oliveirabruno01/intersection-pixel-map-CoT-l-112px-8c-economic

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

0

```palette Key,Color ,#fefefeff a,#ff3a3aff b,#0505ffff c,#5757ffff d,#ff7676ff e,#ff0505ff f,#ffc1c1ff g,#aeaeffff ``` ```image f eed ea ee ed ae ed fef ed ed ed ea ef ae ef de ef fef ef ed ef ee ef ae fe fef fe ed fe ea fe ae fe de fe fef de ed de ee de ae de fef ae ed ae ea ae ae ae de ae fef ea ed ea ee ea ae ea fef ea ed ed ea ed ae ed de fe gbb cbbbcg cbbbc gcbbbc gcbbbc gcbbbg gbbbbg gbbbcg gbbbcg cbbbcg cbbbc cbc bb bbg gbc bb bbg gbc bb cbg gbc bb cbg gbc bb cbg gbc bb cbg gbc bb cbg bc ```

Alright, let's get to work and investigate this image for intersections. Zero, Nada.

0

```palette Key,Color ,#fefefeff a,#0404ffff b,#ff5353ff c,#8080ffff d,#ffa7a7ff e,#ff0505ff f,#3b3bffff g,#c8c8ffff ``` ```image g caa aaf gaac caag faf gaac caag faf gaac caag faf gaac caag faf gaac caag faf gaac gaag aa fag caf gaa fag cac gaf aag fac gaf aa fag caf aa fag cac gaa aag cac gaf aa g eeed deeed beeb beeb deeed deeed beeb beebd deeed dbeeb beeb deeeeeeeeeeeeebbbddd dddbbbeeeeeeeeeeeeeebbdddd dddbbbeeeeeee ```

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.  ```palette Key,Color ,#fefefeff a,#8c96ecff b,#fb0b0bff c,#0505fdff d,#e8776cff e,#b1d7b1ff f,#4a4cebff g,#98c795ff ``` ```image a c c ff c c ff c c ff c c ff c c ff c ggggggggggggggggggggcgggge eeeeeeeeeeeeeeeeeeecfeeeeg eeeeeeeeeeeeeeeeeeaceeeeeg eeeeeeeeeeeeeeeeeeceeeeeeg eeeeeeeeeeeeeeeeecfeeeeeeg eeeeeeeeeeeeeeeeaceeeeeeeg eeeeeeeeeeeeeeeeceeeeeeeeg eeeeeeeeeeeeeeecfeeeeeeeeg eeeeeeeeeeeeeeaceeeeeeeeeg eeeeeeeeeeeeeeceeeeeeeeeeg edb eeeeeeeeeeeeecfeeeeeeeeddbbbbbde eeeeeeeeeeeeaceeedbbbbbbdg eeeeeeeeeegdcbbbbbdeeeeeeg eeeeddbbbbbcfeeeeeeeeeeeeg ddbbbbbdgeeeaceeeeeeeeeeeeeg dbbbbbbdgeeeeeeeeeceeeeeeeeeeeeeeg bbbbdd eeeeeeeeecfeeeeeeeeeeeeeeg b eeeeeeeeaceeeeeeeeeeeeeeeg bd eeeeeeeeceeeeeeeeeeeeeeeeg db eeeeeeecfeeeeeeeeeeeeeeeeg b eeeeeeaceeeeeeeeeeeeeeeeeg b eeeeeeceeeeeeeeeeeeeeeeeeg bd eeeeecfeeeeeeeeeeeeeeeeeeg bb eeeeaceeeeeeeeeeeeeeeeeeeg db eeeeceeeeeeeeeeeeeeeeeeeeg b gggcfgggggggggggggggggggge b ac bd c db ca b ac b c bd ca bb ac db c b ca b ac bd c ggggggggggggggggggdb ca eeeeeeeeeeeeeeeeegbg ac eeeeeeeeeeeeeeeeebeg c eeeeeeeeeeeeeeeebdeg ca eeeeeeeeeeeeeeebbeeg ac eeeeeeeeeeeeeedbeeeg c eeeeeeeeeeeeeebeeeeg ca eeeeeeeeeeeeebgeeeeg ac eeeeeeeeeeeebdeeeeeg c eeeeeeeeeeedbeeeeeeg ca eeeeeeeeeegbeeeeeeeg fc eeeeeeeeeebeeeeeeeeg aaafffccc eeeeeeegabfffccccccccccccccfffaaa ccccccccccfffaageeeeg eeeeeeedbeeeeeeeeeeg eeeeeeebeeeeeeeeeeeg eeeeeebgeeeeeeeeeeeg eeeeebdeeeeeeeeeeeeg eeeedbeeeeeeeeeeeeeg eeegbeeeeeeeeeeeeeeg eeebeeeeeeeeeeeeeeeg eebdeeeeeeeeeeeeeeeg ebbeeeeeeeeeeeeeeeeg dbeeeeeeeeeeeeeeeeeg beeeeeeeeeeeeeeeeeeg bgeeeeeeeeeeeeeeeeeeg ```  This is a magnified view of the region A.  ```palette Key,Color ,#fefefeff a,#a9a7fdff b,#ff0505ff c,#0604fdff d,#f83c42ff e,#ffc2c2ff f,#5550f9ff g,#ff8080ff ``` ```image d gb ebb ebbg dbd dbb gbbe ebbg bbd dbd gbbe ebbe ebbg dbd dbb gbbe ebbg bbd dbd gbbe ebbe ebbg dbd dbb gbbe aaaaa aaaaddfffffffccccccccccc aaaaffffffcccccccccccccccccccccccccccfff ccccccccccccccccccccffffaaaaaa fffffaaaaaa gbbe ebbe ebbg dbd dbb gbbe ebbg bbd dbd gbbe ebbe ebbg dbd dbb gbbe ebbg bbd dbd gbbe ebbe ebbg dbd dbb ```  Eureka! There's definitely an intersection in area A! Alright, let's concentrate on the next area. Let's put area B under the microscope.  ```palette Key,Color ,#fefefeff a,#6864fbff b,#fd0304ff c,#0b0afeff d,#fb4043ff e,#ffbfbfff f,#ff8383ff g,#bbbbffff ``` ```image acc gccg cca acc gccg cca acc gccg cca acc gccg cca acc gccg cca acc gccg cca acc gccg cca eefd acc effddbbbbb gccg effdbbbbbbbbbddf ccaefddbbbbbbbbbdffe eefaccbbbbbbbddffe effdbbbbdccbbddfee effdbbbbbbbbbdccae eefddbbbbbbbbbdffe acc ddbbbbbbbbddfee gccg bbbbddfee cca fe acc gccg cca acc gccg cca acc gccg cca acc gccg cca acc gccg cca acc gccg cca acc gccg ```  Case closed! This is definitely an intersection point in area B. There are precisely two intersections present in the image.

2

```palette Key,Color ,#fefefeff a,#817efcff b,#fe0707ff c,#0404feff d,#fb575bff e,#ffb5b5ff f,#3c37faff g,#c2c2ffff ``` ```image a gc cg ff gc cg ff gc c ff gc c ff gc c ff gc c ff gc c fa gc c fa gc c edb ca edbbbbbde gc edbbbbdde edcbbbbde edbbbbbca edbbbbbde gc edbbbbde c bbbbde ca be gc bd c db ca eb gc b c be ca db ac eb c b ca be ac bd c db ca eb ac b c be ca db ac eb c b ca be ac bd c db cg eb ac b c be cg db ac eb c b cg be ac bd c db cg eb ac b ggaaaffccc ggdaaffcccccccccccccffaaagg cccccccccffaaagg eb b be bd db eb b be db eb b be ```

I have a feeling there might be some intersections in this image. These spots mark what I'd call 'danger zones' - areas where intersections are more likely.  ```palette Key,Color ,#fefefeff a,#fd0707ff b,#0808fbff c,#f15d5aff d,#c8c9feff e,#5e6ce1ff f,#eda8a0ff g,#aed6aeff ``` ```image fa afa fa ac a a a fa af ac a a cc fa a ac cc a be a fa ebb fa ac ebb a a ebb gggggggggggfaggg fa dbbd gggggggggggagggg ac dbbd gggggggggggagggg a dbbd ggggggggggafgggg fa bbd ggggggggggaggggg ac bbeggggggggacggggg a bbeggggggagggggg fa ggbbegggccgggggg ac ggggebbgaggggggg a ggggggebbggggggg fa gggggggaebbggggg ac ggggggfaggebbggg a ggggggagggggebbg fa ggggggaggggggggbbd acgggggggggggggggggggg gggggafgggggggggdbbd gagggggggggggggggggggg gggggagggggggggg bbd gfaggggggggggggggggggg ggggacgggggggggg bbd ggacgggggggggggggggggg ggggaggggggggggg dbbd gggagggggggggggggggggg gggccggggggggggg dbbd gggfaggggggggggggggggg gggagggggggggggg dbbd ggggacgggggggggggggggg fa dbbd gggggagggggggggggggggg a dbbd gggggfaggggggggggggggg fa dbbggggggacgggggggggggggg a dbbgggggagggggggggggggg a gebbgggfaggggggggggggg af gggebbggacgggggggggggg a gggggebbgagggggggggggg cc gggggggebbaggggggggggg a gggggggggebbgggggggggg cc gggggggggggcbbgggggggg a gggggggggggfaebbgggggg fa ggggggggggggacgebbgggg a gggggggggggggagggebbgg fa gggggggggggggfaggggebb af ggggggggggggggacgggggebe a gggggggggggggggagggggg ebe af gggggggggggggggfaggggg eb a ggggggggggggggggacgggg cc gggggggggggggggggagggg a gggggggggggggggggfaggg cc ggggggggggggggggggacgg a gggggggggggggggggggagg fa gggggggggggggggggggfag a ggggggggggggggggggggac fa ggggggggggggggggggggga af fa a ac af a a fa cc ac a a cc fa a c fa a a af a af a cc a cc a fa a ```  Let's zoom in on area A to get a clearer view.  ```palette Key,Color ,#fefefeff a,#fe0303ff b,#0807fdff c,#ff7878ff d,#bebefeff e,#615cfaff f,#ffc2c2ff g,#fa3b40ff ``` ```image faa gac faa gac faaf cag aaf cag aaf cag gac faa e gac bbe faa bbbbe gac debbbed faaf debbbed cag debbbed aaf debbbed cag debbbbgaf ebbbbd ebbbbd faaebbbbe gac dbbbbe faa dbbbbe gac dbbbbed faaf debbbed cag debbb aaf deb cag d aaf caa gac faa gac faa gac faaf cag aaf ```  Amazing! This area was hiding an intersection all along! Let's move forward and inspect another region. Let's take a closer look at area B.  ```palette Key,Color ,#fefefeff a,#fe0000ff b,#0e0dfdff c,#fe6869ff d,#9492fdff e,#911481ff f,#febcbdff g,#fe1f1fff ``` ```image af ag gac faaf cag gac faaf cag gac faaf cag gac faaf cag gac faaf cag gac faaf cag gac bd faaf bbbd cag dbbbbd gac dbbbbd faaf dbbbbd cag dbbbbd gac dbbbbd faaf dbbbbd cag dbbbbdgac dbbbbeaf dbbbbe dbbbbd dbbbbd cebbbbd gaebbbbd faafdbbbbd cag dbbbbd gac dbbbbd faaf dbbbbd cag dbbbbd gac dbbbbd faaf dbbbb cag dbb gac d faaf cag gac faaf cag gac faaf cag gac faaf cag gac faaf cag gac faaf cag gac faa ca ```  Oh my, look at that! It's an intersection in area B! I've identified a total of two intersection points.

2

```palette Key,Color ,#fefefeff a,#fe0707ff b,#0706feff c,#ff7474ff d,#bcbcffff e,#5f5ffeff f,#ffb6b6ff g,#f83d44ff ``` ```image f ca afa fa ac a a a fa af ac a a gc fa a ac cg a be a fa ebe ca ac ebb a a dbb fa fa dbb af ac dbbd a a dbbd af fa bbd a ac bbe gc a bbe a fa ebe cg ac ebe a a ebb fa aebb ac fa dbb a af dbbd fa a dbbd ac af bbd a a bbd fa gc bbd ac a bbd a cg dbbd fa a dbbd ac fa dbbd a a dbb fa fa dbb ac af dbb a a dbb fa af dbb ac a dbb a gc dbba a dbb cg gbb a faebb fa ac ebb a a ebe fa fa ebe af ac ebe a a ebe af fa eb a ac gc a a fa cg ac a a fa fa a ac fa a af fa a ac af a a fa gc ac a a cg fa a g fa a fa af a af a gc a cg a fa a ```

Hmm, I'm not sure what to expect from this image. Let's see if any lines cross. I've noticed 1 areas of interest. These could be potential intersection zones.  ```palette Key,Color ,#fefefeff a,#0606fdff b,#fe0808ff c,#ffaaaaff d,#8c8ff9ff e,#4244f5ff f,#f75f5bff g,#acd4abff ``` ```image c bc b bc cb b cb b eae ff da eae b da eae ff da eae b da eae bc da dae b da dae bc da dae cb a dae b a dae cb a dae b a dae ff a daa b a daa gggbfggggggggggga daa ggggbggggggggggad daa ggggbfggggggggad daa gggggbgggggggadg daa gggggbggggggadgg daa ggggggbggggaeggg daa ggggggbgggaegggg daa ggggggfbgaeggggg daa gggggggbaegggggg d gggggggaeggggggg ggggggaebggggggg gggggaegbfgggggg ggggaagggbgggggg gggaaggggbfggggg ggeaggggggbggggg geagggggggbggggg eagggggggggbgggg eaggggggggggbgggg eagggggggggggfbggg da b da ff da b da ff e b bc b b cb b cb fb b bb ff cbc b bb ff cbc b bb bc cbc b bb b cbc cb bb b cbf cb bb b cbf ff bb b cbf bf bb b cbf bc bb b cbf b bb cb cbf b bb cb bf b fb ff bf b fb bc bf b fb bcbf b ```  Here's a close-up of the area A.  ```palette Key,Color ,#fefefeff a,#0705fdff b,#fe0405ff c,#ff9595ff d,#9191ffff e,#4441fcff f,#f83f46ff g,#e4d6f1ff ``` ```image fbc cbb fbc e cbb ea bbc eaa cbf eaad bbc daad cbf daad gbbg daad fbf daad gbbg daad fbc daad cbb daad fbc daad cbb daae bbcdaae cbfaae faae gaae gaaabg gaaefbf gaae gbbg gaae fbc gaae cbb gaaeg fbc gaaeg cbb geaag bbc geaag cbf eaag bbc eaag fbf eaag gbbg eaag fbf eaag gbbg aag fbc ag cbb d fbc ```  I observe an intersection inside area A. It was tricky, but I finally found one single intersection in the image.

1

```palette Key,Color ,#fefefeff a,#0606feff b,#ff0505ff c,#ff8d8dff d,#8f8fffff e,#4443fdff f,#ff4242ff g,#f8cfd6ff ``` ```image g bc b bg gb b cb b eae cf da eae b da eae fc da eae b da eae bc da dae b da dae bg ga dae gb ga dae b ga dae cb a dae b a dae cf a daa b ag daa fc ag daa b ad daa bc ad daa b ad daa bg ad daa gb ad daa b ad daa cb ae daa bae d ae aeb ae fc ae b ea bc ea b ea bg ea gb ea b ea cb da b da cf da b da fc e b bc b bg gb b cb cb b bb ff cbc b bb fc cbc b bb bc cbc gb bb bg cbc gb bb b cbc cf bb b gbc ff bb b gbc fc bb b gbc bg fb gb gbf bg fb gb gbf b fb cf gbf b fbg ff gbf b fbg fc gbf b fbg bcbf gbg ```

This is the image I'm working with. The goal is to count the intersections. I'd describe these as 'hotspots' for potential intersections.  ```palette Key,Color ,#fefefeff a,#ea5b55ff b,#0b0cfcff c,#ffb0b0ff d,#777ef2ff e,#fc0808ff f,#9cc398ff g,#b1d7b1ff ``` ```image d bb bb dbd dbd bb bb bbd dbd gbb bb bbd dbd dbb fgggggggggggggggggggggggggggggf bb fgggggggggggggggggggggggggggggf bbg fgggggggggggggfeggggggggggggggbbd fgggggggggggggeaeaggggggggggdbb fggggggggggggaeggeegggggggfbbgf fggggggggggggeggggaegggggbbfggf fgggggggggggaegggggfeagbbdggggf fgggggggggggeggggggggabbggggggf fggggggggggeaggggggfbbaeggggggf fggggggggggeggggggbbfggfeaggggf fgggggggggefggggbbdggggggeegggf fggggggggfegggdbdgggggggggaeggf fggggggggeggdbbggggggggggggfeaf fgggggggaedbbggggggggggggggggee fgggggggebbgggggggggggggggggggae fgggggfbbgggggggggggggggggggggfcec fggggbbeggggggggggggggggggggggf ee fggbbfeaggggggggggggggggggggggf ae fbbdgfegggggggggggggggggggggggf cec bbdgggefgggggggggggggggggggggggf ee bbdfgggaeggggggggggggggggggggggggf ae dbd fgggegggggggggggggggggggggggggf cec dbd fggaagggggggggggggggggggggggggf ee dbb fggeggggggggggggggggggggggggggf ae dbb fgeaggggggggggggggggggggggggggf cec dbb ffegggggggggggggggggggggggggggf ee bb fefgggggggggggggggggggggggggggf ae bb aeggggggggggggggggggggggggggggf cec bb e ee bbg aa ae bd e cec ea ee e ae ec cec ce ee e a ae e aa e ec ce e ce e aa e ec e ec ce e aa e ea e ec ce e ae e aa e ec ce e ```  Eureka! Let's inspect this close up of area A  ```palette Key,Color ,#fefefeff a,#fa4247ff b,#0605feff c,#f3cfdaff d,#9390fcff e,#fe0506ff f,#443bf5ff g,#fd8c8eff ``` ```image cc ceea aeeeac d ceegeeeg dbb aea caeea cfbbb geec geeac cfbbbd eeg ceeeg dbbbf gee aeea dbbbfc ceeg geeac dfbbfd aea ceeeg cfbbbd ceec aeeadbbbd aea gabbbfc ceec dfbbbag aeg cfbbbdaeea gee fbbbd geeac eeg dbbbfc ceeeg gea dbbbfc aeea ceec cfbbbd geeac aea fbbbd ceeeg ceec dbbbf aeea aeg dbbbfc geeac gee dbbbfd ceeeg eeg dbbbfd aee gee dbbbbd ge ceedfbbbd c aefbbbd dfbbbd cfbbbd cfbbbfc fbbbfeg dbbbfgee dbbbfcceeg dbbbfd aea dbbbfd ceec dbbbbd aea bbbd ceec bd aeg gee eeg gea ceec aea ceec aeg gee eeg gee ceeg aea ceec aea geec ```  Amazing! This area was hiding an intersection all along! Two intersections have been found!

2

```palette Key,Color ,#fefefeff a,#fa393eff b,#0808feff c,#ffcacaff d,#b0b0ffff e,#fe0203ff f,#5b5bffff g,#ff9393ff ``` ```image d bb bbd fbd dbf dbb bb fbd fbf dbb bb bbd fbf dbb bb bbd ce fbf egeg dbf ge ea bb e ae bbd aa ceg fbd e abf ag dbbae e bb ceg ec fbd ea ce fbf ae e dbb ceg gadbb ea abb ae dbb ceg bbe ea bbdeg ae bbd ce ceg bbd ec ea fbf ge ae fbf e ceg fbf aa ea fbf e ae dbb eg ceg dbb ce ea dbb ec ae bb ge ceg bbd e ea bbd aa ae bd e ceg ag ea e ae ec ceg ce ea e a ga e aa e eg ce ec ge e aa e eg ce ec ge e aa e ag e ec ce e ga e aa e eg ce ec ```

Alright, let's get to work and investigate this image for intersections. My next step is to analyze the details within each area.  ```palette Key,Color ,#fefefeff a,#0707feff b,#ec5d53ff c,#5557faff d,#ffb6b6ff e,#fe0303ff f,#aed5aeff g,#b3b3ffff ``` ```image ffffffffffffffff ffffffffffffffff ffffffffffffffff ffffffffffffffff fffffffffffeeebf ffffffffffebffbeed fffffffffebfffff beed ffffffffebffffff deeb fffffffebfffffff beed ffffffebffffffff eee fffffebfffffffff deeb ffffebffffffffff beed fffebfffffffffff deeb ffebffffffffffff deeb febfffffffffffff beed ebffffffffffffff deeb ebfffffffffffcfff beed edfffffffffffaaaff beed ed fffffffffffafcaf deeb ed ffffffffffacffca beed ed a ga ee ed ag gag ed ga ag ed a ac ed ga ac e a aa e cc ca de a ca de cc ga de a gag de ag ag de a ac de ag ac de ga aa de a ca de ga ca de a ga de ca ga de a ag b cc ag a ac ac aa a aa ag ca a ca ag ga ga ag a ag ga ac a ac cc aa a ca cc ca a ga ag gag a a ag ga a ga a ca a cc a ac a ag a ag ga a ga a cc a cc a ag a ag ga a ```  This close-up might reveal an intersection in area A.  ```palette Key,Color ,#fefefeff a,#0909ffff b,#ff5a5aff c,#a6a6ffff d,#ffa9a9ff e,#ff0202ff f,#4d4dffff g,#ff8181ff ``` ```image d deeeg deeeeeebd deeb dbeee deeb ge deeb deeb deeb deeb deeb deeb deeb deeb geeg geeg geeg geeg geeg geeg geeg geeg geeg beed beed beed eed ed ff d caaa aaaaac caa faac aac faac ```  I don't observe any intersections inside area A. After a thorough analysis, I conclude that there are no intersections in this image.

0

```palette Key,Color ,#fefefeff a,#0404ffff b,#ff5b5bff c,#7a7affff d,#ffb1b1ff e,#ff0303ff f,#3b3bffff g,#c3c3ffff ``` ```image d eeeb eb beed eb beed eb deeb eb beed eb eee eb deeb eb beed ed deeb ed deeb ed beed ed deeb ed f beed ed faa beed ed a fa deeb ed ag ca beed ed ga ga ee ed ag gag ed ga ag ed a ac e ca af e a aa e cf fa e a ca de fc ga de a gag de ac ag de a ac de ag af de ga af de ag fa de ga ca de a ca de cf gag de a ag b ff ac a af fc af a fa ag fa ga ca ag ga ga gag a ac ca ac a af cf aa a fa fc ca a ga ac gag a a ag ga ag ga a cf a ff a fc a ag ga ag ga a ca a cf a fc a ac a ag ga ag ```

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.  ```palette Key,Color ,#fefefeff a,#fd0706ff b,#6c75ebff c,#ee4b44ff d,#a2cca4ff e,#b2d7b2ff f,#0c0dfbff g,#e2988aff ``` ```image ffb fb fb f fb bf ff dffdddgadddffdddddddddddddddddddddddddddddddddddddd ffeeeeagageeffeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeed ffeeeegaeeageeffeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeed fbdeeeeageeeageebfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeed fe deeedaeeeeeaceebfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeed ef deeeageeeeeeaceebfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeed bf deeeaeeeeeeeeaceedfdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeed ff deeageeeeeeeeeaaeedfdeeeeeeeeeeeeeeeeeeeeeeeeeeeeed ff deeaeeeeeeeeeeeaaeedfdeeeeeeeeeeeeeeeeeeeeeeeeeeeed fb deageeeeeeeeeeeecaeeefbeeeeeeeeeeeeeeeeeeeeeeeeeeed fb deaeeeeeeeeeeeeeecaeeefbeeeeeeeeeeeeeeeeeeeeeeeeeed ef daceeeeeeeeeeeeeeecaeeefbeeeeeeeeeeeeeeeeeeeeeeeeed bf daeeeeeeeeeeeeeeeeegaeeeffeeeeeeeeeeeeeeeeeeeeeeeed bf cceeeeeeeeeeeeeeeeeegaeeeffeeeeeeeeeeeeeeeeeeeeeeed ff aeeeeeeeeeeeeeeeeeeeegadeeffeeeeeeeeeeeeeeeeeeeeeed fb cceeeeeeeeeeeeeeeeeeeeedageeffeeeeeeeeeeeeeeeeeeeeed fb adeeeeeeeeeeeeeeeeeeeeeeeageeffeeeeeeeeeeeeeeeeeeeed fe ccdeeeeeeeeeeeeeeeeeeeeeeeeageebfeeeeeeeeeeeeeeeeeeed bf a deeeeeeeeeeeeeeeeeeeeeeeeeaceebfeeeeeeeeeeeeeeeeeed bf gc deeeeeeeeeeeeeeeeeeeeeeeeeeaceebfeeeeeeeeeeeeeeeeed ff a deeeeeeeeeeeeeeeeeeeeeeeeeeeaceedfdeeeeeeeeeeeeeeed ff ga deeeeeeeeeeeeeeeeeeeeeeeeeeeeaaeedfdeeeeeeeeeeeeeed fb a deeeeeeeeeeeeeeeeeeeeeeeeeeeeeaaeedfdeeeeeeeeeeeeed fe ga deeeeeeeeeeeeeeeeeeeeeeeeeeeeeecaeeefbeeeeeeeeeeeed ef a deeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecaeeefbeeeeeeeeeeed bf ga deeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecaeeefbeeeeeeeeeed ff a deeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegaeeeffeeeeeeeeed b a deeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegaeeeffeeeeeeeed a deeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedadeeffeeeeeeed a deeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedageeffeeeeeed ag deeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeageeffeeeeed a deeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeageebfeeeed ag deeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaceebfeeed a deeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaceebfeed ag deeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaceedfdd a deeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaaeedfd cg deeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaaeedf a deeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecaeed cc deeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecaed a deeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecad cc dddddddddddddddddddddddddddddddddddddddddddddddddga a e gc a gc a ga a ga a ga a a a a ag a ag a ag a cg a cc a cc a gc a ga a ga a ga a ```  Eureka! Let's inspect this close up of area A  ```palette Key,Color ,#fefefeff a,#ff0505ff b,#5353feff c,#ff4343ff d,#ffc7c7ff e,#b1b1feff f,#0808feff g,#ff8686ff ``` ```image bffb daacd efff bffe caaaad fffe fffe daadcaad bffe efffe cac caad bffe ffb daad caad bffe fb cac caad bffe b daad caag bffe cac gaag bffb daad gaag effb gac gaag effb aad gaac effb gac daac effb aad daac effb gac daac efff aad daacd efff gac daaad fffe aag dcaad bffe gaa caad bffe aag caad bffe gaa caag bffe cag caag bffe daa gaag bffb cag gaag effb daa gaac effb cag gaac effb daa daac effb cag daac effb daad daac efff cac daacd fff daad daaad fffe cac caad bffe aad caad bffe ac caad bffe ad caag bffe c caag bffe d gaag bffb gaag effb gaac effb gaac effb daac effb daac effb daac efff daaad fffe daaad fffe caad bffe caad bffe caad bffe caag bffe caag bffe gaag bffb gaag effb gaac effb gaac effb daac effb daac effb daac efff daaad fffe daaad fffe caad bffe caad bffe caad bffe caag bffe caag bffe gaag bffb gaag effb gaac effb gaac effb daac effb daac efff daac efff daaad fff daaad ff caad b caad caad caag caag gaag gaag gaa ```  This isn't an intersection in area A, but I'm not discouraged. Zero, Nada.

0

```palette Key,Color ,#fefefeff a,#ff0505ff b,#4e4effff c,#ff4444ff d,#ffc6c6ff e,#acacffff f,#0606ffff g,#ff8888ff ``` ```image ffe fe fb efe fb ef fb bf dad ff ff adad bf fb da ad bf fb ad ag bf fe da ag ef ef ad ac ef bf a ac ef bf ad ac f ff a ca fe fb ag ca fe fe a ca fe efe cg ga fb ef a ga fb bf cg da fb ff a dad ff fb cc ad bf fe a ad bf efe gc ag bf ef a ag ef bf gc ac ef ff a ac ef fb ga aa f fb a ca fe fe da ca fe ef a ca fe bf da ga fb bf ad ga fb e da da fb ad dad ff a ad bf ad ad bf a ag bf ag ag ef a ac ef ag ac ef a aa fe cg ca f a ca cc ca a ga cc ga a d gc a gc a ga a da a da ad da ad a ad a ag a ag a cg a cc a cc a gc a gc a ga a da a ```

I'm on the case! Let's uncover any intersections hidden in this image. These zones indicate regions where lines appear to be in close proximity.  ```palette Key,Color ,#fefefeff a,#f06760ff b,#464af5ff c,#ffb8b8ff d,#fd0a09ff e,#0506feff f,#a3a6f9ff g,#afd6afff ``` ```image a cd d da cd d da cd d dc ad d dc ad d dc aa cd d da cd d da cd d dc ad d dc ad d d da cd d da cd d gggggggggggggggggggggggggggggg dc gggggggggggggggggggggggggggggg ad gggggggggggggggggggggggggggggg d gggggggggggggggggggggggggggggg dc agggggggggggggggggggggggggggggg ad adagggggggggggggggggggggggggggg d gddggggggggggggggggggggggggggg dc gggddggggggggggggggggggggggggg aa ggggadaggggggggggggggggggggggg cd ggggggddaggggggggggggggggggggg d ggggggggddgggggggggggggggggggg da gggggggggaddgggggggggggggggggg cd gggggggggggadagggggggggggggggg d gggggggggggggddggggggggggggggg da fgggggggggggggggddggggggggggggg cd fe begggggggggggggggadaggggggggggg d ee fefgggggggggggggggddgggggggggg dc bef ggeeggggggggggggggggddgggggggg ad feb gggbeggggggggggggggggadagggggg d ee ggggfebggggggggggggggggddagggg dc feb ggggggeegggggggggggggggggddggg ad ee gggggggbegggggggggggggggggaddg d bef gggggggggebgggggggggggggggggada dc feb ggggggggggeeggggggggggggggggggdd da ee gggggggggggbeggggggggggggggggg cdd cd fef gggggggggggggebggggggggggggggg add ee ggggggggggggggeegggggggggggggg c bef gggggggggggggggbeggggggggggggg feb eb ee ee fef fef ee eb bef be feb fef ee eb fef be ee fef bef eb feb be ee fef fef ee ee bef ```  Could this be where the intersection is hiding, in area A?  ```palette Key,Color ,#fefefeff a,#ff4646ff b,#5252ffff c,#ffc8c8ff d,#ff0606ff e,#0707ffff f,#adadffff g,#ff8787ff ``` ```image ac ddac gdddg cadddg caddac gddda adddg caddac gdddac gdddg cadddc cdddac gdddg cadddg cdddac gddda adddg caddac gdddac gdddg f cadddc eef gdddac beeb gdddg beeb cadddg feeef cdddac beeb gddda beeef adddg feeef caddac beeb gdddac feeef gdddg feeef cadddc beeb gdddac feeef gdddg feeef cadddg beeb cdddac feeef gddd feeef cad beeb c feeef beeb beeb feeef beeb beeb feeef beeb ```  No intersection in area A, but I'll keep looking. There's definitely not a single intersection on the image.

0

```palette Key,Color ,#fefefeff a,#ff4040ff b,#4949ffff c,#ffc7c7ff d,#ff0404ff e,#0505ffff f,#a8a8ffff g,#ff8585ff ``` ```image g cd dc aa cd d dg gd d dg gd d dc aa d dc aa cd d da cd d dg gd d dg gd d dc aa cd dc aa cd d dg cd d dg gd d dc g ad gdg d adc dc dd aa gda cd adc d dd aa cda cd adg d ddc dg f cdd gd fe be gdg d ee fef adc dg bef eb dd gd feb be gda d ee fef adc dc feb ee dd aa ee be cda cd bef fef adg dc feb ee dd aa ee be cda cd feb eb gdd ee ee c bef fe feb eb ee ee fef fef ee eb bef be feb fef ee eb fef be ee fef bef eb feb be ee fef fef ee ee bef ```

Hmm, I'm not sure what to expect from this image. Let's see if any lines cross. I'd describe these as 'hotspots' for potential intersections.  ```palette Key,Color ,#fefefeff a,#0707fdff b,#ec7a72ff c,#595defff d,#97c797ff e,#b7b7ffff f,#fb0c0bff g,#b1d6b0ff ``` ```image e ea aea ea ca ae ac a ae ae a a ea cc ca a ac cc ae a a ea ea a ca ea ae ae a a a ae ca a ac cc ae a a cc ea a ca ea ac a ae ea a ae ea a ca ae ae a a cc a a ca cc ac a ae ea a a ea ea ca ae ac a ae ae ddadddddddddddddddd a ggcaggggggggggggggg cc gggcagggggggggggggg a ggggacggggggggggggg cc gggggaggggggggggggg a ggggggagggggggggggg ea ggggggcaggggggggggg a gggggggacgggggggggg ea ggggggggacggggggggg ae gggggggggaggggggggg a gggggggggdagggggggg ae gbbbbbbbffffffffffcaffffggg a bffffffffffffffffffffffbbbbbbbbbbddgggggacgggggg cc ff ggggggggggggadggggg a bfg gggggggggggggaggggg cc ff gggggggggggggcagggg a ff ggggggggggggggcaggg ea bfb gggggggggggggggaggg a ff ggggggggggggggggggg ea bfg ggggggggggggggggggg ae gff ggggggggggggggggggg ddddddddddddadddddddg ff ggggggggggggggggggg gggggggggggacgggggggd bfb ggggggggggggggggggg gggggggggggaggggggggdff ddddddddddddddddddd ggggggggggccgggggggff ggggggggggaggggggbffd gggggggggcagggggffggd gggggggggaggggbfbgggd ggggggggcagggffgggggd ggggggggaggffdggggggd gggggggdabfbggggggggd gggggggaffggggggggggd ggggggbabgggggggggggd gggggfacggggggggggggd gggffdagggggggggggggd gggbgccgggggggggggggd gggggaggggggggggggggd ggggcaggggggggggggggd ggggagggggggggggggggd gggcagggggggggggggggd gggaggggggggggggggggd ggggggggggggggggggggd ggggggggggggggggggggd dgggggggggggggggggggd ```  Let's get to the bottom of what's happening inside area A.  ```palette Key,Color ,#fefefeff a,#0604fcff b,#f64c54ff c,#7a75f9ff d,#feb5b5ff e,#b4b4ffff f,#fd0607ff g,#3c3cfeff ``` ```image cag aae cag aae eaa gac eaa gac db eaa bff cag dfffb aae bfffd cag dfffb aae dbffbd cag bfffd aae dfffb eaa bfffd gac dfffb eaa dbffbd gac bfffd eaa dfffb cagbfffd aafffb caafbd baabd dfbaa bffaae dfffcaa dbffbdgac dffd eaa d gac eaa cag aae cag aae cag aae eaa gac eaa cc ```  Yes! I knew it! There's an intersection right here in area A! Let's move forward and inspect another region. I'm now examining the contents of area B in detail.  ```palette Key,Color ,#fefefeff a,#0504feff b,#fe4545ff c,#7c7afdff d,#ffa5a5ff e,#c5c3fdff f,#fe0405ff g,#3c34f6ff ``` ```image gag eaac eaae caae gag aag eaac caae caae gag eaac eaac caae gaa gag eaac eaae caae gag aag eaac caaeddddddddd bbbbbbbbfffffffffffffgaaffffffffb ffffffffffffffffffffffgagbbbbbbbd dddddddddd eaac eaac caae gaa gag eaac eaae caae gag aag eac e ```  An intersection is present within area B. Two intersections have been found!

2

```palette Key,Color ,#fefefeff a,#0404feff b,#fc4649ff c,#7878ffff d,#ffa4a4ff e,#bdbdffff f,#ff0404ff g,#3a37fbff ``` ```image e ca aea ea ca ae gg a ae ae a a ea gc ca a ac cg ae a a cg ea a gg ea ac ae a a ea ae ca a gg gc ae a a cg ea a ca cg ac a ae ea a ae ea a gg ae ac a a gc ea a ca cg gg a ae ca a a ea ea ca ae ac a ae ae a a ea gc gg a ac cg a a a ea ca a gg ea ae ae a a ea ae dddddddbbbbbbffffffgaffff a dffffffffffffffffffffbbbbbbddddddd ac gc ff ae a bfd a cg dfb ea a ff gg ea dfd a a ff ea bfd ae dfb a ff ae dfd a ff gc bfd a dfb cg ff a dfd ea ff a bfd eadfb abf bad fac bf a d gc a cg a ea a ```

I'm examining this image closely. My goal: find any and all intersections. These spots are like clues. Let's see what they reveal about potential intersections.  ```palette Key,Color ,#fefefeff a,#f73938ff b,#0c0dfdff c,#f79490ff d,#babaffff e,#fe0202ff f,#6770ecff g,#abd4abff ``` ```image c aa ec e e ce aa ec e e ce aa ec e e ce aa ec e b e bf ce fbd aa bb ec bf e dbd e bb ce bf aa dbd ec bb e bb e dbd ce fb aa bb ec dbf e fb e bb ce bf aa fb ec bb e bf bd eggggggggggggggggg dbd dbbbd cegggggggggggggggg bb dbbbd aagggggggggggggggbf dbbbd geaggggggggggggfbd dbbbd ggegggggggggggbbg dbbbd gggegggggggggbbgg dbbbd gggceggggggfbfggg dbbbd ggggcecgggbbggggg dbbbd ggggggeagbbgggggg dbbbd gggggggabfggggggg dbbbdggggggfbaeggggggg dbbbgggbbgggecggggg gfbbbfgggggeagggg ggggggggggggaeggg gggggggggggggcegg gggggggggggggggea ggggggggggggggggee gggggggggggggggggae ggggggggggggggggg cec ggggggggggggggggg ea ae ce ec ea ae ce ea ee ae ec ea ae ce ec ea ae cec ea ee ce e ```  Time to investigate area A up close.  ```palette Key,Color ,#fefefeff a,#fc3d40ff b,#0807fdff c,#fe8384ff d,#b5b5ffff e,#fe0405ff f,#5e5efeff g,#ffc9c9ff ``` ```image a ec eeg ceeg aea eea geec d ceeg fb ceeg fbb aea dbbbd eea fbbf geec fbbf ceec dbbbd ceea fbbbd geeeg fbbf gaeec dbbbd aeea dbbbd ceeafbbf gabbbd dbbbec fbbfceea bfd dbbbf ceeeg bbbbfd dbbbd gaeec dfbbbbbfdfbbf aeec dfbbbbbbf ceeag dfbbd geeeg gaeec aeea ceeag geee ae c ```  Amazing! This area was hiding an intersection all along! I've found a single intersection point in the image.

1

```palette Key,Color ,#fefefeff a,#fd3739ff b,#0a0affff c,#fe9192ff d,#b4b5ffff e,#ff0202ff f,#5555ffff g,#fadbe0ff ``` ```image c aa ec eg ge ce aa ec eg ge ce aa ec eg ge ce aa ec eg b ge bf ce fbg aa bb ec bf eg dbd ge bb ce bf aa dbd ec fb eg bf ge dbd ce fb aa bb ec dbd eg fb ge bb ce gbf aa fbg ec bb eg bf bd ge dbd gfbbd ce bb gbbbd aa bf dbbbd ec dbd dbbbd eg fb dbbbd ge bf dbbbd ce dbd dbbbd ceg fb dbbbd ea bb dbbbd abd dbbbd fbceg dbbbd bb gec dbbbf ea ae ceg gec ee ae gec ea ae ceg gec ea ae ceg ea ee ae gec ea ae ceg gec ea ae ceg ea ee ceg ge ```

I'm examining this image closely. My goal: find any and all intersections. I wonder what's going on inside those areas? Perhaps intersections are hiding there.  ```palette Key,Color ,#fefefeff a,#0708fdff b,#e66659ff c,#a1a6f6ff d,#b1d7b1ff e,#4f57efff f,#f90b0cff g,#9cc396ff ``` ```image gddddddddddddddd ddddddddddddddddddddddddddddddddddddddddd gddddddddddddddd ddddddddddddddddddddddddddddddddddddddddd gddddddddddddddd ddddddddddddddddddddddddddddddddddddddddd gddddddddddddddd ddddddddddddddddddddddddddddddddddddedddd gddddddddddddddd ddddddddddddddddddddddddddddddddddddadddd gddddddddddddddd dddddddddddddddddddddddddddddddddddafdddd gddddddddddddddd ddddddddddddddddddddddddddddddddddgagdddd gddddddddddddddd dddddddddddddddddddddddddddddddddgagddddd gddddddddddddddd ddddddddddddddddddddddddddddddddbfadddddd gddddddddddddddd dddddddddddddddddddddddddddddddbfaddddddd gddddddddddddddd ddddddddddddddddddddddddddddddffeaddddddd gddddddddddddddd dddddddddddddddddddddddddddddffdadddddddd gddddddddddddddd ddddddddddddddddddddddddddddfbdeedddddddd gddddddddddddddd dddddddddddddddddddddddddddfbddaddddddddd gddddddddddddddd dddddddddddddddddddddddddgfgddaeddddddddd gddddddddddddddd ddddddddddddddddddddddddgfgdddadddddddddd gddddddddddddddd dddddddddddddddddddddddbfddddagdddddddddd gddddddddddddddd ddddddddddddddddddddddbfddddcaddddddddddd fddddddddddddddd dddddddddddddddddddddffdddddadddddddddddd bfbddddddddddddd ddddddddddddddddddddffdddddeadddddddddddd gdffdddddddddddd dddddddddddddddddddfbddddddaddddddddddddd gddbfgdddddddddd ddddddddddddddddddfbddddddeeddddddddddddd gddddffddddddddd ddddddddddddddddgfgdddddddadddddddddddddd gdddddffdddddddd dddddddddddddddgfgdddddddaedddddddddddddd gddddddgfbdddddd ddddddddddddddbfdddddddddaddddddddddddddd gddddddddffddddd dddddddddddddbfdddddddddacddddddddddddddd gdddddddddbfgddd ddddddddddddffdddddddddcadddddddddddddddd gdddddddddddffdd dddddddddddffddddddddddaddddddddddddddddd gddddddddddddbfg ddddddddddfbddddddddddeaddddddddddddddddd gdddddddddddddgfb dddddddddfbdddddddddddadddddddddddddddddd gdddddddddddddddff dddddddgfgdddddddddddeedddddddddddddddddd gddddddddddddddd dfb ddddddgfdddddddddddddaddddddddddddddddddd gddddddddddddddd ff dddddbfdddddddddddddaeddddddddddddddddddd gddddddddddddddd bf ddddbfddddddddddddddadddddddddddddddddddd gddddddddddddddd fb dddffddddddddddddddacdddddddddddddddddddd gddddddddddddddd ff ddffddddddddddddddgaddddddddddddddddddddd gddddddddddddddd dfb dfbdddddddddddddddadddddddddddddddddddddd gddddddddddddddd ff fbdddddddddddddddeadddddddddddddddddddddd gddddddddddddddd bfd fgggggggggggggggggaggggggggggggggggggggggg gddddddddddddddd ff df ee gddddddddddddddd bf bf a gddddddddddddddd fb bf ee gddddddddddddddd ff ff a eddddddddddddddd dfff ac eadddddddddddddd b a gaaddddddddddddd a gdaadddddddddddd ca gddaeddddddddddd a gdddaedddddddddd ea gddddaeddddddddd a gdddddacdddddddd ee gddddddagddddddd a gdddddddaddddddd ac gdddddddgagddddg a ca ac ca ca ca a ea ca ea a aa ee ae a ae ac ac a ac ac ac ca a a a ca ca a ca ee ca a ea ae ea a aa ac ae ca ae a ac ca ac a ac ee a a a ee a a caac ca ```  Let's see what secrets area A holds.  ```palette Key,Color ,#fefefeff a,#0707ffff b,#ff3a3aff c,#ababffff d,#ff8484ff e,#4141ffff f,#ff0505ff g,#ffc8c8ff ``` ```image bd gfffd bffb dfff gbfd dfbg fffd bffbg dfffd gbffb dfffg gbffd dffbg gfffd bffb dffg gbfd ffbg gfffd dfff gbf d cc aac eaac eaa eaa eae aae aa cae cae caac caac caac eaac eaac eaac eaa eaa aae ```  Based on this close-up, I can conclude that there's no intersection in area A. One intersection, that's it, but I found it.

1

```palette Key,Color ,#fefefeff a,#0505feff b,#f93e44ff c,#8585ffff d,#ffa3a3ff e,#4040ffff f,#ff0505ff g,#c9c8fdff ``` ```image c a ab gad dag dba bfa bfce fb a fb ee fd a fd ac df ga df ag bf ga b bf a dfd fb ca ff fb a dfd fd ee fb fd a bf df ac dfd df a ff bf ag dfd bf ga fb fb a bf fb ca fb fd a ff fd ee dfd df a ff df ec bfd bf a fb ff ag bf fb ga dfd fb ag ff fd ca dfd fd a fb df ce bf df a fb bf ec ff ff a c dffb ac ea d ga ea ag ae ga ae a ac ce ac a ag ee ag a a ac ga ga ga ag ca ga ca a ea ca ea a ee ee ae a ac ac ac a ag ag ag ga ag a ga ca ga a ga ee ca a ca ec ea a ea ag ae ga ae ag ac ca ac a ag ce ag a a ec ga a gaac ca ```

I have a feeling there might be some intersections in this image. Could these regions be concealing intersection points? Let's find out.  ```palette Key,Color ,#fefefeff a,#5d63f1ff b,#fd0707ff c,#f85956ff d,#afd6afff e,#0909fdff f,#f09f9cff g,#b9b9fdff ``` ```image fcbbbbbf cbbbbf bbf fcbbbc bbf fcbbbcf bbf fbbbbf bbf ddddddddddddddddddd fcbbbcf bbf ddddddddddddddddddd cbbbbf bbc dddddddddddddddddde bbbbc cbc dddddddddddddddddea f cbc ddddddddddddddddead cbc dddddddddddddddeadd cbc ddddddddddddddeeddd cbcdddddddddddddaedddd cbbddddddddddaeddddd dcbbdddddddaedddddd dddcbbdddddeddddddd dddddcbbddedddddddd dddddddcbeddddddddd ddddddddefbbddddddd dddddddeaddfbbddddd ddddddeadddddfbbddd dddddeaddddddddfbbd ddddeedddddddddddfb dddeedddddddddddddd ddaeddddddddddddddd daedddddddddddddddd aeddddddddddddddddd gedddddddddddddddddd eddddddddddddddddddd egddddddddddddddddddd eg ddddddddddddddddddd ea ea ea ee ae ae ge ge e eg eg eg ea ea ee ae ae ge ge e e eg eg ea gea ae ea aeg ee aeg ee geg ee gea ee gea ee ea aeg ee aeg ee aeg ee geg ee gea ee ea ```  I'm going to scrutinize area A for any signs of an intersection.  ```palette Key,Color ,#fefefeff a,#3e3dfdff b,#fe0506ff c,#ff3838ff d,#7f7fffff e,#0504fdff f,#fc9799ff g,#c4c4feff ``` ```image a de dee deed geed geed geea geea aea aee f aeeg bcf aeeg bbbcf deeg fbbbcf deeg fbbbcf deed fbbbcf geed fbbbcf geed fbbbcf geea fbbbbf geea fbbbbfaea fbbeeeg aeebbf aeefcbbbf deeg fcbbbf deeg fcbbbf deed fcbbbf geed fcbbbf geed fcbbbc geea fcbbbc geea fcbb eea fc aea aeeg aeeg deeg deeg deed geed geed geea eea ea a g ```  Aha! I've found an intersection inside area A! After careful examination, I conclude that there is one intersection.

1

```palette Key,Color ,#fefefeff a,#4242ffff b,#fe0808ff c,#ff5f5fff d,#8686ffff e,#0505ffff f,#fcaaacff g,#c9c9feff ``` ```image f fcbbbbbf cbbbbf bbf fbbbbc bbf fcbbbcf bbf cbbbbc bbf fcbbbcf bbc cbbbbf bbc e bbbbc bbc ed f cbc ed cbc ea cbc aa cbc ae cbc de cbb de cbb ge fbb ge fbeg efbb eg fbb ed fbb ea fbb ea fb ae ae de ge ge e eg eg ed ea ea ae ae de ge ge e eg eg ed ed ea ae ae de de ge ge eg eg ed ed gea ae ea aeg ea deg ee ded ee ged ee ged ae gea aeg ea deg ee deg ee ded ee ged ae ea ```

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

0

```palette Key,Color ,#fefefeff a,#ff3838ff b,#0505ffff c,#a7a7ffff d,#ff7878ff e,#5353ffff f,#ff0303ff g,#ffc0c0ff ``` ```image g gdffffa gdaffffdg daffffdg gaffffag gdffffad gdffffadg gdaffffdg gggddaafffffffdg ggddaaffffffffffffaadddgg ffffffffaadddgg e ebbbec cbbbec cebbbc cebbbe ebbbe ebbbec cbbbec cccceeebbbbbbbb cbbbbc cccceeebbbbbbbbbbbbbbbbeeecccc cebbbbbbbbbeeeeccc ```

Time to put on my detective hat and find those intersection points! I can confidently say that there are no intersections in this image.

