -->

Let's examine this image for potential line intersections. It's crucial to examine these regions more closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#f05a55ff b,#0708feff c,#585bf7ff d,#f6a7a3ff e,#fd0808ff f,#abaff7ff g,#afd6afff ``` ```image d e ed cbbc e fbbc bb ggggggggggggggggg e cbbf cbf ggggggggggggggggg de bbc bc ggggggggggggggggg e fbbf bb gggggggggggggggggae cbb fbf ggggggggggggggggge fbbc bc ggggggggggggggggea cbbf cb gggggggggggggggge bbc fbf gggggggggggggggea fbbf bb gggggggggggggggeg cbb cb ggggggggggggggedg fbbc bc gggggggggggggdegg cbbf bb gggggggggggggeggg bbc cbf ggggggggggggaeggg fbbf bc ggggggggggggegggg c bbgggggggggggaagggg fbfgggggggggeggggg gbbgggggggeaggggg ggbbggggggegggggg gggfbcgggedgggggg gggggbbgdeggggggg ggggggcbegggggggg gggggggabcggggggg gggggggegbbgggggg ggggggaaggcbggggg ggggggegggggbcggg gggggeaggggggbbgg gggggeggggggggcbf ggggedggggggggggbc ggggeggggggggggggcb gggeggggggggggggg fbf ggaeggggggggggggg bb ggegggggggggggggg c gaegggggggggggggg geggggggggggggggg eaggggggggggggggg egggggggggggggggg eagggggggggggggggg eggggggggggggggggg edggggggggggggggggg de ggggggggggggggggg e ggggggggggggggggg ae ggggggggggggggggg e ggggggggggggggggg aa e ed e ed de e de e aa e ed e ed de ea e aee de dee e dee aa deed e eed ea eed e eed ed eea de aea e aea de aee e dee aa dee e deed aa eed e eeded ee ``` <!-- end of image --> I'm determined to find out if an intersection exists in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff4040ff b,#0807fdff c,#5754fcff d,#fb8286ff e,#fe0505ff f,#afafffff g,#ffc7c7ff ``` ```image g a ge ae dee eed dea geeg aea geeg aea geeg aed dee eed dee eeg dea f geeg bf aea bbc geeg fbbbf aed fbbbc dee cbbc eed fbbbf dee cbbc eed cbbbf dea fbbbf geeg cbbc aea fbbbf geeg fbbbf aed cbbcee fbbbd dbbbc eecbbc dea fbbbf geeg cbbc aea cbbbf geeg fbbbf aea cbbc geeg fbbbf aed fbbbf dee cbbc eed fbbbf dea fbbb geeg cb aea f geeg aea geeg aed dee eed dee eeg dea geeg aea geeg aed dee eed dee eed ea eg a g ``` <!-- end of image --> I've cracked the case! This area contains the intersection. The final count is: one intersection.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff3f3fff b,#0707ffff c,#5858ffff d,#fd8687ff e,#fe0405ff f,#b4b4ffff g,#ffc8c8ff ``` ```image d e ed cbbc ge fbbc bb eg cbbf cbf ge bbc bc e fbbf bb da cbb fbf e fbbc bc aa cbbf cb e bbc fbf ed fbbf bb ge cbb cb eg fbbc fbc ge cbbf bb e bbc cbf de fbbf bc e c bb aa fbf e bc ed cb e fbf eg bb ge cbe dbc e bb aa cbf e bc ad bb e fbf eg bc ge cb eg fbf de bb e c da e ad e ed ge eg ge e da e aa e ed ge eg ge e de e aa e ed e eg ge ea e dea de dee e deeg aa geeg e geeg ad eed e eed eg aed ge aea eg aea de dea e dee da deeg e geeg ad geeg e eeded ee ``` <!-- end of image -->

I have an image in front of me. I need to determine if there are any intersection segments. These spots mark what I'd call 'danger zones' - areas where intersections are more likely. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd0405ff b,#0707fdff c,#ea8e86ff d,#9aa3edff e,#f03b3aff f,#4d48e3ff g,#afd6afff ``` ```image d fb bb bf bd dbd db fb bb bf bd dbd db fb bb bf bd bd db fb bb bf bd bd db fb bb bf bd bd db fb bb ggggggggggggggggggggggggggggggggggggggggbf gggggggggggggggggggggggggggggggggggggggbf ggggggggggggggggggggggggggggggggggggggbdg ggggggggggggggggggggggggggggggggggggdbggg gggggggggggggggggggggggggggggggggggfbgggg ggggggggggggggggggggggggggggggggdbbbggggg gggggggggggggggggggggggggggggfbbbdggggggg gggggggggggggggggggggggggdbbbfgggceeggggg ggggggggggggggggggggggfbbbfeaaaaaeceagggg ggggggggggggggggggcfbbfaaaecggggggggeaggg gggggggggggceaaebbbfcggggggggggggggggcagg ggggceaaaaaefbbbdgggggggggggggggggggggcag aaaaaecggdbbbfgggggggggggggggggggggggggggag gggggfbbbdgggggggggggggggggggggggggggggggac ggfbbfggggggggggggggggggggggggggggggggggg ac bbbfgggggggggggggggggggggggggggggggggggggg ae dggggggggggggggggggggggggggggggggggggggggg aa ggggggggggggggggggggggggggggggggggggggggg ea ggggggggggggggggggggggggggggggggggggggggg ca ggggggggggggggggggggggggggggggggggggggggg ca a ac ac ae ae ea ea ca ca ac ac ae ae ea ea ca ca a ac ac ae aa ea ca ca a a ``` <!-- end of image --> This is a magnified view of the region A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd0507ff b,#0705fcff c,#fca7a9ff d,#a5a5feff e,#fc5052ff f,#534ffbff g,#85168fff ``` ```image d db fbb fbbd bbbd dbbbd dbbf dbbf fbbf ddfbbd dfbbbbbd dfbbbbbfd dfbbbbbbfd dfbbbbbfd ddfbbbbbfd cceeae dfbbbbbfddccceeaaaaaaaaaac dfbbbbbfgeeaaaaaaaaaaeeeccaaac dfbbbbbbgaaaaaaaaaeeccc eaac cgfbbbbbggaaaaaeeccc eaac cceeegbbbbbbggaeecc eaae ccceeaaaaggbbbbbbgcc caae ccceeaaaaaaaagbbbbbbfd caae ccceeaaaaaaaaaaegfbbbbbffd caae cceeeaaaaaaaaaaeecccdfbbbbbfd caa aaaaaaaaaaeeccc dfbbbbbbfd a aaaeecc dfbbbbbfd ddfbbbbbfd dfbbbbbfdd dfbbbbbfd dfbbbbbbfd bbbbbfd bbfd ``` <!-- end of image --> Wow! I can see an intersection so clearly in area A! My investigation reveals that there is exactly one intersection in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fd0608ff b,#0605feff c,#fdb0b1ff d,#8581faff e,#fe5151ff f,#483df4ff g,#c4c4ffff ``` ```image d fb bb bf bd gbg db fb bb bf bd gbg db fb bb bf bd gbg db fb bb bf bd gbg db fb bb bf bd gbg gb fb fb bf bd gbg gb db gbbb dbbbg gfbbf ccee dbbbdeaaaaaecaa cfbbfaaaec ea ceaaabbbfc ca ceaaaaaefbbfg ca aaaaaecc gfbbd ac dbbbg ac gfbbf ae bbbd ae g aa ea ea ca cac ac ae ae aa ea ea ca ca ac ac ae ae aa ea ea ca cac ac ae ae aa ea ea ca ca a ``` <!-- end of image -->

Hmm, I'm not sure what to expect from this image. Let's see if any lines cross. I'm going to focus my attention on these specific areas. <!-- image --> ```palette Key,Color ,#fefefeff a,#ef6861ff b,#0707fdff c,#fd0909ff d,#545cdfff e,#ffbdbdff f,#babaffff g,#add4adff ``` ```image e ac bf cac b ca c fb c ec bd ce ce bf ec ec b c ce fb ac c bd c ca bf ca c b c aa fb ce c bd ec ac bf c c b ac ec fb c ce bd ca c bf c ca b ce c dbgggggggggacggg aa gbdggggggggcgggg c ggbgggggggacgggg ac gggbggggggcggggg c gggdbggggcaggggg ec ggggbdgggcgggggg ce gggggbggcggggggg c ggggggbacggggggg ce ggggggdbgggggggg c ggggggabdggggggg aa ggggggcgbggggggg c gggggcaggbgggggg ac gggggcgggdbggggg c ggggcgggggbdgggg ec gggacggggggbgggg ce gggcggggggggbggg ec ggacggggggggdbgg ce ggcggggggggggbdg c ca b ca c fb c ce db ac ec bf c c b ec aa fb ce c db ec ca bf ce c b c ce fb ca ec db c c bf aa aa bbf c c fbbf ac ca fbbf c ec fbbf ec ce fbbf ce ec fbbf c c bbf gcagggggggggggggg aa bbf ggcgggggggggggggg c bbf ggaaggggggggggggg ca bbf gggcggggggggggggg ec bbf gggacgggggggggggg ce bbf ggggcgggggggggggg ec bbf ggggacggggggggggg c bbfgggggcggggggggggg bbdggggcgggggggggg gbbdggcaggggggggg gggbbdgcggggggggg gggggbbdagggggggg gggggggbbdggggggg ggggggggabbdggggg gggggggggcgbbdggg gggggggggacggbbgg ggggggggggcgggggg gggggggggggcggggg gggggggggggcagggg ggggggggggggcgggg ggggggggggggcaggg gggggggggggggcggg gggggggggggggacgg ggggggggggggggcgg ``` <!-- end of image --> I wonder what we'll find inside area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#fc5b5eff b,#0504fdff c,#fd0607ff d,#7272ffff e,#ffb8b8ff f,#bab9fdff g,#3736fdff ``` ```image fbbf aca dbbf ecc gbg cca bbd acc fbbf cce dbbf aca gbg ecce bbd aca fbbf ecc dbbf cca gbg acc bbd cce fbbf aca dbbf ecce gbg aca bbdecc fbbaca dbbc bbg acbbd eccfbbf aca dbb ecc gbg cca bbd acc fbbf cce dbb aca gbg ecce fbbd aca fbbf ecc dbb cca gbg acc fbbd cce fbbf aca dbb ecce gbg ``` <!-- end of image --> Wow! I can see an intersection so clearly in area A! Next up, a closer look at another region. Time to investigate area B up close. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff3b3bff b,#0e0cfdff c,#fe0505ff d,#9490fbff e,#fe7b7bff f,#920b77ff g,#febfc0ff ``` ```image ecc cce gcc ace gccg aca gccg eca ccg eca cce ecc ace gccg aca gccg d eca bbd ccg bbbbd eca dbbbbd cce dbbbbd ecc dbbbbd ace dbbbbdgcc dbbbbfce dbbbbfg dbbbbd dbbbbd efbbbbd ccdbbbbd ecc dbbbbd ace dbbbbd gcc dbbbb ace dbd gccg aca gccg eca ccg ecc cce gcc ace gccg aca gccg eca ccg ``` <!-- end of image --> Success! This area contains an intersection point! The final answer is: two intersections found.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff4e4eff b,#0908feff c,#ff0707ff d,#7773fbff e,#fe9292ff f,#c7c7ffff g,#ffd3d3ff ``` ```image g ac bf caa b ce c fb c ec bb cg cg bf ec gc b c ce fb aa c bd c ce bf ce c b gc aa db cg c bd ec ec bf c cg b aa gc db c cg bd ce c bf gc ce b cg c db ec aa bd c c bf aa ec b c c db ce gc bd gc cg bf cg gc fbec ce db c abd aa c bf c ce fb ec gc db c cg bd ec ec b cg c fb gc aa db ce c bd c ce b aa gc fb c cg db aa ec bd c c b ec aa fb cg c db gc ce bd ce gc b c cg fb ce ec db c c bf aa aa bbf c c fbbf ec ce fbbf cg gc fbbf gc cg fbbf cg ec fbbf c c fbbf ce aa fbbf c c bbf aa ce bbf c gc bbf ec cg bbf c ec bbf gc c bbd cg bbd gc bbd ce bbd c bbda bbd ebbd c bbd ec bb cg gc ce c aa c aa c ``` <!-- end of image -->

I'm on the case! Let's uncover any intersections hidden in this image. I've noticed 1 areas of interest. These could be potential intersection zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#df6052ff b,#0000ffff c,#bbbcfeff d,#ff9797ff e,#fd0708ff f,#6f7ae9ff g,#aed5b0ff ``` ```image c fb fb e fb ded fb ee fb ded fb ee fb ded fb ee fb ded fb ee fb ded fb ee fb ded cb ee cb ded cb ee cb ded cb ee cb ded cb ee cb ded cbggggggggggggggggggg ee cbgggggggggggggggggg ded gbggggggggggggggggg ee ggbgggggggggggggggg ded gggbggggggggggggggg ee ggggbgggggggggggggaed gggggbgggggggggggee ggggggbggggggggaeag gggggggbggggggeeggg ggggggggbgggaeagggg gggggggggbeeagggggg ggggggaeeabfggggggg gggaeeaggggbfgggggg aeeaggggggggbfggggg deeeggggggggggggbfgggg deee ggggggggggggggbfggg deeed gggggggggggggggbfgg eeed ggggggggggggggggbfg eeed gggggggggggggggggbf aeed ggggggggggggggggggbc aeed gggggggggggggggggggbc aeed ggggggggggggggggggg bc d bc bc bc bc bc bc bc bc bc bc bc bc bc bc bc bc bc bc bc bc bc bc bc bc bc bc bc bc bc bc bc bc bc bc bc b ``` <!-- end of image --> I'm going to scrutinize area A for any signs of an intersection. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff4343ff b,#0908fdff c,#cecefeff d,#ffbcbcff e,#fd0406ff f,#3c3cfeff g,#fa7a7eff ``` ```image f bf bbf cbbf cbbf cbbf cbbfc cbbfc cbbfc cbbbc cbbbc cfbbc a cfbbc dee cfbbc aeea fbbc deeeg fbbc aeead fbbc deeeg fbbc aeead fbbc daeeeg fbbcdaeeeead fbbeeeegd dgeebbbgd dgeeeeegfbbc dgeeeeegd fbbc dgaeeeead fbbc gaeeeead fbbc gaeeeead fbbc eeeeag fbbc eag fbbc fbbc fbbc fbbc fbbc fbbc fbbc fbbc fbb fb f ``` <!-- end of image --> I observe an intersection inside area A. It was tricky, but I finally found one single intersection in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff4646ff b,#0000ffff c,#bebeffff d,#ffa8a9ff e,#fe0607ff f,#6161ffff g,#fe8282ff ``` ```image c fb fb e fb deg fb ee fb deg fb ee fb deg fb ee fb deg fb ee fb deg fb ee cb deg cb ee cb deg cb ee cb deg cb ee cb deg cb ee cb deg cb ee cb deg cb ee cb deg cb ee b deg bc ee bc deg bc ee bc aeg beeg geegbc geea bc geea bc deea bc deea bc deeed bc deeed bc aeed bc aeed bc aeeg bc aeeg bc g bc bc bc bc bc bc bc bc bc bc bc bc bc bc bc bc bc bc bc bc bc bc bc bc bc bc bc bc bc bc bc bc bc bc bc b ``` <!-- end of image -->

The hunt for intersections begins! Let's analyze this image closely. I've noticed 1 areas of interest. These could be potential intersection zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd0605ff b,#0606fbff c,#e78e83ff d,#5d68e9ff e,#f24a44ff f,#f2efebff g,#b0d6b0ff ``` ```image f ac fa af fa af ca a ce a ec a ac fa af f fa a af ac ca ca a a ce ac a ca ec a a ac ac ea fa fa af af fa ea af fa ca af a ee ce fa a af ec ee a fa ac af fa ee af fa fa af af ee ca fa afffffffffffffffffffffffffffffffffffffffffffaf eegggggggggggggggggggggggggggggggggggggggggaef faggggggggggggggggggggggggggggggggggggggggcagf feegggggggggggggggggggggggggggggggggggggggaggf f fgaggggggggggggggggggggggggggggggggggggggaeggf fdbb fgacggggggggggggggggggggggggggggggggggggcagggf fdbbd fggaggggggggggggggggggggggggggggggggggggaggggf fdbbd fggagggggggggggggggggggggggggggggggggggaeggggf dbbd fggcagggggggggggggggggggggggggggggggggcagggggf dbbd fgggagggggggggggggggggggggggggggggggggagggggdbbd fgggcagggggggggggggggggggggggggggggggaeggdbbdf fggggaggggggggggggggggggggggggggggggcadbbdgggf fggggeeggggggggggggggggggggggggggggdbbdggggggf fgggggagggggggggggggggggggggggggdbbbcggggggggf fgggggeegggggggggggggggggggggdbbdgcagggggggggf fggggggaggggggggggggggggggdbbbggggaggggggggggf bbbbbddddff fggggggacggggggggggggggdbbbggggggacggggggggggf ffgdddbbbbbbbbbbbbddddgagggggggggggdbbbggggggggeagggggggggggf fgddddbbbbbbbbbbbbbbbgggggggggggaggggggggggggf fgggggggcagggggggggggggggggggggacggggggggggggf fggggggggaggggggggggggggggggggeagggggggggggggf fggggggggcagggggggggggggggggggaggggggggggggggf fgggggggggaggggggggggggggggggacggggggggggggggf fgggggggggeeggggggggggggggggeagggggggggggggggf fggggggggggaggggggggggggggggaggggggggggggggggf fggggggggggeeggggggggggggggacggggggggggggggggf fgggggggggggagggggggggggggeagggggggggggggggggf fgggggggggggacggggggggggggaggggggggggggggggggf ffffffffffffafffffffffffafffffffffffffffffff af ee fa fa a af ce ee a fa ee af a ee ec fa a af aae fa ``` <!-- end of image --> This close-up of area A is like examining a piece of evidence. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0303ff b,#0404feff c,#fd7778ff d,#a1a0feff e,#fc3134ff f,#febebeff g,#4945faff ``` ```image e c af fa ae ea aaf caa eac faaf faa eac eac cae faa faaf eac eac cae cae aaf faaf cae aac aaf cae cae faaf faaf aac eac cae faa faaf eac aac faa eae d eac faaf dgbb cae aac dgbbbbb aaf eae dgbbbbbgd cae faaddbbbbbgd aaf egbbbbbgd cae dbbbbbgd faaf dgbbbbgd eac dgbbbbgec faa dgbbbbgdeae eac dgbbbbgd caaf faa dgbbbbgd faac eac dgbbbbgd eae cae dgbbbbgd caa aaf dgbbbbgd faaf cae dgbbbbgd eae bbbgggggddddddaaf dgbbbbgd caa bbbbbbbbbbbbbbbbbbbggggdddddd dgbbbbgd faaf ddddddgggggbbbbbbbbbbbbbbbbbbbbbgbbbbbd eae eacdddddgggggbbbbbbbbbdd caa faa ddd faaf eac eac faa caa eac faaf cae eac aaf caa cae faaf aaf eac cae cae faaf faaf eac eac faa cae eac faaf faa aac eac cae cae faaf ``` <!-- end of image --> Case closed! This is definitely an intersection point in area A. There are precisely two intersections present in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fe0606ff b,#0202ffff c,#fe8f90ff d,#8b8bfeff e,#ff4a4aff f,#f7cfd7ff g,#4a46fbff ``` ```image f ac a af fa a ca a ce a ec a ac a af f fa a a ac ca ca a a ce ac a ca ec a a af ac ea a a af af fa ea a a ca af a ee ee fa a af ec ee a fa ac af a ee af fa fa af a ee ca fa a a ee ae a fa ec a a ae gbb ac fa gbbd a a gbbd af ac gbbd fa ca gbbd a a gbbd ca ac dbbg a cadbbg ee dbbg a dbbgc ec dbbg ca a dbbg a bbbbbggddf ac dbbg ac fddgggbbbbbbbbbbggdddfa dbbgf ca dddggbbbbbbbbbbbbbbf a fa ff ac a ca ca a a af ee ea a a ec af a ea ac a fa af af ee fa fa a af ce ee a fa ee af a ee ec fa a af aae fa ``` <!-- 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,#fe0a0aff b,#0707fdff c,#a7a9faff d,#f26563ff e,#aed4adff f,#febebeff g,#5055f4ff ``` ```image f da ad ad af af a a fa fa da da aa ad ad af af a b fa bc fa gb da bb da bg aa cbc ad bb ad bg af cbc af gb a bb fa cbc fa gb da bb da bg aa cb ad bb ad bg af cbc af gb afeeeeeeeeeeeeeeee bg faeeeeeeeeeeeeeeeecbc faeeeeeeeeeeeeeegb daeeeeeeeeeeeebb edaeeeeeeeeeebge eeeaeeeeeeegbeee eeeeaeeeeebbeeee eeeeeadeebgeeeee eeeeeeadbeeeeeee eeeeeebbaeeeeeee bbbgcc eeeeebbeaaeeeeee ccggbbbbbbbggcc eeecbceeeaaeeeee ccgbbbbbbbbggcc eegbeeeeeedaeeee cggbbbbbbbbgbbeeeeeeeedaeee cggeeeeeeeeeeeaee eeeeeeeeeeeeeead eeeeeeeeeeeeeeead eeeeeeeeeeeeeeeead eeeeeeeeeeeeeeee aa aa da da fa faf af ad ad aa aa da da fa faf af ad ad aa aa da da fa faf a ``` <!-- end of image --> Here's a close-up of the area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff0505ff b,#0505feff c,#9694fcff d,#fa898eff e,#fe3e3eff f,#ebd3e7ff g,#463cf4ff ``` ```image f e ae aae faad daad fg daad cbb daae cbbg daae fgbbc daae cbbbc faaef cbbgf faaaf gbbg feaaf fbbbc eaad cbbgf eaad gbbg daad fgbbc daadbbbf dgbbg fgbbge cbbbcaaef cbbgf faaaf fgbbc feaaf fbbbc eaad cbbgf eaad gbbg daad fbbbc daae bgggbbbf daae bbbbbg daae fcccc faaef faaaf feaa ea e ``` <!-- end of image --> Bingo! This close-up reveals an intersection in area A! It was tricky, but I finally found one single intersection in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0505ff b,#0606feff c,#acacffff d,#fb8588ff e,#fe3e3eff f,#ffc8c8ff g,#5353ffff ``` ```image f ea ae ad ad af af a fa da da ea ae ae ad af af a b fa bc fa gb da bb ea bg ee cbc ae bb ad bg af cbc af gb a bb fa cbc fa gb da bb ea bg ee cb ae bb ad bg ad cbc af gb a bg fa cbc fa gb da bb da bg faf gb faf bb ad bg adbc gbe bbbgcc bg aa ccggbbbbbbbggcc cbc ea ccgbbbbbbbbggcc gb da cggbbbbbbbbgbb da ccc faf af ad ae ae aa ea da da faf af ad ae ae aa ea da da faf af ad ae ae ea ea da da faf a ``` <!-- end of image -->

I'm ready to tackle this image and find those intersections! My analysis shows there's absolutely no intersections in the image

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff6767ff b,#0505ffff c,#ff0909ff d,#7575ffff e,#ffc0c0ff f,#bcbcffff g,#3939ffff ``` ```image d db gb gb gb bg bg bg bd bd bf bf bf fbf fb fb fb db db gb gb c gb ac bg c bg ce bg ca bd ac bd c bd ce bf ca bf ec bf c fb ce fb ca fb ec db c db ce db ac gb ec bbbbgdf gb c ffdgbbbbbbbgdf gb ca ffdgbbbbbbbgdff bg ac ffdgbbbbbbbgdbg ec ffdd c ca ac c ce ca ac c ce ca ec c ce ac ec c ce ac ec c ca ac ec c ca ac c ce ca ec cccae c eaccccae ce eaccccae ca accccae ec accccae c accccae ce accccae ac accc ``` <!-- end of image -->

I have a feeling there might be some intersections in this image. I have a hunch that these areas might contain the intersections we're looking for. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0808ff b,#474af9ff c,#fb9997ff d,#9b9ef8ff e,#f74945ff f,#abd4abff g,#0405feff ``` ```image c a ac ca a ee a ac a a ca a ee a ac ca a ee a ac a a ca a ee a ac ca a ca a ac a ac ca a ee a ac a ac a ac ca ac a ac ee ac a ac ac ac ca ae a ae ee g ae a dgd ae ac bg ae a gb ae a bg ae ca gg ae a dgd ae ee bg ae a gb ae ac bg ae ca gg ae a dgd aa ee gg aa a gb aa ac bg ea ffffffffffffffaf gb ea fffffffffffffaff dgd ea ffffffffffffeaff gg ea ffffffffffffafff dgd eafffffffffffeefff bg eaffffffffffaffff gb eaffffffffacffff dgd feaffffffcafffff gg ffeafffffaffffff dgd fffeafffeaffffffbg ffffeaffaffffffgb fffffeaaeffffbgf ffffffeaffffggff ggbbdd ffffffffffdgdfff ddbbgggggggggbbdd fffffffffggfffff ddbbgggggggggbbbdfffffgbffffff dddbbggggg ``` <!-- end of image --> I'm focusing my attention on this specific region, area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff0404ff b,#6060ffff c,#ff7d7dff d,#b2b2ffff e,#ff4848ff f,#ffb7b7ff g,#0a0affff ``` ```image caa aaf eae faaf eac caa aac cae faaf f eae af faa aaf aac eaaf caa eaaf aaf eaaf eae eaaf faaf eaaf eac eaaf caa eaaf aac eaaf cae eaaf faaf eaaf eae b caaf faa dgg caacaac bggg caaaa dgggb caaf dgggd cc bggb dgggd bggg dgggb bgggd bbbdddd bggb ``` <!-- end of image --> There is no intersection present within area A. There's definitely not a single intersection on the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0707ff b,#4d4dffff c,#ff7a7aff d,#a5a5ffff e,#ff3d3dff f,#ffbfbfff g,#0505ffff ``` ```image c a af fa a ce a ac fa af ca a ee a af fa a ce a ac a af ca a ee a af fa a ce a ec a af fa a ee a ac fa af a ac ca ac a ac ec ac a ac af ac fa ac a ac ee g ac a dgd ae ac bg ae fa gb ae af bgd ae ca gg ae a dgd ae ec gg ae a gb ae af bg ae fa gg ae a dgd ae ce gg aa a gb ea ac bg ea fa gb ea af dgd ea ca gg ea a dgb ea ee bg ea a gb ea af dgd ea fa gg ea a dgd ea ce bg ca a gb caac bg ca gg ggbbdd dgd ddbbgggggggggbbdd gg dddbbgggggggggbbdd gb dddbbggggg ``` <!-- 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,#fc0a0aff b,#0a0afbff c,#e6bed7ff d,#b1d7b1ff e,#6066f2ff f,#ea6661ff g,#98c399ff ``` ```image c af a ff a ca ac ca ac a af a fa a ca ac ca af a ff a fa a ca ac a af a ff a fa ac ca ac a af a fa agdddddddddddddddddddddddddddddddddg be fadddddddddddddddddddddddddddddddddg bb gagddddddddddddddddddddddddddddddddg cbe ggaddddddddddddddddddddddddddddddddg bb gdafdddddddddddddddddddddddddddddddg cbe gddadddddddddddddddddddddddddddddddg bb gddafddddddddddddddddddddddddddddddg cbe gdddaddddddddddddddddddddddddddddddg fa bb gdddfadddddddddddddddddddddddddddddg aaf cbe gddddadddddddddddddddddddddddddddddg caac bb gddddgaddddddddddddddddddddddddddddg faac cbe gdddddagdddddddddddddddddddddddddddg faa bb gddddddadddddddddddddddddddddddddddg aaf cbe gddddddafddddddddddddddddddddddddddg caac bbgdddddddaddddddddddddddddddddddddddg faac cbeddddddffdddddddddddddddddddddddddg faa gbbddddddadddddddddddddddddddddddddg aaf gdgbeddddfadddddddddddddddddddddddgaac gdddbbddddadddddddddddddddddddddfaag gddddgbeddgaddddddddddddddddddfaaddg gddddddbbddafdddddddddddddddaafddddg gdddddddgbedaddddddddddddgaafddddddg gdddddddddbbafdddddddddfaagddddddddg gddddddddddgbbdddddddaaadddddddddddg gddddddddddddbbddddaafdddddddddddddg gdddddddddddddabbfafdddddddddddddddg gdddddddddddddfaabbbgddddddddddddddg gddddddddddddddddddgbbeddddddddddddg gdddddddddddddddddddddebbedddddddddg gddddddddddddddddddddddddbbbgddddddg gddddddddddddddddddddddddddgbbeddddg gdddddddddddddddddddddddddddddebbedg gddddddddddddddddddddddddddddddddbbbc gddddddddddddddddddddddddddddddddddgbbe gddddddddddddddddddddddddddddddddddg ebbe gddddddddddddddddddddddddddddddddddg bbbc gddddddddddddddddddddddddddddddddddg cbbe gddddddddddddddddddddddddddddddddddg ebbe gddddddddddddddddddddddddddddddddddg bbbc gddddddddddddddddddddddddddddddddddg cbbe gddddddddddddddddddddddddddddddddddg ebbe bb ``` <!-- end of image --> This is a magnified view of the region A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0506ff b,#0908fdff c,#fec8c9ff d,#bbbafeff e,#655ff8ff f,#ff8989ff g,#f84147ff ``` ```image ag aaf faa aaf faa gag caac gag caac fag aaf faa aaf caac gag caac gag caac faa aaf faa gaf caac gag caac gag aaf faa aaf faa e gaf bbd caac bbbe gag ebbbd caac dbbbe fag ebbbd aaf dbbbe faa cg ebbbd aaf fgaa dbbbe caa faaaaf ebbbd gag cgaaaaf dbbbe caac cgaaagf ebbbd gag fgaaagc dbbbe caac faaaafc ebbbd fag cgaaaaf dbbbe aaf cgaaagf ebbbdfaa fgaaagc dbbbegaf faaaafc ebbbgac cgaaaaf dbbbbg cgaaagc ebbbd fgaaagc dbbbe faaaafc cebbbed cgaaaaf fabbbbbgaagc aagebbbbed faaaaeebbbbed ggf debbbbbe debbbbed debbbbed debbbbbe debbbbed debbbbed debbbbbe debbbbed debbbbed debbbbbe debbbbed debbb deb ``` <!-- end of image --> Incredible, there's actually an intersection in area A! I've identified a total of two intersection points.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fe0505ff b,#0c0afdff c,#ffb7b7ff d,#c0c0ffff e,#6c6cffff f,#ff7777ff g,#f93a40ff ``` ```image c gf a fg a ca a ca ac a gf a fg a ca ac a af a gg a fa a ca ac a af a gg a fa a ca ac a gf a fg a be ca bb ac dbe a bb ac dbe a bb gf dbe a ga bb fg aaf dbe a caac bb ca faac dbe ac gag bb a aaf dbe af caac bb a faac dbe gg gag bb a aaf dbe fa caac bb a faa dbe ca gag bb ac aaf dbe a caac bbgf faa dbb gag bb aaf abbgac caabbbd dbbe ebbe bbbd dbbe ebbe bbbd dbbe ebbe bbbd dbbe ebbe bbbd dbbe ebbe bb ``` <!-- end of image -->

Alright, let's get to work and investigate this image for intersections. I can confidently say that there are no intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0404ff b,#5252ffff c,#ff8e8eff d,#a5a5ffff e,#0606ffff f,#ffc0c0ff g,#ff4343ff ``` ```image d dee beb beb eeb eed deed dee bee beb beb eed deed deed dee bee bd beb dbeeeeeebdd eeb dbeeeeeebbd eed dbbeeeeeebd deed ddbeeeeeebdddee dbee g caag gaac gaaf faag caac gaaf faag caac gaaf faag caac gaaf faag cag aa caf ag aa caf ag aa caf ag aa caf ag ga caf ag ga faf ag ga faf ag ga fac ag ga fac ag ga fac aa ga fa ``` <!-- end of image -->

Time to put on my detective hat and find those intersection points! Let's take a closer look at what's happening inside these zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#f3494aff b,#5054f6ff c,#a8a9feff d,#faa2a0ff e,#0707feff f,#add4adff g,#fe0605ff ``` ```image c fffebfffffffffffffff ffffefffffffffffffff ffffbbffffffffffffff fffffeffffffffffffff fffffbefffffffffffff fffgafefffffffffffff ffffagaeffffffffffff ffffffaeafffffffffff ffffffffeggdffffffff ffffffffebfggaffffff fffffffffefffaggffff fffffffffbbffffaggff ffffffffffeffffffdggd ffffffffffbeffffffffgga fffffffffffeffffffff aga ffffffffffffefffffff dgg ec dggd e gga ec aga e dgg bb dggd e gg ce dgd e ga ce gg ec ag e dg ec gd e ga bb ag e dg ce gd e ga ce gg ec ag e dgd ec ga e gg bb ag e dg ce gd e ga ce ag ec dg e gd ec ga e gg bb ag e dgd ce ga e gg ce ag ec dg e gd ec ga e ag bb dg e be e ce ec e ec eeb beeb beeb beeb ceeb ceeb ceeb ceeb ceeec ceeec ceeec ceeec ceeec ceeec cee ``` <!-- end of image --> Could this be where the intersection is hiding, in area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#f2404dff b,#5c59fbff c,#b0b0ffff d,#ff8a8aff e,#0a07fcff f,#fecdceff g,#fe0304ff ``` ```image cc cee eeb cee beb ceec beb eec bee eec cee d eeb fggaf cee fagggafbeb fagggaeec fdggeeb daeeaaf beeggaf eeagggad ceefdggggd eeb dggggaf cee dagggaf beb fagggad ceec fdggggd beb dggggaf eec daggga bee fagg eec fd cee eeb cee beb ``` <!-- end of image --> Aha! I've found an intersection inside area A! The image features one single intersection point.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fa474bff b,#4949ffff c,#bebeffff d,#ffa2a2ff e,#0707feff f,#8686ffff g,#ff0505ff ``` ```image c ef e bb e fe ga e agae dea eggd ef gga e aga bb dgg e dggd fe gga e aga ce dgg ec dggd e gga ef aga e dgg bb dggd e gg fe dgd e ga ce gg ec ag e dg ef gd e ga bb ag e dg fe gd e ga ce gg ec ag e dgd ef ga e gg bb ag e dg fe gd e ga ce ag ec dg e gd ef ga e gg bb ag e dgd fe ga e gg ce ag ec dg e gd ef ga e ag bb dg e fe e ce ec e ef eeb feeb feeb feeb feeb feeb feebc feebc feebc ceeec ceeec ceeec ceeec ceeec cee ``` <!-- end of image -->

