Merge pull request #6213 from Firedrake/rogerbw-challenge-168

Solutions for challenge #168

18 files changed, 1635 insertions, 0 deletions

diff --git a/challenge-168/roger-bell-west/javascript/ch-1.js b/challenge-168/roger-bell-west/javascript/ch-1.js
new file mode 100755
index 0000000000..d3fc9016b2
--- /dev/null
+++ b/challenge-168/roger-bell-west/javascript/ch-1.js
@@ -0,0 +1,81 @@
+#! /usr/bin/node
+function deepEqual(a,b)
+{
+    if( (typeof a == 'object' && a != null) &&
+        (typeof b == 'object' && b != null) )
+    {
+        var count = [0,0]
+        for( var key in a) count[0]++
+        for( var key in b) count[1]++
+        if( count[0]-count[1] != 0) {return false}
+        for( var key in a)
+        {
+            if(!(key in b) || !deepEqual(a[key],b[key])) {return false}
+        }
+        for( var key in b)
+        {
+            if(!(key in a) || !deepEqual(b[key],a[key])) {return false}
+        }
+        return true
+    }
+    else
+    {
+        return a === b
+    }
+}
+
+function isprime(candidate) {
+    if (candidate<2) {
+        return false
+    } else if (candidate==2) {
+        return true
+    } else if (candidate==3) {
+        return true
+    } else if (candidate % 2 == 0) {
+        return false
+    } else if (candidate % 3 == 0) {
+        return false
+    }
+    let anchor=0
+    let limit=Math.floor(Math.sqrt(candidate))
+    while (1) {
+        anchor+=6
+        for (let t = anchor-1; t <= anchor+1; t += 2) {
+            if (t > limit) {
+                return true
+            }
+            if (candidate % t == 0) {
+                return false
+            }
+        }
+    }
+}
+
+function perrinprime(n) {
+    let out = new Set;
+    let seq = [3, 0, 2];
+    while (true) {
+        let nv = seq[0] + seq[1];
+        seq.shift();
+        seq.push(nv);
+        if (isprime(nv)) {
+            out.add(nv);
+            if (out.size >= n) {
+                break;
+            }
+        }
+    }
+    let o = [];
+    for (let p of out) {
+        o.push(p);
+    }
+    o.sort((a,b) => a-b);
+    return o;
+}
+
+if (deepEqual(perrinprime(13),[2, 3, 5, 7, 17, 29, 277, 367, 853, 14197, 43721, 1442968193, 792606555396977])) {
+    process.stdout.write("Pass");
+} else {
+    process.stdout.write("FAIL");
+}
+process.stdout.write("\n");
diff --git a/challenge-168/roger-bell-west/javascript/ch-2.js b/challenge-168/roger-bell-west/javascript/ch-2.js
new file mode 100755
index 0000000000..99486914e4
--- /dev/null
+++ b/challenge-168/roger-bell-west/javascript/ch-2.js
@@ -0,0 +1,93 @@
+#! /usr/bin/node
+
+function genprimes(mx) {
+    let primesh=new Set([2,3])
+    for (let i = 6; i <= mx; i += 6) {
+        for (let j = i-1; j <= i+1; j += 2) {
+            if (j <= mx) {
+                primesh.add(j);
+            }
+        }
+    }
+    let q=[2,3,5,7];
+    let p=q.shift();
+    let mr=Math.floor(Math.sqrt(mx));
+    while (p <= mr) {
+        if (primesh.has(p)) {
+            let i=p*p
+            for (let i=p*p; i <= mx; i += p) {
+                primesh.delete(i);
+            }
+        }
+        if (q.length < 2) {
+            q.push(q[q.length-1]+4);
