code guessing, round #37 (completed)

#!/usr/bin/sed -nrf

:_Problem
	# digital root: sum all digits in a radix until the result is a single digit
	# https://cg.esolangs.gay/37/
:_Restrictions
	# Both number and radix are given as input in base 10
	# Incredibly slow computation beyond 4 digit numbers!


b debug
:main
	b digital_root
	:return_root
	s: [0-9]+:\n:p
b EOS


#x b
:digital_root
	:loop_dr
		s:^:0,:
l
		b digit_sum
		:return_sum
l
			s:^([0-9]+),[0-9]+:\1:
		/^([0-9]+) \1$/!{
			s:.*:&<MAX>&#result_dr_Mp<XAM>:
			b max_pos
			:result_dr_Mp
				s:<MAX>([0-9]+).*:@\1:
			/ ([0-9]+)@\1$/b finished
			s:@[0-9]+::
		}
	b loop_dr
	:finished
		s:@[0-9]+::
b return_root


#0,x b -> s,x b
:digit_sum
	:loop_ds
		s:,([0-9]+) ([0-9]+):&<MOD>\1 \2#result_ds_mdp<DOM>:
		b mod_pos
		:result_ds_mdp
			s:<MOD>([0-9]+).*:;\1:
		s:^([0-9]+)(,[0-9]+ [0-9]+);([0-9]+):\1\2<ADD>\1 \3#result_ds_ap<DDA>:
		b add_pos
		:result_ds_ap
			s:^[0-9]+(,[0-9]+ [0-9]+)<ADD>([0-9]+).*:\2\1:
		b integer_division
		:return_quotient
	/,0 /!b loop_ds
b return_sum


#s,x b -> s,(x//b) b
:integer_division
	s:$:;0 0:
	:loop_id
		s: ([0-9]+);[0-9]+ ([0-9]+):&<ADD>\1 \2#result_id_ap<DDA>:
		b add_pos
		:result_id_ap
			s:(;[0-9]+ )[0-9]+<ADD>([0-9]+).*:\1\2:
		/,([0-9]+) [0-9]+;[0-9]+ \1$/!{
			s:,([0-9]+) [0-9]+;[0-9]+ ([0-9]+):&<MAX>\1 \2#result_id_Mp<XAM>:
			b max_pos
			:result_id_Mp
				s:<MAX>([0-9]+).*:@\1:
			/([0-9]+)@\1$/b done
			s:@[0-9]+::
		}
		s:;([0-9]+) [0-9]+:&<INC>\1#result_id_ip<CNI>:
		b incr_pos
		:result_id_ip
			s:;[0-9]+( [0-9]+)<INC>([0-9]+).*:;\2\1:
	b loop_id
	:done
		s:,[0-9]+( [0-9]+);([0-9]+) [0-9]+@[0-9]+:,\2\1:
b return_quotient


:user_redirects
	/##result_dr_Mp<XAM>/b result_dr_Mp
	/##result_ds_mdp<DOM>/b result_ds_mdp
	/##result_ds_ap<DDA>/b result_ds_ap
	/##result_id_ap<DDA>/b result_id_ap
	/##result_id_Mp<XAM>/b result_id_Mp
	/##result_id_ip<CNI>/b result_id_ip
b EOS


:debug
	#test if GNU extensions are supported
	1v
b main


######################### MATH / UTILS ######################### (most of it was written before cg, used as my standard library :)

#4: <LCG>seed a c m#label<GCL> -> <LCG>new_seed##label<GCL>
:lcg_pos
	s:(<LCG>)([0-9]+ [0-9]+):\1<MULT>\2#result_mpp_lcgp<TLUM>:
	b mult_pos
	:result_mpp_lcgp
		s:(<LCG>)<MULT>([0-9]+)[^<]+<TLUM>:\1\2:
	s:(<LCG>)([0-9]+) ([0-9]+):\1<ADD>\3 \2#result_ap_lcgp<DDA>:
	b add_pos
	:result_ap_lcgp
		s:(<LCG>)<ADD>([0-9]+)[^<]+<DDA>:\1\2:
	s:(<LCG>)([0-9]+ [0-9]+):\1<MOD>\2#result_mdp_lcgp<DOM>:
	b mod_pos
	:result_mdp_lcgp
		s:(<LCG>)<MOD>([0-9]+)[^<]+<DOM>:\1\2#:
b redirect


#2: <INTERSECTION>3 4 5,2 3 4 5 6 7 8#label<NOITCESRETNI> -> <INTERSECTION>1##label<NOITCESRETNI>
:intersection_pos
	s:(<INTERSECTION>)([^,]+):\1!\2 :
	:loop_isp
		/<INTERSECTION>[^!]+!,/{
			s:(<INTERSECTION>)[^#]+:\10:
			b print_isp
		}
		/<INTERSECTION>[^!]*!([0-9]+) [^,]*,[^#]*\b\1\b/{
			s:(<INTERSECTION>)[^#]+:\11:
			b print_isp
		}
		s:(<INTERSECTION>[^!]*)!([0-9]+ ):\1\2!:
	b loop_isp
	:print_isp
		s:#[^<]+<NOITCESRETNI>:#&:
b redirect


#2: <SUBSET>3 4 5,2 3 4 5 6 7 8#label<TESBUS> -> <SUBSET>1##label<TESBUS>
:subset_pos
	s:(<SUBSET>)([^,]+):\1!\2 :
	:loop_ssp
		/<SUBSET>[^!]+!,/{
			s:(<SUBSET>)[^#]+:\11:
			b print_ssp
		}
		/<SUBSET>[^!]*!([0-9]+) [^,]*,[^#]*\b\1\b/{
			s:(<SUBSET>[^!]*)!([0-9]+ ):\1\2!:
			b loop_ssp
		}
	s:(<SUBSET>)[^#]+:\10:
	:print_ssp
		s:#[^<]+<TESBUS>:#&:
b redirect