This image seems promising for intersection detection. 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,#5a5cfbff b,#fe0404ff c,#0808feff d,#fbacaaff e,#e8564bff f,#b1b2feff g,#aed5adff ``` ```image d ebe dbb dbbd bbe ebe dbb gggggggggggggggg dbbd gggggggggggggggg bbe gggggggggggggggg ebe gggggggggggggggg ebb gggggggggggggggg dbbd gggggggggggggggg bbd gggggggggggggggg ebeggggggggggggggg ebbggggggggggggg ggebbdgggggggggg gggggbbeeeeeeeeedddddddd gggggggeeeeeeeeeeeeebbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb gggggggggggggggg gggggggggggggggg gggggggggggggggg gggggggggggggggg gggggggggggggggg gggggggggggggggg gggggggggggggggg gggggggggggggggg aaccccccgggggggg faccccccaaf fc faaccccccaf ac faccccccaf ca ccccccaff cf f c c fc ac ca cf c fc ac ca cf c fc ac ca cf c c fc ac ca cf c fc ac ca cf c fc ac ca cf c c fc ac ca cf c fc ac ca cf c fc ac ca cf c ``` <!-- end of image --> Here's a close-up of the area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#4545ffff b,#ff0303ff c,#0505ffff d,#ff8b8bff e,#ff5656ff f,#9e9effff g,#ffcdcdff ``` ```image g beg bbbed gebbbbd dbbbbeg debbbeg gebbbed gebbbbeddddddddddddddd dbbbbbbbbbbbbbbbbbb dddeeeeeeeeeeeeee fffaaccc fffaaccccccccccca ``` <!-- end of image --> No intersection found in area A, but I won't give up. I can confidently say that there are no intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#4141ffff b,#ff0404ff c,#0404ffff d,#ffa4a4ff e,#ff5353ff f,#c8c8ffff g,#8888ffff ``` ```image d ebe dbb dbbd bbe ebe dbb dbbd bbe ebe ebb dbbd bbd ebe ebb dbbd bbeedddddddddddddd eeeeeeeeeeeeebbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb gacccccc fgacccccagf fc fgacccccagf gc fgaccccccagf ca acccccagf cg f c fc gc aa cg cf c fc ac ca cf c fc gc ca cg c fc gc aa cg cf c fc ac ca cf c fc gc aa cg cf fc gc aa cg cf c fc ac ca cf c fc gc aa cg c ``` <!-- 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,#5255f6ff b,#fe0606ff c,#f4a29dff d,#afd6afff e,#f54f4bff f,#0707feff g,#a8aafbff ``` ```image cc ebbbbbbbbbbbeeccc cceebbbbbbbbbbbeeecc cceeebbbbb eb be bc b cb eb bc b b cb ee bc b b eb be bc b cb eb be b b g cb dddddddddddddddddddd aa ee dddddddddddddddddddd fg bc dddddddddddddddddddd f b dddddddddddddddddddd af b dddddddddddddddddddd fg cb dddddddddddddddddddd f be dddddddddddddddddddd gf bcdddddddddddddddddddd fg bdddddddddddddddddddd f cbddddddddddddddddddd gf ebdddddddddddddddddd fa dbeddddddddddddddddd f ddbcdddddddddddddddd f dddbdddddddddddddddd aa dddcbddddddddddddddd fg ddddebdddddddddddddd f dddddbeddddddddddddd af ddddddbddddddddddddd fg dddddddbdddddddddfdd f dddddddebddddddafddd gf ddddddddbeddddffdddd fg dddddddddbcddffddddd f ddddddddddbdfadddddd gf ddddddddddafdddddddd fa dddddddddffebddddddd f ddddddddfaddbedddddd gf ddddddgfgddddbcddddd aa dddddafdddddddbddddd fg ddddffddddddddcbdddd f dddfaddddddddddebddd af dafdddddddddddddbedd fg ffdddddddddddddddbdd f faddddddddddddddddddd gf gfgdddddddddddddddddddd fg af dddddddddddddddddddd f ff dddddddddddddddddddd gf fa dddddddddddddddddddd fa gfg dddddddddddddddddddd f af dddddddddddddddddddd gf ff dddddddddddddddddddd aa fg dddddddddddddddddddd f af dddddddddddddddddddd f ff dddddddddddddddddddd af fa dddddddddddddddddddd fg gfg dddddddddddddddddddd f af dddddddddddddddddddd af ff dddddddddddddddddddd fg fa f gf gf af fa fa fgfg gf ``` <!-- end of image --> Let's see what secrets area A holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#4f48f8ff b,#fe0505ff c,#ffc6c6ff d,#ababfeff e,#fb3a3dff f,#0707feff g,#ff7f7fff ``` ```image c bc be bbe cbbg gbbc gbbc ebe cbbg cbbg gbbc ebb ebe cbbg cbbc gbbc ebe bbe cbbg gbbc gbbc ebe dd bbe aff cbbg dfffd gbbc dfffd ebb affa ebe affd cbbg dfffd cbbg dffa gbbc affa ebbdfffd eefffd affa affabc dfffdgbbc dfff ebe affa bbe affd cbbg dfffd gbbc dffa ebbc affa ebe dfffd cbbg dfffd cbbg affa gbbc affd ebb dfffd ebe dffa cbbg affa cbbc fffd gbb dfffd gc ffa fa d ``` <!-- end of image --> I observe an intersection inside area A. One intersection, that's it, but I found it.

<!-- image --> ```palette Key,Color ,#fefefeff a,#3636ffff b,#ff0808ff c,#ffb0b0ff d,#7c7cfeff e,#ff5b5bff f,#0404ffff g,#c0bffeff ``` ```image cc ebbbbbbbbbbbeeecc ccceebbbbbbbbbbbbeecc ccceebbbbbb eb be bc b cb eb be b b cb be bc b cb eb be bc b cb eb be bc b d cb aa eb fg bc f b df b fg eb f be df bc fd b f cb gf eb ad be f bc gf b aa cb fg eb f be da b fg b f f cb dfg df be af fd bc fa f bgfd gf df ad ffeb f fa be gf gfg bc aa af b fg fa cb f fd eb da dfg be fg af b f fa df gfg fd df f ff gf fd fd gfg f af gf fa aa gfd fg df f af aa fa fg gfg f af df ff fd fd f dfg gf af fd fa fgfg gf ``` <!-- 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,#f73e3bff b,#0606ffff c,#4348edff d,#fe0505ff e,#a5a6feff f,#f4918cff g,#add5adff ``` ```image f add fddf ada fddf dda fddf be dda b fddf b fdda eb addf b fddf eb add b fddf eb add b fddf eb ada b fddf eb fd b d eb df b d eb d b fd eb d b df eb d b d eb fd b d eb af b d eb d b fd ec d ggbggggggggggdag ggccgggggggggdgg gggbggggggggdggg gggccggggggfdggg ggggbggggggdgggg ggggccggggaagggg gggggbggggdggggg gggggccggdfggggg ggggggbgfdgggggg ggggggccdggggggg gggggggbaggggggg gggggggccggggggg ggggggdfbggggggg gggggfdgccgggggg gggggdgggbgggggg ggggaagggccggggg ggggdgggggbggggg gggdfgggggccgggg ggfdgggggggbgggg ggdggggggggccggg gaagggggggggbggg gdggggggggggccgg dfgggggggggggbgg fd ce d b aa be d b df be fd b d be aa b d be df b fd be d b aa be ebbb d b ecbbbce df be ecbbbce d b cbbbbe d be ebbbbc fa b ecbbbce d be ecbbbce df b cbbbbe be ebbbbc bbce ``` <!-- end of image --> Let's get to the bottom of what's happening inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd4547ff b,#0401fcff c,#5555feff d,#fe0606ff e,#cacafeff f,#fc8486ff g,#ffc5c5ff ``` ```image cbc ada bbe gddg cbc adf bbe fdd cbc ddf bbe ada cbc gddg bbe ada cbc fdd bbe ddf cbc ada ebbe gddg cbc ada ebbe fdd cbc ddf ebbe ada cbc gddg ebbe ada cbc fdd ebbe ddf cbcfda ebbddg cbba fbbe dbbc fdabbe gddgcbc ada ebbe fdd cbc ddf ebbe fdd cbc gddg ebbe ada cbc gddg ebbe ddf cbc fdd ebbe gddg cbc ada ebbe gddg cbc ddf ebb fdd cbc gddg ebb ada cbc gddg ebb ddf cbc fdd ebb ``` <!-- end of image --> The close-up clearly shows an intersection point in area A. I've found a single intersection point in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff4b4bff b,#0505ffff c,#423ffbff d,#ff0606ff e,#c1c1ffff f,#ff9f9fff g,#7f7fffff ``` ```image f add fddf add fddf dda fddf be dda eb addf be fdda eb addf be fdda eb add be fddf eb add b fddf eb dda b fddf eb ad b d eb df b d eb d b fd eb d b df gb d b d gb fd b d gb da b d gc d b fd gc d b aa gc d b df gc fd b d gc aa b d gc df b fd ccd ba cc dfb fd cc d b aa cg d b df cg fd b d cg aa b d cg df b fd cg d b aa cg d b df bg fd b d bg aa b d bg df b fd be d b aa be gcbb d b ecbbbce df be ecbbbcg fd b egbbbbg d be gbbbbge aa b ecbbbce d be ecbbbce df b egbbbbg be gbbbbge ebbce ``` <!-- end of image -->

I'm optimistic that I'll find some intersections in this image. I can confidently say that there are no intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#9393ffff b,#ff4242ff c,#0404ffff d,#e7d5edff e,#ff9494ff f,#ff0303ff g,#4040ffff ``` ```image d efffffe effb efffe effb dfffe effb dbffe effbd dbffe effbd dbffe effbd bffe effbd bffe effbd bffb effbd bffb efffd effb efffd effb bd effbd effbd ef a gccc dcg acd gcd cg acg gc cc aca gca cc dcg gcd gcd dca acg cc cc acd aca cg dcc gc gcd aca acg cg cc gcd aca dca dcc cc gcd acd dcg cg cc gc aca aca cc cg cd gc dca cc acd dcg gc aca cg gc dc ``` <!-- end of image -->

Based on a first glance, I suspect there could be intersection regions here. My next step is to analyze the details within each area. <!-- image --> ```palette Key,Color ,#fefefeff a,#f75552ff b,#0a0affff c,#6769faff d,#fe0707ff e,#fbaba9ff f,#acd4adff g,#bcbcffff ``` ```image c gb b bg bc bb cb gb b bg bc cb gb b bg bc bb cb gb g b bb bg bb bc cb cb cb gb cb b fffffffcbfffffff bg ffffffffcbffffff bc ffdffffffcbfffff bb fffdfffffffbffff cb fffadfffffffbfff gb ffffdffffffffbff b fffffdffffffffbf bg fffffadffffffffbg bc ffffffdeffffffffbg cb fffffffdffffffff bc gb fffffffadfffffff bc b ffffffffdaffffff bc bg fffffffffdffffff bc bc fffffffffadfffff bb bb ffffffffffdaffff bb cb fffffffffffdffff bb gb fffffffffffedfff cb b ffffffffffffdaff cb bg fffffffffffffdff cb bc ffffffffffffffdf cb cb aa gb gb d gb b d gb bg e aa gb bc dd de bg bb da d bg cb ade ad bg gb dd de bg b ede d bbg ad ed g da de ede d dd ed da da ad d dd ed ede da ad d da ed ede aa dd d eda d ad ad dd de ede d dd ad da de ad d dd ed ede de ad d da ed ede da dd deda ed ``` <!-- end of image --> This close-up of area A is like examining a piece of evidence. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff5050ff b,#0303ffff c,#8787ffff d,#ff0707ff e,#ffa0a0ff f,#3232ffff g,#f1d8e5ff ``` ```image cbbc cbbc cbbc cbbc cbbc ee cbbf eddg cbbf ada cbbf gdde gbbf eddg gbbf ada gbbfg gdde gfbfg eddg gfbfg ada gfbb gdda fb eddg f add dda edde add dda gdde eddg ada gdde eddg ada gdde eddg ada gdde eddg add gdda edde add dda gdde addg ``` <!-- end of image --> No intersection found in area A, but I won't give up. Zero, Nada.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff5555ff b,#0404ffff c,#8484ffff d,#ff0707ff e,#ffb0b0ff f,#3d3dffff g,#c3c3ffff ``` ```image c gb b bg bc ff cb gb b bg bf fb gb b bg bc ff cb gb g b bf bg fb bf fb fb fb gb cb b cb bg cb bc d gb ff d gb cb aa gb gb de gbg b d bg bg ad bg bf de bc fb d bc gb ad bc b de bf bg d bf bc ed bf ff da bf cb d fb gb ed fb b da fb bg d cb bf ed cb fb aa cb gb d gb b d gb bg e aa gb bc dd de gbg ff da d bg cb ade ad bg gb dd de bc b ede d bbg ad ed c da de ede d dd ed da da ad d dd ed ede da ad d da ed ade aa dd de eda d ad ad dd de ede d dd ad da de ade d dd ed ede de ad d da ed ede da dd deda ed ``` <!-- end of image -->

I'm analyzing this image to identify any points where lines intersect. 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,#f75753ff b,#0607feff c,#fe0909ff d,#a0a2f9ff e,#ffacacff f,#add5adff g,#5052f9ff ``` ```image d gbg gbg gbg gbg gbd gbd bbd bbd bbd bbd bbd bbd bbd bbd bbd bbd bbd bbd bbbd dgbbg gbbg dbbbd dbbbg gbbg dbbbd dbbbd gbbg dbbbdffffffffffffff dbbbgfffffffffff fffgbbgffffffff ffffffgbbbdffff fffffffffdbffff fffffffffffffff ffffffffffcffff fffffffffccffff ffffffffccfffff fffffffacffffff ffffffacfffffff fffffacffffffff ffffacfffffffff fffacffffffffff ffacfffffffffff facffffffffffff acfffffffffffff ecffffffffffffff ecfffffffffffffff ec ec ec c a c ac c ce c cc ce ac ce ece ce ca ce cc ce ec ce ca ce cc ca ac ca ece ca ca ca ac ca ece ca ca ca cc cc ac cc ce cc cc ac ac ac ece ac ca ac cc ac ec ac ca ec ccec ac ``` <!-- end of image --> My goal is to determine if there's an intersection inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff3a3aff b,#0808ffff c,#ff0304ff d,#b5b5ffff e,#ffc6c6ff f,#ff8282ff g,#6161ffff ``` ```image d bbgd bbbbbggd dgbbbbbbgd dgbbbbbgd dgbbbbbggd dgbbbbbbgd dgbbbbb dgbg af aca acce acce acce acce acce acce acce acce acce acce fcce fcce fccf fccf fccf fccf fccf fccf fccf ccf cf f ``` <!-- end of image --> No luck this time. Area A doesn't have an intersection. I can confidently say that there are no intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff3a3aff b,#0707ffff c,#ff0505ff d,#a7a7ffff e,#ffc2c2ff f,#ff7b7bff g,#5858ffff ``` ```image d gbg gbg gbg gbg gbg bbd bbd bbd bbd bbd bbd bbd bbd bbd bbd bbd bbd bbd bbbd dgbbg gbbg dbbbd dbbbg gbbg dbbbd dbbbg gbbg dbbbd dbbbd gbbg gbbbd db a ac ac ac ac ac fc fc fc fc fc ec ec ec ec ec ec f c fc c ecf ce ca ce ac ce ece ce ca ce ac ce fce cf cf cf cc cf ac cf ece cf ca ca ac ca ece ca cf ca cc ca fc aa ecf ac ca ac ac ac ece ac ca ac ac fc fce fc cf fc ccfc fc ``` <!-- end of image -->

Hmm, I'm not sure what to expect from this image. Let's see if any lines cross. The image has some tight areas where segments are too close. I should investigate those closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#0506feff b,#f25c56ff c,#4a4bf6ff d,#f5aaa5ff e,#a2a8f3ff f,#fe0807ff g,#add5adff ``` ```image aa acea ca a ca a ca ac ea a ea ea ea ae a a b a ac bb ae a f ae ea bb ae ae f ac a bf ac cc f ac a df ca ea f ca ae ggbfggggggggggggca a gggfgggggggggggca cc gggdfgggggggggea a ggggfggggggggeag ea ggggdfgggggggagg ae gggggfggggggaggg a ggggggfggggagggg cc ggggggfdggaegggg a gggggggfgaeggggg ea gggggggfacgggggg ae gggggggacggggggg a ggggggacfbgggggg cc gggggaaggfgggggg a ggggcagggfbggggg ea gggcagggggfggggg ae ggcaggggggfbgggg a gcaggggggggfgggg cc eagggggggggbbggg a eagggggggggggfggg ea aggggggggggggbbgg ae a f a bb cc f a bf ea f ae df a f cc df a f ea df ae f a df cc fd a f ea fd ae f a fd cc f a fd ea f ae fd a f cc bb a f ea bb ae f a bb cc f a bb gggggggeaggggggg f ggggggggaegggggg bf gggggggggagggggg f gggggggggccggggg df ggggggggggaggggg f ggggggggggeagggg df gggggggggggagggg f gggggggggggggggg df gggggggggggggggg f gggdbbbfffffgggg df ddbbffffffffffffbbbdgggggggg fd ddbbbfffffffffffbbdd gggggggggggggggg ffffffbbddd gggggggggggggggg gggggggggggggggg gggggggggggggggg gggggggggggggggg ``` <!-- end of image --> Could this be where the intersection is hiding, in area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#0505feff b,#f95258ff c,#433df9ff d,#8887feff e,#c9c9ffff f,#fe0606ff g,#feb6b6ff ``` ```image gff ffb gff d bfb da gff daa bfb eaad gff eaac bfb eaac gffg eaac bfb eaac gffg cac bfb caae gffg caae bfb caae ffg caae bfb daae ffg daad bfbdaad fbaad baad eaacg eaacff eaac ffg eaac gff aac ffg caa gff caae ffg caae gff caae ffb caae gff daae bfb daad gff daad bfb daad gff eaad bfb aac gffg ac bfb c gffg bfb ``` <!-- end of image --> There's no doubt about it - this is an intersection in area A. Moving on to the next area. Could this be where the intersection is hiding, in area B? <!-- image --> ```palette Key,Color ,#fefefeff a,#0808ffff b,#ff3e3eff c,#6060ffff d,#ff8686ff e,#bdbdffff f,#ff0303ff g,#ffc4c4ff ``` ```image aac eaae cac aae caa aac eaae cac aae caa aac eaae cac ac ggggdg gggddddbbbbffffffffb ffffffffffffffffffffbbbd fffffbbbbddddggg gg ``` <!-- end of image --> Based on this close-up, I can conclude that there's no intersection in area B. I've found a single intersection point in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0606feff b,#ff4141ff c,#4b49fcff d,#ff8585ff e,#adadffff f,#ff0404ff g,#ffcacaff ``` ```image aa acea ca ae ca a ca ac ea a ea ea ea ae a a b a ac bb ae a f ae ea db ae ae f ac a db ac cc f ac a df ca ea f ca ae df ca a f ea cc gf ea a fg ea ea gf a ae fg a a gf a cc fg ae a gf ae ea fae ae ac a acfd cc ac f a ca fd ea ca f ae ca bd a ea f cc ea bb a ea f ea a bb ae a f a db cc f a db ea f ae df a f cc df a f ea gf ae fg a gf cc fg a gf ea fg ae f a fg cc f a fd ea f ae bd a f cc bd a f ea bb ae f a bb cc f a db ea f ae db a f cc df a f ea df a f gf fg ggddbbffff gf ggddbbffffffffffbbddgg fg gddbbffffffffffbbddgg gfffffbbddgg ``` <!-- end of image -->

This image looks interesting. I wonder if there are any intersections hidden in there? These zones indicate regions where lines appear to be in close proximity. <!-- image --> ```palette Key,Color ,#fefefeff a,#0607feff b,#fe0505ff c,#f69c97ff d,#a1a4f9ff e,#f84744ff f,#4b4bf0ff g,#add4adff ``` ```image aaa daad a aaf da daad fa aaf af daad ad faf a daad a faa da daad fa faa af daaf ad faad a daaf da aad da ff ad ad a da b fa bc af ee ad cb a b a bc da eb fa b afgggggggggggggbg adgggggggggggbeg gaggggggggggebgg ggagggggggggbggg ggfagggggggbcggg gggfagggggbegggg ggggafgggcbggggg gggggadggbgggggg ggggggagbcgggggg gggggggabggggggg gggggggfaggggggg ggggggbgaagggggg gggggbeggafggggg ggggebggggaggggg ggggbggggggagggg gggbgggggggdaggg ggbeggggggggfagg gcbggggggggggafg gbggggggggggggaf bcggggggggggggga ee a cb da b fa bc af eb ad b a b bc cb b b be cb b bc ee cb b bc eb b b bc bbbe cb cbbbec b cebbbc b cebbbe ee cbbbec cb cebbbc b ebbbec bc cbbbec ee cebb ``` <!-- end of image --> I'm eager to see what's happening in this magnified view of area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0505feff b,#fe0a0aff c,#ffb9b9ff d,#8580f9ff e,#fe6162ff f,#463bf4ff g,#c7c7ffff ``` ```image af ebb aad cbbc daag bbe daag ebb faa ebbc faf cbbc gaaf bbe gaad ebb daag cbbc daag cbbe faa bbe aaf ebb gaad cbbc gaad bbe daag ebb faag ebb faf cbbc aafbbe gaafb daad cbfaag bbefaag ebb faf cbbc gaaf cbbe gaad bbe daag ebb daag cbbc faa bbe faf ebb gaaf ebbc gaad cbbc daag bbe daag ebb faa cbbc aaf cbbc gaad bbe gaa ebb da ``` <!-- end of image --> Area A contains an intersection. After careful examination, I conclude that there is one intersection.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0606ffff b,#ff0404ff c,#ff9696ff d,#9f9fffff e,#fa4145ff f,#4a4affff g,#ecd8eaff ``` ```image g gaaag daad ga gaaf da daad fa aaf af daad ad faf ag daad ga faag da daad fa faag af daaf ad faag a gaaf ga aad da ff ad ag a da b fa bc af ee ad gb ag b ga bc da eb fa gb af bg ad be ag cb ga b da bg fa ee af cb ad b a bc gae gea b ff bc ad cb ag gb a bg da be fa cb af b ad bg ag ee ga cb da b fa bc af eb ad gb a bg bc cb gb bg be cb b bc ee cb b bc eb gb bg bc bbbeg cb gcbbbec gb cebbbc bg gebbbeg ee cbbbec cb cebbbc b gebbbeg bc cbbbec ee cebb ``` <!-- end of image -->

I'm on the case! Let's uncover any intersections hidden in this image. There are 2 regions I'd like to highlight in the image. <!-- image --> ```palette Key,Color ,#fefefeff a,#0707fdff b,#fe0505ff c,#a2a5faff d,#f44441ff e,#f19992ff f,#aed4aeff g,#5053f1ff ``` ```image c a ac ca a gg a ac ca a ag a a ca a a ac ca a ac a a ga ca a ac ac a ca gg a a gg ca db a ac b b ac a b eb ca ca dd bd a ac eb be gg a b b a gg be eb ac a eb db ca ca b be a ac be b gg a eb b a ga b eb ac ac be dd ca a dd fbefffffffffafff gg b ffbffffffffggfff ffafffffffffbfff ffebfffffffaffff ffcafffffffddfff fffdbfffffacffff fffagfffffebffff ffffbdfffgafffff ffffafffffbfffff fffffbfffaffffff ffffgafffbdfffff ffffffbfagffffff fffffaffebffffff ffffffebafffffff ffffffafbfffffff fffffffadfffffff ffffffagefffffff ffffffgabeffffff ffffffdaffffffff ffffffaffbffffff ffffffbcafffffff fffffagfffbfffff fffffbefagffffff fffffaffffdbffff ffffdbfffaffffff ffffaffffffbdfff ffffbffffgafffff fffgafffffffbeff fffbffffffafffff fffafffffffffbff ffddfffffffaffff ffagfffffffffebf ffbffffffffagfff ca db fbffffffffffafff a be bd ca ga b eb ac a b b a ac eb be ga ca bd eb a a be b a gg b be ag a eb eb a ac db b ca ca be be ac a b dd a gg b b gg a eb b a ac dd dd a ca be eb ag a b b agg b be ca db eb bd b be be b eb dd be b ``` <!-- end of image --> Let's take a closer look at area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0706feff b,#fe0505ff c,#b2b1feff d,#fb3e42ff e,#ffc7c7ff f,#fd8284ff g,#554df7ff ``` ```image gag ebbf caac dbd gaa fbbe aag ebbf caac dbd gag fbb aac ebbe caa dbd gag fbb caac ebbe gaa bbf aag dbd caac ebbe gag bbf aac dbd caafbbe gagbf caad fgaa ebbaag dbdcaac fbb gag ebbe aac bbf caa dbb gag ebbe caac bbf gaa dbd aag fbbe caa ebbf gag dbd aac fbbe caa ebbf aag dbd caac ``` <!-- end of image --> Case closed! This is definitely an intersection point in area A. Time for a closer look at another area. Let's see if area B yields any clues. <!-- image --> ```palette Key,Color ,#fefefeff a,#0404feff b,#fe0808ff c,#8181ffff d,#fc5b5dff e,#feb2b3ff f,#c3c3feff g,#3e34f5ff ``` ```image ebbd aac ebbe cag dbbe faaf dbb gag bbd caa ebbe aac ebbe cag dbb faaf bbd gag bbd caa ebbe aac dbbe cag dbb faaf bbd gac ebbdcaa ebbaac dgag faad gagbd caaebbe aac dbbe gag dbb faaf bbd gac ebbd caa ebbe faaf dbb gag dbb faaf bbd gac ebbe caa ebbe faaf dbb gag bbd faaf bbd aac ebbe ``` <!-- end of image --> I've cracked the case! This area contains the intersection. After a long analysis, I found two intersections.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0404ffff b,#fe0809ff c,#8282ffff d,#fd5f60ff e,#ffb9b9ff f,#cdcdfeff g,#3937fcff ``` ```image c a af ca a gc fa af ca a gc fa af ca a a ac fa fa ac af a cg ca a af ac a fa gg a a e cg fa db a ac ebeb ac a b db fa ca bd bd a af eb be gg a b b a gg bd eb ac a eb db fa fa b bd a ac be b gg a db b a ca b db af af be bd ca fa db be a gg b b gg a be eb a fa bd db af ac eb bd ca a b be a cg bd b gc af eb eba fa b ad gge cabe da a b bfa gc eb be ac fa db db a af bd b cg ca be be af a b dd fa ac eb eb gc fa db b a af bd bd ca cg b eb ac a b b a ac db bd cg fa bd eb af af be b fa cg b be gc a eb db a ac db b ca fa bd be af a be db a gg b eb gg a eb b af ac bd bd fa fa be eb gc a b b agg eb bd ca db eb bd b be be b eb db bd b ``` <!-- end of image -->

This is the image I'm working with. The goal is to count the intersections. I wonder what's going on inside those areas? Perhaps intersections are hiding there. <!-- image --> ```palette Key,Color ,#fefefeff a,#6267e4ff b,#fd0404ff c,#f24346ff d,#0a0afbff e,#d89a89ff f,#b1d7b1ff g,#96c797ff ``` ```image a dd da ad dd da ad dd fda ad dd adf dd da ad dd da ad dd da ad gggggggggggggggggggggggggggggggggggggggggggggf dd fffffffffffffffffffffffffffffffffffffffffffffg fdf fffffffffffffffffffffffffffffffffffffffffffffg dd fffffffffffffffffffffffffffffffffffffffffffffgda ffffffffffffffffffffffffffffffffffffffffffffadf fffffffffffffffffffffffffffffffffffffffffffddg ffffffffffffffffffffffffffffffffffffffffffdafg ffffffffffffffffffffffffffffffffffebffffadgffg fffffffffffffffffffffffffffffffffebcbffddffffg ffffffffffffffffffffffffffffffffebffbcdafffffg fffffffffffffffffffffffffffffffebfffadeffffffg ffffffffffffffffffffffffffffffebfffddfbefffffg fffffffffffffffffffffffffffffebffgdafffbfffffg ffffffffffffffffffffffffffffebffadfffffebffffg fffffffffffffffffffffffffffebffddfffffffcbfffg ffffffffffffffffffffffffffebffdafffffffffcbffg fffffffffffffffffffffffffebfadgfffffffffffbcfg ffffffffffffffffffffffffebfddffffffffffffffbeg fffffffffffffffffffffffebfddffffffffffffffffbg ffffffffffffffffffffffebadaffffffffffffffffffb fffffffffffffffffffffebddffffffffffffffffffffeb ffffffffffffffffffffebddfffffffffffffffffffffgcb fffffffffffffffffffebdaffffffffffffffffffffffg cc ffffffffffffffffffeadffffffffffffffffffffffffg be fffffffffffffffffeddfffffffffffffffffffffffffg be ffffffffffffffffedaffffffffffffffffffffffffffg b fffffffffffffffadgfffffffffffffffffffffffffffg b ffffffffffffffddfffffffffffffffffffffffffffffg eb fffffffffffffddffffffffffffffffffffffffffffffg cb fffffffffffgdcfffffffffffffffffffffffffffffffg bc ffffffffffadbffffffffffffffffffffffffffffffffg be fffffffffddbfffffffffffffffffffffffffffffffffg b fffffffgdabffffffffffffffffffffffffffffffffffg b ffffffadgbfffffffffffffffffffffffffffffffffffg b fffffddgbffffffffffffffffffffffffffffffffffffg eb ffffdafbfffffffffffffffffffffffffffffffffffffg cb ffadgfbffffffffffffffffffffffffffffffffffffffg bc fddffbfffffffffffffffffffffffffffffffffffffffg be ddffbffffffffffffffffffffffffffffffffffffffffg b daffbfffffffffffffffffffffffffffffffffffffffffg b ffbffffffffffffffffffffffffffffffffffffffffffg eb gbfffffffffffffffffffffffffffffffffffffffffffg cb bffffffffffffffffffffffffffffffffffffffffffffg cc bgggggggggggggggggggggggggggggggggggggggggggggf be be b b eb cb bc be b b b eb cb bc be b ``` <!-- end of image --> I wonder what we'll find inside area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#5756fdff b,#fe0b0cff c,#f9464cff d,#0806fdff e,#fdc3c4ff f,#b2b0fcff g,#750d96ff ``` ```image f fd add fdddf adddf adda ee fdddf ebbe adda ebbbbe adda ebbccbbe fdddf ebbc cbb adda ebbc bbcddda ebbc egdddf ebbc addge ebbc fdddgbbe ebbc fdddf cbbe ebbc adda cbb ebbc fdddf bbc ebbc fdddf ebbc ebbc adda ebbc ebbc adda ebbe ebbc fdddf cbbe ebbc adda cbbe ebbc adda cbb ebbc fdddf bbc ebbc fdddf ebbc ebbc adda ebbc ebbc fdddf ebbe ebbc fdddf cbbe ebbc adda cbb ebbc adda cb ebbcfdddf b ebbcadda e ebbcadda ebbcdddf ebbgdddf ebbgdda ebbdddf ebgdddf ebgdda ebddda ecdddf egddd egdda fdddf fdddf addg dddg fdddc addgc addgc fdddgc fdddbc addgbc fdddgbc fdddcbc addabbc addabbc fdddfbbc addaebbc addaebbc fdddfebbb fdddfebbb adda ebbb fdddf ebbb fdddf ebbb adda ebbb adda ebbb fdddf ebbb adda ebbb adda ebbb ddf ebbb ff bbb bbb bbb bbbe bbbe bbbe bbbe ``` <!-- end of image --> Oh my, look at that! It's an intersection in area A! There are precisely two intersections present in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#4a44f9ff b,#fd0607ff c,#fb6063ff d,#0706fdff e,#fec0c1ff f,#8a87fcff g,#ccc9fcff ``` ```image f dd da fdg dd gdf ad dd gdf ad da fdg dd da fdg dd gdf adg dd gdf ad da gdf ad da fdg dd gda eb fdg ebcb dd eb bcdf eb adc eb dd be eb gdf b eb ad eb eb dd cb eb df cb eb fdg bc eb dd be eb da be ebgdg b ebad eb ebdd cb ebdf bb ead bc edd be eda b fdg eb ad eb dd cb gdb bc adb bc ddb be gdfb b fdgb eb ddeb cb daeb cb fdgeb bc ad eb be da b be df b b b eb b cb b bb be bc be b eb eb cb bc bc be b eb cb cb bc be b ``` <!-- end of image -->

Let's examine this image for potential line intersections. These zones indicate regions where lines appear to be in close proximity. <!-- image --> ```palette Key,Color ,#fefefeff a,#4648f3ff b,#ed4c46ff c,#fd0707ff d,#0404fdff e,#b0d6afff f,#9399f2ff g,#f49994ff ``` ```image g c c bb gc c cg gc c cg gc c cg bc c a c aa bb d c d c df cb d gc fd c d cg d gc aa c d cg fd gc df c d cg aa bc d c fd c cg df bb cbeeeeeeeedeeeeeeeeeeeeeeeeeeeeeeeeeee c ecbeeeeeeeadeeeeeeeeeeeeeeeeeeeeeeeeee c eecceeeeeeedeeeeeeeeeeeeeeeeeeeeeeeeee cb eeebceeeeeeedeeeeeeeeeeeeeeeeeeeeeeeee gc eeeebceeeeeedaeeeeeeeeeeeeeeeeeeeeeeee c eeeeegceeeeeedeeeeeeeeeeeeeeeeeeeeeeee cg eeeeeeeceeeeefdeeeeeeeeeeeeeeeeeeeeeee gc eeeeeeeecgeeeedfeeeeeeeeeeeeeeeeeeeeee c eeeeeeeeecbeeeedeeeeeeeeeeeeeeeeeeeeee cg eeeeeeeeeecbeeeaaeeeeeeeeeeeeeeeeeeeee gc eeeeeeeeeeecceeedeeeeeeeeeeeeeeeeeeeee c eeeeeeeeeeeebceefdeeeeeeeeeeeeeeeeeeee cg eeeeeeeeeeeeebceedfeeeeeeeeeeeeeeeeeee bc eeeeeeeeeeeeeegceedeeeeeeeeeeeeeeeeeee c eeeeeeeeeeeeeeeecgadeeeeeeeeeeeeeeeeee c eeeeeeeeeeeeeeeeecbdeeeeeeeeeeeeeeeeee bb eeeeeeeeeeeeeeeeeecbdeeeeeeeeeeeeeeeee c eeeeeeeeeeeeeeeeeeecdaeeeeeeeeeeeeeeee c eeeeeeeeeeeeeeeeeeeecdeeeeeeeeeeeeeeee cb eeeeeeeeeeeeeeeeeeeeeadeeeeeeeeeeeeeee gc eeeeeeeeeeeeeeeeeeeeeedceeeeeeeeeeeeee c eeeeeeeeeeeeeeeeeeeeeeedceeeeeeeeeeeee cg eeeeeeeeeeeeeeeeeeeeeeeaacgeeeeeeeeeee gc eeeeeeeeeeeeeeeeeeeeeeeedecbeeeeeeeeee c eeeeeeeeeeeeeeeeeeeeeeeefdecbeeeeeeeee cg eeeeeeeeeeeeeeeeeeeeeeeeedfecceeeeeeeegc eeeeeeeeeeeeeeeeeeeeeeeeeedeebceeeeeeec eeeeeeeeeeeeeeeeeeeeeeeeeeaaeebceeeeecg eeeeeeeeeeeeeeeeeeeeeeeeeeedeeegceeebc eeeeeeeeeeeeeeeeeeeeeeeeeeefdeeeeceece eeeeeeeeeeeeeeeeeeeeeeeeeeeedaeeeeccee eeeeeeeeeeeeeeeeeeeeeeeeeeeeedeeeeebee fd d d aa d fd df d aaf fadddddaff faadddddaff faddddddaf faddddddaf ffadddddaaf ffaddd ``` <!-- end of image --> I'm eager to see what's happening in this magnified view of area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#5047f5ff b,#f93d43ff c,#fe0505ff d,#0706fdff e,#ffc8c8ff f,#a6a4fdff g,#fe8787ff ``` ```image cce ddf bccg fdd bccg ada gccb fddf gccb add eccb ddf eccce fdd ebcce ada bcce ddf bccg fdd gccg dda gccb fddf gccb ada eccbe ddf eccce fdd ebcce ada bccg fddf bccg add gccg ddf gccb fdd eccb ada eccbe ddf eccce fdd bcce dda bccg fddf bccg ada gccb ddf gccb fdd eccb ada eccce fddf ebcce ada bcce ddf bccgfdd gccgada gccbddf gccadd eccddf ecbdd ebada bddf addg ddag fddcb addcb ddbcbe fddbcce adabcce fddfbccg add bccg ddf gccb fdd gccb ada eccb ddf eccce fdd ebcce dda bcce fddf bccg ada gccg e ddf gccb c fdd gccb bc ada eccbe gcc fddf eccce ccg ada ebccebcb ddf bcccce fdd bccg ``` <!-- end of image --> Area A contains an intersection. The image features one single intersection point.

