Merge pull request #3650 from Abigail/abigail/week-102

Abigail/week 102

36 files changed, 1906 insertions, 78 deletions

diff --git a/challenge-102/abigail/README.md b/challenge-102/abigail/README.md
index caf1448381..687594c5f5 100644
--- a/challenge-102/abigail/README.md
+++ b/challenge-102/abigail/README.md
@@ -1,65 +1,52 @@
 # Solution by Abigail
-## [Pack a Spiral](https://perlweeklychallenge.org/blog/perl-weekly-challenge-101/#TASK1)
+## [Rare Numbers](https://perlweeklychallenge.org/blog/perl-weekly-challenge-102/#TASK1)
 
-You are given an array `@A` of items (integers say, but they can be anything).
 
-Your task is to pack that array into an `MxN` matrix spirally
-counterclockwise, as tightly as possible.
+You are given a positive integer `$N`.
 
-'Tightly' means the absolute value `|M-N|` of the difference has to be as
-small as possible
+Write a script to generate all Rare numbers of size `$N` if exists.
+Please checkout [the page](http://www.shyamsundergupta.com/rare.htm)
+for more information about it.
 
 ### Examples
-#### Example 1
 ~~~~
-Input: @A = (1,2,3,4)
-
-Output:
-
-    4 3
-    1 2
+(a) 2 digits: 65
+(b) 6 digits: 621770
+(c) 9 digits: 281089082
 ~~~~
 
-Since the given array is already a `1x4` matrix on its own, but that's
-not as tight as possible. Instead, you'd spiral it counterclockwise into
+### Notes
 
-~~~~
-    4 3
-    1 2
-~~~~
-#### Example 2
-~~~~
-Input: @A = (1..6)
+There is no simple efficient algorithm for spitting out rare numbers;
+at least not one which can be easily found online.
 
-Output:
+The code fragments in the OEIS only give code to check whether a 
+number is a rare number, and they don't suggest anything other
+than "try all numbers" if you want to find all of the numbers of a
+certain length. 
 
-    6 5 4
-    1 2 3
-~~~~
-or
-~~~~
-    5 4
-    6 3
-    1 2
-~~~~
-Either will do as an answer, because they're equally tight.
+Shyam writes: [*I have developed a computer program in Fortran to
+calculate Rare numbers. In fact with refinement of the code over
+the years, the program has been made so powerful that all numbers
+up to 10^14 can be just checked for Rare numbers in less than a
+minute on Pentium III PC. In few hours I have been able to check
+up to 10^18.*](https://www.primepuzzles.net/conjectures/conj_023.htm)
+but he does not publish his code.
 
-#### Example 3
-~~~~
-Input: @A = (1..12)
+Richard Guy writes [*Here are three problems that have come to light
+recently, each of which can consume unlimited amounts of computer time,
+perhaps without revealing anything
+significant*.](https://www.jstor.org/stable/2325149?seq=1)
+The rare numbers are one of the three problems.
+
+So, we just include a [list of all know rare numbers,
+up to 10^22](https://oeis.org/A035519/b035519.txt) 
+and preprocess them so they're bucketed to length. Then it's just
+a matter of reading the desired length, and printing the appropriate
+entry (or the empty string if no rare numbers of that length exist).
+There are only 124 known rare numbers, so preprocessing is very
+feasible.
 
-Output:
-       9  8  7 6
-      10 11 12 5
-       1  2  3 4
-~~~~
-or
-~~~~
-       8  7 6
-       9 12 5
-      10 11 4
-       1  2 3
-~~~~
 
 ### Solutions
 * [AWK](awk/ch-1.awk)
@@ -71,52 +58,38 @@ or
 * [Python](python/ch-1.py)
 * [Ruby](ruby/ch-1.rb)
 
-### Blog
-[Perl Weekly Challenge 101: Pack a Spiral](https://wp.me/pcxd30-r7)
 
+## [Hash-counting String](https://perlweeklychallenge.org/blog/perl-weekly-challenge-102/#TASK2)
 
-## [Origin-containing Triangle](https://perlweeklychallenge.org/blog/perl-weekly-challenge-101/#TASK2)
+You are given a positive integer `$N`.
 
-You are given three points in the plane, as a list of six co-ordinates:
-`A=(x1,y1)`, `B=(x2,y2)` and `C=(x3,y3)`.
+Write a script to produce Hash-counting string of that length.
 