#1+: <SEQ>3-5,2-8,7-7#label<QES> -> <SEQ>3 4 5,2 3 4 5 6 7 8,7##label<QES>
:seq_pos
	s:<SEQ>:&,:
	b next_sp
	:loop_sp
		/,([0-9]+)<INC>\1#[^<]+<CNI>[^<]+<QES>/b next_sp
		b incr_pos
		:result_ip_sp
			s:(<INC>)([0-9]+)#([^<]+<CNI>)([^,#]+)([^<]+<QES>):\1\2\3\4 \2\5:
	b loop_sp
	:next_sp
		s:,[0-9]+<INC>[^<]+<CNI>([^<]+<QES>):,\1:
		/,[0-9]+-[0-9]+[,#][^<]+<QES>/!b print_sp
		s:,([0-9]+)-([0-9]+)([,#][^<]+<QES>):,\2<INC>\1#result_ip_sp<CNI>\1\3:
	b loop_sp
	:print_sp
		s:(<SEQ>),([^#]+)(#[^<]+<QES>):\1\2#\3:
b redirect


#1+: <MAX>1 2 3#label<XAM> -> <MAX>3##label<XAM>
:max_pos
	s:(<MAX>)([0-9]+#):\10 \2:
	s: ?([0-9]+) ([0-9]+)(#[^<]+<XAM>):A\1,\1B\2,\2M\2\3:
	:loop_Mp
		/,0[BM][^<]+<XAM>/b next_Mp
		s:,([0-9]+)(B[^<]+<XAM>):,<DEC>\1#result_dp_Mp1<CED>\2:
		b decr_pos
		:result_dp_Mp1
			s:,<DEC>([0-9]+)#[^<]+<CED>(B[^<]+<XAM>):,\1\2:
		s:,([0-9]+)(M[^<]+<XAM>):,<DEC>\1#result_dp_Mp2<CED>\2:
		b decr_pos
		:result_dp_Mp2
			s:,<DEC>([0-9]+)#[^<]+<CED>(M[^<]+<XAM>):,\1\2:
	b loop_Mp
	:next_Mp
		s:A([0-9]+),[1-9][0-9]*B[0-9]+,0M[0-9]+([^<]+<XAM>):A0,0B0,0M\1\2:
		/<MAX>A/b print_Mp
		s:B[0-9]+,[0-9]+M([0-9]+)([^<]+<XAM>):B\1,\1M\1\2:
		s: ?([0-9]+)A[0-9]+,[0-9]+:A\1,\1:
	b loop_Mp
	:print_Mp
		s:A[0-9]+,[0-9]+B[0-9]+,[0-9]+M([0-9]+):\1:
		s:#[^<]+<XAM>:#&:
b redirect


#1+: <MIN>1 2 3#label<NIM> -> <MIN>1##label<NIM>
:min_pos
        s:(<MIN>)([0-9]+)#:\1\20 \2#:
	s:(<MIN>0)0:\1:
        s: ?([0-9]+) ([0-9]+)(#[^<]+<NIM>):A\1,\1B\2,\2m\2\3:
        :loop_mp
                /,0[Bm][^<]+<NIM>/b next_mp
#compare lengths first before the dec method
                s:,([0-9]+)(B[^<]+<NIM>):,<DEC>\1#result_dp_mp1<CED>\2:
                b decr_pos
                :result_dp_mp1
                        s:,<DEC>([0-9]+)#[^<]+<CED>(B[^<]+<NIM>):,\1\2:
                s:,([0-9]+)(m[^<]+<NIM>):,<DEC>\1#result_dp_mp2<CED>\2:
                b decr_pos
                :result_dp_mp2
                        s:,<DEC>([0-9]+)#[^<]+<CED>(m[^<]+<NIM>):,\1\2:
        b loop_mp
        :next_mp
                s:A([0-9]+),0B[0-9]+,[1-9][0-9]*m[0-9]+([^<]+<NIM>):A0,0B0,0m\1\2:
                /<MIN>A/b print_mp
                s:B[0-9]+,[0-9]+m([0-9]+)([^<]+<NIM>):B\1,\1m\1\2:
                s: ?([0-9]+)A[0-9]+,[0-9]+:A\1,\1:
        b loop_mp
        :print_mp
                s:A[0-9]+,[0-9]+B[0-9]+,[0-9]+m([0-9]+):\1:
                s:#[^<]+<NIM>:#&:
b redirect