0

```palette Key,Color ,#fefefeff a,#ff0606ff b,#0707ffff c,#ff8383ff d,#5e5effff e,#ffc8c8ff f,#ff4242ff g,#b6b7ffff ``` ```image g db bd bg b b gb db bd bd bg b gb db db bd bg b b gb db bd bd bg c b ff gb ae db a db ff bd ae bg ea b ff b a gb ea db ac bd a bd gdbbb ea bg gdbbbbdg ac b gdbbbbdg a gb gdbbbbbd ca db gdbbbbdg ac db gdbbbbdg a bd dbbbbbdg ca bddbbbbdg ae dg a ca ae a f ff aa ae eac a fa ff af ae cae ea aa ff eac a fa ea aa ac eac a fa ea af ac cae a aa ca eac ac fa a aa ca eac ae fa a af ca cae ae aa a eac ff fa ae aa a eac ff fa ae af ea cae ff aa aeac eae ```

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.  ```palette Key,Color ,#fefefeff a,#f94a47ff b,#0708feff c,#fe0404ff d,#6064f7ff e,#fdacabff f,#b5b5ffff g,#abd2abff ``` ```image gggggggggggggggg gddbbbbbbbbbdggg fdbbbbbbdgggggggggdbbbdf fdbbbbbdf ggggggggggggggggdbbbbf fdbbbbbdf gggggggggggggggg fdbbbd fdbbbbbddf gggggggggggggggg dbbbdf bbbdf gggggggggggggggg fbbbbd gggggggacggggggg fdbbbdf gggggggcaagggggg dbbbbf ggggggcegcgggggg fdbbbdf gggggacgggcggggg dbbbb gggggcggggcagggg f ggggcggggggcgggg gggacggggggaaggg gggcggggggggcggg ggcggggggggggcgg gacggggggggggcag c c c aa aa c c ec c ce aa c ec aa c c aa ec ec ce c c ca aa ec c c ec ca ce ec c c aa ce c ec ec c ce ce c ec aa c c ce ec ec ce c c ce aa ac c c ec ce ce ac c c aa ce c aa ec c ce ce c aa aa c c c ec aa ce c c c aa aa c e ec ce c aa c ec ce c aa c ec ce c aa c ec ce c aa c ```  This is a magnified view of the region A.  ```palette Key,Color ,#fefefeff a,#ff2929ff b,#0404feff c,#fe0303ff d,#4e4effff e,#ffbabaff f,#a7a7ffff g,#ff6b6bff ``` ```image ff fffddbbbbbddf ffddbbbbbbbbbbbbbbbbbdff bbbbbbbbbddff fddbbbbbbddf bbddfff ffdbbbbbb fddb aa gccg ecccce acggca gca cce ecce gcc acg acg gca ecce ecce gca acg cce gca gcc ecce acg ccg ecce gca gca ecce cce ccg gcc gca acg ecce ecce ccg gca ```  Darn it! This close-up doesn't show any intersections in area A. My final answer is: no intersections found.

0

```palette Key,Color ,#fefefeff a,#ff4949ff b,#0303ffff c,#ff0303ff d,#7575ffff e,#ffaeaeff f,#babaffff g,#3838ffff ``` ```image f fdbbbbbbbbbd fdgbbbbgdf fgbbbdf dgbbbbbdf dbbbgf fdbbbbbgf fgbbbd fdgbbbbgdf dbbbgf bbgdf fgbbbd ac fdbbbgf caa dbbbgd ce c fgbbbdf ac ec dbbbg c ce f ce c aa aa c c ce ec aa ce c c c aa aa c c ec c ce aa c ec aa c c aa ec ec ce c c ca aa ec c c ec ca ce ec c c aa ce c ec ec c ce ce c ec aa c c ce ec ec ce c c ce aa ac c c ec ce ce ac c c aa ce c aa ec c ce ce c aa aa c c c ec aa ce c c c aa aa c e ec ce c aa c ec ce c aa c ec ce c aa c ec ce c aa c ```

This image seems promising for intersection detection. I'm going to focus my attention on these specific areas.  ```palette Key,Color ,#fefefeff a,#4c4ef5ff b,#fe0909ff c,#fca7a6ff d,#a5a6fbff e,#f7615eff f,#0706feff g,#acd3acff ``` ```image cbbbb ebbbc cb cbbbe bc ebbbc b cbbbe cb ebbbc bc cbbbe b ebbbc eb cbbbe bc ebbec b bc eb bc b eb b b ee b b be b cb be f b fd cb fa be df b f cb f bc fd b af cb df bc f b fd eb aa ggbegggggggggafg gggbgggggggggfgg gggebgggggggfggg ggggbggggggfaggg gggggbggggafgggg gggggebgggfggggg ggggggbggfgggggg gggggggbfagggggg gggggggafggggggg ggggggdfbggggggg ggggggfggbgggggg gggggfdggbeggggg fd ggggfaggggbggggg fd gggafggggggbgggg fa gggfgggggggbeggg fa ggfgggggggggbggg ff gfagggggggggcbgg af af be af df b df f cb df fd bc fd aa b fd df cb fa f bc fa fd b ff fa eb af df bc df f b df f eb fd fa bc fd af b fa df eb fa f b ff fd af aa af df df f df fd fd fa fd af fa f fa f ff fd afaf df ```  I wonder what we'll find inside area A?  ```palette Key,Color ,#fefefeff a,#4c49fcff b,#fd0a0bff c,#ffbabaff d,#8f8cfbff e,#fc6568ff f,#0706fdff g,#ceceffff ``` ```image bbe affg cbbc dffg ebb gffd bbe ffa cbbc aff ebb dffg bbe gffd cbbc gffa ebb afa bbe dffg cbbc dffd ebb gffd bbe afa cbbc affg ebb dffg bbeffd cbffa aff dffbc gffdbb gffa ebe afa cbbc affg ebb dffg bbe gffd cbbc ffa ebb aff bbe dffg cbbc gffd ebb ffa bbe aff cbbc dffg ebb gffd bbe gffa cbbc ```  Case closed! This is definitely an intersection point in area A. I've found a single intersection point in the image.

1

```palette Key,Color ,#fefefeff a,#4341fdff b,#ff0909ff c,#ffb1b1ff d,#8686ffff e,#ff6363ff f,#0606feff g,#ccccffff ``` ```image c cbbbb ebbbc cb cbbbe bc ebbbc b cbbbe cb ebbbc bc cbbbe b ebbbc eb cbbbe bc ebbec b be eb bc b eb bc b ee b cb be b cb be f b fg cb fa be df b gf cb fg bc fd b af cb gf bc f b fd eb aa bc df b f eb fg bc fa b df eb gf bc f bfd af gfb f cb fg be fg aa b fd df cb fd f be fa fg b ff fd cb af df be df gf b df f cb gfg fd bc fg aa b fd gf cb fa f bc fa fg b af fa eb af df bc df gf b gf fg eb gfg fd bc fd af b fd gf eb fa f b ff fd af aa af df df f gfg fg gfg fa fd df fa gf fa fg ff fd afaf df ```

I'm on the case! Let's uncover any intersections hidden in this image. After a thorough analysis, I conclude that there are no intersections in this image.

0

```palette Key,Color ,#fefefeff a,#ff0606ff b,#4f4fffff c,#ff8484ff d,#a2a2ffff e,#ffbfbfff f,#ff4747ff g,#0404ffff ``` ```image d ddbgggggb dbggggggbd dbggggggbd dbbgggggbdd ddbgggggbbd dbggggggbd dbggggggbd dbbgggggbdd ddbgggggbbd dbggggggbd ggbd e af ae a ea ff ac a ea fa ac a a ca af ae a ea ff ae a ea fa ac a ea ca af ae a ca ff ae a ea fa ac a ea ca af ae a ecf ca eecfaaaaaaafc ff ecfaaaaaaafce ae ecfaaaaaaafce a ecfaaaaaaafcee eaaaafce ```

Hmm, I'm not sure what to expect from this image. Let's see if any lines cross. I've spotted 1 narrow regions that might be worth examining further. Let's call them area A.  ```palette Key,Color ,#fefefeff a,#f35c57ff b,#0808feff c,#acacffff d,#fdafaeff e,#fd0908ff f,#585bf9ff g,#add4acff ``` ```image d ed e ea e ea e aa e aa e aa e aa e aa e aa a e de aa e e e ae ed e ea ae ae e de de e e ed de ea e ae de de e e de e e ed de ea e ae de de e e c de ed bf e ea bf de ae bc ed de b de e b ed e cb e ed fb ed ea bb e ae bf ed de bc e e b ed ed b e ea cb ed ae fb e de fb ed e bf e e bc eagggggggggggggg ed b gegggggggggggggg ea b geaggggggggggggg ae cb ggeggggggggggggg de fb ggeagggggggggggg e fb gggegggggggggggg ed bf gggeaggggggggggg ea f bc ggggegggggggggggae bbf bc ggggeagggggggggae cbbc b gggggeggggggggge fbb cb gggggeagggggggeg bbf cb ggggggeggggggeag cbbc fb ggggggaaggggeegg fbb bfgggggggegggaeggg bbf bfggggggaaggegggg cbbc bgggggggegeggggg fbb gbggggggaedggggg bbf ggbggggggagggggg cbbc ggfbgggggggggggg fbb gggfbggggggggggg bbf ggggbbgggggggggg cbbc gggggbfggggggggg fbb bc bbf b cbbc b fbb cbf ```  Let's zoom in on area A to get a clearer view.  ```palette Key,Color ,#fefefeff a,#ff4848ff b,#0807ffff c,#9f9fffff d,#ffcdcdff e,#ff0606ff f,#4d4dffff g,#ff8f8fff ``` ```image gee eeg gee eeg gee eeg gee eeg gee eeg gee aeg gee aeg gee aeg dee aeg deed d aeg e deed ae aea aee deed geed aea deeg deed deea aea aea deed aeed aea geed f deed geeg bc aea deeg bbc deed eea fbbc aea aee fbb deeaeed fbb aeeed bbf deeg bbf gg cbbc cbbc cbbc fbb fbb bbf bbf ```  There is no intersection present within area A. There's definitely not a single intersection on the image.

0

```palette Key,Color ,#fefefeff a,#ff3838ff b,#0808ffff c,#acacffff d,#ffc0c0ff e,#ff0404ff f,#5959ffff g,#ff7777ff ``` ```image d ag e ag e ag e ag e ag e ag e aa e ga e ga g e de ga e e ed ga eg e aa ga ge e de ga e e ed ge eg e ae de de e e de ed e eg de aa e ge de de e e c de ed bf ed eg bf de ae bc ed de b de e b ed ed cb de eg fb ed aa bb de ge bf ed de bc e e b ed ed b e eg cb ed ae fb e de fb ed e bf e ed bc eg eg b e aa b eg ge cb e de fb ag e fb e ed bf ag eg f bc e ae bbf bc ag de cbbc b e e fbb cb ag ed bbf cb e eg cbbc fb ag aa fbb bf e ge bbf bc ag de cbbc bc e e fbb b ged bbf cb g cbbc cb fbb fb bbf bf cbbc bf fbb bc bbf b cbbc b fbb cbf ```

Time to put on my detective hat and find those intersection points! My next step is to analyze the details within each area.  ```palette Key,Color ,#fefefeff a,#0607fdff b,#fb0b0aff c,#8e98eaff d,#b0d6b0ff e,#edf1f0ff f,#e37062ff g,#454cf1ff ``` ```image e edfbbbbfdddddddddddddddddddddddddddddddddddddddddde efbbbfddddbfddddddddddddddddddddddddddddddddddddddddde dbbbbf edddddddbfdddddddddddddddddddddddddddddddddddddddde fbbbbf eddddddddbbddddddddddddddddddddddddddddddddddddddde fbbbfe edddddddddbbdddddddddddddddddddddddddddddddddddddde efbbbfe eddddddddddbbddddddddddddddddddddddddddddddddddddde efbbbfe edddddddddddbbdddddddddddddddddddddddddddddddddddde fbbbbf eddddddddddddfbddddddddddddddddddddddddddddddddddde bbbd edddddddddddddfbdddddddddddddddddddddddddddddddddde eddddddddddddddfbddddddddddddddddddddddddddddddddde edddddddddddddddfbdddddddddddddddddddddddddddddddde edddddddddddddddddbddddddddddddddddddddddddddddddde edddddaddddddddddddbdddddddddddddddddddddddddddddde eddddaaaddddddddddddbfdddddddddddddddddddddddddddde eddddadgaddddddddddddbfddddddddddddddddddddddddddde edddacddgaddddddddddddbfdddddddddddddddddddddddddde eddcaddddgaddddddddddddbfddddddddddddddddddddddddde eddaddddddgaddddddddddddbbdddddddddddddddddddddddde edcadddddddcaddddddddddddbbddddddddddddddddddddddde edadddddddddcaddddddddddddbbdddddddddddddddddddddde egaddddddddddcaddddddddddddbbddddddddddddddddddddde eaddddddddddddcaddddddddddddfbdddddddddddddddddddde ggddddddddddddddaddddddddddddfbddddddddddddddddddde addddddddddddddddacdddddddddddfbdddddddddddddddddde gcdddddddddddddddddacdddddddddddfbddddddddddddddddde aeddddddddddddddddddacddddddddddddbdddddddddddddddde acedddddddddddddddddddacddddddddddddbddddddddddddddde ea eddddddddddddddddddddagddddddddddddbfddddddddddddde ae edddddddddddddddddddddagddddddddddddbfdddddddddddde ca eddddddddddddddddddddddagddddddddddddbfddddddddddde ae edddddddddddddddddddddddagddddddddddddbfdddddddddde ca eddddddddddddddddddddddddaaddddddddddddbbddddddddde a edddddddddddddddddddddddddaaddddddddddddbbdddddddde gg eddddddddddddddddddddddddddaaddddddddddddbbddddddde a edddddddddddddddddddddddddddgaddddddddddddbbdddddde gg eddddddddddddddddddddddddddddgaddddddddddddfbddddde a edddddddddddddddddddddddddddddgaddddddddddddfbdddde ac eddddddddddddddddddddddddddddddgaddddddddddddfbddde ea edddddddddddddddddddddddddddddddgaddddddddddddfbdde ac eddddddddddddddddddddddddddddddddcadddddddddddddbde ea edddddddddddddddddddddddddddddddddcadddddddddddddbe ae eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecaeeeeeeeeeeeee ca eae ae eae ca eae a ac gg ac a ac gc ac a ag ac ag ea ag ae aa ea aa ae g ca a cg a gg a ac ea ac ea ae ca ae ca a gg a gg a ac ea ac ea ae ```  Let's see if area A yields any clues.  ```palette Key,Color ,#fefefeff a,#0707ffff b,#ff0404ff c,#5c5cffff d,#ffbebeff e,#b4b4ffff f,#ff7979ff g,#ff3838ff ``` ```image dfgbbbd dfgbbbbbbbbf fgbbbbbgffd fbbf bbbgfd fbbf fd fbbf dbbg dbbg dbbg dbbg dbbgd dgbbd gbbd gbbd gbbd gbbd fbbf fbbf fbbf fbbf dbbg dbbg dbbg dbbg dbbg dgbbd cae gbbd eaaae gbbd aaaaae gbbd caa caae gbbd aae caae fbbf caa caae fbbf aae caae fbbf cac caae fbbf eaae caae dbbg cac caac dbbg eaa caac dbbg cac eaac dbbg eaa eaac dbbg aac eaac dgbbd eaa eaac gbbd aae eaac gbbd caa eaac gbbd aae eaac gbbd cac eaaa fbbf eaae eaaa fbbf cac aaa fbbf aae aaae fbbf ac aaae fbbg a caae dbbg c caae dbbg caae dbbg caae dbbg caae dbbbd caae gbbd caae gbbd caac gbbd caac gbbd eaac gbbf eaac fbbf eaac fbbf eaac fbbf eaac fbbf eaac dbbg eaaa dbbg eaaa dbbg eaaa dbbg aaae dbbgd aaae gbbd aaae gbbd caae gbbd caae gbbd caae gbbd caae fbbf caae fbbf caae fbbf caac fbbf caac dbbg eaac dbbg eaac dbbg eaac dbbg eaac dbb ```  After careful examination, I've determined that there's no intersection in area A. I'm extremely confident. No intersections at all.

0

```palette Key,Color ,#fefefeff a,#0404ffff b,#ff0707ff c,#7c7cffff d,#ffb3b3ff e,#c1c1ffff f,#ff5a5aff g,#3a3affff ``` ```image d fbbbbd dfbbbf bf dfbbbf bf dbbbbd bf fbbbfd bb fbbbfd bb dfbbbf fb dbbbbd fb bbfd fb db db db g bd aaa bd a ga bd ae ga bf ea ca bf ae ca bf ea ca bb a ea bb cg ea fb a ea fb gg eae fb a ae db gc ae db a ae db ae ac bd a ac bd ae ac bd ea ag bf a ag bf ca ag bf a ag bb cg ga bb a ga fb gc ga fb a ca fb ac ca db a ca db ae ea db ea ea b ae ea ea ea a ae cg ae a ae gg ae a ac gc ac a ac ac ag a ag ae ag ea ga a g ca a cg a gg a gc a ae ea ae ea a ca a cg a gc a ac a ae ea a ```

I'm optimistic that I'll find some intersections in this image. The image has some tight areas where segments are too close. I should investigate those closely.  ```palette Key,Color ,#fefefeff a,#ef645fff b,#5759f2ff c,#0708fdff d,#fc0909ff e,#feb4b4ff f,#b0b1fcff g,#afd6afff ``` ```image gggggggggggggggggg gggggggggggggggggg gggggggggggggggggg gggagggggggggggggg gggcbdddaggggggggg ggggcggadddddagggg ggggbcggggggaddddde gggggcgggggggggggaddddae ggggggcggggggggggg eddddae ggggggcbgggggggggg addddae gggggggcgggggggggg addddae gggggggbcggggggggg add ggggggggcggggggggg aa gggggggggcgggggggg d gggggggggcbggggggg ed ggggggggggcggggggg de ggggggggggbcgggggg d gggggggggggcgggggg aa fc d cf ed c de bb d c ad fc d cf ed c da bb d c ad fc de cf d c da bb d c ed fc de cf d c aa cb d c ed bc de c d c aa cb d c ed bc de c d fc ad cf d c ed bb da c d fc ad cf de c d bb da c d fc ed cf de c d bb aa c d fc ed cf de c d cb aa ccb ggdggggggggggggggg bccf gggdgggggggggggggg fccb gggdaggggggggggggg bcc ggggdggggggggggggg fccf ggggadgggggggggggg bcc gggggdgggggggggggg fccf ggggggdggggggggggg ccb ggggggdagggggggggg bccf gggggggdgggggggggg fccb gggggggadggggggggg bccf ggggggggdggggggggg fccbgggggggggdgggggggg bccgggggggdaggggggg gbccbgggggdggggggg ggggcccgggadgggggg ggggggbccfgdgggggg gggggggggccbdggggg gggggggggggbccgggg gggggggggggggdgggg gggggggggggggggggg gggggggggggggggggg gggggggggggggggggg ```  Let's put area A under the microscope.  ```palette Key,Color ,#fefefeff a,#ff4a4aff b,#4c44f7ff c,#0706fdff d,#fe0303ff e,#e9d5eaff f,#9a96fbff g,#f78f96ff ``` ```image gf fccdaage eccbdddddaage fccggadddddddaage bcb eggadddddddagge eccf eggadddddddagge fcc egaaddddddd ccf egaadd fcce e bcb eccf fcc ccf fcce bcb eccf fcc ccf fcce bcb ecce bcb ccf fcce bcb ecce bcb eccf ```  An intersection is present within area A. Let's inspect the next region. Let's see what secrets area B holds.  ```palette Key,Color ,#fefefeff a,#f2323fff b,#5452fdff c,#0705fcff d,#fe0404ff e,#fecbcbff f,#a5a3fdff g,#fe8282ff ``` ```image eddg gdd adg edde gda ddg gdd ada edde gda ddg gdde ada edde gdd ddg edde ada eddg gdd adg edde ada eddg cbf gdd ccccf adg bccccbf edde fbcccbf gda fbccccb ddg fccccbf gdde fbccccb ada fccccbf edde fbccccf gda bccccbadg fbccccae fbccccb fccb gaa ae ```  The lines cross each other within area B, forming an intersection. I've identified a total of two intersection points.

2

```palette Key,Color ,#fefefeff a,#ff3d3dff b,#5450fbff c,#0707feff d,#fe0405ff e,#ffbebeff f,#a8a8ffff g,#fc7e80ff ``` ```image g cbddag c eadddae fc eadddae c gadddae c gadddae cf gddddge c gddddge bc egdd c aa fc d cf ed c de bb d c aa fc d cf ed c dg bb d c ga fc d cf ed c dg bb d c gd fc de cf d c ag bb d c gd fc de cf d c aa cb d c ed fc de c d c aa cf d c ed bc dg c d fc ga cf d c ed bb dg c d fc gd cf de c d bb ag c d fc gd cf de c d bb aa c d fc ed cf de c d bb aa ccb d bccf ed fccb dg bcc d fccf ga bcc de fccf ed ccb dg bccf d fccb gd bcc de fccb d bcc ag fccf d ccb gd fccf de ccbd bcc d ```

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.  ```palette Key,Color ,#fefefeff a,#f35652ff b,#0607fdff c,#fd0808ff d,#929be9ff e,#fdaaa9ff f,#4c50f6ff g,#add4adff ``` ```image e c ce ec c ec c aa c ce c ce ec c ac c aa c df ce fbbbd ec dbbd b c fbb db ec dbbd bf c ggggggggggggggg fbb b aa ggggggggggggggg dbbd b c ggggggggggggggg fbb fb ce ggggggggggggggg dbbf bd c ggggggggggggggg fbb b ce gggggggggggggdbbf db ec gggggggggggfbbd bf c ggggggggdbbfggg b aa gggcggfbbdggggg b c gggdbbfgggggggg fb ca gggbacggggggggg bd c gggggcagggggggg b ce ggggggcgggggggg dbgggggggggggcgg gggggggcggggggg gbfgggggggggcggg gggggggacgggggg ggbggggggggacggg ggggggggcaggggg gggbgggggggcgggg gggggggggcggggg gggfbgggggaagggg ggggggggggcgggg ggggbdggggcggggg ggggggggggacggg gggggbgggcaggggg gggggggggggccgg gggggdbggcgggggg ce ggggggbfcggggggg c gggggggbcggggggg ec gggggggcbggggggg ac ggggggacfbgggggg ce ggggggcggbdggggg c gggggcagggbggggg c gggggcggggdbgggg ac ggggcegggggbfggg ca ggggcgggggggbggg ce gggcgggggggggbgg c ggacgggggggggfbg ec ggcgggggggggggbd ca aa b ce c db c ce bf ec c b ac ce b ce ec ff c c bd ec aa b ac c db ca ca bf c c b c ce b ec ec ff ca c bd ce ec b c c db ec aa bf aa c b ce ce b c c ff ec ce bd acec b cc db e bf b ```  Let's get to the bottom of what's happening inside area A.  ```palette Key,Color ,#fefefeff a,#f95d63ff b,#0202feff c,#fe0a0aff d,#afacfcff e,#ffbfbfff f,#6360fbff g,#3022f1ff ``` ```image df dgbb dfbbbbf dgbbbgd dfbbbbfd ee dgbbbgd ecc dfbbbbfd ccadgbbbgd dgbbbbfd dbbbgf gfacc cca ecca ecce acc cca ecca ecce acce acc cca ecce acce acc cca ecca ecce acc ```  I can confirm that an intersection exists in area A. Next up, a closer look at another region. I'm analyzing this close-up of area B with precision.  ```palette Key,Color ,#fefefeff a,#fb6063ff b,#0504fdff c,#fd0809ff d,#c4c4ffff e,#ffb8b8ff f,#3c3afdff g,#807efcff ``` ```image gbbd ecce fbf aca bbg ecc dbbd cca gbb acc fbf cce dbbg acc gbbd ecce fbf aca bbg ecce dbbd cca gbb ecc fbf cce dbbg acc gbbd cce fbf aca bbgecce dbbaca gbbc bbf acbbg ccgbbd acc fbf ecce bbg aca dbbd ecce gbb cca fbf ecc dbbg cce gbbd acc fbf cce bbg aca dbbd ecce gbb aca fbf ecc dbbg cca gbbd acc fbf cce bbg ```  There's no doubt about it - this is an intersection in area B. After a long analysis, I found two intersections.

2

```palette Key,Color ,#fefefeff a,#ff3e3eff b,#0908feff c,#fe0506ff d,#b0aefdff e,#ffc0c0ff f,#5b5bffff g,#fd7c7eff ``` ```image g c ce ec c gc c aa c cg c ce ec c ga c ag c df ce fbbbd ec dbbd b c fbb db gc dbbf bf c fbb b aa dbbf b c fbb fb cg dbbf bd c fbbd b ce dbbf db ec fbbd bf c dbbf b ga c fbbd b c dbbf fb ag bgc bd c cg b ce c db ec ec bf c gc b gc ca b c ce fb aa c bd c gc b cg aa db c ce bfce c bc ec cb aa gafb cg c bd c ag b ec c db gc ce bf cg ec b ce c db c gc fb gc c bd aa aa b ce c db c cg bf ec ec b aa ce db cg ec fb c c bd ec ga b gc c db cg ag bf ce c b c ce db gc ec fb ca c bd ce gc b c c db ec aa bf aa c b ce cg db c ec fb ec ce bd acec b cc db g bf b ```

I have a feeling there might be some intersections in this image. I need to zoom in on these areas to get a better look.  ```palette Key,Color ,#fefefeff a,#5b5dfcff b,#fe0909ff c,#ec645bff d,#0606feff e,#bbbbffff f,#ffbcbcff g,#afd6afff ``` ```image eeeeeeeee adadddddddddddddddddddddddddddddddddddddddddd d aa d aa d aa d aa d da d de d de d b de cb d b de bf ed bc de fb ed b d bc ed fb d b ed bf d cb ed b d bf ad cb d b aa bf d cc aa fb d b aa bc d fb aa b d bc da fb d b da bf d cb de b d bf de cb d b de bf ed bc de fb ed b de bc ed fb d b ed bf d cb ed b d bf ad cb d b ad bf d cc aa fb d b aa bc d fb aa b d bc gggdaggggggggg fb gggagggggggggg b gggggggggggggg bf gggggggggggggg cb gggggggggggggg b gggggggggggggg bf gggggggggggggg cb gggggggggggggg b gggggggggggggg bf gggcccccccccccffff bc gggcccccccbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb gggggggggggggg gggggggggggggg gggggggggggggg ```  I'm determined to find out if an intersection exists in area A.  ```palette Key,Color ,#fefefeff a,#9a9affff b,#ff0000ff c,#ff8080ff d,#0b0bffff e,#ff6161ff f,#ffa4a4ff g,#ff4141ff ``` ```image add dda add aa ccccccccfffffffffff bbbbbbbbbbbbbbbbbbb ceeeeeeeegggggggggg ```  Hmm, it seems there's no intersection in area A after all. The image is completely devoid of intersections. Zero.

0

```palette Key,Color ,#fefefeff a,#5555ffff b,#ff0404ff c,#ff8181ff d,#0505ffff e,#b5b5ffff f,#ffc7c7ff g,#ff3e3eff ``` ```image eeeeeeee adaaddddddddddddddddddddddddddddddddddddddddd d aa d aa d aa d aa d da d de d de d b de gg d fb de bf ed gg de fb ed b d bc ed fb d b ed bc d cb ed b d bf ad cb d b aa bf d gg aa fb d b aa gg d fb aa b d bc da cb d b de bc d cb de b d bf de gg d fb de bf ed gg de fb ed b d bc ed fb d b ed bc d cb ed b d bf ed cb d b aa bf d gg aa fb d b aa gg d fb aa b d bc aa cb e b bc cb b bf gg fb bf cccccccfffffffff gg cccgggggggggbbbbbbbbbbbbbbbbbbbbbbbbb ```

Based on a first glance, I suspect there could be intersection regions here. I've spotted 2 narrow regions that might be worth examining further. Let's call them area A,, and B.  ```palette Key,Color ,#fefefeff a,#4548f2ff b,#e07368ff c,#97c697ff d,#969cf3ff e,#b1d7b1ff f,#0505fdff g,#fa0d0cff ``` ```image d fd f fd ecccfcccccccccccccccccccccce cebefeeeeeeeeeeeeeeeeeeeeeec ceggdfeeeeeeeeeeeeeeeeeeeeec ceegbfeeeeeeeeeeeeeeeeeeeeec ceeegaaeeeeeeeeeeeeeeeeeeeec ceeeegfeeeeeeeeeeeeeeeeeeeec ceeeecaaeeeeeeeeeeeeeeeeeeec ceeeeebfeeeeeeeeeeeeeeeeeeec ceeeeeefbeeeeeeeeeeeeeeeeeec ceeeeeeefbeeeeeeeeeeeeeeeeec ceeeeeeefgeeeeeeeeeeeeeeeeec ceeeeeeecfgeeeeeeeeeeeeeeeec ceeeeeeeefbgeeeeeeeeeeeeeeec ceeeeeeeedfggeeeeeeeeeeeeeec ceeeeeeeeefegbeeeeeeeeeeeeec ceeeeeeeeeaaegeeeeeeeeeeeeec ceeeeeeeeeefeegeeeeeeeeeeeec ceeeeeeeeeeaaebgeeeeeeeeeeec ceeeeeeeeeeefeeggeeeeeeeeeec ceeeeeeeeeeefdeegbeeeeeeeeec ceeeeeeeeeeeefeeegceeeeeeeec ceeeeeeeeeeeefceeegeeeeeeeec ceeeeeeeeeeeecfeeebgeeeeeeec ceeeeeeeeeeeeefeeeebgeeeeeec ceeeeeeeeeeeeedfeeeegbeeeeec a ceeeeeeeeeeeeeefeeeeegbeeeec df ceeeeeeeeeeeeeeaaeeeeegeeeec df ceeeeeeeeeeeeeeefeeeeecgeeec f ceeeeeeeeeeeeeeeaaeeeeebgeec f ceeeeeeeeeeeeeeeefeeeeeeggec fd ceeeeeeeeeeeeeeeefdeeeeeegbc fa ceeeeeeeeeeeeeeeeefeeeeeeegc af ecccccccccccccccccfccccccccg df df bg ccccccccccccccccccfcccce f gg eeeeeeeeeeeeeeeeefeeeeec df gb eeeeeeeeeeeeeeeefceeeeec f g eeeeeeeeeeeeeeefdeeeeeec aa g eeeeeeeeeeeeeefaeeeeeeec f bg eeeeeeeeeeeeeafeeeeeeeec ad bg eeeeeeeeeeeeafeeeeeecbgggg f gb eeeeeeeeeeedfebggggggbbc fd g eeeeeeebbggfgggbeeeeeeec f g cbggggggbcfceeeeeeeeeeec f eg bbgggggbbeeeeeefdeeeeeeeeeeeec df bg ebggggggb eeeeeeeefaeeeeeeeeeeeeec f gggggggbe eeeeeeeafeeeeeeeeeeeeeec df b eeeeeeafeeeeeeeeeeeeeeec f eeeeedfeeeeeeeeeeeeeeeec aa eeeeefeeeeeeeeeeeeeeeeec f ceeefceeeeeeeeeeeeeeeeec ad fd f fa fd af f df f df df f f f df fd f fa aa af f df ad df f f fd f f fd f fa df aa f af da df f f aa f f fd ad fa f aa faf f ```  Time to investigate area A up close.  ```palette Key,Color ,#fefefeff a,#3528f1ff b,#f9575dff c,#726ffbff d,#b6b6ffff e,#feb0b0ff f,#0303feff g,#fc080bff ``` ```image cfc dff afc ee dff egge afc bgg dff ggb afd ggbcfa eggeffd eggcfa bggffd ggafc ggff egafc egff bafc bff ffb cfab ffge cfage ffgg cfagb dffggb afcgge dffbgge afcbgg dff ggb ffd ggb cfa egge ffd egge cfa bgg ffd bgg cfc ggb dff eggb afc egge dff bgge afc bgg dfa ggb ffd eggb cfa egge ffd bgge cfa bgg ffd ggb cfc eggb dff egge afc bgge dff bgg afc ggb dfa ggb ffd egge cfa egge ffd bgg cfa bgg ffd ggb cfc eggb dff egge afc bgge dff bgg afc ggb dfa eggb ffd egge cfa bgg ffd bg ```  There is an intersection point visible in this close-up of area A. Okay, on to the next area of interest. Here's a close-up of the area B.  ```palette Key,Color ,#fefefeff a,#0a07fbff b,#ff4343ff c,#5959feff d,#bbbbffff e,#fec0c1ff f,#fc8486ff g,#fe0304ff ``` ```image daac daac aac caa caad caad daad daac daac aac caa caad caad effbbg daad eefbbgggggggg daac effbggggggggggbffe efaaagggggggggbbfee eeffbgggaaagggbbffe effbbggggggggaaafee eefbbgggggggggbbffecaad gggggggggbffe caad ggbbfee daad daac daac aac caa caad caad daad daac daac aac caa ```  The lines cross each other within area B, forming an intersection. The image features two intersection points.

2

```palette Key,Color ,#fefefeff a,#302efcff b,#fa5a5eff c,#6c6bfeff d,#b8b8ffff e,#feababff f,#0303feff g,#fd090aff ``` ```image d ad f fd df e f bgdf gbf gca gf eac bf fb fe fg dfg fbg dagb f ge ca g f g ac eg f bg fd gb f ge fd g df eg f bg da gb c f ge cf ca g df f eg f ac bg fd f gb fd fd ge fc f g aa fd g cf df eg df f gg f da ge fd f g fd ca g fc f eg aa ac bg cf ebgggg f gb df ebgggggbe fd ge ebggfggbe f g eebgggggbefd fd eg ebgggggbe fd df bg ebgggggbe fc f gggggggbe aa da e cf f df cc f f fd ac fd f fc fd aa f cf fd df df f f fd ca fd f fc cc aa f cf ac df f f fd f f fd f fc df aa f cf ca df f f cc f f fd ac fc f aa faf f ```

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.  ```palette Key,Color ,#fefefeff a,#fd0908ff b,#0a0bfbff c,#ffb5b5ff d,#6a73e6ff e,#ed5954ff f,#b1d7b1ff g,#9dc395ff ``` ```image c ac a ac ca a ca a ee a ee a ac a ac ca a ca a ee a ee a ac a ac ca a ca a a ee ea a ca ee ca a a ac ac a ac ac ae ca ae a ea ca ca a ca ee a a ac ee ac d a ae dbf ac aa bb a ea dbd ac ca bb ca ca bb gagggggggggggggggggggggggggggggggggggggf a dbd feaffffffffffffffffffffffffffffffffffffgac bb ffaffffffffffffffffffffffffffffffffffffac fbd ffeeffffffffffffffffffffffffffffffffffae bb fffafffffffffffffffffffffffffffffffffaag bb fffaefffffffffffffffffffffffffffffffeafg dbb dbd ffffaffffffffffffffffffffffffffffffeaffg dbbbd bb ffffagffffffffffffffffffffffffffffgafffg dbbb bbffffaffffffffffffffffffffffffffffaffffg bbbd dbdffagffffffffffffffffffffffffffagffffg dbbbd ffbbfgafffffffffffffffffffffffffaefffffbbbd fffdbdaffffffffffffffffffffffffaeffdbbbd fffffbbaffffffffffffffffffffffaadbbbdffg fffffffbbfffffffffffffffffffgbbbdffffffg fffffffedbdffffffffffffffdbbbefffffffffg ffffffffafbbffffffffffdbbbggaffffffffffg ffffffffaefdbbffffdbbbdffffafffffffffffg fffffffffafffbbdbbbdffffffagfffffffffffg fffffffffagffffdfffffffffaeffffffffffffg fffffffffgafffffffffffffaefffffffffffffg ffffffffffagfffffffffffaaffffffffffffffg ffffffffffgaffffffffffeafffffffffffffffg fffffffffffafffffffffeaffffffffffffffffg fffffffffffeafffffffgafffffffffffffffffg ffffffffffffafffffffaffffffffffffffffffg gfffffffffffeefffffagffffffffffffffffffg a ae ac ae a ea aea a ```  I wonder what we'll find inside area A?  ```palette Key,Color ,#fefefeff a,#fe0404ff b,#0906fcff c,#fe7e7fff d,#aba9fdff e,#f7363dff f,#5a57fbff g,#fec3c3ff ``` ```image gaa eac cae aag cae c aag ga cae gaa gaag gaae eac eae gaa eaa eac caag gaa caag eac caac cae gaac aag gaae bd cae aae bbfd aag eae dbbbf cae eaag fbbbd gaag caag dbbbf eac caag fbbbd gaa caac d dfbbbd eac gaac dffbb dbbbfgaa gaae dfbbbbbf fbbbeac aae dfbbbbbfd dbbbbe eaedfbbbbbbfd dbbbf eebbbbbbfd fbbbd ddbbbbbbfd ebbbf dfbbbbbbfd cafbbbd dfbbbbbbec gaadfbbfd dfbbbbbbfdaac eac dbbbf dfbbbbbfdd gaae gaa fbbbd dfbbbbbfd aae eac dbbbf dfbbbbbbfd eae gaa fbbbd dfbbbbbfd eaag aac fbbbffbbbbbfd caag cae dbbbbbffd caag aag ffd gaac cae gaac aag gaae cae eae gaag eae eac eaag gaa caag eac caag gaa gaac aac gaac cae gaae aag eae cae eae aag eaag cae caag ```  My investigation has led me to an intersection in area A! After a thorough search, I conclude that there are two intersections.

2

```palette Key,Color ,#fefefeff a,#ff0404ff b,#0706feff c,#ff8788ff d,#a9a9ffff e,#fb3c40ff f,#5552fbff g,#ffc8c8ff ``` ```image g ac a ag ga a ca a ce a ec a ac a ag ga a ca a ce a ec a ac a ag ga a ca a e ce ea a ca ec ga a a ac ag a ag ag ac ga ee a ea ca ca a ga ce a a ag ec ac d a ac fbd ag ee bb a ea dbf ag ca bb ga ga bb a a fbd ce ag bb a ac dbf ce ae fbd a ee bb ec ea fbb dbd a ca dbbbd bb ag ga fbbfd dbf a a dfbbf fbd ag ag dbbbd bb ga ac fbbf dbfa ae dbbbd bbe eefbbbd bb dbbbf efbd dbbbe a bb fbbfdga ec dbf dbbbf a a fbfbbbd ag ag f ac a ae ag ee ga ca a ga ce ga a a ee ag a ac ec ae a ea aea ga ```

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.  ```palette Key,Color ,#fefefeff a,#4344eaff b,#fc0a09ff c,#0504fcff d,#868eecff e,#b1d7b1ff f,#e47064ff g,#99c599ff ``` ```image dcca c dccd dc ecca geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecgfeeeeeeaccd eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecbbfeeeeeeegcca eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecdbebgeeeeeeg dccd eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecbgeebeeeeeeg acc eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaabeeefbeeeeeg dccd eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecbeeeeefbeeeeg acc eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaafeeeeeebbeeeg dcca eeeeeeeeeeeeeeeeeeeeeeeeeeeeeecbeeeeeeeebfeeg accd eeeeeeeeeeeeeeeeeeeeeeeeeeeeedceeeeeeeeeebfeg cca eeeeeeeeeeeeeeeeeeeeeeeeeeeeecfeeeeeeeeeeebeg dccd eeeeeeeeeeeeeeeeeeeeeeeeeeeegceeeeeeeeeeeegbg cca eeeeeeeeeeeeeeeeeeeeeeeeeeeecgeeeeeeeeeeeeefb dccd eeeeeeeeeeeeeeeeeeeeeeeeeeefceeeeeeeeeeeeeeefb aca eeeeeeeeeeeeeeeeeeeeeeeeeeecdeeeeeeeeeeeeeeegbf dccd eeeeeeeeeeeeeeeeeeeeeeeeeebceeeeeeeeeeeeeeeeg bf a eeeeeeeeeeeeeeeeeeeeeeeeefcaeeeeeeeeeeeeeeeeg b eeeeeeeeeeeeeeeeeeeeeeeeebceeeeeeeeeeeeeeeeeg b eeeeeeeeeeeeeeeeeeeeeeeebaaeeeeeeeeeeeeeeeeeg b eeeeeeeeeeeeeeeeeeeeeeefbceeeeeeeeeeeeeeeeeeg fb eeeeeeeeeeeeeeeeeeeeeeebdceeeeeeeeeeeeeeeeeeg fb eeeeeeeeeeeeeeeeeeeeeebfceeeeeeeeeeeeeeeeeeeg bf eeeeeeeeeeeeeeeeeeeeegbdceeeeeeeeeeeeeeeeeeeg bf eeeeeeeeeeeeeeeeeeeeebgcgeeeeeeeeeeeeeeeeeeeg b eeeeeeeeeeeeeeeeeeeefbeceeeeeeeeeeeeeeeeeeeeg b eeeeeeeeeeeeeeeeeeeebecdeeeeeeeeeeeeeeeeeeeeg eb eeeeeeeeeeeeeeeeeeebfeceeeeeeeeeeeeeeeeeeeeeg fb eeeeeeeeeeeeeeeeeefbeaaeeeeeeeeeeeeeeeeeeeeeg bb eeeeeeeeeeeeeeeeeebeeceeeeeeeeeeeeeeeeeeeeeeg bf eeeeeeeeeeeeeeeeebfeaaeeeeeeeeeeeeeeeeeeeeeeg be eeeeeeeeeeeeeeeegbeeceeeeeeeeeeeeeeeeeeeeeeeg b eeeeeeeeeeeeeeeebeedceeeeeeeeeeeeeeeeeeeeeeeg b eeeeeeeeeeeeeeefbeeceeeeeeeeeeeeeeeeeeeeeeeeg fb eeeeeeeeeeeeeeebeegceeeeeeeeeeeeeeeeeeeeeeeeg fb eeeeeeeeeeeeeebfeecgeeeeeeeeeeeeeeeeeeeeeeeeg bf eeeeeeeeeeeeefbeeeceeeeeeeeeeeeeeeeeeeeeeeeeg bf eeeeeeeeeeeeebeeecdeeeeeeeeeeeeeeeeeeeeeeeeeg b eeeeeeeeeeeebfeeeceeeeeeeeeeeeeeeeeeeeeeeeeeg b eeeeeeeeeeegbeeeaaeeeeeeeeeeeeeeeeeeeeeeeeeeg b eeeeeeeeeeebeeeeceeeeeeeeeeeeeeeeeeeeeeeeeeeg fb eeeeeeeeeebfeeeaaeeeeeeeeeeeeeeeeeeeeeeeeeeeg bb eeeeeeeeeebeeeeceeeeeeeeeeeeeeeeeeeeeeeeeeeeg bf eeeeeeeeebgeeedceeeeeeeeeeeeeeeeeeeeeeeeeeeeg bf eeeeeeeefbeeeeceeeeeeeeeeeeeeeeeeeeeeeeeeeeeg b eeeeeeeebeeeegceeeeeeeeeeeeeeeeeeeeeeeeeeeeeg b eeeeeeebfeeeecgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg eb eeeeeefbeeeeeceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg fb eeeeeebeeeeecdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg bb eeeeebfeeeeeceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg bf eeeegbeeeeeaaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg be eeeebgeeeeeceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg b eeefbeeeeeaaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg b eeebeeeeeeceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg fb eebfeeeeedceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg f efbeeeeeeceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg ebeeeeeegceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg bfeeeeeecgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg ebeeeeeeeceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg bgggggggcdggggggggggggggggggggggggggggggggggge c ad c da c dc c c c c cd c ad c da c dc c ```  I'm focusing my attention on this specific region, area A.  ```palette Key,Color ,#fefefeff a,#594df2ff b,#f6373fff c,#0706fdff d,#aeadfdff e,#fec2c3ff f,#fe8081ff g,#fe0505ff ``` ```image aca dacccca cc ff accc caeggf da cdbgggf aafggfgge cdgge bgge dcbgb bgb ccgge ggb dccgf eggf acab eggf dccge fgge acag fgge dccgg bgg acage bgb ccbb ggb accg eggf ccbf eggf dccb fgge ccbe fgge cca bgb dcce eggb aca egg fccd fg eaca f bccd eaca gccd fbcc egccd bbcc fgcca egbcc bgaca fgbccd ggaca bgbccd eggaca ggfccd fggdcc eggeccd bgbdcc fgg aca eggfdcc bgb aca egge ccd ggf aca fgb ccd egge dca bgf ccd fgg dcc egge ccd bgb dcc fgge aca ggf dcc bgb aca egge ccd fgg ccd egge dca bgb ccd fgg dcc ggf ccd bgb dcc egge aca ggf dcc fgb aca egge ccd bgb aca fgg ccd eggf dca bgb ccd egge dcc ggf ccd fgb dcc egge aca bgf dcc fgg aca gge ccd gb aca fge ccd gf dcc bg ccd egg dcc ggf ccd fgg dcc egge aca bgb dcc fgg aca ggf ccd bgb aca egge ccd ggf dcc fgb ccd egge dcc fgg dcc egge aca bgb dcc fgge aca ggf ccd fgb ca egge cd bgf dc fgg cd egge dc bgb cc fgg dcc ggf aca bgb dcc egge aca ggf ccd fgg aca egge ccd bgb dcc ```  Incredible, there's actually an intersection in area A! I have found one intersection!

1

```palette Key,Color ,#fefefeff a,#5b58fbff b,#fe3535ff c,#0806fdff d,#b0aefcff e,#ffc4c4ff f,#fe7d7dff g,#fe0303ff ``` ```image d dcca c accd dc cca c f accd cbgf ccc cdg ge dccd cge g acc aab eg dcca cg fg accd ace bb dcca cg gf accd dc ge dcca cf g accd dc eg cca cd fg dccd bc bg ccc cd bb dcca gc gf a fca ge gc g gaa eg egc fg gdc bb bbc gb egdc ge gecd ge fb c g g cd eg ge c fg fg aa bb g c gf bf aa ge eg c g g dc eg bb c fg g dc bg ge cd gb fg c gf g cd ge gf c g eg aa eg g c fg bb aa bb g c gf ge dc ge fb c ge g dc g gf cd eg eg c fg g cd bb bf c gf eg aa ge ge c g fb aa eg g c fg ge dc f fg c g dc bf cd eg c g cd c aa c aa c dc c dc cd c cd c aa c aa c dc c ```

Let's examine this image for potential line intersections. I have a hunch that these areas might contain the intersections we're looking for.  ```palette Key,Color ,#fefefeff a,#fd0a09ff b,#0b0cfbff c,#ea665dff d,#feb2b2ff e,#6e76e9ff f,#b1d7b1ff g,#9ac597ff ``` ```image c a ad a ad da a ca a cc a ad a ad da a d ca ac a a cc ca a a ac da a ad ad a da ac a a da ca a a cc da a ad ac a a e ac fggggggggggggggggggggggggggggggggggggggggggad bb a gfffffffffffffffffffffffffffffffffffffffffga ebe ca gfffffffffffffffffffffffffffffffffffffffffag bb a gffffffffffffffffffffffffffffffffffffffffcaf ebe da gffffffffffffffffffffffffffffffffffffffffaff bb ad gfffffffffffffffffffffffffffffffffffffffcaff ebe a gfffffffffffffffffffffffffffffffffffffffafff bb ac gffffffffffffffffffffffffffffffffffffffacfff ebf a gffffffffffffffffffffffffffffffffffffffaffff bb ca gfffffffffffffffffffffffffffffffffffffacffff ebf a gffffffffffffffffffffffffffffffffffffgaffffgbb da gffffffffffffffffffffffffffffffffffffagfffebf ad gfffffffffffffffffffffffffffffffffffcafffbbf a gfffffffffffffffffffffffffffffffffffaffbbgff ac gffffffffffffffffffffffffffffffffffcafbbffff a gffffffffffffffffffffffffffffffffffabbgfffff ccgfffffffffffffffffffffffffffffffffcbbfffffff agffffffffffffffffffffffffffffffffbbfffffffff daffffffffffffffffffffffffffffffgbbcfffffffff agffffffffffffffffffffffffffffbbgaffffffffff gaffffffffffffffffffffffffffgbefagffffffffff gacffffffffffffffffffffffffbbffgafffffffffff gfaffffffffffffffffffffffebefffaffffffffffff gfcaffffffffffffffffffffbbffffcaffffffffffff gffaffffffffffffffffffebefffffafffffffffffff gffcaffffffffffffffffbbffffffccfffffffffffff gfffagfffffffffffffebefffffffaffffffffffffff gfffgaffffffffffffbbffffffffacffffffffffffff gffffacfffffffffebefffffffffafffffffffffffff gfffffafffffffbbeffffffffffagfffffffffffffff gfffffcafffgbbefffffffffffgaffffffffffffffff gffffffafebbefffffffffffffafffffffffffffffff gffffffebbfffffffffffffffcafffffffffffffffff gffffbbbagfffffffffffffffaffffffffffffffffff gffbbeffgaffffffffffffffcaffffffffffffffffff gbbefffffacfffffffffffffafffffffffffffffffff ebbgffffffffaffffffffffffacfffffffffffffffffff ebb gfffffffffccfffffffffffaffffffffffffffffffff bbe gffffffffffaffffffffffacffffffffffffffffffff bbe gffffffffffcaffffffffgafffffffffffffffffffff ebb gfffffffffffagfffffffagfffffffffffffffffffff ebb gfffffffffffgaffffffcaffffffffffffffffffffff bbe fggggggggggggacgggggaggggggggggggggggggggggg bbe a ca bbf cc a a ac da a aad da ```  Let's get to the bottom of what's happening inside area A.  ```palette Key,Color ,#fefefeff a,#fe0505ff b,#0908fdff c,#fa3f43ff d,#fec7c8ff e,#645ff9ff f,#bcbbfeff g,#ff8383ff ``` ```image g da ca daa cac daad cag gaa aag gaa aad gac daad cac daad cag gaa aag gaa aag gac daad cac fb daad ebb cag fbbbe daa ebbbf aag fbbbe gaa ebbbf aag fbbbe gac ebbef daadfbbbe cacebbef dacbbbf cbbbef ebbbf febbb g ebbbc a fbbbbag ac ebbbeac aad fbbbedaad cac ebbbf cac daad fbbbe daad gaa ebbbf cac aag fbbbe daad gaa ebbbf cag cag fbbbe gaa daad ebbbf aag cac fbbbe gaa daad ebbbf aad gaa fbbbe gac aag ebbbf daad gaa fbbbe cac cag ebbbf daad daad fbbbe cag cac ebbbf gaa daad fbbbe aag gaa ebbbf gaa aag febbbe aag gaa febbbef gac cag fbbbbef daad daad ebbbbef cac cac ebbbbe daad daad febbbbf cag gac febbbef daa aaebbbbef aag ebbbbe gaa febbbbe aag febbbefaad gac fbbbbef cac daad ebbbbe daad cac febbbbe gac daad febbbbf aag cac bbbef gaa daad bef cag cag daad gaa cac aag daad gac gac aad aag cac gaa daad cag cac daad daad cac cag daad gaa gac aag ```  Eureka! There's definitely an intersection in area A! After a thorough search, I conclude that there are two intersections.