+            q.push(q[q.length-1]+2);
+        }
+        p=q.shift();
+    }
+    let primes=[...primesh];
+    primes.sort(function(a,b) {
+        return a-b;
+    });
+    return primes;
+}
+
+function primefactor (n) {
+    let f=new Map()
+    let m=n
+    for (let p of genprimes(1+Math.floor(Math.sqrt(n)))) {
+        while (m % p == 0) {
+            m=Math.floor(m/p)
+            if (f.has(p)) {
+                f.set(p,f.get(p)+1)
+            } else {
+                f.set(p,1)
+            }
+            if (m == 1) {
+                break
+            }
+        }
+    }
+    if (m > 1) {
+        if (f.has(m)) {
+            f.set(m,f.get(m)+1)
+        } else {
+            f.set(m,1)
+        }
+    }
+    return f
+}
+
+function homeprime (n0) {
+    let n = n0;
+    while (true) {
+        let t = primefactor(n);
+        if (t.size == 1 && [...t.values()][0] == 1) {
+            break;
+        }
+        let ns = "";
+        let tk = [...t.keys()];
+        tk.sort((a,b) => a-b);
+        for (let d of tk) {
+            for (let i=0; i<t.get(d); i++) {
+                ns = ns.concat(d);
+            }
+        }
+        n = parseInt(ns);
+    }
+    return n;
+}
+
+if (homeprime(10) == 773) {
+    process.stdout.write("Pass");
+} else {
+    process.stdout.write("FAIL");
+}
+process.stdout.write(" ");
+
+if (homeprime(16) == 31636373) {
+    process.stdout.write("Pass");
+} else {
+    process.stdout.write("FAIL");
+}
+process.stdout.write("\n");
diff --git a/challenge-168/roger-bell-west/kotlin/ch-1.kt b/challenge-168/roger-bell-west/kotlin/ch-1.kt
new file mode 100644
index 0000000000..a8628b4c2d
--- /dev/null
+++ b/challenge-168/roger-bell-west/kotlin/ch-1.kt
@@ -0,0 +1,58 @@
+import kotlin.math.*
+
+fun isprime(candidate: Long): Boolean {
+    if (candidate < 2L) {
+        return false
+    } else if (candidate==2L) {
+        return true
+    } else if (candidate==3L) {
+        return true
+    } else if (candidate % 2L == 0L) {
+        return false
+    } else if (candidate % 3L == 0L) {
+        return false
+    }
+    var anchor=0L
+    val limit = Math.sqrt(candidate.toDouble()).toLong()
+    while (true) {
+        anchor += 6L
+        for (t in anchor-1L..anchor+1L step 2L) {
+            if (t > limit) {
+                return true
+            }
+            if (candidate % t == 0L) {
+                return false
+            }
+        }
+    }
+}
+
+fun perrinprime(n: Long): ArrayList<Long> {
+    var ot = mutableSetOf<Long>()
+    var seq = mutableListOf(3L, 0L, 2L)
+    while (true) {
+        val nv = seq[0] + seq[1]
+        seq.removeAt(0)
+        seq.add(nv)
+        if (isprime(nv)) {
+            ot.add(nv)
+            if (ot.size >= n) {
+                break;
+            }
+        }
+    }
+    var o = ArrayList(ot)
+    o.sort()
+    return o
+}
+
+fun main() {
+    if (perrinprime(13) == listOf(2, 3, 5, 7, 17, 29, 277, 367, 853,
+                                  14197, 43721, 1442968193,
+                                  792606555396977)) {
+        print("Pass")
+    } else {
+        print("FAIL")
+    }
+    println("")
+}