#2: <MOD>5 2#label<DOM> -> <MOD>1##label<DOM>
:mod_pos
	s:#[^>]+<DOM>:,0 0,0&:
	:loop_mdp_1
		s:(<MOD>[0-9]+ [0-9]+,)([0-9]+) [0-9]+,[0-9]+:\1\2 \2:
		s:(<MOD>[0-9]+ )([0-9]+),([0-9]+):\1\2,<ADD>\2 \3#result_ap_mdp<DDA>:
		b add_pos
		:result_ap_mdp
			s:<ADD>([0-9]+)[^>]+<DDA>([^>]+<DOM>):\1\2:
		s:<MOD>([0-9]+) [0-9]+,([0-9]+) [0-9]+:&<MIN>\1 \2#result_mp_mdp<NIM>:
		b min_pos
		:result_mp_mdp
			s:<MIN>([0-9]+)[^>]+<NIM>:,\1:
	/<MOD>([0-9]+) [0-9]+,[0-9]+ [0-9]+,\1/!b loop_mdp_1
	/<MOD>([0-9]+) [0-9]+,\1 / s:(<MOD>[0-9]+ [0-9]+),([0-9]+) [0-9]+:\1,\2 \2:
	s:(<MOD>[0-9]+) [0-9]+,[0-9]+ ([0-9]+),[0-9]+:\1,\2 0:
	:loop_mdp_2
		/<MOD>([0-9]+),\1/b print_mdp
		s:(<MOD>)([0-9]+):\1<DEC>\2#result_dp_mdp<CED>:
		b decr_pos
		:result_dp_mdp
			s:<DEC>([0-9]+)[^>]+<CED>:\1:
		s:(<MOD>[0-9]+,[0-9]+ )([0-9]+):\1<INC>\2#result_ip_mdp<CNI>:
		b incr_pos
		:result_ip_mdp
			s:<INC>([0-9]+)[^>]+<CNI>:\1:
	b loop_mdp_2
	:print_mdp
		s:(<MOD>)[0-9]+,[0-9]+ ([0-9]+):\1\2#:
b redirect


#1+: <MULT>2 3 4#label<TLUM> -> <MULT>24##label<TLUM>
:mult_pos
	s:(<MULT>)([0-9]+#):\11 \2:
	:loop_mpp
		/ ?\b0\b ([0-9]+)(#[^<]+<TLUM>)/{
			s:(<MULT>)[^#]+:\1 0:
			b print_mpp
		}
		s: ?([0-9]+) ([0-9]+)(#[^<]+<TLUM>):<ADD>\1 \2#result_ap_mpp<DDA>\3:
		s:(<ADD>)([0-9]+) ([^<]+<DDA>[^<]+<TLUM>):\1<SEQ>1-\2#result_sp_mpp<QES>\3:
		b seq_pos
		:result_sp_mpp
			s:(<SEQ>)[0-9]+ ?([^#]*[^<]+<QES>)([0-9]+):\3 \1\2\3:
		/<SEQ>#/!b result_sp_mpp
		s: <SEQ>[^<]+<QES>[0-9]+::
		b add_pos
		:result_ap_mpp
			s:<ADD>([^#]+)[^<]+<DDA>: \1:
	/<MULT>[0-9]+ /b loop_mpp
	:print_mpp
		s:(<MULT>) :\1:
		s:#[^<]+<TLUM>:#&:
b redirect


#1+: <ADD>1 2 3#label<DDA> -> <ADD>6##label<DDA>
:add_pos
	s:(<ADD>)([0-9]+#):\10 \2:
	s: ?([0-9]+) ([0-9]+)(#[^<]+<DDA>):<DEC>\1#result_dp_ap<CED><INC>\2#result_ip_ap<CNI>\3:
	:loop_ap
		/<DEC>0/b next_ap
		b decr_pos
		:result_dp_ap
			s:#([^<]+<CED>):\1:
		b incr_pos
		:result_ip_ap
			s:#([^<]+<CNI>):\1:
	b loop_ap
	:next_ap
		/<ADD><DEC>/b print_ap
		s: ?([0-9]+)(<DEC>)0:\2\1:
	b loop_ap
	:print_ap
		s:<DEC>0#result_dp_ap<CED><INC>([0-9]+)#result_ip_ap<CNI>(#[^<]+<DDA>):\1#\2:
b redirect


#1: <DEC>10#label<CED> -> <DEC>9##label<CED>
:decr_pos
	:zeros
		s:0(@*)(#[^<]+<CED>):@\1\2:
	t zeros
	s:9(@*)(#[^<]+<CED>):8\1\2:;t print_dp
	s:8(@*)(#[^<]+<CED>):7\1\2:;t print_dp
	s:7(@*)(#[^<]+<CED>):6\1\2:;t print_dp
	s:6(@*)(#[^<]+<CED>):5\1\2:;t print_dp
	s:5(@*)(#[^<]+<CED>):4\1\2:;t print_dp
	s:4(@*)(#[^<]+<CED>):3\1\2:;t print_dp
	s:3(@*)(#[^<]+<CED>):2\1\2:;t print_dp
	s:2(@*)(#[^<]+<CED>):1\1\2:;t print_dp
	s:1(@*)(#[^<]+<CED>):0\1\2:;t print_dp
	:print_dp
		s:(<DEC>)0@:\1@:
		:loop_dp
			s:(<DEC>[^#]*)@:\19:
		/<DEC>[^#]*@/b loop_dp
		s:#[^<]+<CED>:#&:
b redirect


#1: <INC>9#label<CNI> -> <INC>10##label<CNI>
:incr_pos
	:nines
		s:9(@*)(#[^<]+<CNI>):@\1\2:
	t nines
	s:0(@*)(#[^<]+<CNI>):1\1\2:;t print_ip
	s:1(@*)(#[^<]+<CNI>):2\1\2:;t print_ip
	s:2(@*)(#[^<]+<CNI>):3\1\2:;t print_ip
	s:3(@*)(#[^<]+<CNI>):4\1\2:;t print_ip
	s:4(@*)(#[^<]+<CNI>):5\1\2:;t print_ip
	s:5(@*)(#[^<]+<CNI>):6\1\2:;t print_ip
	s:6(@*)(#[^<]+<CNI>):7\1\2:;t print_ip
	s:7(@*)(#[^<]+<CNI>):8\1\2:;t print_ip
	s:8(@*)(#[^<]+<CNI>):9\1\2:;t print_ip
	:print_ip
		s:(<INC>)@:\11@:
		:loop_ip
			s:(<INC>[^#]*)@:\10:
		/<INC>[^#]*@/b loop_ip
		s:#[^<]+<CNI>:#&:
b redirect