<!-- image --> ```palette Key,Color ,#fefefeff a,#5755fcff b,#fd4143ff c,#fe0506ff d,#0606feff e,#ffcacaff f,#acacffff g,#ff8888ff ``` ```image g ec ce bb ec c cg gc c cg gc c ce bc c a ce aa bb d ec fd ce da bb d ec ad c df cg d gc aa c d cg fd gc df c d ce aa bc d c fd ce ce df bb cg d ec cb ad c cc d bb bc d ec gc da c gc d cg ece fd gc cg df c cg d cg cb aa gc cc d c bc fd ce gc df bb ec d c ecead ce cgd bb cbd ec cda c bd cb ad ec dc c dce cg aace gc d cg c fd cb cg df cc gc d bc c aa gc ce d gc bb fd eceec df cce d g ad df d da d fd df d aaf aadddddaaf faddddddaff faddddddaff faddddddaf ffaddddddaf faaddd ``` <!-- end of image -->

This image might have some surprises. Let's look for intersections carefully. These regions highlight areas that look suspicious. Lines seem to converge within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#0b0cfeff b,#fd0908ff c,#fbaba9ff d,#afd6b0ff e,#c5c5ffff f,#ee5b53ff g,#5c61f4ff ``` ```image ddddddddddddd ddddddddddddd ddddddddddddd ddddddddcdddd dddddfbbbdddd ddbbbfddddddd cbbbfdddddddddd fbbfcddddddddddddd cbbbf ddddddddddddd fbbbc ddddddddddddd cfbbf ddddddddddddd cbbbc ddddddddddddd fbbf ddddddddddddd cbbbf ddddddddddddd fbbbc ddddddddddddd a cfbbf ddddddddddddd ea cbbbc ddddddddddddd addddddddddddddd cbb ddddddddadddd dadddddddddddddd cbb ag dagddddddddddddd cbb ea ddaddddddddddddd cbb a ddagdddddddddddd cbb ag dddadddddddddddd cbb ea dddagddddddddddd fbb a ddddaddddddddddd fbb ag ddddggddddddddddfbf ea dddddaddddddddfbf a dddddgadddddfbfd ag ddddddadddfbfddd ea ddddddgabbfddddd a ddddddbafddddddd ag ddddbbfgaddddddd ea ddbbfdddaddddddd a bbfddddddadddddd ag bfddddddddadddddd ea ddddddddddaddddd a ddddddddddagdddd ag dddddddddddadddd ea dddddddddddagddd a ddddddddddddaddd ag ddddddddddddagdd ea dddddddddddddadd a dddddddddddddgad ag ddddddddddddddad ea ga a a ag ea ea a a ea ag ae ea ea a ae ag a ea ag a a ag ag ea a a gg ag a ea ga a a ag ga ea a a ea ag ae ea ea a ae ag a ea ae a a ag ag ea a a gg ag a ea gg a a ag ga ea a a ea ag a ea ea a aag ea ``` <!-- end of image --> Could this be where the intersection is hiding, in area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#4747ffff b,#fe0808ff c,#feb4b4ff d,#0605feff e,#c7c7ffff f,#f4515bff g,#8282ffff ``` ```image ada edde ada edde gda dde gda ddg gdd ddg gdd ddg edd adg edde ada edde ada edde f ada cfbb edde cfbbbf gda cfbbbfc dde cfbbbfc gdd cfbbbfc ddg cfbbbfc gddcfbbbf ddfbbf cffddf cbbbbddg cbbbbf edd cbbbbf adg cbbbbf edde cbbbbc ada cbbbbc edde bbbbc ada bbc edde c gda dde gda ddg gdd ddg gdd ddg edd adg edde ada edde ada edde ada edde gda ``` <!-- end of image --> An intersection is present within area A. Now, let's turn our attention to the next spot. I'm eager to see what's happening in this magnified view of area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#0d0dffff b,#ff0303ff c,#ffaeaeff d,#ff7777ff e,#f8d6ddff f,#ff3939ff g,#6464ffff ``` ```image cc edfbbf cdfbbbbfd ecfbbbbbfde edfbbbbbdc cdbbbbbfde bbbbbfce bfdc e ge gaa ``` <!-- end of image --> Hmm, it seems there's no intersection in area B after all. It was tricky, but I finally found one single intersection in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#2b2bfeff b,#ff0707ff c,#ffa3a3ff d,#0101ffff e,#c5c5ffff f,#fe5253ff g,#6363ffff ``` ```image c fbbb cfbbf cbbbc fbbf cbbbc fbbbc cfbbf cbbbc fbbf cbbbc fbbbc d cfbbf ed cbbbc de cbb d ed cbb ag de cbb ed d cbb d ag cbb ag d cbb ed ag cbb d d fbf ag gg fbf ed d fbf d ga fbf ag d fbf ed gafbf d fdf ag bbfed ed bbc de d bbc ed ag bc de ed d d de ag d ed ag d d ag ag ed d d ga ag d ed ga d d ag ed ed d d ed ag de ed ed d de ag d ed ag d d ag ag ed d d gg ag d ed ga d d ag ga ed d d ed ag de ed ed d de ag d ed de d d ag ag ed d d ag ag d ed ga d d ag ga ed d d ed ag d ed ed d dag ed ``` <!-- end of image -->

The hunt for intersections begins! Let's analyze this image closely. These zones are intriguing. I bet there's something interesting happening within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd0908ff b,#0404feff c,#f26660ff d,#ffb6b6ff e,#969af6ff f,#aed5aeff g,#4440f3ff ``` ```image ffffffffffffff ffffffffffffff ffffffffffffff ffffffffffffff ddd ffffffffffffcccccccaaaaaaaaaaaaaaaaaaaaa fffaaaaaaaaaaccccdddd ca ffffffffffffff a ffffffffffffff da ffffffffffffff a ffffffffffffff da ffffffffffffff ad ffffffffffffff a fffbefffffffff ac ffffbbffffffff a fffffgbfffffff cc ebe a bb da gb a be da bb ad gb a be ac bb a eb cc bg a bb ca eb a bg da bb ad ebe a bg ad gb a ebe cc bg ffafffffffffffff gb ffcaffffffffffff ebe fffaffffffffffff bg fffcafffffffffff gb ffffafffffffffff ebe fffffaffffffffff gbbbbe fffffacfffffffff egbbbbge ffffffafffffffff egbbbgefffacffffffff fegbbbbgffffffff fffffffgbbbbgeff ffffffffafffegbbbge ffffffffcaffffff egbbbbge fffffffffaffffff ebbbbge ffffffffffafffff eg ffffffffffacffff fffffffffffaffff fffffffffffacfff ffffffffffffafff ffffffffffffcaff 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 --> Time to investigate area A up close. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff0303ff b,#0808ffff c,#ffa6a6ff d,#ffd6d6ff e,#b7b7ffff f,#ff3c3cff g,#6060ffff ``` ```image ddddccc dfffffffaaaaaaaaaaaaa daaaaaaaaaaaaaaaaffff ccccccddddd ee ebbe gbbg gbbbe ebbbe ``` <!-- end of image --> There is no intersection present within area A. Onward to the next region of interest. This close-up of area B is like examining a piece of evidence. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0808ff b,#0404feff c,#fd9d9fff d,#f3d9e5ff e,#9f9fffff f,#fa5459ff g,#4b3beeff ``` ```image faf daac faa aac caa aac caad faf daad faf daac faf daac caa aac ed caad bbbggee faf gbbbbbbbbgeedcaad deegbbbbbbbbggfd eeggbbbbbbbggee deggbbbbbbbbgeed daaceegbbbbbbbbg caa eeggbbb aac de caad aaf caad faf daad faf daac faa aac caa aaf caad faf daad ``` <!-- end of image --> Gotcha! I've found the intersection hiding in area B! After careful examination, I conclude that there is one intersection.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0404ff b,#0505feff c,#ff8383ff d,#ffc7c7ff e,#a7a7ffff f,#ff4040ff g,#4d47f8ff ``` ```image dddd dddccccfffaaaaaaaaaaaaaaaaaafa aaaaaaaaffffcccddd cf a ca ad da ad a be fc bg a gb ff ebe a bb ca gb a ebe da bb ad gb a bg ac bb a gb ff bg a bb ca ebe a bg da bb ad ebe da bg ac bb a ebe ff bg a gb cf ebe a bg da gb ad ebe da gbbbbe ac egbbbbge a ebbbbge fc egbbbbge egbbbbge a egbbbge ca egbbbbge ad ebbbbge da eg ad a fc a ff a ca a da ad a ac a ff a ca a da ad da ac a ff a cf a da ad da ac a fc a cf a ``` <!-- end of image -->

Time to put on my detective hat and find those intersection points! I'm going to focus my attention on these specific areas. <!-- image --> ```palette Key,Color ,#fefefeff a,#575af8ff b,#fe0707ff c,#0808feff d,#f6635fff e,#ffc4c4ff f,#a5a6fcff g,#aed5aeff ``` ```image f fcc acc aca cca gggggggggggggg ccf gggggggggggggg ccf gggccggggggggg fccf ggggaccagggggg fcc gggggggaccgggg fcc gggdgggggfccag acc gggbdgggggggaccf aca ggggbgggggggggfcca cca ggggddgggggggg accf ccf gggggbgggggggg ccc ccf gggggddggggggg fccf fccf ggggggbggggggg acc fcc ggggggdbgggggg fcca acc gggggggbgggggg accf aca gggggggdbggggg fcca aca ggggggggbggggg accf cca ggggggggdbgggg ccf gggggggggbgggg gggggggggdbggg ggggggggggbggg ggggggggggdbgg be eb be eb be b be b bd b bd b dd b dd b dd b db b db b eb b eb be eb be eb be b be b bd b bd e b dbb dd ebbd b dbbe dd ebbd b dbbe dd ebbd b dbbe db ebbd b dbbe db ebbd b dbbe eb ebbd b dbbe eb ebbd be dbbe eb ebbd bedbbe ebd ``` <!-- end of image --> This is a magnified view of the region A. <!-- image --> ```palette Key,Color ,#fefefeff a,#6666ffff b,#ff0505ff c,#0807ffff d,#ff3f3fff e,#ffc1c1ff f,#bebeffff g,#ff8383ff ``` ```image af fccca faccccaf faccccaf faccccaf faccccaf acccccf gg faccccaf ebb acccc dbg fac ebb dbg ebbe dbd ebbe dbd ebbe dbd ebbe gbd bbe gbd bbe gbd bbe gbd bbg gbb bbg gbb bbg gbb dbg ebb dbg ebb ``` <!-- end of image --> The evidence suggests that this is not an intersection point in area A. The image is completely devoid of intersections. Zero.

<!-- image --> ```palette Key,Color ,#fefefeff a,#5f5fffff b,#ff0606ff c,#0808ffff d,#ff5858ff e,#ffc8c8ff f,#afb0ffff g,#ff9090ff ``` ```image f fcc acc aca cca cca ccf cc fccf fcca fcc accf acc g fcca acc dd accf aca b fcca cca dd accf ccf b ccc fccf dd fcca fccf b acc fcc dd fcca acc b accf aca gb fcca aca b accf cca gb ccf b gb b eb be eb be eb be b bg b bg b bg b dd b dd b dd b gb b gb b gb b eb be eb be eb be b bg b bg b bg e b dbb dd ebbd b dbbe dd ebbd b dbbe dd ebbd b dbbe gb ebbd b dbbe gb ebbd b dbbe gb ebbd b dbbe eb ebbd be dbbe eb ebbd bedbbe ebd ``` <!-- end of image -->

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

<!-- image --> ```palette Key,Color ,#fefefeff a,#4444ffff b,#ff0202ff c,#0505ffff d,#a8a8ffff e,#ff7b7bff f,#ffbdbdff g,#ff3939ff ``` ```image d dc c c cd a ca dc ac ca dc cd c c c dc cd aa ca cd ac c dc dc c aa c cd cd c ca dc ac aa dc cd c c c dc cd aa ca cd ac c dc dc c aa c cd cd c ca dc ac aa dc cd c c c dc cd aa ca cd ac c dc dc c aa c g cd cd eb c ca eb dc ac gb aa dc gg cd c bg c c be dc cd be ac ca bf cd ac bf c dc b dc c b ac c fb ccd fb a eb eb gb gg bg be be bf bf b fb fb fb eb gb gb gg bg be be bf bf feggbbb b feggbbbbbbbgeef fb feggbbbbbbbgeef fb feggbbbbbbbgeef fbbbbgeef ``` <!-- end of image -->

Let's examine this image for potential line intersections. Let's take a closer look at what's happening inside these zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#0708feff b,#fc0708ff c,#5a61f1ff d,#f1514bff e,#add4adff f,#eea9a1ff g,#b1b1ffff ``` ```image c a ag ga a cc a ag ga a cc a ag ga a ca a beeeeeeeeeeeeeeee ag fbfeeeeeeeeeeeeee ga ebdeeeeeeeeeeeee a eebdeeeeeeeeeeee ca aceebbeeeeeeeeeee a aeeedbeeeeeeeeee ac caeeefbeeeeeeeee a eaceeeebfeeeeeee ag eeaeeeeebdeeeeee ca eecaeeeeebbeeeee a eeeaceeeeebbeeee ac eeeeaeeeeeedbeee a eeeecaeeeeeefbee ag eeeeeaceeeeeeebd ga eeeeeeaeeeeeeeebd a eeeeeecaeeeeeeeebb cc ac db a a fb ag ga fbf ga ac bf a a bd cc ga bb a ac db ag a fb ga ga bf a cc bd cc a bd a a bb ag cc db ga ag fb a a bf ca ca bb eeeeeeeeeeeeaeee ag dbeeeeeeeeeeeaceee a fbdeeeeeeeeeaeeee ca ebbeeeeeeeaeeeee ag eedbfeeeecaeeeee a eeeebdeeeaeeeeee ca eeeeebbeaceeeeee ag eeeeeefbaeeeeeee a eeeeeeeabbeeeeee ca eeeeeecaedbeeeee ag eeeeeeaeeeebdeee a eeeeeaceeeeebbee ca eeeeeaeeeeeeedbf ag eeeeaeeeeeeeeeebd a eeecaeeeeeeeeeeedb ga eeeaeeeeeeeeeeee fbf ag cc bb a a db ga ag bd ag ga bb a a fbf ga cc bd ac a db a ag fbf gaga bb aa db c bd bb fbf bd db fb ``` <!-- end of image --> I'm analyzing this close-up of area A with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#0808ffff b,#ff0606ff c,#5656ffff d,#ff4545ff e,#ff8e8eff f,#ffcdcdff g,#acacffff ``` ```image f bd bbdf fbbbf dbbe dbbe ebbd ebbd ac fbbbf aag fbbbf gaa dbbe cac dbbe aag ebbd gaa ebbdf cac fbbbf aag fdbbf gaag dbbe cac dbbd aac ebbd gaag fbbdf caa fbbbf aac fdbbe gaag dbbe caa ebbd aac ebbd gaag fbbbf caa fbbbf aac dbbe gaag dbb caa eb aac e ``` <!-- end of image --> I'll move on to the next area. The intersection must be somewhere. Okay, let's direct our attention to the next zone. I'm focusing my attention on this specific region, area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#0303feff b,#fd090aff c,#7978fdff d,#fe5f5fff e,#342df7ff f,#ffb6b6ff g,#bdbdffff ``` ```image gaag eac gaa aac bf cae bbd gaag dbbd eae fbbbf gaa dbbd eac dbbbf cae fbbbf gaag dbbd eae fbbbf gaag fbbbd eac dbbbcae fbbaag eaed gaabbbf eacfbbbd caa dbbd aag fbbbf cae fbbbd gaag dbbbf eac fbbbf caa dbbd aac dbbbf cae fbbb gaag db eac f caa aac ``` <!-- end of image --> Aha! I've found an intersection inside area B! It was tricky, but I finally found one single intersection in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0505ffff b,#fe090aff c,#8181ffff d,#ff5e5eff e,#4141ffff f,#ffbbbbff g,#bdbdffff ``` ```image c a ag ga a ee a ag ga a ee a ac ga a ce a b ac fbf ga bd a bd ca ac bb a a db ac ca fb ga ac bf ag a bd ca ga bb a ac bb ec a db a ga fbf ag ac bf ca a bd a ga bb ee ac db a a db ag ga fbf ga ee bd a a bd ee ga bb a ee db ag a fb ga ga fbf a ee bd ee ag bb a ga bb ac ee db ga ag fbf a a bf ce ee bb a ag db ac a fbd ga ee bb a ag dbf ca a bd a ca bb ac ag fba a abb ca ca db ag a fbd a ec bb ca a dbf ag ag bd a ca bb ca a fbf ac ee bb a a db ca ag fbd ac ga bb a a fbf ga ee bd ac a db a ag fbf gaga bb aa dbf c bd bb fbf bb db fb ``` <!-- end of image -->

I'm on the case! Let's uncover any intersections hidden in this image. These regions highlight areas that look suspicious. Lines seem to converge within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd0706ff b,#0909fbff c,#5e69e7ff d,#e8958aff e,#ee4840ff f,#a3cca1ff g,#b2d7b2ff ``` ```image d da a ad ee da a a ad ea da a ad ae da a a ad ea da a ad ae da a a d ad ea ea da da ad a ae ad aa fffffffffffffffffffffffffffffffffffffffffffff ae ea fgggggggggggggggggggggggggggggggggggggggggggfda dafgggggggggggggggggggggggggggggggggggggggggggfa adgggggggggggggggggggggggcbbgggggggggggggggga faegggggggggggggggggggfbbbfcbggggggggggggggae fgaaggggggggggggggggcbbcggggcbggggggggggggeaf fggeaggggggggggggcbbcggggggggcbggggggggggdagf fgggdafgggggggfbbbfgggggggggggcbgggggggggaggf fggggfadggggcbbcgggggggggggggggcbgggggggadggf fggggggaecbbcgggggggggggggggggggbbgggggaegggf fgggggfbbbfggggggggggggggggggggggbbgggeaggggf fgggcbbcgeagggggggggggggggggggggggbbgfagggggf fcbbcgggggdafggggggggggggggggggggggbbafgggggf gbbbgggggggggfadggggggggggggggggggggggbbggggggf cbbgfggggggggggggaeggggggggggggggggggggeabcgggggf cbbc fgggggggggggggaaggggggggggggggggggdaggbcggggf bbc fggggggggggggggeagggggggggggggggggaggggbcgggf fgggggggggggggggdafggggggggggggggadgggggbcggf fggggggggggggggggfadggggggggggggaegggggggbcgf fggggggggggggggggggaeggggggggggeagggggggggbcf fgggggggggggggggggggaaggggggggfagggggggggggbc fggggggggggggggggggggeagggggggafggggggggggggbg fgggggggggggggggggggggdafggggadgggggggggggggfb fggggggggggggggggggggggfadggeaggggggggggggggf b fffffffffffffffffffffffffaedaffffffffffffffff b aa b b b gb gb cb cb cb cb cb cb bb bb bb bc bc bc bc bc bc bc bg bg b ``` <!-- end of image --> Let's take a closer look at area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0505ff b,#0706fdff c,#9999feff d,#fe8f8fff e,#fc3e40ff f,#f1d5e2ff g,#5251feff ``` ```image ef aaf cc eaad cgbbbg e eaad fgbbbbgbbc da daae fcbbbbbcf cbbc faa daaef cgbbbbgc cbbc faae faaaf fgbbbbgc cbbc eae feaad fcbbbbbcf gbbc daaf eaad cgbbbbgc gbbc daad daae cgbbbbgc gbbc faad daaef fcbbbbbcf gbbc eae faaaf cgbbbbgf gbbc eaaf feaad cgbbbbgc gbbf daaf eaad fcbbbbbcf gbbf faad daaefcgbbbbgf gbbf faae debbbbbgc gbbf eae fgbbbbbc gbbf daaf cgbbbbgeaad bbbf daad cgbbbbgc eaad fbbb faad fgbbbbgc daae fbbb eae fcbbbbbcf daaef fbbgeaaf cgbbbbgc faaaf fbbbaf bbbgc feaad fbbg bcf eaad faabbg daae eaecbbg daaef daaf cbbg faaaf daad cbbg feaad faad cbbg eaad eae cbbg daae eaaf cbbc daaef daaf cbbc faaaf faad cbbc feaad faae cbbc eaad eae cbbc daae daaf gbbc daaef daad gbbc faaaf faad gbb feaad eae gb eaad eaaf g daae daaf daaef faad faaaf faae feaad eae ``` <!-- end of image --> Success! This area contains an intersection point! The image features two intersection points.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0707ff b,#0807feff c,#9898ffff d,#ff9c9cff e,#ff4c4cff f,#f0dbe9ff g,#4d4cfdff ``` ```image d fa a ad ae da fa af ad ea da a ad ae da fa af ad ea da a ad ae da fa af d ad ea ea daf da fad a ae ad aa ae ea da daf fa fad cbb af ae fbbbfcb ad aa gbbc cb ea ea cbbg gb da daf fbbbf gb a fad gbbc gb af aecbbg gb ae fbbbf gb da gbbc ea bb fa cbbc daf bgaf fbbg fad bg gbbc ae eabg cbbc aa da bg bbg ea a bg f daf af bc fad ae bc ae ea bc aa fa bc ea af bf daf ad bf fad ee bf aeda fbf aa fb fb fb cb cb cb cb cb gb gb gb gb bb bg bg bg bg bg bc bc bc bc bc b ``` <!-- end of image -->

Hmm, I'm not sure what to expect from this image. Let's see if any lines cross. I have a hunch that these areas might contain the intersections we're looking for. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd0707ff b,#0505feff c,#fdacabff d,#a2a5f9ff e,#f0564fff f,#4a4df9ff g,#afd6afff ``` ```image ggggggggggggggg ggggggggggggggg ggggggggggggggg ggggggggggdgggg ddffbbbbbbbbfgggg ddffbbbbbbbbfffdggggggggggggg ddfbbbbbbbbbffdd ggggggggggggggg bbbbbbbbffdd ggggggggggagggg bd gggggggggcagggg fb gggggggggaggggg b ggggggggeaggggg bd ggggggggagggggg ff gggggggaegggggg db gggggggaggggggg b ggggggagggggggg bd gggggeagggggggg db gggggaggggggggg b ggggeeggggggggg bd ggggagggggggggg fb gggaegggggggggg b gggaggggggggggg b ggagggggggggggg ff geagggggggggggg db gaggggggggggggg b aeggggggggggggg bd a db ac b ca bd a ff ee b a b ac bf a db a b ca bd a fb ee b a bd ac ff ca db a b ea bf a db ae b a bd ac fb ca b a b ee ff a db ac b ca bd a db ca ggggggbggggggg a gggggbdggggggg ee ggggfbgggggggg a ggggbggggggggg ac gggbgggggggggg ca gggggggggggggg a gggggggggggggg ee gggggggggggggg a gggggggggggggg ac gggggggggggggg a gggggggggggggg ac gggaaegggggggg ca gggggaaegggggg a gggggggaaegggg ee gggggggggeaegg a gggggggggggeae ac gggggggggggggeae ca gggggggggggggg eae a gggggggggggggg eaa ea gggggggggggggg caa a gggggggggggggg caa ae gggggggggggggg caa a gggggggggggggg caa ac gggggggggggggg caac ca gggggggggggggg caac a aac ee aac a aacac aa ``` <!-- end of image --> Could this be where the intersection is hiding, in area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#ff0606ff b,#0404ffff c,#ff8989ff d,#acacffff e,#ff4b4bff f,#4848ffff g,#ffc9c9ff ``` ```image dbbd fbf fbb dbbd bbf fbf dbbd bbd fbf dbb dd g aac gaaaac caaaac caaaac ceaaac geaaacg geaaaeg geaaaeg geaaaeg geaaae geaa ge ``` <!-- end of image --> Area A does not contain any intersection points. Let's shift our focus to the next area. This is a magnified view of the region B. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff0606ff b,#0505ffff c,#ff9191ff d,#ababffff e,#ff4c4cff f,#5555ffff g,#ffcfcfff ``` ```image ddd ddddffffbbbbbbf ffffbbbbbbbbbbbbbbbbbff bbbbbbbbbffffdddd fdddd g gae eae gaag aac caa aac eae gaag eae caag aac caa gaac eae gaag eae caa aac eae gaag eae caag aac caa gaac eae gaag eae caa aac caa gaag eae gaag ``` <!-- end of image --> The evidence suggests that this is not an intersection point in area B. There's definitely not a single intersection on the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0404ff b,#0707ffff c,#ff8080ff d,#adadffff e,#ff3e3eff f,#5757ffff g,#ffc2c2ff ``` ```image d ddffbbbbbbbbf ddffbbbbbbbbbffd dffbbbbbbbbbffdd bbbbbbbbffdd a bd ga fb a b ce bd a ff ac db ga b ag bf ca db a b ee bd a fb ag b ga b a bf ce db a b ec bd a db ag b ga bd a fb ee b a b ac bf ga db ag b ca bd a fb ee b a bd ag ff ga db a b ce bf a db ec b a bd ag fb ca b a bd ee ff a db ac b ga bf a db ca b a bd ec fb a b ag b ga a ce a ac ga g ag aac ca eac a eac ee eae a eae ag eae ga cae a cae ce caa a caa ec gaa a gaag ag gaag ga gaag a gaag ee aag a aacac aa ``` <!-- 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,#fa0b0cff b,#0a0bfcff c,#e4c5dfff d,#616de6ff e,#e66d62ff f,#b1d7b1ff g,#98c59aff ``` ```image c bb bd b cb db bd bc b cb db bd bc b cb db bd ea bc aaae gbgggggggggggggggggeaeggaggggggggggggggggggggg gdbfffffffffffffffaaffffgaffffffffffffffffffff gfbbffffffffffffeaeffffffaafffffffffffffffffff gffbdffffffffffaafffffffffagffffffffffffffffff gfffbgfffffffeaefffffffffffaffffffffffffffffff db gffffbffffffaafffffffffffffeafffffffffffffffff cbb gffffdbfffgaefffffffffffffffaeffffffffffffffff bb gfffffbbfaaffffffffffffffffffaffffffffffffffff bbc gffffffbaafffffffffffffffffffeafffffffffffffff bbd gfffffeabfffffffffffffffffffffaeffffffffffffff dbd gffffaafgbfffffffffffffffffffffaffffffffffffff dbd gffeagfffdbffffffffffffffffffffeafffffffffffff cbb gfaaffffffbbffffffffffffffffffffaeffffffffffff cbb eaeffffffffbdffffffffffffffffffffaffffffffffff bbc aafffffffffffbffffffffffffffffffffgafffffffffff bbc caegfffffffffffgbffffffffffffffffffffaefffffffffdbd aa gffffffffffffdbffffffffffffffffffffafffffffdbb cae gfffffffffffffbdfffffffffffffffffffgaffffdbbff aa gffffffffffffffbgfffffffffffffffffffaafgbbffff cae gfffffffffffffffbffffffffffffffffffffabbgfffff eac gfffffffffffffffdbffffffffffffffffffbbafffffff aa gffffffffffffffffdbfffffffffffffffdbdfeaffffff eac gfffffffffffffffffbdffffffffffffdbdffffaefffff e gffffffffffffffffffbgfffffffffdbbfffffffafffff gfffffffffffffffffffbfffffffgbbfffffffffeaffff gfffffffffffffffffffdbfffffbbgfffffffffffaefff gffffffffffffffffffffbbffbbdffffffffffffffafff gfffffffffffffffffffffbbbdffffffffffffffffeaff gffffffffffffffffffffffdfffffffffffffffffffaeg ac ca ae ac ca ea ac a ea ac a ea ae a ca ae a ca ae ac ca ea ac a ea ac a ea ae a ca ae a ``` <!-- end of image --> This is a magnified view of the region A. <!-- image --> ```palette Key,Color ,#fefefeff a,#f94146ff b,#0706feff c,#9f9ffeff d,#4e4bfcff e,#fe9394ff f,#efd8e7ff g,#fe0505ff ``` ```image bbd eggge eggf fbbc fagga aga cbbc eggge fgge dbbf faggaf eggf dbb eggge aga fbbd faggaf fgge fbbc eggge eggf cbbc aggaf aga dbbf eggge fgge dbd aggaf eggf fbbd fggge agg cbbc egggf gga cbbc fagga fgge dbbf eggge eggf dbd faggaf aga fbbdeggge fgge cbbagaf eggf eabbe aga faggdbbf fgge eggge bbd eggf aggaf fbbd aga fggge cbbc fgge egggf cbbf eggf fagga dbb aga eggge bbd fgge faggaf fbbc eggf eggge cbbc agg ggaf dbbf gga ge dbb fgge f fbbd eggf fbbc aga fd cbbc fgge fdbb dbbf eggf cbbbd dbd aga cbbbdc fbbd fgge cbbbbc cbbc eggf cdbbbc cbbc aga fdbbbc dbbf fggefdbbbdf dbd egdbbbdf fbbd cbbbdc cbbc cbbbbae cbbf cdbbbceggf dbb fdbbbc agg bbd fdbbbdf gga fbbd cbbbdf fgge cbbc cbbbdf eggf cbbf cbbbdc aga dbb cdbbbc fgge bbd fdbbbc eggf fbbc fdbbbd aga cbbc dbbbdf fgge dbbf cbbbdf eggf dbd cbbbdc aga fbbd cdbbbc fgge cbbbbbbc eggf cbbbd aga ``` <!-- end of image --> Oh my, look at that! It's an intersection in area A! There's for sure two intersections on the image you sent me.