-Write a script to find out if the triangle formed by the given three
-co-ordinates contain origin `(0,0)`.
+The definition of a hash-counting string is as follows:
+- the string consists only of digits 0-9 and hashes, `'#'`.
+- there are no two consecutive hashes: `"##"z does not appear in your string
+- the last character is a hash
+- the number immediately preceding each hash (if it exists) is the position
+  of that hash in the string, with the position being counted up from 1
 
-Print `1` if found otherwise `0`.
+It can be shown that for every positive integer `N` there is exactly one
+such length-`N` string.
 
 ### Examples
-#### Example 1
-~~~~
-Input: A=(0,1), B=(1,0) and C=(2,2)
-
-Output: 0 because that triangle does not contain (0,0).
 ~~~~
-
-#### Example 2
-~~~~
-Input: A=(1,1), B=(-1,1) and C=(0,-3)
-
-Output: 1 because that triangle contains (0,0) in its interior.
-~~~~
-
-#### Example 3
-~~~~
-Input: A=(0,1), B=(2,0) and C=(-6,0)
-
-Output: 1 because (0,0) is on the edge connecting B and C.
+(a) "#" is the counting string of length 1
+(b) "2#" is the counting string of length 2
+(c) "#3#" is the string of length 3
+(d) "#3#5#7#10#" is the string of length 10
+(e) "2#4#6#8#11#14#" is the string of length 14
 ~~~~
 