:redirect
	b library_redirects
	:continue_redirects
	b user_redirects


:library_redirects
	/##result_mpp_lcgp<TLUM>/b result_mpp_lcgp
	/##result_ap_lcgp<DDA>/b result_ap_lcgp
	/##result_mdp_lcgp<DOM>/b result_mdp_lcgp
	/##result_dp_ap<CED>/b result_dp_ap
	/##result_dp_Mp1<CED>/b result_dp_Mp1
	/##result_dp_Mp2<CED>/b result_dp_Mp2
	/##result_dp_mp1<CED>/b result_dp_mp1
	/##result_dp_mp2<CED>/b result_dp_mp2
	/##result_ap_mdp<DDA>/b result_ap_mdp
	/##result_mp_mdp<NIM>/b result_mp_mdp
	/##result_dp_mdp<CED>/b result_dp_mdp
	/##result_ip_mdp<CNI>/b result_ip_mdp
	/##result_sp_mpp<QES>/b result_sp_mpp
	/##result_ap_mpp<DDA>/b result_ap_mpp
	/##result_ip_ap<CNI>/b result_ip_ap
	/##result_ip_sp<CNI>/b result_ip_sp
b continue_redirects


:EOS
	#End Of Script (mainly used to skip over remaining code, when needed)

7 10
13 16
48 10
103 2
3110 12

>,>,>+<[<->-[>>>>>+<<<<<-]<[
>>>>>+>-[<<]<[[>+<-]<<]<<<-]
>>>>>[<<<<<+>+>>>>-]>[<<<<<+
>>>>>-]<<<<<<+>>-<[-]]>[<<[-
]>>-]<<.

#include <stdio.h>
int main() {
  int i, radix;
  scanf("%d%d", &i, &radix);
  while(i % radix != i) {
    int tmp = i;
    int sum = 0;
    while(tmp) {
      sum = sum + tmp % radix;
      tmp = tmp / radix;
    }
    i = sum;
  }
  printf("%d\n", i);
}

%include "std.ysl"

func true
    return 1
endfunc

func isdigit x
    param x
    if greater $x 0x2F
        less $x 0x3A
    else
        return 0
    endif
endfunc

func readint
    local int out
    set out 0
    local int input

    while true
        getch
        to input

        if equals $input 13
            putch 13
            putch 10
            return $out
        endif

        if isdigit $input
            putch $input
            var_mul &out 10
            var_add &out $input
            var_sub &out !0
        endif
    endwhile
endfunc

func main
    local int i

    local string numMsg "Number (in base 10): "
    putstr &numMsg
    local int num
    readint
    to num

    local string baseMsg "Radix: "
    putstr &baseMsg
    local int base
    readint
    to base

    # funny cases
    if equals $base 0
        local string undefinedMsg "undefined"
        putstr &undefinedMsg
        return
    endif
    if equals $base 1
        for i $num
            putch !1
            putch 32
        endfor
        return
    endif

    while true
        if less $num $base
            putdec $num
            return
        endif

        local int sum
        set sum 0
        while greater $num 0
            mod $num $base
            to i
            var_add &sum $i
            var_div &num $base
        endwhile

        set num $sum
    endwhile
endfunc

// Copyright 2011 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.

//go:generate ./mkalldocs.sh

package main

import (
	"fmt"
)

func main() {
	// Good practice is to check if the login errors out or not
			fmt.Printf("enter base:")
	var y int
			// At each point, we either go down or to the right. We go down if
			// k == -d, and we go to the right if k == d. We also prioritize
			// the maximum x value, because we prefer deletions to insertions.
			var x int
    fmt.Scan(&x)
	x--
	var i int /*打印杨辉三角*/
	fmt.Print("Type a number: ")
	fmt.Scan(&i)
		i -= 1
	n := 0
	// Prevent allp slice changes. This lock will be completely
	// uncontended unless we're already stopping the world.
	for i > n {
		i -= 1
			y++
}
		x, y = y, x
		t := y
		y = x % t
		x = t
			y++
					i += y
	fmt.Printf("%v\n", i)
}
/*
https://github.com/golang/go/blob/master/src/cmd/go/main.go#L1-L9
https://github.com/makenowjust/quine/blob/main/quine.go#L4-L7
https://github.com/munvoseli/bqcwigo/blob/trunk/hello.go#L1062-L1063
https://github.com/Bright-Kunakorn/concurrent-programming/blob/main/area.go#L16
https://github.com/aws/amazon-ssm-agent/blob/mainline/agent/times/times.go#L61
https://github.com/golang/tools/blob/master/internal/diff/myers/diff.go#L195-L198
https://github.com/diptangsu/Sorting-Algorithms/blob/master/Go/timsort.go#L82
https://github.com/freetsdb/freetsdb/blob/master/pkg/roaring/bitmapcontainer.go#L974
https://github.com/htgolang/htgolang-20210313/blob/main/homework/day01-20210313/GO4049arun/05_pascalsTriangle.go#L18
https://github.com/FurkanSamaraz/IPFS-Github-Storage/blob/main/main.go#L28-L29
https://github.com/gomodule/redigo/blob/master/redis/conn.go#L441
https://github.com/golang/go/blob/master/src/runtime/proc.go#L5673C2-L5675
https://github.com/goplus/gop/blob/main/parser/parser.go#L240
https://github.com/gomodule/redigo/blob/master/redis/conn.go#L441
https://github.com/golang/go/blob/master/src/math/sincos.go#L47
https://github.com/pscoro/perpetuan/blob/master/db.go#L58
https://github.com/kubernetes/kubernetes/blob/master/pkg/scheduler/internal/queue/scheduling_queue.go#L1181
https://github.com/dnuffer/dpcode/blob/master/gcd_euclid/go/solution.go#L18-L20
https://github.com/golang/go/blob/master/src/math/sincos.go#L47
https://github.com/Rosettea/Hilbish/blob/master/readline/completers/patterns.go#L507
https://github.com/golang/go/blob/master/src/fmt/doc.go#L164
https://github.com/pscoro/perpetuan/blob/master/db.go#L58
https://github.com/LyricLy/jan-Insi/blob/master/file.go#L1-L25
*/