2

```palette Key,Color ,#fefefeff a,#fe0505ff b,#0908feff c,#fd4041ff d,#fec7c7ff e,#5957fcff f,#acacffff g,#ff8484ff ``` ```image g a ag da ad da a gc a cc a ag da ad da a d ga cg a a cc gc a a ag da a ad ad a da cg a a ga gc a a cc da a ad cg a a f cg ad bb a da fbf gc ad bb a ga fbf da a bb ad gc ebf a a bb ag cg ebf a a bb cc ag ebf a da bb da ad ebf ad da bb a a ebf ag gc be a aeb cc cbe a eb ga fbbg ad bbda da fbe ad ag bb da a fbe a cc bb ga a fbe a ga bb cc ad fbe a da bb ag ag ebf a a bbe ad cc bbf da a fbbf a ebb ga ebead a bbe da cc fbbf ag a fbb a cg ebb cc a bbe a ad fbbf ga da fbbf ad ad ebb da ga ebe ag a bbe a gc bbf cc a a cg ga a aag da ```

I'm curious to see if this image contains any intersection points. I wonder what's going on inside those areas? Perhaps intersections are hiding there.  ```palette Key,Color ,#fefefeff a,#ed5f56ff b,#464af6ff c,#a1ca9fff d,#959cf0ff e,#b2d7b2ff f,#0606fdff g,#fd0707ff ``` ```image a ag gg ga ga ge eg ag ag gg ga ga ggcccccccccccccccccccccccccccccccccccccc ge agceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeec eg ccgaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeec ag ceeggeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeec ag ceeeagceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeec gg ceeeecgaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeec ga bceeeeeeggeeeeeeeeeeeeeeeeeeeeeeeeeeeeec ga dfdeeeeeeagceeeeeeeeeeeeeeeeeeeeeeeeeeec ge cffeeeeeecgaeeeeeeeeeeeeeeeeeeeeeeeeeec eg cebfceeeeeeggeeeeeeeeeeeeeeeeeeeeeeeeec ag ceecfbeeeeeeagceeeeeeeeeeeeeeeeeeeeeeec ag ceeeeffeeeeeecgaeeeeeeeeeeeeeeeeeeeeeec gg ceeeeedfdeeeeeeggeeeeeeeeeeeeeeeeeeeeec ga ceeeeeeeffeeeeeeagceeeeeeeeeeeeeeeeeeec ga ceeeeeeeebfceeeeecgaeeeeeeeeeeeeeeeeeec ge ceeeeeeeeecfbeeeeeeggeeeeeeeeeeeeeeeeec eg ceeeeeeeeeeeffeeeeeeagceeeeeeeeeeeeeeec ag ceeeeeeeeeeeedfdeeeeecgaeeeeeeeeeeeeeec ag ceeeeeeeeeeeeeeffeeeeeeggeeeeeeeeeeeeec gg ceeeeeeeeeeeeeeebfceeeeeagceeeeeeeeeeec ga ceeeeeeeeeeeeeeeecfbeeeeecgaeeeeeeeeeec ga ceeeeeeeeeeeeeeeeeeffeeeeeeggeeeeeeeeec ge ceeeeeeeeeeeeeeeeeeedfdeeeeeagceeeeeeeceg ceeeeeeeeeeeeeeeeeeeeeffeeeeecgaeeeeeeag ceeeeeeeeeeeeeeeeeeeeeebfceeeeeggeeeegg ceeeeeeeeeeeeeeeeeeeeeeecfbeeeeeagceggc ccccccccccccccccccccccccccffccccccggacc dfd e ff bf fb bf dfd fb ff bf df fd fb bf df fd fb ff bf dfd fb ff bf df fd fb bf df fd fb ff bf dfd fb ff bf df fd fb bf df f ```  I'm now examining the contents of area A in detail.  ```palette Key,Color ,#fefefeff a,#ff3636ff b,#4c4cffff c,#ff7171ff d,#a4a4ffff e,#ffb0b0ff f,#0707feff g,#ff0404ff ``` ```image ga ggge aggc cgga eggge aggc cgga eggge aggc cgga eggge aggc cgga bd eggge ffb aggc dfffd cgga bffb eggge dfffd aggc dfffd cgga bffb eggge dfffd aggc bffb cgga dfffd eggge dfffd aggc bffb cgga dfffd eggge bffb aggc dfffd cgga dfffd eggge bffb aggc dfffd cgga bffb eggge dfffd aggc dfffd cgga bffb eggge dfffd aggc bffb cgga dfffd eggge dfffd aggc bffb cgga dfffd eggge bffb aggc dfffd cgga dfffd eggge bffb aggc dfffd cgga bffb eggge dfffd aggc dfffb cgga a bffb eggge ag dfffd aggc agg bffb cgga egga dfffd egggeegga dfffb agggga ```  After careful examination, I've determined that there's no intersection in area A. There's definitely not a single intersection on the image.

0

```palette Key,Color ,#fefefeff a,#ff4242ff b,#4f4fffff c,#ff7676ff d,#a3a3ffff e,#f5d5dfff f,#0707ffff g,#ff0707ff ``` ```image c ag gg ga gc ege ege cg ag gg ga e gc gg ege cge ege egc cg gg ag cge gg egc ga b gg gc dfd cge ege ff egc ege bfe gg cg efb cge ag ff egc gg dfd gg ga ff cge gc bfe egc ege efb gg ege ff cge cg dfd egc ag ff gg gg bfe cge ga efb egc gc ff gg ege dfd cge ege ff egc cg bfe gg ag efb cge gg ff egga dfd e ff bfe fb ff dfd fb ff bf dfe fd fb bf df efd fb ff bf dfd fb ff bf dfe fd fb bf df efd fb ff bf dfd fb ff bf dfe fd fb bf df ef ```

Based on a first glance, I suspect there could be intersection regions here. These zones indicate regions where lines appear to be in close proximity.  ```palette Key,Color ,#fefefeff a,#fd0605ff b,#5159eeff c,#0607fcff d,#d49984ff e,#b1d7b1ff f,#94c69aff g,#ea4d43ff ``` ```image bcc bcb ec bcb cb bcb d c feeebcbeeeeeeaaffceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef febcbeeeeeeeaddaecbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef bcbeeeeeeeeadeeadecfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef bcbeeeeeeeeeadeeeeaeeceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef bcb feeeeeeeeadeeeeeagebceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef bcb feeeeeeeaeeeeeeeeaeecfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef bcb feeeeedaeeeeeeeeegaeeceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef bcb feeeedaeeeeeeeeeeeaeebceeeeeeeeeeeeeeeeeeeeeeeeeeeeeef bcb feeedaeeeeeeeeeeeedaeecbeeeeeeeeeeeeeeeeeeeeeeeeeeeeef bcb feedaeeeeeeeeeeeeeeadeeceeeeeeeeeeeeeeeeeeeeeeeeeeeeef bcb fedaeeeeeeeeeeeeeeeeaeebceeeeeeeeeeeeeeeeeeeeeeeeeeeef bcb fgaeeeeeeeeeeeeeeeeeggeecbeeeeeeeeeeeeeeeeeeeeeeeeeeef bcb gaeeeeeeeeeeeeeeeeeeeaeeeceeeeeeeeeeeeeeeeeeeeeeeeeeef bcb gaeeeeeeeeeeeeeeeeeeeedaeefceeeeeeeeeeeeeeeeeeeeeeeeeef b gafeeeeeeeeeeeeeeeeeeeeeadeecbeeeeeeeeeeeeeeeeeeeeeeeeef ga feeeeeeeeeeeeeeeeeeeeeeaeeeceeeeeeeeeeeeeeeeeeeeeeeeef ga feeeeeeeeeeeeeeeeeeeeeeageefceeeeeeeeeeeeeeeeeeeeeeeef aa feeeeeeeeeeeeeeeeeeeeeeeaeeecbeeeeeeeeeeeeeeeeeeeeeeef ag feeeeeeeeeeeeeeeeeeeeeeegaeeecfeeeeeeeeeeeeeeeeeeeeeef ag feeeeeeeeeeeeeeeeeeeeeeeeaeeeeceeeeeeeeeeeeeeeeeeeeeef ag feeeeeeeeeeeeeeeeeeeeeeeedaeeebceeeeeeeeeeeeeeeeeeeeef ag feeeeeeeeeeeeeeeeeeeeeeeeeadeeecfeeeeeeeeeeeeeeeeeeeef ag feeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeceeeeeeeeeeeeeeeeeeeef ad feeeeeeeeeeeeeeeeeeeeeeeeeeggeeebceeeeeeeeeeeeeeeeeeef ad feeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeecbeeeeeeeeeeeeeeeeeef ad feeeeeeeeeeeeeeeeeeeeeeeeeeegaeeeeceeeeeeeeeeeeeeeeeef ad feeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeebceeeeeeeeeeeeeeeeef a feeeeeeeeeeeeeeeeeeeeeeeeeeeedaeeeecbeeeeeeeeeeeeeeeef a feeeeeeeeeeeeeeeeeeeeeeeeeeeeeadeeeeceeeeeeeeeeeeeeeef a feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeefceeeeeeeeeeeeeeef a feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeggeeeecbeeeeeeeeeeeeeef ea feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeeceeeeeeeeeeeeeef da feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedaeeeefceeeeeeeeeeeeef da feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeadeeeecbeeeeeeeeeeeef g feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeecfeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeageeeeeceeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeebceeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegaeeeeecfeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeeeceeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedaeeeeebceeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeadeeeeecbeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeeeceeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeggeeeeebceeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeeecbeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedaeeeeeeceeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeadeeeeefceeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeeecbeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeageeeeeeceeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeeefceef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegaeeeeeecbef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeeeecff feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedaeeeeeeecf feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeadeeeeeebc feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeeeece feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeggeeeeeefc feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeeefbc feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedaeeeeef ce feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeadeeeef c feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeef bc feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeageeef c feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeggeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedaef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeadf feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaf feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeag a da a a ad a gg a ```  I'm eager to see what's happening in this magnified view of area A.  ```palette Key,Color ,#fefefeff a,#fe0303ff b,#5959ffff c,#0707ffff d,#ff7070ff e,#babaffff f,#ffbebeff g,#ff3636ff ``` ```image bcccb daf cb ebccbe daag ece ebccbe daaaad cc ebccbe gaaf gad ecce bccbe aaf faaf ecce ccb gaf dag bcb be gaf aa ccb gaa da ecc gaaf faf cb fagf ag ece fag aaf cc faa dag ccb faag aad ecce aag gad ccb fag faaf ecc fag dag bc faa aa bb faad da ece aad faf bcb dad ag ccb dad aaf ecce daa dag bcc aaf aad cc f gad bc faa cb da cce af bcc dg ccb aa bcc gad bc faaf ece dag ece aaf cb ga ecce faf bcc gg ccb faf ecc ag bc faa ece gad cc faaf ccb dag ecce aa bcc gd ecce faf ecc ag bc aaf cb dag ece faa ccb gad ecce faa bcc da ccb af ecc ad cb aa ece gag cc faaf bcb dag ecce aad ecce gad cc faa ece ga bc faf cb dg cce aa ccb gad ecce faaf bcc dag cc aaf ece ga cb faf cce gg ecce faf bcb ag ccb faa bc gad cb faaf ece dag cc aa ccb gd bcc faf ccb ag ecc aaf bc dag bb daa cce gad bcb faa cc da ec af b ad aa gad faaf dag daa ga faf gg faf aad faa gad faaf dag da gd faf ag aaf aa fa g ```  Unfortunately, there's no intersection inside area A. Zero, Nada.

0

```palette Key,Color ,#fefefeff a,#ff0404ff b,#5656ffff c,#0606ffff d,#ff8888ff e,#b7b7ffff f,#ffc8c8ff g,#ff4040ff ``` ```image e bcc bcb ec bcb cb bcb d c bcb aa ec bcb adda bb bcb af af ce bcb af a c bcb af gd bc bcb faf a ce bcb fa dg c bcb fa a bc bcb fa fa ce bcb da ad c bcb da a ec bcb da gg cb bcb da a c bcb ga da ec e ga af cb ga fa c ga ad ec aa a bb ag dg ce ag a c ag fa bc ag af ce ad a c ad gg bc ad a ce ad da c af af ec af fa cb af ad c faf a ec fa gg cb fa a c fa fa ec da af bb g a ce gd c a bc da ce af c fa bc ad ce a c gg ec a cb da c af ec a cb ad c a ec dg bb a ce fa c af bc a ce gg c a bc da ce af c fa ec ad c a gg a fa af a gd a da af fa ad a gg a ```

Here's an image. My task is to find intersections or areas where lines come close together. I'm going to focus my attention on these specific areas.  ```palette Key,Color ,#fefefeff a,#fe0908ff b,#0808feff c,#a9aafcff d,#ffb3b3ff e,#add4adff f,#f65d59ff g,#565bf5ff ``` ```image c gbc bb gbc bb cbc bb cbg bb cbg bb bg gbc bb gbc bb cbc bb cbg bb cbg bb bg gbc bbc bbc bbg gbg gbb cbb cbbc bbc bbg gbg eeeeeeeeeeeeeeeeee gbb eeeeeeeeeeeeeeeeee cbb eeeeeeeeeeeeeeeeee cbbc eeeeeeeeeeeeeeeeee cbbgeeeeeeeeeeeeeeeee bbgeeeeeeeeeeeeeee eebbgeeeeeeeeaeeee eeeegbbeeeefaeeeee eeeeeegbbefaeeeeee eeeeeeeegbbeeeeeee eeeeeeeeaaebbceeee eeeeeeeaaeeeebeeee eeeeeeaaeeeeeeeeee eeeeeafeeeeeeeeeee eeeeafeeeeeeeeeeee eeeafeeeeeeeeeeeee eeafeeeeeeeeeeeeee eaeeeeeeeeeeeeeeee daeeeeeeeeeeeeeeeee daeeeeeeeeeeeeeeeeee da fa fa fa aa aa af af ad ad ad da da d da aaad fa daaf fa daaf aa faaf aa faaf af faaf af faad af faad ad aaad ad daaad ad daaad da daaa da daa ```  I'm analyzing this close-up of area A with precision.  ```palette Key,Color ,#fefefeff a,#fe0405ff b,#0806fdff c,#a9a9ffff d,#ff7d7dff e,#ffc3c3ff f,#fb3539ff g,#5650f8ff ``` ```image c bbc bbbbc cbbbbg ead cgbbbgc eaaf cgbbbgc eaaf cgbbbgc eaaf gbbbbc daad gbbbbc daad cbbbbgaad cbbbbg ffbbbbgc faaecgbbbgc faae gbbbg efaae gbg eaafe eaaf eaaf eaaf daaf daad daad daad faad faae faae faae faae afe f ```  The evidence is clear: this is an intersection in area A. There's only one, but is an intersection after all.

1

```palette Key,Color ,#fefefeff a,#ff0505ff b,#0505feff c,#9393ffff d,#ff9e9eff e,#e9d7ecff f,#ff4949ff g,#4747ffff ``` ```image c gbe ebb gbc bb cbc bb cbc bb ebg gbe ebg gbe ebb gbc bb cbc bb cbc bb ebg gbe ebg gbe ebbc ebbc gbg gbg cbb cbbe ebbe ebbc bbc gbg gbg cbbe cbbe ebbc bbc e gbg da gbg da cbb da cbbe faebbc aa eb af af af ad ad eae eae da da da fa fa aa af af af ad ad eae eae da e da aafe fa daafe fa daaf fa daaf aa faaf af faad af faad af efaad ad efaad ad eaaad eae daaae eae daafeda daa ```

Hmm, I'm not sure what to expect from this image. Let's see if any lines cross. These areas seem to enclose narrow spaces where lines might be close.  ```palette Key,Color ,#fefefeff a,#ed726bff b,#0504fdff c,#fc0a0aff d,#9ba3eeff e,#b2d7b1ff f,#4645ebff g,#98c895ff ``` ```image e ca c ce c c ec d c b ac bd c db aa b c ff aa b c bd ca db c b ce ff c b c bd c db c b ac ff c b ac bd c db aa b c ff c ca b ca c bd cc ca db ac c b ec c ff c c b c c bd ca ec db ca c b ac ac ff ac c egggggggggggggggggggggggggggggbggggggggc aa geeeeeeeeeeeeeeeeeeeeeeeeeeeebdeeeeeeecg c geeeeeeeeeeeeeeeeeeeeeeeeeeedbeeeeeeecag ca geeeeeeeeeeeeeeeeeeeeeeeeeeebeeeeeeecaeg c geeeeeeeeeeeeeeeeeeeeeeeeeeffeeeeeecceeg ca geeeeeeeeeeeeeeeeeeeeeeeeeebeeeeeeaceeeg c geeeeeeeeeeeeeeeeeeeeeeeeebdeeeeegceeeeg ce geeeeeeeeeeeeeeeeeeeeeeeedbeeeeeeceeeeeg c geeeeeeeeeeeeeeeeeeeeeeeebeeeeeecgeeeeeg c geeeeeeeeeeeeeeeeeeeeeeeffeeeeecaeeeeeeg ec geeeeeeeeeeeeeeeeeeeeeeebeeeeecceeeeeeeg c geeeeeeeeeeeeeeeeeeeeeebdeeeeaceeeeeeeeg ac geeeeeeeeeeeeeeeeeeeeedbeeeeaceeeeeeeeeg c geeeeeeeeeeeeeeeeeeeeebeeeeeceeeeeeeeeeg aa geeeeeeeeeeeeeeeeeeeeffeeeeceeeeeeeeeeeg c geeeeeeeeeeeeeeeeeeeebeeeecaeeeeeeeeeeeg aa geeeeeeeeeeeeeeeeeeebdeeecaeeeeeeeeeeeeg c geeeeeeeeeeeeeeeeeedbeeecceeeeeeeeeeeeeg ca geeeeeeeeeeeeeeeeeebeeeaceeeeeeeeeeeeeeg d c geeeeeeeeeeeeeeeeeffeegceeeeeeeeeeeeeeeg bb ce geeeeeeeeeeeeeeeeebeeeceeeeeeeeeeeeeeeeg dbf c geeeeeeeeeeeeeeeebdeecgeeeeeeeeeeeeeeeeg fbd c geeeeeeeeeeeeeeedbeecaeeeeeeeeeeeeeeeeeg bb ec geeeeeeeeeeeeeeebeecceeeeeeeeeeeeeeeeeeg dbd c geeeeeeeeeeeeeeffeaceeeeeeeeeeeeeeeeeeeg bb ac geeeeeeeeeeeeeebeaceeeeeeeeeeeeeeeeeeeeg dbf c geeeeeeeeeeeeebfeceeeeeeeeeeeeeeeeeeeeeg fbd acgeeeeeeeeeeeedbecgeeeeeeeeeeeeeeeeeeeeeg bb cgeeeeeeeeeeeebecaeeeeeeeeeeeeeeeeeeeeeeg dbd aaeeeeeeeeeeefbcaeeeeeeeeeeeeeeeeeeeeeeeg bb ceeeeeeeeeeebcceeeeeeeeeeeeeeeeeeeeeeeeg dbf caeeeeeeeeebfceeeeeeeeeeeeeeeeeeeeeeeeeg fbd gceeeeeeeedbceeeeeeeeeeeeeeeeeeeeeeeeeeg bb gcaeeeeeeebceeeeeeeeeeeeeeeeeeeeeeeeeeeg dbd geceeeeeefbaeeeeeeeeeeeeeeeeeeeeeeeeeeeg bb gecgeeeeebaeeeeeeeeeeeeeeeeeeeeeeeeeeeeg dbf gegceeeebfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg fbd geeceeeabeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg bbgeeacegbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg dbfeecefbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg gbbeacbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg gedbfbfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg geeefbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg egggggggggggggggggggggggggggggggggggggge ```  Let's zoom in on area A to get a clearer view.  ```palette Key,Color ,#fefefeff a,#fd8486ff b,#0705fdff c,#fe0606ff d,#acabfdff e,#fec9caff f,#5249f6ff g,#f73b42ff ``` ```image bbf ec dbb cc bbd gcc fbf gcce dbb acce bbf ecca dbb ecca bbd eccg fbf gcg dbbd gcce bbf acce dbb acca bbd ecca fbf eccg dbbd gcg bbf gcc dbb acce bbd acce fbf ecca dbbd ecca bbf ccg dbb gcg bbd gcce fbf acce dbbd acca bbf ecca dbb eccg bbd gcg fbf gcce dbbd acce fbf acce dbb ecca bbd eccg fbf ccg dbbd gcc fbf gcce dbb acce bbd ecca fbf ecca dbbd eccg fbf gcg dbb gcce bbd acce fbf acca dbbd ecca fbf eccg dbb gcg bbd gcc fbf acce dbbd acce fbf ecca dbb ecca bbd ccg fbf gcg dbbd gcce e fbf acce g dbb acca ce bbdecca cg fbfeccg cce dbbdgcg gca fbfgcce ecc dbbacce gca bbfcce acc fbbcca cca dbbgcg acc fbfcg cce dbbcc acg bbgce cce fbbce acg dbbga ecce fbfa gcg dbbg ecce bbf gca fbbe ecc abbd gca abbf d ecc egbb bf gca ecbbd bbbd acc gfbb fbbfd ccccbbd dbbbf accbbf fbbbd cgbb dbbbfebbd fbbbbb dfbbd dd ```  Area A contains an intersection. After careful examination, I conclude that there is one intersection.

1

```palette Key,Color ,#fefefeff a,#fd8082ff b,#0504feff c,#fe0505ff d,#ababffff e,#ffc4c4ff f,#4e46f7ff g,#ff4040ff ``` ```image e ca c ce ec ce ec f c b ac bd c db ag b c ff ga b c bd ga db c b ce ff c b ce bd ec db c b ac ff c b ag bd c db gg b c ff c ga b ca c bd gg ce db ac c b ec ce ff c ec b ce c bd ca ec db cg c b gc ag ff ac c b ec ag bd c c db ce ga b ca c ff gg ca b ac c bd ec ce db c ec b ce ce ff ca ec b cg c bd gc ac db ec c b ec ag ff c c b ce ga bd cg c db gc ga b ac d c ff ec bb ce b c dbf c bd ce fbd ce db ca bb ec b gg dbd c ff ac bb ac b ec dbf c bd c fbd ag db ce bb c b ca dbd gg ffcg bb c bgc dbf ga bfc fbd c dbc bb ce bc dbd c fbe bb ce ba dbf ec bf fbd c ab bb ec eb dbd c fb bb acb dbfbd fb ```

This is the image I'm working with. The goal is to count the intersections. I've spotted 1 narrow regions that might be worth examining further. Let's call them area A.  ```palette Key,Color ,#fefefeff a,#5053faff b,#fe0706ff c,#0606feff d,#ffaeaeff e,#b3b3ffff f,#f55d58ff g,#aed5adff ``` ```image e ace c ce aa c c c aa ec c ec aa ec c ac aa ac c ac aa ac c ca aa ca c ca aa ce c ce aa ce c ce aa c c c ca ec c ec ce ec c ac ce ac c ac ce ac c ca ce ca c ca ce ce c ce ce ce c ce ce c c c ce ec c ec ce ec ec ac ce ac ec ac ce ac ec ca c ca ec ca c c ec c ec c ec c ec c ec c ec c ac c fbbbb aa dfbbbbfd c dfbbbbfd ggggggacgggggggg dfbbbbfd ggggggcggggggggg dfbbbbfd gggggaaggggggggg dfbbbbbd gggggcgggggggggg dfbbbbfd ggggaagggggggggg fbbbbfd ggggcggggggggggg dbbbf gggaaggggggggggg fbbbd gggagggggggggggg dfbbf gggggggggggggggg dbbbd gggggggggggggggg fbbf gggggggggggggggg dbbbf gggggggggggggggfbbbd ggggggggggggbbbf ggggggggfbbbfggg gggggfbbbggggggg gggbbfgggggggggg gggggggggggggggg gggggggggggggggg gggggggggggggggg ```  This is a magnified view of the region A.  ```palette Key,Color ,#fefefeff a,#5353ffff b,#ff0404ff c,#0101ffff d,#ff8e8eff e,#ffccccff f,#ff4949ff g,#d1d1ffff ``` ```image aca gccg aca gccg aca gccg aca gccg aca gccg aca gccg aca gccg gaa dfb edfbbbb efbbbbbfde edfbbbbbfde edfbbbbbfe dfbbbbbfde dfbbbbbfd ebbbfde fde ```  I'll move on to the next area. The intersection must be somewhere. I've examined the entire image, and there are zero intersections present.

0

```palette Key,Color ,#fefefeff a,#4848ffff b,#ff0505ff c,#0505ffff d,#ffadadff e,#8b8bffff f,#ff5959ff g,#ceceffff ``` ```image g ecg c cg ea cg c gc ea gc c gc aa ec c ec aa ac c ac aa ac c ca aa ca c ca aa ce c ce ae cg c cg ae cg c gc ae gc c gc ce ec c ec ce ac c ac ce ac c ca ce ca c ca ce ce c ce cg cg gc cg cg cg gc gc cg gc gc gc cg ec gc ec cg ac gc ac cg ac gc ca cg ca gc ca cg c gc c ec c ec c ec c ec c ec c ea c dbbbb ea dfbbbbfd c dfbbbbfd ea dfbbbbfd c dfbbbbfd aa dfbbbbbd c dfbbbbfd aa fbbbbfd c dbbbf aa fbbbd a dfbbf dbbbd fbbf dbbbf fbbbd dfbbf dbbbd fbbfd bbf ```

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.  ```palette Key,Color ,#fefefeff a,#f95a57ff b,#0808feff c,#a8a8ffff d,#fcacabff e,#fe0908ff f,#5153fbff g,#acd3adff ``` ```image c cb cb cb b cb b cb cb b fb b bf b bc b ggggggggbggggggg bc gggegggggbgggggg bc gggaagggggbggggg bc ggggegggggfbgggg bc ggggaegggggfbggg bf gggggeggggggbfgg bf gggggaeggggggbfg bf ggggggegggggggbg bf ggggggdegggggggb bf gggggggeggggggggb bb ggggggggegggggggcb fb ggggggggeggggggg fb fb gggggggggegggggg bf fb gggggggggedggggg bc fb a ggggggggggeggggg b fb de ggggggggggeagggg b cb e gggggggggggegggg cb cb e gggggggggggeaggg fb cb ea e fb cb ae aa bf cb de e bc b e aa b b ed e b b ea ae cb bc ae e fb bc e de fb bc e e bf bc ed de bc bc ae e b bf de de b bf e ed cb bf ed e fb bf ea ed bf bb ae e bf bb e ed bc fb e e bfb ed ea b ae e de aa e e ed aa ea e ae ae de e e de ed e aa de de e e de ed ed ea e ae ed de e e ed ed e ea ea de e e aa ed e ea aa ae e de ae e e ed de ea e de de e e e de ea eae e ```  Let's take a closer look at area A.  ```palette Key,Color ,#fefefeff a,#ff3535ff b,#0404ffff c,#aaaaffff d,#ff7c7cff e,#ff0404ff f,#4b4bffff g,#ffbbbbff ``` ```image cbbc fbbc fbb gaa fbf geeg bbf dea cbbf eeg cbbc dea cbbc eeg fbbc dea fbb eeg fbf dea bbf eed cbbf dee cbbc aed cbb gee fb aed f gee aed gee aed geeg aea geeg dea eeg dea eeg dea eeg dea eed dee aed gee aed ```  No intersection in area A, but I'll keep looking. My analysis shows there's absolutely no intersections in the image

0

```palette Key,Color ,#fefefeff a,#ff4343ff b,#0606ffff c,#9898ffff d,#ff9393ff e,#ff0505ff f,#4444ffff g,#edd6e7ff ``` ```image c cb cb cb b cb gb gb cb gb fb gb bf bg bc bg bg bg a b bc aa gb bc e cb bc da fb bc e bf bf de bc bf e bg bf de b bf eg gb bf ge cb fb eg fb fb ge bf fb ed bc fb a e bg cb de ed b cb ge e cb cb eg ad cb cb ed e fb gb ae aa bf gb de e bc gb e aa bg gbg ed e gb bg ea da cb bg de e cb bc ge de ff bc eg e bf bc ed de bc bc aa eg bg bc de ge gb bf e eg cb bf eg ge fb bf ea ed ff bf de e bc fb ge ed bc fb eg e bfb ed ad gb aa e de aa e e eg aa ea e de da ge e e de ed e aa de de eg e ge eg eg ea ge ae ed ge e e ed ed e aa ad de e ge aa eg e ed aa ae e ge da e e ed de aa e de de ge eg eg ge ed eae ge ```

This is the image I'm working with. The goal is to count the intersections. It's crucial to examine these regions more closely.  ```palette Key,Color ,#fefefeff a,#fd0909ff b,#0808feff c,#f56561ff d,#595ef4ff e,#a5a6fcff f,#feb4b4ff g,#add4adff ``` ```image c a af fa af fa a ca a cc a af a af fa a ca a cc a ggggggggggggacgg ggggggggggggaggg gggggggggggagggg gggggggggggagggg ggggggggggaggggg gggggggggcaggggg gggggggggagggggg ggggggggcagggggg eeddbbbddeee ggggggggaggggggg eeddbbbbbbbbbbdddee eeeddbbbbbbbbbbbbbddddegggacggggggg eeddbbbbbbbbbbbddee eedddbbbbbbbbbbbbbddeee bbbbddee ggggggacgggggggdedddbbbb ggggggaggggggggg gggggagggggggggg ggggcagggggggggg ggggaggggggggggg gggcaggggggggggg gggagggggggggggg ggacgggggggggggg ggaggggggggggggg gacggggggggggggg fa af fa a ca a cc a af a af fa a ca a cc a ac a af fa a fa a cc a ac ac a caaaf af faaaf fa faaac a caac fa faaaf a faaac ca caac a caaaf ac faaac a caac af caa ```  I wonder what we'll find inside area A?  ```palette Key,Color ,#fefefeff a,#fe0505ff b,#0704fbff c,#fc7a7cff d,#5958feff e,#9b9bfeff f,#ffc0c0ff g,#f73a41ff ``` ```image faa aac caa aaf cag faaf gag faaf gac faa aac caa aac cag faaf gag faaf gac faa ddddeeeee gac bbbbbbbbbbbbbbbbbbdddeeeee eeedddddbbbbbbbbbbbbbbbbbbbbbbb cggeeedddddbbbbbb aaf cag faaf gag faaf gac caa aac caa aaf cag faaf gag faaf gac faa aac caa ```  Success! This area contains an intersection point! There's only one, but is an intersection after all.

1

```palette Key,Color ,#fefefeff a,#ff0404ff b,#0909ffff c,#ff7b7bff d,#6363ffff e,#adadffff f,#ffbebeff g,#ff3c3cff ``` ```image c a af fa af fa a cg a gc a ac a af fa a cg a gg a ac a af fa a ca a gg eeddbbbdddee a eeddbbbbbbbbbbbddee eedddbbbbbbbbbbbbbdddee gc eeddbbbbbbbbbbbddee eedddbbbbbbbbbbbbbdddee bbbbddee af eedddbbbb fa af ca a cg a gc a af fa af fa a cg a gc a ac a af fa a cg a gg a ac a af fa a ca a gg a gc ac a caagf af caaaf fa fgaac af caagf fa caaaf a fgaac cg gaag a caaaf gc faaac a gaag af caa ```

I'm optimistic that I'll find some intersections in this image. These regions highlight areas that look suspicious. Lines seem to converge within them.  ```palette Key,Color ,#fefefeff a,#0c0cfdff b,#fa3b39ff c,#f68e8aff d,#7375f5ff e,#fe0505ff f,#e2cdeaff g,#add4adff ``` ```image c be bb eb eb ec ec ec ef ef ef fe fe fe ce ce ce be be bb eb eb ec ec d ec faa ef aaf ef aad e dad fe faa fe faa ce aaf ce dad d ce dad daa be faa daaf be aaf faad be aaf daa ebgggggggggggggggg dad daaf ebggggggggggggggg faa faad ebgggggggggggggg faa daa gebgggggggggggggaaf daaf ggebggggggggggaad faad gggeegggggggdaag aaa ggggbegggggaaggg daaf gggggbeggaaggggg faad ggggggbaadgggggg aaa gggggdadeggggggg daaf gggdaaggcegggggg faadgaagggggceggggg aagggggggggegggg ggggggggggggeggg gggggggggggggecg ggggggggggggggec gggggggggggggggec ggggggggggggggggeb eb eb be be be ce ce ce fe fef ef ec ec ec eb eb eb be be be ce ce ce fef fef e ```  Let's put area A under the microscope.  ```palette Key,Color ,#fefefeff a,#0605fdff b,#ff4b4bff c,#febdbdff d,#9292ffff e,#fd0809ff f,#cdcdffff g,#514af8ff ``` ```image b eb eeb ceeb ceeb ceeb ceeb f ceeb fga ceee gaaa ceeec daaagf eeec daaagf beec fgaaad beec fgaaad beec daaagf beecdaaagf beaaaaf fgaaag gaaageeb daaagf ceeb daaagf ceeb fgaaad ceeb ad fgaaad ceeb aaaaaag ceeb dgaagf ceee ff ceeec eeec beec beec beec bee be b ```  Case closed! This is definitely an intersection point in area A. The final count is: one intersection.

1

```palette Key,Color ,#fefefeff a,#0404feff b,#ff4f50ff c,#ffb1b1ff d,#8383ffff e,#ff0909ff f,#cacaffff g,#3e3bfcff ``` ```image c be ee eb eb eb ec ec ec ec e e ce ce ce ce be be be ee eb eb eb ec d ec faa ec aaf ec gad e dad e fag ce aa ce aaf ce gad d be dag gaa be faa daaf be aaf faad be gaf gag eb dad daaf eb fag faad eb faa gag eb aaf daaf eb gad faad ee dag gag be faa daaf be aaf faad baaf gag dage daaf dag ce faadfaa ce gaf ce ec ec ec eb eb eb ee ee be be be ce ce ce e ec ec ec eb eb eb ee ee be be be ce ce ce ec e ```

This is the image I'm working with. The goal is to count the intersections. These zones indicate regions where lines appear to be in close proximity.  ```palette Key,Color ,#fefefeff a,#5962ecff b,#fc0b09ff c,#0809fcff d,#e46e65ff e,#b0b1feff f,#b2d7b1ff g,#9ec9a1ff ``` ```image e ca c c ec ca ce ac c c ca c c ca ec ac ce c c c ca ca c ac ec c ce c c ca aa ac c c ec c ce ca c ac aa c c c ec ca ce ac c ec aa ggggggggggggggggggggggggggggggggggggggggggcgg c gffffffffffffffffffffffffffffffffffffffffcafg ec gfffffffffffffffffffffffffffffffffffffffacffg cegffffffffffffffffffffffffffffffffffffffgcfffg cgffffffffffffffffffffffffffffffffffffffcgfffg acfffffffffffffffgbbdffffffffffffffffffcaffffg cfffffffffffffffbggdbbbbdffffffffffffacfffffg acfffffffffffffbdffffffgdbbbbdffffffgcffffffg gcafffffffffffdbffffffffffffddbbbbdfcfffffffg gfcffffffffffgbffffffffffffffffffddcdbbdffffg gfacfffffffffbgfffffffffffffffffffacffddbbbbd gffcffffffffbdfffffffffffffffffffgcffffffffdbbbbbd gffgcffffffdbffffffffffffffffffffcffffffffffg fdbbbbd gfffcafffffbffffffffffffffffffffcaffffffffffg fdbbbbd gffffcffffbgfffffffffffffffffffacfffffffffffg fdb gffffacffbdfffffffffffffffffffgcffffffffffffg gfffffcfdbffffffffffffffffffffcfffffffffffffg gfffffgcbffffffffffffffffffffcafffffffffffffg gffffffcafffffffffffffffffffacffffffffffffffg gfffffbdcffffffffffffffffffgcfffffffffffffffg gffffdbfacfffffffffffffffffcffffffffffffffffg gffffbfffcgfffffffffffffffcaffffffffffffffffg gfffbdfffgcffffffffffffffacfffffffffffffffffg gffbbfffffcaffffffffffffgcffffffffffffffffffg gfdbfffffffcffffffffffffcfffffffffffffffffffg gfbffffffffacffffffffffcafffffffffffffffffffg gbdfffffffffcgffffffffacffffffffffffffffffffg bbffffffffffgcfffffffgcfffffffffffffffffffffg fbggggggggggggcaggggggcggggggggggggggggggggggg b c ce bd ac ac db c ec b ec c b cce bd a db b b bd db b b bd db b b bd db b b bd db b b ```  I'm determined to find out if an intersection exists in area A.  ```palette Key,Color ,#fefefeff a,#4a4afeff b,#fe0606ff c,#0706feff d,#f74951ff e,#908ffeff f,#cacaffff g,#fda3a4ff ``` ```image fcce aca acc eccf fcce aca acc eccf fcce aca e acc cf g eccf ca bbbbdgg fcce cce dbbbbbbbbbdgg cca ecc dbb ggdbbbbbbbbdgg acc cce gbbg ggdbbbbbbbbdgg eccf fccf bbd ggdbbbbbbbbdgg fcce aca dbd ggdbbbbbbbbdgg cca fcce dbb ggdbbbbbbbbdgg acc ecc gbbg ggdbbbbbbdccgg cce bbd ggddccdbbbbdgg fccf dbd ccagdbbbbbbbddgg aca gbb acc ggdbbbbbbbddg fcce gbbg eccf ggdbbbbb ecc bbd fcce ggd aca dbd cca fccf gbb acc aca gbbg eccf fcce bbd fcce ecc dbb cca aca gbb acc fccf gbbg eccf aca bbd fcce cce dbb cca ecc gbbg acc acagbbg eccf fccdbd fcce accb cca gcce acc gbdcc eccf bbdaca fcce dbb fccf cca gbbg aca acc bbg cce eccf dbd ecc fcce dbb aca cca gbbg fccf acc bbg aca eccf dbd cce fcce dbb ecc cca gbbg aca acc bbd fccf eccf dbd aca fcce dbb cce cca gbbg eccf aca bbd aca eccf dbd fccf fcce ```  The evidence is clear: this is an intersection in area A. Two intersections have been found!

2

```palette Key,Color ,#fefefeff a,#5858ffff b,#ff0707ff c,#0808feff d,#fb4c50ff e,#9e9dfdff f,#e2d9f6ff g,#ffa2a2ff ``` ```image e ca c c ec ca cf ec fc fc ca cf c ca ec ac cf fc fc cf aa ca c ac ec fc ce cf c ca aa ac c fc ec cf ce ca c ac aa fc c cf ec ce ce ac c fc aa cf c ce ec ac ce fc c cf aa fbbg ce c bfgdbbbbg ac ec bd gdbbbbg fc ce db gdbbbbg cf c fb gdcdbbg aa bf ac gdbbbdg c bd fc gdbbbdg ec gb c gdbbbdg ce b ce gdbbbdg c bf ac gdb aa bd fc cfgb c fcb ce ce ac bdc fc gb ac c b cf ce bg fc ac dd ce fc gb c c b ac ce bg cf ac dd fc fc gb ce c b c ce bg ac ac db cf ec gb fc c b cce bg a db fb b bg db fb bf bd db fb bf bd gb b bf bd gb b bg ```

Let's examine this image for potential line intersections. I need to zoom in on these areas to get a better look.  ```palette Key,Color ,#fefefeff a,#4449ebff b,#fa0a0bff c,#0606fdff d,#e16b62ff e,#b1d7b1ff f,#8e99e9ff g,#99c796ff ``` ```image f fc fc c c c cf cf cf ca ca ac ac fc fc d ggggggggggggggggggggggggggggggggggggggfcgggggggggggbb eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegceeeeeeeeeedbde eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeceeeeeeeeeebbeee bd eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecgeeeeeeeedbdeeee bb eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecfeeeeeeeebbeeeeee db eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecfeeeeeeegbdeeeeeee bd eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecaeeeeeeebbeeeeeeeee bb eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecaeeeeeegbdeeeeeeeeee dbe eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecceeeeeebbeeeeeeeeeeee bb eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaceeeeeebbeeeeeeeeeeeee bb eeeeeeeeeeeeeeeeeeeeeeeeeeeeeaceeeeedbgeeeeeeeeeeeeee ebd eeeeeeeeeeeeeeeeeeeeeeeeeeeeaceeeeebbeeeeeeeeeeeeeeee bb eeeeeeeeeeeeeeeeeeeeeeeeeeefceeeedbgeeeeeeeeeeeeeeeee db eeeeeeeeeeeeeeeeeeeeeeeeeefceeeebbeeeeeeeeeeeeeeeeeee bd eeeeeeeeeeeeeeeeeeeeeeeeeeceeedbdeeeeeeeeeeeeeeeeeeee bb eeeeeeeeeeeeeeeeeeeeeeeeeceeebbeeeeeeeeeeeeeeeeeeeeee db eeeeeeeeeeeeeeeeeeeeeeeecfedbdeeeeeeeeeeeeeeeeeeeeeee bd eeeeeeeeeeeeeeeeeeeeeeecfebbeeeeeeeeeeeeeeeeeeeeeeeee bb eeeeeeeeeeeeeeeeeeeeeecagbdeeeeeeeeeeeeeeeeeeeeeeeeee dbe eeeeeeeeeeeeeeeeeeeeecabbeeeeeeeeeeeeeeeeeeeeeeeeeeee bd eeeeeeeeeeeeeeeeeeeecabdeeeeeeeeeeeeeeeeeeeeeeeeeeeee bb eeeeeeeeeeeeeeeeeeeccbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee ebdeeeeeeeeeeeeeeeeeacbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee bbeeeeeeeeeeeeeeeacgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee edbeeeeeeeeeeeeedceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eegbdeeeeeeeeedbceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeebbeeeeeeebbceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeeedbgeeedbdceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeeeeebdebbecgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeeeeeebbdecfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeecfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeecaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeecaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeeeeeecaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeeeeecaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeeeecfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeefcgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeefceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeaceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee ecceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee cceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee cagggggggggggggggggggggggggggggggggggggggggggggggggggg cf cf fc fc ac cc ca cf cf fc fc ac cc ca ca cf c fc ac ac cc ca cf ```  I'm eager to see what's happening in this magnified view of area A.  ```palette Key,Color ,#fefefeff a,#5551fbff b,#fd0506ff c,#0807feff d,#fc8a8cff e,#f73e45ff f,#b0b0feff g,#fecdceff ``` ```image fcca ge fcca dbb fcca gebbe cca dbbbd cca gebbeg ccc dbbbd acc ebbeg accf dbbbd accf ebbeg accf gbbbd accf dbbeg fccf gbbbd fccf dbbbg fcca gebbe fcca dbbbg fcca gebbe cca dbbbd cca gebbeg acc dbbbd acc ebbeg accf dbbbd accf ebbeg accf gbbbd fccf ebbeg fccf gbbbd fcca dbbbg fcca gebbe fcca dbbbg fcca gebbe cca dbbbd ccc gebbeg acc dbbbd acc gebbeg accf dbbbd accf ebbeg accf gbbbd fccf ebbeg fccf gbbbd fcca dbbbg fccagebbe fccadbbbg ccaebbe cccbbbd cccbbeg g accbbd bd accbeg bbe acced dbbeg acceg gbbbd gaccd ebbe eeccf dbbbg gbecca gbbbd dbecca ebbeg gebbcca dbbbg dbbecca gebbd gebbecca dbbeg dbbbdccc gbbbd gebbegacc gebbe dbbbd acc dbbeebbeg accf gbbbbd accf eeg accf fccf fccf fcca fcca fcca fcca fcca fcca acca accf accf cccf fcccf fcca fcca acca acca accf cccf fcccf fccc ```  Gotcha! I've found the intersection hiding in area A! I've found a single intersection point in the image.

