title: Race Around the Track

text:
# Question
Title: Race Around the Track
I'm looking to find the fastest racer around. Show me your fastest lap around this 18x14 track shown below.

```
      ______
     /      \
    /        \
   /   ____   \
  /   /    \   \
 /   /      \   \
|   |        |   |
|   |        |   |
|   |        |   |
|   |        |   |
 \   \      /   /
  \   \____/   /
   \          /
    \        /
     \______/

```

Your job is to move the car below around the track once in all possible positions.

```
 _
| |
|_|

 /\
/ /
\/

 __
|__|

/\
\ \
 \/

```

The car can drive in 3 spaces in a row before turning. Here's an example of what a lap should look like.

```
      ______
     /      \
    /        \
   /   ____   \
  /   /    \   \
 /_  /      \   \
|| ||        |   |
||_||        |   |
|   |        |   |
|   |        |   |
 \   \      /   /
  \   \____/   /
   \          /
    \        /
     \______/
      ______
     /      \
    /        \
   /   ____   \
  /   /    \   \
 /   /      \   \
| _ |        |   |
|| ||        |   |
||_||        |   |
|   |        |   |
 \   \      /   /
  \   \____/   /
   \          /
    \        /
     \______/
      ______
     /      \
    /        \
   /   ____   \
  /   /    \   \
 /   /      \   \
|   |        |   |
| _ |        |   |
|| ||        |   |
||_||        |   |
 \   \      /   /
  \   \____/   /
   \          /
    \        /
     \______/
      ______
     /      \
    /        \
   /   ____   \
  /   /    \   \
 /   /      \   \
|   |        |   |
|   |        |   |
|   |        |   |
| /\|        |   |
 \\ \\      /   /
  \\/ \____/   /
   \          /
    \        /
     \______/
      ______
     /      \
    /        \
   /   ____   \
  /   /    \   \
 /   /      \   \
|   |        |   |
|   |        |   |
|   |        |   |
|   |        |   |
 \ /\\      /   /
  \\ \\____/   /
   \\/        /
    \        /
     \______/
      ______
     /      \
    /        \
   /   ____   \
  /   /    \   \
 /   /      \   \
|   |        |   |
|   |        |   |
|   |        |   |
|   |        |   |
 \   \      /   /
  \ /\\____/   /
   \\ \       /
    \\/      /
     \______/
      ______
     /      \
    /        \
   /   ____   \
  /   /    \   \
 /   /      \   \
|   |        |   |
|   |        |   |
|   |        |   |
|   |        |   |
 \   \      /   /
  \   \____/   /
   \   __     /
    \ |__|   /
     \______/
      ______
     /      \
    /        \
   /   ____   \
  /   /    \   \
 /   /      \   \
|   |        |   |
|   |        |   |
|   |        |   |
|   |        |   |
 \   \      /   /
  \   \____/   /
   \    __    /
    \  |__|  /
     \______/
      ______
     /      \
    /        \
   /   ____   \
  /   /    \   \
 /   /      \   \
|   |        |   |
|   |        |   |
|   |        |   |
|   |        |   |
 \   \      /   /
  \   \____/   /
   \     __   /
    \   |__| /
     \______/
      ______
     /      \
    /        \
   /   ____   \
  /   /    \   \
 /   /      \   \
|   |        |   |
|   |        |   |
|   |        |   |
|   |        |   |
 \   \      /   /
  \   \____//\ /
   \       / //
    \      \//
     \______/
      ______
     /      \
    /        \
   /   ____   \
  /   /    \   \
 /   /      \   \
|   |        |   |
|   |        |   |
|   |        |   |
|   |        |   |
 \   \      //\ /
  \   \____// //
   \        \//
    \        /
     \______/
      ______
     /      \
    /        \
   /   ____   \
  /   /    \   \
 /   /      \   \
|   |        |   |
|   |        |   |
|   |        |   |
|   |        |/\ |
 \   \      // //
  \   \____/ \//
   \          /
    \        /
     \______/
      ______
     /      \
    /        \
   /   ____   \
  /   /    \   \
 /   /      \   \
|   |        |   |
|   |        | _ |
|   |        || ||
|   |        ||_||
 \   \      /   /
  \   \____/   /
   \          /
    \        /
     \______/
      ______
     /      \
    /        \
   /   ____   \
  /   /    \   \
 /   /      \   \
|   |        | _ |
|   |        || ||
|   |        ||_||
|   |        |   |
 \   \      /   /
  \   \____/   /
   \          /
    \        /
     \______/
      ______
     /      \
    /        \
   /   ____   \
  /   /    \   \
 /   /      \  _\
|   |        || ||
|   |        ||_||
|   |        |   |
|   |        |   |
 \   \      /   /
  \   \____/   /
   \          /
    \        /
     \______/
      ______
     /      \
    /        \
   /   ____   \
  /   /    \ /\\
 /   /      \\ \\
|   |        |\/ |
|   |        |   |
|   |        |   |
|   |        |   |
 \   \      /   /
  \   \____/   /
   \          /
    \        /
     \______/
      ______
     /      \
    /        \
   /   ____ /\\
  /   /    \\ \\
 /   /      \\/ \
|   |        |   |
|   |        |   |
|   |        |   |
|   |        |   |
 \   \      /   /
  \   \____/   /
   \          /
    \        /
     \______/
      ______
     /      \
    /      /\\
   /   ____\ \\
  /   /    \\/ \
 /   /      \   \
|   |        |   |
|   |        |   |
|   |        |   |
|   |        |   |
 \   \      /   /
  \   \____/   /
   \          /
    \        /
     \______/
      ______
     /   __ \
    /   |__| \
   /   ____   \
  /   /    \   \
 /   /      \   \
|   |        |   |
|   |        |   |
|   |        |   |
|   |        |   |
 \   \      /   /
  \   \____/   /
   \          /
    \        /
     \______/
      ______
     /  __  \
    /  |__|  \
   /   ____   \
  /   /    \   \
 /   /      \   \
|   |        |   |
|   |        |   |
|   |        |   |
|   |        |   |
 \   \      /   /
  \   \____/   /
   \          /
    \        /
     \______/
      ______
     / __   \
    / |__|   \
   /   ____   \
  /   /    \   \
 /   /      \   \
|   |        |   |
|   |        |   |
|   |        |   |
|   |        |   |
 \   \      /   /
  \   \____/   /
   \          /
    \        /
     \______/
      ______
     /      \
    //\      \
   // /____   \
  / \//    \   \
 /   /      \   \
|   |        |   |
|   |        |   |
|   |        |   |
|   |        |   |
 \   \      /   /
  \   \____/   /
   \          /
    \        /
     \______/
      ______
     /      \
    /        \
   //\ ____   \
  // //    \   \
 / \//      \   \
|   |        |   |
|   |        |   |
|   |        |   |
|   |        |   |
 \   \      /   /
  \   \____/   /
   \          /
    \        /
     \______/
      ______
     /      \
    /        \
   /   ____   \
  //\ /    \   \
 // //      \   \
| \/|        |   |
|   |        |   |
|   |        |   |
|   |        |   |
 \   \      /   /
  \   \____/   /
   \          /
    \        /
     \______/

```

---

## Rules

* The output should show the car in all possible positions. 3 positions in each of the 8 sections of the track mean there are 24 possible positions to show.
* The car positions must be shown in sequence. (You can't teleport to another part of the track!)
* The starting position and direction (clockwise/counter clockwise) are not important.
* Output can be in any reasonable format for text.
* No input.
* Standard code-golf rules. The fewer bytes your code has, the faster your car runs.

# Answer
# Canvas, 131 bytes

```
｛↔］
ø５／２２╋___７１╋__８４╋|¶|１７╋|¶|５７╋２／６５╋╬
３［⁵ __¶|__|²６＋２╋］
３［⁵ _¶| |¶|_|２５²＋╋］
３［⁵ /\¶/ /¶\/６²－２²＋╋］
⁷⁸⇵｛↕］∔⁶｛↕］∔⁸｛↕↔］∔⁷⇵⁴∔⁸⇵⁴∔⁶⁴∔⁸∔

```

Try it here!
> 4 votes

# Answer
# JavaScript (ES6), 371 bytes

Rotates clockwise. Probably still golfable.

```
f=(i=24,A=[])=>i--?A.map(r=>r.join``,g=(s,x,y)=>[...s].map(c=>(j=c.charCodeAt(),d='12221',m=k=>(x-=~-d[j&7],y-=~-d[j-2&7],k--)&&((A[y]=A[y]||Array(18).fill` `)[x]='|/_\\'[j&3],k&&m(k)))(j/8&7)),g('voF`ir@kBdm',5,1),g('fWF`Qb@SBdU',6,4),g(['NFPJAT','MDWFI@S','VFHRAL','UDOFQ@K'][i/3&3],'0x'+'111123678ABCEEECBA876321'[i],'0x'+'678BCDDDDEDC876654222567'[i])).join`
`+f(i):A

```

Try it online!

### Animated version

```
f=(i=24,A=[])=>i--?A.map(r=>r.join``,g=(s,x,y)=>[...s].map(c=>(j=c.charCodeAt(),d='12221',m=k=>(x-=~-d[j&7],y-=~-d[j-2&7],k--)&&((A[y]=A[y]||Array(18).fill` `)[x]='|/_\\'[j&3],k&&m(k)))(j/8&7)),g('voF`ir@kBdm',5,1),g('fWF`Qb@SBdU',6,4),g(['NFPJAT','MDWFI@S','VFHRAL','UDOFQ@K'][i/3&3],'0x'+'111123678ABCEEECBA876321'[i],'0x'+'678BCDDDDEDC876654222567'[i])).join`
`+f(i):A

F = 0;
setInterval(_ => O.textContent = f().substr((F++ % 24) * 285 + 1, 285), 200)
```

```
<pre id=O style="font-size:9px"></pre>
```

### Less golfed

```
// i = frame counter, A[] = drawing matrix
f = (i = 24, A = []) =>
  i-- ?
    A.map(r =>
      r.join``,
      // g() draws the shape described by s, starting at (x, y)
      g = (s, x, y) =>
        [...s].map(c => (
          // j holds the direction in bits 0-2 and the length in bits 3-5
          // a length of 0 means 'move without drawing'
          j = c.charCodeAt(),
          d = '12221',
          // m() either draws a line or just moves the pen by 1 step
          m = k => (
            x -= ~-d[j & 7],
            y -= ~-d[j - 2 & 7],
            k--
          ) && (
            (A[y] = A[y] || Array(18).fill` `)[x] = '|/_\\'[j & 3],
            k && m(k)
          )
        )(j / 8 & 7)),
      // draw the outer boundary of the track
      g('voF`ir@kBdm', 5, 1),
      // draw the inner boundary of the track
      g('fWF`Qb@SBdU', 6, 4),
      // draw the car, using the correct shape for this frame and hard-coded coordinates
      g(['NFPJAT', 'MDWFI@S', 'VFHRAL', 'UDOFQ@K'][i / 3 & 3],
        '0x'+'111123678ABCEEECBA876321'[i],
        '0x'+'678BCDDDDEDC876654222567'[i]
      )
    ).join`\n` + f(i)
  :
    A

```
> 6 votes

# Answer
# Python 2, ~~641~~ ~~639~~ ~~592~~ 576 bytes

```
for i in range(24):
 t='s  ______s  Xs / 642  \s Xs/875310  \sX   /:;8____   \   X  /<9:/s\   \  X />=</s  \   \ X|A@?|ss|   |X|BCB|ss|   |X|DED|ss|   |X|FHG|ss|   |X \ILK\s  /   / X  \KJM\____/   /  X   \MNPRTVs/   Xs\POQSUW  /sXs \______/s '.replace('s',4*' ')
 for c,C in[zip([chr(x)for x in range(48,88)],' '*ord(s)+r+' '*40)for s,r in zip("\0\n	!",'|____|?| ____|?\/\/?/\/\ ?\  / //\ ?_| ||_?_ | |_?_| ||_?\/\/\ ?\/\/?/  \ /\ ?| ____|?| ____|'.split('?'))][abs(12-i)]+zip('\/!','!\/')*(i>12):t=t.replace(c,C)
 print'\n'.join(l[::2*(i<13)-1]for l in t.split('X'))

```

Try it online!

* -2 bytes, thanks to Kevin Cruijssen
* -30 bytes, thanks to Mnemonic
* -16 bytes, thanks to Jonathan
> 3 votes