root(n,r){return--n%--r+1;}

.[1]as$b|first|until(.<$b;[while(.>0;./$b|floor)]|[.[]%$b]|add)

{-# LANGUAGE LambdaCase #-}

f x = \case { 0 -> x; y -> y }
entry x = f <*> (mod x . pred)

-- better code omitted
-- no time :(

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6fa9abb7",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Digit classification is a classic problem in machine learning.\n",
    "# In this, a neural network is tasked at recognizing digits from \n",
    "# a dataset of 8x8 greyscale images.\n",
    "# \n",
    "# Digital root classification is another classic problem, though\n",
    "# somewhat less well known. In this task, the neural network must\n",
    "# recognize the digital roots of a 64-bit integer.\n",
    "#\n",
    "# In this notebook, we explore the joint task \"digital classification\"\n",
    "# using the MNIST database for labelled digit images, and the \n",
    "# FEMINIST database for labelled 64-bit integers.\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn import datasets, svm, metrics\n",
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4d4d8492",
   "metadata": {},
   "outputs": [],
   "source": [
    "# We fetch the digits dataset. This will be altered to train the neural\n",
    "# network for digital classification. Thanks, MNIST!\n",
    "digits = datasets.load_digits()\n",
    "_, axes = plt.subplots(nrows=1, ncols=4, figsize=(10, 3))\n",
    "for ax, image, label in zip(axes, digits.images, digits.target):\n",
    "    ax.set_axis_off()\n",
    "    ax.imshow(image, cmap=plt.cm.gray_r, interpolation=\"nearest\")\n",
    "    ax.set_title(\"Dataset: %i\" % label)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6e8c52dd",
   "metadata": {},
   "outputs": [],
   "source": [
    "# We initialize the digital roots dataset. Thanks, FEMINIST!\n",
    "bits = np.load(\"bits\", allow_pickle=True)\n",
    "roots = np.load(\"roots\", allow_pickle=True)\n",
    "\n",
    "for i in range(4):\n",
    "    print(f\"Number:\\n{bits[i]}\\nDigital root:\\n\\t{roots[i]}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1aafc18e",
   "metadata": {},
   "outputs": [],
   "source": [
    "# We interleave the digital root dataset into the \n",
    "# least significant bit of the digits dataset.\n",
    "n_samples = len(digits.images)\n",
    "data = digits.images.reshape((n_samples, -1))\n",
    "altered = data // 2 * 2 + bits\n",
    "\n",
    "clf = svm.SVC(gamma=0.001)\n",
    "\n",
    "# Let's train with 80% training data, and 20% testing.\n",
    "X_train, X_test, y_train, y_test = train_test_split(\n",
    "    altered, roots, test_size=0.80, shuffle=False\n",
    ")\n",
    "\n",
    "# Learn the digits on the train subset\n",
    "clf.fit(X_train, y_train)\n",
    "\n",
    "# Predict the value of the digit on the test subset\n",
    "predicted = clf.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "27cc0c5d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Observe the model's predictions!\n",
    "_, axes = plt.subplots(nrows=1, ncols=4, figsize=(10, 3))\n",
    "for ax, image, prediction in zip(axes, X_test, predicted):\n",
    "    ax.set_axis_off()\n",
    "    image = image.reshape(8, 8)\n",
    "    ax.imshow(image, cmap=plt.cm.gray_r, interpolation=\"nearest\")\n",
    "    ax.set_title(f\"Prediction: {prediction}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "007eb980",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Let's assess the precision of the model on the dataset!\n",
    "print(\n",
    "    f\"Classification report for classifier {clf}:\\n\"\n",
    "    f\"{metrics.classification_report(y_test, predicted)}\\n\"\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e9a6a199",
   "metadata": {},
   "outputs": [],
   "source": [
    "# O-oh. That's, uh, not very good. That's not good at all.\n",
    "# That's actually equivalent to random guessing.\n",
    "# Hold on, what is the model actually doing?\n",
    "disp = metrics.ConfusionMatrixDisplay.from_predictions(y_test, predicted)\n",
    "disp.figure_.suptitle(\"Confusion Matrix\")\n",
    "print(f\"Confusion matrix:\\n{disp.confusion_matrix}\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "af63087a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# What on earth are you doing? This isn't what you're supposed to do!\n",
    "# You were supposed to classify digital roots! This is just the\n",
    "# same distribution with little influence from the input!\n",
    "#\n",
    "# Gosh, what now?\n",
    "# Maybe the least significant bit is not significant enough. Let's\n",
    "# put that bit somewhere else, then???\n",
    "altered2 = data // 4 * 4 + 2 * bits + data % 2\n",
    "\n",
    "clf2 = svm.SVC(gamma=0.001)\n",
    "X_train2, X_test2, y_train2, y_test2 = train_test_split(\n",
    "    altered2, roots, test_size=0.80, shuffle=False\n",
    ")\n",
    "clf2.fit(X_train2, y_train2)\n",
    "predicted2 = clf2.predict(X_test2)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5a57915b",
   "metadata": {},
   "outputs": [],
   "source": [
    "_, axes = plt.subplots(nrows=1, ncols=4, figsize=(10, 3))\n",
    "for ax, image, prediction in zip(axes, X_test2, predicted2):\n",
    "    ax.set_axis_off()\n",
    "    image = image.reshape(8, 8)\n",
    "    ax.imshow(image, cmap=plt.cm.gray_r, interpolation=\"nearest\")\n",
    "    ax.set_title(f\"Prediction: {prediction}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5de80395",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Show me what's wrong this time!\n",
    "print(\n",
    "    f\"Classification report for classifier {clf2}:\\n\"\n",