diff --git a/challenge-168/roger-bell-west/kotlin/ch-2.kt b/challenge-168/roger-bell-west/kotlin/ch-2.kt
new file mode 100644
index 0000000000..7083d8f76f
--- /dev/null
+++ b/challenge-168/roger-bell-west/kotlin/ch-2.kt
@@ -0,0 +1,94 @@
+import kotlin.math.*
+
+fun genprimes(mx: Int): ArrayList<Int> {
+    var primesh=mutableSetOf<Int>()
+    for (i in 2..3) {
+        primesh.add(i)
+    }
+    for (i in 6..mx+1 step 6) {
+        for (j in i-1..i+1 step 2) {
+            if (j <= mx) {
+                primesh.add(j)
+            }
+        }
+    }
+    var q=ArrayDeque(listOf(2,3,5,7))
+    var p=q.removeFirst()
+    val mr=sqrt(mx.toDouble()).toInt()
+    while (p <= mr) {
+        if (primesh.contains(p)) {
+            for (i in p*p..mx step p) {
+                primesh.remove(i)
+            }
+        }
+        if (q.size < 2) {
+            q.add(q.last()+4)
+            q.add(q.last()+2)
+        }
+        p=q.removeFirst()
+    }
+    var primes=ArrayList(primesh.distinct())
+    primes.sort()
+    return primes
+}
+
+fun primefactor(n: Int): Map<Int,Int> {
+    var f=mutableMapOf<Int,Int>()
+    var m=n
+    for (p in genprimes(sqrt(m.toDouble()).toInt())) {
+        while (m % p == 0) {
+            m /= p
+            if (f.containsKey(p)) {
+                f[p] = f[p]!!+1
+            } else {
+                f[p]=1
+            }
+        }
+        if (m == 1) {
+            break
+        }
+    }
+    if (m > 1) {
+        if (f.containsKey(m)) {
+            f[m] = f[m]!!+1
+        } else {
+            f[m]=1
+        }
+    }
+    return f
+}
+
+fun homeprime(n0: Int): Int {
+    var n = n0
+    while (true) {
+        val t = primefactor(n)
+        val tk = t.keys.sorted()
+        if (t.size == 1 && t[tk[0]] == 1) {
+            break
+        }
+        var ns = ""
+        for (d in tk) {
+            val ds = d.toString()
+            for (i in 1..t[d]!!) {
+                ns += ds
+            }
+        }
+        n = ns.toInt()
+    }
+    return n
+}
+
+fun main() {
+    if (homeprime(10) == 773) {
+        print("Pass")
+    } else {
+        print("FAIL")
+    }
+    print(" ")
+    if (homeprime(16) == 31636373) {
+        print("Pass")
+    } else {
+        print("FAIL")
+    }
+    println("")
+}
diff --git a/challenge-168/roger-bell-west/lua/ch-1.lua b/challenge-168/roger-bell-west/lua/ch-1.lua
new file mode 100755
index 0000000000..2b0f43b734
--- /dev/null
+++ b/challenge-168/roger-bell-west/lua/ch-1.lua
@@ -0,0 +1,102 @@
+#! /usr/bin/lua
+
+-- by Michael Anderson at
+-- https://stackoverflow.com/questions/8722620/comparing-two-index-tables-by-index-value-in-lua
+function recursive_compare(t1,t2)
+  -- Use usual comparison first.
+  if t1==t2 then return true end
+  -- We only support non-default behavior for tables
+  if (type(t1)~="table") then return false end
+  -- They better have the same metatables
+  local mt1 = getmetatable(t1)
+  local mt2 = getmetatable(t2)
+  if( not recursive_compare(mt1,mt2) ) then return false end
+
+  -- Check each key-value pair
+  -- We have to do this both ways in case we miss some.
+  -- TODO: Could probably be smarter and not check those we've 
+  -- already checked though!