<!-- image --> ```palette Key,Color ,#fefefeff a,#f8363cff b,#0a0afeff c,#bebeffff d,#6666ffff e,#ff7a7aff f,#ffc2c2ff g,#fe0405ff ``` ```image c bb bc b cb db bd bc b cb db bd bc b cb db bd eg bc gaaa b egf g cb gg fg db ege aa bd gg gf bc fge g db b ag ea cbb db fge gf bb bb ag g bbc baa eg bbc agb ge dbd ga cb g dbd egf db fg cbb gg bd ge cbb egf bc g bbc gg b fg bbc fge cb aa dbd gg db g dbd fge bd fg cbb ag bc aa cbb fga b gbbc agf cb bba ga db dbd ea egf bd dbd gf e bc cbb g b cbb eg cb bbc ge db bbc g bbbd fg d ge g fg aa gf fg aa gf g eg gf g eg ge g fg ge g fg aa gf fg aa gf g eg gf g eg ge g fg ge g ``` <!-- end of image -->

I'm curious to see if this image contains any intersection points. My analysis shows there's absolutely no intersections in the image

<!-- image --> ```palette Key,Color ,#fefefeff a,#3e3effff b,#ff0808ff c,#ffbebeff d,#7c7cffff e,#0404ffff f,#ff6262ff g,#bebeffff ``` ```image ccccc ffffffbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbf fffcccccc bb fbc bf bb fb cbc bb fb cbc bf bb fbc bf bb fb cbc bb fb cbc bf bb fbc bf bb fb cbc bb fb cbc bf bb fbc b geedg e gdeeeead eg gaeeeeag ed daeeeedg aa gdeeeead de gaeeeeag ge daeeeedg e gdeeeead e gae eg ed aa de ge e eg ed ea ae de ge e eg ed aa de ge e eg eg ea ae de ge e eg ed ea ae ge ge e eg ``` <!-- end of image -->

I'm ready to tackle this image and find those intersections! After a thorough analysis, I conclude that there are no intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0303ff b,#0404ffff c,#ff7f7fff d,#ababffff e,#ff3b3bff f,#5252ffff g,#ffbbbbff ``` ```image d dbbb fbbf dbbbd dbbbd fbbf dbbbf dbbbd fbbf dfbbf dbbbd fbbfd dfbbf dbbbd ddfbbbbbbbfd dffbbbbbbbffdd ddffbbbbbbbffdd bbbbbbffd c aa eag gae ea gac aa cac aa eag gae aa cac aa cag ae eag gae aa cac c aa eaaaeg eag geaaaeg gae ceaaacg ea caaaac gac gcaaaec aa geaaaeg cac geaaaeg aa ceaag ``` <!-- end of image -->

I'm curious to see if this image contains any intersection points. Could these regions be concealing intersection points? Let's find out. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd0808ff b,#0909feff c,#f9a6a3ff d,#b9b9ffff e,#f05a57ff f,#6267f6ff g,#aed4aeff ``` ```image c a a ae ca a ac ea a a ae ca a ac ea a a ae ca b a bdbb gggggggggggggggac bd dbb ggggggggggggggea bd fbb ggggggggggggggag bf fbf gggggggggggggagg bf fbf ggggggggggggaegg bb fbf gggggggggggcaggg fb bbfggggggggggagggg fb bbfgggggggaegggg fb ggbbgggggeaggggg db ggggbbgggagggggg db ggggggbbacgggggg b gggggggebbgggggg bd gggggggagfbbgggg bd ggggggaggggfbbgg bd gggggaeggggggfbb bf ggggeagggggggggfbf bf ggggaggggggggggg fbf bb gggacggggggggggg bbf fb ggeagggggggggggg bbd fb ggaggggggggggggg bbd db gagggggggggggggg bbd db aegggggggggggggg dbb db caggggggggggggggg db b a bd ac bd ea bf a bf a bf ae bb ca fb a fb ac db ea db a b a b ae bd ca bd a bf ac ea a ac eae eae aae aac aac aac aac aac aac aac caac caa caa caa caa caa caa aa ``` <!-- end of image --> Let's zoom in on area A to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0505ff b,#0908fdff c,#ff8484ff d,#a3a1fdff e,#fc3d3fff f,#5852f9ff g,#ffc7c7ff ``` ```image c ga ea caa gaag aac eae caag gaac eae caag gaag aae d eae bbd caag bbbbd gaac dbbbfd eae dbbbfd caag fbbbfd gaac fbbbf eae fbbbf eaa fbbbfaag dfbbbf ebbbbd caadbbbbd gaac dbbbbd eae dbbbbd caa dbbbbd gaag dbbbfd aac fbbbf eae fbb caag f gaac eae caa gaag aac eae caag gaac eae caa gaag aac ae ag ``` <!-- end of image --> Bingo! This close-up reveals an intersection in area A! The final count is: one intersection.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fe0808ff b,#0707ffff c,#ffa1a1ff d,#a3a3ffff e,#fc595cff f,#5757ffff g,#f0dceaff ``` ```image c ga ag ae ca a ac ea ga ag ae ca a ac ea ga ag ae ca gbg a bdbb ac bd dbb ea bd dbf ga bf fbf ag bf fbf ee bf fbf ca fb bbd a fb bbd ac db bbd ca db gbbg a gb gbbac gb ebb bg ga dbb bd ag dbb bd ae fbf bf ca fbf bf a fbf bb ac fbd fb ea bbd fb ga bbd db ag gbbg db ae gbbg gb ca gb bg a bg ac bd ea bd ga bf ag bf ae bb ca fb a fb ac db ea db ga gb ag bg ae bg ca bd a bd ac ea ga ag eae eae aae aac aac aac gaac gaac gaac gaac gaag gaag caag caag caag caa caa aa ``` <!-- end of image -->

I'm on the case! Let's uncover any intersections hidden 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,#f94c4aff b,#0707feff c,#5455f5ff d,#fe0605ff e,#f49a95ff f,#a4a6fbff g,#acd4acff ``` ```image f cbbbcf fbbbbc cbbbbf fcbbbcf fbbbbc cbbbbf fcbbbcf fbbbb bf b cc b fb bf b d cc ad b ed fb d bf d b de cb da b ad b ed bc d b d fb de bf da b ad cc ed b d fb d bf de b da ggcbggggggggggadg gggbgggggggggedgg ggggbggggggggdggg ggggbcggggggdgggg gggggbgggggdegggg gggggcbgggdaggggg ggggggbggadgggggg gggggggbedggggggg gggggggbcgggggggg gggggggdbgggggggg ggggggdecbggggggg gggggdaggbfgggggg ggggadggggbgggggg gggedgggggccggggg gggdgggggggbggggg ggdggggggggfbgggg gdegggggggggbcggg dagggggggggggbggg ad cb ed b d b d bc de b da fb ad bf da ed b edddae d cc eaddde d b adddae de fb edddde da bf eaddda ad b edddae ed cc eaddda d b adddd fb bf b cb b b bc b fb bf b cc b ``` <!-- end of image --> I wonder what we'll find inside area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#fc6163ff b,#0404feff c,#4038f6ff d,#fe0a0aff e,#feb2b3ff f,#8585ffff g,#c5c5feff ``` ```image gbbg dd fbc add bbf adde fbb edde cbc edda gbbg dda fbc ddd bbf add gbbg adde cbc edde gbbg edda fbb dda cbf ddd gbbg add cbc adde bbfedde fbbdda cbca abbg adcbc addebbf edde fbbg edda cbc dda gbbg ddd fbb add bbf adde gbbg edde cbc edda gbbf dda fbb ddd cbf add gbbg adde cbc edde bbf edda fbb dda cbc ``` <!-- end of image --> The close-up clearly shows an intersection point in area A. There's only one, but is an intersection after all.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff5353ff b,#0908fdff c,#5656ffff d,#ff0606ff e,#ffa3a3ff f,#a5a5ffff g,#efdfeeff ``` ```image f cbbbcf fbbbbcg gcbbbbf fcbbbcf fbbbbcg gcbbbbf fcbbbcf fbbbb bf gb cc b fb bf b d cc ad bg ed gb gd bf dg b de cb da bg ad gb ed bc gd b dg fb de bf da b ad cc ed b gd fb dg bf de b da cb ad bg ed gb gd bc dg b de fb da bg ad gbed bb db defb da bf ad b ed cc gd bg dg fb de bf da b ad cb ed bg gd gb dg bc de b da fb ad bf dag ed gb gadddae gd cc eadddag dg b gadddae de fb edddde da bf eadddag ad b edddde ed cc eadddag gd bg gaddddg fb g bf b cb bg gb bc b fb bf gb cc b ``` <!-- end of image -->

I'm on the case! Let's uncover any intersections hidden 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,#585df5ff b,#f55452ff c,#0708fdff d,#f6a29eff e,#fe0908ff f,#aed5aeff g,#b1b2fcff ``` ```image g cc acg cc acg gca cc fffffffffffffffffffff acg fffffffffffffffffffff cc e fffffffffffffffffffff acg edee fffffffffffffffffffffgca be dee ffffffffffffffffffffcc e deefffffffffffffffffaca e bebffffffffffffffccff bb ffbebffffffffffacafff de ffffbebfffffffccfffff e ffffffeebfffccfffffff eb ffffffffeebcaffffffff de fffffffffccedffffffff e fffffffacaffeedffffff ed ffffffccffffffeefffff de ffffacgfffffffffeefff e fffccffffffffffffdeef ed fccffffffffffffffffdee be gcafffffffffffffffffffdee e ccfffffffffffffffffffff deb e acg fffffffffffffffffffff beb bb cc fffffffffffffffffffff beb de gcg fffffffffffffffffffff beb e c eed eb ca eed de gc eed e c e ed cg de ac e c ed cg be aa e gc ed c bb ca e gc e c eb cg de ac e c eb cg de aa e gc ed c be ca e gc ed c be cg e ac e c bb cg de ac e c eb c de ca e gc c ca gc c cg ac c cg aa gc c ca gc c cg ac c cg ``` <!-- end of image --> I'm now examining the contents of area A in detail. <!-- image --> ```palette Key,Color ,#fefefeff a,#443df7ff b,#ff5a5aff c,#0505feff d,#908cfbff e,#fe0607ff f,#ffc1c1ff g,#ccccfeff ``` ```image g ac bf dccc eebf gaccag beeebf dcccd beeebf gaccag fbeeebf dcccd fbeeeb gccca fbeeeb gacccg fbeeeb dcccd fbeeeb gaccag feeeef dcccd feeeedaccag feacccd dcccaeef gaccagbeeebf dcccd beeebf gaccag beeebf dcccd beeebf gccca fbeeebf acccg fbeeeb dcccd fbeeeb gaccag fbeeeb dcccd feee gaccag fe acccd cca ag ``` <!-- end of image --> Yes! I knew it! There's an intersection right here in area A! The image features one single intersection point.

<!-- image --> ```palette Key,Color ,#fefefeff a,#6666ffff b,#ff4343ff c,#0a0afeff d,#fc888aff e,#fe0606ff f,#ffceceff g,#b8b8ffff ``` ```image g cc acg cc ccg gca cc aca cc e acg edee gcc bb dee cc fe deb gca ef deb cc bb beb acg fe bed cc e bed acg ed eedca de ccef e aca eef ed cc feef de acg feef e gcc fee ef cc dee be gca deb fe cc deb ef acg deb bb cc beb fe gcg bed e c bed eb ca eed fe gc eef e c e ed cg de ac e c ed cg de aa e gc ef c bb ca fe gc ef c bb cg fe ac e c ed cg de ac e gc ed c de ca e gc ef c bb ca fe ac ef c bb cg fe ac e c ed c de ca e gc c ca ac c cg ac c cg ca gc c ca gc c cg ac c cg ``` <!-- end of image -->

I'm approaching this image with caution. Intersections might be tricky to spot. These regions highlight areas that look suspicious. Lines seem to converge within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0908ff b,#5454feff c,#f8605dff d,#b0b1fdff e,#ffb5b5ff f,#0707feff g,#afd6aeff ``` ```image e eccaaaaa ecaaaaace ecaaaaacce ecaaaaace ecaaaaace ecaaaaace eaaaace ca aa ac eae ca aa ac eae aa aa eae ggggggggggggg ca ggggggggggggg aa ggggggggggggg ac ggggggggggggg eae ggggggggggggg ca ggggggggggggg aa ggggggggggggg ac ggggggggggggg eae gggggggggggggca ggggggggggggaa gggggggggggac gggggggggcagg ggggggggaaggg gggggggaagggg ggggggacggggg ggggcaggggggg gggaagggggggg ggggggggggggg ggggggggggggg ggggggggggggg ggggggggggggg ggggggggggggg f ggggggggggggg fb ggggggggggggg fd ggggggggggggg dfd ggggggggggggg df ggggggggggggg bf ggggggggggggg bf ggggggggggggg ff ggggggggggggg fb ggggggggggggg fb gggfdgggggggg fd ggggfbggggggg fd ff df bf df dfd bf fb bf ff ff bf fb df fb fd fd fb dfd ff df bf bf dfd bf fb ff ff ff bf fb dfd fd fb fd ff df bf df df bf fd bf fb ff bf fb df fb dfd fd fb fd ffdf bf ``` <!-- end of image --> Let's zoom in on area A to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff0505ff b,#0f0fffff c,#ff6b6bff d,#a5a5ffff e,#ffa1a1ff f,#ff3333ff g,#ffd4d4ff ``` ```image c gfa gaaa eaafg caac gfaae eaaag caafg faac gfaae eaafg caaf gfaac gaaae gafg g d dbbd bbbd ``` <!-- end of image --> Area A doesn't meet the criteria for an intersection. Zero, Nada.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0505ff b,#3333ffff c,#ff5252ff d,#bebeffff e,#ffb0b0ff f,#0303ffff g,#7373ffff ``` ```image e eecaaaac ecaaaaace eccaaaacee ecaaaaace ecaaaaace ecaaaaace eaaaace ca aa ac eae ca aa ac eae ca ac eae ca aa ac eae ca aa ac eae ca aa ae ea ca ac eae ca aa e f fg fd dfd df gf bf bf fb fg fd fg fg fd ff df gf gf dfd gf fg bf fb fb bf fb dfd fg fg fd fb dfd bf df gf gf dfd bf fb bf ff fb gf fg dfd fg fg fd fb dfd bf df dfd gf fg bf fb fb bf fb gf fg dfd fd fb dfd bfdf gf ``` <!-- end of image -->

I'm analyzing this image to identify any points where lines intersect. I'm going to focus my attention on these specific areas. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0403ff b,#0d0efcff c,#7b81f1ff d,#f8ccd2ff e,#b0d6b0ff f,#ec635aff g,#a0c296ff ``` ```image c bb bc bc b db geeeeecbeeeeeeeg eeeeeeecbeeeeeeg eeageeeebbeeeeeg eegaeeeeebceeeeg eeeageeeeebceeeg eeegaeeeeeebeeeg eeeeageeeeegbeeg eeeegaeeeeeecbeg eeeeeageeeeeebbg eeeeegaeeeeeeebb eeeeeeageeeeeeebc eeeeeegaeeeeeeegbd eeeeeeeageeeeeeg b eeeeeeegaeeeeeeg db eeeeeeeeageeeeeg cb eeeeeeeegaeeeeeg bb eeeeeeeeeageeeeg bc eeeeeeeeegaeeeeg bc eeeeeeeeeeageeeg b eeeeeeeeeegaeeeg b eeeeeeeeeeeageeg cb eeeeeeeeeeegaeeg cb eeeeeeeeeeeeageg bb geeeeeeeeeeegaeg bc ad bd da b ad db da cb ad bb da bc ad bc da b ad b da db ad cb da bb ad bc da bbbc ad bbbc da dbbbd ad cbbbd da cbbb ad cbbc da cbbc ad cbbc da cbbc ad cbbcgeeeeeeeeeeeeeeg da bbbceeeeeeeeeeeeg ad egbbbceeeeeeeeeg da eeeecbbbgeeeeeeg ad eeeeeeecbbbeeeeg da eeeeeeeeeecbbbeg ad eeeeeeeeeeeeeceg da eeeeeeeeeeeeeeeg ad eeeeeeeeeeeeefeg da eeeeeeeeeeeaafeg ad eeeeeeeefaafeeeg da eeeeeefaaeeeeeeg ad eeeeaafeeeeeeeeg da efaafeeeeeeeeeeg ad faaeeeeeeeeeeeeeg da daafeeeeeeeeeeeeeeeg ad daad eeeeeeeeeeeeeeeg da faa eeeeeeeeeeeeeeeg ad daaf eeeeeeeeeeeeeeeg da daad eeeeeeeeeeeeeeeg ad faa eeeeeeeeeeeeeeeg da daaf eeeeeeeeeeeeeeeg ad daad eeeeeeeeeeeeeeeg da faa ggggggggggggggge ad daaf da daad adfaa daf ``` <!-- end of image --> I'm now examining the contents of area A in detail. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff0202ff b,#0808ffff c,#b0b0ffff d,#ffbebeff e,#5656ffff f,#ff6b6bff g,#ff3c3cff ``` ```image bbe cbbe cbbc cbbc ebbc dgg ebb aad bbe fag bbe aad cbbe fag cbbc aad ebbc fag ebb aad ebb fag bbe aad cbbe fag cbbc aad cbbc fag ebbc aad ebb fag bb aad b fag c aad fag aad fag aad fag aad fag aad fag aad fag aad fag aad fag aad fag aad fag aad fag aad fag aad fag ``` <!-- end of image --> The lines within area A do not intersect. Next up, a closer look at another region. I'm now examining the contents of area B in detail. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff0606ff b,#0707ffff c,#a9a9ffff d,#ffb9b9ff e,#5757ffff f,#ff4a4aff g,#ff8383ff ``` ```image bec bbbbec cbbbbbec cebbbbbec cebbbbbec cebbbbbec cebbbbbe cebbbbbc cebbbbec cebbbbec cebbe cc dfg dfaaa gaaaafd dfaaaag dfaaafd gaaaafd dfaaaag dfaaafd gaaaafd dfaaaag dfaaafd gaaaafd aaaag afd d ``` <!-- end of image --> There is no intersection present within area B. There's definitely not a single intersection on the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0404ff b,#0707ffff c,#a4a4ffff d,#ffbabaff e,#4c4cffff f,#ff5c5cff g,#f5e0eaff ``` ```image c eb be bc bg gb cb eb ad be ga bc ad bc ga b ad gb ga cb ad eb ga be ad bc ga bg ad gb ga cb ad eb ga eb ad be ga bc ad bg ga gb ad cb ga eb ad be ga bc ad bc ga b ad gb ga cb ad eb ga be ad bc ga bg ad gb ga cb ad eb ga ee ad be ga ebbc ad gbbbc ga cbbbc ad cbbbg ga cbbeg ad cbbe ga cbbe ad ebbe ga ebbc ad ebbc ga gebbc ad gbbbc ga cbbbg ad cbbeg ga cbbe ad c ga ad f ga gaaf ad daad ga faag ad gaaf ga daad ad faag ga gaaf ad daad ga faag ad gaaf ga daad ad faag ga gaaf ad daad ga faag ad gaaf ga daad adfaag gaf ``` <!-- end of image -->

I'm curious to see if this image contains any intersection points. I can confidently say that there are no intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#7373ffff b,#ff0505ff c,#0303ffff d,#ffa9a9ff e,#bcbcffff f,#3232ffff g,#ff5353ff ``` ```image e ff ce c ec ff ce c ac fa ce c ac ca c c ac ca c ec af ca c ec ff ce c ec ff ce c ec ff ce c ec ff ce c ac fa ce c ac ca c c ac cae ffcccccccccfaaee eeaaffcccccccccfaaee eeaaffcccccccccfaaee eeaaff dgb dbbbbd dbbbgd gbbbgd dgbbbg dgbbbd dbbbbd dbbbgd gbbbgd dgbbbg ddddggbbbd ddddggggbbbbbbbbbbbbbbbbggggd bbbbbbbbbggggdddd ``` <!-- end of image -->

I'm ready to tackle this image and find those intersections! Zero, Nada.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0505ffff b,#ff0505ff c,#7d7dffff d,#ffa9a9ff e,#bdbdffff f,#4040ffff g,#ff4f4fff ``` ```image d gb gb gb db db db bd bd bd bd bg bg bg bb gb gb gb db db db b bd bd bd bg bg ae bg a bb ca bb ac gb a gb ea gb ff db ae dbbgd a dbbbbd ca dgbbbd ae dgbbbg a gbbbgd ea dbbbgd ac dgbbbd a dgbbbg ea gbbbgd ff dbbbgd ae dgbb a ca ac a ea ff ae a ca ae a ca ac a ea ff ae a ca ac a ea ff ae a ff ae a ca ac a ea fafccceeee ecccfffaaaaaaaaaaaaaaaaaaafffccceee eeeecccfffaaaaaaaaaa ``` <!-- end of image -->

I'm ready to tackle this image and find those intersections! I wonder what's going on inside those areas? Perhaps intersections are hiding there. <!-- image --> ```palette Key,Color ,#fefefeff a,#3c40f8ff b,#fd0a0aff c,#f06e67ff d,#8388eeff e,#0505feff f,#aed5aeff g,#e9c9dfff ``` ```image g ee aege de de de aa ge ed e e eg ge ed de ea aa aa ed ae e b de ge gb ge de bg e ea gb eg ed bg eg e b ed ge bc ea de b ae ea ffbcffffffffffffae eg fffbfffffffffffde e fffbcffffffffffef ge ffffbfffffffffeff ae ffffcbfffffffefff ea fffffbffffffedfff eg fffffcbffffeaffff e ffffffbfffeafffff ge ffffffcbfaeffffff ae fffffffbdefffffff ed fffffffdeffffffff eg fffffffebffffffff e ffffffeffbfffffff de fffffedffbcffffff ae ffffedffffbffffff ed fffeafffffbcfffff eg ffaefffffffbfffff e faeffffffffbcffff de deffffffffffbffff aa gefffffffffffcbfff ed efffffffffffffbfff eg egfffffffffffffcbff e b de cb aa b ed gb eg bg ge gb de bg aa b ed bc ffffffeffffffff b fffffffefffffff bc fffffffdeffffff b ffffffffeafffff cc fffffffffedffff b ffffffffffeffff cb fffffffffffffff b fffffffffffffff cb fffffffffffffff b fffffffffbbffff gb fffffffbbcfffff bg fffffbbcfffffff gb ffcbbffffffffff bg cbbffffffffffff gb cbbffffffffffffff bg bbc fffffffffffffff b bbc fffffffffffffff bc gbbg fffffffffffffff b gbbg fffffffffffffff cc cbbg fffffffffffffff b cbb fffffffffffffff cc cbc fffffffffffffff b bbc cb bbc b gbbg cb gbbg b cbb gb cbb bgbbc gbc ``` <!-- end of image --> Let's see if area A yields any clues. <!-- image --> ```palette Key,Color ,#fefefeff a,#3733faff b,#fe0707ff c,#ffababff d,#7775fdff e,#0404feff f,#fb5155ff g,#bfbdfdff ``` ```image bbc cbb bbf cbb fbf g cbb ge fbf gee cbbc eea fbf aea bbc aee fbf deeg bbc deeg fbb deeg bbc geed cbb geed bbc geea cbb aea bbc aea cbb aeeg fbf deeg cbbdeeg ffeed geed geeaf eeabbc aea fbf aee bbc deeg fbf deeg bbc deeg cbb geed bbc geed cbb geea bbc aea cbb aea bbf aeeg cbb deeg fbf deeg cbb geed fbf eed cbbc ed fbf a bbc fbf bbc ``` <!-- end of image --> I observe an intersection inside area A. Right then, let's explore the next spot. My goal is to determine if there's an intersection inside area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#6060ffff b,#ff0303ff c,#ff8383ff d,#bcbcffff e,#0a0affff f,#ff2e2eff g,#ffc2c2ff ``` ```image aeed aee eea deea deed aeed aee eea deea deed aeed aee ed cfc cfbbf cbbbbc gcbbbfc gcbbbfg gfbbbfg gfbbbfg cfbbbcg cfbbbc cbbbfc bbbfc bfg g ``` <!-- end of image --> Based on this close-up, I can conclude that there's no intersection in area B. The final count is: one intersection.

<!-- image --> ```palette Key,Color ,#fefefeff a,#4545ffff b,#fe0607ff c,#ff9c9cff d,#9795fdff e,#0606ffff f,#ff5050ff g,#e7d7eeff ``` ```image g eeg aege de de de aa ge ed eg eg eg ge ed de ea ea aa ed ae e b de ge cb ge de bg ge ea gb eg ed bc ed e b ed ge bc ea ae b ae ea bc ae ed b de e ff ge ge b e ae ff eg ea b ed eg cb ea e b ea de cb ae ae bde ea de eg gebg e eggb de eg bc ae ed b ed ea bc eg ae b ge ae ff de de b aa ge ff ed e b eg eg cb ge b de cb aa bg ed cb eg bg ge gb de bc aa b ed bc eg b ge ff de b aa ff ed b e ff b cb b bb cb gbbc bg cbbc gb cbbg bg cbb gb fbf bc fbf b bbc bc gbbc b cbbg ff cbbg b fbb ff fbf b bbf cb gbbc b gbbc cb cbbg bg cbb cb fbf bgfbf gbf ``` <!-- end of image -->

Let's examine this image for potential line intersections. Let's take a closer look at what's happening inside these zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#d66858ff b,#0505fcff c,#3a40e2ff d,#fa0a09ff e,#b1d7b1ff f,#778dcfff g,#a5cba2ff ``` ```image ggggggggggggggggggggggggggggggggggadggggggggggggggggggggggggggggggggggggggggggg geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedadeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedaedgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedefgdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedacbfdaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg geeeeeeeeeeeeeeeeeeeeeeeeeeeeeegdebebedeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg geeeeeeeeeeeeeeeeeeeeeeeeeeeeeedgfcefbadeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg geeeeeeeeeeeeeeeeeeeeeeeeeeeeeadebeeecbdaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg geeeeeeeeeeeeeeeeeeeeeeeeeeeeedefbeeeebcdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg geeeeeeeeeeeeeeeeeeeeeeeeeeeeadebeeeeeebadeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg geeeeeeeeeeeeeeeeeeeeeeeeeeeedefbeeeeeeebdgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg geeeeeeeeeeeeeeeeeeeeeeeeeeedaebgeeeeeeefbdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg geeeeeeeeeeeeeeeeeeeeeeeeeeedefbeeeeeeeeecbaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg geeeeeeeeeeeeeeeeeeeeeeeeeedaebgeeeeeeeeeebceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg geeeeeeeeeeeeeeeeeeeeeeeeegdegbeeeeeeeeeeeebdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg geeeeeeeeeeeeeeeeeeeeeeeeedgebfeeeeeeeeeeeegbgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg geeeeeeeeeeeeeeeeeeeeeeeeadegbeeeeeeeeeeeeeefbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg geeeeeeeeeeeeeeeeeeeeeeeedeebfeeeeeeeeeeeeeeecbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg geeeeeeeeeeeeeeeeeeeeeeeadeebeeeeeeeeeeeeeeeeebfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg geeeeeeeeeeeeeeeeeeeeeeedeebfeeeeeeeeeeeeeeeeeabgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg geeeeeeeeeeeeeeeeeeeeeedaeebeeeeeeeeeeeeeeeeeeedbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg geeeeeeeeeeeeeeeeeeeeeedeecfeeeeeeeeeeeeeeeeeeeeabeeeeeeeeeeeeeeeeeeeeeeeeeeeeg geeeeeeeeeeeeeeeeeeeeedaeebeeeeeeeeeeeeeeeeeeeeeacceeeeeeeeeeeeeeeeeeeeeeeeeeeg geeeeeeeeeeeeeeeeeeeegdeecceeeeeeeeeeeeeeeeeeeeeedbfeeeeeeeeeeeeeeeeeeeeeeeeeeg geeeeeeeeeeeeeeeeeeeedgeebeeeeeeeeeeeeeeeeeeeeeeegdbgeeeeeeeeeeeeeeeeeeeeeeeeeg geeeeeeeeeeeeeeeeeeeadeecceeeeeeeeeeeeeeeeeeeeeeeedabeeeeeeeeeeeeeeeeeeeeeeeeeg geeeeeeeeeeeeeeeeeeedeeebeeeeeeeeeeeeeeeeeeeeeeeeeedfbeeeeeeeeeeeeeeeeeeeeeeeeg geeeeeeeeeeeeeeeeeeadeecceeeeeeeeeeeeeeeeeeeeeeeeeeadcceeeeeeeeeeeeeeeeeeeeeeeg geeeeeeeeeeeeeeeeeedeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeedgbfeeeeeeeeeeeeeeeeeeeeeeg geeeeeeeeeeeeeeeeedaeefbeeeeeeeeeeeeeeeeeeeeeeeeeeeegdebgeeeeeeeeeeeeeeeeeeeeeg geeeeeeeeeeeeeeeeedeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedagbeeeeeeeeeeeeeeeeeeeeeg geeeeeeeeeeeeeeeedaeefbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedefbeeeeeeeeeeeeeeeeeeeeg geeeeeeeeeeeeeeegdeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeadebceeeeeeeeeeeeeeeeeeeg geeeeeeeeeeeeeeedgeefbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedgebfeeeeeeeeeeeeeeeeeeg geeeeeeeeeeeeeeadeeebgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegdeebgeeeeeeeeeeeeeeeeeg geeeeeeeeeeeeeedgeefbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedaegbeeeeeeeeeeeeeeeeeg geeeeeeeeeeeeeadeeebgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedeecbeeeeeeeeeeeeeeeeg geeeeeeeeeeeeedeeegbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeadeebceeeeeeeeeeeeeeeg geeeeeeeeeeeeaaeeebfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedaeebfeeeeeeeeeeeeeeg geeeeeeeeeeeedeeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedeeebeeeeeeeeeeeeeeg geeeeeeeeeeedaeeebfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeadeefbeeeeeeeeeeeeeg geeeeeeeeeegdeeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedgeecbeeeeeeeeeeeeg geeeeeeeeeedgeeebfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegdeeebceeeeeeeeeeeg geeeeeeeeegdeeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedaeeebfeeeeeeeeeeg geeeeeeeeedgeeecceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedeeeebeeeeeeeeeeg geeeeeeeeadeeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeadeeefbeeeeeeeeeg geeeeeeeedeeeecceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedgeeecbeeeeeeeeg geeeeeeeaaeeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegdeeeebceeeeeeeg geeeeeeedeeeecceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedaeeeebfeeeeeeg geeeeeedaeeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedeeeeebeeeeeeg geeeeegdeeeefceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeadeeeefbeeeeeg geeeeedgeeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedaeeeecbeeeeg geeeegdeeeefbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedeeeeebceeeg geeeedgeeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeadeeeeebfeeg geeeadeeeefbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedgeeeeebeeg geeedeeeeebgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegdeeeeefbeg geeaaeeeefbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedaeeeeecbg geedeeeeebgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedeeeeeebc gedaeeeegbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeadeeeeeeb ggdeeeeebfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedgeeeeeg gdgeeeegbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegdeeeeeg gdeeeeebfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedaeeeeg dgeeeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedeeeeg adeeeeebfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeadeeeg dgeeeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedaeeg geeeebfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedeeg geeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeadeg geeecceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedeg geeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegdg geecceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeda gggbggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggd fc e b fc b fb b fb b ``` <!-- end of image --> This is a magnified view of the region A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fb383cff b,#0908feff c,#605cfaff d,#fe0404ff e,#fc7e80ff f,#b5b4feff g,#fec5c5ff ``` ```image dd gdde aaed gdg de gdd eda adeff dd de bbf aa ea bbb gdg gdg cc bc da dd cb fbbgdg de bb cbfaa ae bbf bcdd ed bb bbade da fb cbed gdg bc bbde aa fb bbcd ad bb fbad gdd bc cbd dd cc bbdg de fbf fbca ea cb fbag ad bc cbb dd bf bbg gd bf fbe ae cb bb ed bb bb eda bbf ebc ddg bb bb gdg fb abb ae bf gdbc ad bb abb dd bb dcb de bc adbb gdg cc edbb ad fb acbf ada fbb dabb ddg cbc ddbbc de bbf edfbb de bf gdgcb ed cc da bc da cb gddfbf gdg bb ad cbf aa bb gdg bb ad fb de bb dd bf dd fbf ea bb de bb dg fbb ed bb ed cbc da fbc ada bc eda bb ddg fb dd cb ed fb aa fbc de cb gdg bbf dd bc ad cb da bf gdg bc gdg cc aa fbc gdg cb dd cbf ad bb ad cb dde bf ea bbc da fb de fbb dg bf ddg cbf gdg bb gdd bc ad fbb ed bb de bb gdg cb ed bc da bb de fb dd bbc dd fb ae fbf eda cb gdg cb da bc dde bb gdg bf edd fbf ae cc ad fbf dd cb ea bb da bb de bc ea bbf ad bbf gdg bb gdg cbb dd fb de bc de bf ddg fbf ed fb ada bb ed bb ed bc dd bc ae bc ddg cc da cbb da fb dd cb gdg cb edg bc gd cbc gdg b dd bbf dd c dg bf gdg ea cc aa gdg bf gde gdd bb ade ade bb gdd de fb de ed bf ed d bb dd bb ed bc de cc da fb ddg fbb ad cbc gdg bb aa fbf d ``` <!-- end of image --> An intersection is present within area A. I've found a single intersection point in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#f5424bff b,#0908fdff c,#5f5ffeff d,#fe0606ff e,#fe8889ff f,#b1b1feff g,#fec7c7ff ``` ```image g ed ded aa dg d f d decbfaa gd b b d dgcb fbgd gd b cbde d fb bcd ea b baa d fb bd aa b fbd d fb cbe de bf ba gd b ba dg bf bg gd b fb d bf bb ea b bc d bf eb aa b db d bc ab de b abb gd cc dbf dg b gdb gd cc deb d b dfb ed cc edbc d b dgbf aa fb gd b d b de b de fb d cb gd b ed bc dg fb dg bf gd b d b d fb aa fb ed bf d cb d b gd bc aa bf de bf d b d b de bf aa fb d b dg cb dg bf gd bc gd b de bf d cc d b ed b ed fb d cc dg cb aa b d bc d cc aa bf de b d b d cb ed fb dg b dg cb gd fb d bc d b aa bf ed fb d b d b gd fb aa fb de cb d b d bc de fb ed b d bf dg dg b gd gd bf aa d b d ed bf ed d b dg bc d b aa cc d b gd cc de b d cc g b cb b fb b fb b ``` <!-- end of image -->

Hmm, I'm not sure what to expect from this image. Let's see if any lines cross. I wonder what's going on inside those areas? Perhaps intersections are hiding there. <!-- image --> ```palette Key,Color ,#fefefeff a,#595df8ff b,#ff0505ff c,#ff9f9fff d,#add5adff e,#0808feff f,#f0433cff g,#b8b8ffff ``` ```image c ccffbbbbbbbbbf ccffbbbbbbbbbffcc cccffbbbbbbbbffccc bbbbbfccc bc b bc b bc b bc b bc b bc b bc b bc b bc b bc b bc b bc b e bc ae b ae bc ge b e bc eg b eg bc ea b ae bc ae b ge bc e b eg bc eg b ea fc ae b ae fc ge b e fc eg b eg fc ea b ae fc ge ddddddddddddddbd ge dddddddddddddffd e dddddddddddddbdd eg ddddddddddddffdd ea ddddddddddddbddd ea dddddddddddffddd ae dddddddddddbdddd ge ddddddddddffdddd ge ddddddddddbddddd e dddddddddffddddd eg dddddddddbdddddd ea ddeeadddffdddddd ea ddddeeadbddddddd ae ddddddaeeddddddd ge dddddddbaeeddddd ge ddddddffddaeeddd e ddddddbddddddeea eg dddddffddddddddeea ea dddddbdddddddddd aea ea ddddffdddddddddd aee ae ddddbddddddddddd geeg ge dddffddddddddddd geeg e dddbdddddddddddd eea e ddffdddddddddddd aea eg ddfddddddddddddd aee ea dddddddddddddddd geeg ee dddddddddddddddd geegae dddddddddddddddd ee ``` <!-- end of image --> Let's zoom in on area A to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#372ef5ff b,#fe0102ff c,#ffcfcfff d,#8181ffff e,#0303feff f,#fe5454ff g,#bfbcfbff ``` ```image cbb fbf cbb fbf cbb fbf cbb fbf cbb fbf cbbc fbf cbbc fbf cbbc fbf cbbc fbf cbbc fbf cbbc fbf eag cbbc geeead fbf deeeed cbbc daeeedg fbf gaeeeabbc gaeeeag gaeeead fbfdeeeed cbbc daeeedg fbf gaeeeag cbbc gaeeeag fbf gdeeead cbbc deee fbf da cbbc fbf cbbc fbf cbbc fbf cbbc fbf cbbc fbf cbbc fbf cbbc cff ``` <!-- end of image --> Yes! I knew it! There's an intersection right here in area A! The final count is: one intersection.