1

```palette Key,Color ,#fefefeff a,#4441fbff b,#ff0606ff c,#0504feff d,#fe8e8eff e,#f43a44ff f,#9090ffff g,#e5d4edff ``` ```image f fc fc gc gc cg cg cf cf ca ca ac ac fc fc d gc bb gc dbd cg bb bd cg dbd bb cg bb dbg cf gbd be cf eb bb ca gbe dbd ca ebg be ac gbe eb ac ebg dbd fc be bb fc dbg eb gc bb gbd gc dbd bb cg bb dbg cg dbd gbe cf bb bb cfgbd dbg caeb be cabe eb acbg dbd ace be acg eb ec gbd dec bb bec dbg dbdc gbe bb cg bbd cg cf cf ca ca cf cf gcg fc ac ac ca ca cf gcg fcg fc ac cc ca cf gcf gcg fc ac ac ca ca cf gcg fc fc ac cc ca cf ```

I'm analyzing this image to identify any points where lines intersect. I have a hunch that these areas might contain the intersections we're looking for.  ```palette Key,Color ,#fefefeff a,#fd0807ff b,#3e3ef2ff c,#f39f99ff d,#8993e7ff e,#add4adff f,#ef534fff g,#0404fdff ``` ```image d bg gg a gb afa gd a ac gd ac a dg a a dg ac fa bg a af bg ff a gb a a gb ff ca gd a af g ca ac dg a a bg ca faeeeeeeeeeeeeeebg a eafeeeeeeeeeeeegb a eeaceeeeeeeeeegb a eeeaeeeeeeeeegde a eeecaeeeeeeegdee ac eeeeaaeeeedgeeee a eeeeeaceebgeeeee ac eeeeeeaebgeeeeee a eeeeeecggeeeeeee ff eeeeeegbaeeeeeee eeeeeeeeeeeaeeee eeeeegdeafeeeeee eeeeeeeeeeffeeee eeeegdeeeaeeeeee bd eeeeeeeeeeaeeeee eedgeeeeecaeeeee dgggd eeeeeeeeefaeeeee ebgeeeeeeefaeeee bggb eeeeeeeeeaeeeeee bgeeeeeeeeeafeee dgggd eeeeeeeecaeeeeee ggeeeeeeeeeeeaeee bggbdeeeeeeaeeeeeee gbeeeeeeeeeeeeeaee dgggdeecaeeeeeee gd eeeeeeeeeeeeefae eeeebggbdeeeeeee gd eeeeeeeeeeeeeeaf eeeeeeefgggdeeee dg a eeeeeeaceeebggbd dg a eeeeeeaeeeeeeedgggd bg ca eeeeeafeeeeeeeee bggbgg af eeeeeaeeeeeeeeee db a eeeeffeeeeeeeeee a eeeeaeeeeeeeeeee ca eeeffeeeeeeeeeee af eeeaeeeeeeeeeeee ac eefaeeeeeeeeeeee a a ca ca ff a ac ca a a ca a ff ac ac a a ac ca a fa fc ac a a ff a a fa ff ac a a ca a ca a a ac a ac a ac a ff a ff a ca a ca a ```  Let's see if area A yields any clues.  ```palette Key,Color ,#fefefeff a,#fe0808ff b,#5655feff c,#ffb6b6ff d,#a9a7fdff e,#ff5f5fff f,#8e0070ff g,#0706fdff ``` ```image eae caa eae caac eae aac eae aac eaa aac caa aac caa aae gbdd caa gggggbd eae dbgggggbdd caa dbggggggbd eae dbggggggfd dbggggggbd afbgggggbdd eae dbggggggbd aac dbgggggbd eaa dbgggg aac db caa aac caa aae caa eae caa eae caac eae aac eae ```  Gotcha! I've found the intersection hiding in area A! Let's move forward and inspect another region. I'm analyzing this close-up of area B with precision.  ```palette Key,Color ,#fefefeff a,#fd0607ff b,#514ffcff c,#fec4c5ff d,#a8a8ffff e,#fc8183ff f,#ff4040ff g,#0806fdff ``` ```image aaf caae eaac faa faf d caae dg eaac dgg eaa bggb faf bggd caae bggd caac gggd eaac dggg faf dggb caae dggb caac bggb eaac bggd faf bggd aaegggd caggg dgggc dggbaf bggb aaf bggd caae bggd eaac gggd faa dggg aaf dggb caae dggb eaac bggb faa bggd faf bggd caae gggd eaac ggd faa b faf caae caac eaa ```  I observe an intersection inside area B. I've identified a total of two intersection points.

2

```palette Key,Color ,#fefefeff a,#ff0505ff b,#4846fcff c,#ffbebeff d,#a1a0fdff e,#ff7a7aff f,#fc383bff g,#0605fdff ``` ```image d bg gg ca gb afa gb a ae gd ac a dg a ca dg fe ea bg a ae gg fe ac gb a a gb ef ea gd a af dg ef ac dg a a bg ca ea bg a ff gb ca ac gb ac a gd a ca gd ac ff dg a ac bg fe a bg a cgg fe gbf a gd ae ef gd a bd a dg ca dgggd ef dg fa bggbd a bg ae dgggd ca gg a bggbd a gb ca dgggd ca gd ea bgggd gd ae fgggd dg ac ac bggb dg a a dgggd bg ea ae bggbgg ae a db ac fe a a ea ef ff a ac ef a a ca ca ff a ac ca a ac ca ca ff ac ac a a ac ca a ff fe ae a a fe ca a ea ef ae a a ea a ca a ca ac a ac a fe a fe a ef a ef a ca a ```

This is the image I'm working with. The goal is to count the intersections. I have a hunch that these areas might contain the intersections we're looking for.  ```palette Key,Color ,#fefefeff a,#f85855ff b,#5153fcff c,#0808feff d,#fe0808ff e,#ffb8b8ff f,#9899faff g,#add4adff ``` ```image f bcccccf bcb bcccbf bcb fccccb bcb bcccbf bcb fbcccb bcb fccccf fcb fbcccbf fcb fccccf fcc fbcccbf fcc fccc fcc fcc fcc fcc fcc gggggggbccgggg gggggfccgggggg gggfccgggggggg gggcgggggggggg gggggggggggggg gggggggggggggg gggggggggggggg gggggggggggggg gggagggggggggg gggadggggggggg gggggdaggggggg ggggggddgggggg ggggggggdagggg gggggggggddggg ggggggggggadgg ggggggggggggdd gggggggggggggad ggggggggggggggeda gggggggggggggg dd gggggggggggggg ede gggggggggggggg dd ade da ad eda dd ede dd ade da ad eda dd ede dd ade dd ade dd ade da ad eda dd eda dd eda dd ede dd ede dd ade dd ade dd ade da ad eda dd eda dd ed ```  Let's get to the bottom of what's happening inside area A.  ```palette Key,Color ,#fefefeff a,#ff3e3eff b,#2e2effff c,#0404ffff d,#ff0404ff e,#ffc9c9ff f,#9494ffff g,#ff8787ff ``` ```image fbcccf fbcccf fbcccf fbcccf fbcccf fcccf bf ge eddg addae gdddg eadda gddde eaddg gddae edddg addae gdddg eadda gddde eadd gd e ```  This isn't an intersection in area A, but I'm not discouraged. My analysis shows there's absolutely no intersections in the image

0

```palette Key,Color ,#fefefeff a,#ff3b3bff b,#4d4dffff c,#0606ffff d,#ff0404ff e,#ffc0c0ff f,#9e9effff g,#ff7a7aff ``` ```image f bcccccf bcb fbcccbf bcb fbcccb bcb bcccbf bcb fbcccb bcb fccccf fcb fbcccbf fcb fccccf fcb fbcccbf fcc fccc fcc fcc fcc fcc fcc fcc fcc fcc b g ade da ad edg dd gde da ad eda ad edg dd gde da ad edg dd edg dd gde da ad edg dd ede dd gde dd gde da ade da ad eda ad edg ad edg dd edg dd gde dd gde da gde da ade da ad eda ad edg ad ed ```

Hmm, I'm not sure what to expect from this image. Let's see if any lines cross. My next step is to analyze the details within each area.  ```palette Key,Color ,#fefefeff a,#fd0706ff b,#5a64e0ff c,#e58e82ff d,#0606fbff e,#f1f2edff f,#afd6b0ff g,#ea4c46ff ``` ```image e ac ea ae ea ae ca a cg a gc a ac ea ae ea ae ca a cg a gc a ac ea ae ea ae ca a cg a gc a ac ea ae ea ae ca a gg a gc a ac ea ae ea a ca a gg a gc a ac ea eeeaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee fffcaffffffffffffffffffffffffffffffffffffffffffffffffffffe ffffaffffffffffffffffffffffffffffffffffffffffffffffffffffe ffffcafffffffffffffffffffffffffffffffffffffffffffffffffffe fffffafffffffffffffffffffffffffffffffffffffffffffffffffffe fffffggffffffffffffffffffffffffffffffffffffffffffffffffffe ffffffaffffffffffffffffffffffffffffffffffffffffffffffffffe ffffffagfffffffffffffffffffffffffffffffffffffffffffffffffe fffffffaffffbdbffffffffffffffffffffffffffffffffffffffffffe fffffffabdddbbddddbffffffffffffffffffffffffffffffffffcgaae ffffbdddbfffffffffbddddbffffffffffffffffffffffffffgaaacffe bdddbfffaffffffffffffffbdddbbfffffffffffffffffcaaagffffffe bdddbfffffffcafffffffffffffffffbddddbffffffffffgaaacfffffffffe bdddbe fffffffffaffffffffffffffffffffffbddddbfcaaagfffffffffffffe bdddbe fffffffffcafffffffffffffffffffffffffgddddbfffffffffffffffe bdddbe ffffffffffafffffffffffffffffffffcaaagffffbddddbffffffffffe bdddbe ffffffffffggfffffffffffffffffgaagcffffffffffffbddddbfffffe dddbe fffffffffffafffffffffffffcaaacffffffffffffffffffffbddddbfe e fffffffffffagffffffffcgaagfffffffffffffffffffffffffffffbde ffffffffffffafffffgaaacffffffffffffffffffffffffffffffffffe ffffffffffffaccaaagffffffffffffffffffffffffffffffffffffffe fffffffffffffaacfffffffffffffffffffffffffffffffffffffffffe fffffffffffffffffffffffffffffffffffffffffffffffffffffffffe fffffffffffffffffffffffffffffffffffffffffffffffffffffffffe eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee ```  My goal is to determine if there's an intersection inside area A.  ```palette Key,Color ,#fefefeff a,#fe0405ff b,#524df9ff c,#fd8485ff d,#0604fdff e,#ffc1c1ff f,#a2a1feff g,#fc4346ff ``` ```image eaae gac eaa gac eaa aac caa aae cag aae gag eaae gac eaa gac eaa aac ffbbbf cag ffbdddddddddbff eg aabbddddddbffbbdddddddbff ecgaaa ffbddddddbf ffbdddddddbbf cgaaaaagc ffbddddddbf ffbdddddddbff ecgaaaaagc ffbddddddbf gag fbbddddddbbf ecgaaaaagce fbddddddbf eaae ffbdddddddbff ecgaaaaage ddddbf gac fbbdddddddbff ecgaaaaagce bf eaa fbdddddddbbf ecaaaaaage gac ffbdddddddbff ecgaaaaagce eaa fbbdddddddbff egaaaaaace aac ffbddddddddbgaagce cag cgbddddddddbff aae ecgaaaaagcfbbddddddbbf cag cgaaaaagce ffbdddddddbff aae ecgaaaaagc fbbdddddddbff gag ecgaaaaagce ffbdddddddbbf eaae ecaaaaaage ffbdddddddbff gac ecgaaaaagce fbbddddddbbf eaa egaaaaaace ffbddddd gac ecgaaaaagce fbb caa egaaaaagce aac ecgaaaaagce cag cgaaaaagce aae ecgaaaaagc caaaaaaagce aaaage ece ```  Incredible, there's actually an intersection in area A! Two intersections have been found!

2

```palette Key,Color ,#fefefeff a,#fe0606ff b,#554ff9ff c,#ff8d8dff d,#0504fdff e,#efd0e0ff f,#8c8cffff g,#fc474aff ``` ```image e ac a ae ea a ca a cg a gc a ac a ae ea a ca a cg a gc a ac a ae ea a ca a cg a gc a ac a ae ea a ca a gg a gc a ac ea ae ea a ca a gg a gc a ac ea ae ea a ca a gg a gc a fbf abdddbfbdddbe egaa fdddbe fddddf caaac fdddbe ae ebdddbf eaaag fdddbe ea fddddbe gaaac fdddbe a ebddddf caaac fdddbe cg egddddbe fdddbe a caaac fddddf fdddbe gg egaage ebdddbf dddbe a caaac fbdddbe e gc egaage fd a caaac aeegaage eaac ```

I have an image in front of me. I need to determine if there are any intersection segments. It's crucial to examine these regions more closely.  ```palette Key,Color ,#fefefeff a,#0607fcff b,#fa0e0dff c,#dd7566ff d,#b1d7b1ff e,#8e9fdaff f,#4752e9ff g,#97c895ff ``` ```image c bb bb bc db cb bb bc e bd fae cb a a bb ff a bb a a bc ff ea cb ggggggggggggggggggggggggggggggggaggggggfaggggggggggggggggd bb dddddddddddddddddddddddddddddddffdddddddfadddddddddddddddg bb dddddddddddddddddddddddddddddddadddddddddaaddddddddddddddg bc ddddddddddddddddddddddddddddddffddddddddddafdddddddddddddcb ddddddddddddddddddddddddddddddaddddddddddddafdddddddddddcb dddddddddddddddddddddddddddddffdddddddddddddaedddddddddbbg dddddddddddddddddddddddddddddadddddddddddddddaddddddddbcdg ddddddddddddddddddddddddddddffddddddddddddddddadddddgbcddg ddddddddddddddddddddddddddddadddddddddddddddddeadddcbddddg dddddddddddddddddddddddddddffddddddddddddddddddeadbbdddddg dddddddddddddddddddddddddddaddddddddddddddddddddfabddddddg ddddddddddddddddddddddddddffddddddddddddddddddddbaaddddddg ddddddddddddddddddddddddddadddddddddddddddddddcbddafdddddg dddddddddddddddddddddddddffddddddddddddddddddbbddddafddddg dddddddddddddddddddddddddaddddddddddddddddddbbddddddaedddg ddddddddddddddddddddddddafdddddddddddddddddbcddddddddaeddg ddddddddddddddddddddddddaddddddddddddddddcbgddddddddddaddg dddddddddddddddddddddddafdddddddddddddddcbddddddddddddeadg dddddddddddddddddddddddadddddddddddddddbbddddddddddddddeag ddddddddddddddddddddddafddddddddddddddbbddddddddddddddddfa ddddddddddddddddddddddadddddddddddddgbcddddddddddddddddddfa dddddddddddddddddddddafddddddddddddcbddddddddddddddddddddgaf dddddddddddddddddddddaddddddddddddbbdddddddddddddddddddddg af ddddddddddddddddddddafdddddddddddbbddddddddddddddddddddddg ae ddddddddddddddddddddadddddddddddbbdddddddddddddddddddddddg ae dddddddddddddddddddafddddddddddbcddddddddddddddddddddddddg a dddddddddddddddddddaddddddddddbcdddddddddddddddddddddddddg a ddddddddddddddddddaeddddddddgbgddddddddddddddddddddddddddg a ddddddddddddddddddaddddddddcbddddddddddddddddddddddddddddg ea dddddddddddddddddaedddddddcbdddddddddddddddddddddddddddddg fa dddddddddddddddddadddddddbbddddddddddddddddddddddddddddddg fa ddddddddddddddddaeddddddbbdddddddddddddddddddddddddddddddg af ddddddddddddddddaddddddbbddddddddddddddddddddddddddddddddg af dddddddddddddddaedddddbcdddddddddddddddddddddddddddddddddg ae dddddddddddddddadddddbcddddddddddddddddddddddddddddddddddg a ddddddddddddddaedddgbgdddddddddddddddddddddddddddddddddddg a ddddddddddddddadddcbdddddddddddddddddddddddddddddddddddddg a dddddddddddddaeddcbddddddddddddddddddddddddddddddddddddddg ea dddddddddddddaddbbdddddddddddddddddddddddddddddddddddddddg ea ddddddddddddaedbbddddddddddddddddddddddddddddddddddddddddg fa ddddddddddddadbbdddddddddddddddddddddddddddddddddddddddddg aa dddddddddddaebcddddddddddddddddddddddddddddddddddddddddddg af dddddddddddabcdddddddddddddddddddddddddddddddddddddddddddg ae ddddddddddabdddddddddddddddddddddddddddddddddddddddddddddg a dddddddddcaddddddddddddddddddddddddddddddddddddddddddddddg ddddddddcaeddddddddddddddddddddddddddddddddddddddddddddddg dddddddbbadddddddddddddddddddddddddddddddddddddddddddddddg ddddddbbaedddddddddddddddddddddddddddddddddddddddddddddddg dddddbcdaddddddddddddddddddddddddddddddddddddddddddddddddg ddddbcdaeddddddddddddddddddddddddddddddddddddddddddddddddg dddbcdeadddddddddddddddddddddddddddddddddddddddddddddddddg dcbdddaedddddddddddddddddddddddddddddddddddddddddddddddddg cbdddeaddddddddddddddddddddddddddddddddddddddddddddddddddg cbddddaeddddddddddddddddddddddddddddddddddddddddddddddddddg cddddeadddddddddddddddddddddddddddddddddddddddddddddddddddg ggggaggggggggggggggggggggggggggggggggggggggggggggggggggggd a a a a ea a ea a ea a ```  Let's take a closer look at area A.  ```palette Key,Color ,#fefefeff a,#0605feff b,#fe0708ff c,#fea0a1ff d,#e3d5f0ff e,#9090feff f,#4743fbff g,#fd4b4dff ``` ```image faf eaae daad faad faf faad daad faad faf faf daad daaf faf daaf daad daae faf eaae g daad eaae dgb faf eaad cbbb daad faad cbbgd faf faad gbbg daad faa gbbc faf daa dbbbc aad daf cbbbd af daf cbbg dad aae gbbg dad eaaebbbd fa faabgd daa gfaad fae dgbbfaad daad bbbc faf fae cbgd daaf daad gbg daaf fae gbb daae eaad dbbbc eaae fae cbbbd eaae eaad cbbg eaad fae gbbg faad eaad dgbbc faad fae cbbbc faad eaa cbbgd daaf fae gbbg daaf eaa gbbc daaf fae dbbbc eaa eaa cbbbd ea fae gbbg e eaa gbbc fae dbbbc eaa cbbbd fae cbbg eaa gbbg aae gbbc eaa dbbbc aae dbbbd eaa cbbgd aae cbbg eaa cbbg aae gbbg eaa gbbc aae gbbc eaa dbbbc eaa bbgd aae cbg eaa cbg aae gbb eaa gbbc aae gbbc eaa dbbbc aae dbbbd eaa cbbgd aae cbbg eaa cbbg aae gbbc eaa gbbc aae gbbc eaf dbbbc aae dbbbd eaf cbbg aae cbbg eaf cbbg aae gbbc eaf gbbc aae gbbc eaf dbbbd daae cbbbd eaf cbbg daae cbbg eaf cbbg daaegbbc eafgbbc daagbbc eaabbd daabbd faag caag faf gbaf dgbbad dbbbff cbbbdad cbbg fa cbbg daa gbbg faf gbbc daad gbbc faf dgbbc daad dbbbd faf cbbbd daad cbbg faf cbbg daad gbbg faf gbbc daad bbc faf cc daad ```  Eureka! There's definitely an intersection in area A! The final answer is: two intersections found.

2

```palette Key,Color ,#fefefeff a,#0605feff b,#fd0709ff c,#fe9b9cff d,#e2d5f2ff e,#9998feff f,#4d4dfeff g,#ff4d4dff ``` ```image c gb bg bc cbd gb bb bg e dbc fae gb a ad bb ff ad bg a da dbc ff ea cbd a ea gb ff fa bb a af bc ff af cbd a ae gb ff ae bb a ad bg ff da dbc a da cb ff ea bb a fag ff dbfa a cbd af ff gb af a bb ae fe bg ad a cbd ad fe gb da a bb ea fe bg ea a dbc fa ae cb af a gb af ae bb ae a bg ae ae bg ad a bc da ae dbd da a cb ea ae gb fa a gb fa ae bb af a bg af ae bc ae a bc ad ae dbd ad a cb da ae gb ea a gb ea ae bb fa da bg af aebc af dabc ae abd a ca gad gba bbad bgda bc ad dbc da cbd ad cb da gb ad c da ad da ad da ad da ad da ad da ad ```

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.  ```palette Key,Color ,#fefefeff a,#fe0504ff b,#0a0afdff c,#f38d87ff d,#d4c8f2ff e,#6669f4ff f,#abd3acff g,#fd4a4aff ``` ```image d bbd dbd bd eb bd bb b g dbe db gg ebd db a bb db gg be db a dbd eb gc eb eb a bb eb gc dbe eb a eb bb fffagfffffffffff bb bb ffffafffffffffffbe bb ffffacffffffffebd be fffffafffffffbbf be fffffacfffffbbff be ffffffaffffbefff be ffffffacfebfffff bd fffffffabbffffff bd fffffffbefffffff bd fffffebfafffffff bd ffffbbffacffffff b fffbbffffaffffff db ffbefffffacfffff db ebffffffffafffff db bbfffffffffacffff db dfffffffffffaffff eb fffffffffffacfff eb a eb ad eb da bb ad bb da bb a be da be a be da be a bd ca bd a bd ca bd a b ca db a db ca d a ca a ca a cg a cg a cg a gg a gg a gg a gg a gg a gc a gc a gc a ac a ac aaaaaaaaaaaaaaaaaaaagggggcccccdd ddccccccgggggaaaaaaaaaaaaa ```  I'm now examining the contents of area A in detail.  ```palette Key,Color ,#fefefeff a,#fe0505ff b,#0606feff c,#fe9494ff d,#d0cffeff e,#4745fcff f,#928efaff g,#f22632ff ``` ```image gac caa gac caa d gac fb caa ebb gac debbf caa dbbbd gac fbbed caa ebbe gac dbbbf cag fbbbd aac ebbe cag debbf aafbbbd cgbbed ebbe dbbbgg fbbbdaac ebbe cag debbf aac fbbbd cag fbbed aac ebbf cag dbbbf aac fbbed cag ebbe aac ebbf cag bbd aac ed cag aac cag ```  As I suspected, there's an intersection within area A. There's only one, but is an intersection after all.

1

```palette Key,Color ,#fefefeff a,#ff0303ff b,#0606ffff c,#ff7b7bff d,#b4b4feff e,#5250fdff f,#ffc1c1ff g,#ff3c3cff ``` ```image d bbd dbd bd eb b bb b g bd b gc eb db a bb db gc be db a dbd db gc eb eb a bb eb gc dbd eb a eb eb gc bb bb a be be gc dbd be a eb be ac be be a dbd bd ac eb bd abb bd be bd dbda b eb af b be a b dbd af db eb a db bb af db a db af eb fa eb af eb fa eb af bb fa be af be fa be a be fa bd a bd fa bd a bd fa b a b fa b a db ca d a ca a cg a cg a cg a cg a cg a cg a gg a gc a gc a gc a gc a gc a gc a ac aaaaaaaaaaaaaaaaaaaggggcccccfffff ffffcccccggggaaaaaaaaaaaaa ```

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.  ```palette Key,Color ,#fefefeff a,#5759faff b,#fe0606ff c,#ee9f97ff d,#add5adff e,#0808feff f,#f24d47ff g,#aeaeffff ``` ```image dddddddddddddddd dddddddddddddddd dddddddddddddddd dddddddddddddddd cc dddccccffffffbbbbbbbbbbbbbbbbbbbbbbbbbfbc dddbfffffffccccd bf dddddddddddddddd bf dddedddddddddddd bf dddaeddddddddddd bb ddddeddddddddddd fb ddddaadddddddddd fb dddddedddddddddd fb dddddaaddddddddd cb ddddddeddddddddd cb ddddddeadddddddd cb dddddddedddddddd b eg b e bc eg bc e bc eg bf ge bf e bf ge bb e fb ge fb e fb ge cb e cb aa cb e b aa bc e bc aa bc e bf eg bf e bf eg bb e fb eg fb e fb eg cb ge cb e cb ge b e ge e ge e aa e aa e aa e eg e eg e eg e eg ge e gee ge aeeg e eea ge geeg e aee ge eea e geeg aa aee e geea aa aeeg e eea aa geeg e aee eg geea e aeeg eg eea e geeg egaee ea ```  This close-up of area A is like examining a piece of evidence.  ```palette Key,Color ,#fefefeff a,#5b5bffff b,#ff0101ff c,#ffb4b4ff d,#ff7b7bff e,#0606ffff f,#ff3f3fff g,#c7c7ffff ``` ```image ccccccddddddddffffffffb cbbbbbbbbbbbbbbbbbbbbbbb ffffffffddddddddccccccc g gee eeg aea eeg aea geeg aea geeg aea geeg aea gee aea gee eea gee ```  The lines within area A do not intersect. I'm extremely confident. No intersections at all.

0

```palette Key,Color ,#fefefeff a,#3d3dffff b,#ff0909ff c,#ffb6b6ff d,#7676ffff e,#0404ffff f,#ff5d5dff g,#b8b8ffff ``` ```image cccc ccccffffffbbbbbbbbbbbbbbbbbbbbbbbbbbbc bffffffcccccc bf bf e bf da bb e bb da fb e fb ad fb e cb ad cb e cb eg bc e bc eg bc e bf eg bf ge bf e bb ge bb e fb ge fb e fb da cb e cb da cb e bc aa bc e bc ad bf e bf ad bf e bb eg bb e bb eg fb e fb eg fb ge cb e cb ge cb e ge e da e da e aa e ad e ad e eg e eg e eg ge e gee ge deeg e aea ge geed e dee da eed e deeg da aea e geed ad deeg e eea ad geeg e aee ad geed e deeg eg aea e geed egdee ed ```

Here's an image. My task is to find intersections or areas where lines come close together. I'd describe these as 'hotspots' for potential intersections.  ```palette Key,Color ,#fefefeff a,#f84946ff b,#0606feff c,#5e61f9ff d,#fc9c9bff e,#fe0606ff f,#b9b9ffff g,#b0d6b0ff ``` ```image d aee deed eea aeed deea aeed deed aee deed eea aeed deea aee deed eea deed eea ea e e aa e ed de e aa e ed de e ed de e aa e ed de e aa e e de e ed de e aa e ed de e ed e e aa e ed de e ggggggggggggaagg ggggggggggggeggg c gggggggggggegggg fbbc ggggggggggaegggg cbbf ggggggggggeggggg fbbc gggggggggeaggggg cbbf gggggggggegggggg fbbc ggggggggeggggggg cbbf gggggggaaggggggg bbc gggggggegggggggg cbbf ggggggedgggggggg bbc gggggdeggggggggg fbbf gggggegggggggggg cbb ggggeagggggggggg fbbc ggggeggggggggggg cbb gggbbbbccggggggg fbbc gggggggccbbbbbbbcff cbbf ggggggggggggggggccbbbbbbbcff fbbc gggggggggggggggg fccbbbbbbbcff cbbf gggggggggggggggg fccbbbbc gggggggggggggggg gggggggggggggggg gggggggggggggggg ```  Could this be where the intersection is hiding, in area A?  ```palette Key,Color ,#fefefeff a,#f33a45ff b,#0505ffff c,#584cf3ff d,#fcc3c5ff e,#ff0505ff f,#afaffeff g,#ff8282ff ``` ```image gee deed aea gee eeg aea deed aeg gee deed aea deed eeg gea deed aea gee eeg aea deed eeg gee deed aea geed eeg gea deed aeg gee deeg caaf dbbbbbbbcccfff cccbbbbbbbbbbbbbcccfff fffcccbbbbbbbbbbbbb fffcccbbbb f ```  My analysis confirms the presence of an intersection in area A. The final count is: one intersection.

1

```palette Key,Color ,#fefefeff a,#ff3939ff b,#0606ffff c,#6162ffff d,#ffb7b7ff e,#ff0404ff f,#b9b9ffff g,#ff7878ff ``` ```image d aee geeg eea geed deea aeed deeg aea geeg deea geed deeg aeed deeg aea geed eea ag de e ga e ed de e aa e ed ge e eg de e aa e ed de e ag e ed ga e eg de e aa e ed ge e ag de e ga e ed de e aa e c ed fbbc ge cbbf e fbbc eg cbbf de fbbc e cbbf aa bbc e cbbf ed bbc de fbbf e cbb ag fbbc e cbb bbbbccf fbbc ffcbbbbbbbcff cbbf fccbbbbbbbcff fbbc fccbbbbbbbcff cbbf fccbbbbc ```

I'm approaching this image with caution. Intersections might be tricky to spot. Could these regions be concealing intersection points? Let's find out.  ```palette Key,Color ,#fefefeff a,#fe0707ff b,#0b0cfcff c,#feacacff d,#6870ebff e,#9ec197ff f,#f45e59ff g,#b0d6b1ff ``` ```image fa aff ca a a ca ca a a ca ca ac a a ca af a a ca ff a a ca ca a a ca ca a ac ca a a ac ca a a ff ca a a fa ca a a ca d ca ac bb a a bb ca ac bb a a bd ca ff bd a a bd ca fa bd a a bg ca ca b a ac b ca egeagggggggggggdb g a eggafgggggggggdb bb ca egggaggggggggdbg db eeeeeeeeeeeaeeeg egggafggggggdbgg bd ggggggggggeaggge eggggagggggbbggg bbggggggggggaeggge eggggfagggbbgggg bbggggggggeagggge egggggaggbbggggg dbeggggggaegggge egggggfabbgggggg ggbdggggeaggggge eggggggbdggggggg gggbbgggaeggggge egggggbdaggggggg ggggbbgeagggggge eggggbdgaegggggg gggggdbaegggggge egggbdgggagggggg ggggggebdgggggge eggbeggggafggggg ggggggaebbggggge eebeggggggaggggg gggggeaggbbgggge ebggggggggffgggg gggggaegggdbegge dbggggggggggagggg ggggeaggggggbdge dbeggggggggggfaggg ggggaegggggggbbe db egggggggggggaege gggeagggggggggbb db ca gggaeggggggggggdb bb ac ggeaggggggggggge bd bb a eeaeeeeeeeeeeeeg bb bb ac a db bd a ac gb bd ff a bd bd a ac bb bd fa a db bg a ac gb b ca a bd b ac ac bbgb a a db ac ac a a ff ac a a fa ac a a ca ac ac a ac a af a ff a ```  I'm eager to see what's happening in this magnified view of area A.  ```palette Key,Color ,#fefefeff a,#fe0001ff b,#0404feff c,#fed2d2ff d,#8484ffff e,#3b35f8ff f,#fc5456ff g,#c7c7ffff ``` ```image faf caac faf caac faf eg caac bbg faf ebbd caac dbbe faf dbbeg caac gbbbg faf ebbd caac dbbe faf dbbeg caac gbbbg faf ebbd caac dbbe faf dbbeaac gbbbf cebbd faebbe caacdbbeg faf gbbbg caac ebbd faf dbbe caac dbbeg faf gbbbg caac ebbd faf dbbe caac dbbe faf geb caac e faf caac faf caac faf ```  Area A contains an intersection. Let's shift our focus to the next area. Could this be where the intersection is hiding, in area B?  ```palette Key,Color ,#fefefeff a,#fe0505ff b,#0706feff c,#ff8f8fff d,#9e9bfbff e,#4c47f9ff f,#fa4044ff g,#ead5eaff ``` ```image gaag faf gaag caf d aac db caa dbb aac ebbd caag ebbd fac ebbd gaag ebbd faf ebbd gaag gebbg faf gbbbg gaac gbbbg caa gbbbg aac gbbeg caadbbe ffbbe dbbe dbbef dbbeaag ebbd faf ebbd gaac ebbd caf ebbd aac ebbd caa gebbg fac gbbbg caag gbbbg faf gbbeg gaag dbbe faf dbbe gaac bbe caf be aac e caa aac ```  I've cracked the case! This area contains the intersection. I can confirm there's two intersections in there.

2

```palette Key,Color ,#fefefeff a,#fe0707ff b,#0707feff c,#ffa3a3ff d,#a2a2ffff e,#4b4afdff f,#ff5454ff g,#f5d9e2ff ``` ```image g ca aff ca a a ca ca ag a ga ca ac a a ca af a a ca ff a a ca ca a ag ca ga a ac ca ga a ac ca a a ff ca a a ca ca ag a ca e ca ag eb a ga bb ca ac be ag a be ca ff be ag a bd ca fa bd ag a bd ca ca gbg ag ag db ca ga db d ag ac db eb ca a eb dbg ag ff eb gbd ca a eb be ag ff bb eb ga a bb dbg ag cabe gbd ga be be ag bea eb ga bd ac dbag bd a gbd gbd af agbb gbg a ga eb db ff ag dbg db a ga bd db ca ag bb eb ag ga eb eb ga ag dbg eb ac ga be bb ga ag bb be ac ga eb be a ag dbg be ff ga be bd a ag bb bd ca ga eb bd a ag dbd gbg ca ga be gbg ag ac bbdb ga ga eb ac ac a ga ff ac a ga fa ac a ga ca ac ag ga ac a ff a ff a ```

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

0

```palette Key,Color ,#fefefeff a,#0606ffff b,#ff0707ff c,#8b8bffff d,#ff5656ff e,#ffb3b3ff f,#c7c7ffff g,#4b4cffff ``` ```image f gaaaac a fgaaagf af caaaac ca fgaaagf a caaaac gg fgaaagf fa caaaac af fgaaagf ca caaaac a fgaaa ac fa a gg a af ca a ac fa a gg a af ca a ac fa af gg a ac ca a gg fa af ee ca eddbbbbbbd a eedbbbbbbdde ac eddbbbbbbdee fa eedbbbbbbdde a eddbbbbbbdee gg bbde a bb af bb ca bb a bb ac db fa db a db gg db a db af db ca db a db ag db fa db af eb eb eb eb eb eb eb eb eb eb b b b b be be be be be be be be ```

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

0

```palette Key,Color ,#fefefeff a,#ff0505ff b,#4f4fffff c,#ff4141ff d,#a7a7ffff e,#ff8383ff f,#ffc4c4ff g,#0808ffff ``` ```image d bg bg bg bg bg gg gg gg gb gb gb gb f gb a gb af gd ea gd a gd ae gd ea gd a gd ae gd fa g a g ae dg fa dg a dg cc dg fa dg a dg cc dg fa bg af bg cc gggb bg a bgggd bg af dgggb bg cc dgggd bg a bggbd gg af dgggb gg ea bgggd gb a dbggbd gb af dgggb gb ea bggggb a dd ae e ea ea a ea ae ea fa ea a ea ae fa fa fa a fa cc fa fa fa a faf cc af fa af af af cc af a ae af ae cc ae a ae af ae ea ac a ac af ac ea ac a ac ae aa ea ca a ca ae ca fa ca a ca ae ca fa ea a eacc ea ```

Let's examine this image for potential line intersections. These zones are intriguing. I bet there's something interesting happening within them.  ```palette Key,Color ,#fefefeff a,#0809fdff b,#e55c53ff c,#6168efff d,#feb7b6ff e,#fc0807ff f,#b1d7b1ff g,#99c696ff ``` ```image ffffffffffffffff ffffffffffffffff ffffffffffffffff dffffffffffffffff befffffffffffffff eeffffffffffffff feefffffffffffff ffebffffffffffff fffebfffffffffff ffffebffffffffff fffffebfffffffff ffffffebffffffff fffffffegfffffff ffffffffegffffff fffffffffegfffff ffffffffffefffff cffffffffffgeffff caffffffffffgefff agffffffffffgeff gafffffffffffbef fcafffffffffffbe ffaffffffffffffbe ffgaffffffffffffbe fffacfffffffffff be ffffafffffffffff be ffffcaffffffffff ee fffffacfffffffff eb ffffffafffffffff eb ffffffcaffffffff eb gggggggacggggggg eb a ed ca ed a ed a ed cc e a e a de ac de a de fa de ac be a be ca be af de a de gffffffffffffffffffffffg ca de gffffffffffffffffffffffg a de gffffffffffffffffffffffg a ed gffffffffffffffffffffffg cc edgffffffffffffffffffffffg ca a ebffffffffffffffffffffffg cac a ebfffffffffffffffffffffg aa ac gebffffffffffffffffffffg aa a gfebfffffffffffffffffffg aaf fa gffebffffffffffffffffffgcac ac gfffeeffffffffffffffffcac a gffffeefffffffffffffcaag ca gfffffeefffffffffffaaffg af gffffffbeffffffffaagfffg a gfffffffbefffffaacfffffg ca gffffffffbeffcacfffffffg a gfffffffffbbaafffffffffg a gffffffffgaaeffffffffffg cc gfffffffaaffgefffffffffg a gfffffaacffffgeffffffffg a gfffcacffffffffegffffffg ac gfcacfffffffffffegfffffg a caaffffffffffffffebffffg fa aafffffffffffffffffebfffg ac aa gffffffffffffffffffebffg a cac gfffffffffffffffffffebfg ca cac gffffffffffffffffffffebg acaa gfffffffffffffffffffffee a gffffffffffffffffffffffee gffffffffffffffffffffffgee gffffffffffffffffffffffg be gffffffffffffffffffffffg be gffffffffffffffffffffffg be gffffffffffffffffffffffg de fggggggggggggggggggggggf de de de ed e ```  Could this be where the intersection is hiding, in area A?  ```palette Key,Color ,#fefefeff a,#0606ffff b,#ff3939ff c,#a6a6ffff d,#ff8585ff e,#ff0505ff f,#5050ffff g,#ffccccff ``` ```image dg eeg beeg beeg bebg gbeb geeb geeb geeb geeb geeb geed geed deed deed deed deed deeg deeg beeg beeg beeg beeg beeg beb gbeb ff geeb aac geeb faa geeb aaf geeb caac geeb faf geed aac deed caa dee faf de aac d caa faf aac caa aaf caac faa aaf caac faf aac caa faf aac caa faf ```  No luck this time. Area A doesn't have an intersection. Alright, let's concentrate on the next area. I'm now examining the contents of area B in detail.  ```palette Key,Color ,#fefefeff a,#0a09feff b,#f73a41ff c,#b8b7feff d,#ff8282ff e,#fe0505ff f,#6767ffff g,#ffc2c2ff ``` ```image g ed eed deed deed deed deeb geeb geeb geeb geeb f geeb caa geeeg caaaa beeg cfaaac beeg faaaf beeg faaaf beeg faaafc beeg caaaac beed caaaac deed cfaaaf deed faaaf deed faaafc debaaaac caaaac cfaaabeb faaaf geeb faaaf geeb faaafc geeb caaaac geeb caaaac geeeg cfaaaf beeg faaaf beeg faaafc beeg caaaac beeg caaaac beeg aaaf beed af deed deed deed deed deeb geeb geeb gee ge g ```  As I suspected, there's an intersection within area B. I've found a single intersection point in the image.

1

```palette Key,Color ,#fefefeff a,#0707feff b,#fb3e42ff c,#9b9bffff d,#ff8f8fff e,#fe0505ff f,#5252ffff g,#eed5e5ff ``` ```image d be be eb eb eb ed ed ed ed eg eg geg f ge fa ge ag ge a de ff de ag de ga be af be a be ca bb ac eb a eb ca eb ac ed a ed fa ed ag eg a eg ff eg ag geg ga ge af ge a de ca de ac de a de ca de ac de a de fa ge ag geg ga geg ff eg fa ag ed caf ga ed gaa af ed aag a eb aac ca eb fac ac eb caf a ee caa ca be gaa ac be aag a be fac fa de faf ag dbaf ga gaae ff aag ge ag aac geg ga fac geg af caf eg a caa ed ca gaa ed ac aag ed a fac eb ca faf eb afaf eb a ee be be be de de de ge geg geg e ```

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.  ```palette Key,Color ,#fefefeff a,#f4615cff b,#0304feff c,#fc0a0aff d,#8a8df7ff e,#4145f8ff f,#feb7b6ff g,#aed5aeff ``` ```image a fc c cf ca ac fc c c cf bbd ca ebbd ac ebbd fc ebbd c ebbd cf ebbd ca ebbd ac ebbd fc ebbd c ebbd gggggggggggggggg cf ebbd gggggggggggggggg ca ebbd gggggggggggggggg ac ebd gggggggggggggggg fc be ggggggggggggggggfc bb ggggggggggggggggc eb gggggggggggggggcf db ggggggggggggggcc bdgggggggggggggacg bbggggggggggggcgg ebggggggggggcggg gdbggggggggcaggg gggbdgggggcagggg ggggbegggacggggg gggggbbgacgggggg ggggggebcggggggg gggggggcbdgggggg ggggggcagbeggggg gggggccgggbbgggg ggggacgggggebggg ggggcgggggggdbgg gggcggggggggggbe ggcagggggggggggbe gccgggggggggggggeb acgggggggggggggg db fcggggggggggggggg bd cgggggggggggggggg be cfgggggggggggggggg bb ca gggggggggggggggg eb ac gggggggggggggggg db fc gggggggggggggggg bd c gggggggggggggggg bb cf eb ca db ac bd cc be ca eb acf db cc b fcf cc fca ac cc acf cc fca cc ca acf cc fcf cc fca ac ca acf cc fcf cc ca ```  I wonder what we'll find inside area A?  ```palette Key,Color ,#fefefeff a,#fe9596ff b,#0806fdff c,#fe0708ff d,#a1a1feff e,#4f4cfbff f,#f2d6e3ff g,#ff4a4aff ``` ```image a ac fcc ccg gccf accf e acca bbf fcca bbbd fccg ebbd gcc ebbe gccf dbbef acca dbbbd fcca febbd fccg ebbe gcg dbbe gccf dbbbf accf fbbbd acca ebbdfccg ebbecg dbbbf acbbbd accaebbd fcca ebbe fccg dbbef gcc dbbbf gccf fbbbd acca ebbe fcca dbbe fccg dbbbf gcg fbbbd gccf ebbd accf ebb acca db fccg d ccg gccf accf acca cca cg c f ```  I've cracked the case! This area contains the intersection. There's one and only one intersection present in the image.

1

```palette Key,Color ,#fefefeff a,#ff8585ff b,#0303ffff c,#fe0405ff d,#9090ffff e,#4242ffff f,#fac9ceff g,#ff3c3cff ``` ```image a fc c cf ca gg ac fc cf ca bbd gg ebbd ac ebbd fc ebbd c ebbd cf ebbd cg ebbd gc ebbd fc ebbd c ebbd cf ebbd ca ebbd gg ebd ac be fc bb cf eb ca dbf gg bd ac be fc eb c db cf bd cg be gc eb fc dbc cbd ca be gg bb ac eb fc db cf bd ca be gg eb ac db fc bd c be cf bb cg eb gc dbf fc bd c bb cf eb ca db gg bd gc be cg eb acf db cc fb aca cc fca gc cg acf cc fca gc fcg gcf cg acf cc fca gc cg acf cc fca gc cg ```

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

0

```palette Key,Color ,#fefefeff a,#ff3a3aff b,#0707ffff c,#b0b0ffff d,#ff7a7aff e,#5e5effff f,#ff0404ff g,#ffc2c2ff ``` ```image g gdfffa dffffd dafffdg gafffag gdfffad dffffdg gafffag gafffag gdffffd afdg fa fa fd fg gfg gf df af af fa fa fd fd fg gfg gf df af af fa fa fd fg gfg gf df df af ff fa fd fd bb cbbc bbe ebe ebb cbbc bbe bbe ebb cbbc cbbc bbe ebb cbbc cbbc bbe ebbe ebbe ebbbc cbbbc ebbe ebbec cbbbc cbbbe ebbe cbbbc cbbbe ebbe ebbbc cbb ```

Here's an image. My task is to find intersections or areas where lines come close together. These zones indicate regions where lines appear to be in close proximity.  ```palette Key,Color ,#fefefeff a,#0607feff b,#fb3635ff c,#abaef9ff d,#f6a29eff e,#5558f8ff f,#fe0403ff g,#add4adff ``` ```image cc cceeaaaaaaaaaaa cceeaaaaaaaaaaeecc ee aaaaaaaaaaeecc a c ca ggagggggggggggggg gggaggggggggggggg d gggacgggggggggggg dbffb ggggagggggggggggg dbffbd ggggaeggggggggggg dbffbd gggggaggggggggggg dbffbd gggggeegggggggggg dbffbd ggggggagggggggggg dbffbd ggggggeagggggggdbfffd gggggggagggdbfffd ggggggggafffdgggg gggdbfffacggggggg bfffdggggaggggggg fbggggggggaegggggg bfggggggggggagggggg df ggggggggggeeggggg f gggggggggggaggggg fd gggggggggggeagggg bb ggggggggggggagggg df ggggggggggggcaggg f gggggggggggggaggg f ggggggggggggggagg fd ac bb a df ee f a f ea fd a bb ca df ac f a fd ac fb a df ee df a f ee fd a bb ca df a f ca f ac fd a bb ae df a f ee fd a fb ca bf a df ca f ac fd a bb ac df a f ee f a fd ea bb a df ca b ac a ac a ee a ea a ca ac a ac a ee a ee a ```  I'm analyzing this close-up of area A with precision.  ```palette Key,Color ,#fefefeff a,#0a08fcff b,#fc4c4eff c,#5e5effff d,#ff8c8cff e,#ffcbcbff f,#fe0506ff g,#b4b2fdff ``` ```image aac gaa cac gaag cac aag caa aag gaa aac gaa cac gaag cac aag caa aag gaa edb aac edbffff gaa edbffffffbd cac edbffffffbde gaaffffffbde edbffaaafbde edbffffffbaag edbffffffbde caa bffffffbde aag fffbde caa be aac gaa aac gaag cac gaag cac aag caa aag gaa aac gaa cac gaag cac aag ```  Incredible, there's actually an intersection in area A! One intersection, that's it, but I found it.

1

```palette Key,Color ,#fefefeff a,#0404feff b,#ff3c3cff c,#8383ffff d,#ffa8a8ff e,#3e3effff f,#ff0505ff g,#c5c3fdff ``` ```image gg gcceeaaaaaaaaaa gcceeaaaaaaaaaeccg ce eaaaaaaaaeeccg a g ca ag ga d ag dbffb a dbffbd ec dbffbd a dbffbd ee dbffbd a dbfffd ca dbfffd a dbfffd gafffd dbfffag bfffd a fb ac bf a df ee f a fd ca fb a df ga f ag f a fd ac bb a df ee f a f ce fd a bf ga df ag f ga fd ac fb a bf ec df a f ce fd a bb ca df ag f ga f ag fd a bb ec df a f ee fd a fb ca bf a df ga f ag fd a bb ac df a f ee f a fd ca bb a df ga b ag a ac a ee a ce a ga ag ga ac a ec a ce a ```

I'm on the case! Let's uncover any intersections hidden in this image. I've spotted 1 narrow regions that might be worth examining further. Let's call them area A.  ```palette Key,Color ,#fefefeff a,#5361ddff b,#da6156ff c,#0708fbff d,#b1d7b1ff e,#f8090aff f,#9cc09aff g,#eff6f0ff ``` ```image b beb beeggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggg gbeefdddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddfg gddfeefddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddg gddddfeebddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddg gdddddddeebddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddg gdddddddddbebddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddg gdddddddddddbeeddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddg gdddddddddddddbeefdddddddddddddddddddddddddddddddddddddddddddddddddddddddddddg gdddddddddddddddfeefdddddddddddddddddddddddddddddddddddddddddddddddddddddddddg cccccccccccccccaaaaaafeebdddddddddddddddddddddddddddddddddddddddddddddddddddddddg gddddddddfffaaaaaaccccccccccccccccdddddddddddddddddddddddddddddddddddddddddddg gddddddddddddddddddddddeebdddddddcaddddddddddddddddddddddddddddddddddddddddddg gddddddddddddddddddddddddbeeddddddcddddddddddddddddddddddddddddddddddddddddddg gddddddddddddddddddddddddddbeeddddacdddddddddddddddddddddddddddddddddddddddddg gddddddddddddddddddddddddddddbeefddcfddddddddddddddddddddddddddddddddddddddddg gddddddddddddddddddddddddddddddfeeddcddddddddddddddddddddddddddddddddddddddddg gddddddddddddddddddddddddddddddddbedacdddddddddddddddddddddddddddddddddddddddg gdddddddddddddddddddddddddddddddddeedcfddddddddddddddddddddddddddddddddddddddg gddddddddddddddddddddddddddddddddddebfcddddddddddddddddddddddddddddddddddddddg gdddddddddddddddddddddddddddddddddddebcadddddddddddddddddddddddddddddddddddddg gddddddddddddddddddddddddddddddddddddefcdddddddddddddddddddddddddddddddddddddg gdddddddddddddddddddddddddddddddddddddefcddddddddddddddddddddddddddddddddddddg gdddddddddddddddddddddddddddddddddddddfecadddddddddddddddddddddddddddddddddddg gddddddddddddddddddddddddddddddddddddddbecdddddddddddddddddddddddddddddddddddg gdddddddddddddddddddddddddddddddddddddddbbcddddddddddddddddddddddddddddddddddg gddddddddddddddddddddddddddddddddddddddddecadddddddddddddddddddddddddddddddddg gdddddddddddddddddddddddddddddddddddddddddecdddddddddddddddddddddddddddddddddg gddddddddddddddddddddddddddddddddddddddddddbcddddddddddddddddddddddddddddddddg gdddddddddddddddddddddddddddddddddddddddddddcadddddddddddddddddddddddddddddddg gdddddddddddddddddddddddddddddddddddddddddddfcdddddddddddddddddddddddddddddddg gddddddddddddddddddddddddddddddddddddddddddddacddddddddddddddddddddddddddddddg gdddddddddddddddddddddddddddddddddddddddddddddcedddddddddddddddddddddddddddddg gddddddddddddddddddddddddddddddddddddddddddddddceddddddddddddddddddddddddddddg gddddddddddddddddddddddddddddddddddddddddddddddacedddddddddddddddddddddddddddg gdddddddddddddddddddddddddddddddddddddddddddddddcebddddddddddddddddddddddddddg gddddddddddddddddddddddddddddddddddddddddddddddddcebdddddddddddddddddddddddddg gddddddddddddddddddddddddddddddddddddddddddddddddacefddddddddddddddddddddddddg gdddddddddddddddddddddddddddddddddddddddddddddddddcfeddddddddddddddddddddddddg gdddddddddddddddddddddddddddddddddddddddddddddddddfcfedddddddddddddddddddddddg gddddddddddddddddddddddddddddddddddddddddddddddddddcabeddddddddddddddddddddddg gdddddddddddddddddddddddddddddddddddddddddddddddddddcdbedddddddddddddddddddddg gdddddddddddddddddddddddddddddddddddddddddddddddddddfcdeeddddddddddddddddddddg gddddddddddddddddddddddddddddddddddddddddddddddddddddcadebdddddddddddddddddddg gdddddddddddddddddddddddddddddddddddddddddddddddddddddcddebddddddddddddddddddg gdddddddddddddddddddddddddddddddddddddddddddddddddddddacddefdddddddddddddddddg gddddddddddddddddddddddddddddddddddddddddddddddddddddddcaddedddddddddddddddddg gdddddddddddddddddddddddddddddddddddddddddddddddddddddddcddfeddddddddddddddddg gdddddddddddddddddddddddddddddddddddddddddddddddddddddddacddbedddddddddddddddg gddddddddddddddddddddddddddddddddddddddddddddddddddddddddcaddbeddddddddddddddg gdddddddddddddddddddddddddddddddddddddddddddddddddddddddddcdddeedddddddddddddg gdddddddddddddddddddddddddddddddddddddddddddddddddddddddddacdddebddddddddddddg gddddddddddddddddddddddddddddddddddddddddddddddddddddddddddcfdddebdddddddddddg gdddddddddddddddddddddddddddddddddddddddddddddddddddddddddddcddddefddddddddddg gdddddddddddddddddddddddddddddddddddddddddddddddddddddddddddacddddeddddddddddg gddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddcfdddfedddddddddg gddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddfcddddbeddddddddg gdddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddcaddddbedddddddg gddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddcdddddeeddddddg gddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddfcdddddebdddddg gdddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddcadddddebddddg gddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddcddddddefdddg gddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddfcddddddedddg gdddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddcadddddfeddg gddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddcddddddbedg gddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddacddddddbeg gfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffcaffffffeg c ac cg gc ac cg gc aa cg gc ca c ```  Let's put area A under the microscope.  ```palette Key,Color ,#fefefeff a,#4137f5ff b,#fa484cff c,#0404feff d,#fea8a8ff e,#fc0608ff f,#7a7afeff g,#bcbafdff ``` ```image ed eeeb dbeeb beebd beeed deee deeeb dbeebd deeed beeed deee beeb deeed cccccccccccccccaaaafffffgggeeed fffaaaacccccccccccccccccccccccccccaaaaafffffgggg gggggfffffaaaacccccccccccccccccccccc beebd gcc dbeeb fc beebd aa deeed cc deee acf dbeeb gcc dbeed cf bee gcg be ca eb gcc eeb ac dee cf ded ca eedccg beefcc ebgcg ebfc deeccg deacc becc beaa eecf eccg ecc dbcg baa cc ac gcb cad cce fccd gcee fceb cae acaed cceed gcbee cfbe ccgeb acaeeb fc ded aa ded gcg eed acf be gcc eb fc eb gcg dee ca ded gcc eed ac bee cf ee ca deb ccg ee fcc ded gcg eed fc bee cf ee fcc deb cc eed gcg dee cf bed cc ee ac beb gcg deb ca ded ccf eed ac bed gcg be fc eb ccg dee fcc ded ac ded fa bee cf be ccg be cc eeb gcg dee aa ded cc e ```  Oh my, look at that! It's an intersection in area A! I can confirm there's two intersections in there.

2

```palette Key,Color ,#fefefeff a,#4848feff b,#f7434bff c,#0504fdff d,#fe9899ff e,#fd0507ff f,#9491fbff g,#ebd4e8ff ``` ```image d beb dee deeg geed geed eeb beb bee deeg deeg ccccccccccccccaaaaffffeed ggffffaaaaccccccccccccccc beb cf beb c deeg fc deeg cg gee c be aa eb cg edgc edaa egcg gegc geaa dec bbc ecf ec bc cf gc fc cb ce acb ceb gced aaeg cge gcge aade c be gc eb cf eb c ed fc eg cf e c ge fc de cf be c bb fc eb cg ed c eg aa e cg ge gc de aa be c bb gc eb ca ed c eg fc e cf ge c de fc be cf b c fc cf c aa cg gc aa cg gc aa c ```

Let's examine this image for potential line intersections. Let's take a closer look at what's happening inside these zones.  ```palette Key,Color ,#fefefeff a,#0807fdff b,#f73a36ff c,#5a59f6ff d,#ff9e9eff e,#ff0303ff f,#aed4acff g,#a4a6faff ``` ```image deee deeb de deeb ed deeb e deeb de deeb ed deeb e deeb de deeb ed deeb e deebd de deeed ed bd e de ed e de ed e de ed e de ed e de ed e bb ed e bb ed e bb ed e bb e e bbfffffffffffffff efffffffffffffff feffffffffffffff g fbbfffffffffffff aaaaac ffefffffffffffff ac caaacg fffeffffffffffff ac gaaaag fffbbfffffffffff ag gcaaac ffffefffffffffff ag caaacg fffffeffffffffff ag gaaaagfffffbbfffffffff ag gcaaacffefffffffff ag fffcaaaagfffffff ag fffffffcaaaacfff a ffffffffeffgaaaac a fffffffffeffffffc a fffffffffbbfffff ga ffffffffffefffff ga fffffffffffeffff ga fffffffffffbbfff ga ffffffffffffefff ga fffffffffffffeff ga fffffffffffffbbf ca ffffffffffffffef ca fffffffffffffffe ca bb ca e ca ca aa aa aa ac ac ac ac ac ac ag ag ```  Here's a close-up of the area A.  ```palette Key,Color ,#fefefeff a,#0905fbff b,#fd3e40ff c,#5e55f5ff d,#fd9294ff e,#fe0404ff f,#fadadeff g,#abaafeff ``` ```image eb eed deef beb feed deef beb feed deef beb feed deef beb feed deef beb feed deef f beb aacgg feed aaaaaaccg deef ggcaaaaaaacgbeb fgcaaaaaaaacg gccaaaaaaccg gcaaaaaaaacgf feedgcaaaaaaacgg deef gccaaaaa beb ggca feed deef beb feed deef beb feed deef beb feed deef beb feed dee beb feed dee be ```  My investigation has led me to an intersection in area A! There's one and only one intersection present in the image.