# Answer
# Deadfish~, 26942 bytes

```
{iii}iicccccc{iiiiii}iiicccccc{{d}ii}dddddc{ii}iiccccc{i}iiiiic{d}dddddcccccc{iiiiii}c{{d}ii}ddc{ii}iicccc{i}iiiiic{d}dddddcccccccc{iiiiii}c{{d}ii}ddc{ii}iiccc{i}iiiiic{d}dddddccc{iiiiii}iiicccc{dddddd}dddccc{iiiiii}c{{d}ii}ddc{ii}iicc{i}iiiiic{d}dddddccc{i}iiiiic{d}dddddcccc{iiiiii}c{dddddd}ccc{iiiiii}c{{d}ii}ddc{ii}iic{i}iiiiic{iiiii}ddc{dddddd}dddcc{i}iiiiic{d}dddddcccccc{iiiiii}c{dddddd}ccc{iiiiii}c{{d}ii}ddc{{i}}{i}iiiicc{{d}i}ddc{{i}d}iicc{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiicc{ddd}ic{iii}dcc{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{ii}iic{iiiiii}c{dddddd}ccc{iiiiii}c{dddddd}cccccc{i}iiiiic{d}dddddccc{i}iiiiic{dddd}iiic{ii}iicc{iiiiii}c{dddddd}ccc{iiiiii}ciiicccc{ddddd}iic{d}dddddccc{i}iiiiic{dddd}iiic{ii}iiccc{iiiiii}c{dddddd}{c}{i}iiiiic{dddd}iiic{ii}iicccc{iiiiii}c{dddddd}cccccccc{i}iiiiic{dddd}iiic{ii}iiccccc{iiiiii}ciiicccccc{ddddd}iic{dddd}iiic{ii}iicccccc{iiiiii}iiicccccc{{d}ii}dddddc{ii}iiccccc{i}iiiiic{d}dddddcccccc{iiiiii}c{{d}ii}ddc{ii}iicccc{i}iiiiic{d}dddddcccccccc{iiiiii}c{{d}ii}ddc{ii}iiccc{i}iiiiic{d}dddddccc{iiiiii}iiicccc{dddddd}dddccc{iiiiii}c{{d}ii}ddc{ii}iicc{i}iiiiic{d}dddddccc{i}iiiiic{d}dddddcccc{iiiiii}c{dddddd}ccc{iiiiii}c{{d}ii}ddc{ii}iic{i}iiiiic{d}dddddccc{i}iiiiic{d}dddddcccccc{iiiiii}c{dddddd}ccc{iiiiii}c{{d}ii}ddc{{i}}{i}iiiic{{d}i}ddc{iiiiii}iiic{dddddd}dddc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiicc{{d}i}ddc{{i}d}iicc{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiicc{ddd}ic{iii}dcc{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{ii}iic{iiiiii}c{dddddd}ccc{iiiiii}c{dddddd}cccccc{i}iiiiic{d}dddddccc{i}iiiiic{dddd}iiic{ii}iicc{iiiiii}c{dddddd}ccc{iiiiii}ciiicccc{ddddd}iic{d}dddddccc{i}iiiiic{dddd}iiic{ii}iiccc{iiiiii}c{dddddd}{c}{i}iiiiic{dddd}iiic{ii}iicccc{iiiiii}c{dddddd}cccccccc{i}iiiiic{dddd}iiic{ii}iiccccc{iiiiii}ciiicccccc{ddddd}iic{dddd}iiic{ii}iicccccc{iiiiii}iiicccccc{{d}ii}dddddc{ii}iiccccc{i}iiiiic{d}dddddcccccc{iiiiii}c{{d}ii}ddc{ii}iicccc{i}iiiiic{d}dddddcccccccc{iiiiii}c{{d}ii}ddc{ii}iiccc{i}iiiiic{d}dddddccc{iiiiii}iiicccc{dddddd}dddccc{iiiiii}c{{d}ii}ddc{ii}iicc{i}iiiiic{d}dddddccc{i}iiiiic{d}dddddcccc{iiiiii}c{dddddd}ccc{iiiiii}c{{d}ii}ddc{ii}iic{i}iiiiic{d}dddddccc{i}iiiiic{d}dddddcccccc{iiiiii}c{dddddd}ccc{iiiiii}c{{d}ii}ddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddc{iiiiii}iiic{dddddd}dddc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiicc{{d}i}ddc{{i}d}iicc{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiicc{ddd}ic{iii}dcc{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{ii}iic{iiiiii}c{dddddd}ccc{iiiiii}c{dddddd}cccccc{i}iiiiic{d}dddddccc{i}iiiiic{dddd}iiic{ii}iicc{iiiiii}c{dddddd}ccc{iiiiii}ciiicccc{ddddd}iic{d}dddddccc{i}iiiiic{dddd}iiic{ii}iiccc{iiiiii}c{dddddd}{c}{i}iiiiic{dddd}iiic{ii}iicccc{iiiiii}c{dddddd}cccccccc{i}iiiiic{dddd}iiic{ii}iiccccc{iiiiii}ciiicccccc{ddddd}iic{dddd}iiic{ii}iicccccc{iiiiii}iiicccccc{{d}ii}dddddc{ii}iiccccc{i}iiiiic{d}dddddcccccc{iiiiii}c{{d}ii}ddc{ii}iicccc{i}iiiiic{d}dddddcccccccc{iiiiii}c{{d}ii}ddc{ii}iiccc{i}iiiiic{d}dddddccc{iiiiii}iiicccc{dddddd}dddccc{iiiiii}c{{d}ii}ddc{ii}iicc{i}iiiiic{d}dddddccc{i}iiiiic{d}dddddcccc{iiiiii}c{dddddd}ccc{iiiiii}c{{d}ii}ddc{ii}iic{i}iiiiic{d}dddddccc{i}iiiiic{d}dddddcccccc{iiiiii}c{dddddd}ccc{iiiiii}c{{d}ii}ddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddc{i}iiiiic{iiii}iiiiic{iii}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{ii}iic{iiiiii}cc{dddddd}c{iiiiii}cc{dddddd}cccccc{i}iiiiic{d}dddddccc{i}iiiiic{dddd}iiic{ii}iicc{iiiiii}cc{dddd}dddddc{d}dddddc{iiiiii}ciiicccc{ddddd}iic{d}dddddccc{i}iiiiic{dddd}iiic{ii}iiccc{iiiiii}c{dddddd}{c}{i}iiiiic{dddd}iiic{ii}iicccc{iiiiii}c{dddddd}cccccccc{i}iiiiic{dddd}iiic{ii}iiccccc{iiiiii}ciiicccccc{ddddd}iic{dddd}iiic{ii}iicccccc{iiiiii}iiicccccc{{d}ii}dddddc{ii}iiccccc{i}iiiiic{d}dddddcccccc{iiiiii}c{{d}ii}ddc{ii}iicccc{i}iiiiic{d}dddddcccccccc{iiiiii}c{{d}ii}ddc{ii}iiccc{i}iiiiic{d}dddddccc{iiiiii}iiicccc{dddddd}dddccc{iiiiii}c{{d}ii}ddc{ii}iicc{i}iiiiic{d}dddddccc{i}iiiiic{d}dddddcccc{iiiiii}c{dddddd}ccc{iiiiii}c{{d}ii}ddc{ii}iic{i}iiiiic{d}dddddccc{i}iiiiic{d}dddddcccccc{iiiiii}c{dddddd}ccc{iiiiii}c{{d}ii}ddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{ii}iic{iiiiii}c{dddddd}c{i}iiiiic{iiii}iiiiicc{dddddd}cccccc{i}iiiiic{d}dddddccc{i}iiiiic{dddd}iiic{ii}iicc{iiiiii}cc{dddddd}c{iiiiii}cciiicccc{ddddd}iic{d}dddddccc{i}iiiiic{dddd}iiic{ii}iiccc{iiiiii}cc{dddd}dddddc{d}dddddcccccccc{i}iiiiic{dddd}iiic{ii}iicccc{iiiiii}c{dddddd}cccccccc{i}iiiiic{dddd}iiic{ii}iiccccc{iiiiii}ciiicccccc{ddddd}iic{dddd}iiic{ii}iicccccc{iiiiii}iiicccccc{{d}ii}dddddc{ii}iiccccc{i}iiiiic{d}dddddcccccc{iiiiii}c{{d}ii}ddc{ii}iicccc{i}iiiiic{d}dddddcccccccc{iiiiii}c{{d}ii}ddc{ii}iiccc{i}iiiiic{d}dddddccc{iiiiii}iiicccc{dddddd}dddccc{iiiiii}c{{d}ii}ddc{ii}iicc{i}iiiiic{d}dddddccc{i}iiiiic{d}dddddcccc{iiiiii}c{dddddd}ccc{iiiiii}c{{d}ii}ddc{ii}iic{i}iiiiic{d}dddddccc{i}iiiiic{d}dddddcccccc{iiiiii}c{dddddd}ccc{iiiiii}c{{d}ii}ddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{ii}iic{iiiiii}c{dddddd}ccc{iiiiii}c{dddddd}cccccc{i}iiiiic{d}dddddccc{i}iiiiic{dddd}iiic{ii}iicc{iiiiii}c{dddddd}c{i}iiiiic{iiii}iiiiicciiicccc{ddddd}iic{d}dddddccc{i}iiiiic{dddd}iiic{ii}iiccc{iiiiii}cc{dddddd}c{iiiiii}c{dddddd}ccccccc{i}iiiiic{dddd}iiic{ii}iicccc{iiiiii}cc{dddd}dddddc{d}dddddcccccc{i}iiiiic{dddd}iiic{ii}iiccccc{iiiiii}ciiicccccc{ddddd}iic{dddd}iiic{ii}iicccccc{iiiiii}iiicccccc{{d}ii}dddddc{ii}iiccccc{i}iiiiic{d}dddddcccccc{iiiiii}c{{d}ii}ddc{ii}iicccc{i}iiiiic{d}dddddcccccccc{iiiiii}c{{d}ii}ddc{ii}iiccc{i}iiiiic{d}dddddccc{iiiiii}iiicccc{dddddd}dddccc{iiiiii}c{{d}ii}ddc{ii}iicc{i}iiiiic{d}dddddccc{i}iiiiic{d}dddddcccc{iiiiii}c{dddddd}ccc{iiiiii}c{{d}ii}ddc{ii}iic{i}iiiiic{d}dddddccc{i}iiiiic{d}dddddcccccc{iiiiii}c{dddddd}ccc{iiiiii}c{{d}ii}ddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{ii}iic{iiiiii}c{dddddd}ccc{iiiiii}c{dddddd}cccccc{i}iiiiic{d}dddddccc{i}iiiiic{dddd}iiic{ii}iicc{iiiiii}c{dddddd}ccc{iiiiii}ciiicccc{ddddd}iic{d}dddddccc{i}iiiiic{dddd}iiic{ii}iiccc{iiiiii}c{dddddd}ccc{iiiiii}iiicc{dddddd}dddccccc{i}iiiiic{dddd}iiic{ii}iicccc{iiiiii}c{dddddd}c{{i}d}iic{ddd}icc{iii}dc{{d}i}ddccc{i}iiiiic{dddd}iiic{ii}iiccccc{iiiiii}ciiicccccc{ddddd}iic{dddd}iiic{ii}iicccccc{iiiiii}iiicccccc{{d}ii}dddddc{ii}iiccccc{i}iiiiic{d}dddddcccccc{iiiiii}c{{d}ii}ddc{ii}iicccc{i}iiiiic{d}dddddcccccccc{iiiiii}c{{d}ii}ddc{ii}iiccc{i}iiiiic{d}dddddccc{iiiiii}iiicccc{dddddd}dddccc{iiiiii}c{{d}ii}ddc{ii}iicc{i}iiiiic{d}dddddccc{i}iiiiic{d}dddddcccc{iiiiii}c{dddddd}ccc{iiiiii}c{{d}ii}ddc{ii}iic{i}iiiiic{d}dddddccc{i}iiiiic{d}dddddcccccc{iiiiii}c{dddddd}ccc{iiiiii}c{{d}ii}ddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{ii}iic{iiiiii}c{dddddd}ccc{iiiiii}c{dddddd}cccccc{i}iiiiic{d}dddddccc{i}iiiiic{dddd}iiic{ii}iicc{iiiiii}c{dddddd}ccc{iiiiii}ciiicccc{ddddd}iic{d}dddddccc{i}iiiiic{dddd}iiic{ii}iiccc{iiiiii}c{dddddd}cccc{iiiiii}iiicc{dddddd}dddcccc{i}iiiiic{dddd}iiic{ii}iicccc{iiiiii}c{dddddd}cc{{i}d}iic{ddd}icc{iii}dc{{d}i}ddcc{i}iiiiic{dddd}iiic{ii}iiccccc{iiiiii}ciiicccccc{ddddd}iic{dddd}iiic{ii}iicccccc{iiiiii}iiicccccc{{d}ii}dddddc{ii}iiccccc{i}iiiiic{d}dddddcccccc{iiiiii}c{{d}ii}ddc{ii}iicccc{i}iiiiic{d}dddddcccccccc{iiiiii}c{{d}ii}ddc{ii}iiccc{i}iiiiic{d}dddddccc{iiiiii}iiicccc{dddddd}dddccc{iiiiii}c{{d}ii}ddc{ii}iicc{i}iiiiic{d}dddddccc{i}iiiiic{d}dddddcccc{iiiiii}c{dddddd}ccc{iiiiii}c{{d}ii}ddc{ii}iic{i}iiiiic{d}dddddccc{i}iiiiic{d}dddddcccccc{iiiiii}c{dddddd}ccc{iiiiii}c{{d}ii}ddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{ii}iic{iiiiii}c{dddddd}ccc{iiiiii}c{dddddd}cccccc{i}iiiiic{d}dddddccc{i}iiiiic{dddd}iiic{ii}iicc{iiiiii}c{dddddd}ccc{iiiiii}ciiicccc{ddddd}iic{d}dddddccc{i}iiiiic{dddd}iiic{ii}iiccc{iiiiii}c{dddddd}ccccc{iiiiii}iiicc{dddddd}dddccc{i}iiiiic{dddd}iiic{ii}iicccc{iiiiii}c{dddddd}ccc{{i}d}iic{ddd}icc{iii}dc{{d}i}ddc{i}iiiiic{dddd}iiic{ii}iiccccc{iiiiii}ciiicccccc{ddddd}iic{dddd}iiic{ii}iicccccc{iiiiii}iiicccccc{{d}ii}dddddc{ii}iiccccc{i}iiiiic{d}dddddcccccc{iiiiii}c{{d}ii}ddc{ii}iicccc{i}iiiiic{d}dddddcccccccc{iiiiii}c{{d}ii}ddc{ii}iiccc{i}iiiiic{d}dddddccc{iiiiii}iiicccc{dddddd}dddccc{iiiiii}c{{d}ii}ddc{ii}iicc{i}iiiiic{d}dddddccc{i}iiiiic{d}dddddcccc{iiiiii}c{dddddd}ccc{iiiiii}c{{d}ii}ddc{ii}iic{i}iiiiic{d}dddddccc{i}iiiiic{d}dddddcccccc{iiiiii}c{dddddd}ccc{iiiiii}c{{d}ii}ddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{ii}iic{iiiiii}c{dddddd}ccc{iiiiii}c{dddddd}cccccc{i}iiiiic{d}dddddccc{i}iiiiic{dddd}iiic{ii}iicc{iiiiii}c{dddddd}ccc{iiiiii}ciiicccc{ddddd}iicc{iiii}iiiiic{dddddd}c{i}iiiiic{dddd}iiic{ii}iiccc{iiiiii}c{dddddd}ccccccc{i}iiiiic{d}dddddc{i}iiiiicc{dddd}iiic{ii}iicccc{iiiiii}c{dddddd}cccccc{iiiiii}c{dddd}dddddcc{dddd}iiic{ii}iiccccc{iiiiii}ciiicccccc{ddddd}iic{dddd}iiic{ii}iicccccc{iiiiii}iiicccccc{{d}ii}dddddc{ii}iiccccc{i}iiiiic{d}dddddcccccc{iiiiii}c{{d}ii}ddc{ii}iicccc{i}iiiiic{d}dddddcccccccc{iiiiii}c{{d}ii}ddc{ii}iiccc{i}iiiiic{d}dddddccc{iiiiii}iiicccc{dddddd}dddccc{iiiiii}c{{d}ii}ddc{ii}iicc{i}iiiiic{d}dddddccc{i}iiiiic{d}dddddcccc{iiiiii}c{dddddd}ccc{iiiiii}c{{d}ii}ddc{ii}iic{i}iiiiic{d}dddddccc{i}iiiiic{d}dddddcccccc{iiiiii}c{dddddd}ccc{iiiiii}c{{d}ii}ddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{ii}iic{iiiiii}c{dddddd}ccc{iiiiii}c{dddddd}cccccc{i}iiiiicc{iiii}iiiiic{dddddd}c{i}iiiiic{dddd}iiic{ii}iicc{iiiiii}c{dddddd}ccc{iiiiii}ciiicccc{ddddd}iicc{d}dddddc{i}iiiiicc{dddd}iiic{ii}iiccc{iiiiii}c{dddddd}cccccccc{iiiiii}c{dddd}dddddcc{dddd}iiic{ii}iicccc{iiiiii}c{dddddd}cccccccc{i}iiiiic{dddd}iiic{ii}iiccccc{iiiiii}ciiicccccc{ddddd}iic{dddd}iiic{ii}iicccccc{iiiiii}iiicccccc{{d}ii}dddddc{ii}iiccccc{i}iiiiic{d}dddddcccccc{iiiiii}c{{d}ii}ddc{ii}iicccc{i}iiiiic{d}dddddcccccccc{iiiiii}c{{d}ii}ddc{ii}iiccc{i}iiiiic{d}dddddccc{iiiiii}iiicccc{dddddd}dddccc{iiiiii}c{{d}ii}ddc{ii}iicc{i}iiiiic{d}dddddccc{i}iiiiic{d}dddddcccc{iiiiii}c{dddddd}ccc{iiiiii}c{{d}ii}ddc{ii}iic{i}iiiiic{d}dddddccc{i}iiiiic{d}dddddcccccc{iiiiii}c{dddddd}ccc{iiiiii}c{{d}ii}ddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}ii}iiic{iiii}iiiiic{dddddd}c{{i}d}iic{{d}}{d}ddddc{ii}iic{iiiiii}c{dddddd}ccc{iiiiii}c{dddddd}cccccc{i}iiiiicc{d}dddddc{i}iiiiicc{dddd}iiic{ii}iicc{iiiiii}c{dddddd}ccc{iiiiii}ciiicccc{ddddd}iic{d}dddddc{iiiiii}c{dddd}dddddcc{dddd}iiic{ii}iiccc{iiiiii}c{dddddd}{c}{i}iiiiic{dddd}iiic{ii}iicccc{iiiiii}c{dddddd}cccccccc{i}iiiiic{dddd}iiic{ii}iiccccc{iiiiii}ciiicccccc{ddddd}iic{dddd}iiic{