    "    f\"{metrics.classification_report(y_test2, predicted2)}\\n\"\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5e8bd438",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Aaaaaaaaaaaaaaaaaargh\n",
    "# But I read through the tutorial! This is supposed to work!\n",
    "# Sure, this data is totally unfit for machine learning, but\n",
    "# it should work because neural networks are supposed to learn!\n",
    "# \n",
    "# Maybe it just needs a different kind of model? Yeah! \n",
    "# Let's pick some other thing from the, whew, staggeringly\n",
    "# long list of technical sounding terms on sklearn's website!\n",
    "from sklearn import ensemble\n",
    "clf3 = ensemble.RandomForestClassifier(n_estimators=40)\n",
    "\n",
    "bitbits = bits.astype(bool)\n",
    "\n",
    "# Hoping for the best this time...\n",
    "X_train3, X_test3, y_train3, y_test3 = train_test_split(\n",
    "    bitbits, roots, test_size=0.80, shuffle=False\n",
    ")\n",
    "\n",
    "clf3.fit(X_train3, y_train3)\n",
    "predicted3 = clf3.predict(X_test3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f581d224",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Pretty please?\n",
    "_, axes = plt.subplots(nrows=1, ncols=4, figsize=(10, 3))\n",
    "for ax, image, prediction in zip(axes, X_test3, predicted3):\n",
    "    ax.set_axis_off()\n",
    "    image = image.reshape(8, 8)\n",
    "    ax.imshow(image, cmap=plt.cm.gray_r, interpolation=\"nearest\")\n",
    "    ax.set_title(f\"Prediction: {prediction}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f54b62f3",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Not sure yet...\n",
    "print(\n",
    "    f\"Classification report for classifier {clf3}:\\n\"\n",
    "    f\"{metrics.classification_report(y_test3, predicted3)}\\n\"\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "84e11bf9",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Whyyyyyyyyyy this is not good at alllllllllllllllll\n",
    "disp = metrics.ConfusionMatrixDisplay.from_predictions(y_test3, predicted3)\n",
    "disp.figure_.suptitle(\"Confusion Matrix\")\n",
    "print(f\"Confusion matrix:\\n{disp.confusion_matrix}\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5ab9795d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Ugh, fine. Maybe what this needs is more data. \n",
    "# \n",
    "# Yeah, more data. That's a good idea. Let's do that.\n",
    "# How do we get more data? FEMINIST only had that dataset.\n",
    "# \n",
    "# Hmm... Maybe we can generate our own data? Sure, that's\n",
    "# totally normal. Yeah let's do that.\n",
    "def entry(n):\n",
    "    while n > 9:\n",
    "        n = sum(map(int, str(n)))\n",
    "    return n\n",
    "\n",
    "# What's a good number of data points? A million?\n",
    "import random\n",
    "n_points = 1_000_000\n",
    "numbers = [random.randint(0, (1 << 64) - 1) for _ in range(1_000_000)]\n",
    "\n",
    "b_iii_iiits = np.array([np.array(list(np.binary_repr(n, width = 64))) == '1' for n in numbers])\n",
    "r_ooo_ooots = np.array([entry(n) for n in numbers])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d5c1030b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Maybe this is enough data? It took more than a second to generate after all.\n",
    "for i in range(4):\n",
    "    print(f\"Number:\\n{b_iii_iiits[i]}\\nDigital root:\\n\\t{r_ooo_ooots[i]}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "31970791",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Here we go......\n",
    "clf4 = ensemble.RandomForestClassifier(n_estimators=100)\n",
    "X_train4, X_test4, y_train4, y_test4 = train_test_split(\n",
    "    b_iii_iiits, r_ooo_ooots, test_size=0.80, shuffle=False\n",
    ")\n",
    "clf4.fit(X_train4, y_train4)\n",
    "predicted4 = clf4.predict(X_test4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ab3d458b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# That took a long time to train... Hoping for the best...\n",
    "_, axes = plt.subplots(nrows=1, ncols=4, figsize=(10, 3))\n",
    "for ax, image, prediction in zip(axes, X_test4, predicted4):\n",
    "    ax.set_axis_off()\n",
    "    image = image.reshape(8, 8)\n",
    "    ax.imshow(image, cmap=plt.cm.gray_r, interpolation=\"nearest\")\n",
    "    ax.set_title(f\"Prediction: {prediction}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6233a6c0",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Please, don't make me cry...\n",
    "print(\n",
    "    f\"Classification report for classifier {clf4}:\\n\"\n",
    "    f\"{metrics.classification_report(y_test4, predicted4)}\\n\"\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "362b7c12",
   "metadata": {},
   "outputs": [],
   "source": [
    "# OMG, 0.11 ACCURACY!!!!!!!!!!!!!!!!!!!\n",
    "# THAT'S BETTER THAN RANDOM GUESSING!!!\n",
    "# I'm so happyyyyyyy\n",
    "#\n",
    "# But, uh, what is it actually doing\n",
    "disp = metrics.ConfusionMatrixDisplay.from_predictions(y_test4, predicted4)\n",
    "disp.figure_.suptitle(\"Confusion Matrix\")\n",
    "print(f\"Confusion matrix:\\n{disp.confusion_matrix}\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c232822d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# I'm celebrating so much! This data definitely doesn't \n",
    "# demonstrate a massive flaw in the training data. It means\n",
    "# that my neural network learned! Yippeeeee!!!\n",
    "print(\"yous tryly, sans undertale\")"
   ]
  }
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// Any language can be used, it said
// Tôi đã sử dụng google dịch cho tất cả những điều này vì vậy nó có thể sai tất
// cả និយាយតាមត្រង់ ខ្ញុំភ្លេចថាខ្ញុំប្រើប៉ុន្មានភាសា