<!-- image --> ```palette Key,Color ,#fefefeff a,#3f3efdff b,#ff0707ff c,#ffa5a5ff d,#8989ffff e,#0606ffff f,#ff5454ff g,#cdcdffff ``` ```image c ccffbbbbbbbbbf ccffbbbbbbbbbffccc ccffbbbbbbbbbbffcc bbbbbffcc bc b bc b bc b bc b bc b bc b bc b bc b bc b bc b bc b bc b e bc aa b de bc ge b e bc eg b ed bc ea b ae bc de b ge bc e b eg bc ed b ea bc ae b de bc ge b e bc eg b ed fc ea b ae ff de b ge ff e b eg ff ed b ea ff ae b de ff ge b e ff eg g b ed eed ff ea aed b ae aea de bdee ge ff deeg e b geed eg ff eed ed b aea aa ff dee ae b deeg de ff geed ge b eed eg ff aea eg f dee ed deeg aa geedde ee ``` <!-- end of image -->

Alright, let's get to work and investigate this image for intersections. These zones are intriguing. I bet there's something interesting happening within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0504ff b,#0707fdff c,#f28d89ff d,#4c54efff e,#f4403bff f,#989df5ff g,#acd4adff ``` ```image f b b bd fb b c bf ea dd aca b ee ac b a a bd ce ee fb a a b ce a bf a ac dd ce a fb a ce b ce a bf a a fb ca ac b a a bf ca ca dd a a fb ca a b a ec bf ca a fb a ca b ca ggagggggggggggbg a gggagggggggggbdg ca gggeegggggggfbgg a ggggagggggggbggg a ggggcagggggbdggg a gggggacgggdbgggg a ggggggagggbggggg a ggggggeegbgggggg a gggggggabdgggggg a gggggggcbggggggg a gggggggbacgggggg bb ac ggggggbdgagggggg dbf ggggggggggggaggg gggggdbggeeggggg bb gggggggggggacggg gggggbggggaggggg fbf gggggggggggagggg ggggbgggggcagggg bbggggggggggacgggg gggbdggggggacggg fbdggggggggaggggg ggfbggggggggaggg gbbggggggacggggg ggbgggggggggeegg ggfbdggggagggggg gbdggggggggggagg ggggbbggacgggggg dbgggggggggggcag gggggfbdaggggggg b ac gggggggbbggggggg b a gggggggagbdggggg bd ee ggggggeeggdbgggg fb a ggggggagggggbbgg b ca gggggeeggggggdbf bf ac gggggagggggggggbb db a ggggeeggggggggggdbf b ce ggggaggggggggggg bb b a gggeeggggggggggg fbf bd a gggagggggggggggg bb fb ac ggeegggggggggggg fbf b a a bb bf ce ee fbddb a a bb a ce ac a a ce ca a a ce a a ec ce a a ca ca a a a ca ee a a ca ca a ac ca a a ee ca a a ``` <!-- end of image --> Let's take a closer look at area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0404ff b,#0908fdff c,#ff7c7cff d,#5b5bfeff e,#f22e3aff f,#b4b4feff g,#ffb0b0ff ``` ```image aag cae aag cae aag cae aag cae f aag bdf cae bbbd aag dbbbf cae fbbbd aag dbbbf cae fbbbd aag dbbbf caa fbbbd aac dbbbf gaa fbbbdeac dbbbe fbbbd gaebbbf eacfdbbd gaa fbbbf eac dbbdf gaa fbbbd eac dbbbf gaa fbbbd eac dbbb gaa fbb eac d gaa eac gaa eac gaa eac gaa eac ``` <!-- end of image --> Amazing! This area was hiding an intersection all along! Time for a closer look at another area. Let's get to the bottom of what's happening inside area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0a0bff b,#0404feff c,#ff6565ff d,#8884faff e,#3f35f5ff f,#c7c7ffff g,#ffb9b9ff ``` ```image aac ebe gaag dbbf caa fbbd aag ebe caa dbbf aac fbbf gaag bbd caa ebe aag dbbf gaa fbbd aac ebe gaag dbb caa fbbf aac bbd gaa ebe aac dbbf gaagfbbd caaebe aebb dbbd bbec ebeaag dbbfcaa fbbd aac ebe gaa dbb cac fbbf gaag bbd caa ebe aac dbbf gaag fbbd cac ebe gaag dbb caa fbbf aac bbd gaag ebe cac dbbf aag fbbd caa ``` <!-- end of image --> There is an intersection point visible in this close-up of area B. After a long analysis, I found two intersections.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fe0505ff b,#0a0afeff c,#fd8081ff d,#6a6afeff e,#ff3e3eff f,#b9b9ffff g,#ffc7c7ff ``` ```image d fb b bd db b c bf ea db aga fb ee ac b a a bd ce ce db a a b ce ga bf a ac db ce a fb a ce b ce ag bd a ga db ca ac b a a bf ca ca bb a ag fb ca ga b a ec bd ga a db a ca b ga ag bf a a bd ga ec fb ag a b ga ca bd ag ag db ga a b ag ee bf ga abd ag cb ga bag bb ag bd a dbf a db ee bb ag b a dbf a bf ga bb ag bd ag fbd a fb a bb ac b ee fbd a bf a bb ac db ga fbda b ac bb bf a afbd bd ee ec dbf fb a a bb b ga ec dbf bf ac a bb db a ec dbf b ce a bb bf a ec dbf bd ga a bb fb ac ee fbd b a a bb bf ce ee fbddb ag a bb ga ce ac a a ce ca a ag ce ga a ec ce a a ca ca ag a a ca ec a a ca ca a ag ga a a ee ga a a ``` <!-- end of image -->

I'm on the case! Let's uncover any intersections hidden in this image. I'm extremely confident. No intersections at all.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0404ff b,#0808ffff c,#ff8686ff d,#acacffff e,#ffcacaff f,#ff3d3dff g,#5c5cffff ``` ```image d dgbbbbb dgbbbbbgd dgbbbbbgd dgbbbbbgd dgbbbbbgd dgbbbbbgd dbbbbbgd bbb gbbd bbg gbbd dbbg gbbd dbbg c gbbd caa dbbg caf gbb faf dbbd faf bbb fac gbbd aac bbg aac d eaae eaae caae caa caf faf faf fac aac aac eaae eaae eaae aa ae ac ff ca ea ae ac ff ca ea a ae af fa ea a ae ac ff ca ea ae ac ff ca ea a ae af fa ea a ae ac ff ca ea ae ac ff ca ea a ae ``` <!-- end of image -->

Here's an image. My task is to find intersections or areas where lines come close together. These spots are like clues. Let's see what they reveal about potential intersections. <!-- image --> ```palette Key,Color ,#fefefeff a,#ed4a42ff b,#0b0cfcff c,#e59a8eff d,#7076e7ff e,#a1cda2ff f,#b2d7b2ff g,#fd0605ff ``` ```image cga g ag eeeeeeeeeeeeeeeeeeeeeee b cg cgc efffffffffffffffffffffe dbd g gg efffffffffffffffffffffe bb g ag efffffffffffffffffffffe bd gc gc efffffffffffffffffffffe db g gg efffffffffffffffffffffe bb ac cgcefffffffffffffffffffffebd g gaffffffffffffffffffffdb aa ggffffffffffffffffffbbe g ecgcffffffffffffffdbdfe cg effggffffffffffffbbfffe g efffagffffffffffbbffffe cg effffcgaffffffdbdfffffe g effffffggffffbbfffffffe g efffffffageebdffffffffe gc effffffffedbefffffffffe g effffffffbbggfffffffffe ac effffffebdffcgcfffffffe g efffffbbefffffgaffffffe aa effffbbffffffffagfffffe g effdbdffffffffffcgcfffe cg efbbffffffffffffffggffe eeeeeeeeeeeeeeeeeeeg ebbffffffffffffffffagee efffffffffffffffffcg dbeffffffffffffffffffega efffffffffffffffffge bbefffffffffffffffffffffgg effffffffffffffffege bd efffffffffffffffffffffecg effffffffffffffffgce db efffffffffffffffffffffe ga effffffffffffffffgfe bb efffffffffffffffffffffe gg efffffffffffffffaafe fbd efffffffffffffffffffffe cgc efffffffffffffffgffe bb efffffffffffffffffffffe ga effffffffffffffaaffe bb efffffffffffffffffffffe ag effffffffffffffgfffe dbf eeeeeeeeeeeeeeeeeeeeeee c efffffffffffffcgfffe bb efffffffffffffgffffe bbd effffffffffffcgffffe dbd effffffffffffgeffffe bb effffffffffffgfffffe bb efffffffffffgcfffffedbd efffffffffffgfffffdbb effffffffffaafffebbe effffffffffgfffbbefe efffffffffaafdbdfffe efffffffffgebbfffffe effffffffcbbeffffffe efffffffbbdffffffffe efffffdbdgfffffffffe efffebbfgcfffffffffe effbbeffgffffffffffe edbdfffgcffffffffffe dbbfffffgfffffffffffe bbefffffaafffffffffffe bbf efffffgffffffffffffe dbd effffaaffffffffffffe d effffgfffffffffffffe efffcgfffffffffffffe efffgffffffffffffffe effcgffffffffffffffe effgcffffffffffffffe effgfffffffffffffffe efgcfffffffffffffffe efgffffffffffffffffe eaaffffffffffffffffe egfffffffffffffffffe aafffffffffffffffffe gffffffffffffffffffe cgffffffffffffffffffe geeeeeeeeeeeeeeeeeeee g gc g gc g aa g ca g cg g ``` <!-- end of image --> I'm determined to find out if an intersection exists in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff4242ff b,#0706fdff c,#fe8888ff d,#a8a8feff e,#ffccccff f,#5549f3ff g,#fe0405ff ``` ```image a eg ag egg aga egge cga gge cga ggc cgg agc egg agc egge aga egge cga gge cga ggc cgg agc egg agc egge aga egge cga gge cga ggc cgg d agc dbb egg dfbbb agc fbbbd egge dbbbf aga dbbbfd egge fbbbd cga fbbbf gge dbbbf cgadfbbbd ggfbbbd cfbbbf dbbbfd dfbbbd fbbbfc dbbbfgge dbbbfdaga fbbbd egge fbbbf cga dbbbf gge dfbbbd cga fbbbd ggc dbbbf cgg dbbbfd agc bbbd egg bd agc egge aga egge cga gge cga ggc cgg agc egg agc egge aga egge cga gge cga ggc cgg agc egg agc egge aga egge cga gge cga ggc cgg agc ``` <!-- end of image --> Aha! I've found an intersection inside area A! Time to investigate another area. I'm now examining the contents of area B in detail. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe4e4eff b,#0606feff c,#ff9f9fff d,#9793fbff e,#e7d5edff f,#4942f7ff g,#fe0707ff ``` ```image e gc d gga fb cgggc ebbb egggc dbbbe aggae efbbf cgggc ebbbd eagga dbbfe aggae efbbf cgggc dbbbd eagga fbbfe cggge efbbd egggc dbbbd aggae fbbfe cgggc ebbbd eagga dbbbe aggae efbbf cgggdbbbd eafbbfe efbbfge dbbbdgggc fbbfe agga efbbd cgggc dbbbe egggc fbbf aggae ebbbd cgggc dbbfe eagga efbbf aggae dbbbd cgggc fbbfe eagga efbbd cggge dbbbd egggc fbbfe aggae ebbbd cgggc dbbbe eagg bbf ag bd c e ``` <!-- end of image --> Incredible, there's actually an intersection in area B! I can confirm there's two intersections in there.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff3f3fff b,#0707feff c,#fe8282ff d,#a7a7feff e,#ffc3c3ff f,#544ffaff g,#ff0505ff ``` ```image e cga g ag b eg egc dbd ge gg bb g ag bf ge egc dbd g gg bb ac cge bf g ga fb ca ag bb g ege dbd ca ga fb g ag bf eg egc dbd ge gg bb g cge bf ge fb g bbgg ac dbd cge g fb ga ca bb ag g dbd egc cg fb gg g bf ag eg dbd egc ge bb gg g bf cge ge fb ga g bb ag ac dbd cge g fb ga ca bf ag g dbd e cg bb g fbd eg dbf ge bb g bb ge fbd g dbf ac bb g bbd ca fbf gdbb cbb fbd dbfg bb ge bb g fbd gc dbf g bb ac bbd g fbf ca f g cg g eg ge g gc g ac g ca g eg g eg ge g gc g ac g ca g eg g ``` <!-- end of image -->

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

<!-- image --> ```palette Key,Color ,#fefefeff a,#0707ffff b,#ff3939ff c,#b3b3ffff d,#ffb5b5ff e,#ff0303ff f,#5b5bffff g,#ff7474ff ``` ```image d beeeeeg deeeg geebd geebd dbeeg dbeeg geeed geeed dbeeb beeb geeeg deeeg dbeebd geebd deeeg dbeeg geebd geeed deeeg eeb geeed dbeeb ge ccffaaaaaaaaac ccffaaaaaaaaaffcc af ccffaaaaaaaaaffcc aa affcc fa fa ca ac af aa aa fa ca ac af af aa fa ca cac af af aa fa ca cac ac af aa fa fa cac ac af aa fa fa ca a ``` <!-- 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,#0607fcff b,#fd0707ff c,#babaffff d,#f2655fff e,#575af0ff f,#97c796ff g,#b2d7b1ff ``` ```image c cac a ac ca ac ac ac a ac ac ac a ac ee ac a ac ee a a a ca a a a ca ca ac ca a ca ac ca a ca ee ca a ca ee ca a ca ca ca a ca ca ca ac ca a ca ac ea a ea ee ea bb gfffffffffffafff ea dbd fggggggggggeeggg geaffffffffffffffff dbd fggggggggggagggg fgeaggggggggggggggg bbg fgggggggggeagggg fggeagggggggggggggg bb fgggggggggaggggg fgggeaggggggggggggg gbbggggggggfaggggg fggggeagggggggggggg dbdggggggafggggg fgggggeaggggggggggg fgdbdggggagggggg fggggggeagggggggggg fgggbbfgaegggggg fgggggggaaggggggggg fgggggbbaggggggg fggggggggaagggggggg fggggggaebgggggg fgggggggggaadbbgggg fggggggagdbdgggg fggggggfdbbaafggggg fgggggeegggdbdgg fggdbbbbdgggaaggggg fgggggaggggggbbf gdbbbdfggggggggaagggg fggggeaggggggggbb dbbbbdfgggggggggggggagggg fggggagggggggggggbb gdbbbd fgggggggggggggggggg fgggfagggggggggg dbd dbbbbd fgggggggggggggggggg fgggafgggggggggg dbd gdbbbd fgggggggggggggggggg fgggaggggggggggg bbg dbbbbd fgggggggggggggggggg fggaeggggggggggg bbgdbbbd fgggggggggggggggggg gffaffffffffffff bd fgggggggggggggggggg ee gffffffffffffffffff a ee a ca a ca ac a ac a ee a ee a ca a ca ac a ac a ee a ee a ca a ``` <!-- end of image --> Let's zoom in on area A to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#0504feff b,#fd0b0cff c,#8989ffff d,#fe6b6cff e,#4741f8ff f,#cdcdffff g,#fdbcbdff ``` ```image faaf eae faaf cae aaf cae aac caa eac faa eac bg faaf bbbg eae dbbbdg faaf dbbbd cae gdbbbd aaf gbbbbg cae gbbbbg aac dbbbdgcaa dbbbaac gdbaad eaebbg faagbbbbg eae dbbbdg faaf dbbbd cae gdbbbd aaf gbbbbg cae gbbbbg aac dbbb caa db eac g faa eac faaf eae faaf cae aaf cae aac ``` <!-- end of image --> Aha! I've found an intersection inside area A! Okay, let's direct our attention to the next zone. I'm going to scrutinize area B for any signs of an intersection. <!-- image --> ```palette Key,Color ,#fefefeff a,#0b09fcff b,#fd0203ff c,#bbbbffff d,#fb8185ff e,#4c4cffff f,#ff3d3dff g,#fac1c5ff ``` ```image eaac eaac eaac eaac eaac eaac eaac eaac eaac eaac eaac eaac eaac eaac eaac eaac eaac eaac eaac gdg eaagdfbbbf gddaaabbbbfd gdfbbbbbaaadg gddfbbbbbbfdggaaa gdfbbbbbbffdg aaa gddfbbbbbbfdg aaa bbbbbffdg aaa bfdg aaa ac ``` <!-- end of image --> I am surprised, so clear, an intersection has appeared in area B. The image features two intersection points.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0606feff b,#fe0808ff c,#9696ffff d,#ff6363ff e,#514dfbff f,#cfcfffff g,#ffb5b5ff ``` ```image f cac a af fa af af af fa af ac af a af ec af a af ee af a faf ca faf a fa fa fa af fa a fa ac fa a fa ec fa a fa ee fa a ca ca ca a ca fa ca af ca a ca ac ca a ca ec ca bb a ea dbd ee ea dbd a ea bbg ca ea bb a ea gbb fa ea dbd af ea dbd a ea bbg ac ea bba ea eeb eadbb a dbd gdbbaag ee dbd dbbbbg aa a bbg gdbbbdg aa ca bb dbbbbg a a gbb gdbbbdg fa gbd dbbbbg af dbd gdbbbdg a bbg dbbbbg ac bbgdbbbdg a gbg ee a ee a ca a fa af a ac a ee a ce a ca a fa af a ac a ee a ce a ca a ``` <!-- end of image -->

I'm analyzing this image to identify any points where lines intersect. I've noticed 1 areas of interest. These could be potential intersection zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd0909ff b,#0606feff c,#f56560ff d,#5659f4ff e,#add4acff f,#ffb6b6ff g,#b2b2ffff ``` ```image f ac a ecaeeeeeeeeeeeee eeaeeeeeeeeeeeee eeeaeeeeeeeeeeee eeeaceeeeeeeeeee gdbb eeeeaeeeeeeeeeee gdbbbbdg db eeeecaeeeeeeeeee gdbbbbdg gb eeeeeaceeeeeeeeegdbbbbdg bg eeeeeeaeeeeddbbbbdg bg eeeeeedbbbbddeee bd dbbbbbdaeeeeeeee bd ddeeeeeeaeeeeeee bb eeeeeeeeaceeeeee db eeeeeeeeeaeeeeee db eeeeeeeeecaeeeee gb eeeeeeeeeeaeeeee bg eeeeeeeeeeeaeeee bg eeeeeeeeeeeaceee bd eeeeeeeeeeeeaeee bd eeeeeeeeeeeecaee bb af db a db cc gb a bg fa bg af bd a bd ca bb a db fa db ac gb a bg ca bg af bd a bd ac bb a db fa db af gb a bg cc bg a bd fa bd af b a ca a fa ac a ca af a ac a fa af aa caa faaf faaf aac aac cac caa faa faaf faaf aac aac cac caa faa faaf aaf aac cac ca ``` <!-- end of image --> I'm focusing my attention on this specific region, area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0304ff b,#0503fdff c,#ff7474ff d,#4d49faff e,#ff3434ff f,#febcbcff g,#9c99fbff ``` ```image cae aac caa eac faaf cae aac faa eae faaf cae eac faaf eae aaf caa gg eac ggddbbbb faaf ggdbbbbbbbbdd ggdbbbbbbbbbdgg ggdbbbbbbbbddgg gddbbbbbbbbdggaa bbbbbddgg eac dgg faaf cae aac faa eae faaf cae eac faaf eae aaf caa eac faaf cae ``` <!-- end of image --> The close-up clearly shows an intersection point in area A. I've found a single intersection point in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fe0505ff b,#0605feff c,#ff8585ff d,#5654fdff e,#ff4040ff f,#ffc6c6ff g,#b6b6ffff ``` ```image f ec a ca af a ee gdbb a gdbbbbdg db fa gdbbbbdg gb ac gdbbbbdg gbg a gdbbbbdg bg gdbbbbdg bd gdbbbbda bd dg fa bb ac db a db ca gb af gbg fa bg ec bd a bd ca bb af db a db ee gb a gbg fa bg ac bd a bd ee bb a db fa db ac gb a gbg ca bg af bd fa bd ec bb a db ca db af gb a gbg ee bg a bd fa bd ac b a ee a fa ac a ca af fa ec a ca af ae caa faaf faaf aac eac eae caa caa faaf faac aac eae eae caa caaf faaf faac aac eae ea ``` <!-- end of image -->

The hunt for intersections begins! Let's analyze this image closely. I need to zoom in on these areas to get a better look. <!-- image --> ```palette Key,Color ,#fefefeff a,#0606feff b,#fe0c0bff c,#8687fdff d,#dcccefff e,#4142fbff f,#f67874ff g,#add4adff ``` ```image gggggggggggggggg gggggggggggggggg gggggggggggggggg gggggggggggggggg ggggggbbbbbfgggg gggfbbfggggfbbbf gfbbgggggggggggbbbfd bbbgggggggggggggg fbbbf dbbfgggggggggggggggg fbbbf fbbd gggggggggggggggg dbbbfd bbf gggggggeaggggggg fbbbf dbbf gggggggacagggggg dfbbbd fbbd ggggggaggagggggg fbbbf bbb gggggeagggaggggg fbbbf dbbf gggggaggggaegggg dbbbbd fbbd ac a fbbbf bbb ca ca f dbbf a ad fbbd ac da bb da ec a a ee ca a ad ad da ca ac a a ac ca ca ad a da ac ac da a a ca ee ad da da ad ac ce a a ca ac ad ca da a ac ac a da ce a ad ee da da ac ad a ee ce a ad ad da ca ac a a ac ce da a a da ee ac da a ad ee ee a a da ad ac ca a a ee ac a da da a ac ee a d ee a da ac a ee a da ac a ee a da ac a ee a ``` <!-- end of image --> Could this be where the intersection is hiding, in area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#0b0bffff b,#ff0505ff c,#6e6effff d,#ffc9c9ff e,#ff4141ff f,#ff8080ff g,#bfbfffff ``` ```image dd debbbefd fbbbbbbbbbbfd dfbbbbfd dfebbbbbefd debbbef dfebbbbbe fbbbbed dfebbb dfbbbbfd df debbbef bbbed bfd gg gaag caaa gaaaag aaccaa caa aac gaag gaag aac caa caa aag gaag caa ``` <!-- end of image --> This close-up reveals that there are no intersections in area A. Zero, Nada.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0404ffff b,#ff0707ff c,#7d7dffff d,#ffb6b6ff e,#3535ffff f,#ff6161ff g,#c9c9ffff ``` ```image d bbbbbf dbbd fbbbd fbb dfbbfd bbf dbbbf dbbd fbbbd fbbd g dbbbf bbf ea fbbbf dbbf aca fbbbd fbbd ag ag dbbbf fbf ce ga fbbbd dbbf a ec dfbbfd fbbd ac a dbbbf fbb ca ca f dbbf a ag dbbd ec ga bb ga ec a a ee ca a ag ag ga ce ec a a ag ce ca ag a ga ac ec ga a a ce ee ag ga ga ag ac ce a a ce ag ag ca ga a ac ac a ga ce a ag ee ga ga ac ag a ce ce a a ag ga ca ac a a ac ce ga a a ga ee ac ga a ag ce ce a a ga ag ac ca a a ce ac a ga ga a ac ec a g ee a ga ac a ee a ga ag a ee a ga ag a ee a ``` <!-- 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,#5458efff b,#ee4b43ff c,#0708fdff d,#a5a9f7ff e,#fe0302ff f,#f6928eff g,#aed5aeff ``` ```image d cd c cd dc c dc c aa c aa c cd c cd dc c dc c aa c aa c cd c cd dc c dc c aa c aa c cd c c dc c f ggacgggggggggggg ebeef gggcgggggggggggg be beef gggaaggggggggggg eb beef ggggcggggggggggbef beef ggggcaggggggggee beef gggggggggggggggggg gggggcgggggggebg beef gggggggggggggggggg gggggcdggggbeggg beef gggggggggggggggggg ggggggcgggeegggg beef gggggggggggggggggg ggggggcgfefggggg beef gggggggggggggggggg ggggggdceggggggg beebggggggggggggggggg ggggggecgggggggg beebgggggggggggggg ggggbegacggggggg gggbeebggggggggggg gggeegggcggggggg ggggggbeebgggggggg gfebggggaagggggg gggggggggbeebcgggg begggggggcgggggg gggggggggggacagggg ebggggggggcaggggg ggggggggggccgggggg fefggggggggggcggggg ggggggggacdggggggg ee ggggggggggcdgggg ggggggdcaggggggggg ef gggggggggggcgggg gggggccggggggggggg be gggggggggggcgggg gggacagggggggggggg eb ggggggggggggcggg ggccgggggggggggggg fef c ccgggggggggggggggg ee dc dcaggggggggggggggggg eb c cc gggggggggggggggggg be aa acd gggggggggggggggggg ee c dca ad cc c acd cd cc c cc c dca dc cc c acd dc dca c cc aa acd c cc cd cc c dca cdcc cd ``` <!-- end of image --> I wonder what we'll find inside area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#514cf9ff b,#ff4b4bff c,#0706feff d,#e2d7f4ff e,#fd0507ff f,#fea0a1ff g,#9494ffff ``` ```image ccg gcc ccg gca dccd aca dccd aca dccd acg fe gcc fee ccg dbeeb gcc feeef ccg beebd gca feeef dccd feeef aca dbeeb dccd feeef acabeebd dcceef fccaf beecc feeefccg beebd gcc dbeeb ccg feeef gca beeb dccd feeef aca feeed dccd dbeeb aca feeef dccd eebd acg ef gcc f ccg gcc ccg gca dccd aca dccd ``` <!-- end of image --> Yes! I knew it! There's an intersection right here in area A! Now, let's scrutinize the next spot. I'm eager to see what's happening in this magnified view of area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#392df2ff b,#fe6364ff c,#0404feff d,#c3c0fcff e,#fe0808ff f,#ffbbbbff g,#7777feff ``` ```image f eebf eeeeebf fbeeeeebf fbeeeeebf fbeeeeebf fbeeeeebf fbeeeeebf fbeeeeebf fbeeeeebdag fbeeaccc gcccab daccadff gcccg dcccg daccad gcccg daccad gcccd gcccg daccad gcccg dcccg daccad gcccg daccad gcccd ccg ad ``` <!-- end of image --> Success! This area contains an intersection point! There are precisely two intersections present in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#3a36fbff b,#ff4949ff c,#0404feff d,#c7c7ffff e,#ff0303ff f,#ff8f8fff g,#8282feff ``` ```image d cg c cd dc c gc c ga c ag c cg c cd dc c gc c ga c ag c cg c cd dc c gc c ga c ag c cd c cd dc c f ga ebeef c be beef ga eb beef c fef beef ag ee beef c eb beef cd be beef c ee beef cdfef beef dce beef ec beef fe ga beef ee c beef fef ga beeba be c gca eb ag cc fef c acd ee cd dca ef c cc be cd gcg eb dc dca fef c acd ee ga gcg eb c cc be ga acd ee c dca ag cc c gcg cd dca c acd cd gcg dc cc c acd ga dca c cc ga gcg c dca ag acd c gcg cdcc dcd ``` <!-- end of image -->

I have a feeling there might be some intersections in this image. I wonder what's going on inside those areas? Perhaps intersections are hiding there. <!-- image --> ```palette Key,Color ,#fefefeff a,#0c0efaff b,#f90c0cff c,#d87767ff d,#6d7dddff e,#b1d7b1ff f,#98c59bff g,#eff4f0ff ``` ```image e ad ag ga aa ag ga da ag ga da ae a da ad a da ad a da ad ag ga adfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffg faeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg ffaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg feaaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg feeafeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg feefaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg feeeaaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg feeeeafeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg feeeeeaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg feeeeedaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg feeeeeeadeeeeeeeeeeeefeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg feeeeeeeaeeeeeeeecbbbbceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg feeeeeeedaeeefcbbbceeebfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg feeeeeeeeacbbbceeeeeeeebfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg feeeeecbbbafeeeeeeeeeeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg fefbbbbceedaeeeeeeeeeeeefbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg cbbbceeeeeeeadeeeeeeeeeeeefbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg cbbbcfeeeeeeeeeeeaeeeeeeeeeeeeecbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg gbbbbg feeeeeeeeeeedaeeeeeeeeeeeeecbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg gcbbbc feeeeeeeeeeeeadeeeeeeeeeeeeecbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg bbbc feeeeeeeeeeeeeaeeeeeeeeeeeeeecbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg g feeeeeeeeeeeeedaeeeeeeeeeeeeeecbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg feeeeeeeeeeeeeeadeeeeeeeeeeeeeecbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg feeeeeeeeeeeeeeeaeeeeeeeeeeeeeeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg feeeeeeeeeeeeeeefaeeeeeeeeeeeeeeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg feeeeeeeeeeeeeeeeaaeeeeeeeeeeeeeeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg feeeeeeeeeeeeeeeeeafeeeeeeeeeeeeeeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeg feeeeeeeeeeeeeeeeefaeeeeeeeeeeeeeeeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeg feeeeeeeeeeeeeeeeeeaaeeeeeeeeeeeeeeeebceeeeeeeeeeeeeeeeeeeeeeeeeeg feeeeeeeeeeeeeeeeeeeafeeeeeeeeeeeeeeeebceeeeeeeeeeeeeeeeeeeeeeeeeg feeeeeeeeeeeeeeeeeeefaadeeeeeeeeeeeeeeebceeeeeeeeeeeeeeeeeeeeeeeeg feeeeeeeeeeeeeeeeeeeeefaaadeeeeeeeeeeeeebceeeeeeeeeeeeeeeeeeeeeeeg feeeeeeeeeeeeeeeeeeeeeeeefaaadeeeeeeeeeeebceeeeeeeeeeeeeeeeeeeeeeg feeeeeeeeeeeeeeeeeeeeeeeeeeefaaadeeeeeeeeebceeeeeeeeeeeeeeeeeeeeeg feeeeeeeeeeeeeeeeeeeeeeeeeeeeeefaaadeeeeeeebfeeeeeeeeeeeeeeeeeeeeg feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefaaadeeeeebfeeeeeeeeeeeeeeeeeeeg feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefaaadeeebeeeeeeeeeeeeeeeeeeeg feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefaaadfbeeeeeeeeeeeeeeeeeeg feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefaaabeeeeeeeeeeeeeeeeeg feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefaaadeeeeeeeeeeeeeeg feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecbaaadeeeeeeeeeeeg feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecbefaaadeeeeeeeeg feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecbeeefaaadeeeeeg feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecbeeeeefaaadeeg feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecbeeeeeeefaaag feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeeeeeeeefg feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeeeeeeeeg feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeeeeeeeg feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeeeeeeg feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeeeeeg feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebceeeeeg feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebceeeeg feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebceeeg feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebceeg feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebceg feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebcg feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefbg ggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggg ``` <!-- end of image --> My goal is to determine if there's an intersection inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0303feff b,#fe0405ff c,#fe9495ff d,#9190feff e,#3f39f9ff f,#fd4143ff g,#ecd6e8ff ``` ```image ea gad dag aad daag eae gaad daag eae gaad ea gad dag ae aad daag aad daag gg daa gcfbbc ea ccfbbbbbbg gad gcfbbbbfc fbbg da gcfbbbbbfc fbbg ae cfbbbbbfc fbbg gceaabbfc fbg gcfbbbbaaeg gffg gcbbbbbfggaad gbfg gcfbbbbfcc daag bbf gcbbbbbbfg eae gbbf fbbbbfcg gaad gbbf c ea gbb gad cbf dag cbf ae bbc aad cbbc daag cbbc eae cbbc daag cbb eaa fbc aae fbg gaa bbg da fbbg ee fbbg aag fbbg eae gfbf gaad gbbg daag gbf eae gbf gaad bbf ea gbbf gad cbbf dag cbb aed cbc aaaaed cbc gdeaaaad bbc gdeaaaed cbbc gdeaaaed cbbc gdaaaaed fbbc gdeaaaad fbb gdeaaaed fbg geaaaaed fbg gdeaaaed bbg deaaaad fbbg gdeaaaed gfbfg geaaaaed gbbf gdeaaaed gbb gdeaaaedbf deaaaaff gdeaaaed ceaaaaed cbbeeaaaed cbbcdeaaaae cbb gdeaaaed cbc gdaaaaed cbc gdeaaaed cbbc deaaaae fbbc gdeaaaed fbbg gdaaa fbbg gde fbb fbg fbg fbfg gbbfg gbbf gbbf gbb gbf bbf cbbf cbbc cbbc cbbc cbb cbc bbc fbb fb ``` <!-- end of image --> Eureka! There's definitely an intersection in area A! I can confirm there's two intersections in there.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0303feff b,#fe0707ff c,#ffa3a3ff d,#9996fcff e,#3535feff f,#fb4c50ff g,#e0d6f4ff ``` ```image d ee ag ga ee ag ga ee ag a de ad a da ad a da ad a da ad a ga ee ag ga ee ag ga ee ag ga ee ag g a cbbbbc da gfbbbc bg adbbbc bg cbbbag b gfbbfc da gb fbbbc ad gb cbbbf a cb cfbbfc da cb fbbbc ad cb bbbf a cb g da fb ee fb a fb ga fb ee bb ag bf ga bf ee bf ag bf gaad bc geaad bc geaad bc geaad bc geaad bg geaad bg geaad b geaadgb geaaf geaad cbeaad cb geaad cb geaad fb geaad fb geaa fb g fb bb bf bf bf bf bc bc bc bc b ``` <!-- end of image -->