ii}iicccccc{iiiiii}iiicccccc{{d}ii}dddddc{ii}iiccccc{i}iiiiic{d}dddddcccccc{iiiiii}c{{d}ii}ddc{ii}iicccc{i}iiiiic{d}dddddcccccccc{iiiiii}c{{d}ii}ddc{ii}iiccc{i}iiiiic{d}dddddccc{iiiiii}iiicccc{dddddd}dddccc{iiiiii}c{{d}ii}ddc{ii}iicc{i}iiiiic{d}dddddccc{i}iiiiic{d}dddddcccc{iiiiii}c{dddddd}ccc{iiiiii}c{{d}ii}ddc{ii}iic{i}iiiiic{d}dddddccc{i}iiiiic{d}dddddcccccc{iiiiii}c{dddddd}ccc{iiiiii}c{{d}ii}ddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddc{iiiiii}iiic{dddddd}dddc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iicc{{d}i}ddc{{i}d}iicc{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iicc{ddd}ic{iii}dcc{{d}}{d}ddddc{ii}iic{iiiiii}c{dddddd}ccc{iiiiii}c{dddddd}cccccc{i}iiiiic{d}dddddccc{i}iiiiic{dddd}iiic{ii}iicc{iiiiii}c{dddddd}ccc{iiiiii}ciiicccc{ddddd}iic{d}dddddccc{i}iiiiic{dddd}iiic{ii}iiccc{iiiiii}c{dddddd}{c}{i}iiiiic{dddd}iiic{ii}iicccc{iiiiii}c{dddddd}cccccccc{i}iiiiic{dddd}iiic{ii}iiccccc{iiiiii}ciiicccccc{ddddd}iic{dddd}iiic{ii}iicccccc{iiiiii}iiicccccc{{d}ii}dddddc{ii}iiccccc{i}iiiiic{d}dddddcccccc{iiiiii}c{{d}ii}ddc{ii}iicccc{i}iiiiic{d}dddddcccccccc{iiiiii}c{{d}ii}ddc{ii}iiccc{i}iiiiic{d}dddddccc{iiiiii}iiicccc{dddddd}dddccc{iiiiii}c{{d}ii}ddc{ii}iicc{i}iiiiic{d}dddddccc{i}iiiiic{d}dddddcccc{iiiiii}c{dddddd}ccc{iiiiii}c{{d}ii}ddc{ii}iic{i}iiiiic{d}dddddccc{i}iiiiic{d}dddddcccccc{iiiiii}c{dddddd}ccc{iiiiii}c{{d}ii}ddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddc{iiiiii}iiic{dddddd}dddc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iicc{{d}i}ddc{{i}d}iicc{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iicc{ddd}ic{iii}dcc{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{ii}iic{iiiiii}c{dddddd}ccc{iiiiii}c{dddddd}cccccc{i}iiiiic{d}dddddccc{i}iiiiic{dddd}iiic{ii}iicc{iiiiii}c{dddddd}ccc{iiiiii}ciiicccc{ddddd}iic{d}dddddccc{i}iiiiic{dddd}iiic{ii}iiccc{iiiiii}c{dddddd}{c}{i}iiiiic{dddd}iiic{ii}iicccc{iiiiii}c{dddddd}cccccccc{i}iiiiic{dddd}iiic{ii}iiccccc{iiiiii}ciiicccccc{ddddd}iic{dddd}iiic{ii}iicccccc{iiiiii}iiicccccc{{d}ii}dddddc{ii}iiccccc{i}iiiiic{d}dddddcccccc{iiiiii}c{{d}ii}ddc{ii}iicccc{i}iiiiic{d}dddddcccccccc{iiiiii}c{{d}ii}ddc{ii}iiccc{i}iiiiic{d}dddddccc{iiiiii}iiicccc{dddddd}dddccc{iiiiii}c{{d}ii}ddc{ii}iicc{i}iiiiic{d}dddddccc{i}iiiiic{d}dddddcccc{iiiiii}c{dddddd}ccc{iiiiii}c{{d}ii}ddc{ii}iic{i}iiiiic{d}dddddccc{i}iiiiic{d}dddddcccccc{iiiiii}c{dddddd}cc{iiiiii}iiicdddc{{d}ii}ddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iicc{{d}i}ddc{{i}d}iicc{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iicc{ddd}ic{iii}dcc{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{ii}iic{iiiiii}c{dddddd}ccc{iiiiii}c{dddddd}cccccc{i}iiiiic{d}dddddccc{i}iiiiic{dddd}iiic{ii}iicc{iiiiii}c{dddddd}ccc{iiiiii}ciiicccc{ddddd}iic{d}dddddccc{i}iiiiic{dddd}iiic{ii}iiccc{iiiiii}c{dddddd}{c}{i}iiiiic{dddd}iiic{ii}iicccc{iiiiii}c{dddddd}cccccccc{i}iiiiic{dddd}iiic{ii}iiccccc{iiiiii}ciiicccccc{ddddd}iic{dddd}iiic{ii}iicccccc{iiiiii}iiicccccc{{d}ii}dddddc{ii}iiccccc{i}iiiiic{d}dddddcccccc{iiiiii}c{{d}ii}ddc{ii}iicccc{i}iiiiic{d}dddddcccccccc{iiiiii}c{{d}ii}ddc{ii}iiccc{i}iiiiic{d}dddddccc{iiiiii}iiicccc{dddddd}dddccc{iiiiii}c{{d}ii}ddc{ii}iicc{i}iiiiic{d}dddddccc{i}iiiiic{d}dddddcccc{iiiiii}c{dddddd}c{i}iiiiic{iiii}iiiiicc{{d}ii}ddc{ii}iic{i}iiiiic{d}dddddccc{i}iiiiic{d}dddddcccccc{iiiiii}cc{dddddd}c{iiiiii}cc{{d}ii}ddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{ddd}ddc{dddd}dddddc{d}dddddc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{ii}iic{iiiiii}c{dddddd}ccc{iiiiii}c{dddddd}cccccc{i}iiiiic{d}dddddccc{i}iiiiic{dddd}iiic{ii}iicc{iiiiii}c{dddddd}ccc{iiiiii}ciiicccc{ddddd}iic{d}dddddccc{i}iiiiic{dddd}iiic{ii}iiccc{iiiiii}c{dddddd}{c}{i}iiiiic{dddd}iiic{ii}iicccc{iiiiii}c{dddddd}cccccccc{i}iiiiic{dddd}iiic{ii}iiccccc{iiiiii}ciiicccccc{ddddd}iic{dddd}iiic{ii}iicccccc{iiiiii}iiicccccc{{d}ii}dddddc{ii}iiccccc{i}iiiiic{d}dddddcccccc{iiiiii}c{{d}ii}ddc{ii}iicccc{i}iiiiic{d}dddddcccccccc{iiiiii}c{{d}ii}ddc{ii}iiccc{i}iiiiic{d}dddddccc{iiiiii}iiicccc{dddddd}dddc{i}iiiiic{iiii}iiiiicc{{d}ii}ddc{ii}iicc{i}iiiiic{d}dddddccc{i}iiiiic{d}dddddcccc{iiiiii}cc{dddddd}c{iiiiii}cc{{d}ii}ddc{ii}iic{i}iiiiic{d}dddddccc{i}iiiiic{d}dddddcccccc{iiiiii}cc{dddd}dddddc{d}dddddc{iiiiii}c{{d}ii}ddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{ii}iic{iiiiii}c{dddddd}ccc{iiiiii}c{dddddd}cccccc{i}iiiiic{d}dddddccc{i}iiiiic{dddd}iiic{ii}iicc{iiiiii}c{dddddd}ccc{iiiiii}ciiicccc{ddddd}iic{d}dddddccc{i}iiiiic{dddd}iiic{ii}iiccc{iiiiii}c{dddddd}{c}{i}iiiiic{dddd}iiic{ii}iicccc{iiiiii}c{dddddd}cccccccc{i}iiiiic{dddd}iiic{ii}iiccccc{iiiiii}ciiicccccc{ddddd}iic{dddd}iiic{ii}iicccccc{iiiiii}iiicccccc{{d}ii}dddddc{ii}iiccccc{i}iiiiic{d}dddddcccccc{iiiiii}c{{d}ii}ddc{ii}iicccc{i}iiiiic{d}dddddcccccc{i}iiiiic{iiii}iiiiicc{{d}ii}ddc{ii}iiccc{i}iiiiic{d}dddddccc{iiiiii}iiiccccdddc{dddddd}c{iiiiii}cc{{d}ii}ddc{ii}iicc{i}iiiiic{d}dddddccc{i}iiiiic{d}dddddcccc{iiiiii}cc{dddd}dddddc{d}dddddc{iiiiii}c{{d}ii}ddc{ii}iic{i}iiiiic{d}dddddccc{i}iiiiic{d}dddddcccccc{iiiiii}c{dddddd}ccc{iiiiii}c{{d}ii}ddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{ii}iic{iiiiii}c{dddddd}ccc{iiiiii}c{dddddd}cccccc{i}iiiiic{d}dddddccc{i}iiiiic{dddd}iiic{ii}iicc{iiiiii}c{dddddd}ccc{iiiiii}ciiicccc{ddddd}iic{d}dddddccc{i}iiiiic{dddd}iiic{ii}iiccc{iiiiii}c{dddddd}{c}{i}iiiiic{dddd}iiic{ii}iicccc{iiiiii}c{dddddd}cccccccc{i}iiiiic{dddd}iiic{ii}iiccccc{iiiiii}ciiicccccc{ddddd}iic{dddd}iiic{ii}iicccccc{iiiiii}iiicccccc{{d}ii}dddddc{ii}iiccccc{i}iiiiic{d}dddddccc{iiiiii}iiicc{dddddd}dddc{iiiiii}c{{d}ii}ddc{ii}iicccc{i}iiiiic{d}dddddccc{{i}d}iic{ddd}icc{iii}dc{{d}i}ddc{iiiiii}c{{d}ii}ddc{ii}iiccc{i}iiiiic{d}dddddccc{iiiiii}iiicccc{dddddd}dddccc{iiiiii}c{{d}ii}ddc{ii}iicc{i}iiiiic{d}dddddccc{i}iiiiic{d}dddddcccc{iiiiii}c{dddddd}ccc{iiiiii}c{{d}ii}ddc{ii}iic{i}iiiiic{d}dddddccc{i}iiiiic{d}dddddcccccc{iiiiii}c{dddddd}ccc{iiiiii}c{{d}ii}ddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{ii}iic{iiiiii}c{dddddd}ccc{iiiiii}c{dddddd}cccccc{i}iiiiic{d}dddddccc{i}iiiiic{dddd}iiic{ii}iicc{iiiiii}c{dddddd}ccc{iiiiii}ciiicccc{ddddd}iic{d}dddddccc{i}iiiiic{dddd}iiic{ii}iiccc{iiiiii}c{dddddd}{c}{i}iiiiic{dddd}iiic{ii}iicccc{iiiiii}c{dddddd}cccccccc{i}iiiiic{dddd}iiic{ii}iiccccc{iiiiii}ciiicccccc{ddddd}iic{dddd}iiic{ii}iicccccc{iiiiii}iiicccccc{{d}ii}dddddc{ii}iiccccc{i}iiiiic{d}dddddcc{iiiiii}iiicc{dddddd}dddcc{iiiiii}c{{d}ii}ddc{ii}iicccc{i}iiiiic{d}dddddcc{{i}d}iic{ddd}icc{iii}dc{{d}i}ddcc{iiiiii}c{{d}ii}ddc{ii}iiccc{i}iiiiic{d}dddddccc{iiiiii}iiicccc{dddddd}dddccc{iiiiii}c{{d}ii}ddc{ii}iicc{i}iiiiic{d}dddddccc{i}iiiiic{d}dddddcccc{iiiiii}c{dddddd}ccc{iiiiii}c{{d}ii}ddc{ii}iic{i}iiiiic{d}dddddccc{i}iiiiic{d}dddddcccccc{iiiiii}c{dddddd}ccc{iiiiii}c{{d}ii}ddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{ii}iic{iiiiii}c{dddddd}ccc{iiiiii}c{dddddd}cccccc{i}iiiiic{d}dddddccc{i}iiiiic{dddd}iiic{ii}iicc{iiiiii}c{dddddd}ccc{iiiiii}ciiicccc{ddddd}iic{d}dddddccc{i}iiiiic{dddd}iiic{ii}iiccc{iiiiii}c{dddddd}{c}{i}iiiiic{dddd}iiic{ii}iicccc{iiiiii}c{dddddd}cccccccc{i}iiiiic{dddd}iiic{ii}iiccccc{iiiiii}ciiicccccc{ddddd}iic{dddd}iiic{ii}iicccccc{iiiiii}iiicccccc{{d}ii}dddddc{ii}iiccccc{i}iiiiic{d}dddddc{iiiiii}iiicc{dddddd}dddccc{iiiiii}c{{d}ii}ddc{ii}iicccc{i}iiiiic{d}dddddc{{i}d}iic{ddd}icc{iii}dc{{d}i}ddccc{iiiiii}c{{d}ii}ddc{ii}iiccc{i}iiiiic{d}dddddccc{iiiiii}iiicccc{dddddd}dddccc{iiiiii}c{{d}ii}ddc{ii}iicc{i}iiiiic{d}dddddccc{i}iiiiic{d}dddddcccc{iiiiii}c{dddddd}ccc{iiiiii}c{{d}ii}ddc{ii}iic{i}iiiiic{d}dddddccc{i}iiiiic{d}dddddcccccc{iiiiii}c{dddddd}ccc{iiiiii}c{{d}ii}ddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{ii}iic{iiiiii}c{dddddd}ccc{iiiiii}c{dddddd}cccccc{i}iiiiic{d}dddddccc{i}iiiiic{dddd}iiic{ii}iicc{iiiiii}c{dddddd}ccc{iiiiii}ciiicccc{ddddd}iic{d}dddddccc{i}iiiiic{dddd}iiic{ii}iiccc{iiiiii}c{dddddd}{c}{i}iiiiic{dddd}iiic{ii}iicccc{iiiiii}c{dddddd}cccccccc{i}iiiiic{dddd}iiic{ii}iiccccc{iiiiii}ciiicccccc{ddddd}iic{dddd}iiic{ii}iicccccc{iiiiii}iiicccccc{{d}ii}dddddc{ii}iiccccc{i}iiiiic{d}dddddcccccc{iiiiii}c{{d}ii}ddc{ii}iicccc{i}iiiiicc{iiii}iiiiic{dddddd}cccccc{iiiiii}c{{d}ii}ddc{ii}iiccc{i}iiiiicc{d}dddddc{i}iiiiic{iiiii}ddcccc{dddddd}dddccc{iiiiii}c{{d}ii}ddc{ii}iicc{i}iiiiic{d}dddddc{iiiiii}c{dddd}dddddcc{d}dddddcccc{iiiiii}c{dddddd}ccc{iiiiii}c{{d}ii}ddc{ii}iic{i}iiiiic{d}dddddccc{i}iiiiic{d}dddddcccccc{iiiiii}c{dddddd}ccc{iiiiii}c{{d}ii}ddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{ii}iic{iiiiii}c{dddddd}ccc{iiiiii}c{dddddd}cccccc{i}iiiiic{d}dddddccc{i}iiiiic{dddd}iiic{ii}iicc{iiiiii}c{dddddd}ccc{iiiiii}ciiicccc{ddddd}iic{d}dddddccc{i}iiiiic{dddd}iiic{ii}iiccc{iiiiii}c{dddddd}{c}{i}iiiiic{dddd}iiic{ii}iicccc{iiiiii}c{dddddd}cccccccc{i}iiiiic{dddd}iiic{ii}iiccccc{iiiiii}ciiicccccc{ddddd}iic{dddd}iiic{ii}iicccccc{iiiiii}iiicccccc{{d}ii}dddddc{ii}iiccccc{i}iiiiic{d}dddddcccccc{iiiiii}c{{d}ii}ddc{ii}iicccc{i}iiiiic{d}dddddcccccccc{iiiiii}c{{d}ii}ddc{ii}iiccc{i}iiiiicc{iiii}iiiiic{dddddd}c{iiiiii}iiicccc{dddddd}dddccc{iiiiii}c{{d}ii}ddc{ii}iicc{i}iiiiicc{d}dddddc{i}iiiiicc{d}dddddcccc{iiiiii}c{dddddd}ccc{iiiiii}c{{d}ii}ddc{ii}iic{i}iiiiic{d}dddddc{iiiiii}c{dddd}dddddcc{d}dddddcccccc{iiiiii}c{dddddd}ccc{iiiiii}c{{d}ii}ddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{ii}iic{iiiiii}c{dddddd}ccc{iiiiii}c{dddddd}cccccc{i}iiiiic{d}dddddccc{i}iiiiic{dddd}iiic{ii}iicc{iiiiii}c{dddddd}ccc{iiiiii}ciiicccc{ddddd}iic{d}dddddccc{i}iiiiic{dddd}iiic{ii}iiccc{iiiiii}c{dddddd}{c}{i}iiiiic{dddd}iiic{ii}iicccc{iiiiii}c{dddddd}cccccccc{i}iiiiic{dddd}iiic{ii}iiccccc{iiiiii}ciiicccccc{ddddd}iic{dddd}iiic{ii}iicccccc{iiiiii}iiicccccc{{d}ii}dddddc{ii}iiccccc{i}iiiiic{d}dddddcccccc{iiiiii}c{{d}ii}ddc{ii}iicccc{i}iiiiic{d}dddddcccccccc{iiiiii}c{{d}ii}ddc{ii}iiccc{i}iiiiic{d}dddddccc{iiiiii}iiicccc{dddddd}dddccc{iiiiii}c{{d}ii}ddc{ii}iicc{i}iiiiicc{iiii}iiiiic{dddddd}c{i}iiiiic{d}dddddcccc{iiiiii}c{dddddd}ccc{iiiiii}c{{d}ii}ddc{ii}iic{i}iiiiicc{d}dddddc{i}iiiiicc{d}dddddcccccc{iiiiii}c{dddddd}ccc{iiiiii}c{{d}ii}ddc{{i}}{i}iiiic{{d}i}ddc{iiiiii}c{dddd}dddddc{{i}dd}dddc{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{{i}}{i}iiiic{{d}i}ddccc{{i}d}iic{{d}i}ddcccccccc{{i}d}iic{{d}i}ddccc{{i}d}iic{{d}}{d}ddddc{ii}iic{iiiiii}c{dddddd}ccc{iiiiii}c{dddddd}cccccc{i}iiiiic{d}dddddccc{i}iiiiic{dddd}iiic{ii}iicc{iiiiii}c{dddddd}ccc{iiiiii}ciiicccc{ddddd}iic{d}dddddccc{i}iiiiic{dddd}iiic{ii}iiccc{iiiiii}c{dddddd}{c}{i}iiiiic{dddd}iiic{ii}iicccc{iiiiii}c{dddddd}cccccccc{i}iiiiic{dddd}iiic{ii}iiccccc{iiiiii}ciiicccccc{ddddd}iic