 ### Solutions
 * [AWK](awk/ch-2.awk)
 * [Bash](bash/ch-2.sh)
-* [Befunge-93](befunge-93/ch-2.bf93)
 * [C](c/ch-2.c)
 * [Lua](lua/ch-2.lua)
 * [Node.js](node/ch-2.js)
 * [Perl](perl/ch-2.pl)
 * [Python](python/ch-2.py)
 * [Ruby](ruby/ch-2.rb)
-
-### Blog
-[Perl Weekly Challenge 101: Origin-containing Triangle](https://wp.me/pcxd30-s8)
diff --git a/challenge-102/abigail/awk/ch-1.awk b/challenge-102/abigail/awk/ch-1.awk
new file mode 100644
index 0000000000..ccfb3cd023
--- /dev/null
+++ b/challenge-102/abigail/awk/ch-1.awk
@@ -0,0 +1,151 @@
+#!/usr/bin/awk
+
+#
+# See ../README.md
+#
+
+#
+# Run as: awk -f ch-1.awk < input-file
+#
+
+#
+# Load the list of all known rare numbers. Note that we're using
+# strings instead of numbers, since the largest number exceed
+# the largest integer AWK stores losslessly.
+#
+BEGIN {
+    rare_numbers [ 2] =                     "65\n"
+    rare_numbers [ 6] =                 "621770\n"
+    rare_numbers [ 9] =              "281089082\n"
+    rare_numbers [10] =             "2022652202\n" \
+                                    "2042832002\n"
+    rare_numbers [12] =           "868591084757\n" \
+                                  "872546974178\n" \
+                                  "872568754178\n"
+    rare_numbers [13] =          "6979302951885\n"
+    rare_numbers [14] =         "20313693904202\n" \
+                                "20313839704202\n" \
+                                "20331657922202\n" \
+                                "20331875722202\n" \
+                                "20333875702202\n" \
+                                "40313893704200\n" \
+                                "40351893720200\n"
+    rare_numbers [15] =        "200142385731002\n" \
+                               "204238494066002\n" \
+                               "221462345754122\n" \
+                               "244062891224042\n" \
+                               "245518996076442\n" \
+                               "248359494187442\n" \
+                               "403058392434500\n" \
+                               "441054594034340\n" \
+                               "816984566129618\n"
+    rare_numbers [16] =       "2078311262161202\n" \
+                              "2133786945766212\n" \
+                              "2135568943984212\n" \
+                              "2135764587964212\n" \
+                              "2135786765764212\n" \
+                              "4135786945764210\n" \
+                              "6157577986646405\n" \
+                              "6889765708183410\n" \
+                              "8052956026592517\n" \
+                              "8052956206592517\n" \
+                              "8191154686620818\n" \
+                              "8191156864620818\n" \
+                              "8191376864400818\n" \
+                              "8650327689541457\n" \
+                              "8650349867341457\n"
+    rare_numbers [17] =      "22542040692914522\n" \
+                             "67725910561765640\n" \
+                             "86965750494756968\n"
+    rare_numbers [18] =     "225342456863243522\n" \
+                            "225342458663243522\n" \
+                            "225342478643243522\n" \
+                            "284684666566486482\n" \
+                            "284684868364486482\n" \
+                            "297128548234950692\n" \
+                            "297128722852950692\n" \
+                            "297148324656930692\n" \
+                            "297148546434930692\n" \
+                            "497168548234910690\n" \
+                            "619431353040136925\n" \
+                            "619631153042134925\n" \
+                            "631688638047992345\n" \
+                            "633288858025996145\n" \
+                            "633488632647994145\n" \
+                            "653488856225994125\n" \
+                            "811865096390477018\n" \
+                            "865721270017296468\n" \
+                            "871975098681469178\n" \
+                            "898907259301737498\n"
+    rare_numbers [19] =    "2042401829204402402\n" \
+                           "2060303819041450202\n" \
+                           "2420424089100600242\n" \
+                           "2551755006254571552\n" \
+                           "2702373360882732072\n" \
+                           "2825378427312735282\n" \
+                           "6531727101458000045\n" \
+                           "6988066446726832640\n" \
+                           "8066308349502036608\n" \
+                           "8197906905009010818\n" \
+                           "8200756128308135597\n" \
+                           "8320411466598809138\n"
+    rare_numbers [20] =   "22134434735752443122\n" \
+                          "22134434753752443122\n" \
+                          "22134436953532443122\n" \
+                          "22136414517954423122\n" \
+                          "22136414971554423122\n" \
+                          "22136456771730423122\n" \