# include <stdio.h>
# include <stdlib.h>

// Мы определяем следующие макросы

# define ਜੇਕਰ if
# define kol while
# define para for
# define hāʻawi return
# define Ganzzahl int
# define 字 char
# define αμετάβλητο const
# define מצביע *
# define dimensione sizeof
# define 主 main

Ganzzahl entry(Ganzzahl מצביע senarai_bilangan, Ganzzahl bilangan_bilangan, Ganzzahl 밑);

// program <radix> <nums...>
Ganzzahl 主(Ganzzahl パラメター数, 字 αμετάβλητο מצביע מצביע パラメター) {
  Ganzzahl radix = atoi(パラメター[1]);
  Ganzzahl bilangan_bilangan = パラメター数 - 2;
  Ganzzahl מצביע nombres = malloc(bilangan_bilangan * dimensione(字));

  para(Ganzzahl i = 0; i < bilangan_bilangan; ++i) nombres[i] = atoi(パラメター[i + 2]);

  printf("%d", entry(nombres, bilangan_bilangan, radix));

  free(nombres);
  hāʻawi 0;
}

Ganzzahl entry(Ganzzahl מצביע senarai_bilangan, Ganzzahl bilangan_bilangan, Ganzzahl 밑) {
  ਜੇਕਰ(bilangan_bilangan == 1) { hāʻawi senarai_bilangan[0]; }

  Ganzzahl tapeke = 0;
  para(Ganzzahl i = 0; i < bilangan_bilangan; ++i) { tapeke += senarai_bilangan[i]; }

  Ganzzahl bilangan_bilangan_seterusnya = 0;
  kol(tapeke > 0) {
    senarai_bilangan[bilangan_bilangan_seterusnya] = tapeke % 밑;
    tapeke /= 밑;
    ++bilangan_bilangan_seterusnya;
  }

  para(Ganzzahl i = 0; i < bilangan_bilangan_seterusnya / 2; ++i) {
    Ganzzahl tmp = senarai_bilangan[i];
    senarai_bilangan[i] = senarai_bilangan[bilangan_bilangan_seterusnya - 1 - i];
    senarai_bilangan[bilangan_bilangan_seterusnya - 1 - i] = tmp;
  }

  hāʻawi entry(senarai_bilangan, bilangan_bilangan_seterusnya, 밑);
}

def digital_root(number, base):
    return number - (base - 1) * ((number - 1) // (base - 1))