1

```palette Key,Color ,#fefefeff a,#0908fdff b,#ff3e3eff c,#6460fbff d,#ff9090ff e,#ff0404ff f,#ffd0d0ff g,#b7b7ffff ``` ```image f deee deeb de deeb ed deeb e deebf de deebf ed deebf e deebf de deebf ed deebf e feeef de feeef ed bf e de ed e de ed e de ed e de ef e de ef e de ef e bb ef e bb ef e bb ef fe bb ef fe g bb aaaaac ef ac gcaaacg fe ac caaaag bb ag gcaaac ef ag gcaaacg fe ag caaaag bb ag gcaaac ef ag gcaaaag ag caaaag ag ef gcaaac a fe gc ga bb ga e ga fe ga bb ga e ga fe ca bb ca e ca fe ca bb ca e ca aa aa aa aa aa ac ac ac ac ac ac ag ```

This image seems promising for intersection detection. The image has some tight areas where segments are too close. I should investigate those closely.  ```palette Key,Color ,#fefefeff a,#0808fdff b,#f44c47ff c,#b0b0feff d,#eea098ff e,#5860eeff f,#fd0707ff g,#acd3acff ``` ```image d df df df df f f f f d f ff fd ff fd fb fd fb fd fb aac ggggggggggggggfb fb accaaac gggggggggggggfbg fb ca eaae ggggggggggggfbgg fb a eaaac gggggggggggfbggg fb ea caaacggggggggggffgggg fb a eaaeggggggffggggg fb ee ggeaaaggbfgggggg fb a gggggeaaaegggggg fb ae ggggggbfgeaaeggg fd a gggggbfgggggeaaac fd ac ggggbfgggggggggeaaac fd ca gggdfggggggggggg eaae fd a ggdfgggggggggggg eaaac fbgggggggggeaggg gdfggggggggggggg caa gfdggggggggagggg gfgggggggggggggg ggfdggggggeagggg fggggggggggggggg gggfdgggggaggggg f ggggfdgggeeggggg f gggggfdggagggggg f ggggggfdaegggggg fd gggggggfaggggggg fd gggggggafggggggg fd gggggggagfgggggg fd ggggggagggfggggg fb gggggeaggggfgggg fb gggggaggggggfggg fb ggggeagggggggfgg fb ggggagggggggggfg fb gggaeggggggggggf bf a df bf ac df bf a dfbf ac df ca a ca a ee a ae a ac a ac ca a ea a ee a ae a ac ca a ca a ea a ee a ac a ac ca a ```  I'm eager to see what's happening in this magnified view of area A.  ```palette Key,Color ,#fefefeff a,#0605fdff b,#ff4f4fff c,#9291fdff d,#ffb0b0ff e,#4844faff f,#fd0c0dff g,#f0dceaff ``` ```image ffd eac bffd caag bffd aac bffd caa bffd aac bffd cae bffd gaac bffd eae bffd gaag bffd eae bffd caag bffd eac bffd caa bffd aac bffcaa bfaac eaag gaaffg eaebffg gaaggbffg eae gfffg caag gfffg eac gfffg caa gfffg aac gfffg caa gfffg gaac gfffg eae gfffg gaag gfffg eae gffbg gaag gffb eae gff ```  Wow! I can see an intersection so clearly in area A! Now, let's dive into another area. I'm analyzing this close-up of area B with precision.  ```palette Key,Color ,#fefefeff a,#0807feff b,#ff5656ff c,#a6a6ffff d,#ffaeaeff e,#5958fdff f,#fe0707ff g,#a02381ff ``` ```image df dff dffb dffb dffb dffb dffb dffb dffb ffb fff aec fff aaaaec fff ceaaaaaec bff ceaaaaaaec bff ceaaaaaegffd ceaaaaaec ggaaaaaaec bffd ceaaaaaec bffd ceaaaaaec bffd ceaaaaaa bffd ceaa dffd c dffd dffb dffb dffb dffb dffb dffb dffb ffb ```  Bingo! This close-up reveals an intersection in area B! There are precisely two intersections present in the image.

2

```palette Key,Color ,#fefefeff a,#0808feff b,#fc3d3fff c,#aeaeffff d,#ff8787ff e,#5c5cffff f,#fe0505ff g,#ffc8c8ff ``` ```image d df df gf gf gf gf f fg g fg bf fg bb fg fb fd fb fd fb aac fd fb accaaac fb fb ca eaae fb fb a eaaac fb fb ea caaac fb fb a eaae bf fb ee eaaac bf fd a caaac fd ae bf eaae fd a df eaaac fd ac df caaac fd ca df eaae fd a gf eaaac fd ca gf caa fd a gf fg ea gf fg a f fg ee fg fg a fg fgac fg fa fg abg fd ca fg fd a fg fd ca fg fb a gf fb ee gf fb a gf fb ee gf bf a gf bf ac gf bf a gfbf ac gf ca a ca a ee a ae a ac a ac ca a ea a ee a ae a ac ca a ca a ea a ee a ac a ac ca a ```

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

0

```palette Key,Color ,#fefefeff a,#ff3f3fff b,#0707ffff c,#ff0505ff d,#6161ffff e,#b5b5ffff f,#ffc4c4ff g,#ff8080ff ``` ```image e edbbbbbbbd edbbbbbde dbb edbbbbbde ebbe eddbbbbde bbd edbbbbbde dbb bbbbbde ebbe bbd dbb ebbe bbd dbbe ebbd dbb dbbe ebbd dbb ebbe bbd db ac ccgc cg ac gcf aa ac ca ca cg fcf cf ac cf ca c fcg fc gc fc cc gc ca ac fcf ac ac ca ca cg fcg cg gc cf cc c cg fc gcf fc ac gc ca gc fcf ac ac ca cc cg cg cg gcf cf a cf c fc gc gc ac ca ca cg cf cf c fc fc gc ac aa ca cg cf c ```

I'm analyzing this image to identify any points where lines intersect. These spots are like clues. Let's see what they reveal about potential intersections.  ```palette Key,Color ,#fefefeff a,#0a0bfcff b,#fc0909ff c,#5f6ae7ff d,#b7b7feff e,#e67066ff f,#9fcca1ff g,#b2d7b2ff ``` ```image d ca aca ac a a da ad a da da a ad ca a a ac ac a a cc ad a da da a a ca da a ad ac afffffffffffffffffff a acgggggggggggggggggf ad fagggggggggggggggggf da fccggggggggggggggggf a fgaggggggggggggggggf ca fgcagggggggggggggggf a fggagggggggggggggggf ac fggcaggggggggggggggf e a fgggafgggggggggggggf ebbe ad fgggfagggggggggggggf bbb da fggggacggggggggggggf ebbe a fgggggaggggggggggggf ebbe ca fgggggacgggggggggggf bbb ffffffffffffffffffafffff fggggggaggggggggggebbe fggggggggggggggggacggggf fggggggcaggggggebbef fgggggggggggggggfagggggf fgggggggagggfbbbfggf fgggggggggggggggafgggggf fgggggggcaebbegggggf fggggggggggggggcaggggggf fggggggebaeggggggggf fggggggggggggggagggggggf fgggfbbbffaggggggggf fgggggggggggggcagggggggf fgebbeggggacgggggggf fgggggggggggggaggggggggf ebbeggggggggagggggggf fggggggggggggacggggggggf bbbfggggggggggacggggggf fgggggggggggfagggggggggf ebbg fgggggggggggaggggggf fgggggggggggafgggggggggf ebbe fgggggggggggcagggggf fggggggggggcaggggggggggf ebbbb fggggggggggggagggggf fggggggggggagggggggggggf ebbbeg fggggggggggggcaggggf fgggggggggcaggggggggggfebbbe fgggggggggggggafgggf fgggggggggagggggggfebbbe fgggggggggggggfagggf fggggggggacgggebbbbegggf fggggggggggggggacggf fgggggggfaebbbbegggggggf fgggggggggggggggaggf fgggggebabbegggggggggggf fgggggggggggggggacgf fgebbbecaggggggggggggggf fggggggggggggggggagf bbbefgggagggggggggggggggf fggggggggggggggggcaf fgggggcagggggggggggggggf fgggggggggggggggggaf fgggggaggggggggggggggggf ffffffffffffffffffca fggggacggggggggggggggggf a fgggfagggggggggggggggggf da fgggafgggggggggggggggggf ad fggcaggggggggggggggggggf a fggagggggggggggggggggggf ac fgcagggggggggggggggggggf a fgaggggggggggggggggggggf cc facggggggggggggggggggggf a fagggggggggggggggggggggf ca afgggggggggggggggggggggf a daggggggggggggggggggggggf da afggggggggggggggggggggggf ad ffffffffffffffffffffffff a ad a cc a ca a da ad da ad a ac a ca a ```  I wonder what we'll find inside area A?  ```palette Key,Color ,#fefefeff a,#0706feff b,#fd0608ff c,#9493fdff d,#d7d7ffff e,#ffafafff f,#4c4afcff g,#ff5b5bff ``` ```image faf caad aac caa daac faf daad faf caad aac caa daac faf daad faf caad aac caa daac faf daad faf caad aac caa daac faf daad eegbb faf eegbbbbbb caad eggbbbbbbgge aac eggbbbbbbgee caa egbbbbbbbgee daacegbbbbbbbge efaabbbbbbge eegbbaabbgge eggbbbbbaafe eggbbbbbbgecaad egbbbbbbbgee aac bbbbbbge caa bgge daac faf daad faf caad aac caa daac faf daad faf caad aac caa daac faf daad faf caad aac caa daac faf daad faf caad aac aa dd ```  Gotcha! I've found the intersection hiding in area A! Let's move forward and inspect another region. Let's take a closer look at area B.  ```palette Key,Color ,#fefefeff a,#0505feff b,#fd0506ff c,#8787ffff d,#c9c9ffff e,#feaeafff f,#423efaff g,#fd5254ff ``` ```image aac caa aac caa fac daad faf daad caf aac caa aac caa fac daad faf daad faf daad caf aac caa fac daad faf daad faf egb daad gbbbb caf egbbbbge aac egbbbbge caa gbbbbbe aac egbbbbge daaegbbbbge efafbbbe egbbaage egbbbbgfaf egbbbbge daad egbbbbge caf egbbbbge aac egbbbbge caa egbbbbge aac bbbge caa ge fac daad faf daad caf aac caa aac caa fac daad faf daad faf daad caf aac caa fac daad faf daad faf daad caf aa ```  Eureka! There's definitely an intersection in area B! There's for sure two intersections on the image you sent me.

2

```palette Key,Color ,#fefefeff a,#0303feff b,#fe0708ff c,#7473feff d,#babaffff e,#ffa5a5ff f,#3131ffff g,#fd5a5cff ``` ```image d ca acf fc a a da ad a da da a ad cf a a fc fc a a cf ad a da ca a a cf da a ad fc a a fc ad a da ff a a cf cf a a fc da g a ad ebbg ad a bbb da ac gbbe a a ebbg cf fc bbb a a gbbe fc cf ebbg a a bbb ad dagbbe da ebag a bbb da cf gbbe ad a ebbg a fc ebbg fc a gbbe a ad ebbg cf da ebbbg a a gbbbge da cf gbbbg a a egbbbg da fc egbbbe ad aebbbbe a ebabge fc gbbbgca a bbbg a cf cf a a ca ac a a da ad ad da a a fc cf a a ff ac a a cf ad a da da a ad a ac a fc a cf a da ad da ad a fc a cf a ```

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.  ```palette Key,Color ,#fefefeff a,#e93c35ff b,#0a0bfaff c,#5c6cdeff d,#e48274ff e,#fb0908ff f,#b1d7b1ff g,#97c699ff ``` ```image f ed e e e e de e da e ad e ed e e e e de e da e ad e ed e e e e de e da e ad e ed c b egggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggbb b egfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffbba bf gefffffffffffffffffffffffffffffffffffffffffffffffffffffffffcbaaf bc geffffffffffffffffffffffffffffffffffffffffffffffffffffffffbbeaff bc gdeffffffffffffffffffffffffffffffffffffffffffffffffffffffbbeafff bc gfeffffffffffffffffffffffffffffffffffffffffffffffffffffgbceaffff bb gfaaffffffffffffffffffffffffffffffffffffffffffffffffffcbfeafffff bb gffefffffffffffffffffffffffffffffffffffffffffffffffffbbfeaffffff cb gffadfffffffffffffffffffffffffffffffffffffffffffffffbcfeafffffff cb gfffefffffffffffffffffffffffffffffffffffffffffffffcbgfeaffffffff cb gfffedfffffffffffffffffffffffffffffffffffffffffffbbffeafffffffff fb gffffeffffffffffffffffffffffffffffffffffffffffffbcffeaffffffffff b gffffegfffffffffffffffffffffffffffffffffffffffcbgffeafffffffffff bfgffffdeffffffffffffffffffffffffffffffffffffffbbfffeaffffffffffff bcfffffefffffffffffffffffffffffffffffffffffffbbfffeefffffffffffff bcffffdeffffffffffffffffffffffffffffffffffgbcfffeeffffffffffffff gbbffffefffffffffffffffffffffffffffffffffcbffffeefffffffffffffff gfbbfffaafffffffffffffffffffffffffffffffbbffffeeffffffffffffffff gffbbfffeffffffffffffffffffffffffffffffbcffffeefffffffffffffffff gfffbbffadfffffffffffffffffffffffffffcbgffffaeffffffffffffffffff gffffcbffeffffffffffffffffffffffffffbbfffffaefffffffffffffffffff gfffffcbfedffffffffffffffffffffffffbcfffffaeffffffffffffffffffff gffffffcbgeffffffffffffffffffffffcbgfffffaefffffffffffffffffffff gfffffffgbegffffffffffffffffffffbbffffffaeffffffffffffffffffffff gfffffffffbafffffffffffffffffffbbffffffaefffffffffffffffffffffff gffffffffffbcffffffffffffffffgbcffffffaeffffffffffffffffffffffff gffffffffffdbcffffffffffffffcbfffffffaefffffffffffffffffffffffff gfffffffffffebcffffffffffffbbfffffffaeffffffffffffffffffffffffff gfffffffffffaabbfffffffffgbcfffffffaefffffffffffffffffffffffffff gffffffffffffefbbfffffffcbgfffffffaeffffffffffffffffffffffffffff gffffffffffffadfbbfffffbbffffffffaefffffffffffffffffffffffffffff gfffffffffffffeffcbfffbcffffffffaeffffffffffffffffffffffffffffff gfffffffffffffedffcbcbgffffffffaefffffffffffffffffffffffffffffff gffffffffffffffefffcbfffffffffaeffffffffffffffffffffffffffffffff gffffffffffffffegffffffffffffaefffffffffffffffffffffffffffffffff gffffffffffffffdefffffffffffaeffffffffffffffffffffffffffffffffff gfffffffffffffffeffffffffffaefffffffffffffffffffffffffffffffffff gfffffffffffffffdeffffffffdeffffffffffffffffffffffffffffffffffff gffffffffffffffffefffffffdefffffffffffffffffffffffffffffffffffff gffffffffffffffffaafffffdeffffffffffffffffffffffffffffffffffffff gfffffffffffffffffeffffdefffffffffffffffffffffffffffffffffffffff gfffffffffffffffffadffdeffffffffffffffffffffffffffffffffffffffff gffffffffffffffffffefdefffffffffffffffffffffffffffffffffffffffff gffffffffffffffffffeaeffffffffffffffffffffffffffffffffffffffffff gffffffffffffffffffgeffffffffffffffffffffffffffffffffffffffffffg ```  I'm focusing my attention on this specific region, area A.  ```palette Key,Color ,#fefefeff a,#fb383bff b,#0807feff c,#b2b0fdff d,#fd7f80ff e,#fe0404ff f,#fec6c7ff g,#5653fcff ``` ```image ea g eef cbb dea cbbb feef bbbe fee cbbaea ae gbbgea fe gbbgea ad cbbbcee da bbgfeea ef gbgfeea ea cbbcfeea dea gbbg eea feef cbbbc fea aed cbbbc fea fee bbg fee aed gbg feea fee cbbc feea aed gbbg feea eef cbbbc feea dea bbbc eea ee gbg fea de cbbc fea fef cbbb fee ad gbbg feea fe gbbg feea bc ee bbg feea bbg aed gbg eea gbbg dea cbbc fea cbb eef cbbb faa cbg dea gbbg ae cbg eef cbbbc aea bbb dea bbbc aeaf bbbc aed gbg aeef gbbc fee cbbb aeef gbb aed gbbg aeef gbc fee gbbg eef gbg aed cbbbc aef bbg dea bbbc aef cbbg ee gbg aee cbbgfef cbbb aeef cbbbda gbbg aeef cbbbef gbbg aeef bbed bbbc eef gba gbg aef bbd gbg aef gbbc cbbb aee dgbbg gbbg aeef eabbg bbbc aeef deabb cbbc aeef eecbg gbg aeef deacbb gbb eef feefbbb cbbbc aef aed bbbc gbbg aef ae gbbc bbbc aeef fe gbbc cbbc aeef ed gbb gbg aeef da gbg cbbb aeef ef cbgcbbbc eef ea bbbbg def eef cbbg def feef deef aed deed fee deed aed deed fee eed eed ded dea ded dea deed eef deed dea deed fee deed ae deed fe eed ad ded ed dee ea deed eeaeed deeed ```  An intersection is present within area A. The final count is: one intersection.

1

```palette Key,Color ,#fefefeff a,#fd4142ff b,#0606feff c,#9493feff d,#fe8787ff e,#fe090aff f,#e7d1e9ff g,#4643fcff ``` ```image f ed e ef fe e de e da e ad e ed e ef fe e de e da e ad e ed e ef fe e de e da e ad e ed c bf e bb fbf ef bga bc fe cbea bc e gbea bg de bgea bg e fbcea bb da gb ea gb e bb ea gb ad fbc ea cb e cbf ea cb ed bb ea fb e bg ea fbf ef cbf ea bc fe gb ea bc e bg ea bg de fbc ee bg e gb ee bg da bb ae gb e fbc ae gb ad cbf ae gb e bb ae cb ed bg ae cbfe cbf ae fbef gb ae ba bg ae bc fbc ae dbc gb ae ebg bb ae aabg fbc ae e bb cbf ae ad gb bb ae e gb bg ae ed cbcbf ae fe cb ae ef de fe de e de da de e de aa de e de ad de e de eae fe ```

Let's examine this image for potential line intersections. My next step is to analyze the details within each area.  ```palette Key,Color ,#fefefeff a,#0807fdff b,#fc0909ff c,#555ceeff d,#e86761ff e,#b1d6b1ff f,#b0b0ffff g,#97c598ff ``` ```image fa afa fa ac a af a a af ca a af cc a a fa cc ac a a fa a db a ca bbd fa af bbd a a ebbe a gcaeeeeeeeeeeeeg dbb af geaceeeeeeeeeeee dbb a geeaeeeeeeeeeeee bbd cc geegaeeeeeeeeeee bbd a geeecaeeeeeeeeegbbe cc geeeeageeeeeedbbe a geeeeeaeeeedbbee fa geeeeecaedbbeeee a geeeeeeaddeeeeee fa geeeebbdaeeeeeee af gegbbdeegaeeeeee a dbbgeeeeeaceeeee af dbbeeeeeeeeeageeee a dbd geeeeeeeeeeaeeee cc bbd geeeeeeeeeecaeee a bbd geeeeeeeeeeeacee cc dbe geeeeeeeeeeeeaee a eb geeeeeeeeeeeecag fa b ac a b a fa bd a af bd ca a db af af db a a b fa cc b ac a b a cc bd fa a bd cc fa db af eggggggggggggggggagggggggdb a geeeeeeeeeeeeeeegaeeeeeegbg ca geeeeeeeeeeeeeeeageeeeeebeg af geeeeeeeeeeeeeeeaeeeeeebgeg a geeeeeeeeeeeeeeaceeeeebdeeg fa geeeeeeeeeeeeeeaeeeeebbeeeg ac geeeeeeeeeeeeecceeeedbeeeeg af geeeeeeeeeeeeeaeeeedbeeeeeg a geeeeeeeeeeeecceeegbeeeeeeg ca geeeeeeeeeeeeaeeeebeeeeeeeg af geeeeeeeeeeecaeeebgeeeeeeeg a geeeeeeeeeeeaeeebdeeeeeeeeg fa geeeeeeeeeegaeebbeeeeeeeeeg ac geeeeeeeeeeagedbeeeeeeeeeeg a geeeeeeeeeeaedbeeeeeeeeeeeg a geeeeeeeeeacebeeeeeeeeeeeeg ca geeeeeeeeeaebeeeeeeeeeeeeeg a geeeeeeeeccbdeeeeeeeeeeeeeg geeeeeeeeabdeeeeeeeeeeeeeeg geeeeeeecabeeeeeeeeeeeeeeeg geeeeeeeabeeeeeeeeeeeeeeeeg geeeeeecaeeeeeeeeeeeeeeeeeg geeeeeeaeeeeeeeeeeeeeeeeeeg geeeeebaeeeeeeeeeeeeeeeeeeg geeeebageeeeeeeeeeeeeeeeeeg geeebdaeeeeeeeeeeeeeeeeeeeg geebbaceeeeeeeeeeeeeeeeeeeg gedbeaeeeeeeeeeeeeeeeeeeeeg gedecceeeeeeeeeeeeeeeeeeeeg geeeaeeeeeeeeeeeeeeeeeeeeeg geecaeeeeeeeeeeeeeeeeeeeeeg a fa a ```  I'm going to scrutinize area A for any signs of an intersection.  ```palette Key,Color ,#fefefeff a,#0906fcff b,#fe0606ff c,#5c55f7ff d,#f63e46ff e,#fec9c9ff f,#adacfdff g,#fd8a8cff ``` ```image faa gb cac ebb faa ebbd cac bbd aaf dbd cac dbbe aaf gbbe faa gbbg aaf ebbg faa ebbd aaf bbd faa dbb cac dbbe faa gbbe cac gbbg aaf ebbg cac ebbd aaf bbd faa dbb aaf dbbe faa gbbe aaf gbbg faa ebbg cac ebbd faa dbd cac dbb aaf dbbe cac gbbe aaf ebbg faa ebbg aaf ebbd faa dbd aaf dbbe faa gbbe cacgbbe faagbbg cacbbd aadbd caabd aadbe faabe aadg faag eaac daa daac dbaa gbcac gbbaaf ebbcac ebbdaaf bbdfaa dbb aaf dbbefaa gbbe cac ebbg faa dg cac faa cac aaf cac ```  Bingo! This close-up reveals an intersection in area A! Okay, let's proceed to the next area. I'm analyzing this close-up of area B with precision.  ```palette Key,Color ,#fefefeff a,#0404feff b,#ff0606ff c,#7d7dffff d,#f2434fff e,#fd9e9fff f,#c2c1fdff g,#3837fdff ``` ```image gag faac caaf gag aac faaf caa gag faac caaf gag aac ed faaf edbb cag ebbbbd gac ebbbbe faaf dbbbbe caa edbbbde gagdbbbde eaadbd ebbdaaf ebbbbegag dbbbbe aac edbbbde faaf edbbbde caa edbbbd gag bbbbe faac bbe caaf e gag aac faaf caa gag faac caaf gag aac faaf ```  Oh my, look at that! It's an intersection in area B! My analysis indicates that there are two intersections in this image.

2

```palette Key,Color ,#fefefeff a,#0505feff b,#fe0708ff c,#7a79fdff d,#fa5559ff e,#feb1b1ff f,#bebeffff g,#3d3cfdff ``` ```image f ca afa fa gg af af a a af ca a ac gc a a fa cg ac a a cg fa db a gg bbd fa af ebbe af a ebbe a ca ebb af ac dbb a a dbd gc fa bbd a gg ebbe cg af ebbe a a dbb ca ca dbd a add fa bbea af ebbe fa a ebbe gg af dbb af a dbd a gc bbd ca a bbe af cg dbe a a eb fa ca b ac a be a fa be fa af bd gg a db af af eb a a eb ca gc b ac a be a cg be fa a bd gg fa db af a eb a fa eb ca af b ac a be a af bd fa a bd gg gc db af a eb a cg b ca a b af fa be a a bd fa fa bd ac af db a a eb fa af b gg a b a gcbe abd cgb ab ca a ba baf bda dbac db a d gc a cg a fa a ```

The hunt for intersections begins! Let's analyze this image closely. These areas seem to enclose narrow spaces where lines might be close.  ```palette Key,Color ,#fefefeff a,#575ee4ff b,#f91816ff c,#efefecff d,#a0cba5ff e,#cf9981ff f,#0808fcff g,#b1d7b2ff ``` ```image e bb bc cb bb bc cb eb bc b eb be b eb be b eb be bc cb bb bc cb bb bccccccccccccccccccccccccccccccccccccccccccccccccccccc cbddddddddddddddddddddddddddddddddddddddddddddddddddddc bbggggggggggggggggggggggggggggggggggggggggggggggggggdc cbegggggggggggggggggggggggggggggggggggggggggggggggggdc cdbgggggggggggggggggggggggggggggggggggggggggggggggggdc cdebgggggggggggggggdggggggggggggggggggggggggggggggggdc cdgbeggggggggggggdffdgggggggggggggggggggggggggggggggdc cdggbgggggggggggafdgfdggggggggggggggggggggggggggggggdc cdggebgggggggggffgggdfggggggggggggggggggggggggggggggdc cdgggbeggggggdfagggggafgggggggggggggggggggggggggggggdc cdggggbgggggffggggggggafggggggggggggggggggggggggggggdc cdggggebgggffggggggggggffgggggggggggggggggggggggggggdc cdgggggbeafdggggggggggggfaggggggggggggggggggggggggggdc cdggggggffgggggggggggggggfagggggggggggggggggggggggggdc cdggggdfabggggggggggggggggfdggggggggggggggggggggggggdc cdgggafdgbbggggggggggggggggfdgggggggggggggggggggggggdc cdggffggggbdgggggggggggggggdfgggggggggggggggggggggggdc cdafagggggebggggggggggggggggafggggggggggggggggggggggdc cffggggggggbbggggggggggggggggafgggggggggggggggggggggdc cfaggggggggggbeggggggggggggggggffggggggggggggggggggggdc afcdggggggggggdbgggggggggggggggggfagggggggggggggggggggdc ff cdgggggggggggbbgggggggggggggggggfaggggggggggggggggggdc cfa cdggggggggggggbegggggggggggggggggfdgggggggggggggggggdc af cdgggggggggggggbggggggggggggggggggfdggggggggggggggggdc cfa cdgggggggggggggebgggggggggggggggggdfggggggggggggggggdc afc cdggggggggggggggbegggggggggggggggggafgggggggggggggggdc ff cdgggggggggggggggbggggggggggggggggggafggggggggggggggdc cfa cdgggggggggggggggebggggggggggggggggggffgggggggggggggdc afc cdggggggggggggggggbeeeeeeeeeeeeeeeeeeefaeeeeeeeeeeeeegccccccccc ff cdgggggggggggggggggbbbbbbbbbbbbbbbbbbbbfabbbbbbbbbbbbbbbbbbbbbb gfg cdggggggggggggggggggggggggggggggggggggggfdggggggggggdc ff cdgggggggggggggggggggggggggggggggggggggggfdgggggggggdc c cdgggggggggggggggggggggggggggggggggggggggdfgggggggggdc cdggggggggggggggggggggggggggggggggggggggggdfggggggggdc cdgggggggggggggggggggggggggggggggggggggggggafgggggggdc cdggggggggggggggggggggggggggggggggggggggggggafggggggdc cdgggggggggggggggggggggggggggggggggggggggggggfagggggdc cdggggggggggggggggggggggggggggggggggggggggggggfaggggdc cdgggggggggggggggggggggggggggggggggggggggggggggfdgggdc cdggggggggggggggggggggggggggggggggggggggggggggggfdggdc cdggggggggggggggggggggggggggggggggggggggggggggggdfggdc cdgggggggggggggggggggggggggggggggggggggggggggggggdfgdc dddddddddddddddddddddddddddddddddddddddddddddddddafd af fa fa fg fc cf cf af af fa fa fg f ```  Let's take a closer look at area A.  ```palette Key,Color ,#fefefeff a,#5551fbff b,#fd2728ff c,#fec4c4ff d,#b1b1ffff e,#fb7578ff f,#0807feff g,#fe0101ff ``` ```image e gc gb bge cggc egb bge cggc egb d bge dffd cggc affffd egg dfffdaff bgb affad aff cgge dfffa ffa eggc dfffd dffa bgb affa dffa cgge dfffd dffd eggc afffd dffd bgb affa affd gge dfffd aff cggc affa aff egb dfffa ffa bge dfffd dffa cggaffa dffa efffd dffd afffe dffd dfffaggc affd dfffd egb aff affa bge aff dfffd cggc ffa afffd egg dffa affa bgb dffa dfffd cgge dffd affa eggc dffd dfffa bgb affd fffd cgge aff fa eggc aff d bgb ffa gge ffa cggc dffa egb dffd bge dffd cggc affd egb affd bge aff cggc ffa egb ffa bge dffa cggc dffd egg dffd bgb affd cggc affd eggc aff bgb ffa cggecccccccccccccccccccccccccccccccccccccffacccccccccccccccccccccccccc egggggggggggggggggggggggggggggggggggggggbffaggggggggggggggggggggggggg ebbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbffabbbbbbbbbbbbbbbbbbbbbbbb dffd affd affd aff ffa ffa dffa dffa dffd affd affd aff fff ffa dffa dffa dffd affd affd aff fff ffa dffa dffa dffd ```  The close-up clearly shows an intersection point in area A. My analysis indicates that there are two intersections in this image.

2

```palette Key,Color ,#fefefeff a,#3c37faff b,#ff1818ff c,#ffc4c4ff d,#c0c0ffff e,#ff6f6fff f,#0404feff g,#7b79fdff ``` ```image c be bc cb bb bc b eb bc b eb bc b eb be b cb be b cb be b cb bb bc b eb bc b eb d bc ffd b gfd f eb ff df be dfg df b af gf cb fa aa begfd fa ff fg dfgb fd af be f fa b df dfd cb df af bb gf fa bc aa gfd b fa ff eb fg dfg bc fd af b f fa eb df gfd bc df ff b gf dfg eb af af beccccccccccccccccccfaccccccccccccccccccccccc fa bbbbbbbbbbbbbbbbbbbbfabbbbbbbbbbbbbbbbbbbbbb dfd fd af f d df df gf af fa fg fd f f df gf af fa fg fd fd f df gf af aa fg fd f ```

I have an image in front of me. I need to determine if there are any intersection segments. Could these regions be concealing intersection points? Let's find out.  ```palette Key,Color ,#fefefeff a,#fd0606ff b,#0706fdff c,#fb9f9dff d,#a7a9fbff e,#aed5adff f,#f3534dff g,#535af1ff ``` ```image caa a caa ca caf a faf a fac ac aac a aa fc aa a caa ff caf a fac ca aac a aa ca aa eeeeeeeeeeeee a caa eeeeeeeeeeeee a caf eeeeeeeeeeeee ac faf eeeeeeeeeeeee a fac eeeeeeeeeeeee fc aaeeeeeeeeeeeee a aaeeeeeeeeeee ff ecaaeeeeeeeee a eeefaaeeeeeee ca eeeeefafeeeee a eeeeeeefaeeee ca eeeeeeeeeeeee a eeeeeeeeeeeee a eeeeeeeeeeeee ac eeeeeeeeeeeee a eeeeeeeeeeeee fc eeeeeeeeeeeee a eeeeeeeeeeeee ff eeeeeeeeeeeee a eeeeeeeegeeee ca eeeeeegbbeeee a dbbg ca dbbd a gbb a bbg ac dbbd a gbb ff bbg a dbbd ff dbbd a gbg eeeeeeeeeeefaeee bbg eeeeeeeeeeeaeeee dbbd eeeeeeeeeeeaeeee gbb eeeeeeeeeeaeeeee bbg eeeeeeeeeeaeeeee dbbd eeeeeeeeeaceeeee gbb eeeeeeeeeaeeeeee bbg eeeeeeeeffeeeeee dgbbd eeeeeeeeaeeeeeee dggbbbbbgd eeeeeeeffeeeeeeggbbbbbbgd eeeeeeeagbbbbbbgd dggbbbbbbgdeeeeee bbbbggeeeeaeeeeeeeee eeeeeeaeeeeeeeee eeeeeaeeeeeeeeee eeeeeaeeeeeeeeee eeeeafeeeeeeeeee eeeeaeeeeeeeeeee eeeffeeeeeeeeeee eeeaeeeeeeeeeeee eeffeeeeeeeeeeee eeaeeeeeeeeeeeee ca a a ac a ac a ff a cf a ca a ```  I'm going to scrutinize area A for any signs of an intersection.  ```palette Key,Color ,#fefefeff a,#fe0404ff b,#0605fdff c,#fd8486ff d,#aeaefeff e,#ffccccff f,#f63f47ff g,#5c5cfeff ``` ```image caa fac eaa fac eaae faf eaae caf aae caf aac caa fac eaa fac eaae faf eaae caf aae ddgggbbb cffggbbbbbbbbbbb ddgggbbbbbbbbbbbgggdd dddggbbbbbbbbbbbbggdd bbbbbbbbbggdddfac bgggdd eaa fac eaae faf eaae caf aae caf aac caa fac eaa fac eaae faf eaae caf aae caf ```  The close-up clearly shows an intersection point in area A. I'm ready to analyze the next area. Could this be where the intersection is hiding, in area B?  ```palette Key,Color ,#fefefeff a,#ff0404ff b,#1212ffff c,#ff7070ff d,#8787ffff e,#fbd5d9ff f,#ff3c3cff g,#ffa8a8ff ``` ```image fe aafe caaace efaaac efaaag gfaafg gaaafg caaafe ecaaace efaaac efaaa gfc dd edbbb ```  Darn it! This close-up doesn't show any intersections in area B. One intersection, that's it, but I found it.

1

```palette Key,Color ,#fefefeff a,#ff0505ff b,#0706feff c,#ff8080ff d,#a0a0ffff e,#ffc3c2ff f,#fc4042ff g,#5757feff ``` ```image e caa a eaa ea caf ae caf a fac ae aae a aae fc eaa a eaf cf caf a fac ca fae a aae ea eaa ae eaa a caf ae fac a fac fc aae a aa cf eaa a caf ca caf a fa ea ae a ae a fc a cf a d ca gbg a bbg ea dbbd ae gbb a bbg ae dbbd a gbb fc bbg a dbbd cf dbb a gbg ca bbg a dbbd ea gbb ae bbg a dbbd ac gbb a bbg fc dgbbd a dggbbbbbgd cf dgbbbbbbgd fgbbbbbbgd dgbbbbbbgd bbbbgd a ea ae a ac a fc a cf a ea a ea ae a ac a fc a cf a ea a ```

This is the image I'm working with. The goal is to count the intersections. There are 2 regions I'd like to highlight in the image.  ```palette Key,Color ,#fefefeff a,#0707feff b,#fd0a09ff c,#8f90fdff d,#f06b64ff e,#e3cde8ff f,#aed5adff g,#4b4dfbff ``` ```image fffffffffffffff fffffffffffffff fffffffffffffff fffdfffffffffff fffdbbfffffffff fffffdbbfffffff ffffffffbbdffff ffffffffffbbdff ffffffffffffdbb ffffffffffffffdbbe fffffffffffffff ebbd fffffffffffffff bbd fffgfffffffffff dbbe fffagffffffffff ebbe a ebbd gg dbb a dbbe gg ebbd a bbd fffffffffffffff gg dbbde fffffffffffffff a edbbbbbde fffffffffffffff gg edbbbbbde fffffffffffffff a edbbbbbde fffffffffffffff cg edbbbbbde fffffffffffffff a edbbbbbdefffffffffffffff ca edbbbbbddfffffffff a ffffdbbbbbdffff ca ffffffffffdffff a fffffffffffffff ca fffffffffffffff a fffffffffffffff ca ffffffffffgffff a fffffffffcaffff ca fffffffffafffff ae ffffffffaffffff ea fffffffafffffff ae ac ea ag ae ga ea ca ae ea ea a ae ae ea ac ac ag a ga ac ca a ea ac a a ae ac ac a ag ac ga a ca gc ea a a gg ae a ac gg ag a ga gg ca a ea gg a a ae cg ac a ag ca ga a ca ca ea a a ca ae a ac ca ag a ga ca ca ae ca ea ea ae ae ea ac ae ag ea ga aga ea ```  My goal is to determine if there's an intersection inside area A.  ```palette Key,Color ,#fefefeff a,#1010ffff b,#ff0303ff c,#8d8dffff d,#ff6a6bff e,#ffd8d8ff f,#ff3636ff g,#ffa1a1ff ``` ```image ge ebbfg efbbbfg edbbbbde gfbbbde gfbbbfg edbbbfg edbbbbde gfbbbde gfbbbfg edbbb edb cc caa aac ```  This close-up reveals that there are no intersections in area A. I'm ready to analyze the next area. Let's put area B under the microscope.  ```palette Key,Color ,#fefefeff a,#1010ffff b,#ff0202ff c,#7272ffff d,#ff7e7eff e,#ffbbbbff f,#b2b2ffff g,#ff3b3bff ``` ```image bbgdde bbbbbbbbgdde eedggbbbbbbbbgdde eedggbbbbbbbbgdd eedggbbbbg eedd c caa faaf faac faac aaa aaa ```  Area B is clear of intersections, but the search continues. After a thorough analysis, I conclude that there are no intersections in this image.

0

```palette Key,Color ,#fefefeff a,#0505ffff b,#ff0a0aff c,#8b8bffff d,#ff6e6eff e,#ffc2c2ff f,#cacaffff g,#4747ffff ``` ```image d dbb dbbe ebbd bbd dbb ebbe ebbd bbd c dbb gc ebbe a bbd gg dbb a dbbe gg ebbe a bbd gg dbbde a edbbbbbde gg edbbbbbde a edbbbbbde cg edbbbbbde a edbbbbbde cg edbbbbbde a edbbbbbd ca ed a ca a ca c a ca fa fa af a fa af af ac fa ag af ga fa ca af fa fa a af af a ac af ag a ga ac ca a fa ac a a af ac ac a ag gc ga a ca gc fa a a gg af a ac gg ag a ga gg ca a fa gg a a af cg ac a ag cg ga a ca ca fa a a ca af a ac ca ag a ga fa ca a fa fa a af af fa ac af ag fa gg aga fa ```

I'm analyzing this image to identify any points where lines intersect. I can confidently say that there are no intersections in this image.

0

```palette Key,Color ,#fefefeff a,#0808ffff b,#ff3434ff c,#5f5fffff d,#ff7b7bff e,#ffc1c1ff f,#ff0202ff g,#b2b2ffff ``` ```image g cag aa gaa cag aa gaa cac aag aa gac aag aa gac cag aa gac cag aa gaa cac aag gaaaaaaaaaccgg ggccaaaaaaaaaccgg ggccaaaaaaaaaaccgg ggccaaaaaaa fffffbdde edbfffffffbdde edbbffffffbdde eddbffffffbd ebf dfe fb bf efd ff dfe efd ff dfe fb bf efd fb df efd ff dfe fb bf efe fb bf efd ff dfe fb bf efe fb bf ef ```

Time to put on my detective hat and find those intersection points! There are 1 regions I'd like to highlight in the image.  ```palette Key,Color ,#fefeffff a,#0a09faff b,#d36257ff c,#686cdeff d,#b2d7b2ff e,#fa0908ff f,#eef5f0ff g,#a3cca2ff ``` ```image c fa af ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffcad fggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggagef fgddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddacegf fgdddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddcaebgf fgdddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddaeedgf fgddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddaceddgf fgdddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddcaedddgf fgdddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddaegdddgf fgddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddabbddddgf fgdddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddcaedddddgf fgdddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddaeddddddgf fgddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddacdddddddgf fgdddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddgabdddddddgf fgdddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddabddddddddgf fgddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddaadddddddddgf fgdddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddgaddddddddddgf fgdddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddagddddddddddgf fgddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddaadddddddddddgf fgdddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddbaddddddddddddgf fgddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddbagddddddddddddgf fgddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddcadddddddddddddgf fgdddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddeaddddddddddddddgf fgddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddeacddddddddddddddgf fgdddddddddddddddddddddddddddddddddddddddddddddddddddddddddddbbadddddddddddddddgf fgddddddddddddddddddddddddddddddddddddddddddddddddddddddddddgeaddddddddddddddddgf fgddddddddddddddddddddddddddddddddddddddddddddddddddddddddddeacddddddddddddddddgf fgdddddddddddddddddddddddddddddddddddddddddddddddddddddddddecadddddddddddddddddgf fgddddddddddddddddddddddddddddddddddddddddddddddddddddddddeeaddddddddddddddddddgf fgdddddddddddddddddddddddddddddddddddddddddddddddddddddddbeacddddddddddddddddddgf fgddddddddddddddddddddddddddddddddddddddddddddddddddddddgegadddddddddddddddddddgf fgddddddddddddddddddddddddddddddddddddddddddddddddddddddegagdddddddddddddddddddgf fgdddddddddddddddddddddddddddddddddddddddddddddddddddddebacddddddddddddddddddddgf fgddddddddddddddddddddddddddddddddddddddddddddddddddddbegadddddddddddddddddddddgf fgdddddddddddddddddddddddddddddddddddddddddddddddddddgedagdddddddddddddddddddddgf fgdddddddddddddddddddddddddddddddddddddddddddddddddddedcaddddddddddddddddddddddgf fgddddddddddddddddddddddddddddddddddddddddddddddddddebgadddddddddddddddddddddddgf fgdddddddddddddddddddddddddddddddddddddddddddddddddebdagdddddddddddddddddddddddgf fgddddddddddddddddddddddddddddddddddddddddddddddddbedcaddddddddddddddddddddddddgf fgdddddddddddddddddddddddddddddddddddddddddddddddgeddadddddddddddddddddddddddddgf fgdddddddddddddddddddddddddddddddddddddddddddddddegdacdddddddddddddddddddddddddgf fgddddddddddddddddddddddddddddddddddddddddddddddebdcaddddddddddddddddddddddddddgf fgdddddddddddddddddddddddddddddddddddddddddddddbeddadddddddddddddddddddddddddddgf fgddddddddddddddddddddddddddddddddddddddddddddbeddacdddddddddddddddddddddddddddgf fgddddddddddddddddddddddddddddddddddddddddddddeddcaddddddddddddddddddddddddddddgf fgdddddddddddddddddddddddddddddddddddddddddddegddadddddddddddddddddddddddddddddgf fgddddddddddddddddddddddddddddddddddddddddddebddacdddddddddddddddddddddddddddddgf fgdddddddddddddddddddddddddddddddddddddddddbeddgaddddddddddddddddddddddddddddddgf fgddddddddddddddddddddddddddddddddddddddddgedddadddddddddddddddddddddddddddddddgf fgddddddddddddddddddddddddddddddddddddddddegddacdddddddddddddddddddddddddddddddgf fgdddddddddddddddddddddddddddddddddddddddebddgaddddddddddddddddddddddddddddddddgf fgddddddddddddddddddddddddddddddddddddddeedddagddddddddddddddddddddddddddddddddgf fgdddddddddddddddddddddddddddddddddddddbedddaadddddddddddddddddddddddddddddddddgf fgddddddddddddddddddddddddddddddddddddgedddgaddddddddddddddddddddddddddddddddddgf fgddddddddddddddddddddddddddddddddddddegdddagddddddddddddddddddddddddddddddddddgf fgdddddddddddddddddddddddddddddddddddebdddcadddddddddddddddddddddddddddddddddddgf fgddddddddddddddddddddddddddddddddddbeddddaddddddddddddddddddddddddddddddddddddgf fgdddddddddddddddddddddddddddddddbeeeddddacddddddddddddddddddddddddddddddddddddgf fgdddddddddddddddddddddddddgbeeeebbdddddcadddddddddddddddddddddddddddddddddddddgf fgddddddddddddddddddddgbeeeebgddddddddddaddddddddddddddddddddddddddddddddddddddgf fgdddddddddddddddgbeeeebgddddddddddddddacddddddddddddddddddddddddddddddddddddddgf fgddddddddddgbeeeebgddddddddddddddddddcadddddddddddddddddddddddddddddddddddddddgf fgdddddbbeeeebgdddddddddddddddddddddddaddddddddddddddddddddddddddddddddddddddddgf fgbeeeeebddddddddddddddddddddddddddddacddddddddddddddddddddddddddddddddddddddddgf eeebggggggggggggggggggggggggggggggggcaggggggggggggggggggggggggggggggggggggggggggf faf faaad faaac daaad caaaf caaaf caaaf caacf caacf caac fcaac fcaac aac ```  I'm eager to see what's happening in this magnified view of area A.  ```palette Key,Color ,#fefefeff a,#0b08fcff b,#fd5658ff c,#6462fcff d,#feb0b0ff e,#fe0708ff f,#bfbffeff g,#930a75ff ``` ```image ca aace aa e fafbe cadee aaeeb cabe faced faaeb aage aaed ageb caeb agd cae fagb aad fag cab faa aad fag aa aa daa bac bga gaa eaa beaf dga eaa bega eeaf deaa beaac eeaa ebac beca eeaa dedca eefaf eedaa dedfaf eb ac eefaa dedcac ee ac bee ca ded aa deb aa ee faf ded ca ded faa beb aa ee faf ded ac ee aa ee ac ded ac ee ca be aac ded aa dee faf ee ca be aa ee ca eb faf be aa dee faf eeb cc be aa ded cac eb ac be ca bed faf eeb aa eb faf bed ca dbeeee faa dbeeeeebd aac dbbeeeeebd faf ddbeeeeeedd cc ddbeeeeebdd aa dbeeeeebbd ac dbbeeeeebb ac dbeeeeeedd ca dbbeeeeebd faa beeeeebbd aa ```  Amazing! This area was hiding an intersection all along! There's one and only one intersection present in the image.