+                          "61952807156239928885\n" \
+                          "61999171315484316965\n" \
+                          "65459144877856561700\n"
+    rare_numbers [21] =  "208393425242000083802\n" \
+                         "219518549668074815912\n" \
+                         "257661195832219326752\n" \
+                         "286694688797362186682\n" \
+                         "837982875780054779738\n"
+    rare_numbers [22] = "2414924301133245383042\n" \
+                        "2414924323311045383042\n" \
+                        "2414946523311023183042\n" \
+                        "2576494891793995836752\n" \
+                        "2576494893971995836752\n" \
+                        "2620937863931054483162\n" \
+                        "2620937863931054483162\n" \
+                        "2620955641393276283162\n" \
+                        "2622935621573476481162\n" \
+                        "2622935643751276481162\n" \
+                        "2622937641933274481162\n" \
+                        "2622955841933256281162\n" \
+                        "2622957843751254281162\n" \
+                        "2727651947516658327272\n" \
+                        "2747736918335953517072\n" \
+                        "2788047668617596408872\n" \
+                        "2788047848617776408872\n" \
+                        "2788047868437576408872\n" \
+                        "2788047888617376408872\n" \
+                        "2939501759705522349392\n" \
+                        "2939503375709360349392\n" \
+                        "2939503537707740349392\n" \
+                        "2939521359525562149392\n" \
+                        "2939521557527542149392\n" \
+                        "2939523577527340149392\n" \
+                        "2939523779525320149392\n" \
+                        "2959503377707360349192\n" \
+                        "6344828989519887483525\n" \
+                        "8045841652464561594308\n" \
+                        "8045841654642561594308\n" \
+                        "8655059576513659814468\n" \
+                        "8655059772157639814468\n" \
+                        "8655079374155679614468\n" \
+                        "8655079574515659614468\n" \
+                        "8888070771864228883913\n"
+}
+
+
+#
+# Print the numbers of the appropriate length.
+#
+{
+    if ($1 in rare_numbers) {
+        printf "%s", rare_numbers [$1]
+    }
+}
diff --git a/challenge-102/abigail/awk/ch-2.awk b/challenge-102/abigail/awk/ch-2.awk
new file mode 100644
index 0000000000..e673437860
--- /dev/null
+++ b/challenge-102/abigail/awk/ch-2.awk
@@ -0,0 +1,36 @@
+#!/usr/bin/awk
+
+#
+# See ../README.md
+#
+
+#
+# Run as: awk -f ch-2.awk < input-file
+#
+
+#
+# Working from the end of the required string backwards, we alternate
+# placing a hash, and placing a number. We place them in an array out,
+# and at the end, print out said array in reverse order.
+#
+
+{
+    idx  = $1
+    hash = 0
+    i    = 0
+    while (idx) {
+        i ++
+        if (hash = !hash) {
+            out [i] = "#"
+            idx --
+        }
+        else {
+            out [i] =       idx + 1
+            idx  -= length (idx + 1)
+        }
+    }
+    for (; i; i --) {
+        printf "%s", out [i]
+    }
+    printf "\n"
+}
diff --git a/challenge-102/abigail/bash/ch-1.sh b/challenge-102/abigail/bash/ch-1.sh
new file mode 100644
index 0000000000..874ae78998
--- /dev/null
+++ b/challenge-102/abigail/bash/ch-1.sh
@@ -0,0 +1,146 @@
+#!/bin/sh
+
+#
+# See ../README.md
+#
+
+#
+# Run as: bash ch-1.sh < input-file
+#
+
+#
+# Put the known rare numbers into an array
+#
+declare -a rare_numbers
+
+rare_numbers[ 2]="65\n"
+rare_numbers[ 6]="621770\n"
+rare_numbers[ 9]="281089082\n"
+rare_numbers[10]="2022652202\n"\
+"2042832002\n"
+rare_numbers[12]="868591084757\n"\
+"872546974178\n"\
+"872568754178\n"
+rare_numbers[13]="6979302951885\n"
+rare_numbers[14]="20313693904202\n"\
+"20313839704202\n"\
+"20331657922202\n"\
+"20331875722202\n"\
+"20333875702202\n"\
+"40313893704200\n"\
+"40351893720200\n"
+rare_numbers[15]="200142385731002\n"\
+"204238494066002\n"\
+"221462345754122\n"\
+"244062891224042\n"\
+"245518996076442\n"\
+"248359494187442\n"\
+"403058392434500\n"\
+"441054594034340\n"\
+"816984566129618\n"
+rare_numbers[16]="2078311262161202\n"\
+"2133786945766212\n"\
+"2135568943984212\n"\
+"2135764587964212\n"\
+"2135786765764212\n"\
+"4135786945764210\n"\
+"6157577986646405\n"\
+"6889765708183410\n"\
+"8052956026592517\n"\
+"8052956206592517\n"\
+"8191154686620818\n"\
+"8191156864620818\n"\
+"8191376864400818\n"\
+"8650327689541457\n"\
+"8650349867341457\n"
+rare_numbers[17]="22542040692914522\n"\
+"67725910561765640\n"\
+"86965750494756968\n"
+rare_numbers[18]="225342456863243522\n"\
+"225342458663243522\n"\
+"225342478643243522\n"\
+"284684666566486482\n"\
+"284684868364486482\n"\
+"297128548234950692\n"\
+"297128722852950692\n"\
+"297148324656930692\n"\
+"297148546434930692\n"\
+"497168548234910690\n"\
+"619431353040136925\n"\
+"619631153042134925\n"\
+"631688638047992345\n"\
+"633288858025996145\n"\
+"633488632647994145\n"\
+"653488856225994125\n"\
+"811865096390477018\n"\
+"865721270017296468\n"\