```
> 0 votes

---
Tags: code-golf, ascii-art, kolmogorov-complexity
---


# Question
Title: Fizz Buzz with unique characters in columns
*Inspired by Digits in their lanes and 1, 2, Fizz, 4, Buzz*

# Introduction

Your task is to generate exactly the following output:

```
1
2
Fizz
4
  Buzz
    Fizz
7
8
      Fizz
        Buzz
 11
          Fizz
   13
    14
            FizzBuzz
     16
      17
              Fizz
       19
                  Buzz
                    Fizz
 22
    23
                      Fizz
                        Buzz
   26
                          Fizz
     28
      29
                            FizzBuzz
       31
      32
                              Fizz
34
                                  Buzz
                                    Fizz
 37
  38
                                      Fizz
                                        Buzz
        41
                                          Fizz
  43
   44
                                            FizzBuzz
      46
       47
                                              Fizz
         49
                                                  Buzz

```

# Challenge

This challenge is based on the Fizz Buzz challenge, and here is a recap: output the numbers from 1 to 100 inclusive, each number on its own line, but if the number is a multiple of 3, you should output "Fizz" instead of the original number, if the number is a multiple of 5, you should output "Buzz" instead of the original number. If the number is a multiple of 15, you should output "FizzBuzz" instead of the original number.

However, in addition to the requirement above, you should also indent each line using spaces to make that every column contains unique characters (excluding spaces and newlines) only. The spaces prepended to each line are the minimum required to make all the lines appeared before it (inclusive) has unique characters in each column.

For example, `1,2,Fizz,4` does not need any indentation because they already have unique characters in each column (column 1: `12F4`, column2: `i`, column3: `z`, column4: `z`), but when adding `Buzz` we need to indent by two spaces because otherwise we would have two `z`'s in both the 3rd and the 4th column. Since two spaces is enough to achieve the goal you should not indent it by three spaces. `7` and `8` does not need any indentation but when outputting `11` we need to indent by one space because the 1st column already has a `1`. `13` then needs to be indented by three spaces because now 1st, 2nd and 3rd column all have a `1`. Indentation for the remaining lines follow the same rule.

**To make the challenge simpler, The upper limit has been changed to 50.**

# Specs

* You can write a program or a function. Neither of them should take any non-empty input. Taking an empty input is fine.
* Since this is a KC challenge you need to produce the output as specified in the Introduction section. A single trailing newline is fine. No heading newlines or extra heading spaces. No extra trailing spaces for each line.
* Your program can exit with error or have non-empty STDERR output as long as STDOUT conforms to the specification.
* This is intra-language , the program with lowest number of bytes wins in its language.
* Default loopholes apply.

# Answer
> 9 votes
# Python 2, 127 bytes

```
i=0;exec"print ord('<<<<>@<<BD=F?@HABJCNP=@RT?VABXCBZ<^`=>bdDf>?hBCjEn'[i])%60*' '+(i%3/2*'Fizz'+i%5/4*'Buzz'or`-~i`);i+=1;"*50

```

Try it online!

A fifty-byte lookup table seems to hurt the code size less than the logic necessary to track which characters have occurred in each column.

# Answer
> 5 votes
# Python 2, ~~167~~ ~~166~~ ~~163~~ ~~161~~ 157 bytes

```
a=eval(`[{0}]*99`);i=0
exec"f=i%3/2*'Fizz'+i%5/4*'Buzz'or`i+1`;i+=1;g=0\nwhile any(b>{c}for b,c in zip(a[g:],f)):g+=1\nmap(set.add,a[g:],f);print' '*g+f;"*50

```

Try it online!

Edits:

* `while` is shorter than `for..range()` by 1 byte.
* Thanks to @ovs for shaving off 3 bytes. I always forget `exec`...
* Adapted `i%3/2` trick from Lynn's answer (-2 bytes).
* @Lynn suggested `a=map(set,[[]]*99)`, but I found another way using `eval` and `repr` with same bytes (-4 bytes).

Use a list of sets to track the chars used for each column, and set inequality for membership. The rest follows the exact spec given.

# Answer
> 4 votes
# C (gcc), ~~145~~ 144 bytes (143 for hex)

```
i;main(){for(;i++<50;printf("%*s%s%.d\n","000402800:81>34@56B7BH14JH3N56P76R0RX12ZX8^23`67b9b"[i]-48,i%3?"":"Fizz",i%5?"":"Buzz",i%3*i%5?i:0));}

```

Try it online!

```
0000h: 69 3B 6D 61 69 6E 28 29 7B 66 6F 72 28 3B 69 2B ; i;main(){for(;i+
0010h: 2B 3C 35 30 3B 70 72 69 6E 74 66 28 22 25 2A 73 ; +<50;printf("%*s
0020h: 25 73 25 2E 64 5C 6E 22 2C 22 FE FE FE 02 FE 00 ; %s%.d\n","......
0030h: 06 FE FE 08 06 FF 0C 01 02 0E 03 04 10 05 10 16 ; ................
0040h: FF 02 18 16 01 1C 03 04 1E 05 04 20 FE 20 26 FF ; ........... . &.
0050h: 63 28 26 06 2C 00 01 2E 04 05 30 07 30 22 5B 69 ; c(&.,.....0.0"[i
0060h: 5D 2B 32 2C 69 25 33 3F 22 22 3A 22 46 69 7A 7A ; ]+2,i%3?"":"Fizz
0070h: 22 2C 69 25 35 3F 22 22 3A 22 42 75 7A 7A 22 2C ; ",i%5?"":"Buzz",
0080h: 69 25 33 2A 69 25 35 3F 69 3A 30 29 29 3B 7D    ; i%3*i%5?i:0));}

```

# Answer
> 3 votes
# Ruby, 129 bytes

```
puts (1..50).map{|n|" "*(".<<<<>@<<BD=F?@HABJCNP=@RT?VABXCBZ<^`=>bdDf>?hBCjEn"[n].ord%60)+("FizzBuzz
"[i=n**4%-15,i+13]||n.to_s)}

```

Try it online!

Double credit goes to Lynn here, for the lookup table approach and the fizzbuzz algorithm.

The FizzBuzz algorithm is very interesting, and it hinges on the remarkable coincidence that all positive, non-composite numbers less than 15 (other than 3 and 5), when raised to the 4th power, are 1 more than a multiple of 15. In fact:

```
 n     n**4  n**4%15  n**4%-15
 1        1     1       -14
 2       16     1       -14
 3       81     6        -9
 4      256     1       -14
 5      625    10        -5
 6     1296     6        -9
 7     2401     1       -14
 8     4096     1       -14
 9     6561     6        -9
10    10000    10        -5
11    14641     1       -14
12    20736     6        -9
13    28561     1       -14
14    38416     1       -14
15    50625     0         0

```

The values `3**4%15` and `5**4%15` are exactly 4 apart: the length of the string "Fizz". We can exploit this by using them to index from the end of a string, at least 9 characters in length. Multiples of 3 will index from the beginning of the string, and multiples of 5 will index from 5 characters from the end. Every other number will attempt to index from before the beginning of the string, and fail, returning `nil`. Then 15, of course, indexes from the 0th character. The fact that "FizzBuzz" is only 8 characters long is a small obstacle; we use a newline character to pad it, which will later be ignored by `puts`.

It's possible that the lookup table can be out-golfed by a more procedural approach, but my attempt was in the neighborhood of 190 bytes.

# Answer
> 2 votes
# \[JavaScript (Node.js) REPL\], 144 bytes

```
(f=(i,s=[['Fizz'][i%3]]+[['Buzz'][i%5]]||i+[],b=i>1?f(i-1):[])=>[...s].some((p,j)=>b.some(w=>w[j]==p&0!=p))?f(i,' '+s):b.push(s)&&b)(50).join`

```

\`

Try it online!

Warning program itself runs unacceptable time

# JavaScript (Node.js), 132 bytes by Arnauld

```
f=(a=n=[],s=`${b=++n%5?'':'Buzz',n%3?b||n:'Fizz'+b}
`)=>n>50?'':a.some(x=>[...x].some((c,i)=>c!=0&c==s[i]))?f(a,' '+s):s+f([s,...a])

```

Try it online!

# Answer
> 2 votes
# Java (JDK 10), 185 bytes

```
v->{for(int n=0,l;n<50;System.out.printf((l>0?"%"+l:"%")+"s%s%n","",(n%3<1?"Fizz":"")+(n%5<1?"Buzz":n%3<1?"":n)))l="####%'##)+$-&'/()1*57$'9;&=()?*)A#EG$%IK+M%&O)*Q,U#".charAt(n++)-35;}

```

Try it online!

## Credits

# Answer
> 1 votes
# Haskell, ~~190 187 186 178~~ 176 bytes

```
unlines$foldl(\a x->a++[[z|z<-iterate(' ':)x,all(\m->null[p|(p,q)<-m`zip`z,p==q&&p>' '])a]!!0])[]$h<$>[1..50]
a%b=a`mod`b<1
h n|n%15="FizzBuzz"|n%3="Fizz"|n%5="Buzz"|1<2=show n

```

Try it online!

The slightly more readable (and annotated) version:

```
-- check if a is evenly divisible by b
a%b=a`mod`b<1
-- produce correct FizzBuzz output for a number
h n|n%15="FizzBuzz"|n%3="Fizz"|n%5="Buzz"|1<2=show n
-- test if all chars distinct between two strings
x#y=null[a|(a,b)<-x`zip`y,a==b&&a>' ']
-- given a new string and all previous strings
-- shift the new string to the right until all
-- chars are distinct
x!y=[z|z<-iterate(' ':)y,all(z#)x]!!0
g=h<$>[1..50]
f'=foldl step[]g
  where step acc x = acc++[acc!x]

```

Edit: I ended up inlining some functions in the golfed version to save more bytes.

# Answer
> 1 votes
# Jstx, 122 bytes

```
◄50-☺6*ø($♥:ø↕♂Fizz♀☺(◙$♣:ø↕♂Buzz♀6☺(◙"ø↕$6◙♂<<<<>@<<BD=F?@HABJCNP=@RT?VABXCBZ<^`=>bdDf>?hBCjEn'[i])%60*♀&P◄59▼ö,► 7.☻a0.2

```

Try it online!