1

```palette Key,Color ,#fefefeff a,#0909feff b,#fd4f50ff c,#6d69faff d,#ffb0b0ff e,#fe0505ff f,#bcbafdff g,#6d0294ff ``` ```image c a af cad ade afe caed abb ace fae aed agb fae ae ag fad ab ag fa af ga ba daf ga ea eaf bga dea eac eca bba deac efa eda ebac befa de af e ca ed a eb af de ca e a e af ed ca be a de ac e fa ed a eb ac be fa de a e ac ed fa bb a de cc e a ed af eb ca be a dbee af deeeebd ca dbeeeebd a dbeeeebd af dbeeeeb fa dbeeeed a dbeeebd ac eebd fa a faaaf faaaf faaaf faaaf faaaf caaaf caac caac caac caac caac aac ```

Time to put on my detective hat and find those intersection points! I'd describe these as 'hotspots' for potential intersections.  ```palette Key,Color ,#fefefeff a,#636cecff b,#fd0706ff c,#e8998eff d,#090afdff e,#96c896ff f,#b1d6b2ff g,#e94847ff ``` ```image f da d d ad da d fd da d d ad da d fd da d efedfffffffffffffffe effadffffffffffffffe efffdafffffffffffffe effffdfffffffffffffe effffadffffffffffffe efffffdafffffffffffe effffffdfffffffffffe efffffffdffffffffffe ccgbbb efffffffadfffcggbbbbbbbgc bg efffcggbbdgbbbgccffe bc ccgbbbbbbbgceffdffffffffe b bbbbggc efffffffffadfffffffe b effffffffffdaffffffe gb efffffffffffdffffffe bg efffffffffffedfffffe bc effffffffffffadffffe b efffffffffffffdafffe cb effffffffffffffdfffe gb effffffffffffffadffe bc feeeeeeeeeeeeeeedaef b d b d cb ad gg df bc d b ad b da cb d bg d bc ad beeeeeeeeeeeeeeeeeeee df ebfffffffffffffffffff d egbffffffffffffffffff ad efbgfffffffffffffffff da effbcffffffffffffffff ddda efffbffffffffffffffff adda efffcbfffffffffffffff addd effffgbffffffffffffff adddf efffffbgfffffffffffff fdddaeffffffbeffffffffffff addafffffbffffffffffff efadddefcbfffffffffff effffadddgbffffffffff efffffffedddaffffffff effffffffffbadddfffff efffffffffffbffadddaf efffffffffffgbffffaddda effffffffffffbgffffff adda efffffffffffffbcfffff ad effffffffffffffbfffff effffffffffffffcbffff efffffffffffffffgbfff effffffffffffffffbgff efffffffffffffffffbcf effffffffffffffffffbf effffffffffffffffffcb feeeeeeeeeeeeeeeeeeegb bc b b cb gg bc b ```  Eureka! Let's inspect this close up of area A  ```palette Key,Color ,#fefefeff a,#4742f9ff b,#fd0203ff c,#fd9c9eff d,#0605feff e,#ded3f3ff f,#9292ffff g,#fb4447ff ``` ```image ada eddf fdde add dda eddf fdde ada eddf fdde add dda eddf fdde ada eddf fdde eccc add ecccgggbbbbbb eddagggbbbbbbbbbbbbggg ecccgggbbbbddgbbbbbgggccce ccgggbbbbbbbbbbbbgaddcce bbbbbbbbgggccce ada ggccce eddf fdde ada dda eddf fdde ada eddf fdde ada edda eddf fdde ada eddf fdde ada ```  My analysis confirms the presence of an intersection in area A. Okay, let's direct our attention to the next zone. Let's take a closer look at area B.  ```palette Key,Color ,#fefefeff a,#635df8ff b,#fe0505ff c,#ff8181ff d,#0907fcff e,#ffc6c6ff f,#b6b6feff g,#f93a40ff ``` ```image be bg bbg ebbc cbbe cbbe gbg bbg ebbc cbbe gbbe gbg ebbc ebbc cbbe gbb gbg ebbc ebbe cbbe daf gbg ddddaf bbg fadddddaff ebbc faddddddaf cbbe fadddddaf cbbe fadddddagbg faddddddaf faadddddaf addddddaf gbgadddddaf gbg faddddddaf ebbc ffadddddaf ebbc faddddda cbbe faddd gbb fa gbg ebbc ebbe cbbe gbg bbg ebbc cbbe cbbe gbg bbg ebbc cbbe gbb gbg ebbc ebb cb ```  I am surprised, so clear, an intersection has appeared in area B. My analysis indicates that there are two intersections in this image.

2

```palette Key,Color ,#fefefeff a,#5b5bfeff b,#fe0404ff c,#ff8484ff d,#0808feff e,#ffc5c5ff f,#b0b0ffff g,#f83c42ff ``` ```image f da df d ad df d fd da df d ad df d fd da d d ad df d fd da d d ecgbbb ad ecgbbbbbbggce gg ecgbbdgbbggce be ecgbbbbbbgcce d b bbbbgcce fd eb da cb d bg fd be ad b df eb d gb fd bc da be d b fd cb ad gg df bc d be fd eb da cb d gg fd be aa b df eb d cb ad bg da be dddf b adda eb addaf gb fdddf bc fddda be adda b adddf cb fdddgg fadda badda eb fdddf cb fdddf gg adda be ad b eb cb bg be b eb gb bc be b cb gg bc b ```

Time to put on my detective hat and find those intersection points! I wonder what's going on inside those areas? Perhaps intersections are hiding there.  ```palette Key,Color ,#fefefeff a,#fd0a09ff b,#0403fdff c,#f26c67ff d,#5256f5ff e,#9ac596ff f,#fec3c3ff g,#b1d7b1ff ``` ```image c fa f a ac ac a ca fa fa ac a a ac ca ca af fa a a ca ac af ca a fa ac a a ac fa ca ac fa a a ca ac af ca a fa ca a af ac a ca cc fa a a fa ac ac ca a fa fa a af ac a ca ca fa aeeeeeeeeeeeeeeeeeeeeeeeeeee a eagggggggggggggggggggggggggg ac eaaggggggggggggggggggggggggg ca egaggggggggggggggggggggggggg fa egeagggggggggggggggggggggggg a eggacggggggggggggggggggggggg ac egggaggggggggggggggggggggggg ca egggcaggggggggggggggggggggggfa eggggacggggggggggggggggggggga egggggaggggggggggggggggggggac egggggcaggggggggggggggggggca eggggggaeggggggggggggggggeag egggggggaggggggggggggggggagg g egggggggaaggggggggggggggacgg dbbd eggggggggagggggggggggggcaggg dbbbd eggggggggeagggggggggggeagggg dbbbg egggggggggacggggggggggaggggg gbbbd eggggggggggagggggggggacggggg dbbbd eggggggggggcagggggggcagggggg dbbbegggggggggacgggggeaggggggg edbbbdgggggggagggggagggggggg eggggdbbbdgggcagggacgggggggg egggggggedbbdeaegcaggggggggg egggggggggggdbbbdagggggggggg eggggggggggggggcbbdggggggggg egggggggggggggggegdbdggggggg egggggggggggggggggggdbdggggg egggggggggggggggggggggdbdggg egggggggggggggggggggggggdbdg egggggggggggggggggggggggggdbd egggggggggggggggggggggggggggdbd eggggggggggggggggggggggggggg dbd eggggggggggggggggggggggggggg dbd eggggggggggggggggggggggggggg dbd eggggggggggggggggggggggggggg dbd eggggggggggggggggggggggggggg dbd eggggggggggggggggggggggggggg dbd eggggggggggggggggggggggggggg dbd eggggggggggggggggggggggggggg dbd eggggggggggggggggggggggggggg dbd eggggggggggggggggggggggggggg dbd eggggggggggggggggggggggggggg dbd eggggggggggggggggggggggggggg dbd egggggggggggggggggggggggggge dbd dbd db ```  This close-up of area A is like examining a piece of evidence.  ```palette Key,Color ,#fefefeff a,#fe0303ff b,#0504fdff c,#ff7171ff d,#5652faff e,#f93035ff f,#febfbfff g,#b4b2fdff ``` ```image ac aaf cae aac faaf eae faaf caa eac faaf cae eac faaf cae aac faaf eae faaf caa eac f faaf e cae ca eac faa faaf faac cae eae aac caa faaf faaf eae faac faaf eae caa caa eac faaf faaf faac cae eae eac caa faaf faaf cae faac aac eae faaf caa g eae faaf bbbdg faaf faac dbbbbbdgg caa eae gdbbbbbbdg eac caa ggdbbbbbddg faaf faaf gddbbbbbdg cae faac gdbbbbbbdg eac eae ggdbbbbbddgfaaf caa gdbbbbbbdee faaf gdbbbbbbdaac gddbbbbd eebbbbd faagdbbbd ff gdbbbd gdbbbd gdbbbd gdbbbd gdbbbd gdbbbd gdbbbd gdbbb gdb g ```  As I suspected, there's an intersection within area A. Two intersections have been found!

2

```palette Key,Color ,#fefefeff a,#ff0808ff b,#0403fdff c,#ff8d8dff d,#5554feff e,#fe5555ff f,#ffd5d5ff g,#a9a8ffff ``` ```image c fa c a ee ac a ea fa fa ac a a ac ca ea ac fa a a ea ac af ea fa fa ee a a ac fa ea ac fa a a ca ac ac ea a fa ea a af ac fa ea ee fa a a fa ac ac ea a fa ca af ac ac a ea ea fa af af fa ac ee ea a fa fa af ac ac a ea ca fa ac af a ac ea ea af fa fa af g ee ac dbbdg af ea gbbbd fa fa dbbbg ae af gbbbd a ac gbbbg ca ea dbbbg ac fa gbbbd a af dbbbg ca ac gdbbdgaf ea gbbbda ebbd f dbd dbd dbd dbd dbd dbd dbd dbd dbd dbd dbd dbd dbd dbd dbd dbd dbd dbd dbd dbd db ```

I'm curious to see if this image contains any intersection points. These regions highlight areas that look suspicious. Lines seem to converge within them.  ```palette Key,Color ,#fefefeff a,#e75a56ff b,#666df0ff c,#fd0808ff d,#edeff0ff e,#faa7a5ff f,#0a0bfcff g,#afd5afff ``` ```image b df fd fb bf f fd bf df fd fb bf f fd bf df fd fb bf f fd bf df fd fb bf f fd e bf cce df ec cd fd c dc dddddddddddddddfb ce ec gggggggggggggggbf ac ecgggggggggggggggfd dc acgggggggggggggfbd ce ccgggggggggggffgd aa gcaggggggggggfggd dc ggcaggggggggfgggd cd gggcgggggggfbgggd ca ggggcgggggbfggggd ec gggggcggggfgggggd c gggggacggfggggggd ce ggggggacffggggggd ac gggggggafgggggggd dc gggggggfcaggggggd cd ggggggfbgcagggggd ca gggggbfgggcgggggd ec gggggfgggggcggggd c ggggfgggggggcgggd ce gggffgggggggacggd ec gggfgggggggggacgd c ggfgggggggggggccd ce gfbggggggggggggca ac bfggggggggggggggce dc dfgggggggggggggggdce cd fggggggggggggggggd cd ddddddddddddddddddca fb ddddddddddddddd dc dgggggggggggggggggacd df ec dgggggggggggggggggcgd fd ac dggggggggggggggggcagd fb ac dgggggggggggggggacggd bf ca dgggggggggggggggcgggd bf ca dggggggggggggggcggggd bffb ce dgggggggggggggcaggggd bffb cd dggggggggggggecgggggd bffbd dc dggggggggggggcggggggd dfffd ec dgggggggggggcaggggggd dfffd ec dggggggggggacgggggggdbffb ac dggggggggggcggggggbffb ca dgggggggggcegggbffbgd ca dggggggggacgbffbggggd ce dggggggggafffgggggggd cd dggggggfffggggggggggd dcd dgggfffaagggggggggggd ec dggfbgacggggggggggggd ec dgggggcgggggggggggggd ac dggggcagggggggggggggd cc dgggacggggggggggggggd ca dgggcgggggggggggggggd c dggcggggggggggggggggd dgggggggggggggggggggd dgggggggggggggggggggd dgggggggggggggggggggd ```  Let's see if area A yields any clues.  ```palette Key,Color ,#fefefeff a,#f93e44ff b,#564af3ff c,#fe0505ff d,#a7a7feff e,#fec5c5ff f,#0706feff g,#fc8386ff ``` ```image c ac gcc eccg aca gcce eccg aca gcc ecce ccg aca gcce eccg aca gcc ecce cca acc ecce eccg aca gcce eccg d aca dbff gcc dbfffff ecce dbfffffbd ccg dfffffbd aca dbffffbd gccedbffffbd ecabffffbd dbffffbd dbfffffd dbfffffbg dfffffbaca dffffbd acc fbd ecce ccg aca gcce eccg aca gcc ecce ccg aca ecce gg ```  Area A contains an intersection. Okay, let's proceed to the next area. This close-up might reveal an intersection in area B.  ```palette Key,Color ,#fefefeff a,#fc4e50ff b,#4d45f6ff c,#fe0707ff d,#d1d1ffff e,#feadadff f,#0707feff g,#9292feff ``` ```image g df e ff ce bff cc gffd acc dffg cca bfb cca gffd ecca dffg ecce ffb ecce bff acce gffd acce dffg acc bfb cca gffd cca dffg ecca ffb ecce bff ecce gffd acce dffg accebfb acbffd affg ffba bffcca gffdecca dffg ecce bfb ecce gffd acce dffg acc ffb acc bff cca gffd ecca dffg ecca bfb ecce gffd ecce dffg acce ffb acc bff acc gffd cc dffg c bfb e gffd dffg ffb ff ```  Amazing! This area was hiding an intersection all along! I've identified a total of two intersection points.

2

```palette Key,Color ,#fefefeff a,#f95056ff b,#3c3cffff c,#fe0707ff d,#c6c6ffff e,#ffb0b0ff f,#0404feff g,#8181ffff ``` ```image g df f fg gf f fd bb df f fg gf f fd bb df f fg gf f fd bb df f fg gf f fd e bb cce df ec c f c c fg ce ec gf ac ec f c ac fd ce ca bb aa ca df ec ce f c ce fg ca c gf ec ec f c ec fd ce acbb ac af c fca c fg ce ca gf ce ec f c c fd ec ce bb ec ac df ac c f ac ce fg ca aa gf ce ec f ce c fd c ca bb c ec df ec c f ac ce fg ac ac gf ca c bf ca ce gffg ce aa gffb c ec gffb c c dffbd ec ca dbffd ec ec bffd ac c bffg ca ce gffg ca ac gffb ce affb ce dfffd c dbffaa ec fg ec ec c ac ce cc ac ca c c ce ```

This image looks interesting. I wonder if there are any intersections hidden in there? My next step is to analyze the details within each area.  ```palette Key,Color ,#fefefeff a,#3f49e9ff b,#fa0d0cff c,#0505fdff d,#d97568ff e,#8c9ae1ff f,#b1d7b1ff g,#97c896ff ``` ```image fffffffffffffffffffffffffff fffffffffffffffffffffffffff fffffffffffffffffffffffffff dffffffffffffffffffffffffff bbfffffffffffffffffffffffff fbdffffffffffffffffffffffff ffbffffffffffffffffffffffff ffdbfffffffffffffffffffffff fffbbffffffffffffffffffffff ffffbgfffffffffffffffffffff fffffbfffffffffffffffffffff fffffdbffffffffffffffffffff cccccaddfffffffffffffffffff ffffgeaccccccaeffffffffffff ffffffffbfffeaacccccaaeffff ffffffffdbffffffffffeaccccccae fffffffffbdffffffffffffffffeeacccccae ffffffffffbffffffffffffffff ec fffffffffffbfffffffffffffff c fffffffffffdbffffffffffffff aa ffffffffffffbdfffffffffffff c fffffffffffffbfffffffffffff ec fffffffffffffgbffffffffffff ca ffffffffffffffdbfffffffffff c fffffffffffffffbdffffffffff ec ffffffffffffffffbffffffffff ca ffffffffffffffffgbfffffffff c fffffffffffffffffbbffffffff ec ffffffffffffffffffbdfffffff ce fffffffffffffffffffbfffffff c fffffffffffffffffffdbffffff ec ffffffffffffffffffffbbfffff ce fffffffffffffffffffffbdffff c ffffffffffffffffffffffbffff ec ffffffffffffffffffffffdbfff ce fffffffffffffffffffffffbbff c ffffffffffffffffffffffffbdf ec fffffffffffffffffffffffffbf ce fffffffffffffffffffffffffdb fgggggcggggggggggggggggggggggggggggg ggggggggggggggggggggggggggbd gfffffecffffffffffffffffffffffffffff b gffffffcefffffffffffffffffffffffffff b gfffffffcfffffffffffffffffffffffffff db gfffffffecffffffffffffffffffffffffff bd gffffffffcefffffffffffffffffffffffff b gfffffffffcfffffffffffffffffffffffff b gfffffffffacffffffffffffffffffffffff db gffffffffffcefffffffffffffffffffffff bd gfffffffffffcfffffffffffffffffffffff b gfffffffffffacffffffffffffffffffffff b gffffffffffffcefffffffffffffffffffff db gfffffffffffffcfffffffffffffffffffff bd gfffffffffffffacffffffffffffffffffff bbbd gffffffffffffffcefffffffffffffffffff bbbd gfffffffffffffffcfffffffffffffffffff bbbdffffffffffffffacffffffffffffffffff gbbbdffffffffffffcefffffffffffffffff gfffbbbdffffffffffcfffffffffffffffff gffffffdbbdfffffffacffffffffffffffff gfffffffffdbbdfffffcefffffffffffffff gffffffffffffdbbbfffcfffffffffffffff gfffffffffffffffdbbbacffffffffffffff gffffffffffffffffffdbcbgffffffffffff gfffffffffffffffffffffcbbbdfffffffff gfffffffffffffffffffffaafdbbbdffffff gffffffffffffffffffffffcefffdbbbdfff gfffffffffffffffffffffffcffffffgbbbd gfffffffffffffffffffffffaaffffffffgb gffffffffffffffffffffffffcgfffffffff gfffffffffffffffffffffffffcfffffffff gfffffffffffffffffffffffffaaffffffff gffffffffffffffffffffffffffcffffffff gffffffffffffffffffffffffffgcfffffff gfffffffffffffffffffffffffffaaffffff gffffffffffffffffffffffffffffcffffff gffffffffffffffffffffffffffffgcfffff gfffffffffffffffffffffffffffffaaffff gffffffffffffffffffffffffffffffcffff gffffffffffffffffffffffffffffffecfff gfffffffffffffffffffffffffffffffcaff gffffffffffffffffffffffffffffffffcff gffffffffffffffffffffffffffffffffecf gfffffffffffffffffffffffffffffffffca gffffffffffffffffffffffffffffffffffc gfffffffffffffffffffffffffffffffffff gfffffffffffffffffffffffffffffffffff fggggggggggggggggggggggggggggggggggg ```  Here's a close-up of the area A.  ```palette Key,Color ,#fefefeff a,#5353feff b,#f9353bff c,#0504feff d,#fd797aff e,#a6a6feff f,#fe0404ff g,#ffc0c0ff ``` ```image gg gff bfb gffd gffg dff bfb gffd gffg dff bfb gffd dffg bfb bfb gffd dffg ccaaeee bfb ecccccccccaaabbd eeeaacccccccccccaaeee eeaaccccccccccccaaeee bfbeeaacccccccccccaaaee ffd eeaaacccccccccccaaeee gffg eeeaacccccccccccaaaee dffg eeeaacccccccc bfb eeaaa ffd gffg dff bfb gffd gffg dff bfb gffd gffg dff bfb gffd dffg dff bfb gffd dffg bfb bfb gffd dffg bfb ffd gffg dffg bfb ffd gffg dffg bfb ffd gffg dff bfb gffd gffg dff bfb gffd gffg dff bfb gff df ```  I observe an intersection inside area A. Okay, on to the next area of interest. I'm now examining the contents of area B in detail.  ```palette Key,Color ,#fefefeff a,#423ffbff b,#fd5859ff c,#0505feff d,#cecefeff e,#8a89feff f,#fd0607ff g,#ffababff ``` ```image aca dcce eccd aca dcce eccd aca dcce eccd aca dcce eccd aca dcce ecc aca dcce ecc aca dcce ecc aca dccd ecc aca dccd ecc aca dccd ecc cce g dccd ffbg ecc bffffbg cce gbfffffbg dccd gbfffffbg ecc gbfffffbg cce gbfffffbg dccd gbfffffbg aca gbfffffbg cce gbfffffbg dccd gbfffffbg aca gbfffffbg cce gbfffffbg dccd gbffffbgaca gbffffcce gbffccbbg gaccfffbg ccafffffbg eccdgbfffffbg aca gbfffffbg cce gbfffffbg eccd gbfffffbg aca gbfffffbg dcce gbfffffb eccd gbff aca g dcce eccd aca dcce eccd aca dcce eccd aca dcce eccd aca dcce eccd aca dcce eccd aca dcce ecc aca dcce ecc aca dccd ecc aca dccd ecc ac dc e ```  Case closed! This is definitely an intersection point in area B. I can confirm there's two intersections in there.

2

```palette Key,Color ,#fefefeff a,#4d4cfeff b,#f8383eff c,#0505feff d,#fd7d7eff e,#a6a6ffff f,#ff0505ff g,#ffc5c5ff ``` ```image g bb fg f df bb fg f df cccccabd eaccccccae f eeacccccaee df eaccccccae fd eeacccccae fg ec gf ec df aa fd c f ec gf ca bf c fd ec f ca gf c bb ec fd ca f c gf ec bb ce fg c f ec gf ce bb c fg ec f ce df c bb ec fg ce f c df ec fd ce fg c f ec df ce fd c fg ec gf ce df c fd ac fffg ce gbffd c gbffd ac bffd ce bffd c dffd ac dffb ce dffb c dffbaa dfcbg cfffg aa gfffg c gfffg c gbffd aa gb c c aa c c aa c c aa c ec aa c ec ca c ```

I'm optimistic that I'll find some intersections in this image. I've noticed 1 areas of interest. These could be potential intersection zones.  ```palette Key,Color ,#fefefeff a,#ee3c36ff b,#1011faff c,#fe0303ff d,#8593e2ff e,#f1f4eeff f,#dc9c8bff g,#b1d7b0ff ``` ```image f c cf ec ce fc ce fa c aa c cf ec ce e fc bd ce b fa db c bd aa b c db cf bd ec b cf db ec bd ce aeeeeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee fc acgggggdbgggggggggggggggggggggggggggggggggggggggggge c ecfgggggbdggggggggggggggggggggggggggggggggggggggggge aa egcggggggbggggggggggggggggggggggggggggggggggggggggge c egacgggggdbgggggggggggggggggggggggggggggggggggggggge af eggcfgggggbdggggggggggggggggggggggggggggggggggggggge ec egggcggggggbggggggggggggggggggggggggggggggggggggggge cf egggaagggggbbgggggggggggggggggggggggggggggggggggggge ec eggggcfgggggbdggggggggggggggggggggggggggggggggggggge ce egggggcggggggbggggggggggggggggggggggggggggggggggggge fc egggggaagggggbbgggggggggggggggggggggggggggggggggggge c eggggggcfgggggbgggggggggggggggggggggggggggggggggggge aa egggggggcggggggbggggggggggggggggggggggggggggggggggge c egggggggaagggggbbgggggggggggggggggggggggggggggggggge af eggggggggcfgggggbgggggggggggggggggggggggggggggggggge c egggggggggcggggggbggggggggggggggggggggggggggggggggge cf egggggggggaagggggbbgggggggggggggggggggggggggggggggge ec eggggggggggcfgggggbgggggggggggggggggggggggggggggggge ce egggggggggggcgggggdbggggggggggggggggggggggggggggggge fc egggggggggggaagggggbbgggggggggggggggggggggggggggggge ce eggggggggggggcfgggggbgggggggggggggggggggggggggggggge fa egggggggggggggcgggggdbggggggggggggggggggggggggggggge c egggggggggggggaagggggbdgggggggggggggggggggggggggggge aa eggggggggggggggcfgggggbgggggggggggggggggggggggggggge c egggggggggggggggcgggggdbgggggggggggggggggggggggggggecf egggggggggggggggaagggggbdggggggggggggggggggggggggggec eggggggggggggggggcggggggbggggggggggggggggggggggggggce egggggggggggggggggcgggggdbggggggggggggggggggggggggfc egggggggggggggggggaagggggbdgggggggggggggggggggggggce eggggggggggggggggggcggggggbggggggggggggggggggggggace egggggggggggggggggggcgggggdbgggggggggggggggggggggcge egggggggggggggggggggaagggggbdgggggggggggggggggggaage eggggggggggggggggggggcggggggbgggggggggggggggggggcgge egggggggggggggggggggggcgggggdbgggggggggggggggggcfgge dbb egggggggggggggggggggggaagggggbdggggggggggggggggcggge dbbbbd eggggggggggggggggggggggcggggggbgggggggggggggggcfggge dbbbbd eggggggggggggggggggggggfcgggggdbgggggggggggggfcgggge dbbbbd egggggggggggggggggggggggaagggggbdggggggggggggcggggge dbbbbd eggggggggggggggggggggggggcggggggbgggggggggggfcggggge dbbbbd eggggggggggggggggggggggggfcgggggdbggggggggggcgggggge dbbbbd egggggggggggggggggggggggggaagggggbdggggggggaaggggdbbbbd eggggggggggggggggggggggggggcggggggbggggggggcgdbbbbde eggggggggggggggggggggggggggfcgggggbbgggggdbbbbdgggge egggggggggggggggggggggggggggaagggggbddbbbbagggggggge eggggggggggggggggggggggggggggcggggggbbdggcfgggggggge eggggggggggggggggggggggggggggfcgggggggggfcggggggggge egggggggggggggggggggggggggggggaaggggggggcgggggggggge eggggggggggggggggggggggggggggggcgggggggfcgggggggggge eggggggggggggggggggggggggggggggfcggggggcggggggggggge egggggggggggggggggggggggggggggggaaggggaaggggggggggge eggggggggggggggggggggggggggggggggcggggcgggggggggggge eggggggggggggggggggggggggggggggggfcggaagggggggggggge egggggggggggggggggggggggggggggggggaagcggggggggggggge eggggggggggggggggggggggggggggggggggccfggggggggggggge eggggggggggggggggggggggggggggggggggfcgggggggggggggge eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee ```  Here's a close-up of the area A.  ```palette Key,Color ,#fefefeff a,#fc4143ff b,#5f5ffeff c,#fe0505ff d,#b7b7ffff e,#fed4d4ff f,#fe9090ff g,#0808feff ``` ```image cce dggd acc bgg ccf ggb ecce dggd acc bgg ccf ggb ecce dggd aca bgg ccf ggb ecce dggd aca bgg ccf ggb fcce dggd aca bgg ccf ggb fcce dggd aca bgg ccf ggb fcce dggd aca bgb ccf ggb fcce dggd aca bgb ccf ggd fcce dgg aca bgb eccf ggd fcce dgg aca bgb eccf dggd fcce bgg aca bgb eccf dggd fcce bgg aca ggb eccf dggd fcce bgg aca ggb eccf dggd fcce bgg aca ggb eccf dggd fcce bgg aca ggb eccf dggd fcce bgg aca ggb eccf dggd fcce bgg aca ggb eccf dggd fcce bgg aca ggb eccf dggd fcce bgg aca ggb f eccf dggd c fcce bgb fc aca ggd ecc eccf dgg aca fcce bgb ecce aca ggd aca eccf dgg ecce fcce bgb acf aca dggd fcc eccf bgg ccf fcce bgb fcc aca dggd ccf eccf bgg fca fcce ggb ecce aca dggd aca eccf bgg ecce fcce ggb aca aca dggd fcce eccf bgg ccf fcce ggb fcc aca dggd ccf eccf bgg fca fcce ggb ecce aca dggd aca ddb eccf bgg ecce ddbgggg fcce ggb aca ddbggggggbb aca dggd fcabggggggbbd eccf bgg ddbggggggbbd fcce ggb dbbggggggbbd aca dggddbbggggggbacf eccf bgggggggbdd fca fcce gggbdd eccf aca d aca eccf ecce fcce aca aca ecce eccf acf fcce fcc aca ccf eccf fcc fcc eccf aca aca eccf ecce fcc aca aca ecce eccf acf fcc fcce aca ccf eccffcc fccccf acca ```  Yes! I knew it! There's an intersection right here in area A! After careful examination, I conclude that there is one intersection.

1

```palette Key,Color ,#fefefeff a,#ff4545ff b,#4040feff c,#fe0304ff d,#a5a5ffff e,#ffd5d4ff f,#ff9292ff g,#0605feff ``` ```image f c cf ec ce fc c fa c aa c cf ec ce ec gd c g fc dg c gd aa g c dg cf gd c g ce dg ec gd ce a g fc ac dg c ce gd aa c g c aa bg af ce gd c c g cf aa bb ec ce gd ce c g fc aa bb c ce g aa c g c aa bb aa ce g c ec g cf aa bb ec ce g ce ec dg fc aa bb c ce g fa ec dg c aa gb aa ce g c ec dg cf aa gd ec ce g ce ec dg ec aa gd c ce g fc ec dg c aa gd aa ce g c ec dg cf dbg aa gd c dbgggd ce g ce dbgggd ec dg ec dbggbd aa gd ce dbggbd ce g fc dbggbd ec bg c dgggbd aa gd aa dgggbd ce g c dgggbd ec bb dgggbd aa gddgggbc ce gbd cf ec ec aa ce ce fc ec c aa aa c c ec aa aa c ccf ec ```

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.  ```palette Key,Color ,#fefefeff a,#5d60f2ff b,#f1514dff c,#fca8a7ff d,#0909fdff e,#bdbefeff f,#fe0606ff g,#acd4acff ``` ```image c fc f bb d b f dda cf bb d d f f da ed bb bb d da f f aa d f bb d ed bb f aa da f bb d d f f ed ed bb cf d da f f ed d fc cf d ed bf f ed da f cf de d fc f d ed bf cf de aa f f d de fc cf de d cf fc d aa f f aa de fc fc d d cf f aa ad f fc d de fc f ad d cf fc d gadgggggggggfggg f ed ggdggggggggfbggg gggfbggggggdgggg gggdggggggcfgggg ggggfggggggdgggg gggadgggggfggggg ggggfbggggdggggg ggggdggggfbggggg gggggfggggdggggg gggggdggcfgggggg gggggbbggdgggggg gggggadgfggggggg ggggggfggdgggggg ggggggdbbggggggg ggggggbbdagggggg gggggggdgggggggg gggggggfdggggggg ggggggfadggggggg gggggggdaggggggg gggggfbgdagggggg gggggggdfggggggg gggggfgggdgggggg ggggggaabbgggggg ggggfggggadggggg ggggggdggfgggggg gggbbgggggdagggg gggggadggbfggggg gggfgggggggdgggg gggggdggggfggggg ggfggggggggadggg ggggadggggbfgggg gbbgggggggggdagg ggggdggggggfgggg f d gggadggggggbfggg f ed gggdggggggggfggg bb da ed cf f d de f fc ed d cf bf da de f f d d cf fc ed de fc bf da d f f d aa fc fc ed d f cf da aa fc f d d f fc ed ad fc cf da d f f d ed fc fc ed d f cf da ed bb f d de f fc ed ed bb cf aa de f f de d bb fb ed de fcf a d bf da c d aa d aa d ad d ed d ```  Let's zoom in on area A to get a clearer view.  ```palette Key,Color ,#fefefeff a,#4f46f5ff b,#f9363cff c,#ff9898ff d,#0706fdff e,#c7c5fdff f,#fe0506ff g,#8a88fdff ``` ```image ffc gdd cff ddg ffc edd cff adg bfc edd cff adg bfc edde cff ada bfc edde cff ada bfc dde cff gda bfb dde cff gda bfb ddg ffgdd bfddg bdd dda eddfc adafb eddeffc ada cfb edde ffc ada cfb edde ffc gda cfb dde ffc gda cfb dde ffc gdd cff ddg ffc gdd cff ddg bfc edd cff ```  The close-up clearly shows an intersection point in area A. Onward to the next region of interest. This is a magnified view of the region B.  ```palette Key,Color ,#fefefeff a,#5c5afdff b,#f93c41ff c,#fec5c6ff d,#0807fdff e,#b4b4ffff f,#fe0506ff g,#ff8585ff ``` ```image edde ffg add bfb dda gffc edde ffg add bfb dda cffc edde ffg add bfb dda cffc edde ffg add bfb dda cffc edde ffg add gff ddacffc eddbfg addb cdda bfdde gffadd cffc dda bfb edde gff add cffc ada bfb edde gff add cffg ada bfb edde gff edd cffg ada bfb dde gffc edd cffg ada ```  As I suspected, there's an intersection within area B. The image features two intersection points.

2

```palette Key,Color ,#fefefeff a,#5f5dfcff b,#fc3c3eff c,#febebeff d,#0909feff e,#b3b3ffff f,#fe0404ff g,#ff7b7bff ``` ```image c bg f bg d b f dda cf bg d d f f da ed bb bb d da cf f aa d f gb d ed bb f aa da f gb d d fc f ed ed bb gb d da f f ed d fc gf d ed gb f ed da f cf de d fc f d ed gf cf de aa f fc d d fc cf de d gf fc d aa f cf aa de fc fc d d gf f aa ad f fc d de fg f ad d gf fc d ad f f ed de fg fg d d cf f ed ad f bg d de fg f d d cf bg de ad f f d dbg bbde cd fd fad da bb de df cf d aagb f ad d f bb de aa gb cf d d f fc ed ed gf bb de d f f d ed cf fc ed d f bb da ed cf f d de f fc ed d cf gb da de fc f d d cf fc ed de fc gf da d f f d aa fc fc ed d f gf da aa fc f d d f fc ed ad fg gf da d f f d ed bg fg ed d f cf da ed bg f d d f fg ed d bg cf aa de f f d d bb fg d de fcf a d gf da c d aa d aa d ed d ed d ```

I'm analyzing this image to identify any points where lines intersect. These spots are like clues. Let's see what they reveal about potential intersections.  ```palette Key,Color ,#fefefeff a,#4344fcff b,#fe0707ff c,#faa3a1ff d,#0202feff e,#d2d2ffff f,#aed5aeff g,#f85653ff ``` ```image ffffffffffffffff ffffffffffffffff ffffffffffffffff fffffffffffcffff fffffffgbbbbffff ffcgbbbgffffffff cbbbbgffffffffffff cgbbbgcffffffffffffffff cbbbbc ffffffffffffffff cgbbbgc ffffffffffffffff cbbbbc ffffffffffffffff cgbbbgc ffffffffffffffff cbbbbc ffffffffffffffff cbbbgc ffffffffffffffff bbg ffffffffffffffff gbbc ffffffffffffffff cbbg ffffffffffffffff bbb fffffffffffdffff gbbc ffffffffffaaffff cbbg ffffffffffdfffff gbbc fffffffffdffffff cbbc ffffffffaaffffff bbg ffffffffdfffffff gbbc fffffffdffffffff cbbg ffffffadffffffff bbb ed gbbc de bg aa ed de aa ed de aa ed de aa ed de aa ed de aa ed de aa ed de aa ed de aa ed de aa ed de aa ed de aa ed de aa ed a de add aa edde ed edde de edde aa dda ed ada de ada aa edde ed edde de edde aa dda ed ada de ada aa add ed edde d eddeaa dd ```  I've examined the entire image, and there are zero intersections present.

0

```palette Key,Color ,#fefefeff a,#4040ffff b,#ff0707ff c,#ffa3a3ff d,#0101ffff e,#8e8effff f,#dedafaff g,#ff5656ff ``` ```image c gbbbb cgbbbgf cbbbbc cgbbbgf cbbbbc cgbbbgc cbbbbc cgbbbgc cbbbbc cbbbgc fbbg gbbc cbbg bbbf d gbbc aa cbbg fd gbbc df cbbc aa fbbg fd gbbc df cbbg aa bbbf fd gbbc df bg aa fd df aa fd df aa fd df aa fd df aa fd df aa fd df aa fd df aa fd df aa fd df aa fd df aa fd df aa fd df aa fd e df eda aa eddf fd fddf df fdde aa dde fd ada df ada aa eddf fd eddf df fdde aa dde fd ada df ada aa eddf fd eddf df fddeaa fdd ```

This image looks interesting. I wonder if there are any intersections hidden in there? I did not find anything, there's no intersections

0

```palette Key,Color ,#fefefeff a,#ff4242ff b,#0101ffff c,#ff0505ff d,#a6a6ffff e,#ffccccff f,#4e4effff g,#ff8888ff ``` ```image d fbbbd dfbbfd dbbbf fbbbd fbbbd dfbbfd dbbbf fbbbd fbbbd dfbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb ga eccaace gccg ca ecca ace acce eca gccg ac acce ecg gccg cc ecca gcg acce cc ecca gce acce cc gccg gce ecca ca ccg ace eca ac ecg cc ecg cc gcg cc gce ca ace eca ac eca cc ec ```

I have an image in front of me. I need to determine if there are any intersection segments. These zones indicate regions where lines appear to be in close proximity.  ```palette Key,Color ,#fefefeff a,#f18680ff b,#0c0bfaff c,#fe0505ff d,#747cefff e,#fec3c3ff f,#aed5aeff g,#f64541ff ``` ```image e ac cgg ec c c ac ec ce ce ec c ce ca c c ga ga c c gg ag c c ac ac c c ec ec ce ce c c ca ce c c gg ga c c ac gg c c ec ag ce c c ec ca c c ec gg ce c c ag ce c c ec ga ce c ec gg ca c c ag ga c c ec ag c c ec ac ce ce c ec ca ce c c fffffffffffggfff ga fffffffffffcffff c ffffffffffggffff gg ffffffffffcfffff c fffffffffacfffff ac fffffffffcffffff c ffffffffacffffff ec ffffffffcfffffff ce ffffffffcfffffff c bbbbbddfffcafffffff ca fddbbbbbbbbddfff c ffffffcaffddbbbbbbbdd gg ffffffcfffffffff fddbbbbbbbdd c fffffggfffffffff ddbbbbbd ac fffffcffffffffff bbb c ffffggffffffffff dbbf ec ffffcfffffffffff bbd ce fffacfffffffffff dbb c fffcffffffffffff dbbf fffcafffffffffff ffacffffffffffff bbd ffffcfffffffffff ffcfffffffffffff dbb ffffggffffffffff ec dbbd fffffcffffffffff ce bbd fffffgcfffffffff c dbb ffffffcfffffffff ga dbbd ffffffacffffffff c bbd fffffffcffffffff gg dbbffffffffcfffffff c dbbdfffffcaffffff ag ffbbbffffcffffff c ffffdbbffggfffff ec ffffffdbbdcfffff c fffffffffbbbffff fffffffffffbffff ffffffffffffffff ffffffffffffffff ffffffffffffffff ```  Eureka! Let's inspect this close up of area A  ```palette Key,Color ,#fefefeff a,#ff7c7cff b,#0606feff c,#fe0404ff d,#5849efff e,#ffc6c6ff f,#b2b2feff g,#f63d45ff ``` ```image gca ecc gca ecce acg cce acg cce acg cca ecc gca ecc gca ecce gcg ecce f acg bbbbdddfff cce bbbbbbbbbbbbbdddggf fffdddbbbbbbbbbbbbdddfff ffdddbbbbbbbbbbbbbd cca fffdddbbbbb ecc ff gca ecc gca ecce gcg ecce acg cce acg cce acc gca ecc gca ecc gca ecce ```  My investigation has led me to an intersection in area A! Hmm, interesting. Let's check out another area. Could this be where the intersection is hiding, in area B?  ```palette Key,Color ,#fefefeff a,#fda6a7ff b,#0808feff c,#fe0708ff d,#5b5bfeff e,#710896ff f,#aaaafeff g,#fe5253ff ``` ```image cca acc ccg acc gcg acca gcg cca gcc cca acc cca acc gcg acc gcg d cca bbdf gcg dbbbbf cca fdbbbbd acc fbbbbdf cca fdbbbbf acc dbbbbd gcg fbbbbdf acc fdbbbbfgcg dbbbbeca fbbbbef fdbbb aee ga ```  I can confirm that an intersection exists in area B. The final answer is: two intersections found.

2

```palette Key,Color ,#fefefeff a,#ff8585ff b,#0706feff c,#ff0505ff d,#5752faff e,#ffc6c6ff f,#a5a5ffff g,#ff4242ff ``` ```image e ac cgg ec c ce ac ec ce ce ec c ce ca c c ga ga c c gg ag c c ac ac c c ec ec ce ce c c ca ce c c gg ga c c ac gg c c ec ag ce c c ac ca c c ec gg ce c c ag ce c c ec ga ce c ec gg ca c c ag ga c c ec ag c c ec ac ce ce c ec ca ce c c ga ga c c ag gg c c ag ac c c ec ec ce ce ec c bbbbddf ce ca fddbbbbbbdff c ca fdbbbbbbbdf gg c ffdbbbbbbddf c ga fddbbbbf ac c dbd c ag fbbf ec c fbbd ce ac dbb c c fbbf ca ec bbd c ce dbb gg c fbbf c ce bbd ag c dbb c ga fbbf ec c bbd ce gg dbb ec c fbbf ca ag bbd c c dbb ga ac fbbfc c bbb d ```

I have a feeling there might be some intersections in this image. It's crucial to examine these regions more closely.  ```palette Key,Color ,#fefefeff a,#fd0505ff b,#6767efff c,#eb9f96ff d,#090afcff e,#b0d6b1ff f,#f74441ff g,#96c59bff ``` ```image eeeeeeeeeeeeeeeeeg eeeeeeeeeeeeeeeeeg eeeeeeeeeeeeeeeeeg eeeeeeeeeeeeefeeeg bb eeeeeeeeeeeeeaeeeg dbbddddb eeeeeeeeeeeeaceeeg bd bddddbb eeeeeeeeeeegaeeeeg d bbddddbe eeeeeeeeeeeageeeeg d bdddddb eeeeeeeeeecaeeeeeg db ebddddbeeeeeeeeeeeaeeeeeeg bd bdddddbgeeefaeeeeeeg d eeegbdddddbeeeeeeg de eeeeeeeefbddddeeeg bd eeeeeeeeaeeeeeeeeg ed eeeeeeeaceeeeeeeeg d eeeeeeeaeeeeeeeeeg db eeeeeeaceeeeeeeeeg bd eeeeecaeeeeeeeeeeg d eeeeeaeeeeeeeeeeeg d eeeefaeeeeeeeeeeeg db eeeeaeeeeeeeeeeeeg bd eeeffeeeeeeeeeeeeg d eeeaeeeeeeeeeeeeeg de eeafeeeeeeeeeeeeeg bd eeaeeeeeeeeeeeeeeg ed eaceeeeeeeeeeeeeeg d caeeeeeeeeeeeeeeeg db agggggggggggggggge bd ca geeeeeeeeeeeeeeg d a eeeeeeeeeeeeeeeg d ff eeeeeeeeeeeeeeegdb a eeeeeeeeeeeeeeebd fc eeeeeeeeeeeeeeed a ceeeeeeeeeeeeedg ac afeeeeeeeeeeeddg a eaceeeeeeeeegdeg a eeaeeeeeeeeedeeg ca eecaeeeeeeedbeeg a eeeafeeeeebdeeeg ff eeeeaceeegdeeeeg a eeeeeaeeedgeeeeg ff eeeeecaedbeeeeeg a eeeeeeabdeeeeeeg ac eeeeeeedceeeeeeg a eeeeeedgaeeeeeeg a eeeeeddecaeeeeeg ca eeeegdeeeafeeeeg a eeeedeeeeeaceeeg cf eeedbeeeeeeaeeeg a eebdeeeeeeecaeeg ff egdeeeeeeeeeafeg a edgeeeeeeeeeeacg ac dbeeeeeeeeeeeeag a geeeeeeeeeeeeeca ac eeeeeeeeeeeeeeeaf ca eeeeeeeeeeeeeeegac a eeeeeeeeeeeeeeeg a ca eeeeeeeeeeeeeeeg ca a geeeeeeeeeeeeeeg ff ff ac a a ac ca a ff ac ac ca a a ca ca ff a ac ff a a ca fc ff a ac ac a a ca a ff ca ac a a ff ca a ff ff ac a aac ca ```  Let's see if area A yields any clues.  ```palette Key,Color ,#fefefeff a,#fe0a0bff b,#3833faff c,#fb5f63ff d,#0504feff e,#c5c5feff f,#7777ffff g,#febdbdff ``` ```image e b fd gg edd gaa eddf aac bdb gaac fdde gaag edde caa ddf aac bdb gaac fdde gaag eddf caa bdb aac fdd gaac edde gaag eddf caa bdb aac fdde gaac edde gaag ddf caa bdb aacdde gaddf bdbg fddaa eddeaac eddf gaac bdb gaag fdde caa edde aac ddf gaac bdb gaag fdde caa eddf aac bdb gaac fdd gaag edde caa eddf aac bdb gaac fdde gaag edde caa ddf aac edb gaa ee ga c ```  Oh my, look at that! It's an intersection in area A! Let's continue our search in the next region. Let's take a closer look at area B.  ```palette Key,Color ,#fefefeff a,#fe0506ff b,#6056f4ff c,#ff7d7dff d,#0907fdff e,#aaaafeff f,#fe3a3aff g,#ffc0c0ff ``` ```image c gaa aac caa aag caf gaag faf gaag fac gaa fac caa ddbbee aac ddddddddbbee caf ebbdddddddddbee gaag eebbdddddddddbee ebbdddddddddbee fabbbddddddd gaa eebdb fac caa aac caf aag caf gaag faf gaag fac caa aac caf aag caf gaag faf gaag fac gaa aac caa aag caf gaag faf gaag fac ```  I can confirm that an intersection exists in area B. The final answer is: two intersections found.

2

```palette Key,Color ,#fefefeff a,#ff0202ff b,#5451fbff c,#fa757aff d,#0706feff e,#a8a8feff f,#fe3535ff g,#feb5b5ff ``` ```image c be a dbbddddbe ag bd ebddddbe ga d ebddddbe ag d eddddde ga db ebddddbe a ed ebddddb cf d ebddddde de fcbddd bb a ed ac d a de ag bd ga d a d cf db a ed ff d a de fc bb a ed ag d ga de a bd ca d a d cf db a ed fc d a g de ag ff bb ga ag ed a a d ga ga de a ff bd cf ag d a a d fc ga db a fbd ag dg ga dea ag bb ga ga ed ff a d ag cf de a a bd ga fc d ff a d ag ac db a a ga ag ff ga ag a a cf ga a ff ff ag a a fc ga a ff ag ag ga a a ga ca ff a ag cf a a ga fc ff a ag ag a ga ga a ff ga ag a a cf ga a ff fc ag a aag ga ```

I'm curious to see if this image contains any intersection points. The image is completely devoid of intersections. Zero.

0

```palette Key,Color ,#fefefeff a,#3e3effff b,#ff0808ff c,#ceceffff d,#ffb2b2ff e,#0404ffff f,#ff5d5dff g,#8888ffff ``` ```image d fbf fbb dbb dbbd dbbd bbd bbf fbf fbb fbb dbb dbbd bbd bbf bbf fbf fbb dbbd dbbd bbf fbf fbb dbbd bbf fbf fbb dbbd dbbd bbf fbb ce fbb eaa dbbd ec ea bbf eg eg fbf ea eg fbb aa ec dbbd ae ec db ge ce ce ce ce ge ec ge ec ae eg aa ea ea aa eg ae ec ge ec ce e ce ce ec ce ec ge eg ae ea ae aa ea ae eg ge eg ce ec ce ec ec e ec ce eg ge ea ge aa ae ae aa ge ea ce eg ce eg ec ec ec ec eg ce ea ce c ge ge ae ea ea eg ec e ```

Let's examine this image for potential line intersections. These regions highlight areas that look suspicious. Lines seem to converge within them.  ```palette Key,Color ,#fefefeff a,#e64e49ff b,#585ff0ff c,#f4948fff d,#0908fbff e,#add4adff f,#adaefcff g,#fe0706ff ``` ```image f eedbeeeeeeeeeeeeee eeedeeeeeeeeeeeeee eeebdeeeeeeeeeeeee eeeedeeeeeeeeeeeee eeeebdeeeeeeeeeeee eeeeedeeeeeeeeeeee eeeeeedeeeeeeeeeee eeeeeedbeeeeeeeeee eeggacedeeeeeeeeee eeecaagddggaceeeee eeeeeeeedeeaagggggac eeeeeeeebdeeeeeeeecagggggac eeeeeeeeedeeeeeeee cagggggac eeeeeeeeeedeeeeeee caggggg eeeeeeeeeedbeeeeee gc eeeeeeeeeeedeeeeee g eeeeeeeeeeedbeeeee cg eeeeeeeeeeeedeeeee gc eeeeeeeeeeeebdeeee g d cg fd gc df g d cg db gc d g bb cg d gc fd g df cg d gc df g d cg bb gc d g fd cg d gc fd g df cg d gc db g d cg bd gc d g fd cg df gc d g db cg d gc bb g d cg fd gc df g d cg df gc d g bb cg d gc fd g d cg fd gc df egeeeeeeeeeeeeee d ecgeeeeeeeeeeeee db eegaeeeeeeeeeeee ddddbf eeegeeeeeeeeeeee fbddddb eeecgeeeeeeeeeee fbddddbf eeeegaeeeeeeeeee bddddbf eeeeegeeeeeeeeee fbddddb eeeeecgeeeeeeeee fbddddbeeeegaeeeeeeee ebddddbaeeeeeeee eeeeeebdddddbeee eeeeeeeegaefbdee eeeeeeeeegeeeeee eeeeeeeeecgeeeee eeeeeeeeeegaeeee eeeeeeeeeeegeeee eeeeeeeeeeecgeee eeeeeeeeeeeegaee eeeeeeeeeeeeegee eeeeeeeeeeeeeeee ```  I'm eager to see what's happening in this magnified view of area A.  ```palette Key,Color ,#fefefeff a,#f8656bff b,#322af6ff c,#fcbcbeff d,#0302feff e,#7070ffff f,#b7b7ffff g,#fd0809ff ``` ```image bde fdd bde fddf edb ddf edb bde fdd bde fddf edb ddf edb dde c fdd gggaaacc bde cggggggggggddacc ccaaggggbdbgggggaacc ccddagggggggggggaacc edb ccaaagggggggggg ddf ccaaaggg edd c bde fdd bde fddf edb ddf edb bde fdd bde fddf edb ddf ```  The evidence is clear: this is an intersection in area A. Let's shift our focus to the next area. My goal is to determine if there's an intersection inside area B.  ```palette Key,Color ,#fefefeff a,#fe6767ff b,#544ffaff c,#ffbcbcff d,#0605feff e,#f51c26ff f,#a6a6ffff g,#fe0000ff ``` ```image cggc age ega cggc age ega cggc age ega cggc age ega cggc age ega cggc f age dddbbff ega bddddddddbff cggc fbbddddddddbbee ffbddddddddbbff ffbbddddddddbff aeebbdddddddb ega ffbddb cggc age ega cggc age ega cggc age ega cggc age ega cggc age ac ```  Aha! I've found an intersection inside area B! After a thorough search, I conclude that there are two intersections.