I'm analyzing this image to identify any points where lines intersect. These zones indicate regions where lines appear to be in close proximity. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0505ff b,#090afcff c,#f1807cff d,#f0c7d4ff e,#add4adff f,#f2403cff g,#6a71efff ``` ```image d ca acf cf a a ca ca ad a da ca ad a a ca fc a a da ff a a da ca a a da da d a ad gb da a gb ad ac gb da a bb ad ff bb da a bg ad ca bg da a bg ad da bd da ad db ad da db da ac gb ad eeaeeeeeeeeeeeeegb a eeffeeeeeeeeeeebb ad eeeaeeeeeeeeeebb a eeeffeeeeeeeebbe ad eeeeaeeeeeeebgee a eeeecaeeeeebgeee ad eeeeeaeeeebgeeee da eeeeeeaeebeeeeee eeeeeeeeeeeaceee eeeeeeacbeeeeeee eeeeeeeeeeeaeeee eeeeeegbeeeeeeee bb eeeeeeeeeeaceeee eeeeegbffeeeeeee dbb eeeeeeeeeeaeeeee eeeegbeeaeeeeeee dbbdeeeeeeeeeaceeeee eeebbeeeffeeeeee dbbeeeeeeeeaeeeeee eebbeeeeeaeeeeee ebbeeeeeaceeeeee ebbeeeeeecaeeeee eeebbeeeaeeeeeee bgeeeeeeeeaeeeee eeeeebbfceeeeeee bgeeeeeeeeeeaeeee eeeeeeebbgeeeeee bgeeeeeeeeeeeaceee eeeeeefcebbgeeee bd eeeeeeeeeeeeaeee eeeeeeaeeeebbgee db fc eeeeeffeeeeeebbg gb a eeeeeaeeeeeeeeebbg gb ff eeeeffeeeeeeeeee bbg gb a eeeeaeeeeeeeeeee bbg bb ca eeeffeeeeeeeeeee bbg bb a eeeaeeeeeeeeeeee bbg bb da eeffeeeeeeeeeeee gbg bg ad a gbbg a ff d ac a a cf ff a a cf ca a a cf da a ad cf da a ac cf a a fc cf a a cf ca a a da ca ad a da ac a fc a cf a ``` <!-- end of image --> I'm focusing my attention on this specific region, area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0809ff b,#0605fdff c,#ffa1a1ff d,#cfcefeff e,#9292ffff f,#fa4f54ff g,#514dfaff ``` ```image caa aac caa aac caa aac caa aac caa aac gd caa bbgd aac gbbbgd caa dgbbbgd aac dgbbbgd caa dgbbbgd aac dgbbbgd caa dgbbbgfac dgbbbbd dgbbbgd caagbbbge fac ebbbge caa ebbbbe faf ebbbbe caa ebbbbe faf ebbbb caa ebb faf e caa faf caa faf caa faf caa faf caa ``` <!-- end of image --> The evidence is clear: this is an intersection in area A. Time to investigate another area. Time to investigate area B up close. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0304ff b,#0505feff c,#fc7c7fff d,#a2a1feff e,#ffc7c7ff f,#fb383bff g,#4843faff ``` ```image caa fac eaae fac eaae faf b eaae dbb caf dbbg aac dbbg caa dbbg fac dbbg eaa gbbd fac gbbd eaae gbbd faf gbbd eaae gbbd caf bbb aacbbg cfbbg dbbg dbbga dbbgfac gbbd eaae gbbd faf gbbd eaae gbbd caf gbbd aae bbb caf dbbg aac dbbg caa dbbg fac dbbg eaae dbbg faf bbd eaae bd caf d eaae caf aac ``` <!-- end of image --> The evidence is clear: this is an intersection in area B. My analysis indicates that there are two intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff0505ff b,#0808feff c,#fd8284ff d,#b7b7feff e,#ffc6c6ff f,#fd4143ff g,#5e5effff ``` ```image e ca acf ca a a ca ca ae a ea ca ae a a ca fc a a ea ff a a ea ca a a ea ea d a ae db ea a gb ae ac gb ea a bb ae ff bb ea a bg ae ca bg ea a bd ae ea bd ea ae db ae a db ea ac gb ae a gb a ff gb ae a bb a cf bb ae a bg a ea bg ae ae bd a ea bd ac acb a db bb ac gbfc dbb a gb a dbb ac gb cf dbbd a bb a dbbd ac bg ca dbbd a bg ae bbfc bg ea bbd bd ae fc bbd bd a a bbd db fc fc bbd db a a bbd gb ff fc bbg gb a a bbg bb ca fc bbg bb a a gbg bg ea ff gbg bg ae a gbbg a ff d ac a a ff ff a a cf ca a a cf ea a ae cf a a ac cf a a ff cf a a cf ca a a ea ca ae a ea ac a fc a cf a ``` <!-- end of image -->

Time to put on my detective hat and find those intersection points! I've noticed 2 areas of interest. These could be potential intersection zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#0808feff b,#fa0c0dff c,#585ef2ff d,#ee7c74ff e,#97c598ff f,#b4b4feff g,#b1d6b0ff ``` ```image f ca acc ac a a fa af a fa fa a af cc a a ac af a fa cc a a ca fa a a ac fa a af bg af a b fa ac b a a db cc cc bb a a bd af ca bd fa a b a fa b ca af db a a bbggggggggggacge af ebbgggggggggaggg a egbdgggggggaeggg cc eggbggggggcagggg a egggbgggggaggggg ca egggdbgggccggggg a eggggdbggagggggg fa egggggbbacgggggg af eggggggbaggggggg a eggggggabegggggg af egggggcagbgggggg a egggggaggdbggggg ac eggggacgggdbgggg a eggggagggggbbggg cc egggaeggggggbdgg a eggcaggggggggbeg fa eggaggggggggggbe a egccggggggggggeb geeaeeeeeeeeeeeeg a db eggacggggggggggge af bb egggaggggggggggge fa bd egggacgggggggggge a bg eggggagggggggggge ca b eggggccggggggggge a b egggggaggggggggge dbbb ac db egggggcaggggggdbbbbd a db eggggggaggdbbbbde af bd eggggdbbabdegggge fa bd edbbbbdgaegggggge a b dbbbbdgggggggagggggge cc b dbbbbd eggggggggacggggge a db dbbbbd egggggggggaggggge af db dbbbbd egggggggggccgggge fa bbbbbd eggggggggggagggge a g eggggggggggcaggge ca egggggggggggaggge a egggggggggggeagge af a af a cc a ca a fa af fa af a ac a cc a ``` <!-- end of image --> Let's zoom in on area A to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#0505feff b,#fd0506ff c,#9494feff d,#ff9292ff e,#453ef7ff f,#efd4e3ff g,#ff3e3eff ``` ```image bd eae bbf caaf gbbf aac gbg caa fbbg faac fbbd eae dbbd faaf dbbf eae gbbf caa gbg aac fbbg cae fbbd faac dbbd eae dbbf caaf gbbf aac gbg caa fbbgfaac fbbeae dbaaf eaed caabbf aacgbbf cae gbg faac fbbg eae fbbd caaf dbbd aac dbbf caa gbbf faac gbg eae fbbg faaf fbbd eae dbbd caa dbbf aac gbbf cae gbg faac fbbg eae fbb ``` <!-- end of image --> As I suspected, there's an intersection within area A. Next up, a closer look at another region. I'm determined to find out if an intersection exists in area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#0303feff b,#fc0406ff c,#7e7effff d,#ffa6a6ff e,#3831f7ff f,#bfbfffff g,#ff5151ff ``` ```image faaf cae aaf cae aac caa eac faa eac faaf eae faaf cae aac caa dgg eac ddgbbbbb faa dggbbbbbbggd eaebbbbbbbgdd dggbbaabbggd ddgbbbbbbbeae dggbbbbbbggd faaf bbbbbbgdd cae bggd aaf cae eac faa eac faaf eae faaf cae aaf cae aac caa eac ``` <!-- end of image --> Wow! I can see an intersection so clearly in area B! The final answer is: two intersections found.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0505feff b,#fd0608ff c,#8484ffff d,#ffb1b1ff e,#3e3effff f,#cacaffff g,#ff5757ff ``` ```image f ca ace ac a fa ca af af ca fa a af ee a a ec af a fa ee a a ce ca a a ac fa fa af bd af a b ca ac db a a db ee ee gb a a bg ac ca bd fa a b a fa b ce af db a fa gb ac ac bg fa a bd af ee b ca a b a ce db ee a gb a fa bgac af ba fa abd ac ce b a a db ec ec gb a a bg ce af bg a ca bd ca a b af ee db fa a gb af ac gb a fa bg ec a bd a ce b ee a db a gbbb ec db ca dgbbbgd a gb a gbbbbd af bg dgbabg ca bd gbbbgd af a b dgbbbg a ee b gbbbgd ac a db dbbbbg a ac gb dgbbbgd ee fa bbbbbg a af d ca ca a e fa af fa ac a ee a ce a fa af fa ac a ec a ce a ``` <!-- end of image -->

Based on a first glance, I suspect there could be intersection regions here. These spots mark what I'd call 'danger zones' - areas where intersections are more likely. <!-- image --> ```palette Key,Color ,#fefefeff a,#f8514eff b,#0909feff c,#afafffff d,#fd0909ff e,#5f5ffeff f,#ffb0b0ff g,#add5aeff ``` ```image gggggggggggggggg gggggggggggggggg gggggggggggggggg gggggggggggagggg ggggggggggadgggg gggggggggadggggg ggggggggadgggggg gggggggadggggggg ggggggddgggggggg gggggddggggggggg ggggddgggggggggg gggddggggggggggg ggddgggggggggggg gdaggggggggggggg da dagggggggggggggg da daggggggggggggggg dd dagggggggggggbgggg ad da ggggggggggebgggg ad df ggggggggggbggggg fd df gggggggggbgggggg fdf df eb df df b da df bc da df eb dd df b ad d bc ad fd eb fd fd b df fd bc df fd cb da fd b da fd bc dd fd cb ad ad b ad ad bc fd ad cb df ad b df ad be da ad cb da dd b dd dd be ad dd cb fd da b fd da be df da cb dda b f be cb b ee b b ee b bc bb eb eb b cbc bc bb eb eb b cbc bc be eb bb b cbc bc be eb bb b eb bc be cb bb b eb bc cbc cb bb b eb be cbc cb be b bb be cbc cb be b bb be eb cb be b bbbe eb ``` <!-- end of image --> I'm focusing my attention on this specific region, area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff2929ff b,#0c0cffff c,#8787ffff d,#ff0303ff e,#fcdcdeff f,#ffafafff g,#ff5757ff ``` ```image fe gda gddf gddf gddf gddf gddf gddf addf addf eadde eadde eadae eadae eadae eadae eadae eddae eddae fdda fdda fddg fddg fddg ddg dg c g cbb bbc cbb cbbe bbc ``` <!-- end of image --> Hmm, it seems there's no intersection in area A after all. The image is completely devoid of intersections. Zero.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff3535ff b,#0909ffff c,#b1b1ffff d,#ff0505ff e,#6161ffff f,#ffb6b6ff g,#ff6e6eff ``` ```image g gd gd ad ad ad ad aa da da da dg da da dg dd dg b ad dg eb gd dg b fd df bc fdf df eb df df b dg df bc da df eb ad df b ad d bc gd fd eb fd fd b fdf fd bc df fd eb dg fd b da fd bc ad gd cb ad gd b gd gd bc fd gd cb df ad b df ad be dg ad cb da ad b ad aa be ad da cb gd da b fd da be df da cb ddg b f be cb b ee b b ee b bc bb eb eb b cbc bc bb eb eb b cbc bc be eb bb b cbc bc be eb bb b eb bc be cb bb b eb bc cbc cb bb b eb be cbc cb be b bb be cbc cb be b bb be eb cb be b bbbe eb ``` <!-- end of image -->

I'm on the case! Let's uncover any intersections hidden in this image. These areas seem to enclose narrow spaces where lines might be close. <!-- image --> ```palette Key,Color ,#fefefeff a,#f6514eff b,#0a0afeff c,#6769f4ff d,#fba8a7ff e,#acd3acff f,#b6b6ffff g,#fe0808ff ``` ```image c dagg b dagggd ag bf dggggd gd fb dgggad g b agggad g bc aggga dg b daggga ga bf dagggd gd cb dggggd g b ad dg bc ag b ga bf gd cb g b dg bc ag fb gd b g cb g b dg bf ga fb gd b g cb egeeeeeeeeeebeee eageeeeeeeebceee eegaeeeeeecbeeee eeegeeeeeebeeeee eeeegeeeecbeeeee eeeeageeebeeeeee eeeeeggebceeeeee eeeeeegcbeeeeeee eeeeeeebeeeeeeee eeeeeebcgeeeeeee eeeeeebeageeeeee eeeeebeeegaeeeee eeeecbeeeegdeeee eeeebeeeeeegeeee eeebceeeeeedgeee eeebeeeeeeeeagee eebeeeeeeeeeegae cb gd b g bc dg b aa bf gd cb g b dg bc ag fb ga b gd cb g b dg bf ag fb gd b g cb g b d bf fb b cc b bf fb b cc b bf fb b bc fcbb fcbbbbc fbbbbbf cbbbbcf cbbbbcf fcbbbbcf fcbbbbcf bbbc ``` <!-- end of image --> My goal is to determine if there's an intersection inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff4d4dff b,#0605fdff c,#8e8afbff d,#ffa1a1ff e,#4641faff f,#e6d7efff g,#fd0608ff ``` ```image dggd ebc dggd cbb aggf fbbc aga ebe fgga fbbf dggd bbc dggf cbb agg fbbc gga ebe fggd cbbf dggd bbc aggf cbb aga fbbc fgga ebe dggcbbf dgbbc ebbf fbbga ebegga cbbfdggd bbc aggf cbe agg fbbf gga ebe fggd cbbf dggd fbbc aggf ebe aga fbbf fgga ebe dggd cbbf dggf fbbc agg ebe gga ``` <!-- end of image --> I am surprised, so clear, an intersection has appeared in area A. My investigation reveals that there is exactly one intersection in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff5151ff b,#0505ffff c,#8684fcff d,#ffaaaaff e,#4444feff f,#c5c5ffff g,#ff0707ff ``` ```image c dagg b dagggd ag bf dggggd gd cb dgggad g b agggad g ee aggga dg b daggga ga bf dagggd gd cb dggggd g b ad dg bc ag fb ga bf gd cb g b dg bc ag fb gd b g ce g b dg bc ga fb gd b g ee dg b ag bc ga fb gd b g ee dg b aa bf gcb b eeg b ag bf ga cb gd b g ee dg b ag bf ga cb g b g bc dg fb aa bf gd cb g b dg bc ag fb ga bf gd ce g b dg bc ag fb gd b g ee g b d bc fb b ee b bf fb b ee b bf cb b ee febb febbbec cebbbec cebbbef fcbbbbef fcbbbbef febbbbcf bbbc ``` <!-- end of image -->

I have an image in front of me. I need to determine if there are any intersection segments. My next step is to analyze the details within each area. <!-- image --> ```palette Key,Color ,#fefefeff a,#fba4a3ff b,#484afbff c,#fe0505ff d,#acadfbff e,#0808feff f,#fa4c49ff g,#aed5aeff ``` ```image cc caac ac ca fc c cf ff ca c ac ac fc ca cc c cf fc aca c fc c cc ff cf c ca ac ac ca fc c cf ff ca c ac ac fc ca cc c cf ac aca ca fc c cc ff cf c ca ac ac ca f c fc c c ff c ac dd ca dbeeeeb c dbeeed eb ff dbeeed eb c dbeeed eb ac dbeeed ee ca dbeeed ee c dbeeed be ac deeebd be ca eeebd be c d be ff be c de ac de ca de c de fc de c e c ed ff ed c ed ac ed ca ed c eb ggffgggggggggg eb gggcgggggggggg eb ggggcggggggggg eb ggggcfgggggggg eb gggggcgggggggg ee gggggfcggggggg ee ggggggcagggggg be gggggggcgggggg be gggggggffggggg beggggggggcggggg begggggggacgggg begggggggcgggg gbeggggggggggg ggdegggggggggg gggdeggggggggg gggggegggggggg ggggggeggggggg e ed e ``` <!-- end of image --> I'm analyzing this close-up of area A with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff7e7eff b,#5353ffff c,#ff0505ff d,#a0a0ffff e,#0202ffff f,#ff3e3eff g,#ffc1c1ff ``` ```image cca gccg fcf cca acc fcf gccg acf cca gccg fcf gccg acc fca gccg acf cca acc fcf gccg d acc ed cca eed gccg beed fcf deed ca deeb deeb deeb deeb deeb deeb deeb deeb deeb ``` <!-- end of image --> Area A doesn't meet the criteria for an intersection. I've examined the entire image, and there are zero intersections present.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff7c7cff b,#3c3cffff c,#ff0505ff d,#ababffff e,#0404ffff f,#ff3f3fff g,#ffc1c1ff ``` ```image g cc gcgac ac cg fc c cf ff ca c gcg gc fc ca cc c ca ac gcg cg ac c cc fa cf c gcg gc ac cg fc c cf ff ca c gcg gc fc ca cc c ca ac gcg cg ac c cc ff cf c gcg gc ac ca f c ac cg gc fa c gc dd cg dbeeeeb c dbeeed eb ff dbeeed eb c dbeeed eb gc dbeeed eb ca dbeebd be c dbeebd be ac dbeebd be cg beebd be c d be ff de c de gc de ca de c de af de cg e gc ed fa ed c ed ac ed cg ed c ed ff eb c eb gc eb ca eb c eb ac be cg be c be ff be c be gc de c de de de de de e ed e ``` <!-- end of image -->

Alright, let's get to work and investigate this image for intersections. It's crucial to examine these regions more closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#f04c45ff b,#0606feff c,#fd0606ff d,#7a85e7ff e,#b1d7b1ff f,#95c898ff g,#ea9e94ff ``` ```image d dbbb dbbbd dbbbe dbbbd dbbbe dbbbd dbbbe dbbbd dbbb dbbbd dbbb dbbbd dbb db db db db db db efffffffffffffffffffffffffdbfffffccff feeeeeeeeeeeeeeeeeeeeeeeedbeeeeeacgce feeeeeeeeeeeeeeeeeeeeeeedbeeeeegceeaa feeeeeeeeeeeeeeeeeeeeeedbeeeeeeceeeecg feeeeeeeeeeeeeeeeeeeeedbeeeeeeceeeeefc feeeeeeeeeeeeeeeeeeeedbeeeeeecgeeeeeegc feeeeeeeeeeeeeeeeeeedbeeeeeecaeeeeeee ca feeeeeeeeeeeeeeeeeedbeeeeeeaceeeeeeee c feeeeeeeeeeeeeeeeedbeeeeeeaceeeeeeeee c feeeeeeeeeeeeeeeedbeeeeeegceeeeeeeeee ac feeeeeeeeeeeeeeedbeeeeeeeceeeeeeeeeee cg feeeeeeeeeeeeeedbeeeeeeecgeeeeeeeeeee c feeeeeeeeeeeeedbeeeeeeecaeeeeeeeeeeee gc feeeeeeeeeeeedbeeeeeeecaeeeeeeeeeeeee aa feeeeeeeeeeedbeeeeeeeaceeeeeeeeeeeeee cg feeeeeeeeeedbeeeeeeegceeeeeeeeeeeeeee c feeeeeeeeedbeeeeeeeeceeeeeeeeeeeeeeee gc feeeeeeeedbeeeeeeeeceeeeeeeeeeeeeeeee ca feeeeeeedbeeeeeeeecgeeeeeeeeeeeeeeeee c feeeeeedbeeeeeeeecaeeeeeeeeeeeeeeeeee c feeeeedbeeeeeeeeaceeeeeeeeeeeeeeeeeee gc feeeefbeeeeeeeeaceeeeeeeeeeeeeeeeeeee cg feeefbeeeeeeeegceeeeeeeeeeeeeeeeeeeee c feefbeeeeeeeeeceeeeeeeeeeeeeeeeeeeeee c fefbeeeeeeeeecgeeeeeeeeeeeeeeeeeeeeee ac ffbeeeeeeeeecaeeeeeeeeeeeeeeeeeeeeeee cg fbeeeeeeeeecaeeeeeeeeeeeeeeeeeeeeeeee c beeeeeeeeeaceeeeeeeeeeeeeeeeeeeeeeeee gc bfeeeeeeeegceeeeeeeeeeeeeeeeeeeeeeeeee aa b feeeeeeeeceeeeeeeeeeeeeeeeeeeeeeeeeee cg feeeeeeeceeeeeeeeeeeeeeeeeeeeeeeeeeee c feeeeeecgeeeeeeeeeeeeeeeeeeeeeeeeeeee gc feeeeecaeeeeeeeeeeeeeeeeeeeeeeeeeeeee ca feeeeaceeeeeeeeeeeeeeeeeeeeeeeeeeeeee c feeeaceeeeeeeeeeeeeeeeeeeeeeeeeeeeeee c feegceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee ac feeceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee cg fecgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee c fcaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee gc caeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee aa acffffffffffffffffffffffffffffffffffff cg gc c a gc ca c c ac cg c gc aa cg c gc ca c c gc cg c ``` <!-- end of image --> Let's put area A under the microscope. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff3b3bff b,#0303ffff c,#ff0505ff d,#b1b2ffff e,#ffc6c6ff f,#5656ffff g,#ff7e7eff ``` ```image dbbf ecce dbbf acca dbbf accccg dbbf gcceecce dbbf gcce gcce dbbf eccg aca dbbf eccg ecc dbbf cca ec dbbf aca g dbbf acce dbbf gcce dbbf gccg dbbf eccg dbbf ecca dbbf aca dbbf acc dbbf gcce dbbf gcce dbbf eccg dbbf eccg dbbf cca dbbf aca dbbf acce dbbf gcce dbbf gcce dbbf eccg dbbf ecca dbbf aca dbbf acc dbbf gcce dbbf gcce dbbf eccg dbbf eccg dbbf ecca dbbf aca dbbf acce dbbf gcce dbbf gcce dbbf eccg dbbf ecca dbbf aca dbbf aca dbbf acce dbbf gcce dbbf eccg dbbf eccg dbbf ecca dbbf aca dbbf acce dbbf gcce dbbf gcce dbbf eccg dbbf eccg dbbf cca bbf aca bf acce f gcce eccg eccg ecca aca acc gcce gcce eccg eccg cca aca acce gcce gccg eccg ecca aca acc gcce gcce eccg eccg cca ``` <!-- end of image --> My analysis shows that the lines in area A do not cross. The image is completely devoid of intersections. Zero.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff4a4aff b,#0505ffff c,#ff0707ff d,#b8b8ffff e,#ffd1d1ff f,#7575ffff g,#ff9595ff ``` ```image d fbbb dbbbf fbbbd dbbbf fbbbd dbbbf fbbbd dbbbf fbbbd dbbbf fbbbd fbbbf fbfd fb fb fb fb fb fb fb cc fb acec fb gc aa fb ec ce db ce c db cg gc db ca ca db ac ce db gc ec db ec ac db c cg db ce c db cg ec db ca aa db ac cg db gc c db ec gc db ce ca db cg ce db ca c db ac gc db gc cg db ec c db c ec db ce ac db cg cg db ca c db ac gc db gc aa b ec ce ce c cg gc ca ca ac ce gc ec ec ac c cg ce c cg ec ca aa ac ce gc c a gc ca ce ec ac cg c ec aa cg c gc ca ce c gc cg c ``` <!-- end of image -->

Based on a first glance, I suspect there could be intersection regions here. Let's take a closer look at what's happening inside these zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#d68a78ff b,#0809faff c,#fc0605ff d,#4e5ad9ff e,#b1d7b1ff f,#96c59aff g,#e1433dff ``` ```image a ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeca eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefce eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecfe eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeacee eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeceee eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegceee eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeceeee eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeggeeee eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeceeeee eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecaeeeee eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeceeeeee eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecaeeeeee eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaceeeeeed eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeceeeeeebb eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaceeeeebbe eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeceeeeebdee eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeggeeeebfeee eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeceeefbfeeee eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecaeedbeeeeee eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeceedbeeeeeee eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecaebbeeeeeeee eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeacebdeeeeeeeee eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecfbdeeeeeeeeee eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeagbfeeeeeeeeeee egeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegbeeeeeeeeeeeee egceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedbeeeeeeeeeeeeee eecaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeeeeeeeeeeeeee eeeceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbgeeeeeeeeeeeeeee eeegceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebdceeeeeeeeeeeeeeee ebeecaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebdcaeeeeeeeeeeeeeeee efbbeceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefbffceeeeeeeeeeeeeeeee eeedbdceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedbeecfeeeeeeeeeeeeeeeee eeeeebbaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedbeeaceeeeeeeeeeeeeeeeee eeeeeefbbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeeceeeeeeeeeeeeeeeeeee eeeeeeeagbdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeeggeeeeeeeeeeeeeeeeeee eeeeeeeecabbfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebdeeeeceeeeeeeeeeeeeeeeeeee eeeeeeeeeceebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebdeeeeggeeeeeeeeeeeeeeeeeeee eeeeeeeeeaceefbbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefbfeeeeeceeeeeeeeeeeeeeeeeeeee eeeeeeeeeecgeeedbdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedbeeeeeecaeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeceeeeebbfeeeeeeeeeeeeeeeeeeeeeeeeeeeeedbeeeeeefceeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeaceeeeefbbeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeeeeeecfeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeecgeeeeeedbdeeeeeeeeeeeeeeeeeeeeeeeebdeeeeeeeaceeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeeeceeeeeeeebbfeeeeeeeeeeeeeeeeeeeeebdeeeeeeeeceeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeeeaceeeeeeeeebbeeeeeeeeeeeeeeeeeefbfeeeeeeeegceeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeeeecgeeeeeeeeedbdeeeeeeeeeeeeeeefbeeeeeeeeeeceeeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeeceeeeeeeeeeedbdeeeeeeeeeeeedbeeeeeeeeeeggeeeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeefceeeeeeeeeeeebbeeeeeeeeeebbeeeeeeeeeeeceeeeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeeeggeeeeeeeeeeeefbbeeeeeeebbeeeeeeeeeeecaeeeeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeeeeceeeeeeeeeeeeeedbdeeeebdeeeeeeeeeeeeceeeeeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeeeefceeeeeeeeeeeeeeebbfebdeeeeeeeeeeeecaeeeeeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeeeeeggeeeeeeeeeeeeeeeebbfeeeeeeeeeeeeaceeeeeeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeeeeeecfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeceeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeeeeeeeceeeeeeeeeeeeeeeeeeeeeeeeeeeeeaceeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeeeeeeeggeeeeeeeeeeeeeeeeeeeeeeeeeeeeceeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeeeeeeeecaeeeeeeeeeeeeeeeeeeeeeeeeeeggeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeeeeeeeeeceeeeeeeeeeeeeeeeeeeeeeeeeeceeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeeeeeeeeegceeeeeeeeeeeeeeeeeeeeeeeecaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeeeeeeeeeecaeeeeeeeeeeeeeeeeeeeeeeeceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeeeeeeeeeeeceeeeeeeeeeeeeeeeeeeeeecaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeeeeeeeeeeegceeeeeeeeeeeeeeeeeeeeaceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeeeeeeeeeeeecaeeeeeeeeeeeeeeeeeeeceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeeeeeeeeeeeeeceeeeeeeeeeeeeeeeeeaceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeeeeeeeeeeeeegceeeeeeeeeeeeeeeeeceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeeeeeeeeeeeeeecaeeeeeeeeeeeeeeeggeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeeeeeeeeeeeeeeeceeeeeeeeeeeeeeeceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeeeeeeeeeeeeeeeaceeeeeeeeeeeeecgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee fffffffffffffffffffffffffffffcaffffffffffffcfffffffffffffffffffffffffffffffffffff c ca ac c ca c c ac ac c ca ag c c ec ga ca c cca c ``` <!-- end of image --> I wonder what we'll find inside area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#fc6c6eff b,#0908fdff c,#fe0303ff d,#5f5fffff e,#ffb6b6ff f,#babaffff g,#f82c33ff ``` ```image e c c ece ac cc ec ga cc acg cg ece ec gc ce ag ce cc ca ga d ec fb cg bb ce dbd ece dbb gc bbf gca bb cc fbd ca dbd ce dbf ac bbf cg fbb ecefbb ec dbd gcdbf gbbf a abb ece gbd gca bb ecc bba ga bbba ece fbbc gc bbacg d ece dbfcce bbbf cg fbb ece fbbdcc fbb ga fdbbg dbd gc bbba dbd cc dbb bb ca gbbb fbbf ce egbbd bbb ac ccadbbf dbd ca ecc fbbf bb ece ca fbbf bbf ec ece fbbdf fbb gc cc dbbd bb ce ece fbbf dbd ag ca bbd bbb ac cc fdbb fbbf cc ac bbdf fbb ca ece dbbf dbd ga cg fbbb dbd ac ece dbb bbf acg ac dbbf bbf cce cce dbbd fbd ece acc bbf dbb ga ece bbb dbf gc ac dbbd bbf cc cg fbbf fbb ce ac bbd bb ce gg fdbb dbd ac cc dbbdbb ca gc dbbbf ec ece ec cg cc ece ce ag ag cc gc ac ecc ca gca cg ca gca ag ac ac ga cc cg ece gc ga ac gc ca cc ac ag ga ce ece ac gc ca ece ec cg ec ``` <!-- end of image --> Incredible, there's actually an intersection in area A! After a long analysis, I found two intersections.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fd7678ff b,#0808feff c,#ff0404ff d,#5a55faff e,#ffb9b9ff f,#b4b4ffff g,#f73239ff ``` ```image a c ce ec ce ec c ag c ga c ca c ce ec d c bb ag bd c bd gg bf c fb ca db c db ce bb ec bd c bd agbf g gb ac db ce db c bba ac bdc b ce bfce fbb c fbfec dbdc fb c bba db ec bb bb c egbd bd ag cadbf bd c c bb bf ga ec fbd fbf c ca dbf fb ce c bb db ec ec fbb bb ce ga dbd bd ec c bbf bd c ec bb bf ag ga fbd fb c c dbf db ga ec bb db c gg fbb bb ca c dbd bd c ec bbf bf ce gg bbf ec ce c c ag gg c ce gg c c ag ga ce c c ce ac ec ce c c ac ac c ce ag c c ac ga ca c c ce ec ec ca c c ec ec c ca ag c c ec ga ga c cce ec ``` <!-- end of image -->

I'm ready to tackle this image and find those intersections! I've noticed 1 areas of interest. These could be potential intersection zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#6064ebff b,#fd0b0aff c,#ed746cff d,#d1c3f1ff e,#090afdff f,#96c599ff g,#b1d7b1ff ``` ```image a de ed ae e ed ae e ed ae e ed ae e ed ae e ed ae e ed ae e ea de e ea ed de e e de ea de de ae e ae ea ee de ea e ea ea ed de ed e ed ea de de de e de aa ae de ae ed ee aa ea de feagggggggggggggggggggggggggggggged fgeaggggggggggggggggggggggggggggae fggefgggggggggggggggggggggggggggef fgggeggggggggggggggggggggggggggeff fgggfeggggggggggggggggggggggggaegf fggggfegggggggggggggggggggggggeggf fgggggaegggggggggggggggggggggefggf fggggggaegggggggggggggggggggaegggf fgggggggeeggggggggggggggggggeggggf fggggggggeeggggggggggggggggefggggf fgggggggggeaggggccbbbfggggaegggggf fgggggggfcbeabbbbcfggbbgggeggggggf fccbbbbbbccgeaggggggggfbbeaggggggf ccbbbbbbccgggggggggefgggggggggaebggggggf dcbbbbbbccd fgggggggggggggegggggggggegcbbggggf bbbcc fgggggggggggggfegggggggeagggcbcggf fggggggggggggggfegggggaeggggggcbcf fgggggggggggggggaeggggegggggggggbbc fggggggggggggggggaeggeaggggggggggfbbc fgggggggggggggggggeeaegggggggggggf bbd fggggggggggggggggggeeggggggggggggf bb fggggggggggggggggggggggggggggggggf dbb fggggggggggggggggggggggggggggggggf dbb fggggggggggggggggggggggggggggggggf cbb fggggggggggggggggggggggggggggggggf cbc gffffffffffffffffffffffffffffffffg cbc bbc bbc bbd bb dbb dbb cbb cb ``` <!-- end of image --> I'm analyzing this close-up of area A with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#3837feff b,#fe0505ff c,#feb8b8ff d,#c2c2ffff e,#0404feff f,#7a77fcff g,#f5535dff ``` ```image deea deef deef d feef e feed ae feed dee feed eef aeed aea aee deed aea eef deea fea deea deed deef eef deef fea feef deed feed eef feed fea aeed deed aeed aef aea fea aea deed deea ccc aef deea ccgggbbbbbgc fee deefccgggbbbbbbbbbbbbbbgc deed cccgggeegbbbbbbbgggcc gbbbg aef ccgggbbbbbbbbgeeggccc cgbbbg fee cccggbbbbbbbbbbbgggcc feed cgbbbgeed bbbbbbbbbbbgggcc feed cgbeea bbbbggccc aeed feebbc c aeed deefbbbbc aea aea cbbbgc aea fee gbbbgc deea deed gbbbgc deea aea gbbbg deef fee cgbbbg deef deed cgbbb feef aea cgb feed fee c feed deef aeed aea aeedfeed aeaeef aeea deed ``` <!-- end of image --> Yes! I knew it! There's an intersection right here in area A! After a thorough search, I conclude that there are two intersections.