# Answer
> 0 votes
# Deadfish~, 3041 bytes

```
{i}c{iiii}cdc{dddd}ic{iiii}iiic{dddd}dddcc{iiiiii}iiic{iiii}dddciiiiicdddc{d}iiic{i}dc{d}dddcdc{{d}iii}iic{iiiiii}iiiiiic{ii}iiic{{d}i}ic{iii}iiiiiic{iiii}dddcddciic{i}icdc{{d}ii}dddc{{i}ddd}iiiciiiiic{{d}ii}iic{{i}dd}iiiic{d}ddcdddciiiic{i}dc{{d}ii}ddc{{i}ddd}iiiiiic{d}dc{i}iiic{d}ic{i}iiiic{{d}ii}dddc{iiiiii}iiiiic{i}iiic{d}c{{d}iii}iic{ii}dddcdddddc{d}ddc{ii}ddcddddddc{d}ddc{iiii}ddc{iii}iiiiic{ii}dddcc{{d}ii}iic{d}ddc{ii}c{d}iic{d}ddc{iii}iiiic{iiiii}iciiiiicc{{d}}{d}ddc{iiiiii}iiic{iiii}dddciiiiiicddcdddc{d}dc{ii}dddc{dd}iic{ii}dddc{d}dciiiiiicdc{{d}}cc{{i}dd}dc{ii}iiciiiiiicdddc{{d}ii}ddc{{i}dd}iiiic{dd}ic{ii}ddc{d}iic{{d}iii}dddddc{{i}ddd}iiic{i}c{{d}ii}dddc{{i}dd}iiiicdddddc{{d}ii}ic{{i}ddd}icddc{i}dc{d}ic{i}iiic{dd}iiic{ii}dc{d}dddddc{{d}iii}ic{{i}ddd}dc{ii}dc{dd}dddciic{ii}dddc{d}iic{i}iiic{{d}i}ic{{i}dd}iiiic{d}ddcdddc{{d}iii}ic{{i}ddd}c{i}dcdddcciiic{i}ddc{d}ddddciiiiic{d}iiic{{d}iii}dc{{i}dd}dciiiiiicdcddddciiiiicdc{dddddd}iic{ddddd}iicc{iiii}dc{dddd}ic{iiii}c{dddd}c{iiiiii}c{iii}iiiiic{ii}dddcc{{d}}{d}ddc{iiii}iic{dddd}ddc{ii}iicc{iii}iiiic{iiiii}iciiiiicc{{d}}{d}ddc{ii}iicccc{iiii}ddc{iii}iiiiic{ii}dddcc{{d}}{d}ddc{iiii}iiiiic{dddd}dddddc{iiii}iiiiiic{dddd}ddddddc{ii}iicccccc{iiii}ddc{iii}iiiiic{ii}dddcc{{d}}{d}ddc{ii}iicccccccc{iii}iiiic{iiiii}iciiiiicc{{d}}{d}ddc{ii}iic{ii}dddcc{dddd}ic{ii}ii{c}{iiii}ddc{iii}iiiiic{ii}dddcc{{d}}{d}ddc{ii}iiccc{ii}dddciic{dddd}dc{ii}iicccc{ii}dddciiic{dddd}ddc{ii}ii{c}cc{iiii}ddc{iii}iiiiic{ii}dddcc{ddddd}ddddddc{iiiii}iciiiiicc{{d}}{d}ddc{ii}iiccccc{ii}dddciiiiic{dddd}ddddc{ii}iicccccc{ii}dddciiiiiic{dddd}dddddc{ii}ii{c}cccc{iiii}ddc{iii}iiiiic{ii}dddcc{{d}}{d}ddc{ii}iiccccccc{ii}dddc{i}ddc{ddddd}iiic{ii}ii{c}cccccccc{iii}iiiic{iiiii}iciiiiicc{{d}}{d}ddc{ii}ii{cc}{iiii}ddc{iii}iiiiic{ii}dddcc{{d}}{d}ddc{ii}iic{ii}ddcc{dddd}c{ii}iicccc{ii}ddcic{dddd}dc{ii}ii{cc}cc{iiii}ddc{iii}iiiiic{ii}dddcc{{d}}{d}ddc{ii}ii{cc}cccc{iii}iiiic{iiiii}iciiiiicc{{d}}{d}ddc{ii}iiccc{ii}ddciiiic{dddd}ddddc{ii}ii{cc}cccccc{iiii}ddc{iii}iiiiic{ii}dddcc{{d}}{d}ddc{ii}iiccccc{ii}ddciiiiiic{dddd}ddddddc{ii}iicccccc{ii}ddc{i}dddc{ddddd}iiic{ii}ii{cc}cccccccc{iiii}ddc{iii}iiiiic{ii}dddcc{ddddd}ddddddc{iiiii}iciiiiicc{{d}}{d}ddc{ii}iiccccccc{ii}dcddc{dddd}ic{ii}iicccccc{ii}dcdc{dddd}c{ii}ii{cc}{c}{iiii}ddc{iii}iiiiic{ii}dddcc{{d}}{d}ddc{iiii}icic{dddd}ddc{ii}ii{cc}{c}cccc{iii}iiiic{iiiii}iciiiiicc{{d}}{d}ddc{ii}ii{cc}{c}cccccc{iiii}ddc{iii}iiiiic{ii}dddcc{{d}}{d}ddc{ii}iic{ii}dciiiic{dddd}dddddc{ii}iicc{ii}dciiiiic{dddd}ddddddc{ii}ii{cc}{c}cccccccc{iiii}ddc{iii}iiiiic{ii}dddcc{{d}}{d}ddc{ii}ii{cc}{cc}{iii}iiiic{iiiii}iciiiiicc{{d}}{d}ddc{ii}iicccccccc{ii}cdddc{dddd}ic{ii}ii{cc}{cc}cc{iiii}ddc{iii}iiiiic{ii}dddcc{{d}}{d}ddc{ii}iicc{ii}cdc{dddd}dc{ii}iiccc{ii}cc{dddd}ddc{ii}ii{cc}{cc}cccc{iiii}ddc{iii}iiiiic{ii}dddcc{ddddd}ddddddc{iiiii}iciiiiicc{{d}}{d}ddc{ii}iicccccc{ii}ciic{dddd}ddddc{ii}iiccccccc{ii}ciiic{dddd}dddddc{ii}ii{cc}{cc}cccccc{iiii}ddc{iii}iiiiic{ii}dddcc{{d}}{d}ddc{ii}iiccccccccc{ii}ciiiiic{ddddd}iiic{ii}ii{cc}{cc}{c}{iii}iiiic{iiiii}iciiiiicc{{d}}{d}ddc

```

---
Tags: code-golf, kolmogorov-complexity
---


title: Golf the Chinese 9*9 multiple table

text:
# Question
Title: Golf the Chinese 9*9 multiple table
Output the following table:

```
一一得一
一二得二 二二得四
一三得三 二三得六 三三得九
一四得四 二四得八 三四十二 四四十六
一五得五 二五一十 三五十五 四五二十 五五二十五
一六得六 二六十二 三六十八 四六二十四 五六三十 六六三十六
一七得七 二七十四 三七二十一 四七二十八 五七三十五 六七四十二 七七四十九
一八得八 二八十六 三八二十四 四八三十二 五八四十 六八四十八 七八五十六 八八六十四
一九得九 二九十八 三九二十七 四九三十六 五九四十五 六九五十四 七九六十三 八九七十二 九九八十一

```

Or you can use the first three letters in its English word, in case that some languages don't support Chinese characters:

```
OneOneGetOne
OneTwoGetTwo TwoTwoGetFou
OneThrGetThr TwoThrGetSix ThrThrGetNin
OneFouGetFou TwoFouGetEig ThrFouTenTwo FouFouTenSix
OneFivGetFiv TwoFivOneTen ThrFivTenFiv FouFivTwoTen FivFivTwoTenFiv
OneSixGetSix TwoSixTenTwo ThrSixTenEig FouSixTwoTenFou FivSixThrTen SixSixThrTenSix
OneSevGetSev TwoSevTenFou ThrSevTwoTenOne FouSevTwoTenEig FivSevThrTenFiv SixSevFouTenTwo SevSevFouTenNin
OneEigGetEig TwoEigTenSix ThrEigTwoTenFou FouEigThrTenTwo FivEigFouTen SixEigFouTenEig SevEigFivTenSix EigEigSixTenFou
OneNinGetNin TwoNinTenEig ThrNinTwoTenSev FouNinThrTenSix FivNinFouTenFiv SixNinFivTenFou SevNinSixTenThr EigNinSevTenTwo NinNinEigTenOne

```

You can output in any reasonable format, e.g. plain text separated with space/comma/tab and newline, 2D array where empty places are empty or don't exist (The 2\*1 place is empty so there shouldn't be anything in the array).

Code golf, shortest code in bytes win. GBK encoding is allowed, where each Chinese character use 2 bytes.

Converting Table:

| Character | Number |
| --- | --- |
|  | One |
|  | Two |
|  | Thr |
|  | Fou |
|  | Fiv |
|  | Six |
|  | Sev |
|  | Eig |
|  | Nin |
|  | Ten |
|  | Get |

# Answer
> 8 votes
# Stax, 66 characters

```
9mYF"得一二三四五六七八九"cacy*~@ny@\p;11AH:b!n;A/X@]z?px'十z?p,A%sn@]z?' +qD

```

Number of bytes depends on the encoding used for Chinese characters.

Run and debug online!

## Explanation

```
9mYF...D    Loop `n` times and print a newline after each loop, `n`=1..9

"..."cay*~@ny@\p
"..."c              Push the string and duplicate it
      ay            Fetch the outer loop variable
        *           Multiply with the inner loop variable
         ~          Move the product to input stack for later use
          @         Take character at the index specified by inner loop variable
           ny@      Take character at the index specified by outer loop variable
              \p    Print the two characters

;11AH:b!n;A/X@]z?p
;11AH:b!        ?p    Is the product not in range [11,20)?
                      Output (*) if true, (**) if false.
        n;A/X@        Character at the index of the "ten" digit of product
              ]       Convert character to string (*)
               z      Empty string (**)

x'十z?p,A%sn@]z?' +q
x'十z?p                Print "十" if the "ten" digit is non-zero, nothing otherwise
       ,A%sn@]z?       Get the character specified by the last digit if that digit is non-zero, empty string otherwise
                ' +q   Append a space and print

```

## Alternative version (Stax 1.0.6), 59 bytes (by @recursive)

This uses a feature that is inspired by this challenge and is only included in Stax 1.0.6 which postdates the challenge.

```
éz░╖▐5à{│`9[mLùÜ•ëO╞îπl▼Γ─§╥|▒╛Δ◙Φµ'r╠eƒÿQ╫s♪Ω]£ï♪D3╚F◙δÿ%‼

```

The ASCII version is

```
9mX{x\_x*YA/]yA-y20<*!*+y9>A*+yA%]0-+"NT|,,t.%,p&()(!'^pq kzi !X6"!s@mJ

```

This version constructs the index array and then uses it to index the string of Chinese characters to avoid redundant stack operations (`c`,`a`,`n`) and multiple `@`s.

## Explanation

```
9mX{...m    Loop `n` times and map `1..n` to a list of strings, `n`=1..9
        J   Join the strings with space and print with a newline

x\_x*YA/]yA-y20<*!*+y9>A*+yA%]0-+"..."!s@
x\                                           A pair: (inner loop variable, outer loop variable)
  _x*Y                                       Product of inner and outer loop variable
      A/                                     floor(product/10)
        ]                                    [floor(product/10)]
         yA-                                 Product does not equal 10
            y20<                             Product is less than 20
                *!                           `Nand` of them
                                             This is true (1) if the product is in the range {10}U[20,81]
                  *                          Repeat [floor(product/10)] this many times
                                             This results in itself if the predicate above is true, or empty array if it is false
                   +                         Add it to the list of [inner loop var, outer loop var]
                                             This list will be used to index the string "得一二三四五六七八九十"
                    y9>A*                    Evaluates to 10 if the product is larger than 9, 0 otherwise
                                             When indexed, they become "十" and "得", respectively
                         +                   Append to the list of indices
                          yA%                Product modulo 10
                             ]0-             [Product modulo 10] if that value is not zero, empty array otherwise
                                +            Append to the list of index
                                 "..."!      "得一二三四五六七八九十"
                                       s@    Index with constructed array

```

# Answer
> 6 votes
# Python 3, ~~151~~ ~~149~~ 146 bytes

-3 bytes thanks to Rod.

```
l=" 一二三四五六七八九"
for i in range(1,10):print([l[j//i]+l[i]+('得',l[j//10][10<j<20:]+'十')[j>9]+l[j%10]for j in range(i,i*i+1,i)])

```

Try it online!

# Answer
> 3 votes
## Javascript, 190 bytes

```
(_="得一二三四五六七八九十")=>{for(i=1;i<10;i++){for(t="",v=0;v<i;t+=_[++v]+_[i]+[...(v*i+'')].map((a,b,c) => c.length>1&&b==0?(a>1?_[a]+'十':'十'):b==0?'得'+_[a]:_[a]).join``+' ');console.log(t)}}

```

```
a=(_=" 一二三四五六七八九")=>{for(i=1;i<10;i++){for(t="",v=0;v<i;t+=_[++v]+_[i]+[...(v*i+'')].map((a,b,c) => c.length>1&&b==0?(a>1||c[1]==0?_[a]+'十':'十'):b==0?'得'+_[a]:_[a]).join``+' ');console.log(t)}}
a()
```

# Answer
> 2 votes
# Yabasic, ~~250~~ ~~242~~ 238 bytes

A answer with unicode characters?! What?

An anonymous function and declared helper function, `c(n)` that takes no input and outputs to STDOUT

```
For r=1To 9
For c=1To r
c(c)
c(r)
If!r*c>9Then?"得";Fi
c(r*c)
?" ";
Next
?
Next
Sub c(n)
s$="一二三四五六七八九"
If n>19Then?Mid$(s$,Int(n/10)*3-2,3);Fi
If n=10Then?"一";Fi
If n>9Then?"十";Fi
?Mid$(s$,Mod(n,10)*3-2,3);
End Sub

```

Try it online!

# Answer
> 2 votes
# Ruby, 166 bytes

```
->{(1..9).map{|a|(1..a).map{|b|p=a*b;([b,a]+(p<10?[0,p]:p<11?[1,10]:p<20?[10,p%10]:[p/10,10]+(p%10<1?[]:[p%10]))).map{|d|"得一二三四五六七八九十"[d]}*""}}}

```

Try it online!

A lambda returning a 2D array of strings.

```
->{
  (1..9).map{|b|                  # b is the multiplier
    (1..b).map{|a|                # a is the multiplicand
      p=a*b;                      # p is the product
      (                           # We will build an array of indexes into a ref string:
        [a,b] + (                 #   The first two indexes will be a and b
        p<10 ? [0,p] :            #   Case 1: abGp (single digit sums)
        p<11 ? [1,10] :           #   Case 2: 251X (only happens once)
        p<20 ? [10,p%10] :        #   Case 3: abXd (12-18, d is the ones digit)
        [p/10,10]+(               #   (Cases 4 and 5 share a prefix)
          p%10<1 ? [] :           #   Case 4: abcX (20, 30, 40, c is the tens digit)
          [p%10]))                #   Case 5: abcXd (two-digit product, p = 10*c+d)
      ).map{|d|
        "得一二三四五六七八九十"[d] # Fetch the character for each index
      }*""                        # Join the characters into words
    }
  }
}

```

# Answer
> 1 votes
# Python 3, 196 bytes

```
lambda c=' 一二三四五六七八九':[[c[j]+c[i]+[('得'+c[(i*j%10)]),((c[(int(i*j/10))]*((i*j>19)or(i*j==10)))+'十'+(c[i*j%10])*(i*j%10!=0))][i*j>9]for j in range(1,i+1)]for i in range(1,10)]

```

Try it online!

# Answer
> 1 votes
# Retina, 100 characters, 122 bytes

```

9*
_
$`_$n
_
$%`_$.%=
(_+)(.)
$.1,$2,$.($.1*$2*)
\B.
:$&
:0
:
1:\b
:
,(. )
,0$1
T`,d:`_得一二三四五六七八九十

```

Try it online! Explanation:

```

9*

```

Insert nine `_`s.

```
_
$`_$n

```

Expand to 9 rows of 1 to 9 `_`s.

```
_
$%`_$.%=

```

(note trailing space) Expand to 9 rows of 1 to i `_`s plus i as a digit.

```
(_+)(.)
$.1,$2,$.($.1*$2*)

```

Convert the `_`s to decimal and multiply by i.

```
\B.
:$&

```

Insert a `:` if the answer has two digits. This will become the `ten` character.

```
:0
:

```

Delete zero units.

```
1:\b
:

```

Delete the `1` from `1:` unless it's `1:0` which had its zero removed.

```
,(. )
,0$1

```

Inser a `0` for single-digit answers; this will become the `get` character.

```
T`,d:`_得一二三四五六七八九十

```

Fix up all the characters.

# Answer
> 1 votes
# JavaScript (Node.js), 141/130 bytes

```
(s=[...'得一二三四五六七八九'])=>s.map((A,i)=>s.map((B,j)=>i<j|!j?'':B+A+[s[(q=i*j)/10|-(q>11&q<19)]]+(q>9?'十':'')+[s[q%10||s]]))

```

Try it online!

# Answer
> 1 votes
# Python 3, 142 bytes

Structure is similar to ovs's 146 byte answer, but the middle terms work in a different way.

```
n=" 一二三四五六七八九"
for x in range(1,10):print([n[y//x]+n[x]+n[y//10][20>y!=10:]+'得十'[y>9]+n[y%10]for y in range(x,x*x+1,x)])

```

Try it online!

# Explanation

The most interesting term is the term for the number of tens:

```
n[y//10][20>y!=10:]

```

Note that `20>y!=10` means `20 > y and y != 10`, which is `False` when the number of tens should be included and `True` otherwise.

`False` has an integer value of `0` and `True` has an integer value of `1`, so whereas `n[y//10]` is always one character long, the subscript `[20>y!=10:]` is equivalent to `[0:1]` (i.e. "the character") when the number of tens should be included and `[1:1]` (i.e. "no characters") otherwise.