2

```palette Key,Color ,#fefefeff a,#ff5e5eff b,#3832f8ff c,#ff9c9cff d,#0303ffff e,#7878ffff f,#bdbdffff g,#fe0708ff ``` ```image f be d eb d fd df d de ggac d ccagbbggac d cagggggac ed cagggggac d cagggggacc fd caggggg df gc d g be cg d gc eb g d cg fd gc df g d cg be gc d g eb cg d gc fd g df cg fd gc de g d cg bb gc d g ed cg d gc fd g df cg d gc be g d cg eb gc d g fd cg df gc d g be cg d gc eb g d cg fd ga df g fd cg de ga d g bb cg d ga ed g d cg fd ga df g d cg be ga bdddbe g fbddddef cg feddddef ga ebdddbf g fbdddbe cg feddddef ga feddddbg ebdddbe ga fbd g cg ga g cg ga g ```

The hunt for intersections begins! Let's analyze this image closely. These zones indicate regions where lines appear to be in close proximity.  ```palette Key,Color ,#fefefeff a,#fc0b0aff b,#4d52f4ff c,#ea6d68ff d,#0708fdff e,#9ea3f0ff f,#ffb7b7ff g,#add4adff ``` ```image f caa a caf af aa ca caf a aa af caf ca aa a caf af aa ca fac a aa af fac ca aa a fac af aa ca fac a aa ggggggggggggggggg af fac ggggggggggggggggg ca aa gggggggggggggdggg a faagggggggggggdbggg af aagggggggggbdgggg ca ggaagggggggdggggg a gggaagggggdeggggg af gggggaaggdbgggggg ca ggggggaaedggggggg a ggggggggdaggggggg d af gggggggdbcagggggg ed ca ggggggbdgggaagggg db a ggggggdgggggcaggg d af gggggdggggggggggg edgggggggggggcag ggggdbggggggggggg gdbggggggggggagg gggedgggggggggggg ggdgggggggggacgg gggdggggggggggggg gggdgggggggcaggg ggdeggggggggggggg gggbdggggggagggg gbdgggggggggggggg ggggdeggggacgggg gdggggggggggggggg gggggdgggcaggggg d gggggbdggagggggg db ggggggdeacgggggg ed gggggggdaggggggg d gggggggcdggggggg de ggggggacdbgggggg bb gggggcaggdgggggg ed gggggagggedggggg d ggggacggggdbgggg de gggcaggggggdgggg bd gggagggggggedggg d ggacggggggggdbgg d gcaggggggggggdgg db gaggggggggggggdg ed ac bb d fa de de a d bd ac bd d f de d d db ed ed de d d de ed bb db ed d d ed de bb bd d d d d bb db de ed d d bd de de bd d d ed d de db d ed ed d db de dbb ed ```  Eureka! Let's inspect this close up of area A  ```palette Key,Color ,#fefefeff a,#fe0404ff b,#4a49feff c,#ff9393ff d,#0706fdff e,#ecd9ebff f,#f93d43ff g,#9a96fbff ``` ```image eddg caae gdde eaac bdb faf eddg caae gdde eaac bdb faf eddg caae gdde eaac bdb faf eddg caae gdde eaac bdd faf ddb caae gddg eaac bdd faf ddb caae eddgeaac gddfaf bddae eddg ffdde caabdb eaaceddg faf gdde caae bdb eaac eddg faf gdde caae bdd eaac ddb faf gddg caae bdd eaac ddb faf eddg caae gdde eaac bdb faf eddg caae gdde aac bdb ```  I've cracked the case! This area contains the intersection. Right then, let's explore the next spot. Let's zoom in on area B to get a clearer view.  ```palette Key,Color ,#fefefeff a,#fe0404ff b,#4e4cfcff c,#ff9393ff d,#0706fdff e,#a2a0fdff f,#fb3c3fff g,#efdaeaff ``` ```image be bdd c edde afg gddb aaac bdb gfaafg eddg caaac gdde gfaafg ddb caaac bdd gfaafg edde caaac gdde gfaafg bdb caaac eddg gfaafedde caaddb gbddfg eddfaac gddegfaafg bdb caaac bddg gfaafg edde caaac gddb faaf bdb cac eddg gdde ddb bdd edde gdde bdb eddg edde ddb bdd ```  There's no doubt about it - this is an intersection in area B. My analysis indicates that there are two intersections in this image.

2

```palette Key,Color ,#fefefeff a,#fd0a0bff b,#3b3bffff c,#ff6a6aff d,#0505feff e,#c1c0feff f,#ffb2b2ff g,#7a7affff ``` ```image f caa a caf af aa ca caf a aa af caf ca aa a faf af aa ca fac a aa af fac ca aa a fac af aa ca fac a aa af fac ca aa d a fac dg af aa gd ca fac d a ca de af aa bb ca caed a da d af dgcaf ed ca gd aa dg a d ca d af de ed ca bb bb a ed de af d ed fa de bb a bb de af ed d fa d gd a dg deac gd da d ad de acdg bb fa d ed a ed d ac dg dg fa d gd a ed d ac bb de fa de bb a ed ed ac bb d fa de de a d bb ac gd ed f de d d dg gd gd dg d d de ed bb dg ed d d ed dg bb gd de d ed de bb bb de ed d d gd de de bb d ed gd d dg dg d gd ed d dg de dbb ed ```

This image looks interesting. I wonder if there are any intersections hidden in there? I need to zoom in on these areas to get a better look.  ```palette Key,Color ,#fefefeff a,#575df2ff b,#f4605bff c,#b6b7feff d,#0707fdff e,#ffb1b1ff f,#fd0909ff g,#add4adff ``` ```image c cd daa cd d d cd d dc dc cd d dc aa d d aa aa d d aa cd d d cd f cd dc fe dc cd fb d dc ff dc d bf d aa ef aa d f d ad f aa d fe d cd fb cd dc fb d cd bf cd dc bf dc d ef d aa f dc d f d gadggggggggggggfe aa ggdgggggggggggfb d ggadgggggggggffg aa gggdggggggggbfgg d ggggdggggggbfggg cd ggggdagggggfgggg d gggggdggggfggggg cd gggggdaggfgggggg dc ggggggdgfbgggggg d ggggggadbggggggg dc ggggggfdgggggggg d gggggbfadggggggg aa ggggbfggdggggggg d ggggfggggdgggggg aa gggfgggggdaggggg d ggfgggggggdggggg cd gfbgggggggdagggg d fbgggggggggdgggg cd ffggggggggggadggg dc bfggggggggggggdggg d ef cd dc ef dc d f d aa fe dc gggggggggggdgggg fe d ggggggggggaagggg fb aa ggggggggggdggggg bf d gggggggggadggggg bf ad gggggggggdgggggg ef d gggggggggdgggggg f cd ggggggggdggggggg f dc ggggggggdggggggg fe d gggggggdaggggggg fb dc ffffffffdfffffffffffffbbbbbbeeeeee fb d ggggggaagggggggg eeeeeebbbbbbffffff aa ggggggdggggggggg d gggggadggggggggg ad gggggdgggggggggg d ggggadgggggggggg cd ggggdggggggggggg dc ggggdggggggggggg d gggdgggggggggggg dc gggdgggggggggggg d ggdagggggggggggg aa d d aa ad d d aa cd d dc cd d d a ```  Let's zoom in on area A to get a clearer view.  ```palette Key,Color ,#fefefeff a,#4646ffff b,#f54852ff c,#ceceffff d,#0504fdff e,#feaaabff f,#fe0606ff g,#8782f9ff ``` ```image cddc ada cddc gda ddc gda ddg gdd adg cdd adg cddc ada cddc gda ddc gda ddg fffffbbbbbbbbbbgddeeeeeeeeeeee fffffffffffffffddbfffffffffffffff eeeeeeeeeeeebddbbbbbbbbbfffffff adg cddc ada cddc gda ddc gda ddg gdd adg cdd adg cddc ada cddc gda ddc ```  I've cracked the case! This area contains the intersection. Time to investigate another area. I'm now examining the contents of area B in detail.  ```palette Key,Color ,#fefefeff a,#4747ffff b,#f54750ff c,#e5d4eeff d,#0605fdff e,#ff9f9fff f,#fe0808ff g,#8e8bfcff ``` ```image gda ddg e gdd ef ddg cff gddc cffb ada bff cddc bffc ada bffc cddc effe gda effe ddg effb gdd cffb ddg ffb gddc bff ada bffc cddc bffe ada effe cddgffe gddfb cddb fbdd bffddg bffcgddc effe ada effe cddc effe ada cffb cddc cffb gda ffb ddg bffc gdd bffc ddg effe gddc effe ada effe cddc cffb ada cffb cddc bff gda ffc ddg ```  The lines cross each other within area B, forming an intersection. There are precisely two intersections present in the image.

2

```palette Key,Color ,#fefefeff a,#3737ffff b,#ff5757ff c,#b8b8ffff d,#0404feff e,#ffababff f,#fe0808ff g,#6f6fffff ``` ```image c gd dga cd d d cd d dc dc cd d dc ag d d ag ga d d ga ga d d cd f cd dc fe dc cd fb d dc bf dc d bf d ag ef ag d f d ga f ga d fe d cd fe ca dc fb d cd bf cd dc bf dc d ef d ag f dc d f d ga fe ag d fb d cd fb ga dc bf d cd ef ca dc ef d d f cd ag f dc d fe d gdb dc fd d bfcd ag ef dc d ef d ga f dc d fe d cd fe ag d fb d cd ff ga dc bf d d ef cd dc f dc d f d ag fe dc d fe d ga fb ag d bf d cd bf ga d ef d cd f cd dc f dc d fe d dc fb dc ffffffffdfffffffffffffbbbbbbeeeeee fb d ag eeeeeebbbbbbfffff ag d d ga ga d d cd cd d dc cd d dc dc d d ac ag d d ag ga d d ga cd d dc cd d d a ```

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.  ```palette Key,Color ,#fefefeff a,#f84f4cff b,#0505fdff c,#fe0606ff d,#4548f5ff e,#939af1ff f,#f7a3a0ff g,#aed5aeff ``` ```image e dbbbbde ebbbbde edbbbbde edbbbde edbbbbde edbbbbe edbbb db bd be b b ebgggggggggggggggggggggg dbggggggggggggggggggggg bdgggggggggggggggggggg gbeggggggggggggggggggg ggbggggggggggggggggggg ac gggbgggggggggggggggggg accf gggebggggggggggggggggg fcca ggggdbgggggggggggggggg fcca gggggbdggggggggggggggg cccf ggggggbeggggggggggggggaccf gggggggbgggggggggggacca ggggggggbgggggggfccagg ggggggggebggggcccggggg gggggggggdbaccfggggggg ggggggggacbdgggggggggg gggggfccaggbeggggggggg gggcccggggggbggggggggg accfgggggggggbgggggggg accaggggggggggggebggggggg fcca ggggggggggggggdbgggggg ac gggggggggggggggbdggggg fc ggggggggggggggggbegggg c gggggggggggggggggbgggg cf ggggggggggggggggggbggg ca ggggggggggggggggggebgg fc gggggggggggggggggggdbg c ggggggggggggggggggggbd c gggggggggggggggggggggbe ca ggggggggggggggggggggggb ac b c eb c db cf bd ac be fc b c b cf eb aa db fc bd c be cf b ca b ac eb c db c bd cf be ac b fc c cf aa fc c cf ca fc c c cf ac fc c cf aa fc c cf ```  I'm focusing my attention on this specific region, area A.  ```palette Key,Color ,#fefefeff a,#ff4949ff b,#0605fdff c,#fe0405ff d,#3f3dfdff e,#908ffdff f,#fd9799ff g,#ded3f4ff ``` ```image e bg bbg dbd gbbd gbbe ebbe ebbg dbbg dbd gbbd gbbe ebbe ebbg dbbg dbd gbbd gbbe ebbe ebbg ga dbbg gfccc dbd facccca gbbd faccccaf gbbe faccccaf ebbe gfcccccfg ebbg faccccaf dbbfaccccaf fbbbccaf gfcccbbdg faccccaebbe faccccaf ebbe faccccaf ebbg gfcccccfg dbbg gfaccccag dbd faccccaf gbbd cccaf gbbe afg ebbe ebbg dbbg dbd gbbd gbbe ebbe ebbg dbbg dbd gbbd gbbe ebbe ebbg dbbg dbd gbb gb e ```  There's no doubt about it - this is an intersection in area A. My investigation reveals that there is exactly one intersection in this image.

1

```palette Key,Color ,#fefefeff a,#ff5050ff b,#0706feff c,#ff0606ff d,#504efdff e,#a0a0ffff f,#ff9f9fff g,#efddedff ``` ```image e dbbbbde gebbbbdeg edbbbbde gebbbbbeg edbbbbde gedbbbbeg edbbb db bd be bg gb eb db bd be bg gac gb accf eb fcca db fcca bd gcccg be accf bg fcca gb fcca eb gcccg dbaccf acbd fcca be gcccg bg accf gb accf eb fcca db acg bd fc be c bg cf gb ca eb fc db gc bd cg be ca bg ac gb gc eb cg db cf bd ac be fc bg c gb cf eb aa db fc bd gc be cg bg ca gb ac eb gc db cg bd cf be ac b fc c cf aa fc c cg ca fc gc cg cf ac gc c cf aa fc c cf ```

I'm curious to see if this image contains any intersection points. There are 1 areas where the lines seem to converge. We should take a closer look at area A.  ```palette Key,Color ,#fefefeff a,#4f52f9ff b,#f55657ff c,#0708feff d,#fca7a6ff e,#fe0707ff f,#9b9ef7ff g,#add4adff ``` ```image f aca aca aca aca aca aca aca fcc fcc fcc fcc fcc fcc fcc fcc fcc fcc fcc cf c fc aa cf c fc eed cf eeb c deed fc eeb aa bee cf deed c eeb gggacggggggggggggggg beed ggggcagggggggggggggg deeb gggggcgggggggggggggg bee gggggfcggggggggggggg deed ggggggcagggggggggggg eeb gggggggcgggggggggggg beed ggggggggcggggggggggg deeb ggggggggacggggggggggdddbbbbeeeeeeeeeee bee ddddbbbeeeeeeecbeeeeeeeeebbbbdddd deebbbbbbdgggggggcggggggggg ggggggggggfcgggggggg gggggggggggcaggggggg ggggggggggggcggggggg gggggggggggggcgggggg gggggggggggggacggggg ggggggggggggggcfgggg gggggggggggggggcgggg gggggggggggggggfcggg ca c c ac cf c fc ca c c ac cf c fc ca c c ac cf c fc ca c c aa cf c fc ca c ```  This close-up might reveal an intersection in area A.  ```palette Key,Color ,#fefefeff a,#3b38fcff b,#f24c59ff c,#0504feff d,#feb1b2ff e,#fe0506ff f,#c2c2ffff g,#7d7dffff ``` ```image ccg fccf gcc aca fccg gccf aca ccg fccf gcc aca fccg gccf aca ccg fccf gcc ddddacadbbbbbbbbeeeeeeee bbbbbeeeeeeeeeeeeeccbeeeeeeeeeeeeeeee eeeeeeeeeeeeeeeebbbccbbbdddddddd dddddddd aca ccg fccf gcc aca fccg gccf aca ccg fccf gcc aca fccg gccf aca ccg ```  My analysis confirms the presence of an intersection in area A. There's one and only one intersection present in the image.

1

```palette Key,Color ,#fefefeff a,#5959ffff b,#f94146ff c,#0909feff d,#ff8888ff e,#ff0505ff f,#a6a6ffff g,#ffc8c8ff ``` ```image f aca aca aca aca aca aca acc acc fcc fcc fcc fcc fcc fcc fcc fcc fcc fcc ca c fc aa cf c ac eed cf beb c deeg fc geed aa bee cf deed c beb ac deeg cf geed c bee fc deed ca eeb cf deeg c geed ac gggdddbbbeeeeeeeeeee beegggdddbbbeeeeeecbeeeeeeeeebbbdddggg deebbbdddggg c fc ca c c ac cf c fc ca c c ac cf c fc ca c c ac cf c fc ca c c ac cf c fc ca c c ac cf c fc ca c ```

I'm approaching this image with caution. Intersections might be tricky to spot. I need to zoom in on these areas to get a better look.  ```palette Key,Color ,#fefefeff a,#0506fdff b,#fd0504ff c,#8c9bdfff d,#e9423cff e,#d49380ff f,#b1d7b1ff g,#454feaff ``` ```image c a ac a a ca a d cg ebffffffffffffffffffffffffffffffffffffffffffffffffffffff a befffffffffffffffffffffffffffffffffffffffffffffffffffff gg fbfffffffffffffffffffffffffffffffffffffffffffffffffffff a fbdffffffffffffffffffffffffffffffffffffffffffffffffffff ac affbffffffffffffffffffffffffffffffffffffffffffffffffffff a cafebfffffffffffffffffffffffffffffffffffffffffffffffffff a acfbeffffffffffffffffffffffffffffffffffffffffffffffffff ca caffbffffffffffffffffffffffffffffffffffffffffffffffffff a facfbdfffffffffffffffffffffffffffffffffffffffffffffffff ca ffaffbfffffffffffffffffffffffffffffffffffffffffffffffff a ffacfebffffffffffffffffffffffffffffffffffffffffffffffff gg fffaffbefffffffffffffffffffffffffffffffffffffffffffffff a fffagffbfffffffffffffffffffffffffffffffffffffffffffffff ac ffffaffddffffffffffffffffffffffffffffffffffffffffffffff a ffffggffbffffffffffffffffffffffffffffffffffffffffffffff ac fffffaffebfffffffffffffffffffffffffffffffffffffffffffff ca fffffggffbeffffffffffffffffffffffffffffffffffffffffffff a ffffffafffbffffffffffffffffffffffffffffffffffffffffffff ca ffffffgaffddfffffffffffffffffffffffffffffffffffffffffff a fffffffafffbfffffffffffffffffffffffffffffffffffffffffff gg fffffffcaffebffffffffffffffffffffffffffffffffffffffffff a ffffffffafffbefffffffffffffffffffffffffffffffffffffffff ac ffffffffcafffbfffffffffffffffffffffffffffffffffffffffff a fffffffffacffddffffffffffffffffffffffffffffffffffffffff ac ffffffffffafffbffffffffffffffffffffffffffffffffffffffff a ffffffffffacffebfffffffffffffffffffffffffffffffffffffff a fffffffffffafffbeffffffffffffffffffffffffffffffffffffff ca fffffffffffagfffbffffffffffffffffffffffffffffffffffffff a ffffffffffffafffddfffffffffffffffffffffffffffffffffffff gg ffffffffffffggfffbfffffffffffffffffffffffffffffffffffff a fffffffffffffafffebffffffffffffffffffffffffffffffffffff gg fffffffffffffggfffbefffffffffffffffffffffffffffffffffff a ffffffffffffffaffffbfffffffffffffffffffffffffffffffffff ac ffffffffffffffgafffddffffffffffffffffffffffffffffffffff a fffffffffffffffaffffbffffffffffffffffffffffffffffffffffa fffffffffffffffcafffebffffffffffffffffffffffffffffffffca ffffffffffffffffaffffbefffffffffffffffffffffffffffffffa ffffffffffffffffcaffffbffffffffffffffffffffffffffffffga fffffffffffffffffacfffddfffffffffffffffffffffffffffffaf fffffffffffffffffcaffffbffffffffffffffffffffffffffffggf ffffffffffffffffffacfffebfffffffffffffffffffffffffffaff fffffffffffffffffffaffffbefffffffffffffffffffffffffacff fffffffffffffffffffacffffbfffffffffffffffffffffffffafff eb ffffffffffffffffffffaffffddfffffffffffffffffffffffacfff dbb ffffffffffffffffffffagffffbffffffffffffffffffffffcaffff ebbe fffffffffffffffffffffaffffebfffffffffffffffffffffafffff ebbd fffffffffffffffffffffggffffbefffffffffffffffffffgafffff dbb ffffffffffffffffffffffafffffbfffffffffffffffffffaffffff dbbe ffffffffffffffffffffffggffffddfffffffffffffffffggffffff ebbd fffffffffffffffffffffffafffffbfffffffffffffffffafffffff bbb fffffffffffffffffffffffgaffffebfffffffffffffffagfffffff dbbe ffffffffffffffffffffffffafffffbeffffffffffffffaffffffebbd ffffffffffffffffffffffffcafffffbfffffffffffffacfffebbbf fffffffffffffffffffffffffafffffddfffffffffffcaffdbbefff fffffffffffffffffffffffffcafffffbfffffffffffaebbdffffff ffffffffffffffffffffffffffacffffebffffffffedadfffffffff fffffffffffffffffffffffffffafffffbefffffdbbafffffffffff fffffffffffffffffffffffffffacfffffbffebbdfggfffffffffff ffffffffffffffffffffffffffffafffffdbbdffffaffffffffffff ffffffffffffffffffffffffffffagfffffefffffagffffffffffff fffffffffffffffffffffffffffffafffffffffffafffffffffffff fffffffffffffffffffffffffffffggfffffffffacfffffffffffff ffffffffffffffffffffffffffffffaffffffffcaffffffffffffff ffffffffffffffffffffffffffffffggfffffffafffffffffffffff a ca ca a a gg ca a a gg ca a aac a ```  Let's put area A under the microscope.  ```palette Key,Color ,#fefefeff a,#0404feff b,#fe0607ff c,#7a79fdff d,#fd5153ff e,#feacacff f,#bebeffff g,#3835fcff ``` ```image bbe ebb bbd ebb be eb bd cc bbe aa dbd gac bbe faa ebb faa ebbe ga dbd faf bbe cg ebb af bb ag ebe aaf dd cag be caa bbd gac ebbe faa dbd gac bbe faa ebb gac dbd faa ebbe faf bbe cg ebb faf db ag ebe aaf dd cag be aaf bb caa dbd caa dbd gac bbe faa ebb gac dbd faa ebbe gac dbb faa bb faf dd cg ebe af bb ag bbe aaf ebb cag dbd aac ebbe caa dbb faa ebb gac dbd faa ebbe gac dbb faa bb ga eb faf dd faf bb ag bbe aaf ebb cag dbd aaf ebbe caa dbb aac bbe gac dbd g faa bb ca gac db aa faaf bd cag gac eb aaf faa bd cag ga bbe aaf faf dbb ac af ebb gc ag dbd ca aaf bbe aa cag dbb cag aac bbd aaf caa ebb cag gac dbd faaf gac db faaf faa bd gac gac eb faa faa bd aac ga bbe ag faf ebb af cg bbd cg faf ebbe faf aaf bbe faa cag ebb gac aaf bbd faa caa ebbe gac aac dbd caa faa bb aaf edb gac eb cag ebbbb gac ebe gag edbbbbe faaf bd faaf ebbbbde gac bbe gac edbbbde faa ebb aaedbbbbe ga bbd agbbbde faf ebbe eddabde cg dbd edbbace af bbe dbbbbga aaf bbd ebbbbd cag cag ebbedbbbbde faaf aac dbbbbde gac caa bbd faa gac gac faa caa gac aac gac aaf faaf ag gag faf faa gg ```  My investigation has led me to an intersection in area A! There's one and only one intersection present in the image.

1

```palette Key,Color ,#fefefeff a,#0505feff b,#ff0606ff c,#8383ffff d,#fb4e52ff e,#feaaabff f,#c4c4ffff g,#4141ffff ``` ```image c a ac fa af fa a b cg eb a be gg b a bd ac a b a fa eb af af be fa fa b a af bd ca a b a ac eb gg a be a gc b ac a dd a gg b af a eb fa cg be a a b ca ca dd a a b gg fa eb a af be gc fa b a af dd af a b fa af eb af a be ca ac b a a dd cg gc b a a eb gc gg be a a b ac cg dd fa a b af ca eb fa a be a fa b cg af dd a fa b gg af eb a a be ac ac b a eb a dd af dbbe gc b fa dbbe a eb a ebbd gg be ca bbb a b a dbbe cg dd gg ebbd a b a bbb ca eb ac dbbe a be a ebbd fa b af bbb af dd fa dbbe fa b aebbd af eb edad a be dbba af b ebbd gg a dbbd a ac e gc a a gc af a fa gg af a ca cg a a cg ca a a gc fa a aac fa ```

I'm on the case! Let's uncover any intersections hidden in this image. It's crucial to examine these regions more closely.  ```palette Key,Color ,#fefefeff a,#0808fdff b,#f06d66ff c,#b6b6feff d,#b1d6b0ff e,#5b61f0ff f,#fd0a0aff g,#97c698ff ``` ```image ff bf df ff bf fb fd bf f ff bf bfd fb ff f fb f bf bf ff fb ggggggggggggggggd dfb f ddddddddddddddddg ff df ddadddddddddddddg fb fb ddgaddddddddddddgbf f dddagdddddddddddff f ddddadddddddddgfb bf ddddaedddddddbfdg fb dddddaddddddffddg f dddddaedddbfbdddg f ddddddaddffdddddg bf ddddddeafbddddddg fd ddddddbagdddddddg f dddddffeadddddddg bf dddgfbddadddddddg fb ddffddddgaddddddg f ddbddddddagdddddg f ddddddddddadddddg bf ddddddddddaeddddg fb dddddddddddaddddg f dddddddddddeedddg df ddddddddddddadddg fb ddddddddddddeaddg f gddddddddddddagdg f ca bf ac fb ca f ac f a bf ae fd a fgggggggggggggggd ee bfddddddddddddddg a fbdddddddddddddg ea dfgddddddddddddg a ddfddddddddddddg ca ddbfdddddddddddg ac dddfbddddddddadg a ddddfddddddeagdg ac ddddgfddddaadddg a dddddffdgaeddddg ae ddddddfeaddddddg a ddddddaadddddddg ee ddddgaebfddddddg a dddeadddfbdddddg ca ddaadddddfdddddg a eaeddddddgfddddg ca aadddddddddbfdddg ac aedddddddddddfbddg a cac ddddddddddddfddg ac aa ddddddddddddbfdg a ae dddddddddddddfdg ee eac dddddddddddddddg a aa gggggggggggggggd ea cae a ea ca aa a cac ca ea ac aa a cac ae aa a ae ee cac a aa ea ae a eac ca aa acae ca ```  Let's put area A under the microscope.  ```palette Key,Color ,#fefefeff a,#0504feff b,#f7545bff c,#8787ffff d,#feb2b2ff e,#4444feff f,#fd080aff g,#c8c8ffff ``` ```image cc gaa eac gaag eae gaag d eae bf gaag dfff cae dfffd aac bffb caa dfffd aac bfffd gaa bffb eae dfffd gaag bffb eae dfffb gaag dfffd caebffb aaffd bbaad dfffaac dfffdcaa bffb eac dfffd gaag bfffd eae bffb gaag dffd eae d gaag cae aac caa aac caa eac gaag eae gaag eae gaag cae aac ```  Yes! I knew it! There's an intersection right here in area A! Alright, let's examine the next area. Let's see if area B yields any clues.  ```palette Key,Color ,#fefefeff a,#0605fdff b,#fa4c50ff c,#9191ffff d,#ff9d9dff e,#4240fcff f,#fe0707ff g,#ecd9ebff ``` ```image fg fb ffd dffg bff ffb gffd dffg bfb gffb dffd bffg ffb cg gffd geae dffg gaaac bff caaeg gffb geaae dffd caaac dffg caaeg bfb geaac gffd caaac dffeaaeg baaac caaab eaaeffd gaaac dffg caaag bfb geaae gffb gaaac dffd caaeg bffg geaae bfb caaac gffd caaeg dffg eaac bff aac ffb eg dffd dffg bfb gffd dffd bff bd ```  Case closed! This is definitely an intersection point in area B. I've identified a total of two intersection points.

2

```palette Key,Color ,#fefefeff a,#0505feff b,#ff4545ff c,#9191ffff d,#ff9797ff e,#4443feff f,#ff0505ff g,#e6d5eeff ``` ```image g ff dfggf ff bb gfd fd bf f fb df dfd fb ff fg gfb gf bfg bf ff fd dfd f bf df ag fb bb ga dfg fg ag ff f ga gfd df ac bf fd a fb f ee dfd gf a ff bb eefb fd dag f ffca df gfd ag fb bf ga fg d ag gf ga bf ac fd a f ee df a bb ce fg a f ca df ag fd ga f ac gf a bb ec fd a f ee df a fb ca fg a gf ca bf ag fd ga ga f cag ac df aa a bb gac ec feag a aa ee gacdf a ea fd ca ae fg ag cac gf ga ea bb ag ae fd ga cag f ac aa df a gae b ee cag a aa ce gac a eag ca aa ag gac ga ea ac ae a cac ac ea a ae ee cag a aa ce gae a cag ca aa acac gag ```

This image seems promising for intersection detection. These zones indicate regions where lines appear to be in close proximity.  ```palette Key,Color ,#fefefeff a,#5455f0ff b,#fd0909ff c,#f0615aff d,#aeb0fbff e,#aed4aeff f,#0607fdff g,#ffb6b6ff ``` ```image g bc bg b cb bc b gb cb bg b gb bc bg b cb bc b gb cb bg b gb bc bg b cb bg b gb cc bg b eeeeeeeeeeeeeeeeeeeeeee gbeeeeeeeeeeeeeeeeeeeeeee bceeeeeeeeeeeeeeeeeeeeee beeeeeeeeeeeeeeeeeeeeee ebeeeeeeeeeeeeeeeeeeeee ecbeeeeeeeeeeeeeeeeeeee eebceeeeeeeeeeeeeeeeeee eeebeeeeeeeeeeeeeeeeeee eeecbeeeeeeffaeeeeeeeee eeeebbeeeefeeafffffadee eeeeebeeefeeeeeeeeeafffffad eeeeeebefeeeeeeeeeeeeee daffffad eeeeeecfaeeeeeeeeeeeeee daffffadd eeeeeefaceeeeeeeeeeeeee dafffffad eeeeefaebeeeeeeeeeeeeee dafffffad eeeeffeeebeeeeeeeeeeeee daffff eeeafeeeecbeeeeeeeeeeee eeafeeeeeebceeeeeeeeeee eafeeeeeeeebbeeeeeeeeee efeeeeeeeeeeebbceeeeeee dfeeeeeeeeeeeeeebbceeeee feeeeeeeeeeeeeeeeecbbeee fdeeeeeeeeeeeeeeeeeeecbbe fd eeeeeeeeeeeeeeeeeeeeecbbg fd eeeeeeeeeeeeeeeeeeeeeeegbbg fa eeeeeeeeeeeeeeeeeeeeeee bbc fa cbc ff cbb af gbbg af gbbg df bbc df cbc f cbb f gbbg fd gbbg fd bbc fd bbc fa cbb fa g af af af df df f f fd fd ```  I'm going to scrutinize area A for any signs of an intersection.  ```palette Key,Color ,#fefefeff a,#4d45f6ff b,#fe0707ff c,#fea4a4ff d,#9f9efeff e,#fb5256ff f,#0606ffff g,#e8daf1ff ``` ```image c bg bb bbe cbbc ebbg ebe gbbc cbbc ebb bbe gbbc cbbg ebb gbbe gg cbbc gffffaaddg ebbg gfffffffffffaaddg ebe gffa gddafffffffffaaddg gbbc affg gddaaffffffff cbbc affg gddaaff ebb affg g bbe affd cbbaffd ceffd dffa dffabe gffacbbc gffa ebbg gffa bbe gffag gbbc affg cbbg affg ebb affg bbe affd cbbc dffd cbbeg dffd ebbbec dffd cebbbec dffa gebbbbc gffa gcbbbbcg gffa cbbbbeg ffa cebbbec ffg cebbbec fg gebbbbc g gebbbb cbb c ```  Aha! I've found an intersection inside area A! The final count is: one intersection.

1

```palette Key,Color ,#fefefeff a,#5d59fbff b,#ff0404ff c,#ff7e7eff d,#b5b5ffff e,#ff3a3aff f,#0808ffff g,#ffc3c3ff ``` ```image g ee bg b cb bc b gb ee bg b gb ee bg b cb bc b gb ee bg b cb ee bg b cb bc b gb ee bg b cb bc bg gb cb bc b gb dffad ee f dafffffad bg f daaffffad b fd daffffad cfd dafffffad fac dafffffad fa b dafffffad ff gb daffff af ee af bg df bbg df gbbc df ebc f ebe fd cbb fd gbbg fd gbbc fa bbc fa ebe ff cbb af cbbg af gbbg df bbc df ebe f cbe f cbbg fd gbbg fd bbc fd ebe fa cbe fa c ff af af df df f f fd fd ```

I'm on the case! Let's uncover any intersections hidden in this image. After a thorough analysis, I conclude that there are no intersections in this image.

0

```palette Key,Color ,#fefefeff a,#5555ffff b,#ff3e3eff c,#0505ffff d,#ff7d7dff e,#ff0303ff f,#aeaeffff g,#ffc0c0ff ``` ```image ff faaccccccccccccccaff faacccccccaaf ffaccccccaaf ffacccccccaaff faaccccccaff cccccccaff ffaccccccaaf faaccccccaff ffac gdd gddbeeeeeeeebbd gddbeeeeeeeebbdgg gddbeeeeeeeebbdgg geeeeebbdgg e eg eg ed eb bb be de ge e e eg ed eb bb be de ge ge e eg ed ed eb be de ge ge e eg eg ed eb be de ge ge e eg eg ```

I have an image in front of me. I need to determine if there are any intersection segments. Let's take a closer look at what's happening inside these zones.  ```palette Key,Color ,#fefefeff a,#fb0909ff b,#0c0cf9ff c,#f1eeecff d,#b1d7b1ff e,#e85a50ff f,#6875e4ff g,#9dc196ff ``` ```image e ca ac ee ca ac ee ca ac ee ca ac ee ca ac ee ca ac aeggggggggggggggggggggggggggggggggggggggggggggggggggd ea caddddddddddddddddddddddddddddddddddddddddddddddddddg ca cgadddddddddddddddddddddddddddddddddddddddddddddddddg ac cdaaddddddddddddddddddddddddddddddddddddddddddddddddg ea cddagdddddddddddddddddddddddddddddddddddddddddddddddg ca cdddadddddddddddddddddddddddddddddddddddddddddddddddg ac cdddeaddddddddddddddddddddddddddddddddddddddddddddddg ea bbdddaedddddddddddddddddddddddddddddddddddddddddddddg ca cfbfddagddddddddddddddddddddddddddddddddddddddddddddg ac cddbbddaddddddddddddddddddddddddddddddddddddddddddddg ea cdddfbfeadddddddddddddddddddddddddddddddddddddddddddg ca cdddddbbaeddddddddddddddddddddddddddddddddddddddddddg ac cddddddgbbgdddddddddddddddddddddddddddddddddddddddddg ea cddddddddbbgddddddddddddddddddddddddddddddddddddddddg ca cdddddddddebbdddddddddddddddddddddddddddddddddddddddg ac cddddddddddabbgdddddddddddddddddddddddddddddddddddddg ea cdddddddddddagbbddddddddddddddddddddddddddddddddddddg ca cddddddddddddadfbfddddddddddddddddddddddddddddddddddg ac cddddddddddddeaddbbdddddddddddddddddddddddddddddddddg ea cdddddddddddddaeddfbfdddddddddddddddddddddddddddddddg ca cddddddddddddddagdddbbddddddddddddddddddddddddddddddg ac cddddddddddddddgaddddfbfddddddddddddddddddddddddddddgea cdddddddddddddddeadddddbbdddddddddddddddddddddddddddga cddddddddddddddddaedddddgbfdddddddddddddddddddddddddac cdddddddddddddddddagddddddbbdddddddddddddddddddddddea cdddddddddddddddddgadddddddgbbdddddddddddddddddddddag cddddddddddddddddddeaddddddddbbgddddddddddddddddddagg cdddddddddddddddddddaedddddddddbbddddddddddddddddeadg cddddddddddddddddddddaddddddddddfbfddddddddddddddaddg cddddddddddddddddddddgadddddddddddbbddddddddddddagddg cdddddddddddddddddddddeadddddddddddfbfdddddddddeadddg cddddddddddddddddddddddaeddddddddddddbbddddddddaddddg cdddddddddddddddddddddddadddddddddddddbbddddddagddddg cdddddddddddddddddddddddgadddddddddddddgbfdddeadddddg cddddddddddddddddddddddddeaddddddddddddddbbddaddddddg cdddddddddddddddddddddddddaeddddddddddddddfbagddddddg cddddddddddddddddddddddddddadddddddddddddddebbddddddg cddddddddddddddddddddddddddgaddddddddddddddadbbdddddg cdddddddddddddddddddddddddddeaddddddddddddagddgbfdddg cddddddddddddddddddddddddddddaeddddddddddeadddddbbddg cdddddddddddddddddddddddddddddaddddddddddadddddddfbgg cdddddddddddddddddddddddddddddgaddddddddagdddddddddbb cddddddddddddddddddddddddddddddaaddddddeadddddddddddbb cdddddddddddddddddddddddddddddddagdddddaddddddddddddgdbf cddddddddddddddddddddddddddddddddaddddagddddddddddddg bb cddddddddddddddddddddddddddddddddeaddeadddddddddddddg fbc cdddddddddddddddddddddddddddddddddaedaddddddddddddddg cbf cgdddddddddddddddddddddddddddddddddaagddddddddddddddg bb cccccccccccccccccccccccccccccccccccaccccccccccccccc fbf bb fbc cbf bb fbd bb fbc cbf bb fbc bb bbc cb ```  Could this be where the intersection is hiding, in area A?  ```palette Key,Color ,#fefefeff a,#fe0203ff b,#0b09fdff c,#febdbdff d,#babafeff e,#fe6f70ff f,#6561fbff g,#fa2a2fff ``` ```image aac eaac gag aae caac eaa gag caae caac eaa gag caae caac bf eaa bbbd gag dfbbfd caae dbbbf caac fbbbd eag dbbbf gag fbbbd caae dbbbf caac fbbbdeag dbbbfgag fbbbgae dbbbbac fbbbg dbbbbd fbbbf ebbbbd ggbbbf gabbbbd caafbbbf eaacfbbbd gag dbbbf gae fbbbd caac dbbbf eaac fbbbd gag dbbbf aae fbbbd caac dfbbfd eaac dbbbf gag fbbbd aae dbbbf caac fbbbd eaa dbbbf gag fbbbd aae dbbbf caac fbbbd eaa dbbbf e gag fbbbd ca caae dfbbfd ga caac dbbbf eag eaa fbbbd caac gag dbbbf gae caae fbbbd eag caac dbbbf caac eag fbbbd gae gag dbbbf eag caae fbbbd caac caac dbbbf gae eag fbbbd eag gag dbbbf caac caae fbbbd gae eaac dbbbd eag eag fbbf caac gae fbbbd gae caae dbbbf eag eaac fbbbd caac gag dbbbd gae gae fbbf eag caac fbbbgac eaac dbbbf gag ebbbf gae caafbbbd caac gae fbbf eaac eag fbbbd gag caac dbbbf aae gae fbbf caac eag dbbbd eaac caac dbbbf gag gae fbbbd aae eag dbbb caac caac fb eaac gae d gag eag aae caac caac gae eaa eag gag caac caae gae caac eaa eaa caac gag gae caaeeaa ```  Oh my, look at that! It's an intersection in area A! The image features two intersection points.

2

```palette Key,Color ,#fefefeff a,#ff0101ff b,#0606ffff c,#febfc0ff d,#ababffff e,#fd6667ff f,#4e4afaff g,#fc2b2dff ``` ```image e a ac gg a ac gg a ac eg a ac eg a ac eg a ac ac eg a a ca ac gg eg ac a a ac ca eg bb gg a dbd ac ac bb a eg dbfca a bbge ac dbfc eg fb a ebf ac gfbd eg acbb a a fbd ac ea bb eg ae dbd a ac bb ac a dbf eg ea bb a ae dbf ac a fb eg ca bf a ea fbd ac ae bb eg a fbd a ca bb ac eg dbd eg ae bf a a fb ac ca dbf eg eg bb a ac dbgc a ebf ca a fb gg ac dbd ac eg bb a a fbd ca ac bf gg eg fb ac a dbd a ac bb ca eg fb gg a bf aac bb g dbd bb fb bf bb dbd bf fb dbf bb dbd bf fb db ```

I'm on the case! Let's uncover any intersections hidden in this image. I have a hunch that these areas might contain the intersections we're looking for.  ```palette Key,Color ,#fefefeff a,#fe0505ff b,#0304feff c,#fa8381ff d,#6b75ebff e,#fec9c9ff f,#f8413eff g,#aed5aeff ``` ```image e ac a ae ea a ca a cf a fc a ac a ae ea ae gggcaggggggggggg ggggaggggggggggg ggggffgggggggggg gggggagggggggggg gggggffggggggggg gdbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb ggggggaggggggggg gdbbbbbd ggggggacgggggggddbbbbbd gggggggagddbbbbbd gggddbbbbbdggggg ddbbbbbdgggaggggggg bbd ggggggggaggggggg ggggggggcagggggg gggggggggagggggg gggggggggffggggg ggggggggggaggggg ggggggggggffgggg gggggggggggagggg ac a ae ea a ca a a cf ac a ae fc eae a ea ae ca a fa ae fa ea af a af ca ac a eae cf eae a ca fc ca a fa ae aa a af ae ac ea ac a eae cf ea a ca cf fa a fa fc af a af ae ac a ae ae eae ea ca a ca cf fa a aa ff af a ac fc ac a eae aca ea ```  This is a magnified view of the region A.  ```palette Key,Color ,#fefefeff a,#fd090bff b,#0302feff c,#ff9e9eff d,#9c9cffff e,#ecd8eaff f,#fc595bff g,#4d41f2ff ``` ```image aac caa aac caa aac faf eaae faf eaae faf caa aac caa aac e caa eddggbb aac eddggbbbbbbbb edggbbbbbbbbbggdde eddggbbbbbbbbggdde eddggbbbbbbbbgggaf bbbbbbbggdde eaae bggdde faf caa aac caa aac caa aac faf eaae faf eaae faf caa aac ```  Case closed! This is definitely an intersection point in area A. I've found a single intersection point in the image.

1

```palette Key,Color ,#fefefeff a,#ff0505ff b,#0000ffff c,#ff8686ff d,#9a9affff e,#ffc9c9ff f,#ff4141ff g,#4645ffff ``` ```image e ac a ae ea a ca a cf a fc a ac a ae ea a ca a cf a fc dgbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb a dgbbbbgd ac dgbbbbgd a dgbbbbgd dgbbbbgd dgbbbbgd ea bgd a ca a cf a fc a ac a ae ea a ca a a cf ac a ac fc eae a ea ae ca a fa ae fa ea af a af ca ac a eae cf eae a ca fc fa a fa ae aa a af ae ac ea ac a eae cf ea a ca ff fa a fa fc af a af ae ac a ae ae eae ea ca a ca cf fa a aa ff af a ac fc ac a eae aca ea ```

I'm ready to tackle this image and find those intersections! The image has some tight areas where segments are too close. I should investigate those closely.  ```palette Key,Color ,#fefefeff a,#4e50fbff b,#fa4745ff c,#0505feff d,#fe0606ff e,#fca3a2ff f,#aed5aeff g,#a9a9ffff ``` ```image e bde dd ede dd edb bde dd ede dd edb bde dd ede dd edb bde g dd aa ede c dd gc edb c bde gc dd cg ed c de aa de c db gc db cg dd c bd cg ed c ed aa de c de gc db cg db c dd aa bd c bd gc ed c ed gc de cg de c db aa dd c bd gc bd cg ed c ed cg de c de aa db fffffffffffff c db fffffffffffff gc bdfffffffffffff cg bdffffffffffff c bdfffffffffff aa fedffffffffff c fffdfffffffff gc ffffdefffffff c fffffdbffffff gc ffffffdbfffff cg fffffffddffff c ffffffffbffff aa fffffffffffff c fffffffffffff gc fffffffffffff cg fffffffffffff c fffffffffffff ca fffffffffffff c fffffffffffff aa ffffffffaffff c fffaccccaffff gc accccafffffffff cg gaccccag c gacccca aa gaccccg c gaccccg gc gacccag c gacccag gccag ```  Eureka! Let's inspect this close up of area A  ```palette Key,Color ,#fefefeff a,#4c4cffff b,#ff4141ff c,#0707ffff d,#ff0606ff e,#ffc5c5ff f,#ff8383ff g,#9d9dffff ``` ```image e de ddf fddf fddb fddb eddb eddde eddde bdde bddf bddf fddf fddb eddb eddbe eddde bdd be ggg ggacccca ggaccccccccag ```  Area A doesn't meet the criteria for an intersection. I can confidently say that there are no intersections in this image.

0

```palette Key,Color ,#fefefeff a,#6565ffff b,#ff4141ff c,#0a0affff d,#ff0606ff e,#ffc8c8ff f,#ff8686ff g,#b6b6ffff ``` ```image f bde dd fdf dd edb bde dd fdf dd edb bde dd fdf dd edb bde g dd ca fdf c dd ac edb c bde gc dd cg fde c ede aa df c db gc db cg bd c bd ca fd c ed ac ede c df gc df cg db c dd ca bd c fd ac fd c ede gc de cg df c db aa dd c bd gc bd cg fd c ede ca ede c df ac db c db gc bd cg bd c fd ca ed c ede ac df c df gc db cg dd c b aa c gc cg c ca c ac a c acccca gc gaccccag cg gaccccag c gaccccag ca gacccca c gacccca ac gaccccg c gccccag gccag ```

This image seems promising for intersection detection. These regions highlight areas that look suspicious. Lines seem to converge within them.  ```palette Key,Color ,#fefefeff a,#fd0b0aff b,#0101feff c,#f06962ff d,#8a93ecff e,#383afaff f,#aed5adff g,#ffbbbbff ``` ```image g aa gaca a a ag ga ac ag ca ga ga ag a a ac ac ca a ga cc a a ag ca aa a ga ga a ag ag a ac ac ca a a cc a a ac fcafffffffffffff ca ffafffffffffffff ga ffcaffffffffffff a fffaffffffffffff ag ffffafffffffffff d aa ffffacffffffffff debbbe ga fffffaffffffffff debbbed a fffffacfffffffff debbbed ag ffffffaffffffdebbbed ac ffffffcadebbbedf ca fffdebbbedffffff ffffffffffffffa debbbedffcafffffff fffffffffffffaf debbbedffffffffafffffff ffffffffffffacf dbbbed fffffffffaffffff fffffffffffcaff dbe fffffffffacfffff fffffffffffafff ebe ffffffffffafffff ffffffffffaffff ebe ffffffffffacffff fffffffffacffff bbd fffffffffffaffff ffffffffaafffff bbd fffffffffffcafff fffffffcaffffff bbd ffffffffffffafff fffffffafffffff dbb ffffffffffffcaff ffffffaffffffff dbb a fffffacffffffff dbe ga ffffcafffffffff ebe ag ffffaffffffffffebe a fffafffffffffebd ac fffffffffffbbdf a fffffffffbbdfff cc ffffffdbbdfffff a ffffdbbffffffff ca fffbbffffffffff a fffffffffffffff ga ag a ac a cc a ca a ga ag a ag a cc a ca a ga ag ga ag a ac a ca a ```  I'm eager to see what's happening in this magnified view of area A.  ```palette Key,Color ,#fefefeff a,#ff0505ff b,#0606ffff c,#ff8585ff d,#a0a0ffff e,#4a4affff f,#ff3f40ff g,#ffc2c2ff ``` ```image ga aa faf caag gaag gaac faf faa caag gaac aaf faa caag gaac aaf faf caag gaag gaac faf caa caag gaac faf faa caag gaac aaf faf de gaag dbbb cg dbbbbd dbbbbd ebbbbd ebbbed debbbed debbbed debbbe debbbe dbbbbd dbbbd ```  Darn it! This close-up doesn't show any intersections in area A. I'm ready to analyze the next area. Time to investigate area B up close.  ```palette Key,Color ,#fefefeff a,#fe0404ff b,#0402fdff c,#ff7b7bff d,#b0b0feff e,#5655feff f,#fd393bff g,#ffc0c0ff ``` ```image aag caf aac caa fac gaag faf gaag caf aag caf aac caa fac gaa fac gaag faf ddeeb gaag ddeebbbbbb cafddeebbbbbbbeed ddebbbbbbbbeed ddeebbbbbbbeed ddeebbbbbbbeedfac bbbbbbbeed gaa bbeed fac gaag faf gaag caf aag caa aac gaa fac gaag faf gaag caf aag caf aac ```  The lines cross each other within area B, forming an intersection. One intersection, that's it, but I found it.