+"871975098681469178\n"\
+"898907259301737498\n"
+rare_numbers[19]="2042401829204402402\n"\
+"2060303819041450202\n"\
+"2420424089100600242\n"\
+"2551755006254571552\n"\
+"2702373360882732072\n"\
+"2825378427312735282\n"\
+"6531727101458000045\n"\
+"6988066446726832640\n"\
+"8066308349502036608\n"\
+"8197906905009010818\n"\
+"8200756128308135597\n"\
+"8320411466598809138\n"
+rare_numbers[20]="22134434735752443122\n"\
+"22134434753752443122\n"\
+"22134436953532443122\n"\
+"22136414517954423122\n"\
+"22136414971554423122\n"\
+"22136456771730423122\n"\
+"61952807156239928885\n"\
+"61999171315484316965\n"\
+"65459144877856561700\n"
+rare_numbers[21]="208393425242000083802\n"\
+"219518549668074815912\n"\
+"257661195832219326752\n"\
+"286694688797362186682\n"\
+"837982875780054779738\n"
+rare_numbers[22]="2414924301133245383042\n"\
+"2414924323311045383042\n"\
+"2414946523311023183042\n"\
+"2576494891793995836752\n"\
+"2576494893971995836752\n"\
+"2620937863931054483162\n"\
+"2620937863931054483162\n"\
+"2620955641393276283162\n"\
+"2622935621573476481162\n"\
+"2622935643751276481162\n"\
+"2622937641933274481162\n"\
+"2622955841933256281162\n"\
+"2622957843751254281162\n"\
+"2727651947516658327272\n"\
+"2747736918335953517072\n"\
+"2788047668617596408872\n"\
+"2788047848617776408872\n"\
+"2788047868437576408872\n"\
+"2788047888617376408872\n"\
+"2939501759705522349392\n"\
+"2939503375709360349392\n"\
+"2939503537707740349392\n"\
+"2939521359525562149392\n"\
+"2939521557527542149392\n"\
+"2939523577527340149392\n"\
+"2939523779525320149392\n"\
+"2959503377707360349192\n"\
+"6344828989519887483525\n"\
+"8045841652464561594308\n"\
+"8045841654642561594308\n"\
+"8655059576513659814468\n"\
+"8655059772157639814468\n"\
+"8655079374155679614468\n"\
+"8655079574515659614468\n"\
+"8888070771864228883913\n"
+
+#
+# Read a length, and print the rare numbers of that length
+#
+while read length
+do    printf "${rare_numbers[$length]}"
+done
diff --git a/challenge-102/abigail/bash/ch-2.sh b/challenge-102/abigail/bash/ch-2.sh
new file mode 100644
index 0000000000..9a9072a56c
--- /dev/null
+++ b/challenge-102/abigail/bash/ch-2.sh
@@ -0,0 +1,37 @@
+#!/bin/sh
+
+#
+# See ../README.md
+#
+
+#
+# Run as: bash ch-2.sh < input-file
+#
+
+
+#
+# Working from the end of the required string backwards, we alternate
+# placing a hash, and placing a number. We place them in an array out,
+# and at the end, print out said array in reverse order.
+#
+
+while read index
+do    declare -a out
+      hash=0
+      i=0
+      while ((index > 0))
+      do    ((i ++))
+            if   ((hash = !hash))
+            then out[$i]="#"
+                 ((index --))
+            else number=$((index + 1))
+                 out[$i]=$number
+                 ((index -= ${#number}))
+            fi
+      done
+      for ((; i; i --))
+      do  printf "%s" ${out[$i]}
+      done
+      echo
+done
+      
diff --git a/challenge-102/abigail/c/ch-1.c b/challenge-102/abigail/c/ch-1.c
new file mode 100644
index 0000000000..564ffc732a
--- /dev/null
+++ b/challenge-102/abigail/c/ch-1.c
@@ -0,0 +1,164 @@
+# include <stdlib.h>
+# include <stdio.h>
+# include <string.h>
+
+/*
+ * See ../README.md
+ */
+
+/*
+ * Run as: cc -o ch-1.o ch-1.c; ./ch-1.o < input-file
+ */
+
+# define NR_OF_KNOWN_RARE_NUMBERS  124
+# define MAX_RARE_NUMBER_LENGTH     22
+
+/*
+ * Create a list of all known rare numbers.
+ */
+char * rare_numbers [23];
+
+int main () {
+    rare_numbers [ 0] =                       NULL;
+    rare_numbers [ 1] =                       NULL;
+    rare_numbers [ 2] =                     "65\n";
+    rare_numbers [ 3] =                       NULL;
+    rare_numbers [ 4] =                       NULL;
+    rare_numbers [ 5] =                       NULL;
+    rare_numbers [ 6] =                 "621770\n";
+    rare_numbers [ 7] =                       NULL;
+    rare_numbers [ 8] =                       NULL;
+    rare_numbers [ 9] =              "281089082\n";
+    rare_numbers [10] =             "2022652202\n" \
+                                    "2042832002\n";
+    rare_numbers [11] =                       NULL;
+    rare_numbers [12] =           "868591084757\n" \
+                                  "872546974178\n" \
+                                  "872568754178\n";
+    rare_numbers [13] =          "6979302951885\n";
+    rare_numbers [14] =         "20313693904202\n" \
+                                "20313839704202\n" \
+                                "20331657922202\n" \
+                                "20331875722202\n" \
+                                "20333875702202\n" \
+                                "40313893704200\n" \
+                                "40351893720200\n";
+    rare_numbers [15] =        "200142385731002\n" \
+                               "204238494066002\n" \
+                               "221462345754122\n" \
+                               "244062891224042\n" \
+                               "245518996076442\n" \
+                               "248359494187442\n" \
+                               "403058392434500\n" \
+                               "441054594034340\n" \
+                               "816984566129618\n";