The following term,

```
'得十'[y>9]

```

is easier to understand; note that:

* The output for every result \<= 9 should contain
* The output for every result \> 9 should contain
* can be handled after the 'tens' term because the 'tens' term always evaluates to an empty string when there is a

### Note on trailing spaces

The trailing spaces for multiples of ten stretch the specification slightly - as mentioned by rod, this could be made visually perfect by using a zero-width space, but then you would also have to unpack the arrays using `print(*[...])` as the zero-width space is represented as a literal `"\u200b"` when printed in an array.

# Answer
> 1 votes
# APL (Dyalog), ~~75~~ 100 characters, ~~97~~ 122 bytes

```
k t←' 一二三四五六七八九得十'10
∘.{⍺<⍵:''⋄(s=10)∨19<s←⍺×⍵:k[1+⍵⍺(⌊s÷t)11,t|s]⋄9<s:k[1+⍵⍺,11,t|s]⋄k[⍵⍺t s+1]}⍨⍳9

```

Try it online!

# Answer
> 0 votes
# JavaScript, 190 bytes

```
(s="得一二三四五六七八九十",o="")=>eval(`for(i=1;i<10;i++){for(j=1;j<=i;j++){o+=s[j]+s[i]+(i*j<10?s[0]:i*j<11?s[1]+s[10]:i*j<20?s[10]:s[i*j/10|0]+s[10])+(i*j%10?s[i*j%10]:"")+" "}o+="\\n"}`)

```

I will try to golf this later.

# Answer
> 0 votes
# Ruby, 136 bytes

Byte count in UTF-8, should be 128 bytes with Han characters counted as 2 instead of 3.

```
1.upto(9){|x|p (1..x).map{|y|[y,x,x*y/10,?X,x*y%10].join.sub(/(?<=0)X|1(?=X[1-9])|0$/,'').tr"0-9X","得一二三四五六七八九十"}}

```

Try it online!

1. Construct the strings from multipliers' and products' digits with the latter separated by `X` as a placeholder for .
2. Do some regex fun to drop `X` for products \<10, leading ones for "-teen" products, and trailing zeroes.
3. Translate digits and `X` to Han characters.

# Answer
> 0 votes
# ///, 301 bytes (GBK\*)

```
/*/\/\///1/一*2/二*3/三*4/四*5/五*6/六*7/七*8/八*9/九*0/十*=/得*I/
1*t/ 2*T/ 3/11=1I2=2t2=4I3=3t3=6T3=9I4=4t4=8T402 4406I5=5t510T505 4520 55205I6=6t602T608 46204 5630 66306I7=7t704T7201 47208 57305 67402 77409I8=8t806T8204 48302 5840 68408 78506 88604I9=9t908T9207 49306 59405 69504 79603 89702 99801

```

Try it online!

\*Spec explicitly allows GBK → Unicode conversion.

# Answer
> 0 votes
# Pyth, 49 characters, 71 bytes

```
J" 一二三四五六七八九"jmj;m+s@LJkr6>3+\得j\十@LJj*FkT,RdSdS9

```

Uses UTF-8 encoding. Try it online here.

In the following explanation, the `?` characters are substitutes for the correct Chinese characters - I'm too lazy to make everything line up properly...

```
J" ?????????"jmj;m+s@LJkr6>3+\?j\?@LJj*FkT,RdSdS9
J" ?????????"                                       Assign space + glyphs for 1-9 to J
                                               S9   [1-9]
              m                                     Map each element, as d, using:
                                             Sd       [1-d]
                                          ,Rd         Pair each element of the above with d
                                                        e.g. for d=3, yields [[1,3],[2,3],[3,3]]
                 m                                    Map each element, as k, using:
                                      *Fk               Get the product of the pair
                                     j   T              Get decimal digits of the above (convert to base 10)
                                  @LJ                   Map each digit to its index in J
                               j\?                      Join the above on ? ("Ten")
                            +\?                         Prepend ? ("Get")
                          >3                            Take the last 3 characters of the above
                        r6                              Strip whitespace
                  +                                     Prepend to the above...
                   s@LJk                                Concatenated digits of k in lookup string
               j;                                     Join result on spaces
             j                                      Join result on newlines, implicit print

```

# Answer
> 0 votes
# Deadfish~, 5210 bytes

```
{{i}dd}dc{iii}ic{d}ic{dd}ddc{iii}ic{d}ic{ddd}c{iii}c{i}iiiiic{dddd}iiic{iii}ic{d}ic{{d}i}dc{{i}ddd}dc{iii}ic{d}ic{dd}iiic{iii}iiiiic{d}iic{dddd}c{iii}c{i}iiiiic{ddd}ddc{iii}iiiiic{d}iic{{d}ii}ic{iiiii}iic{iii}iiiiic{d}iic{ddd}iiic{iii}iiiiic{d}iic{dddd}c{iii}c{i}iiiiic{dddd}ddddddc{iiii}iciiiiiic{{d}}{d}iiic{{i}ddd}dc{iii}ic{d}ic{dd}iiic{ii}c{i}c{dddd}dddc{iii}c{i}iiiiic{ddd}ddc{ii}c{i}c{{d}ii}ddc{iiiii}iic{iii}iiiiic{d}iic{ddd}iiic{ii}c{i}c{dddd}dddc{iii}c{i}iiiiic{ddd}dddc{ii}iic{i}iiiiic{{d}i}iic{iiiii}iic{ii}c{i}c{ddd}c{ii}c{i}c{dddd}dddc{iii}c{i}iiiiic{dddd}iic{iii}dddciiiiic{{d}}c{{i}ddd}dc{iii}ic{d}ic{ddd}dc{iiii}iciiiiiic{dddd}ddddddc{iii}c{i}iiiiic{dddd}ddddddc{iiii}iciiiiiic{{d}ii}dddddc{iiiii}iic{iii}iiiiic{d}iic{dddd}dc{iiii}iciiiiiic{dddd}ddddddc{iii}c{i}iiiiic{ddddd}iiic{iii}iiiiiicddc{{d}iii}dc{iiiii}iic{ii}c{i}c{dddd}ddddc{iiii}iciiiiiic{ddd}dddc{ii}dddc{i}dc{dd}ddddddc{iii}iiiiic{d}iic{{d}ii}ic{iiii}ddc{iiii}iciiiiiic{ddddd}iiic{iiii}iciiiiiic{ddd}dddc{ii}dddc{i}dc{ddd}iiic{ii}iic{i}iiiiic{{d}}{d}c{{i}ddd}dc{iii}ic{d}ic{ddd}dc{iii}iiiiic{i}iiic{ddddd}iiic{iii}c{i}iiiiic{dddd}ddddddc{iii}iiiiic{i}iiic{{d}ii}ddddddc{iiiii}iic{iii}iiiiic{d}iic{dddd}dc{iii}iiiiic{i}iiic{dddd}ic{iii}ic{d}ic{dd}iiic{ii}dddc{i}dc{{d}ii}iic{iiiii}iic{ii}c{i}c{dddd}ddddc{iii}iiiiic{i}iiic{ddd}ddddc{ii}dddc{i}dc{dddd}c{iii}iiiiic{i}iiic{{d}ii}ddddddc{iiii}ddc{iiii}iciiiiiic{ddddd}iiic{iii}iiiiic{i}iiic{ddd}ddddc{iii}iiiiic{d}iic{ddd}iiic{ii}dddc{i}dc{{d}ii}iic{iiii}ddc{iii}iiiiic{i}iiic{ddddd}iic{iii}iiiiic{i}iiic{ddd}ddddc{iii}iiiiic{d}iic{ddd}iiic{ii}dddc{i}dc{dddd}c{iii}iiiiic{i}iiic{{d}}{d}iic{{i}ddd}dc{iii}ic{d}ic{dd}iic{ii}iic{i}iiiiic{ddddd}ic{iii}c{i}iiiiic{ddd}dddc{ii}iic{i}iiiiic{{d}i}iic{iiiii}iic{iii}iiiiic{d}iic{ddd}iic{ii}iic{i}iiiiic{ddd}ddddddc{ii}dddc{i}dc{dd}ddddddc{iii}iiiiic{d}iic{{d}ii}ic{iiiii}iic{ii}c{i}c{ddd}dc{ii}iic{i}iiiiic{ddd}ddddddc{ii}dddc{i}dc{dddd}dc{iii}iiiiiicddc{{d}iii}dc{iiii}ddc{iiii}iciiiiiic{ddd}ddddc{ii}iic{i}iiiiic{ddd}ddddddc{iii}iiiiic{d}iic{ddd}iiic{ii}dddc{i}dc{dddd}c{iiii}iciiiiiic{{d}ii}dddddc{iiii}ddc{iii}iiiiic{i}iiic{ddd}dddddc{ii}iic{i}iiiiic{ddd}ddddddc{ii}c{i}c{ddd}c{ii}dddc{i}dc{{d}ii}iic{iiiii}ic{ii}iic{i}iiiiic{dddd}iiic{ii}iic{i}iiiiic{ddd}ddddddc{ii}c{i}c{ddd}c{ii}dddc{i}dc{ddd}iiic{ii}iic{i}iiiiic{{d}}{d}c{{i}ddd}dc{iii}ic{d}ic{dd}iic{ii}ddc{ii}dddc{ddddd}iiic{iii}c{i}iiiiic{ddd}dddc{ii}ddc{ii}dddc{{d}ii}ddddddc{iiiii}iic{iii}iiiiic{d}iic{ddd}iic{ii}ddc{ii}dddc{ddd}ddddc{ii}dddc{i}dc{dddd}c{iiii}iciiiiiic{{d}ii}dddddc{iiiii}iic{ii}c{i}c{ddd}dc{ii}ddc{ii}dddc{ddd}ddddc{iii}iiiiic{d}iic{ddd}iiic{ii}dddc{i}dc{ddd}dc{iii}ic{d}ic{{d}iii}ic{iiii}ddc{iiii}iciiiiiic{ddd}ddddc{ii}ddc{ii}dddc{ddd}ddddc{iii}iiiiic{d}iic{ddd}iiic{ii}dddc{i}dc{dddd}dc{iii}iiiiiicddc{{d}iii}dc{iiii}ddc{iii}iiiiic{i}iiic{ddd}dddddc{ii}ddc{ii}dddc{ddd}ddddc{ii}c{i}c{ddd}c{ii}dddc{i}dc{dddd}c{iii}iiiiic{i}iiic{{d}ii}ddddddc{iiiii}ic{ii}iic{i}iiiiic{dddd}iiic{ii}ddc{ii}dddc{ddddd}iic{iiii}iciiiiiic{ddd}dddc{ii}dddc{i}dc{dd}ddddddc{iii}iiiiic{d}iic{{d}ii}ic{iiiii}ic{ii}ddc{ii}dddc{ddd}dddddc{ii}ddc{ii}dddc{ddddd}iic{iiii}iciiiiiic{ddd}dddc{ii}dddc{i}dc{ddd}ddc{iii}dddciiiiic{{d}}c{{i}ddd}dc{iii}ic{d}ic{ddd}ddc{iii}iiiiiicddc{ddd}ddc{iii}c{i}iiiiic{ddddd}iiic{iii}iiiiiicddc{{d}iii}dc{iiiii}iic{iii}iiiiic{d}iic{dddd}ddc{iii}iiiiiicddc{dd}ic{ii}dddc{i}dc{ddd}iiic{ii}iic{i}iiiiic{{d}i}iic{iiiii}iic{ii}c{i}c{dddd}dddddc{iii}iiiiiicddc{dd}ic{iii}iiiiic{d}iic{ddd}iiic{ii}dddc{i}dc{dddd}c{iiii}iciiiiiic{{d}ii}dddddc{iiii}ddc{iiii}iciiiiiic{ddddd}iic{iii}iiiiiicddc{dd}ic{ii}c{i}c{ddd}c{ii}dddc{i}dc{dd}ddddddc{iii}iiiiic{d}iic{{d}ii}ic{iiii}ddc{iii}iiiiic{i}iiic{ddddd}ic{iii}iiiiiicddc{ddd}dddc{iiii}iciiiiiic{ddd}dddc{ii}dddc{i}dc{{d}ii}iic{iiiii}ic{ii}iic{i}iiiiic{ddddd}dc{iii}iiiiiicddc{ddd}dddc{iiii}iciiiiiic{ddd}dddc{ii}dddc{i}dc{dddd}dc{iii}iiiiiicddc{{d}iii}dc{iiiii}ic{ii}ddc{ii}dddc{ddddd}ic{iii}iiiiiicddc{ddd}dddc{iii}iiiiic{i}iiic{ddd}ddddc{ii}dddc{i}dc{ddd}iiic{ii}iic{i}iiiiic{{d}i}iic{iiii}dddc{iii}iiiiiicddc{ddd}ddddc{iii}iiiiiicddc{dd}c{ii}iic{i}iiiiic{ddd}ddddddc{ii}dddc{i}dc{dddd}c{iiii}iciiiiiic{{d}}{d}iiic{{i}ddd}dc{iii}ic{d}ic{dd}dddc{iii}dddciiiiic{dddd}ic{iii}c{i}iiiiic{dddd}iic{iii}dddciiiiic{{d}ii}iic{iiiii}iic{iii}iiiiic{d}iic{ddd}dddc{iii}dddciiiiic{dd}ddddddc{ii}dddc{i}dc{dddd}dc{iii}iiiiiicddc{{d}iii}dc{iiiii}iic{ii}c{i}c{ddd}ddddddc{iii}dddciiiiic{dd}ddddddc{iii}iiiiic{d}iic{ddd}iiic{ii}dddc{i}dc{ddd}iiic{ii}ddc{ii}dddc{{d}ii}ddddddc{iiii}ddc{iiii}iciiiiiic{dddd}ic{iii}dddciiiiic{dd}ddddddc{ii}c{i}c{ddd}c{ii}dddc{i}dc{ddd}iiic{ii}iic{i}iiiiic{{d}i}iic{iiii}ddc{iii}iiiiic{i}iiic{dddd}c{iii}dddciiiiic{dddd}c{iiii}iciiiiiic{ddd}dddc{ii}dddc{i}dc{dddd}c{iii}iiiiic{i}iiic{{d}ii}ddddddc{iiiii}ic{ii}iic{i}iiiiic{dddd}ddc{iii}dddciiiiic{dddd}c{iii}iiiiic{i}iiic{ddd}ddddc{ii}dddc{i}dc{dddd}c{iiii}iciiiiiic{{d}ii}dddddc{iiiii}ic{ii}ddc{ii}dddc{dddd}c{iii}dddciiiiic{ddd}iiic{ii}iic{i}iiiiic{ddd}ddddddc{ii}dddc{i}dc{dd}ddddddc{ii}c{i}c{{d}ii}ddc{iiii}dddc{iii}iiiiiicddc{dd}dddddc{iii}dddciiiiic{ddd}iiic{ii}ddc{ii}dddc{ddd}ddddc{ii}dddc{i}dc{dd}ddddddc{iii}iiiiic{d}iic{{d}ii}ic{iiii}iiiiiic{iii}dddciiiiic{ddd}ddc{iii}dddciiiiic{dddd}dc{iii}iiiiiicddc{dd}ic{ii}dddc{i}dc{ddd}dc{iii}ic{d}ic{{d}i}dc

```

---
Tags: code-golf, kolmogorov-complexity
---


# Question
Title: Continued Fraction of Digit-wise Sum of Square Roots
# Introduction

Your task is to generate the first 1000 terms in the continued fraction representation of digit-wise sum of square root of 2 and square root of 3.