<!-- image --> ```palette Key,Color ,#fefefeff a,#3c38fbff b,#ff0606ff c,#ffababff d,#ccccffff e,#0404feff f,#8685fdff g,#ff5454ff ``` ```image f de ed aa e ed aa e ed fa e ed fe e ed fe e ef fe e ef fe e ef fe e ef ed de e e de ef fe de fe e ae af aa de ea e ef aa ef de ed e ed aa de de de ed fe aa fe de ae ed aa aa ea de ef ed ef aa ed e ed ed de aa de e fe ed fe fa ae e aa ed ea cgbbbc fe ccgeabbbgcc bb e cgbbbbbbgc ed cbbed cgbbbbbbgc ed feb ccgbbbbbgcc e e cbg bbbgc de ef gbg de fe gbg fe e gbc fe ef bbc aefe bbc ae bb cbb cbb cbg gbg gbg gbc bbc bbc bb cbb cbb cbb gb ``` <!-- end of image -->

The hunt for intersections begins! Let's analyze this image closely. These areas seem to enclose narrow spaces where lines might be close. <!-- image --> ```palette Key,Color ,#fefefeff a,#5759fbff b,#fe0606ff c,#0606feff d,#f1746eff e,#b1d7b0ff f,#98c797ff g,#b5b5ffff ``` ```image g gaaccccccca gaacccccccaagg gaacccccccaagg gaacccccccaagg gcccaagg c cg ac c c ca efffacffffffffff feeeceeeeeeeeeee feecfeeeeeeeeeee feaceeeeeeeeeeee ffceeeeeeeeeeeee fceeeeeeeeeeeeee caeeeeeeeeeeeeee aceeeeeeeeeeeeeef cfeeeeeeeedbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb cgfeeeeeeeebeeeeee aa feeeeeeebdeeeeee gc feeeeeeebeeeeeee c feeeeeebfeeeeeee cg feeeeedbeeeeeeee ac feeeeebeeeeeeeee c feeeebdeeeeeeeee cg feeeebeeeeeeeeee ca feeebfeeeeeeeeee gc feedbeeeeeeeeeee c feebeeeeeeeeeeee cg febdeeeeeeeeeeee ac febeeeeeeeeeeeee gc fbfeeeeeeeeeeeee c dbeeeeeeeeeeeeee ca beeeeeeeeeeeeeee gc bdfffffffffffffff c b cg b aa db gc b c bd ca b ac b c db cg b ca bd gc b c b cg db ac b c bd c b ca b g db b bd b b db b bd b b db b bd b b db b bd b b db b bd b b ``` <!-- end of image --> Let's put area A under the microscope. <!-- image --> ```palette Key,Color ,#fefefeff a,#5a5affff b,#ff0303ff c,#0909ffff d,#ff8989ff e,#ffcfcfff f,#ff3c3cff g,#aeaeffff ``` ```image gccg gccg cca acc gccg cca acc gcc gccg cca acc gccg cca ca c g fbbbbbbbbbbb dbbbbbbbbbbbb ebbd fbf ebbe fbd dbb ebbd fbf ebbe fbd dbb ebbd fbf ebbe fbd dbb ebbd fbf ebbe fbd dbb ebbd fbf ebbe fbd dbb ebbd fbf ebbe fbd dbb bbd bf ``` <!-- end of image --> It's a shame, but area A doesn't contain an intersection. I've examined the entire image, and there are zero intersections present.

<!-- image --> ```palette Key,Color ,#fefefeff a,#6e6effff b,#ff0606ff c,#0404ffff d,#ff7b7bff e,#edd9ebff f,#3939ffff g,#a8a8ffff ``` ```image eg egafcccccccf egafcccccccfage egafcccccccfage egafcccccccfage gcccfage c cg af ec ce ca gc c cg ff ec c ca ac c dbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb ce b ff bd gc eb c be cg db ac b ec bd ce eb fa be gc db c b cg bd ff eb ec be ce db ca b gc bd c eb cg be ff db gc b c bd ca eb ac be ec db ce b ff bd gc eb c be cg db ac b ec bd ce eb ca be e db b bd eb be db b bd eb be db b bd eb be db b bd eb be db b bd eb be ``` <!-- end of image -->

I'm approaching this image with caution. Intersections might be tricky to spot. These zones indicate regions where lines appear to be in close proximity. <!-- image --> ```palette Key,Color ,#fefefeff a,#0809fcff b,#e26c5dff c,#4d56ecff d,#fb0907ff e,#b1d7b1ff f,#99c795ff g,#8b9bdeff ``` ```image bbdddddddfffffffffffffffffffffffffffffffffffffffffff bbdddddddbfeeeeebdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee bbddddddbb feeeeeeeadbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee bbddddddbb feeeeeeaagdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee ddddbb feeeeegaeabdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee feeeeeaeeccdfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee feeeecaeeeaedeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee feeeeaeeeecabdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee feeeaceeeeeaedfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee feeeaeeeeeegaedeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee feeageeeeeeeagdbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee fegaeeeeeeeeeaedeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee feaeeeeeeeeeeccfdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee fcaeeeeeeeeeeeaedbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee faeeeeeeeeeeeecaedeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee aceeeeeeeeeeeeeaebdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee aeeeeeeeeeeeeeegaedbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee ageeeeeeeeeeeeeeeagedeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee afeeeeeeeeeeeeeeeeaebdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee a feeeeeeeeeeeeeeeeacedbeeeeeeeeeeeeeeeeeeeeeeeeeeeeee ga feeeeeeeeeeeeeeeeeaeedeeeeeeeeeeeeeeeeeeeeeeeeeeeeee a feeeeeeeeeeeeeeeeecaebdeeeeeeeeeeeeeeeeeeeeeeeeeeeee cc feeeeeeeeeeeeeeeeeeaeedfeeeeeeeeeeeeeeeeeeeeeeeeeeee a feeeeeeeeeeeeeeeeeegaeedeeeeeeeeeeeeeeeeeeeeeeeeeeee ag feeeeeeeeeeeeeeeeeeeagebdeeeeeeeeeeeeeeeeeeeeeeeeeee a feeeeeeeeeeeeeeeeeeeeaeedfeeeeeeeeeeeeeeeeeeeeeeeeee a feeeeeeeeeeeeeeeeeeeeacefdeeeeeeeeeeeeeeeeeeeeeeeeee ga feeeeeeeeeeeeeeeeeeeeeaeedbeeeeeeeeeeeeeeeeeeeeeeeee a feeeeeeeeeeeeeeeeeeeeecaeedeeeeeeeeeeeeeeeeeeeeeeeee cc feeeeeeeeeeeeeeeeeeeeeeaeefdeeeeeeeeeeeeeeeeeeeeeeee a feeeeeeeeeeeeeeeeeeeeeegaeedbeeeeeeeeeeeeeeeeeeeeeee ac feeeeeeeeeeeeeeeeeeeeeeeageedeeeeeeeeeeeeeeeeeeeeeee a feeeeeeeeeeeeeeeeeeeeeeeeaeebdeeeeeeeeeeeeeeeeeeeeee ag feeeeeeeeeeeeeeeeeeeeeeeeaceedbeeeeeeeeeeeeeeeeeeeee ga feeeeeeeeeeeeeeeeeeeeeeeeeaeeedeeeeeeeeeeeeeeeeeeeee a feeeeeeeeeeeeeeeeeeeeeeeeecaeebdeeeeeeeeeeeeeeeeeeee ga feeeeeeeeeeeeeeeeeeeeeeeeeeaeeedbeeeeeeeeeeeeeeeeeee a feeeeeeeeeeeeeeeeeeeeeeeeeegaeeedeeeeeeeeeeeeeeeeeee cc feeeeeeeeeeeeeeeeeeeeeeeeeeeageebdeeeeeeeeeeeeeeeeee a feeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeedfeeeeeeeeeeeeeeeee ag feeeeeeeeeeeeeeeeeeeeeeeeeeeeaceeedeeeeeeeeeeeeeeeee a feeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeebdeeeeeeeeeeeeeeee a feeeeeeeeeeeeeeeeeeeeeeeeeeeeecaeeedeeeeeeeeeeeeeeee ga feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeefdeeeeeeeeeeeeeee a feeeeeeeeeeeeeeeeeeeeeeeeeeeeeegaeeedbeeeeeeeeeeeeee cc feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeageeedeeeeeeeeeeeeee a feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeefdeeeeeeeeeeeee ag feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaceeedbeeeeeeeeeeee a feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeedeeeeeeeeeeee ag feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecaeeebdeeeeeeeeeee ga feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeedbeeeeeeeeee a feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegaeeeedeeeeeeeeee ca feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeageeebdeeeeeeeee a feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeedfeeeeeeee cc feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaceeeedeeeeeeee a feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeebdeeeeeee ag feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecaeeeedfeeeeee a feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeedeeeeee a feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegaeeeedbeeeee ga feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeageeeedeeeee a feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeefdeeee cc feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaceeeedbeee a feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeedeee ag feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecaeeeebdee a feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeedbe a feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegaeeeeede feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeageeeebd effffffffffffffffffffffffffffffffffffffffffffafffffd ag a cc a ga a a ag a cc a ``` <!-- end of image --> This close-up of area A is like examining a piece of evidence. <!-- image --> ```palette Key,Color ,#fefefeff a,#0606feff b,#ff4242ff c,#4c4cffff d,#ff0505ff e,#fe9292ff f,#ead6ebff g,#9898feff ``` ```image ffebbddddf eebdddddddddddb ddddddbbeeff dde gbdb fagdde cacedd faaagbd cagaafde aag gaafdb gaa cacdde faag faaedd cac ca dde faaf fageddf aaf ag dd ag aafedf ga cac bb ag faaffde ca cac ddf cac gaafdde gaaf aa eddf cac gaf bdb gaaf cc fdd aag faf ed fag aag fdf cc gaa db faf aag dde ca gaafeddf aa cac bdb a ca edf g fag bb ga fde ag ddf aaf bdb faaf edd cac bdb faa fdd ga ed ag de ac db aaf dde cac eddf faag bdb gaa fdde gaa bd ca fde faf edf cc db fag dde aag bdb gaaf fdde cac edd faaf dd cac edf ga de ag ddf ga bdb ac fdde aaf eddf cac bdb gaa edf aag bb gaa fde ca dd gaf bdb fag bdb aa dde aag edd gaa bd cac fde cac db faa dde ca eddf ag bdb ga fdde aaf bd cac fde faag ed cac de aag ddf aa dde gaf eddf cc bdb fag fdd ac edf gaa fde aag ddf gaaf bdb cac fdde faa edd fag fdd ga ed ag de aaf edf cac db cac eddf faag bdb gaa fdde aa edd gaf bd faf edf ac db aag dde gaa edd aag bdb cac bdb faa dd ca edf fag bb ga fde aaf bdb cac fdd faaf ed ``` <!-- end of image --> Area A is clear of intersections, but the search continues. After a thorough analysis, I conclude that there are no intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0202ffff b,#ff4e4eff c,#7171ffff d,#ff0606ff e,#ffa4a4ff f,#2e2effff g,#babafeff ``` ```image ebddddddd ebddddddbee ed ebddddddbee ade ebddddddbee aagd ddddbee ga aed a fcde cf a d a cfbb fc a d a ga d ag agbb ga a d a fced cf a db a cf d fc a ed a ga de ag ag d ga a ed ag fc de ca a d a cf bd cf a de a ga d fc ag bb a a d ag fc d ga a bb a cf d cf a ed a ga db fc ag d a a ed ag fc de ga a d a cf ed cf a de a ga d fc ag bd a a de ag fc d ga a bb ag cf d ga a d a ga bb cf ag d a a ed fc fc de a a d ag cf ed ga a de a ga d cf ag ed a a de fc fc d a a bb ag cf d ga a d a ga bb ca ag d a a ed ff fc db a a d ac cf ed a a de ag ga d ag ed a d fc a cf a ga ag a fc a cf a ``` <!-- end of image -->

Let's examine this image for potential line intersections. Could these regions be concealing intersection points? Let's find out. <!-- image --> ```palette Key,Color ,#fefefeff a,#5359f4ff b,#fc0d0dff c,#0809fbff d,#babaffff e,#f5726dff f,#add4adff g,#ffd5d5ff ``` ```image acd dc cd c cd cd cd ac cd c cd cd cd b ca c be dc c gb c c bg cd dc eb ac dc b dc dc be c dc gb ca dc bg ac dc eb c dc b cd dc be aa dc gb dc dc bg c dc eb cd ac b ac acffffffffffbefff c acfffffffffbffff c facfffffffbfffff ca ffacfffffebfffff dc fffacffffbffffff c ffffacffbeffffff cd fffffacfbfffffff ac ffffffacffffffff dc ffffffeccfffffff c ffffffbfccffffff ca fffffbeffccfffff ac fffffbffffccffff c ffffbffffffccfff cd fffebfffffffccff ca fffbfffffffffccf dc ffbeffffffffffcc fffffffffffcffff ffbffffffffffffca ffffffffffcaffff bg ca fffffffffacfffff eb ca fffffffffcffffff b ca ffffffffcfffffff be ca fffffffcafffffff gb ca fffbbfacffffffff bg c ffffbbcfffffffff eb fffffcbfffffffff b ffffacbbffffffff be ffffcffbbfffffff gb fffcffffbbffffff bg fffffffffbbfffff eb ffffffffffebffff b fffffffffffebfff be ffffffffffffebff gb fffffffffffffebf bg eb eb gb b gb be gbg gb gbg bg gbg eb bg b bg be bg gb be bg be eb be b be be be gb bb bg bb eb bb b bb be bb gb eb bg eb eb eb b ebbe eb ``` <!-- end of image --> Here's a close-up of the area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#493cf1ff b,#fa373cff c,#0606feff d,#9795fcff e,#ff8787ff f,#ff0404ff g,#ecd4e6ff ``` ```image gccd aca dccg gccd cca acc dccg gccd aca dccg dccd g cca gbb aca gffb dccg gffb gccd gffbaca gfacc dccbg gccafbg acagbffg dccg gbffg gccd gbffg cca bffg dcc bffg gg bffg bffe bffe bffe effe effe effe effe effe ``` <!-- end of image --> The lines cross each other within area A, forming an intersection. Moving on to the next area. Eureka! Let's inspect this close up of area B <!-- image --> ```palette Key,Color ,#fefefeff a,#5353ffff b,#fd0708ff c,#0c0bfdff d,#aaaaffff e,#fe9494ff f,#fb464aff g,#eadef2ff ``` ```image cd fbf ccd ebbg accd bbe accd ebb accd gbbe accd fbf accd ebbg accd bbe accd ebb accd gbbe accd fbf accd ebbg accd bbe accd ebb accdgbbe accfbf accbg gcccg ebcccg gbbeaccg fbf gaccg ebbg gcccg bbe gcccg ebb gcccg gbbe gcccg fbf gcccg ebbg gcccg bbe gcccg ebb gcccg gbbe gccag fbf gcca ebbg gcc bbe gc ``` <!-- end of image --> I've cracked the case! This area contains the intersection. After a long analysis, I found two intersections.

<!-- image --> ```palette Key,Color ,#fefefeff a,#5757ffff b,#fd2426ff c,#0908feff d,#b9b9ffff e,#ff7a7aff f,#ff0101ff g,#ffd7d7ff ``` ```image acd dc cd c cd cd cd ac cd c cd cd cd f ca c be dc c gf c c fg cd dc eb ac dc f dc dc be c dc gf ca dc fg ac dc eb c dc f cd dc be aa dc gf dc dc fg c dc eb cd ac f ac ac be c ac gf c ac fg ca ac eb dc ac f c ac be cd acgf ac acg dc ecc c f ac ca be cc ac gf cc c fg cc cd eb cc ca f ca dc be ca c gf ca cd fg ca ac eb ca dc f ca c be ca g ca gf ca fb dc fg c fbc eb cb f aabb be dc bb gf c bf fg bf eb ef f ef be ef gf ef fg ef eb gf f gf be gfg gf gfg fg gfg eb fg f fg be fe gf fe fg fe eb fe f fe be fb gf fb fg fb eb bb f bb be bf gf bf fg ef eb ef f efbe ef ``` <!-- end of image -->

I have an image in front of me. I need to determine if there are any intersection segments. I wonder what's going on inside those areas? Perhaps intersections are hiding there. <!-- image --> ```palette Key,Color ,#fefefeff a,#0607feff b,#fd0c0bff c,#adadffff d,#f57772ff e,#5255f6ff f,#b1d7b1ff g,#95c49bff ``` ```image ea aca ac ac ca a a ee ee a a ca ac ac ca a a ea ae a ca a a ae ee a a ca ac ac ca a b a ee bb ee a bd a ca db ac ac bb ca a bb a eaggggggggggggggf bd ae agfffffffffffffg db ca gafffffffffffffg bb a faeffffffffffffg bb ee ffaffffffffffffg bd a ffeafffffffffffdb ac fffagfffffffffbb ca ffffaffffffffbbg a ffffeeffffffbdfg ee fffffaffffdbgffg a fffffgaffbbffffg ac ffffffaebbfffffg ca fffffffadffffffg a fffffdbeaffffffg ae ffffdbffagfffffg ca fffbbfffgafffffg a ffbdfffffaeffffg ea gbdfffffffaffffg a dbfffffffffeafffg ac bbfffffffffffagffg ca bd ffffffffffffaffg a bd ffffffffffffeefg ee db fffffffffffffafg a bb fffffffffffffgag ac bd ffffffffffffffae ca bd ggggggggggggggga a db ea ae bb ac ca bb a a bd ae ea db a a bb ca ac bd ac ca db a a bb ee ee bd a c db ca bb ac bd a db ea bb ac bd a db ee bb a bd ca db ac bb a bd ee db a bb bd db bb bd db bb bd ``` <!-- end of image --> Let's zoom in on area A to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#0303feff b,#fd0607ff c,#7978fdff d,#ff4a4aff e,#3530faff f,#ffaaaaff g,#c1c1feff ``` ```image ag ae aac gaag eae gaag caa eac gaag cae aac caa eac d gaag db cae fbbb aac fbbbf gaag fbbd eae dbbd gaag bbbf caa fbbbf eac fbbd gaag dbbd cae dbbf aacfbbbf caabbd eaed dbaag fbbbcae fbbd eac dbbd gaag dbbf eae fbbbf gaag fbbd caa dbbd eac dbbf gaag fbbbf cae fbbd aac bbd caa bf eae f gaag cae eac gaag eae gaag caa eac gaag cae aa ``` <!-- end of image --> I observe an intersection inside area A. I've found a single intersection point in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0505ffff b,#ff0909ff c,#8f8fffff d,#ff6d6dff e,#4948feff f,#ffd4d4ff g,#ccccffff ``` ```image g ea aca ac ag ca a a ee ee a a ga ag ac ca a a ee ac ag ga ga ag ac ee a a ca ac ag ca a b a ee bb ee a fbd a ga dbf ag ac bb ca a bb a ca fbd ac ag dbf ga ga db ag ae bb ee a bd a ca fbf ac ag db ga a bb a ee bd ee a fbf a ga db ag acbb ca ad a fbea ac db ag ga bb ga ag bd ee ee fbf a a db ca ac bb ag ga bd a a fbf ee ee db a a bb ga ag bd ac ca fbf a a db ca ac bb ag ga bd ga ag fbd ee ee dbf a a bb ca ac fbd ag ga dbf a a bb ee ee fbd a c dbf ga bb ac fbd a dbf ca bb ag fbd ga dbf ee bb a fbd ca dbf ac bb a fbd ee dbf a bb fbd dbf bb fbd dbf bb bd ``` <!-- end of image -->

I'm approaching this image with caution. Intersections might be tricky to spot. There are 1 areas where the lines seem to converge. We should take a closer look at area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0808fdff b,#fe0606ff c,#5b5ef1ff d,#e3574bff e,#f0a7a0ff f,#b7b7ffff g,#afd6b0ff ``` ```image ggggggggggggggggggggggggggggggg ggggggggggggggggggggggggggggggg ggggggggggggggggggggggggggggggg ggggggggggggggggggggggggggggggg gggggggggggggcagggggggggggggggg gggggggggggggagaggggggggggggggg gggggggggggggagaagggggggggggggg ggggggggggggagggagggggggggggggg ggggggggggggaggggaggggggggggggg gggggggggggacggggcagggggggggggg gggggggggggaggeeedacddddddddddddddbbbbbbbbbbbbbbbbbbbbbbbb ggggggggggacbbbddddadddddddddddeeeeee gggggggdbbadggggggggagggggggggg gggebbbdgccgggggggggcaggggggggg dbbbeggggagggggggggggacgggggggg ebbbdgggggggcaggggggggggggagggggggg dbbde ggggggggaggggggggggggggaggggggg ebbbe ggggggggaggggggggggggggaagggggg edbbd gggggggaggggggggggggggggagggggg dbbbe gggggggagggggggggggggggggaggggg ebbbd ggggggacgggggggggggggggggcagggg de ggggggagggggggggggggggggggacggg gggggacggggggggggggggggggggaggg gggggaggggggggggggggggggggggagg cc ca a af fa a a fa fa cc af af a a af ca a ac cc a a fa cc ca a af fa a a fa fa ac af af a a af ca a ac cc a a fa cc ca a af fa a a fa fa ac af af a a af ca a ac cc a a fa cc ca a af fa a a fa fa ac af af a a af f a cc a cc a fa a fa af a af a cc a cc a fa a ``` <!-- end of image --> This is a magnified view of the region A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0404feff b,#fb0508ff c,#7d7dffff d,#fd5b5dff e,#fe999aff f,#c1c1ffff g,#3e36f6ff ``` ```image f aaf caag aaaag faafaaf gac caaf faa gag gac aac faaf faaf cag caa aaf gag cag faac aaf caaf cag gag gac eeeeeeeeaageeeeeeddddddddddddddd faa edbbbbbbbbbbbaabbbbbbbbbbbbbbbbbbbbb gagbbbbbbddddddddgaadddddddddeeeeeeeeeee edbaabbbde gag edbbbbgage aac edbbbbbddaaf faaf edbbbbbbde cag caa edbbbbbde aaf gag edbbbbbbde cag faac bbbbde aaf caaf bde cag gag gac aac faa faaf gac caaf faa gag gac faac faaf faaf cag caa aaf gag cag faac aaf caaf cag gag gac aac faa faaf gac caa faa gag gac faac ``` <!-- end of image --> My analysis confirms the presence of an intersection in area A. Two intersections have been found!

<!-- image --> ```palette Key,Color ,#fefefeff a,#0505feff b,#ff0505ff c,#7d7dffff d,#fd5758ff e,#ffa7a7ff f,#bebeffff g,#403cfaff ``` ```image f ca afa fa gg af af a a af ca a eeeeageeddddddddddddbbbbbbbbbbbbbbbbbbbbbbbb ggbbdddddaddddddeeeeeeeeeeee dbbae a ebbbd cg ca dbbbe a ac ebbbd cg a dbbde a fa ebbbe fa gg edbbd af af dbbbe a a ebbbd af ca de a ac gc a a fa cg ca a ac ca a a fa fa gg af af a a af ca a ac gc a a fa cg ga a af ca a a fa fa gg af af a a af ca a ac gc a a fa cg gg a af fa a a fa fa gg af af a a af ca a ac gc a a fa cg gg a af fa a a fa fa gg af af a a ac f a gc a cg a fa a fa af a ac a gc a cg a fa a ``` <!-- end of image -->

The hunt for intersections begins! Let's analyze this image closely. My final answer is: no intersections found.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff5d5dff b,#0606ffff c,#ff0707ff d,#8e8effff e,#ffb3b3ff f,#4d4dffff g,#d0d0ffff ``` ```image dg fbbbbbbfdg gdfbbbbbbfdg gdfbbbbbbfdg gdfbbbbbbfdg gdfbbbb gbd bb fbg gbd bb dbg gbf bb dbg bf bb dbg bf fb gbd bb fb gbd bb fbg gbd bb dbg gbf bb dbg bf bb dbg bf fb gb ccccccccccccccccccccccccccaaaaaaeeeeeee ca eeeeeeaaaaaaaccccccccc ece ac cc cc ca ece ac cc ca ce ec ac cc ca ece ac cc ca ce ece ac cc ca ece ec ac cc ca ``` <!-- end of image -->

I'm optimistic that I'll find some intersections in this image. These spots mark what I'd call 'danger zones' - areas where intersections are more likely. <!-- image --> ```palette Key,Color ,#fefefeff a,#f65955ff b,#4c50f6ff c,#faa4a1ff d,#9b9ef8ff e,#0607feff f,#fd0707ff g,#add5adff ``` ```image c f fc f f cf f af f aa f fc f fc cf f cf f aa f fc f fc cf f cf f aa f fa e f de fc be cf ed f e cf e f de aa eb f ed aa e f de fc be f ed f e cf e f de af eb f ed aa e f de fc be f ed fc e cf e f de cf eb f ed aa e f de fc be f ed fc e cf e f de cf eb f ed aa ggeggggggggggggggfgg ggdeggggggggggggfagg gggbegggggggggggfggg ggggebgggggggggfcggg gggggegggggggggfgggg db ac ggggggegggggggfggggg dbbeeeeebd cffffa ggggggbegggggafggggg ddbeeeeebbd affffc gggggggebggggfgggggg ddbeeeeeebd cafffac ggggggggedggafggggggddbeeeeeebd cafffac gggggggggeggfdbeeeeeebd cffffa gggggggggdeeebbggggg affffagggggggfgggggggg ggcafffacgfagggggggg gggggggafffggggggggg gggggggggggggggggggg gggggggggggggggggggg gggggggggggggggggggg ``` <!-- end of image --> I'm now examining the contents of area A in detail. <!-- image --> ```palette Key,Color ,#fefefeff a,#fb474aff b,#4a4affff c,#ff9393ff d,#9c99fcff e,#0605feff f,#fd0608ff g,#efd3e3ff ``` ```image beeg gffg beb afa geeb cffg deed ffc deeg cff bee ffc eeb cff geed gffc deed afa beeg gffg beb afa geeb cffg deed afc deeg cff bee ffc eeb cff geed gffc deed afa beeg gffg gdddbbe beb afaddbbeeeeeeeee geebbeeeeeeeeeeebbbddg deeeeeeebbddg facg dddffg ffffffacg ffc gcafffffffaacg cff ccafffffffaccg ffc gccafffffffafa gcaaffffg gcc ``` <!-- end of image --> The evidence is clear: this is an intersection in area A. I have found one intersection!

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff4040ff b,#4e4effff c,#ff8686ff d,#9f9fffff e,#0707feff f,#fe0405ff g,#ffc7c7ff ``` ```image c f fc gf fg gf f ca f aa f fc gf fg gf f cf f aa f fc f fg gf f cf f aa f ac e f de fg be gf ed fg e cf e f de ca eb f ed ac e f de fc be gf ed fg e gf e f de ca eb f ed aa e f de fc be gf ed fg e gf e f de cf eb f ed aa e f de fc be f ed fg e gf e f de cf eb f ed aa e f de ac be f ed fg e gf db ag e fg dbbeeeeebd cafffcg de cf ddbeeeeebbd gcffffc eb f ddbeeeeeebd gafffac ed ca dbeeeeeebd cafffag e fdbeeeeeebd cffffcg deeebdd gcfffac f gafffag fc caff ``` <!-- end of image -->

Here's an image. My task is to find intersections or areas where lines come close together. These areas seem to enclose narrow spaces where lines might be close. <!-- image --> ```palette Key,Color ,#fefefeff a,#fc0808ff b,#0807fcff c,#efa199ff d,#a7a9fbff e,#b0d6b0ff f,#f25751ff g,#5a62eeff ``` ```image eeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeeeeeeeeeeeeeeeeee d eeeeeeeeeeeeeeeeeeeeeeeeeeeeeee gbbbg eeeeeeeeeeeeeeeeeeeeeeeeeeeeeee gbbbg eeeeeeeeeeeeeeeeeeeeeeeeeeeeeee gbbbgd eeeeeeeeeeeeeeeeeeeeeeeeeeeeeee dbbbbd eeeeeeeeeeeeeeeeeeeeeeeeeeeeeee dbbbbd eeeeeeeeeeeeeeeeeeeeeeeeeeeeeee dgbbbg eeeeeeeecaeeeeeeeeeeeeeeeeeeeee gbbbgeeeeeafaeeeeeeeeeeeeeeeeeeee eegbbbgeaefaeeeeeeeeeeeeeeeeeee eeeeeegbbbgafeeeeeeeeeeeeeeeeee eeeeeeeaeebbbfeeeeeeeeeeeeeeeee eeeeeeaceeeegbbeeeeeeeeeeeeeeee eeeeeeaeeeeeeeabbgeeeeeeeeeeeee eeeeeaceeeeeeecaebbbeeeeeeeeeee eeeeeaeeeeeeeeefaeegbbdeeeeeeee eeeeaceeeeeeeeeeaaeeeebbgeeeeee eeeeaeeeeeeeeeeeeafeeeeegbbeeee eeeaceeeeeeeeeeeeeaceeeeeegbbge eeeaeeeeeeeeeeeeeeeaeeeeeeeeebbg eeafeeeeeeeeeeeeeeecaeeeeeeeeeegbb eeaeeeeeeeeeeeeeeeeefaeeeeeeeee dbbd eafeeeeeeeeeeeeeeeeeeaaeeeeeeee bbg eaeeeeeeeeeeeeeeeeeeeeafeeeeeee gbbd afeeeeeeeeeeeeeeeeeeeeeaceeeeee dbbg aeeeeeeeeeeeeeeeeeeeeeeeaeeeeee gbb ffeeeeeeeeeeeeeeeeeeeeeeeeaeeeee dbbd aeeeeeeeeeeeeeeeeeeeeeeeeefaeeee bbg ffeeeeeeeeeeeeeeeeeeeeeeeeeefaeee gbb a eeeeeeeeeeeeeeeeeeeeeeeeeeeafee d ff eeeeeeeeeeeeeeeeeeeeeeeeeeeeace a eeeeeeeeeeeeeeeeeeeeeeeeeeeeeae ff eeeeeeeeeeeeeeeeeeeeeeeeeeeeeea a ca cf fa a af ca ac a a ca a a ca ca fa a af ca ac a a ca a a ca a fa a af a af ac ac a a ac ca a ca ac fa a af ac ac a a ac a a ca ac f a ff a ff a ff a ff a ff a cf a ca a ca a ca a ca a ``` <!-- end of image --> Time to investigate area A up close. <!-- image --> ```palette Key,Color ,#fefefeff a,#fe0505ff b,#0907fcff c,#fe7c7dff d,#acabfdff e,#fec4c4ff f,#f9383eff g,#605cfbff ``` ```image cf eaaf bgd faaac bbbbbgd eaacaac dgbbbbbbbgdd fac caae dggbbbbbbgddaae faae dggbbbbbbbgd faf ddgbbbbbbdeaaf fafdgbbbbgaac eaae dbbbbbfc caf dgbbbbg eaae gbbbbgd caf fbbbbgd eaae afgbbbbg caf eaacgbbbbgd aae eaac dgbbbbd caf caae dgbbbbg aae caae dbbbbgd caf faa dgbbbbd aae faf gbbbbg caf eaaf dbbbbgd aae eaac dgbbbbd caf caae gbbbbgd aae caae dbbbbgd caf faa dgbbbb aac faf gbb caa eaaf d aac eaac caa eaae fac caae eaa faae fac faf eaa aaf fac eaac eaa eaac fac caae eaa faae fac faf aa aaf ac eaac ae eaac c caae e caae faa faf eaac eaac caae caae faa fa ea ``` <!-- end of image --> There is an intersection point visible in this close-up of area A. I've identified a total of two intersection points.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fe0404ff b,#0806fdff c,#fe7b7bff d,#a8a6fdff e,#ffbfbfff f,#ff3838ff g,#5c5cfeff ``` ```image d gbbbg gbbbg gbbbgd dbbbbd dbbbbd dgbbbg ea gbbbg aca gbbbgda fa dbbbdaf ea bbbc ae gbbd a abbd ae ea gbg a ca dbbd ae ff bbg a ac gbb ae ae dbbd a a bbg ac ea gbb a ca dbbd fc ff bbg a ac gbbd fc ae dbbg a a gbb fc ea dbbd a ca bbg fc ff gbb a ac d cf ae a a cf ea a ea cf fa a af cf ac a ae ca a a ea ea ca a ff ea ac a ae ea a a ea ea ca ae ff ea ac ae ae a a ae ea a ca ae ff a ac ae ae a a fc ea a ca fc c a fc a fc a ff a cf a cf a cf a cf a ca a ea a ea a ``` <!-- end of image -->