+  for k1,v1 in pairs(t1) do
+    local v2 = t2[k1]
+    if( not recursive_compare(v1,v2) ) then return false end
+  end
+  for k2,v2 in pairs(t2) do
+    local v1 = t1[k2]
+    if( not recursive_compare(v1,v2) ) then return false end
+  end
+
+  return true  
+end
+
+function isprime(candidate)
+   if candidate<2 then
+      return false
+   elseif candidate==2 then
+      return true
+   elseif candidate==3 then
+      return true
+   elseif candidate % 2 == 0 then
+      return false
+   elseif candidate % 3 == 0 then
+      return false
+   end
+   local anchor=0
+   local limit=math.floor(math.sqrt(candidate))
+   while true do
+      anchor = anchor + 6
+      for t = anchor-1,anchor+1,2 do
+         if t > limit then
+            return true
+         end
+         if candidate % t == 0 then
+            return false
+         end
+      end
+   end
+end
+
+function hammingweight(x0)
+   local x = x0
+   local count = 0
+   while x > 0 do
+      x = x & (x-1)
+      count = count + 1
+   end
+   return count
+end
+
+function perrinprime(n)
+   local out={}
+   local ol = 0
+   local seq = {3, 0, 2}
+   while true do
+      local nv = seq[1] + seq[2]
+      seq[1] = seq[2]
+      seq[2] = seq[3]
+      seq[3] = nv
+      if isprime(nv) then
+         if out[nv] == nil then
+            ol = ol + 1
+         end
+         out[nv] = true
+         if ol >= n then
+            break
+         end
+      end
+   end
+   local o = {}
+   for k,v in pairs(out) do
+      table.insert(o,k)
+   end
+   table.sort(o)
+   return o
+end
+
+if recursive_compare(perrinprime(13), {2, 3, 5, 7, 17, 29, 277, 367,
+                                       853, 14197, 43721, 1442968193,
+                                       792606555396977}) then
+   io.write("Pass")
+else
+   io.write("FAIL")
+end
+print("")
diff --git a/challenge-168/roger-bell-west/lua/ch-2.lua b/challenge-168/roger-bell-west/lua/ch-2.lua
new file mode 100755
index 0000000000..978f8ed462
--- /dev/null
+++ b/challenge-168/roger-bell-west/lua/ch-2.lua
@@ -0,0 +1,101 @@
+#! /usr/bin/lua
+
+function genprimes(mx)
+   local primesh = {}
+   for i = 2, 3 do
+      primesh[i] = true
+   end
+   for i = 6, mx, 6 do
+      for j = i-1, i+1, 2 do
+         if j <= mx then
+            primesh[j]=true
+         end
+      end
+   end
+   local q={2,3,5,7}
+   local p=table.remove(q,1)
+   local mr=math.floor(math.sqrt(mx))
+   while p <= mr do
+      if primesh[p] ~= nil then
+         for i = p*p,mx,p do
+            primesh[i] = nil
+         end
+      end
+      if #q < 2 then
+         table.insert(q,q[#q]+4)
+         table.insert(q,q[#q]+2)
+      end
+      p=table.remove(q,1)
+   end
+   local primes = {}
+   for k,v in pairs(primesh) do
+      table.insert(primes,k)
+   end
+   table.sort(primes)
+   return primes
+end
+
+function primefactor(n)
+   local f={}
+   local m=n
+   for k,p in pairs(genprimes(1+math.floor(math.sqrt(m)))) do
+      while m % p == 0 do
+         m=math.floor(m/p)
+         if f[p] == nil then
+            f[p]=1
+         else
+            f[p] = f[p] + 1
+         end
+         if m==1 then
+            break
+         end
+      end
+   end
+   if m>1 then
+      if f[m] == nil then
+         f[m]=1
+      else
+         f[m] = f[m] + 1
+      end
+   end
+   return f
+end
+