In other words, produce exactly the following list (but the output format is flexible)

```
[2, 6, 1, 5, 7, 2, 4, 4, 1, 11, 68, 17, 1, 19, 5, 6, 1, 5, 3, 2, 1, 2, 3, 21, 1, 2, 1, 2, 2, 9, 8, 1, 1, 1, 1, 6, 2, 1, 4, 1, 1, 2, 3, 7, 1, 4, 1, 7, 1, 1, 4, 22, 1, 1, 3, 1, 2, 1, 1, 1, 7, 2, 7, 2, 1, 3, 14, 1, 4, 1, 1, 1, 15, 1, 91, 3, 1, 1, 1, 8, 6, 1, 1, 1, 1, 3, 1, 2, 58, 1, 8, 1, 5, 2, 5, 2, 1, 1, 7, 2, 3, 3, 22, 5, 3, 3, 1, 9, 1, 2, 2, 1, 7, 5, 2, 3, 10, 2, 3, 3, 4, 94, 211, 3, 2, 173, 2, 1, 2, 1, 14, 4, 1, 11, 6, 1, 4, 1, 1, 62330, 1, 17, 1, 5, 2, 5, 5, 1, 9, 3, 1, 2, 1, 5, 1, 1, 1, 11, 8, 5, 12, 3, 2, 1, 8, 6, 1, 3, 1, 3, 1, 2, 1, 78, 1, 3, 2, 442, 1, 7, 3, 1, 2, 3, 1, 3, 2, 9, 1, 6, 1, 2, 2, 2, 5, 2, 1, 1, 1, 6, 2, 3, 3, 2, 2, 5, 2, 2, 1, 2, 1, 1, 9, 4, 4, 1, 3, 1, 1, 1, 1, 5, 1, 1, 4, 12, 1, 1, 1, 4, 2, 15, 1, 2, 1, 3, 2, 2, 3, 2, 1, 1, 13, 11, 1, 23, 1, 1, 1, 13, 4, 1, 11, 1, 1, 2, 3, 14, 1, 774, 1, 3, 1, 1, 1, 1, 1, 2, 1, 3, 2, 1, 1, 1, 8, 1, 3, 10, 2, 7, 2, 2, 1, 1, 1, 2, 2, 1, 11, 1, 2, 5, 1, 4, 1, 4, 1, 16, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 8, 1, 2, 1, 1, 22, 3, 1, 8, 1, 1, 1, 1, 1, 9, 1, 1, 4, 1, 2, 1, 2, 3, 5, 1, 3, 1, 77, 1, 7, 1, 1, 1, 1, 2, 1, 1, 27, 16, 2, 1, 10, 1, 1, 5, 1, 6, 2, 1, 4, 14, 33, 1, 2, 1, 1, 1, 2, 1, 1, 1, 29, 2, 5, 3, 7, 1, 471, 1, 50, 5, 3, 1, 1, 3, 1, 3, 36, 15, 1, 29, 2, 1, 2, 9, 5, 1, 2, 1, 1, 1, 1, 2, 15, 1, 22, 1, 1, 2, 7, 1, 5, 9, 3, 1, 3, 2, 2, 1, 8, 3, 1, 2, 4, 1, 2, 6, 1, 6, 1, 1, 1, 1, 1, 5, 7, 64, 2, 1, 1, 1, 1, 120, 1, 4, 2, 7, 3, 5, 1, 1, 7, 1, 3, 2, 3, 13, 2, 2, 2, 1, 43, 2, 3, 3, 1, 2, 4, 14, 2, 2, 1, 22, 4, 2, 12, 1, 9, 2, 6, 10, 4, 9, 1, 2, 6, 1, 1, 1, 14, 1, 22, 1, 2, 1, 1, 1, 1, 118, 1, 16, 1, 1, 14, 2, 24, 1, 1, 2, 11, 1, 6, 2, 1, 2, 1, 1, 3, 6, 1, 2, 2, 7, 1, 12, 71, 3, 2, 1, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 3, 5, 5, 1, 1, 1, 1, 4, 1, 1, 1, 3, 1, 4, 2, 19, 1, 16, 2, 15, 1, 1, 3, 2, 3, 2, 4, 1, 3, 1, 1, 7, 1, 2, 2, 117, 2, 2, 8, 2, 1, 5, 1, 3, 12, 1, 10, 1, 4, 1, 1, 2, 1, 5, 2, 33, 1, 1, 1, 1, 1, 18, 1, 1, 1, 4, 236, 1, 11, 4, 1, 1, 11, 13, 1, 1, 5, 1, 3, 2, 2, 3, 3, 7, 1, 2, 8, 5, 14, 1, 1, 2, 6, 7, 1, 1, 6, 14, 22, 8, 38, 4, 6, 1, 1, 1, 1, 7, 1, 1, 20, 2, 28, 4, 1, 1, 4, 2, 2, 1, 1, 2, 3, 1, 13, 1, 2, 5, 1, 4, 1, 3, 1, 1, 2, 408, 1, 29, 1, 6, 67, 1, 6, 251, 1, 2, 1, 1, 1, 8, 13, 1, 1, 1, 15, 1, 16, 23, 12, 1, 3, 5, 20, 16, 4, 2, 1, 8, 1, 2, 2, 6, 1, 2, 4, 1, 9, 1, 7, 1, 1, 1, 64, 10, 1, 1, 2, 1, 8, 2, 1, 5, 4, 2, 5, 6, 7, 1, 2, 1, 2, 2, 1, 4, 11, 1, 1, 4, 1, 714, 6, 3, 10, 2, 1, 6, 36, 1, 1, 1, 1, 10, 2, 1, 1, 1, 3, 2, 1, 6, 1, 8, 1, 1, 1, 1, 1, 1, 1, 2, 40, 1, 1, 1, 5, 1, 3, 24, 2, 1, 6, 2, 1, 1, 1, 7, 5, 2, 1, 2, 1, 6, 1, 1, 9, 1, 2, 7, 6, 2, 1, 1, 1, 2, 1, 12, 1, 20, 7, 3, 1, 10, 1, 8, 1, 3, 1, 1, 1, 1, 2, 1, 1, 6, 1, 2, 1, 5, 1, 1, 1, 5, 12, 1, 2, 1, 2, 1, 2, 1, 1, 3, 1, 1, 1, 8, 2, 4, 1, 3, 1, 1, 1, 2, 1, 11, 3, 2, 1, 7, 18, 1, 1, 17, 1, 1, 7, 4, 6, 2, 5, 6, 4, 4, 2, 1, 6, 20, 1, 45, 5, 6, 1, 1, 3, 2, 3, 3, 19, 1, 1, 1, 1, 1, 1, 34, 1, 1, 3, 2, 1, 1, 1, 1, 1, 4, 1, 2, 1, 312, 2, 1, 1, 1, 3, 6, 6, 1, 2, 25, 14, 281, 4, 1, 37, 582, 3, 20, 2, 1, 1, 1, 2, 1, 3, 7, 8, 4, 1, 11, 2, 3, 183, 2, 23, 8, 72, 2, 2, 3, 8, 7, 1, 4, 1, 4, 1, 2, 2, 1, 2, 1, 8, 2, 4, 1, 2, 1, 2, 1, 1, 2, 1, 1, 10, 2, 1, 1, 5, 2, 1, 1, 1, 2, 1, 1, 2, 1, 3, 2, 9]

```

# Challenge

The following general introduction to continued fraction is taken from the challenge Simplify a Continued Fraction.

> Continued fractions are expressions that describe fractions iteratively. They can be represented graphically:
>
> Or they can be represented as a list of values: `[a<sub>0</sub>, a<sub>1</sub>, a<sub>2</sub>, a<sub>3</sub>, ... a<sub>n</sub>]`

This challenge is to find out the continued fraction of the digit-wise sum of `sqrt(2)` and `sqrt(3)`, the digit-wise sum is defined as follows,

Take the digits in the decimal representation of `sqrt(2)` and `sqrt(3)`, and obtain the sum digit by digit:

```
    1.  4  1  4  2  1  3  5  6  2  3 ...
+   1.  7  3  2  0  5  0  8  0  7  5 ...
=   2. 11  4  6  2  6  3 13  6  9  8 ...

```

Then only keep the last digit of the sum and compile them back to the decimal representation of a real number

```
    1.  4  1  4  2  1  3  5  6  2  3 ...
+   1.  7  3  2  0  5  0  8  0  7  5 ...
=   2. 11  4  6  2  6  3 13  6  9  8 ...
->  2.  1  4  6  2  6  3  3  6  9  8 ...

```

The digit-wise sum of `sqrt(2)` and `sqrt(3)` is therefore `2.1462633698...`, and when it is expressed with continued fraction, the first 1000 values (i.e. `a<sub>0</sub>` to `a<sub>999</sub>`) obtained are the ones listed in the introduction section.

# Specs

* You may write a function or a full program. Neither should take inputs. In other words, the function or the program should work properly with no inputs. It doesn't matter what the function or program does if non-empty input is provided.
* You should output to STDOUT. Only if your language does not support outputting to STDOUT should you use the closest equivalent in your language.
* You don't need to keep STDERR clean, and stopping the program by error is allowed as long as the required output is made in STDOUT or its equivalents.
* You can provide output through any standard form.
* This is , the lowest number of bytes wins.
* As usual, default loopholes apply here.

# Answer
> 2 votes
# Python 2, ~~193~~ ... ~~179~~ 178 bytes

```
d=10
u=d**2000
v=u*u
def s(n,a=d,i=9):
 while a-i:i,a=a,(a+n/a)/2
 return a
p,q,r,t=s(2*v),s(3*v),1,0
while p:t+=(p+q)%d*r;p/=d;q/=d;r*=d
for i in range(1000):print t/u;t=v/(t%u)

```

Try it online!

Calculating `sqrt(2)` and `sqrt(3)` to such a precision with a short code is a tough job in Python and other languages.

~~2000 digits is needed to ensure the expansion is correct~~ (1020 suffices, but I'm not going to modify it because no improvement), and lines 4-6 is the integer square root.

**193 \> 180 : The digit-wise modulo sum is now carried by a loop instead of array manipulation**

**180 \> 179 : Replaced the 6 occurrences of `10` using `d` with the cost of defining with 5 bytes, cutting 1 byte in total**

**179 \> 178 : Just realized that `a!=i` can be replaced by `a-i`**

# Answer
> 2 votes
# Kotlin 1.1 script, ~~304~~ 293 bytes

```
import java.math.BigDecimal as b
import java.math.*
val m=MathContext(1022)
var B=b(2)
var A=b((""+B.sqrt(m)).zip(""+b(3).sqrt(m)).joinToString(""){(a,b)->if(a=='.')".";else ""+(a-'0'+(b-'0'))%10})
val g=b(1).setScale(1022)
repeat(1000){println(B);A=g/(A-B);B=A.setScale(0,RoundingMode.FLOOR)}

```

A bit verbose unfortunately :/

Must be run with JDK 9, as `sqrt` was added to `BigDecimal` in this release. Interestingly, I couldn't find a TIO site with both Kotlin 1.1 and JDK 9 features (Ideone and repl.it both run Kotlin 1.0, which did not support destructuring in lambdas, and TIO complains that `sqrt` does not exist.)

Prints each element separated by a newline.

Edit (`-11`): moved `println` to the beginning of the loop body and added an additional iteration to avoid repeating the method call. An extra calculation is done, but it is not used for anything.

# Answer
> 1 votes
# Haskell 207 bytes

I Couldn't find an easy way to compute the continued fraction lazilly, so I worked as well with 2000 digits.

```
import Data.Ratio
r#y|x<-[x|x<-[9,8..],r>(y+x)*x]!!0=x:(100*(r-(y+x)*x))#(10*y+20*x)
c r|z<-floor r=z:c(1/(r-z%1))
main=print.take 1000.c$foldl1((+).(10*))(take 2000$(`mod`10)<$>zipWith(+)(3#0)(2#0))%10^1999

```

# Answer
> 1 votes
# Jelly, 32 bytes

```
ȷ*`
%¢¢²¤:
2,3×Ñ×ÑÆ½DS%⁵ḌÇȷÐ¡Ṗ:Ñ

```

Try it online!

---

Basically use fixed-point arithmetic. M may work better here, but somehow `floor(HUGE_NUMBER × sqrt(2)` doesn't want to evaluate for too large `HUGE_NUMBER`. Anyway the fixed-point division is definitely better.

---

Explanation:

```
-------
ȷ*`       Calculate the base for fixed-point arithmetic.
ȷ         Number 1000.
 *        Raise to the power of...
  `       self. (so we have 1000 ** 1000 == 1e3000) Let B=1e3000.

-------
%¢¢²¤:    Given f × B, return a number approximately (1/frac(f)) × B.
          Current value: f × B.
%¢        Modulo by B. Current value: frac(f) × B.
  ¢²¤     B² (that is, 1e6000)
     :    integer-divide by. So we get B²/(frac(f)×B) ≃ 1/frac(f) × B.

-------
2,3×Ñ×ÑÆ½DS%⁵ḌÇȷÐ¡Ṗ:Ñ  Main link.
2,3                    The list [2,3].

    Ñ                  This refers to the next link as a monad, which is the
                       first link (as Jelly links wraparound)
   ×                   Multiply by. So we get [2,3]×1e3000 = [2e3000,3e3000]
     ×Ñ                Again. Current value = [2e6000,3e6000] = [2B²,3B²]

       Æ½              Integer square root.
                       Current value ≃ [sqrt(2B²),sqrt(3B²)]
                                     = [B sqrt(2),B sqrt(3)]

         DS            Decimal digits, and sum together.
           %⁵          Modulo 10.
             Ḍ         Convert back from decimal digits to integer.

                Ð¡     Repeatedly apply...
              Ç          the last link...
               ȷ         for 1000 times, collecting the intermediate results.
                  Ṗ    Pop, discard the last result.
                   :Ñ  Integer divide everything by B.