Time to put on my detective hat and find those intersection points! The image has some tight areas where segments are too close. I should investigate those closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#fd0606ff b,#0b0cfcff c,#ea968cff d,#737aefff e,#b1d7b1ff f,#f24741ff g,#97c797ff ``` ```image dbbb dbbd db dbbd bd dbbd b bbbd db bbbd be ebbbd b ebbbd db dbbbe b dbbb b dbbb db bbb b b bd b eb a bd aac b ac a db af ca bd ff ff b fa a db ca a bd a ff b a ac db ac a be ac ca b af ac db fa a b ca cagggggggggbgggggggggggggggggggggge a afeeeeeeeebbeeeeeeeeeeeeeeeeeeeeeg a gageeeeeeeebeeeeeeeeeeeeeeeeeeeeeg a geaeeeeeeeegbeeeeeeeeeeeeeeeeeeeeg ac gefaeeeeeeeebdeeeeeeeeeeeeeeeeeeeg af geeaceeeeeeeebeeeeeeeeeeeeeeeeeeeg fa geeeaeeeeeeeedbeeeeeeeeeeeeeeeeeeg ca geeecaeeeeeeeebdeeeeeeeeeeeeeeeeeg ca geeeeafeeeeeeeebeeeeeeeeeeeeeeeeeg a geeeeeaeeeeeeeedbeeeeeeeeeeeeeeeeg a geeeeecaeeeeeeeebdeeeeeeeeeeeeeeeg ac geeeeeeafeeeeeeeebeeeeeeeeeeeeeeeg af geeeeeeeageeeeeeedbeeeeeeeeeeeeeeg ff geeeeeeeeaeeeeeeeebdeeeeeeeeeeeeeg fa geeeeeeeefaeeeeeeeebeeeeeeeeeeeeeg ca geeeeeeeeeaceeeeeeedbeeeeeeeeeeeeg a geeeeeeeeeeaeeeeeeeebgeeeeeeeeeeeg a geeeeeeeeeecaeeeeeeeebeeeeeeeeeeeg ac geeeeeeeeeeeafeeeeeeebbeeeeeeeeeeg ac geeeeeeeeeeeeaeeeeeeeebeeeeeeeeeeg af geeeeeeeeeeeecaeeeeeeegbeeeeeeeeeg fa geeeeeeeeeeeeeffeeeeeeebdeeeeeeeeg ca geeeeeeeeeeeeeeageeeeeeebeeeeeeeeg a geeeeeeeeeeeeeeeaeeeeeeedbeeeeeeeg a geeeeeeeeeeeeeeefaeeeeeeebdeeeeeeg a geeeeeeeeeeeeeeeeaceeeeeeebeeeeeeg ac geeeeeeeeeeeeeeeeeaeeeeeeedbeeeeeg af geeeeeeeeeeeeeeeeecaeeeeeeebdeeeeg fa geeeeeeeeeeeeeeeeeeafeeeeeeebeeeeg c geeeeeeeeeeeeeeeeeeeaeeeeeeedbeeeg geeeeeeeeeeeeeeeeeeecaeeeeeeebdeeg geeeeeeeeeeeeeeeeeeeeffeeeeeeebeeg geeeeeeeeeeeeeeeeeeeeeageeeeeedbeg geeeeeeeeeeeeeeeeeeeeeeaeeeeeeebgg geeeeeeeeeeeeeeeeeeeeeefaeeeeeeebg geeeeeeeeeeeeeeeeeeeeeeeaceeeeeebb geeeeeeeeeeeeeeeeeeeeeeeeaeeeeeeeb geeeeeeeeeeeeeeeeeeeeeeeecaeeeeeegb geeeeeeeeeeeeeeeeeeeeeeeeeafeeeeegd geeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeeg geeeeeeeeeeeeeeeeeeeeeeeeeecaeeeeg geeeeeeeeeeeeeeeeeeeeeeeeeeeffeeeg geeeeeeeeeeeeeeeeeeeeeeeeeeeeageeg geeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeg geeeeeeeeeeeeeeeeeeeeeeeeeeeeefaeg geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeacg geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeag geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeca ac a ``` <!-- end of image --> Time to investigate area A up close. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff0505ff b,#0909ffff c,#ff7d7dff d,#5d5dffff e,#b3b3ffff f,#ff3d3dff g,#ffc2c2ff ``` ```image ac dbd aag bbe caa ebb faf dbd gaac ebbe caag dbb faf bbd gaac ebbe gaag dbb faf bbd aac ebbe gaag dbb caa bbd faf ebbe gaac dbb caag bbd faf ebbe aac dbd gaag bbe faf ebb aac dbd gaag ebbe caa dbb faf bbd gaac ebbe caag dbb faf bbd aac ebbe gaag dbb faf bbd aac ebbe gaag dbb caa bbd faf ebbe gaac dbd caag bbe faf ebb aac dbd gaag bbe faa ebb aac dbd gaag ebbe caa dbb faf bbd gaac ebbe caag dbb faf bbd aac ebbe gaag dbb caa bbd aac ebbe gaag dbb caa bbe faf ebb gaac dbd caag bbe faf ebb aac dbd gaag ebbe caa dbb faf bbd gaag ebbe caa dbb faf bbd gaac ebbe caag dbb faf bbd aac ebbe gaag dbb caa bbd faf ebb gaag db caa b faf e gaac caag faf aac gaag caa faf gaag caa faf gaac caag faf aac gaag caa faf gaag caag faf gaa ``` <!-- 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,#ff0505ff b,#0808ffff c,#ff7d7dff d,#5d5dffff e,#b5b5ffff f,#ff3c3cff g,#ffc2c2ff ``` ```image e dbbb dbbd eb dbbd be dbbd b dbbd db ebbbe be ebbbe b ebbbe db ebbbe be ebbbe b ebbbe dd bbd b eb bd b eb a bd aac b ag a eb ac ga be ff ff b ca ag eb ga ga be ga ff b a ag db ag a be ac ca b af ac db fa a be ca ga b ga ff dd a ag b ag ga eb ac ff bd af ag b fa a eb ca ca bd ga ac b a a eb ag ga be ag ff b ac ag db ff a be ca ff b ga ag db ga a be a ca b ag ac dd ac a b af ga eb fa ff bd ca ag b ga a eb a ca bd ag ag b ac a eb af ca be fa ac b g a db ga be ff b ag db a be ca b ag dd a b ca eb ac d a ga ff ag a ca ag a ca ac a ``` <!-- end of image -->

This image might have some surprises. Let's look for intersections carefully. I can confidently say that there are no intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ff5151ff b,#4646ffff c,#ff0606ff d,#0505ffff e,#8a8affff f,#ffa6a6ff g,#c6c6ffff ``` ```image f acf cc acf cc fcf cc fca fcc cc accf fca fcca ac ccc ca fccf acf fcca cc accf acf fcca cc acc fcf fccf cc cca fca accf cc fcca fca acc ac fccf ca cca acaccf a gbdg ebdddegdde edddbg bdd gbdddbg edde gbddde bdb edddde eddg edddbg gddb gbdddbg bddg gbddde gdde be bddg gdde bdb edde ddb eddg gddb bddg gdde bd ``` <!-- end of image -->

The hunt for intersections begins! Let's analyze this image closely. I can confidently say that there are no intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0707ffff b,#ff4141ff c,#b4b4ffff d,#ff8686ff e,#ff0505ff f,#5454ffff g,#ffcbcbff ``` ```image g eeg deg e ee ge ged de be bb eb ed ged eg be e eb ge deg de ee be ged eb beg eg ee eg ged ge be de eb be deg eb ee ed geb eg deg e ee ge ged f de be aac bb eb ac a ed deg ac ca eg b af fa e af af ge af ac de af a be af ca eb af ff ed af ac eg af a ge aa ca ge aa fa be aa af eb fa ac ed fa a eg fa ca e fa ff ge fa ac de fa a bb fa ca ed ca fa eg ca af e ca ac ge ca a de ca ca be ca ff eb ca ac ed ca a e ca ca a fa a af a ac ac a ac ca ac fa ac ac a ca fa af ac a ca fa ac a ca fa af ac a ca fa ac a ``` <!-- end of image -->

Alright, let's get to work and investigate this image for intersections. I did not find anything, there's no intersections

<!-- image --> ```palette Key,Color ,#fefefeff a,#0707ffff b,#ff0606ff c,#ffb5b5ff d,#ff5d5dff e,#8c8cffff f,#4747ffff g,#c9c9ffff ``` ```image c dbb cbbd dbbc cbbd dbbc cbbd dbbc cbbd dbbc cbbd dbbc bbd dbbc bbd dbbc bbd cbbc dbbb cdbbbd cdbbbd cbbbbc cbbbdc dbbbdc cdbbbd cdbbbd cbbbbc dc ga ea fa aa af ae gag ea fa aa af ae gag ea ag fa aa aa eae af aa ae eae gag aa ea gaf fa fag aa aa af fag ae aa gag eae ea aa fa gaf aa fag af gaf ae fag gag aa ea eae fa aa aa eae af aa ae gafgag fa ``` <!-- end of image -->

I have an image in front of me. I need to determine if there are any intersection segments. I've noticed 1 areas of interest. These could be potential intersection zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#454cf0ff b,#fd0706ff c,#eff1efff d,#0707fdff e,#8e98e9ff f,#eb6359ff g,#b0d6b0ff ``` ```image e ed ed ed cd cd cdc cdc dc dc de de de da da da da b dd gbg ad bb ad bf cggggggggggggggggggggggggggggggadgggggggggggfbg dc cgggggggggggggggggggggggggggggadgggggggggggbbgc cde cggggggggggggggggggggggggggggedgggggggggggbfggc dd cgggggggggggggggggggggggggggedggggggggggfbggggc ede cggggggggggggggggggggggggggedggggggggggbbgggggc dd cgggggggggggggggggggggggggedggggggggggbfggggggc adc cgggggggggggggggggggggggggdgggggggggfbggggggggc cda cggggggggggggggggggggggggdgggggggggbbgggggggggc adc cgggggggggggggggggggggggdgggggggggbfggggggggggc cda cggggggggggggggggggggggdegggggggfbggggggggggggc dd cgggggggggggggggggggggdegggggggbbgggggggggggggc ede cggggggggggggggggggggdegggggggbfggggggggggggggc dd cgggggggggggggggggggdeggggggfbggggggggggggggggc ede cggggggggggggggggggdaggggggbbgggggggggggggggggc cda cgggggggggggggggggdaggggggbfggggggggggggggggggc adc cggggggggggggggggdagggggfbggggggggggggggggggggc cda cgggggggggggggggdagggggbbgggggggggggggggggggggc dd cggggggggggggggddgggggbfggggggggggggggggggggggc ede cgggggggggggggddggggfbggggggggggggggggggggggggc dd cggggggggggggadggggbbgggggggggggggggggggggggggc edecgggggggggggadggggbfggggggggggggggggggggggggggc ddggggggggggadgggfbggggggggggggggggggggggggggggc adggggggggadgggbbgggggggggggggggggggggggggggggc cgdagggggedgggbfggggggggggggggggggggggggggggggc cggadgggedggfbggggggggggggggggggggggggggggggggc cgggedaedggbbgggggggggggggggggggggggggggggggggc cgggggddggbfggggggggggggggggggggggggggggggggggc cgggggggfbggggggggggggggggggggggggggggggggggggc cggggggbbgggggggggggggggggggggggggggggggggggggc cgggggbfggggggggggggggggggggggggggggggggggggggc cggggbggggggggggggggggggggggggggggggggggggggggc cggfbgggggggggggggggggggggggggggggggggggggggggc cgfbggggggggggggggggggggggggggggggggggggggggggc cbbgggggggggggggggggggggggggggggggggggggggggggc bfggggggggggggggggggggggggggggggggggggggggggggc cbfccccccccccccccccccccccccccccccccccccccccccccc cbc fbc fb bb bf cbf cbc fbc fb bb bf bf cbc fbc fb bb bf bf cbc fbc fb bb bf bf ``` <!-- end of image --> Let's see what secrets area A holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#5d5dffff b,#fe0606ff c,#ffccccff d,#0707ffff e,#b0b0ffff f,#ff4545ff g,#ff8c8cff ``` ```image adde gbb adde fbbf adde cfbbg adde gbbbc edde fbbf edda cfbbg edda gbbbc edda fbbf edda cbbbg edda gbbbc edda fbbf edda cbbbg dda gbbbc ddd fbbf ddd cbbbg ddd gbbbc add fbbf adde cbbbg adde gbbfc adde fbbf adde cbbbg adde gbbfc adde fbbf adde cbbbg edde gbbfc edda cfbbf edda cbbbg edda gbbfc edda cfbbg edda cbbbg edda gbbfc edda cfbbg edda cbbbc ddd gbbfc ddd cfbbg ddd gbbbc ddd gbbfc add cfbbg adde gbbbc adde fbbfc adde cfbbg adde gbbbc e adde fbbf da adde cfbbg ddde adde gbbbc eddde edde fbbf adda edda cbbbg eddde edda gbbbc adda edda fbbf addde edda cbbbg eddda edda gbbbc addddda fbbf eddda cbbbg aa gbbbc fbbf cbbbg gbbfc fbbf fbbg cfbbc cbbbc gbbfc gbbf fbbg fbbg cfbbc cbbbc bbfc ``` <!-- end of image --> No intersection in area A, but I'll keep looking. My analysis shows there's absolutely no intersections in the image

<!-- image --> ```palette Key,Color ,#fefefeff a,#5454ffff b,#ff0707ff c,#ffccccff d,#0808ffff e,#adaeffff f,#ff4b4bff g,#ff8a8aff ``` ```image e ed ed ed ed ed d d de de de de de da da da da b dd cbc ad fb ad bf ad gbc d ad fb eda ed bf dd ed gbc ede ed bb dd ed bf ade d gbc da d bb ad d bf eda de gbc dd de bb ede de bf dd de gbc ade da bb dd da cbf ad da gbc da da bb dd dd cbg ede ad fbc dd ad bb ede ad cbg dd ad fb ade ed bb da ed cbg ad ed fb edaed bb dd cbg fb bb bg cbc gb fb bb bf bg cbc gb fb bb bf bg cbc gb fb bb bf bg cbc gb fb bb bf bg cbc gb fb bb bf bg ``` <!-- end of image -->

Here's an image. My task is to find intersections or areas where lines come close together. My next step is to analyze the details within each area. <!-- image --> ```palette Key,Color ,#fefefeff a,#5360e5ff b,#fc0908ff c,#d78875ff d,#b1d7b1ff e,#b4b4ffff f,#0809fcff g,#95c59bff ``` ```image e fe f fe f a fe ef ef f d f af bcggfggggggggggggggggggggggggggggggggggggggggggd f bddfddddddddddddddddddddddddddddddddddddddddddg fe bcdafdddddddddddddddddddddddddddddddddddddddddg ef dbddfdddddddddddddddddddddddddddddddddddddddddg f dbcdafddddddddddddddddddddddddddddddddddddddddg af ddbddfddddddddddddddddddddddddddddddddddddddddg f ddbcdaadddddddddddddddddddddddddddddddddddddddg fe dddbddfdddddddddddddddddddddddddddddddddddddddg ef dddbcdaaddddddddddddddddddddddddddddddddddddddg f ddddbddfddddddddddddddddddddddddddddddddddddddg aa ddddbcdfadddddddddddddddddddddddddddddddddddddg f dddddbddfdddddddddddddddddddddddddddddddddddddg fe dddddbcdfaddddddddddddddddddddddddddddddddddddg ef ddddddbddfddddddddddddddddddddddddddddddddddddg f ddddddbcdfgdddddddddddddddddddddddddddddddddddg aa dddddddbdgfdddddddddddddddddddddddddddddddddddg f dddddddbcdfgddddddddddddddddddddddddddddddddddg fe ddddddddbdgfddddddddddddddddddddddddddddddddddg ef ddddddddbcdfddddddddddddddddddddddddddddddddddg f dddddddddbdafdddddddddddddddddddddddddddddddddg fa dddddddddbcdfdddddddddddddddddddddddddddddddddg f ddddddddddbdafddddddddddddddddddddddddddddddddg fe ddddddddddbcdfddddddddddddddddddddddddddddddddg ef dddddddddddbdafdddddddddddddddddddddddddddddddg f dddddddddddbcdfdddddddddddddddddddddddddddddddg fa ddddddddddddbdaaddddddddddddddddddddddddddddddg f ddddddddddddbcdfddddddddddddddddddddddddddddddg fe dddddddddddddbdfadddddddddddddddddddddddddddddg af dddddddddddddbcdfdddddddddddddddddddddddddddddg f ddddddddddddddbdfaddddddddddddddddddddddddddddg fa ddddddddddddddbcdfddddddddddddddddddddddddddddg ef dddddddddddddddbdfadddddddddddddddddddddddddddg f dddddddddddddddbcdfdddddddddddddddddddddddddddg af ddddddddddddddddbdfgddddddddddddddddddddddddddg f ddddddddddddddddbcgfddddddddddddddddddddddddddg fe dddddddddddddddddbdfgdddddddddddddddddddddddddg ef dddddddddddddddddbcgfdddddddddddddddddddddddddg f ddddddddddddddddddbdfdddddddddddddddddddddddddg aa ddddddddddddddddddbcafddddddddddddddddddddddddg f dddddddddddddddddddbdfddddddddddddddddddddddddg fe dddddddddddddddddddbcafdddddddddddddddddddddddg ef ddddddddddddddddddddbdfdddddddddddddddddddddddg f ddddddddddddddddddddbcaaddddddddddddddddddddddg aa dddddddddddddddddddddbdfddddddddddddddddddddddg f dddddddddddddddddddddbcaadddddddddddddddddddddg fe ddddddddddddddddddddddbdfdddddddddddddddddddddg ef ddddddddddddddddddddddbcfaddddddddddddddddddddg f dddddddddddddddddddddddbdfddddddddddddddddddddgaa dddddddddddddddddddddddbcfadddddddddddddddddddgf ddddddddddddddddddddddddbdfdddddddddddddddddddfe ddddddddddddddddddddddddbcfgdddddddddddddddddaf dddddddddddddddddddddddddbdfdddddddddddddddddfg dddddddddddddddddddddddddbcfgdddddddddddddddfag ddddddddddddddddddddddddddbgfddddddddddddddgfdg ddddddddddddddddddddddddddbcfddddddddddddddfgdg dddddddddddddddddddddddddddbgfddddddddddddafddg dddddddddddddddddddddddddddbcfddddddddddddfdddg ddddddddddddddddddddddddddddbafddddddddddfadddg ddddddddddddddddddddddddddddbcfdddddddddgfddddg dddddddddddddddddddddddddddddbafddddddddfgddddg dddddddddddddddddddddddddddddbcfdddddddafdddddg ddddddddddddddddddddddddddddddbaaddddddfddddddg ddddddddddddddddddddddddddddddbcfdddddfaddddddg dddddddddddddddddddddddddddddddbaadddgfdddddddg dddddddddddddddddddddddddddddddbcfdddfddddddddg ddddddddddddddddddddddddddddddddbfadafddddddddg cbbbbb ddddddddddddddddddddddddddddddddbcfdfdddddddddg cbbbbbbcc dddddddddddddddddddddddddddddddddbffadddddddddg cbbbbbbcc dddddddddddddddddddddddddddddddddbcfddddddddddg cbbbbbbcc ddddddddddddddddddddddddddddddddddbdddddddddgcbbbbbbcc ddddddddddddddddddddddddddddddddddbcdgcbbbbbbcc gdddddddddddddddddddddddddddddddddgbbbbcgdddddg ``` <!-- end of image --> Let's get to the bottom of what's happening inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#4343ffff b,#fe0303ff c,#fe9495ff d,#8585ffff e,#c6c6ffff f,#0606ffff g,#ff2b2bff ``` ```image bb fd gb ff gc eff cb afd bc dff gbc df cbb fe gb da cb fe cg ffe bc afa bg effe gbc afa gbc af cbg ef gb ad gc fd cg ff bc ffd bg dff cbg df gbc fe cbg da cb fa gc ffe cg afa bc effe gbc eff cbg af gb ef cb ad cg fd bc ff bg ffd cbg ffd bbc dfa cbg ff bb df bc da cg efe bc fa bg ffe cbg eff bbc af cbg ef cb ef bc fd cg ff bc ffd bbc ffe cbg dfa bb ff bc fe cg aa bc efe bg fa cbg afd bbceff cbg afd bb eff bc df cg fd bc df bbc fa cbg ffe bbcdfa cbg ff cb efe bc aa cg efe bg ffe bbcafd cbgeff bb afd bc af cg df bc fd bg df cbg fa bbcffe d cbgdfa f cb dfa ff bceff fd cg af df bcefe efd bbcef eff cbg fd ffd bbcff ff cbgafd efe cb ff efe bcdf ff cg fd dff bg fe afa bbcfa ffe cbgffe fd bbdfa da bcafa af cgeff dff bcaf ffd bbcad ffe cbgef fa bbcfd df cbgff fd cbdff eff bcffdafd cgdffff bcfffd bbcfe cbge bbc cc bb cccgbbbbbbbgg cbggbbbbbbbggcc ``` <!-- end of image --> I had hoped to find an intersection in area A, but there isn't one. The image is completely devoid of intersections. Zero.

<!-- image --> ```palette Key,Color ,#fefefeff a,#3c3cffff b,#ff0707ff c,#fea8a8ff d,#8080ffff e,#c7c7ffff f,#0404ffff g,#ff4c4cff ``` ```image e fd f fe f a fe ef ef fe c fe da bc ef f b f fd bc df ef b f f bc da da b f f bc da fd b f ef bc ad f b f aa bc ad f b f fe bc fd ef b f f bc fe aa b ef f bc fe fe b ef df bc f f b ef ad bc f f b da fe bc f df b da f bc f ad b aa ef bc f fe b ad df bc f f b ad fd bc f ef b fe fe bc f da b fe f bcef fd b fe ef bcef f b f aa bcdf f b f fe bcda ef b f f bcda aa b f f bcad fe b f df bcad f b f aa bcfd f b f fe bcfe df b f f bcfe ad bef ef bcf fe bef df bcf f bdf fd bcf ef bda fe bcf da bda f bcf fd bad ef bcf f bad aa ccgbbbb bcf f ccgbbbbbgc bffd ccgbbbbbgc bcf ccgbbbbbgc b ccgbbbbbgc bc ccgbbbbbgc bbbgc ``` <!-- 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,#f53939ff b,#0c0dfcff c,#747cefff d,#ef9790ff e,#fe0202ff f,#b1d7b1ff g,#96c897ff ``` ```image fffffffffffffffg fffffffffffffffg fffffffffffffffg fffffffffffffffg fffffffffffffffg cbbbbbb fffffffffffffffg ccbbbbbcf cb fffffffffffffffg cbbbbbbc b fffffffffffffccbbbbbcc cb fffffffcbbbbbbcg b fffbbbbbcffffffg b fffdeffffffffffg bc ffffeffffffffffg b ffffdefffffffffg bc fffffedffffffffg b ffffffeffffffffg cb ffffffedfffffffg b fffffffefffffffg cb fffffffaaffffffg b ffffffffeffffffg fb ffffffffaafffffg bf fffffffffefffffg b fffffffffdeffffg bc ffffffffffeffffg b ffffffffffdefffg cc fffffffffffegffg b ggggggggggggeggf cb ed b e fb ad b e b aa bc e b da bc e b de cb e b de cb ed b e b ed bc e b ad bc e b aa cb e b da cb e b de b e bc e b ed bc e b ad fbbgggggggggggggggg e gfbffffffffffffffff aa gfcbfffffffffffffff e gffbfffffffffffffff da gffgbffffffffffffff e gfffbcfffffffffffff de gffffbfffffffffffff e gffffbcffffffffffff de gfffffbffffffffffff ed gfffffbbfffffffffff e gffffffbfffffffffff ed gffffffcbffffffffff e gfffffffbffffffffff ad gfffffffcbfffffffff e gffffffffbgfffffdae aa gfffffffffbdaeeeadf e gfffffdaeebadffffff da gdaeeeadfffbfffffff e daeeeadffffffffbcffffff de daeeead gfffffffffffbffffff e daeeead gfffffffffffcbfffff e daeeead gffffffffffffbfffff eddaeeead gffffffffffffcbffff ead gfffffffffffffbgfff gfffffffffffffgbfff gffffffffffffffbcff gfffffffffffffffbff gfffffffffffffffbcf gffffffffffffffffbf gffffffffffffffffcb gfffffffffffffffffb gffffffffffffffffff fgggggggggggggggggg ``` <!-- end of image --> I'm analyzing this close-up of area A with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#ff3c3cff b,#0402fcff c,#9e9bfcff d,#f9b9beff e,#ff0404ff f,#ff7878ff g,#4a47fbff ``` ```image ccgg cccggbbbbbb ccggbbbbbbbbbggcc dccggbbbbbbbbbggcc dbbbbbbbggccc bbgcc dee aef dee aef deed aea deed fea eed fea eef fee aef dee aef deed aea deed fea eed fea eed fee eef dee aef dee aef deed aea ``` <!-- end of image --> Incredible, there's actually an intersection in area A! Alright, let's examine the next area. Let's see if area B yields any clues. <!-- image --> ```palette Key,Color ,#fefefeff a,#fb5458ff b,#0605feff c,#9593fdff d,#ffa1a1ff e,#fe0203ff f,#e2d5f2ff g,#4d4afcff ``` ```image gbg fbbc cbg bbc cbb bbc cbbf gbg fbbf gbg fbbf gbg fbbc cbb bbc cbbf gbg fbbf gbg fbbf gbg fbbc cbb bbc cbb gbc cbbf gbg fbbf fdaae gbg fdaaeeeeee fbbcdaaeeeeeeeaadf fdagbbeeeeeaadf fdaaeeeeebbaadf fdaaeeeeeeeaadcbb fdaaeeeeeeeaadf bbc aeeeeeeeaadf cbbf eeeaadf gbg df fbbf gbg fbbc cbg bbc cbb bbc cbbf gbg fbbf gbg fbbf gbg fbbc cbb bbc cbbf gbg fbbf gbg fbb gb fb c ``` <!-- end of image --> Wow! I can see an intersection so clearly in area B! My analysis indicates that there are two intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#fc4548ff b,#0303feff c,#7575ffff d,#ffa4a4ff e,#ff0404ff f,#bfbfffff g,#3838ffff ``` ```image f fcgbbbbb fgbbbbbcf cg fcgbbbbgcf b fcbbbbbcf fb cgbbbbgcf bf bbbbgf fb de bf e b de gc ed b e cg ed b e cb aa b e fb aa bf e b de gc e b de gg e b e cg ed b e fb ed bf e b aa bc e b aa gc e b de cg e b de fb ed bf e fb ed bf e b aa gc e b aa cg e b de fb e bf de fb e bf e b ed gc e b ed cg e b aa cb e b aa fb e bf de b e bc de b ed gg e b ed cg e b aa fb e bf dae aa bdaeeead e daeebad de daeeead b e daeeead gc de daeeead b e daeeead cg e daeeead b eddaeeead fb ead bf fb bf b gc b cg b ``` <!-- end of image -->

Time to put on my detective hat and find those intersection points! These zones are intriguing. I bet there's something interesting happening within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#676ad7ff b,#fb0a09ff c,#0809fcff d,#e67064ff e,#b1d7b1ff f,#99c697ff g,#eff1efff ``` ```image a gc cg ac gc cg ac gc cg gffffffffffffffffffffffffffffffffffffffffffffacffffbg geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeceeeebdg geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecfeeebbeg geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaceeedbeeg geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeceeeebeeeg geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecfeeebdeeeg geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaceeebbeeeeg geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeceeedbeeeeeg geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecfeeebeeeeeeg d geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaceeebfeeeeeeg db geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeceeebdeeeeeeeg bd geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecfeedbeeeeeeeeg bg geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaceeebeeeeeeeeeg gb geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeceeebfeeeeeeeeeg db geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecaeebdeeeeeeeeeeg bd geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaceedbeeeeeeeeeeeg bg geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeceeebeeeeeeeeeeeeg gb geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecaeebfeeeeeeeeeeeeg db geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaceebdeeeeeeeeeeeeeg bd geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeceedbeeeeeeeeeeeeeeg bg geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecaefbeeeeeeeeeeeeeeeg gb geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaceebeeeeeeeeeeeeeeeeg db geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeceebdeeeeeeeeeeeeeeeeg bd geeeeeeeeeeeeeeeeeeeeeeeeeeeeecaedbeeeeeeeeeeeeeeeeeg bg geeeeeeeeeeeeeeeeeeeeeeeeeeeeacefbeeeeeeeeeeeeeeeeeeg gb geeeeeeeeeeeeeeeeeeeeeeeeeeeeceebeeeeeeeeeeeeeeeeeeeg db geeeeeeeeeeeeeeeeeeeeeeeeeeecaebdeeeeeeeeeeeeeeeeeeeg bd geeeeeeeeeeeeeeeeeeeeeeeeeeacebbeeeeeeeeeeeeeeeeeeeeg bg geeeeeeeeeeeeeeeeeeeeeeeeeecedbeeeeeeeeeeeeeeeeeeeeeg gb geeeeeeeeeeeeeeeeeeeeeeeeecaebeeeeeeeeeeeeeeeeeeeeeeg db geeeeeeeeeeeeeeeeeeeeeeeeacebdeeeeeeeeeeeeeeeeeeeeeeg bd geeeeeeeeeeeeeeeeeeeeeeeecebbeeeeeeeeeeeeeeeeeeeeeeeg bg geeeeeeeeeeeeeeeeeeeeeeecadbeeeeeeeeeeeeeeeeeeeeeeeeg gb geeeeeeeeeeeeeeeeeeeeeeacebeeeeeeeeeeeeeeeeeeeeeeeeeg db geeeeeeeeeeeeeeeeeeeeeecebfeeeeeeeeeeeeeeeeeeeeeeeeeg bd geeeeeeeeeeeeeeeeeeeeecabbeeeeeeeeeeeeeeeeeeeeeeeeeeg bg geeeeeeeeeeeeeeeeeeeeacdbeeeeeeeeeeeeeeeeeeeeeeeeeeeg gb geeeeeeeeeeeeeeeeeeeecebeeeeeeeeeeeeeeeeeeeeeeeeeeeeg db geeeeeeeeeeeeeeeeeeecabfeeeeeeeeeeeeeeeeeeeeeeeeeeeeg bd geeeeeeeeeeeeeeeeeeacbdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg bg geeeeeeeeeeeeeeeeeecdbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg gb geeeeeeeeeeeeeeeeecabeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg db geeeeeeeeeeeeeeeeacbfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg bd geeeeeeeeeeeeeeeecbdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg bggeeeeeeeeeeeeeeecabeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg gbgeeeeeeeeeeeeeeacbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg dbeeeeeeeeeeeeeecbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg bdeeeeeeeeeeeecadeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg gbeeeeeeeeeeeacbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg gfbeeeeeeeeeecbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg gedbeeeeeeeecaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg geebdeeeeeeacdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg geeebeeeeeecbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg geeefbeeeecaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg geeeedbeeaceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg geeeeebdecdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg geeeeeebcaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg geeeeeacceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg geefccceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg gcccaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg accaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg ecca geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg gcccg geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg acce geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg acca geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg gccag geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg gcccg geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg acca geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg acca geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg gcccg gfffffffffffffffffffffffffffffffffffffffffffffffffffg cce ``` <!-- end of image --> I'm now examining the contents of area A in detail. <!-- image --> ```palette Key,Color ,#fefefeff a,#5755fdff b,#fd0709ff c,#0807fdff d,#fc5255ff e,#b0aefdff f,#74048eff g,#feb0b1ff ``` ```image aca d ecce gb cc bd ece db ca dbg ac gbb cca dbd acc dbb cce bbg ca bd ac dd cc gbb acc gbbd ecce bbd cca bb cce gbg ca bb ac dbb ece gbbg acc bd ecce db cca gbg cc gbb ece bbd ac dbbg ecc bbg cca bd acc dd ca gbb ac bbd ece dbd cc bb ecce gbd cca bb acc dbb cce gbbg ca bbg ece db cc gbg acc gbb ecce bbd cc gbbg ece bbg aa bd ec db aca gbb ecc bbd cce dbd ca bb ec gbg ac db ecc dbb ccegbbg aca bbd cce db ca gbg ec gbb ce bbd eccgbbg ccebbg aca bd cc db aagbb ecebbd ccdbb acabbg eccgbg acadb ccdbb cabbg aabbd ccbb accbg eccbd g ccfb bd ecbbg bb cfbg gbg acbd db eccb bd ccfg gbbg ccbd dbb cfb bbd acbg gbb ecbg db acc bd eccb bbg ccfg gbbg accd bb cf gbg acg gbgecd bbcc dfcc eacccae eaccca eccccae ecccca cc e ``` <!-- end of image --> The close-up clearly shows an intersection point in area A. My analysis indicates that there are two intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#6968feff b,#fe0a0aff c,#0909feff d,#fe7071ff e,#aeaefeff f,#791095ff g,#fed1d1ff ``` ```image a c c ac c ce ac c ce ac b c bd ce db ac gb c b ce bg ac bb c gb ce b d ac bg db c bd bd ce db bg ac b gb c bg db ce bd bd ac db bg c gb gb ce bg db ac bd bd c db bg ce gb gb ac bg db c bd bd ce db bg ac gb gb c b db ce bd bd ac db bg c gb gb ce b db ac bg bd c bb bg cegb gb ec b db c bg bd cebd bg ecdb gb c b db cebg bd ecbd bg cdb gb cab db ecbg bd cbd b cfb gb ecb db cbg bd cfd b ecb gb cb db cf bd ecd b cb gb cf db ec bd cg bcf ecc eccc acce acca ecca ccc acce acca ecca ccce acce ecca eccc cce ``` <!-- end of image -->