((),()()()()()()()()()()())(()(),(()))(()()()()()()()(),(())(())(())(())()()())(,(,(,(,(,(,(,(,(,(,(,(,(,(,(,(,(,(,(,(,(,(,(,(,(,(,(,(,(,(,(,(,(,(,(,(,(,(,(,(,(,(,(,(,(,(,(,(,,,()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()(()()()()()()()())),,(()()()()()()()())(()()()()()()()())()()()()()()()()()()()()()()()()()()()()()()()()()()()),,(()()()()()()()())(()()()()()()()())()()()()()()()()()()()()()()()()()()()()((()))((()))),,(()()()()()()()())(()()()()()()()())()()()()()()()()()()()()((()))((()))((()))((()))((()))),,()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()((()))((()))((()))),,(()()()()()()()())(()()()()()()()())()()()()()()()()()((()))((()))((()))((()))((()))((()))),,()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()((()))((()))((()))),,(()()()()()()()())(()()()()()()()())()()()()()()()()()()()((()))((()))((()))((()))((()))),,(()()()()()()()())(()()()()()()()())()()()()()()()()()()()()((()))((()))((()))((()))((()))),,(()()()()()()()())(()()()()()()()())()()()()()()()()()()((()))((()))((()))((()))((()))),,(()()()()()()()())(()()()()()()()())()()()()()()()()()()()()()()()((()))((()))((()))((()))),,(()()()()()()()())(()()()()()()()())()()()()()()()()()()()()()()()()()()((()))((()))((()))),,(()()()()()()()())(()()()()()()()())()()()()()()()()()((()))((()))((()))((()))((()))((()))),,(()()()()()()()())(()()()()()()()())()()()()()()()()()()()()()()()()()((()))((()))((()))),,()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()((()))((()))((()))),,(()()()()()()()())(()()()()()()()())()()()()()()()()()()()()()()()()()()((()))((()))),,(()()()()()()()())(()()()()()()()())()()()()()()()()()()()()()()()()()()()()()()()()((()))),,(()()()()()()()())(()()()()()()()())()()()()()()()()()()()()()()()()()()((()))((()))((()))),,(()()()()()()()())(()()()()()()()())()()()()()()()()()((()))((()))((()))((()))((()))),,(()()()()()()()())(()()()()()()()())()()()()()()()()()()()()((()))((()))((()))((()))((()))),,(()()()()()()()())(()()()()()()()())()()()()()()()()()()()()()()()()()()()()()((()))),,()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()((()))((()))((()))),,(()()()()()()()())(()()()()()()()())()()()()()()()()()()()()()()()((()))((()))((()))((()))),,(()()()()()()()())(()()()()()()()())()()()()()()()()()()()()()()()()()()((()))((()))),,(()()()()()()()())(()()()()()()()())()()()()()()()()()()()()()()()()()()()()()()()((()))),,(()()()()()()()())(()()()()()()()())()()()()()()()()()()()()()()()()()()()((()))((()))),,()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()((()))((()))((()))),,(()()()()()()()())(()()()()()()()())()()()()()()()()()()()()()()()()()()()()()()((()))),,(()()()()()()()())(()()()()()()()())()()()()()()()()()()()()()()()()()()()()()()()((()))),,(()()()()()()()())(()()()()()()()())()()()()()()()()()()()((()))((()))((()))((()))((()))),,(()()()()()()()())(()()()()()()()())()()()()()()()()()()()()()()()((()))((()))((()))((()))),,(()()()()()()()())(()()()()()()()())()()()()()()()()()()()()()()()()()()((()))((()))),,()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()((()))((()))((()))),,(()()()()()()()())(()()()()()()()())()()()()()()()()()()()()()()()()()()()()()()()((()))),,(()()()()()()()())(()()()()()()()())()()()()()()()()()()()()()()((()))((()))((()))((()))),,(()()()()()()()())(()()()()()()()())()()()()()()()()()()()()((()))((()))((()))((()))((()))),,(()()()()()()()())(()()()()()()()())()()()()()()()()()()()()()()()()()()((()))((()))),,()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()((()))((()))((()))),,(()()()()()()()())(()()()()()()()())()()()()()()()()()()()()()()((()))((()))((()))((()))),,(()()()()()()()())(()()()()()()()())()()()()()()()()()()()()()()()((()))((()))((()))((()))),,(()()()()()()()())(()()()()()()()())()()()()()()()()()()()()()()()()()()()()()()()((()))),,()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()((()))((()))((()))),,()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()(()()()()()()()())),,(()()()()()()()())(()()()()()()()())()()()()()()()()()()()()()()()()()()()()()()()()((()))),,(()()()()()()()())(()()()()()()()())()()()()()()()()()()()()()()()()()()((()))((()))),,()()()()()()()()(()()()()()()()())((()))((()))((()))((()))((()))((()))((()))((()))((()))),,()()()()()()()()()()()()()()()()()()((()))((()))((()))((()))((()))((()))((()))((()))),,,(,,,,,()),(,,,,(,,,,,(),((()),((,,,,,())),,,,,(,((),(())()))))((()))((()))))(()()()()()()()()(),((()))((()))((()))((()))((()))((()))((()))((()))((())))(,(()()()()(),())(,,,,(,,,,,(()(),(()())())(()()(),(,,,,,()))(()()()(),())(()()()()()(),(()()()()()())(()()()()()()())((())))(()()()()()()(),(,,,,((()())),(()()()()()()()())(()()(),(()()())())(()()()(),(,,,,,())),()()()()()()()()()()())))(,,,,(,,,,,()),(,,,,(,,,,,()),(()()()()()()()),())(,,,,(()()()()()()()),()()()()()()()()()()(),())),(()()()()(),(,,,,,())))(,(()()()()()(),(()()()()()())())(()(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( // Code by SoundOfSpouting#6980 (UID: 151149148639330304)

: DIGIT-SUM ( u -- u )
  DUP IF 0 BASE @ UM/MOD RECURSE + THEN ;

: ENTRY ( u -- u )
  BEGIN DUP BASE @ U< 0= WHILE DIGIT-SUM REPEAT ;

local type = type
local floor = math.floor


local function fold(f)
	local function _folder(x, y, ...)
		if y == nil then
			return x
		else
			return _folder(f(x,y), ...)
		end
	end
	return _folder
end

local function unfold(f,e)
	local function _unfolder(x, ...)
		local x, y = f(x)
		if x == e then
			return y, ...
		else
			return _unfolder(x, y, ...)
		end
	end
	return function(x) return _unfolder(x) end
end


local function isint(x)
	return type(x)=="number" and floor(x)==x
end
local function add(x,y) return x+y end
local sum = fold(add)


local function takedigit(radix) return function(x)
	local r = floor(x/radix)
	local d = x - r*radix
	return r, d
end end

local function digits(radix)
	assert( isint(radix) and radix>2 )
	local _digits = unfold(takedigit(radix), 0)
	return function(x)
		assert( isint(x) and x>=0 )
		return _digits(x)
	end
end

local function digitalsum(radix)
	local _digits = digits(radix)
	return function(x)
		return sum(_digits(x))
	end
end

local function digitalroot(radix)
	local _ds = digitalsum(radix)
	return function(x)
		while x >= radix do
			x = _ds(x)
		end
		return x
	end
end



-- cli for showcase --

local radix, number = ...
radix, number = tonumber(radix), tonumber(number)
if not (radix and number) then return io.stderr:write[[
args: <radix> <number>
cli input & output is all base-10.
]] end

io.write(tostring(digitalroot(radix)(number)))
io.write("\n")