```

# Answer
> 0 votes
# Deadfish~, 15503 bytes

```
{iiiii}c{dd}iic{ii}iic{dd}ddc{ii}dddc{dd}iiic{ii}ic{dd}dc{ii}iiic{dd}dddc{ii}ddc{dd}iic{ii}c{dd}c{ii}c{dd}c{ii}dddc{dd}iiic{ii}dddcc{dd}iiic{ii}iiciic{dd}ddddc{ii}dddciiiiiic{dd}dddc{ii}dddc{dd}iiic{ii}dddc{i}ddc{dd}dddddc{ii}ic{dd}dc{ii}iic{dd}ddc{ii}dddc{dd}iiic{ii}ic{dd}dc{ii}dc{dd}ic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}dc{dd}ic{ii}ddcdc{dd}iiic{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}ddc{dd}iic{ii}iiiiic{dd}dddddc{ii}iiiic{dd}ddddc{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}iic{dd}ddc{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}c{dd}c{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}dc{dd}ic{ii}iiic{dd}dddc{ii}dddc{dd}iiic{ii}c{dd}c{ii}dddc{dd}iiic{ii}iiic{dd}dddc{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}c{dd}c{ii}ddcc{dd}iic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dc{dd}ic{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}iiic{dd}dddc{ii}ddc{dd}iic{ii}iiic{dd}dddc{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}dc{dd}ic{ii}dddciiic{dd}c{ii}dddc{dd}iiic{ii}c{dd}c{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddciiiic{dd}dc{ii}dddc{dd}iiic{ii}iiiiic{d}iic{dd}iiic{ii}dc{dd}ic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}iiiic{dd}ddddc{ii}iic{dd}ddc{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dc{dd}ic{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}iciiic{dd}ddddc{ii}dddc{dd}iiic{ii}iiiic{dd}ddddc{ii}dddc{dd}iiic{ii}ic{dd}dc{ii}ddc{dd}iic{ii}ic{dd}dc{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}iiic{dd}dddc{ii}ddc{dd}iic{ii}dc{dd}ic{ii}dc{dd}ic{ii}ddcc{dd}iic{ii}ic{dd}dc{ii}dc{dd}ic{ii}dc{dd}ic{ii}dddc{dd}iiic{ii}iiiiic{dd}dddddc{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}iiic{dd}dddc{ii}ic{dd}dc{ii}ddc{dd}iic{ii}dc{dd}ic{ii}dddcdc{d}ddddddc{ii}ddc{dd}iic{ii}dc{dd}ic{ii}dc{dd}ic{ii}c{dd}c{ii}iiiiicdddddc{dd}c{ii}ddcdcc{dd}iiic{ii}dc{dd}ic{ii}ddc{dd}iic{ii}dddciiiiiicddddc{dd}ic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}dddciiic{dd}c{ii}c{dd}c{ii}dddc{dd}iiic{ii}dddcc{dd}iiic{ii}iic{dd}ddc{ii}dddc{dd}iiic{ii}c{dd}c{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}iicddddciccdddc{d}ddddddc{ii}dddc{dd}iiic{ii}dddciiiiiic{dd}dddc{ii}dddc{dd}iiic{ii}ic{dd}dc{ii}ddc{dd}iic{ii}ic{dd}dc{ii}ic{dd}dc{ii}dddc{dd}iiic{ii}iiiiic{dd}dddddc{ii}dc{dd}ic{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}ic{dd}dc{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddcc{dd}iiic{ii}iiiic{dd}ddddc{ii}ic{dd}dc{ii}dddcic{dd}iic{ii}dc{dd}ic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}iiiic{dd}ddddc{ii}iic{dd}ddc{ii}dddc{dd}iiic{ii}dc{dd}ic{ii}dddc{dd}iiic{ii}dc{dd}ic{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}iiicic{dd}ddddc{ii}dddc{dd}iiic{ii}dc{dd}ic{ii}ddc{dd}iic{ii}ccddc{dd}iic{ii}dddc{dd}iiic{ii}iiic{dd}dddc{ii}dc{dd}ic{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}dc{dd}ic{ii}dddc{dd}iiic{ii}dc{dd}ic{ii}ddc{dd}iic{ii}iiiiic{dd}dddddc{ii}dddc{dd}iiic{ii}iic{dd}ddc{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}ddc{dd}iic{ii}ddc{dd}iic{ii}ic{dd}dc{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}iic{dd}ddc{ii}ddc{dd}iic{ii}dc{dd}ic{ii}dc{dd}ic{ii}ddc{dd}iic{ii}ddc{dd}iic{ii}ic{dd}dc{ii}ddc{dd}iic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}iiiiic{dd}dddddc{ii}c{dd}c{ii}c{dd}c{ii}dddc{dd}iiic{ii}dc{dd}ic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}ic{dd}dc{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}c{dd}c{ii}dddcic{dd}iic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}c{dd}c{ii}ddc{dd}iic{ii}dddciiiic{dd}dc{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}dc{dd}ic{ii}ddc{dd}iic{ii}ddc{dd}iic{ii}dc{dd}ic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddciic{dd}ic{ii}dddcc{dd}iiic{ii}dddc{dd}iiic{ii}ddcic{dd}ic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddciic{dd}ic{ii}c{dd}c{ii}dddc{dd}iiic{ii}dddcc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}dc{dd}ic{ii}dddciiic{dd}c{ii}dddc{dd}iiic{ii}iiiccdddc{dd}c{ii}dddc{dd}iiic{ii}dc{dd}ic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}dc{dd}ic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}iiiic{dd}ddddc{ii}dddc{dd}iiic{ii}dc{dd}ic{ii}dddcdc{d}ddddddc{ii}ddc{dd}iic{ii}iiic{dd}dddc{ii}ddc{dd}iic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}dddcc{dd}iiic{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}ic{dd}dc{ii}dddc{dd}iiic{ii}c{dd}c{ii}dddc{dd}iiic{ii}c{dd}c{ii}dddc{dd}iiic{ii}dddciiiiic{dd}ddc{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}iiiic{dd}ddddc{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}ddcc{dd}iic{ii}dc{dd}ic{ii}dddc{dd}iiic{ii}iiiic{dd}ddddc{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}iiiiic{dd}dddddc{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}c{dd}c{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}dc{dd}ic{ii}ic{dd}dc{ii}dddc{dd}iiic{ii}dc{dd}ic{ii}dddc{dd}iiic{ii}iiicc{dd}dddc{ii}dddc{dd}iiic{ii}iiic{dd}dddc{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}ddciiiiic{dd}dddc{ii}dddciiiiic{dd}ddc{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}dddcdc{d}ddddddc{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}ic{dd}dc{ii}dddc{dd}iiic{ii}iic{dd}ddc{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}c{dd}c{ii}dddciiic{dd}c{ii}dcc{dd}ic{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}ddc{i}dddc{dd}dddddc{ii}ddc{dd}iic{ii}ic{dd}dc{ii}dc{dd}ic{ii}iiic{dd}dddc{ii}dddc{dd}iiic{ii}ciiicddddddc{dd}iiic{ii}dddc{dd}iiic{ii}icdddddc{d}ddddddc{ii}ic{dd}dc{ii}dc{dd}ic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dc{dd}ic{ii}dddc{dd}iiic{ii}dc{dd}ic{ii}dciiic{dd}ddc{ii}dddciiiic{dd}dc{ii}dddc{dd}iiic{ii}ddc{i}dddc{dd}dddddc{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}iiiiic{dd}dddddc{ii}ic{dd}dc{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}dddciiiic{dd}dc{ii}dddc{dd}iiic{ii}ddcc{dd}iic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}iiic{dd}dddc{ii}dddc{dd}iiic{ii}ic{dd}dc{ii}iiiiic{dd}dddddc{ii}dc{dd}ic{ii}dddc{dd}iiic{ii}dc{dd}ic{ii}ddc{dd}iic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}iiiic{dd}ddddc{ii}dc{dd}ic{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}c{dd}c{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}iic{dd}ddc{ii}dddc{dd}iiic{ii}iic{dd}ddc{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}ic{dd}dc{ii}iiic{dd}dddc{ii}iicddc{dd}c{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddcicddc{d}ddddddc{ii}dddc{dd}iiic{ii}c{dd}c{ii}ddc{dd}iic{ii}iiic{dd}dddc{ii}dc{dd}ic{ii}ic{dd}dc{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}iiic{dd}dddc{ii}dddc{dd}iiic{ii}dc{dd}ic{ii}ddc{dd}iic{ii}dc{dd}ic{ii}dddciic{dd}ic{ii}ddc{dd}iic{ii}ddc{dd}iic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}cdc{dd}ic{ii}ddc{dd}iic{ii}dc{dd}ic{ii}dc{dd}ic{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}c{dd}c{ii}dddciiic{dd}c{ii}ddc{dd}iic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}ddcc{dd}iic{ii}c{dd}c{ii}ddc{dd}iic{ii}dddcic{dd}iic{ii}dddc{dd}iiic{ii}iiiiic{dd}dddddc{ii}ddc{dd}iic{ii}iic{dd}ddc{ii}dddcdc{d}ddddddc{ii}c{dd}c{ii}iiiiic{dd}dddddc{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}iic{dd}ddc{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddciiic{dd}c{ii}dddc{dd}iiic{ii}ddcc{dd}iic{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddcc{i}dddc{dd}ddddc{ii}dddc{dd}iiic{ii}dddciiiiic{dd}ddc{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddciiic{dd}c{ii}ddc{dd}iic{ii}ddciic{dd}c{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}dddcc{dd}iiic{ii}dddc{dd}iiic{ii}iic{dd}ddc{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dc{dd}ic{ii}iic{dd}ddc{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}ddc{dd}iic{ii}iiic{dd}dddc{ii}dddc{dd}iiic{ii}dddcic{dd}iic{ii}iiicddddddc{dd}iiic{ii}dc{dd}ic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}iiiiic{dd}dddddc{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}iiic{dd}dddc{ii}dddc{dd}iiic{ii}dc{dd}ic{ii}ic{dd}dc{ii}ic{dd}dc{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}c{dd}c{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dc{dd}ic{ii}dddc{dd}iiic{ii}c{dd}c{ii}ddc{dd}iic{ii}dddc{i}ddc{dd}dddddc{ii}dddc{dd}iiic{ii}dddciiiiic{dd}ddc{ii}ddc{dd}iic{ii}dddciiiic{dd}dc{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dc{dd}ic{ii}ddc{dd}iic{ii}dc{dd}ic{ii}ddc{dd}iic{ii}c{dd}c{ii}dddc{dd}iiic{ii}dc{dd}ic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}iiic{dd}dddc{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}ddc{dd}iic{ii}dddcciiiiiic{dd}dddc{ii}ddc{dd}iic{ii}ddc{dd}iic{ii}iiiic{dd}ddddc{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}ic{dd}dc{ii}dddc{dd}iiic{ii}dc{dd}ic{ii}dddcic{dd}iic{ii}dddc{dd}iiic{ii}dddcdc{d}ddddddc{ii}dddc{dd}iiic{ii}c{dd}c{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}ic{dd}dc{ii}ddc{dd}iic{ii}dcc{dd}ic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{i}dddc{dd}ddddc{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}c{dd}c{ii}ddciciiic{dd}ddc{ii}dddc{dd}iiic{ii}dddcc{dd}iiic{ii}c{dd}c{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddcc{dd}iiic{ii}dddciic{dd}ic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}ic{dd}dc{ii}dddc{dd}iiic{ii}dc{dd}ic{ii}ddc{dd}iic{ii}ddc{dd}iic{ii}dc{dd}ic{ii}dc{dd}ic{ii}iiic{dd}dddc{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}iiiic{dd}ddddc{ii}ic{dd}dc{ii}dddciiic{dd}c{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}iic{dd}ddc{ii}iiic{dd}dddc{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}iic{dd}ddc{ii}dddciiic{dd}c{ii}ddcc{dd}iic{ii}iiiic{dd}ddddc{ii}dciiiiic{dd}ddddc{ii}c{dd}c{ii}iic{dd}ddc{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}iiic{dd}dddc{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}ddcddc{d}ddddddc{ii}ddc{dd}iic{ii}ddciiiiiic{dd}ddddc{ii}c{dd}c{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}c{dd}c{ii}ddc{dd}iic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}dc{dd}ic{ii}dddc{dd}iiic{ii}dddciic{dd}ic{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}ic{dd}dc{ii}dddc{dd}iiic{ii}c{dd}c{ii}dddc{dd}iiic{ii}dc{dd}ic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}cddddc{i}ddc{dd}ddddc{ii}dddc{dd}iiic{ii}ddc{i}dddc{dd}dddddc{ii}dddc{dd}iiic{ii}iic{dd}ddc{ii}iicic{dd}dddc{ii}dddc{dd}iiic{ii}iic{dd}ddc{ii}ddciiicddddc{dd}iiic{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}iiiic{dd}ddddc{ii}dddciic{dd}ic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddciiiic{dd}dc{ii}dddc{dd}iiic{ii}dddciiiiic{dd}ddc{ii}ddcic{dd}ic{ii}dddcic{dd}iic{ii}dddc{dd}iiic{ii}dc{dd}ic{ii}ic{dd}dc{ii}ddcddc{d}ddddddc{ii}dddciiiiic{dd}ddc{ii}c{dd}c{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}iiiic{dd}ddddc{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}ddc{dd}iic{ii}iic{dd}ddc{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}c{dd}c{ii}dddc{dd}iiic{ii}iiiiic{dd}dddddc{ii}dddc{dd}iiic{ii}iiic{dd}dddc{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}iicddc{dd}c{ii}dddcdc{d}ddddddc{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}iiiic{dd}ddddc{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}ic{dd}dc{ii}c{dd}c{ii}ddc{dd}iic{ii}ic{dd}dc{ii}iic{dd}ddc{ii}iiic{dd}dddc{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}c{dd}c{ii}dddcc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}c{dd}c{ii}dddc{dd}iiic{ii}iiicddddddciiic{dd}c{ii}iic{dd}ddc{ii}dc{dd}ic{ii}dddcdc{d}ddddddc{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}iic{dd}ddc{ii}dciiic{dd}ddc{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddcdc{d}ddddddc{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dc{dd}ic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}iic{dd}ddc{ii}dddc{dd}iiic{ii}iiiic{dd}ddddc{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}cddddc{d}ddddddc{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}ic{dd}dc{ii}dddc{dd}iiic{ii}dc{dd}ic{ii}ddciic{dd}c{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}iic{dd}ddc{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}iiic{dd}dddc{ii}ic{dd}dc{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}iic{dd}ddc{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}iiiiic{dd}dddddc{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}iiic{dd}dddc{ii}iic{dd}ddc{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}dddcic{dd}iic{ii}dddc{dd}iiic{ii}ddcddc{d}ddddddc{ii}iiic{dd}dddc{ii}dc{dd}ic{ii}dddc{dd}iiic{ii}dddcdc{d}ddddddc{ii}dddc{dd}iiic{ii}iiiic{dd}ddddc{ii}dddc{dd}iiic{ii}dc{dd}ic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}iic{dd}ddc{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}ic{dd}dc{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}ic{dd}dc{ii}dddcic{dd}iic{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dc{dd}ic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}iiiic{dd}ddddc{ii}ddc{dd}iic{ii}c{dd}c{ii}dddc{dd}iiic{ii}dc{dd}ic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}dddcc{dd}iiic{ii}dc{dd}ic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}iiic{dd}dddc{ii}dddc{i}dddc{dd}ddddc{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddciiiiiic{dd}dddc{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}iiic{dd}dddc{ii}c{dd}c{ii}iic{dd}ddc{ii}ddc{dd}iic{ii}ic{dd}dc{ii}iic{dd}ddc{ii}c{dd}c{ii}c{dd}c{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}iic{dd}ddc{ii}ddcddc{d}ddddddc{ii}dddc{dd}iiic{ii}cic{dd}dc{ii}ic{dd}dc{ii}iic{dd}ddc{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dc{dd}ic{ii}ddc{dd}iic{ii}dc{dd}ic{ii}dc{dd}ic{ii}dddc{i}ddc{dd}dddddc{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dcic{dd}c{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dc{dd}ic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}c{dd}c{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}dcddcic{dd}iic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dc{dd}ic{ii}iic{dd}ddc{ii}iic{dd}ddc{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}ddciiic{dd}dc{ii}dddciiic{dd}c{ii}ddciiiiiic{d}iiic{dd}iiic{ii}c{dd}c{ii}dddc{dd}iiic{ii}dciiiic{dd}dddc{ii}iciiicddddddc{dd}iic{ii}dc{dd}ic{ii}ddcddc{d}ddddddc{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}dc{dd}ic{ii}iiic{dd}dddc{ii}iiiic{dd}ddddc{ii}c{dd}c{ii}dddc{dd}iiic{ii}dddcc{dd}iiic{ii}ddc{dd}iic{ii}dc{dd}ic{ii}dddc{i}dddcdddddc{dd}ic{ii}ddc{dd}iic{ii}ddcic{dd}ic{ii}iiiic{dd}ddddc{ii}iiicdddddc{dd}iic{ii}ddc{dd}iic{ii}ddc{dd}iic{ii}dc{dd}ic{ii}iiiic{dd}ddddc{ii}iiic{dd}dddc{ii}dddc{dd}iiic{ii}c{dd}c{ii}dddc{dd}iiic{ii}c{dd}c{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}iiiic{dd}ddddc{ii}ddc{dd}iic{ii}c{dd}c{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddcdc{d}ddddddc{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}ic{dd}dc{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}dddc{dd}iiic{ii}ddc{dd}iic{ii}dddc{dd}iiic{ii}dc{dd}ic{ii}ddc{dd}iic{ii}iiiiic

```

---
Tags: code-golf, math, kolmogorov-complexity, number-theory
---