1

```palette Key,Color ,#fefefeff a,#ff0505ff b,#0202ffff c,#ff8f8fff d,#a1a1ffff e,#4141feff f,#fe4545ff g,#fdd1d2ff ``` ```image g fa caff a a ag ca af ag ca ga ga ac ag a ac fc fa a ga ff a a ac ca ff ag ca ga a ag ag a af ac ca a ga ff ag a ac ca fa a ga ga a ag ac ga d ff ac debbbe ca a debbbed a ff debbbed ag a debbbed af cfdebbbed ca debbbed ga debbbed ca ag debbbed ag ac dbbbed ga fa ebe ac ga ebe a a ebe fc ac bbd a ff bbd ff ca dbbd a a dbbg ca ag dbb ag af dbb ga ca ebe ac ga ebe a ag ebe fc bbd a bbd ff dbbd a dbb ca bb ag ga ag a ac a ff a ca a ga ag ga ac a ff a cf a ca ag ga ac a fc a ff a ```

This image might have some surprises. Let's look for intersections carefully. I wonder what's going on inside those areas? Perhaps intersections are hiding there.  ```palette Key,Color ,#fefefeff a,#f75d5aff b,#0707feff c,#fd090aff d,#a3a6f9ff e,#feb3b2ff f,#add4adff g,#555af5ff ``` ```image d b bd e b ca b c db ec b aa gb ce b c gg ac b ce bd c b ac bd ce db c b ec db ca b c gg ec b ca bd c b ec bd aa db ce b c db ac b ce gg c b ac bg ce b c bd ec db ce b c db ec b ca gg c b ec gg ca b c bd c b ac b ce db c b ac gb ce b c gg ac ffffffffffffffbff ce fffffffffffffbgff c fffffffffffffbfff ec ffffffffffffbffff ca fffffffffffdbffff c fffffffffffbfffff ec ffffffffffgbfffff ca ffffffffffbffffff accfffffffffggffffff eccaffffffbfffffff ffaccfffbgfffffff fffffccabffffffff fffffffbccaffffff ffffffdbffcccffff ffffffbfffffaccaf fffffgbffffffffccc fffffbfffffffffffecca ffffggfffffffffff acce ffffbffffffffffff ecca fffbgffffffffffff acce fffbfffffffffffff ecca ffbdfffffffffffff acce ffbffffffffffffff ccc fbfffffffffffffff ecca bg gbfffffffffffffff acc dgbbbbgd b e dbbbbgd gg dgbbbbg b dgbbbbgd gg dbbbbbd b dgbbbbgd bd gbbb ```  This close-up of area A is like examining a piece of evidence.  ```palette Key,Color ,#fefefeff a,#fd4a4bff b,#0404feff c,#fd0406ff d,#8282ffff e,#fe9e9eff f,#c6c5fdff g,#3e3afaff ``` ```image fbbf gbd dbb bbd dbg bbf dbg fbbf gbg fbbf gbd dbb bbd dbg bbf dbg fbbf e gbg ccae fbbf acccca gbd eccccae dbb eaccccae bbd eacccce dbb eaccccabbd eacgbbe fbbcccae gbgeacccca fbbf eccccae gbd eaccccae fbb eccccae gbd eaccc dbb ea bbd dbg fbbf gbg fbbf gbg fbbf gbd dbb bbd dbg bbf dbg fbbf gbg fbbf ```  Incredible, there's actually an intersection in area A! There's one and only one intersection present in the image.

1

```palette Key,Color ,#fefefeff a,#fe5758ff b,#0505feff c,#fe0809ff d,#8282ffff e,#ffb1b1ff f,#c4c4ffff g,#4141ffff ``` ```image d b bd e fb ca bf c fb ec b aa dg ce b c gg ac b ce bd c b ac bf ce fb c b ec db ca b c gg ec b ca bd c b ec bf aa fb ce b c db ac b ce gg c b ac gd ce b c bf ec fb ce bf c db ec b ca dg c b ec gd ca b c bd c fb aa bf ce fb c b ac dg ce b c gg ac b ce bd c b ec bf ca fb c b ec db ca b acc gg ecca b acce bd eccab bcce fb cca b ecce db acc b ecca gg acce b ecca gd acce b ecca bf acce fb ccc bf ecca bdf db acc fdbbbbgf b e dgbbbgd dg fgbbbbdf b fdbbbbgf gd dgbbbgd b fgbbbbdf bd fdbbb ```

Let's examine this image for potential line intersections. There are 1 areas where the lines seem to converge. We should take a closer look at area A.  ```palette Key,Color ,#fefefeff a,#0a0bfeff b,#fe0a09ff c,#8f8ffdff d,#f86a66ff e,#ffbfbfff f,#b1d7b1ff g,#98c697ff ``` ```image e edbbbbbb edbbbbbbde db eddbbbbbde b edbbbbbde eb edbbbbbdde bd bbbde b db b eb be b dd b eb be b bd b db be ac eb a bd ca b ac db a b ca eb ac be a b ca dd ac b a eb ca be ac b a bd ca b ac db a be ca eb ac bd a b ca db ac b a eb ca be ac b a dd ca b ac eb a be ca b ac bd a b ca db ac be a eb ca bd ac b a db ca b ac eb a fbdggggggggggg ca gfbfffffffffff ac gfbdffffffffff a gffbffffffffff ca gffdbfffffffff ac gfffbgffffffff a gffffbffffffff ca gffffbdfffffff ac gfffffbfffffff a gfffffdbffffff ca gffffffbgfffff ac gffffffgbfffff a gfffffffbdffff caacc gffffffffbffff ccaaaaaaaacc gffffffffgffff ccaaaaaaaacc gfffffffffffff ccaaaaaaaacc gfffffffffffff cccaaaaaaaacgfffffff gffgcaaaaaffff gfffffffffffff gfffffffffffff fggggggggggggg ```  This close-up of area A is like examining a piece of evidence.  ```palette Key,Color ,#fefefeff a,#0404ffff b,#ff0505ff c,#a7a7ffff d,#ff8585ff e,#ffc6c6ff f,#5858ffff g,#ff4343ff ``` ```image gbg ebbe dbb bbd ebbe gbg ebbe dbg bbd dbb gbg ebbe gbg bbd dbb gbd ebbe gbg ebbe dbb bbd ebbe gbg ebbe dbg bbd dbb gbg ebg e ffccc aaaaaaaafffccc cfffaaaaaaaaaaaaafffc cccfffaaaaaaaf cccfc ```  This isn't an intersection in area A, but I'm not discouraged. My final answer is: no intersections found.

0

```palette Key,Color ,#fefefeff a,#0606ffff b,#ff0505ff c,#9797ffff d,#ff8484ff e,#ffc7c7ff f,#5050ffff g,#ff4343ff ``` ```image e egbbbbbb edgbbbbgde db edgbbbbbde be dgbbbbbgd eb edbbbbbgde bd bbgde b gg b eb be b gg b db be b gd b db be ac eb a bd ca b ac gg a b ca eb ac be a b ca gg ac b a db ca be ac b a gd ca b ac db a be ca eb ac bd a b ca gg ac b a eb ca be ac b a gg ca b ac db a be ca b ac gd a b ca db ac be a eb ca bd ac b a gg ca b ac eb a be ca b ac gg a b ca db ac be a b ca gd ac b a db ca be ac eb a bd caffc b ccfaaaaaaffc e ccfaaaaaaafc ccfaaaaaaafc ccfaaaaaaafcc ccfaaaa ```

I'm analyzing this image to identify any points where lines intersect. I can confidently say that there are no intersections in this image.

0

```palette Key,Color ,#fefefeff a,#ff0404ff b,#0606ffff c,#ff7e7eff d,#afafffff e,#5b5bffff f,#ffc3c3ff g,#ff3a3aff ``` ```image f gg af a ca gg af a ca ac af fa ca ac a fa ga ac a fa gg af a fa gg af a ca gg aa af faaf a faaf ca faaf ac faa af caa a caa ca cag ac cag a gag fa gag ca gac ac gac a aac fa aac gg aaf af faaf a faaf fa faaf gg faa acaa g e ebbd ebbe ebbe ebbe ebbe ebbe dbbe dbbe dbbe dbbbd dbbbd dbbbd dbbbd bbbd dbbbd dbbbd ebbed ebbe dbbbd dbbbd ebbe debbe dbbbd ebbbd ebbe bbe ```

This image looks interesting. I wonder if there are any intersections hidden in there? These spots mark what I'd call 'danger zones' - areas where intersections are more likely.  ```palette Key,Color ,#fefefeff a,#0607fdff b,#fe0707ff c,#f89a97ff d,#585df4ff e,#b9bafeff f,#ef514cff g,#aed5afff ``` ```image d a ae ea a dd a ae ea a dd a ae b ea b a bc da b a bc ad b a ff ae b ea ff a b ad cb a b ae cb ea b a b dd bc a b ae bc ea b a ff dd b a ff ae b ea cb a b da cb a b ad b ea bc ae b da bc a b ad ff a b ae ff ea b a cb dd b a cb ae b ea b a bc dd b a bfgggggggggggggggggggggad bgggggggggggggggggggggag c ffgggggggggggggggggggagg cbb d gbggggggggggggggggggdagg cbb daae gffgggggggggggggggggaggg cbb eaad ggbggggggggggggggggadggg cbb daae ggfbgggggggggggggggagggg cbb eaad gggbggggggggggggggaggggg cbb daae gggcbggggggggggggdaggggg cbb eaad ggggbggggggggggggagggggg cbb daae gggggbggggggggggadgggggg cbf eaad gggggbcgggggggggaggggggg fbf daaeggggggbggggggggagggggggg fbf eaadggggbfggggggdagggggggg fbf gdaagggbggggggaggggggggg fbf ggggaadffggggadggggggggg fbf ggggggdaaggggagggggggggg fbf ggggggggfaadaggggggggggfbf gggggggggbgdaggggggggfbf gggggggggfbggggggggfbfgg ggggggggggbggggggbbfgggg ggggggggggcbgggbbfgggggg gggggggggggbgbbfgggggggg ggggggggggggbfgggggggggg gggggggggggggggggggggggg gggggggggggggggggggggggg gggggggggggggggggggggggg ```  Could this be where the intersection is hiding, in area A?  ```palette Key,Color ,#fefefeff a,#0706feff b,#fe0404ff c,#fd7779ff d,#534ef9ff e,#ababfeff f,#fb3437ff g,#ffb8b8ff ``` ```image bb e fbc a gbb da fbc eaa gbb dad fbc eaa gbbg aae fbf dad gbbg eaae cbf dad bbg eaa cbf aae bbg daa cbb eaae fbc dad gbb eaa fbc aae gbb daa fbc aae gbbg dad fbf eaa gbbg aad cbf eaa bbg aae cbf dad e bbg eaae ade cbb aad aaaade fbc eaa eaaaade gbb aae edaaaade fbc dad eaaaade gbb eaae edaaaadefbc dad eaaaadfbg eaa edaaaade aae eaaaade daa cdaaaadeaae bbdaaaaad gf cbf edaa gfbb bbg gfbbbc cbb gfbbbc fbc gfbbbc gbb gfbbbc fbc gfbbbc gbb gfbbbc fbc gfbbbc gbbggfbbbc fbbbbbc gbbbc gc ```  I am surprised, so clear, an intersection has appeared in area A. There's one and only one intersection present in the image.

1

```palette Key,Color ,#fefefeff a,#0807feff b,#ff0202ff c,#fd7475ff d,#6464ffff e,#c0c0ffff f,#ff3030ff g,#ffc1c1ff ``` ```image d a ae ea a dd a ae ea a da a ad bg ea gb a bg da b a fc ad b ea fc ae b da cf a b ad cf a b ae gb ea bg a gb dd bg a b ae fc ea b a fc dd b a cf ae b ea cf a b da gb a bg ad gb ea bg ae b da fc a b ad fc a b ae cf ea b a cf dd b a gb ae bg ea gb a bg dd b a fc ae b ea g fc a gbb d b da gbb daae cf a gbb eaad b ad cbb daae cf ea cbf eaad b ae cbf daae gb da cbf eaad bg a cbf daae gb ad cbf eaad bg a cbf daae b ae cbf eaad fc da cbf daae b a cbf eaadfc ad cbf daae a fbc caadae fbc b da fbc cf fbc b fbc gb fbc bgfbc gbc ```

Hmm, I'm not sure what to expect from this image. Let's see if any lines cross. These zones are intriguing. I bet there's something interesting happening within them.  ```palette Key,Color ,#fefefeff a,#bf3957ff b,#0607fcff c,#fd0202ff d,#f0847dff e,#4847e8ff f,#8f98ecff g,#afd6afff ``` ```image d dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc gggggggggggggggggggggggggggggggggggggggggggdc ggggggggggggggggggggggggggggggggggggggggggdc gggggggggggggggggggggggggggggggggggggggggdcg ggggggggggggggggggggggggggggggggggggggggdcgg gggggggggggggggggggggggggggggggggggggggdcggg ggggggggggggggggggggggggggggggggggggggdcgggg gggggggggggggggggggggggggggggggggggggdcggggg ggggggggggggggggggggggggggggggggggggdcgggggg ggggggggggggggggggggggggggggggggebbbaggggggg ggggggggggggggggggggggggggggfbbbeaccbegggggg gggggggggggggggggggggggggebbbacccagggbbggggg gggggggggggggggggggggfbbbeacccdgggggggebgggg ggggggggggggggggggebbbacccdggggggggggggfbggg ggggggggggggggfbbbecccaggggggggggggggggggbfg gggggggggggebbbacccdggggggggggggggggggggggbe gggggggfbbbecccdgggggggggggggggggggggggggggbb ggggebbbaccaggggggggggggggggggggggggggggggggeb fbbbecccdggggggggggggggggggggggggggggggggggg fb bbaccdggggggggggggggggggggggggggggggggggggggg bf caggggggggggggggggggggggggggggggggggggggggggg be bb eb fb bf be bb eb fb bf bf be eb fb fb bf be bb eb fb bf be bb eb fb b ```  I'm going to scrutinize area A for any signs of an intersection.  ```palette Key,Color ,#fefefeff a,#96278fff b,#0606feff c,#fc0406ff d,#fd9ea0ff e,#544cf6ff f,#a097f5ff g,#fb5e61ff ``` ```image d dc dcc dccg dccg dccg dccg dccg dccg dccg dccg dccg dccg dccg febbfccg febbbbbbbag febbbbbefdabbe febbbbbbefgccccabbe febbbbbefdgcccccgd fbbb febbbbbbefgccccccgd bbbf febbbbbefgccccccgd ebbf febbbbbbeagcccccggd ebbe febbbbbefgccccccgd fbbe febbbbbbeaccccccgd fbbb febbbbbeagcccccggd bbbf febbbbbbeaccccccgd ebbf febbbbbeagcccccgd ebbe febbbbbbeaccccccgd fbb febbbbbeaccccccgd fb febbbbbbeacccccgd f febbbbbeaccccccgd febbbbbbaacccccgd febbbbbeacccccgd febbbbbbaacccccgd ebbbbbeacccccgd bbbaaccccgdd acccccgd ```  My investigation has led me to an intersection in area A! One intersection, that's it, but I found it.

1

```palette Key,Color ,#fefefeff a,#b9246aff b,#0101feff c,#fe0303ff d,#fd8687ff e,#645bf5ff f,#afafffff g,#2423fdff ``` ```image d dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc ebbba fgbbedccbg ebbgdcccd gb fgbbeaccc eb ebbgacccd fb fgbbecccd bf ebbgacccd be fgbbecccd gg ebbgaccd eb fgbbecccd fb bgaccd bf cd be bg gb fb fbf be bg gb eb fbf be bg gb eb fbf bf bg gb eb fb bf be gg eb fb b ```

I'm analyzing this image to identify any points where lines intersect. I wonder what's going on inside those areas? Perhaps intersections are hiding there.  ```palette Key,Color ,#fefefeff a,#e48073ff b,#0607fcff c,#fd0504ff d,#b1d7b1ff e,#ef3a34ff f,#4c56e8ff g,#97c599ff ``` ```image a c cd ac c ca a c ea c c ae ae c c ca ac gggggggggggggggggggggggggggggggggggggggggggggggggac c dddddddddddddddddddddddddddddddddddddddddddddddddcg c ddddddddddddddddddddddddddddddddddddddddddddddddeeg ca ddddddddddddddddddddddddddddddddddddddddddddddddcdg c dddddddddddddddddddddddddddddddddddddddddddddddcgdg ea ddddddddddddddddddddddddddddddddddddddddddddddacddg c ddddddddddddddddddddddddddddddddddddddddddddddcdddg ae dddddddddddddddddddddddddddddddddddddddddddddcadddg db c ddddddddddddddddddddddddddddddddddddddddddddgcddddg fb ac ddddddddddddddddddddddddddddddddddddddddddddcdddddg fb c dddddddddddddddddddddddddddddddddddddddddddeedddddg fb c dddddddddddddddddddddddddddddddddddddddddddcddddddgbb cd ddddddddddddddddddddddddddddddddddddddddddcaddddddbf c dddddddddddddddddddddddddddddddddddddddddacddddddbf ea dddddddddddddddddddddddddddddddddddddddddcddddddbfg c ddddddddddddddddddddddddddddddddddddddddeedddddbfdg ee ddddddddddddddddddddddddddddddddddddddddcdddddbgddg c dddddddddddddddddddddddddddddddddddddddcgdddgbgdddg ac ddddddddddddddddddddddddddddddddddddddacdddgbdddddg c ddddddddddddddddddddddddddddddddddddddcdddfbddddddg dc dddddddddddddddddddddddddddddddddddddcaddfbdddddddg cd ddddddddddddddddddddddddddddddddddddgcddfbddddddddg c ddddddddddddddddddddddddddddddddddddcddbbdddddddddg ca dddddddddddddddddddddddddddddddddddeedbbddddddddddg c dddddddddddddddddddddddddddddddddddcdbfdddddddddddg ee ddddddddddddddddddddddddddddddddddcabfddddddddddddg c dddddddddddddddddddddddddddddddddacbfdddddddddddddg ae dddddddddddddddddddddddddddddddddcbgddddddddddddddg c ddddddddddddddddddddddddddddddddebgdddddddddddddddg ac dddddddddddddddddddddddddddddddgbdddddddddddddddddg c ddddddddddddddddddddddddddddddfbgdddddddddddddddddg c dddddddddddddddddddddddddddddfbcddddddddddddddddddg ca ddddddddddddddddddddddddddddfbcdddddddddddddddddddg c dddddddddddddddddddddddddddbbcadddddddddddddddddddg eaddddddddddddddddddddddddddbbgcddddddddddddddddddddg cdddddddddddddddddddddddddbfdcdddddddddddddddddddddg aedddddddddddddddddddddddbfdeedddddddddddddddddddddg cddddddddddddddddddddddbfddcddddddddddddddddddddddg acddddddddddddddddddddbgddcaddddddddddddddddddddddg dcgdddddddddddddddddgbgddacdddddddddddddddddddddddg dgcddddddddddddddddgbddddcddddddddddddddddddddddddg ddcaddddddddddddddfbddddeeddddddddddddddddddddddddg dddcdddddddddddddfbdddddcdddddddddddddddddddddddddg dddeadddddddddddfbdddddcgdddddddddddddddddddddddddg ddddcddddddddddbbdddddacddddddddddddddddddddddddddg ddddeeddddddddbbddddddcdddddddddddddddddddddddddddg dddddcdddddddbfddddddcadddddddddddddddddddddddddddg dddddacddddfbfddddddgcddddddddddddddddddddddddddddg ddddddcddgbbddddddddcdddddddddddddddddddddddddddddg ddddddacbbgddddddddeedddddddddddddddddddddddddddddg ddddddfbfddddddddddcddddddddddddddddddddddddddddddg dddddbbdcdddddddddcaddddddddddddddddddddddddddddddg dddbbgddcadddddddacdddddddddddddddddddddddddddddddg dfbfdddddcdddddddcddddddddddddddddddddddddddddddddg bbdddddddeedddddeeddddddddddddddddddddddddddddddddg fbgdddddddddcdddddcdddddddddddddddddddddddddddddddddg dbf ddddddddddacdddcgdddddddddddddddddddddddddddddddddg bb dddddddddddcddacddddddddddddddddddddddddddddddddddg fbd dddddddddddacdcdddddddddddddddddddddddddddddddddddg dbf ddddddddddddccadddddddddddddddddddddddddddddddddddg bb dddddddddddddcddddddddddddddddddddddddddddddddddddg fbd ggggggggggggggggggggggggggggggggggggggggggggggggggd dbf bb fbd dbf bb fbd bf ```  I'm now examining the contents of area A in detail.  ```palette Key,Color ,#fefefeff a,#fe8081ff b,#0605feff c,#fe0506ff d,#a9a7fdff e,#f93f44ff f,#504af8ff g,#fec2c2ff ``` ```image e gc cc acc gccg ece cca ece ccg ca ac gcg ec gcc cca acc gccg acc cca ece gccg eca acc gccg d ece db gccg dbb cca dbbf cc fbbf ee bbd ac fbd cc fbd ece bbb gccg dbbb eca dbbf acc dbbf gccg dbbf ece dbbf gccg fbbf cca fbbd gccg fbd ece fbd acc bbb cca dbbb ece dbbf gccg dbbf eca dbbf cc dbbf gcgfbbf eefbbd gcfbbd acbbd gcbbd ebbb abbf dbbf dbbf dbbfg fbbfa fbbec fbbecg fbbece bbdccg dbb ace dbbfgccg g dbbf ece e dbbf cc cg dbbf ca ce fbbf ee ccg fbbd gcg acc fbbd cc cca fbbd acc acc bbd gccg eca bbd ece ece dbbf cca gcc dbbf ace ec dbbf gccg cg dbbf ece ae dbbf acc ca fbbd cca cc fbbd ece eca fbbd gccg gcc fbbd cca ece bbd acc gccg bb ccg gccg dbbf gcg ace dbbf ca cca fbbf ac acc dbbbd gcc cca dbbbf ece gcc fbbbd acc eca bbbf cca gccdbbf ece efbbd gccg dbbbf cca dbbbfce acc dbbbf ac ece fbbfd ca gccg fbbd gc cca dbbf ca ace dfbbf ccg gccg fbbbd ece ece bbf gccg acc fd ace cca ccg ce acc gcg cca ca eca gcc gccg ece eceaccg gcccca ecce ccg ```  Yes! I knew it! There's an intersection right here in area A! Two intersections have been found!

2

```palette Key,Color ,#fefefeff a,#fe9292ff b,#0606feff c,#fe0506ff d,#a4a3feff e,#fd4647ff f,#4c4bfeff g,#f6d8e0ff ``` ```image a gc cg ac c ca a gc ee cg c ee ae c c ca ac ac cg c gc ee ca gc c cg ea ac c c g ee ca db c gc db ac cg fb cg ee fb gc c bb ca ca bf c ac bf ca c bf c ee bd ee gc bd c cg gbg ac ac db cg c db gc ca fb cg gc fb gc cg bb ca ee bf c c bf ee cabf c acbd ae cbd c ebg ac db cg dbg gc fbc ca fbc c bbca ee bfgc c bf cg ee bf ee c bd c ac bd ca cg gbg ac gc db c ca db ee c fb gc ea fb cg c bb ac ee bf c c bf ca ac dbd gc cg gbb cg gcbbg ee dbf c gbbgc ca fbg ca ac dbf c c bb ee ee fbd c gc dbf ac cg bb c ac fbd ac c dbf cca bb gc fbd dbf bb fbd dbf bb fbd bf ```

I'm ready to tackle this image and find those intersections! I'd describe these as 'hotspots' for potential intersections.  ```palette Key,Color ,#fefefeff a,#fe0808ff b,#0405feff c,#f6605bff d,#a8a9fcff e,#ffb5b5ff f,#aed5adff g,#4f53f7ff ``` ```image dd ffffffffffffffff gbbbbbbbbbbggdd ffffffffffffffff ddgggbbbbbbbbbggddd ffffffffffffffff ddggbbbbbbbbbfffffffff ffffffdbbgffffff fffffffffgbbgfff ffffffffffffgbbg fffffffffffffffbbb ffffffffffffffff dbbg ffffffffffffffff gbbd ffffffffffffffff gbbd ffffffafffffffff dbbb fffffaacffffffff dbbg fffffafaffffffff gbbd ffffaffcafffffff gbbd fffcafffafffffff dbbg fffafffffaffffff dbbg ffacfffffccfffff gbbd ffafffffffafffff gbbd fafffffffffaffff dbb cafffffffffacfff afffffffffffafff cafffffffffffcaff afffffffffffffacf acffffffffffffffaf a ffffffffffffffca ae fffffffffffffffae ea ffffffffffffffffa a ffffffffffffffffcc cc ffffffffffffffff a a ffffffffffffffff ea ae ffffffffffffffff ac ea ffffffffffffffff a a ffffffffffffffff ea ca ffffffffffffffff ae a ffffffffffffffff a cc ca a ae ae a ea ca a ae ca a a cc ac a a ea ae ac ea a a ea cc ae a a ac ca a ae ae a ea cc a a cc ea a ac ae a ea ea a ae ca a a ca cc ae a a ae cc ea a a ea ca ac a a ac ea a ae ae a ea ca a ae a ca a a ac a ```  Here's a close-up of the area A.  ```palette Key,Color ,#fefefeff a,#ff0505ff b,#0606ffff c,#ff8686ff d,#a6a6ffff e,#ffcacaff f,#ff4141ff g,#5555ffff ``` ```image bbbggggdddd bbbbbbbbbbbbbbgd dddddggggbbbbbbbd dgbbbbgd dgbbbbgd dbbbbbgd dgbbbbbd dgbbbbg dgbb d aae caaf eaaaac fafcaa eaae faf fac eaae caa caa aac aac caf eaae eaae faf faf aac eaae caae fac faf caa eaac aac caa caf faf eaae eaae faf caa eaae aac aac eaae caa faf aac aac af caae ae faf f eaac caa faf eaa ca f e ```  This isn't an intersection in area A, but I'm not discouraged. There's definitely not a single intersection on the image.

0

```palette Key,Color ,#fefefeff a,#ff0404ff b,#0606ffff c,#ff7e7eff d,#afafffff e,#ffc3c3ff f,#ff3b3bff g,#5959ffff ``` ```image dd gbbbbbbbbbbggdd ddggbbbbbbbbbbgggdd ddggbbbbbbbbbd dbbg dbbg gbbd bbbd dbbg gbbg gbbd a dbbb aae dbbg ea a gbbd a cf gbbd cf ae dbbg a a dbbg fc ff gbbd a a bbbd ae ea dbb ea ac a a cf ea a ac ac a ea ca ae ae ca a a ff ff a a ea ac fc ea a ae ea ca ac a a fc ca a ae ae a ea ff a ae cf ea a ff fc a a ea ae ac ea a a ca ff ae a a ac cf ea ae ae a ca ff a a ff ea a ac ac a ea ca a ac ca a a ca fc ae a a ae ff ea a a ea cf fc a a fc ea a ac ae a ea ca a ae a ff ae ea ff a ```

Alright, let's get to work and investigate this image for intersections. There are 1 areas where the lines seem to converge. We should take a closer look at area A.  ```palette Key,Color ,#fefefeff a,#0506fcff b,#df685dff c,#7a8bdcff d,#b1d7b1ff e,#fb0a09ff f,#98c699ff g,#3c42eaff ``` ```image fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffd dddddddddddddddddddddddddddddddddddddddddddddddddddddddddddf dddddddddddddddddddddddddddddddddddfdddddddddddddddddddddddf ddddddddddddddddddddddddddddddddddaadddddddddddddddddddddddf dddddddddddddddddddddddddddddddddgaggddddddddddddddddddddddf ddddddddddddddddddddddddddddddddcaddaddddddddddddddddddddddf ddddddddddddddddddddddddddddddddadddcadddddddddddddddddddddf dddddddddddddddddddddddddddddddafddddafddddddddddddddddddddf ddddddddddddddddddddddddddddddacdddddfaddddddddddddddddddddf dddddddddddddddddddddddddddddagdddddddacdddddddddddddddddddf ddddddddddddddddddddddddddddgadddddddddadddddddddddddddddddf dddddddddddddddddddddddddddcaddddddddddagddddddddddddddddddf dddddddddddddddddddddddddddaddddddddddddaddddddddddddddddddf ddddddddddddddddddddddddddafddddddddddddggdddddddddddddddddf dddddddddddddddddddddddddacddddddddddddddadddddddddddddddddf ddddddddddddddddddddddddagdddddddddddddddcaddddddddddddddddf be dddddddddddddddddddddddgadddddddddddddddddaddddddddddddddddf beeeb ddddddddddddddddddddddcaddddddddddddddddddcadddddddddddddddf beeeb ddddddddddddddddddddddaddddddddddddddddddddacddddddddddddddf dbeeeb dddddddddddddddddddddafdddddddddddddddddddddaddddddddddddddfdeeeeb ddddddddddddddddddddacddddddddddddddddddddddacddddddddddbeeeed dddddddddddddddddddagddddddddddddddddddddddddaddddddbeeeefdf ddddddddddddddddddgadddddddddddddddddddddddddggdbeeebfdddddf dddddddddddddddddcaddddddddddddddddddddddddfbeaebddddddddddf dddddddddddddddddadddddddddddddddddddddfeeeebdcadddddddddddf ddddddddddddddddafdddddddddddddddddbeeeebddddddadddddddddddf dddddddddddddddacdddddddddddddddbeeebddddddddddcaddddddddddf ddddddddddddddagdddddddddddddbeeedddddddddddddddacdddddddddf dddddddddddddgadddddddddddbeebdddddddddddddddddddadddddddddf ddddddddddddcadddddddddbeebddddddddddddddddddddddacddddddddf ddddddddddddadddddddbeebddddddddddddddddddddddddddaddddddddf dddddddddddafddddeeebdddddddddddddddddddddddddddddggdddddddf ddddddddddacdfeeebdddddddddddddddddddddddddddddddddadddddddf dddddddddageeebddddddddddddddddddddddddddddddddddddgaddddddf dddddddfgaebddddddddddddddddddddddddddddddddddddddddaddddddf ddddbeebadddddddddddddddddddddddddddddddddddddddddddcadddddf dbeeefdadddddddddddddddddddddddddddddddddddddddddddddafddddf eeefdddafdddddddddddddddddddddddddddddddddddddddddddddfaddddf dddddacdddddddddddddddddddddddddddddddddddddddddddddddacdddf ddddagdddddddddddddddddddddddddddddddddddddddddddddddddadddf dddgaddddddddddddddddddddddddddddddddddddddddddddddddddggddf ddcaddddddddddddddddddddddddddddddddddddddddddddddddddddaddf ddadddddddddddddddddddddddddddddddddddddddddddddddddddddggdf dafddddddddddddddddddddddddddddddddddddddddddddddddddddddadf acdddddddddddddddddddddddddddddddddddddddddddddddddddddddcaf agdddddddddddddddddddddddddddddddddddddddddddddddddddddddddaf ddddddddddddddddddddddddddddddddddddddddddddddddddddddddddfa dddddddddddddddddddddddddddddddddddddddddddddddddddddddddddac dddddddddddddddddddddddddddddddddddddddddddddddddddddddddddfa dddddddddddddddddddddddddddddddddddddddddddddddddddddddddddfgc dddddddddddddddddddddddddddddddddddddddddddddddddddddddddddf a dddddddddddddddddddddddddddddddddddddddddddddddddddddddddddf gg dddddddddddddddddddddddddddddddddddddddddddddddddddddddddddf a dddddddddddddddddddddddddddddddddddddddddddddddddddddddddddf ca dddddddddddddddddddddddddddddddddddddddddddddddddddddddddddf a dddddddddddddddddddddddddddddddddddddddddddddddddddddddddddf da dddddddddddddddddddddddddddddddddddddddddddddddddddddddddddf ad fddddddddddddddddddddddddddddddddddddddddddddddddddddddddddf a ac a gg a ca a ca a a ac a gg a cg a ca a a ac a gc a cg a ```  Could this be where the intersection is hiding, in area A?  ```palette Key,Color ,#fefefeff a,#0605feff b,#fb5a5eff c,#8484feff d,#feadaeff e,#fe0607ff f,#c9c9feff g,#403cfbff ``` ```image ff faaf aaag gaafcag aaf aac fac caa fac aac aa caa gag gac gaaf faaf caaf gag faac faaf faac gag aag faaf gag cag gaaf aac faac ga faac faf aag gg gag faf gaaf ag aaf aaf fac cag fac aac aa caa gag gac gaaf faa caaf gac faac faaf aag faaf gag cag gaaf aac caaf caa db faac aac ddbeeee faac caa ddbeeeeebb aag gac dbbeeeeebbd gag faaf dbbeeeeeebd gaaf gag beeeeeeebdd aaf faabeeeeebd fac ddbeegaaebd fac ddbeeeeeebaac aa dbeeeeeebbd caa gag dbbeeeeebdd aa caaf dbeeeeeebd gc faac deeeeebd faf faac dbeeeebd ag aag dbeeeeeb aaf gag dbeeeeebd gag gaaf dbeeeeebd faaf caaf dbeeeebd cag faac dbeeeebd aac faac dbeeeeeb caa aag dbeeeeebd gac gag dbeeeeebd faaf gaaf dbeeeebd gag aaf dbeeeeb faaf fac dbeeeeebd faaf faabeeeeebd cag gaaeeebd aac dbgaaebd caa dbeegaabd aac dbeeeebaac faa beeeeebdaac gac dbeeeebd faag faaf dbeeeebd gag gag eeeeebd gaaf faaf ebd caaf cag caac aa faac ca faag ac gaaf ac aaf aaf cac gag fac faaf faa cag gag aaf gaaf caa caaf aac caac caa faac gac aag faa ag ga ff fa f ```  Case closed! This is definitely an intersection point in area A. Two intersections have been found!

2

```palette Key,Color ,#fefefeff a,#0606feff b,#fb4c4fff c,#9e9effff d,#ff9d9dff e,#fe0404ff f,#e2dbf8ff g,#4f4dfcff ``` ```image f aa gagg ca a fa ca af af ac fa ag ac ga a ca ac fa a af gg ac a ag ca de ga af beeebf ca fa fbeeebf fa ac dbeeed af fa dbeeed ac ac deeebd ag a deeebd ga gg beeebf ca fbeaeb fa dbeeed ca af dbeeed af ac deebd ca ag deeb af ga beeb fa ca beeb ac fa beeb a af beed gg ac fbeed a ageeed gg dgaed a deeba ca deeedfa af eebf af fa ac ac ag a ga gg ca a fa gg af a ac ca ag af f fa ac a ac a gg a ca af fa ac fa ac a gg a ca af ca af fa ac a gg a gg a ca af fa ac a gg a gg a ```

I have a feeling there might be some intersections in this image. I'm going to focus my attention on these specific areas.  ```palette Key,Color ,#fefefeff a,#0607feff b,#fe0707ff c,#abadfbff d,#ec5551ff e,#5155f7ff f,#aed5aeff g,#faa8a6ff ``` ```image aa acee ca a ea ca aa a ae ca ac ac ca a ea ae aa a ae ee ac a ca ca ea a aa ca ae ac cac a ca ac ea a aa ee ae a cac ca ea a ea ca ae ac ae a cac ac ea a aa ee ae a ea a ca ac a ac a ee a ee a ca a ca ac a ae a g ee bbdbbg a gbbg bbbg fffffeafffffffffffffff gbb gbbd ffffffafffffffffffffff gbb gbbd fffffffaffffffffffffff dbb dbbg fffffffacfffffffffffff dbd dbbg ffffffffafffffffffffff bbd gbbb ffffffffaeffffffffffff bbg gbbdffffffffaffffffffffff gbbg dbbdfffffeefffffffffff gbbg fffdbbdfffafffffffffff gbb ffffffbbbfeaffffffffff dbb ffffffffgbbaffffffffff dbd fffffffffffdabdfffffff bbd ffffffffffffafdbbdffff bbg fffffffffffffafffdbbgf bbg fffffffffffffaefffffbb bbg ffffffffffffffafffffff ffffffffffffffeeffffff fffffffffffffffaffffff fffffffffffffffeafffff ffffffffffffffffafffff ffffffffffffffffcaffff fffffffffffffffffaffff ca ac a ee a ee a ```  Let's zoom in on area A to get a clearer view.  ```palette Key,Color ,#fefefeff a,#0504feff b,#fc0709ff c,#7e7bfbff d,#fe6262ff e,#3d35f7ff f,#c1c1feff g,#ffb6b6ff ``` ```image caa eac faa eac faaf eae faaf cae aaf caa aac faa bdg eac bbbbdg faaf gdbbbbbdg eae gdbbbbbd faaf gdbbbbdg cae gdbbbbdg aaf dbbbbbdg cae gdbbbbbdaac gdbbbbaa gdbaaedg caabbbdg eaebbbbbdg faafgdbbbbbd cae gdbbbbdg aaf gdbbbbdg cae dbbbbb aac gdbb caa g eac faa eac faaf eae faaf cae aac caa eac faa eac faaf ```  Incredible, there's actually an intersection in area A! After careful examination, I conclude that there is one intersection.

1

```palette Key,Color ,#fefefeff a,#0504feff b,#ff0808ff c,#8383ffff d,#fc676aff e,#3e3effff f,#c9c9feff g,#ffbfbfff ``` ```image f aa facce caf a ea ca aa af ae fa faf af ca a ea ec aa a ae ee faf a ca ca ea a ae fa ac af faf a ca ac ea a ae ee ac a faf ca ca a ea fa ae af ac fa faf ac ca a ea ee ae a ce a fa af fa ac a ec a ce a ca af fa af a ec a d ee bbdbbg a gbbg gbbbg ca gbbg gbbd a dbb dbbd fa dbb dbbd af dbd bbbg a bbd gbbbg ac bbd gbbd a gbbg dbbd ee gbbg dbbg a dbb gbbbgca dbb gbba dbd dabd bbd afdbbd bbd fa dbbg gbbg ac gbb bbg a ee a ce a fa af fa ac a ec a ce a ```

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

0

```palette Key,Color ,#fefefeff a,#3b3bffff b,#ff0606ff c,#ffa9a9ff d,#c4c4ffff e,#0303ffff f,#ff5a5aff g,#8989ffff ``` ```image d ee gedde ae ge ea aa ged ed ae e ea de ded ge ae ea ea ed ded e ae de ea aa ded eg ae ed ea e deg ge ae aa ea eg deg e ae de ea ge deg aa ae ed ee e deg de ae ae g eg ed e de aa eg ed e ge aa eg e de ge ea ed e de ae eg ed e ge aa eg ed de ge a bbbf fbbbc fbbbc cfbbbc cbbbfc cff cbbbfc ccfbbbbbbbffc cbbbf ccfbbbbbbbffc fbbbf cffbbbbbbbfcc fbbbc ccfbbbbbbbffc fbbbbbfcc ```

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.  ```palette Key,Color ,#fefefeff a,#5e68eaff b,#fd0707ff c,#090afdff d,#ea4c46ff e,#e5978dff f,#b1d7b1ff g,#95c699ff ``` ```image e b b be eb b b bd eb b be dd b b be eb b b bd eb b be dd eb b c be ccc db ac ca b c ca b cf cf bd ac c eb fggggggggggggggggggcggggggggcgggggggggggggggbf d gfffffffffffffffffcaffffffffgcfffffffffffffbeg ebe gffffffffffffffffacffffffffffacfffffffffffddfg bd gffffffffffffffffcffffffffffffacfffffffffebffg bb gfffffffffffffffcafffffffffffffccffffffffbfffg eb gffffffffffffffacfffffffffffffffcaffffffbefffg be gffffffffffffffcfffffffffffffffffcaffffdbffffg bb gfffffffffffffcaffffffffffffffffffcgffgbfffffg db gffffffffffffacffffffffffffffffffffcffbffffffg ebe gffffffffffffcffffffffffffffffffffffcbdffffffg bdgfffffffffffcaffffffffffffffffffffffecfffffffg bbffffffffffacfffffffffffffffffffffffbacffffffg dbfffffffffcfffffffffffffffffffffffbefacfffffg gfbdffffffcaffffffffffffffffffffffbdfffccffffg gffbbffffacffffffffffffffffffffffebfffffcafffg gfffdbfffcfffffffffffffffffffffffbfffffffcaffg gffffebecaffffffffffffffffffffffbeffffffffcgfg gffffffdcffffffffffffffffffffffdbffffffffffcgg gffffffcbbffffffffffffffffffffgbffffffffffffcg gfffffcafdbfffffffffffffffffffbfffffffffffffgc gffffacffffbdffffffffffffffffbdffffffffffffffac gffffcffffffbbffffffffffffffdbfffffffffffffffgac gfffcafffffffdbfffffffffffffbffffffffffffffffg cc gffgcfffffffffebeffffffffffbeffffffffffffffffg ca gffcffffffffffffbdffffffffbdfffffffffffffffffg ca gfcafffffffffffffbbffffffebffffffffffffffffffg cf ggcfffffffffffffffdbfffffbfffffffffffffffffffg c gcgffffffffffffffffgbdffbefffffffffffffffffffg c ca bbdb c fc db ac c ac ca cc c ca c ca ca cf c c c c ca c c ac c ac aa cc c ca c ca aa c c c ac c c ```  Let's put area A under the microscope.  ```palette Key,Color ,#fefefeff a,#8a8afeff b,#fe0b0cff c,#0505feff d,#fd6566ff e,#ffb9b9ff f,#403bfaff g,#d0d0feff ``` ```image gccg fcf eb fcf gccf bb acc gccf dbb gcca gcca ebbe fcf acca bbd acc acca bbd gcca accg dbb fcf fccg ebbe accg fccg bbd gcca fcf dbb fcf gccf dbbe accg gccf ebbe gcca gcca bbd fcf acca dbb accg acca ebbe gcca accg ebbd fcf fccg bbd accg fccg dbb gcca fcf ebbe fcf gccfbbd accg gccfb gcca dccf e fcf ebbcca be accg bbdacca bbd gcca dbb accg dbbb fcf ebbe fccg ebbbe accg ebbd fccg bbbd gcca bbd fcf dbbd fcf dbb gccf ebbbe accg ebbe gccf ebbbe gcca bbd gcca dbbd fcf dbb acca dbbb accg dbbe acca ebbbegcca ebbe accg bbbfcf bbd fccg dbccg dbb fccg ccfbe ebbe fcf fcfbbbe ebbd gcc accg dbbd bbd gc cca dbbb dbb g fcf ebbbe ebbe gccg bbbd bbd cca dbbd dbb fcf ebbbe dbbe gccg ebbbe ebbe cca dbbd bbd fcf dbbb dbb gccg ebbbe ebbe cca bbbd ebbd acf dbbd bbd gccg ebbbe dbb cca ebbbe ebbe acc dbbd bbd gccg dbbb dbb cca ebbbe dbb acc bbbd ebbe ```  My analysis confirms the presence of an intersection in area A. My analysis indicates that there are two intersections in this image.

2

```palette Key,Color ,#fefefeff a,#8787feff b,#fd0a0bff c,#0505feff d,#fd6566ff e,#ffb9b9ff f,#4141ffff g,#ccccffff ``` ```image d eb b bd db b be bd eb b be db eb b bd db b be bd eb b be db eb b c bd ccf db ac cf b c ca b cg cg bd ac cg eb c gc b b cg gc be ebe ac ac bd bd c fc eb bb ca ff b db ac cf be bd c ca db bb ca cg eb db ac cg b ebe c gcbd bd ca dc bb ac bac db c be fc bd ca bd ff bb ac eb cf db c b ca ebeca be cg bc db cg cbb eb gc ca db b gc gc bd bd ac c bb db fc ca db b ff gc ebe be cf c bd bd ca ca bb eb cg gc db b cg c bd be c ff bbdb gc gc db ac c fc ff fc gc cf c ca ff cg gc cg c c ff gc gc ac cg ac ff fc gc cf cg ca ff c gc cg ff c cg ```

I'm examining this image closely. My goal: find any and all intersections. I have a hunch that these areas might contain the intersections we're looking for.  ```palette Key,Color ,#fefefeff a,#f44944ff b,#0405feff c,#f69b97ff d,#4737e0ff e,#fe0505ff f,#aed5aeff g,#828aefff ``` ```image c e ec ec e e e e ce ce e e ca ce e e aa ca e e ec aa e e ec ac ce e e ec ce e e ec aa e e e ec ce e e ec ce ce e e ca ce e e aa aa e e ac ac e e ec ec e e ec e e ce e e ce aa e e ce aa e e ca ec e e aa e e ce ac e e ca ec e e aa ec e e ec e e ce ec e ce ce e e ce ca e e aa bb aafffffffffffffffffffffef dbbg feffffffffffffffffffffeaf gbbg faafffffffffffffffffffeff gbbg ffeffffffffffffffffffecff gbbd ffecffffffffffffffffcefff bbb fffeffffffffffffffffeffff dbbg fffecffffffffffffffaeffff dbbg ffffeffffffffffffffefffff gbbg ffffefffffffffffffaafffff gbbd ffffceffffffffffffefffffgbbd fffffefffffffffffeafffbbb fffffceffffffffffefdbbgff ffffffefffffffffdbbgfffff ffffffaafffffdbbdffffffff ffffgggddddbbdfefffffffff ggggddbbbbbbbbbbbbbbbbddddggfffcefffffffff bbbbbbbbddgggg ffffffffefffffeffffffffff ffffffffaafffaaffffffffff fffffffffefffefffffffffff fffffffffecfaafffffffffff ffffffffffefeffffffffffff ffffffffffeecffffffffffff fffffffffffefffffffffffff fffffffffffffffffffffffff fffffffffffffffffffffffff fffffffffffffffffffffffff ```  Let's take a closer look at area A.  ```palette Key,Color ,#fefefeff a,#ff4c4cff b,#0404feff c,#fea0a0ff d,#4949feff e,#fe0606ff f,#7f1897ff g,#a9a7fcff ``` ```image aea ae eec cee aea aea ee cee aea eec cee cee aec eec cee aea eec eec cee aea eec cee cee aea eec cee cea eec eec cee aea eec eec aea aea eec ee aea aea ceec cee aea aec cee gdb cee eec gdbbbb aec cee gdbbbbdg cee eec gdbbbbdg eec cefdbbbbdg cee gfbbbbdg eec gdbbbbbg cea gbbbbbfg eec gdbbbbdfea ggggggfffdddddbbbbbdg cee dbbbbbbbbbbbbbbbbbbbbbbbdg aea bbbbbbbbbddddddfffggggg cee gg ee eec aea cee cee eec aec aea cee eec aec aea cee cee eec aea cee cee eec eec ceacee eeeec aeea eec cc ```  Area A contains an intersection. After a thorough search, I conclude that there are two intersections.

2

```palette Key,Color ,#fefefeff a,#ff4545ff b,#0505ffff c,#ff8b8bff d,#5442edff e,#ff0505ff f,#ffceceff g,#a1a1ffff ``` ```image c e ec ef fe fe ef ef ce fe e e ca ce e e aa ca e e ec aa fe e ef ac fe e e ec ce e e ef aa fe e ef ec fe e e ef ce fe e ef ca ce e e aa aa e e ac ac e e ec ef e fe ef ef fe ce ef e fe aa e e ce ac e e ca ec e fe aa ef e ce ac e e ca ec e e aa ef e fe ec ef fe fe ef e fe ce e e ce ca e e aa bb aa e dbbg e ec dbbg ac e gbbd e ef gbbd ec fe gbbb e ef dbbg ef ce dbbg fe e dbbg ef aa gbbd fe e gbbd e ac bbbg ce e dbbg e dbbg ca gbbd gggddddbbd ef ggggdddbbbbbbbbbbbbbbbbddddgg ce bbbbbbbbdddgggg e e ac aa e e ec ac e e eec fe ```

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.  ```palette Key,Color ,#fefefeff a,#0606feff b,#fe0706ff c,#5c5ef5ff d,#f95754ff e,#b9b9ffff f,#f8a5a2ff g,#acd4acff ``` ```image e eae a ae ea ae ae ae a a ae a a ea cc ea a ea cc ea a ea ea ea a ca ea ca ae ca a ca ae ca a ca cc aa a aa cc aa a ac ea ac a ac ea ac ae ac a ac ae ae a ae cc ae a ae cc ae a ae ea a a a ea ea ae ea a ea ae ea a ea cc ea a ca cc ca a ca ea ca a c ea ae a ae a cc a cc a gggggggggggcagggg gggggggggggaggggg gggggggggggaggggg ggggggggggagggggg ggggggggggagggggg gggggggggacgggggg gggggggggaggggggg gdggggggccggggggg gdbbdgggagggggggg ggggdbbcagggggggg gggggggabbbfggggg f ggggggcaggfbbbfgg fdbbbb ggggggagggggggbbbf fbbbbdf ggggggaggggggggggdbbd dbbbbdf gggggaggggggggggg dbbd fdbbbbdf gggggaggggggggggg dbbd fdbbbbf ggggacggggggggggg fbbd fbbbbdf ggggagggggggggggg fbbbf dbbbbdf gggccgggggggggggg fbbbf fdbbbbdf gggaggggggggggggg fbbbf ggcaggggggggggggg a ea a ```  I'm analyzing this close-up of area A with precision.  ```palette Key,Color ,#fefefeff a,#0504feff b,#fc0608ff c,#8a89feff d,#ff5a5aff e,#ceceffff f,#ffababff g,#4641faff ``` ```image cag aac caa gac eaa gac eaae gag eaae cag aae cag aac caa gac eaa df gac fbbbdf eaae dbbbbbdf gag fdbbbbbdf eaae fdbbbbgag fdbaabbdf caabbbbbdf aac fdbbbbbdf caa fdbbbbbdf gac fdbbbbbdf eaa fdbbbb gac fd eaae gag eaae cag aae cag aac caa gac eaa gac eaae gag eaae ```  Area A contains an intersection. I've found a single intersection point in the image.

1

```palette Key,Color ,#fefefeff a,#0404ffff b,#fe0808ff c,#7f7fffff d,#ff6565ff e,#c2c2ffff f,#ffb8b8ff g,#423efbff ``` ```image e cae a ae ea ae ae ae a a ae a a ea gc ea a ea cg ea a ea cg ca a ca ea ca ae ca a ga ae ga a ga gc ga a gg cg ag a ag ca ag a ag ea ac ae ac a ac ae ac a ae gc ae a ae cg ae a ae ca a a a ea ea ae ea a ea ae ea a ea gc ca a ca cg ca a ca ca ga a g ea ae a ac a gc a cg a ea a ea ae a ac a d gc dbbd a dbbgg abbbf f ea fbbbf fdbbbb a fbbbd dbbbbdf ea dbbd fdbbbbdf ae dbbd fdbbbbdf a dbbd fdbbbbd ac dbbbf dbbbbdf a fbbbf fdbbbbdf gc fbbbf fdbbbbdf a fbbbd cg a ea a ```