+    rare_numbers [16] =       "2078311262161202\n" \
+                              "2133786945766212\n" \
+                              "2135568943984212\n" \
+                              "2135764587964212\n" \
+                              "2135786765764212\n" \
+                              "4135786945764210\n" \
+                              "6157577986646405\n" \
+                              "6889765708183410\n" \
+                              "8052956026592517\n" \
+                              "8052956206592517\n" \
+                              "8191154686620818\n" \
+                              "8191156864620818\n" \
+                              "8191376864400818\n" \
+                              "8650327689541457\n" \
+                              "8650349867341457\n";
+    rare_numbers [17] =      "22542040692914522\n" \
+                             "67725910561765640\n" \
+                             "86965750494756968\n";
+    rare_numbers [18] =     "225342456863243522\n" \
+                            "225342458663243522\n" \
+                            "225342478643243522\n" \
+                            "284684666566486482\n" \
+                            "284684868364486482\n" \
+                            "297128548234950692\n" \
+                            "297128722852950692\n" \
+                            "297148324656930692\n" \
+                            "297148546434930692\n" \
+                            "497168548234910690\n" \
+                            "619431353040136925\n" \
+                            "619631153042134925\n" \
+                            "631688638047992345\n" \
+                            "633288858025996145\n" \
+                            "633488632647994145\n" \
+                            "653488856225994125\n" \
+                            "811865096390477018\n" \
+                            "865721270017296468\n" \
+                            "871975098681469178\n" \
+                            "898907259301737498\n";
+    rare_numbers [19] =    "2042401829204402402\n" \
+                           "2060303819041450202\n" \
+                           "2420424089100600242\n" \
+                           "2551755006254571552\n" \
+                           "2702373360882732072\n" \
+                           "2825378427312735282\n" \
+                           "6531727101458000045\n" \
+                           "6988066446726832640\n" \
+                           "8066308349502036608\n" \
+                           "8197906905009010818\n" \
+                           "8200756128308135597\n" \
+                           "8320411466598809138\n";
+    rare_numbers [20] =   "22134434735752443122\n" \
+                          "22134434753752443122\n" \
+                          "22134436953532443122\n" \
+                          "22136414517954423122\n" \
+                          "22136414971554423122\n" \
+                          "22136456771730423122\n" \
+                          "61952807156239928885\n" \
+                          "61999171315484316965\n" \
+                          "65459144877856561700\n";
+    rare_numbers [21] =  "208393425242000083802\n" \
+                         "219518549668074815912\n" \
+                         "257661195832219326752\n" \
+                         "286694688797362186682\n" \
+                         "837982875780054779738\n";
+    rare_numbers [22] = "2414924301133245383042\n" \
+                        "2414924323311045383042\n" \
+                        "2414946523311023183042\n" \
+                        "2576494891793995836752\n" \
+                        "2576494893971995836752\n" \
+                        "2620937863931054483162\n" \
+                        "2620937863931054483162\n" \
+                        "2620955641393276283162\n" \
+                        "2622935621573476481162\n" \
+                        "2622935643751276481162\n" \
+                        "2622937641933274481162\n" \
+                        "2622955841933256281162\n" \
+                        "2622957843751254281162\n" \
+                        "2727651947516658327272\n" \
+                        "2747736918335953517072\n" \
+                        "2788047668617596408872\n" \
+                        "2788047848617776408872\n" \
+                        "2788047868437576408872\n" \
+                        "2788047888617376408872\n" \
+                        "2939501759705522349392\n" \
+                        "2939503375709360349392\n" \
+                        "2939503537707740349392\n" \
+                        "2939521359525562149392\n" \
+                        "2939521557527542149392\n" \
+                        "2939523577527340149392\n" \
+                        "2939523779525320149392\n" \
+                        "2959503377707360349192\n" \
+                        "6344828989519887483525\n" \
+                        "8045841652464561594308\n" \
+                        "8045841654642561594308\n" \
+                        "8655059576513659814468\n" \
+                        "8655059772157639814468\n" \
+