+function homeprime(n0)
+   local n = n0
+   while true do
+      local pfc = 0
+      local ns = ""
+      local t = primefactor(n)
+      local kl = {}
+      for k,v in pairs(t) do
+         pfc = pfc + v
+         table.insert(kl,k)
+      end
+      table.sort(kl)
+      if pfc == 1 then
+         break
+      end
+      for k,v in pairs(kl) do
+         for i = 1,t[v] do
+            ns = ns .. v
+         end
+      end
+      n = 0 + ns
+   end
+   return n
+end
+
+if homeprime(10) == 773 then
+   io.write("Pass")
+else
+   io.write("FAIL")
+end
+io.write(" ")
+
+if homeprime(16) == 31636373 then
+   io.write("Pass")
+else
+   io.write("FAIL")
+end
+print("")
diff --git a/challenge-168/roger-bell-west/perl/ch-1.pl b/challenge-168/roger-bell-west/perl/ch-1.pl
new file mode 100755
index 0000000000..3d2d398a9d
--- /dev/null
+++ b/challenge-168/roger-bell-west/perl/ch-1.pl
@@ -0,0 +1,56 @@
+#! /usr/bin/perl
+
+use strict;
+use warnings;
+use experimental 'signatures';
+
+use Test::More tests => 1;
+
+is_deeply(perrinprime(13),
+          [2, 3, 5, 7, 17, 29, 277, 367, 853, 14197, 43721,
+           1442968193, 792606555396977],
+          'example 1');
+
+sub isprime {
+  my $candidate=shift;
+  if ($candidate<2) {
+    return 0;
+  } elsif ($candidate==2) {
+    return 1;
+  } elsif ($candidate==3) {
+    return 1;
+  } elsif ($candidate % 2 == 0) {
+    return 0;
+  } elsif ($candidate % 3 == 0) {
+    return 0;
+  }
+  my $anchor=0;
+  my $limit=int(sqrt($candidate));
+  while (1) {
+    $anchor+=6;
+    foreach my $t ($anchor-1,$anchor+1) {
+      if ($t > $limit) {
+        return 1;
+      }
+      if ($candidate % $t == 0) {
+        return 0;
+      }
+    }
+  }
+}
+
+sub perrinprime($n) {
+  my %out;
+  my @seq = (3, 0, 2);
+  while (1) {
+    push @seq,$seq[0]+$seq[1];
+    shift @seq;
+    if (isprime($seq[-1])) {
+      $out{$seq[-1]} = 1;
+      if (scalar keys %out >= $n) {
+        last;
+      }
+    }
+  }
+  return [sort {$a <=> $b} keys %out];
+}
diff --git a/challenge-168/roger-bell-west/perl/ch-2.pl b/challenge-168/roger-bell-west/perl/ch-2.pl
new file mode 100755
index 0000000000..0191fac52f
--- /dev/null
+++ b/challenge-168/roger-bell-west/perl/ch-2.pl
@@ -0,0 +1,80 @@
+#! /usr/bin/perl
+
+use strict;
+use warnings;
+use experimental 'signatures';
+
+use Test::More tests => 2;
+
+is(homeprime(10),773,'example 1');
+is(homeprime(16),31636373,'example 2');
+
+sub genprimes($mx) {
+  my @primes;
+  {
+    my %primesh=map {$_ => 1} (2,3);
+    for (my $i=6;$i <= $mx+1; $i += 6) {
+      foreach my $j ($i-1,$i+1) {
+        if ($j <= $mx) {
+          $primesh{$j}=1;
+        }
+      }
+    }
+    my @q=(2,3,5,7);
+    my $p=shift @q;
+    my $mr=int(sqrt($mx));
+    while ($p <= $mr) {
+      if ($primesh{$p}) {
+        my $i=$p*$p;
+        while ($i <= $mx) {
+          delete $primesh{$i};
+          $i += $p;
+        }
+      }
+      if (scalar @q < 2) {
+        push @q,$q[-1]+4;
+        push @q,$q[-1]+2;
+      }
+      $p=shift @q;
+    }
+    @primes=sort {$a <=> $b} keys %primesh;
+  }
+  return \@primes;
+}
+
+sub primefactor($n) {
+  my %f;
+  my $m=$n;
+  foreach my $p (@{genprimes(int(sqrt($n)))}) {
+    while ($m % $p == 0) {
+      $f{$p}++;
+      $m=int($m/$p);
+      if ($m == 1) {
+        last;
+      }
+    }
+  }
+  if ($m > 1) {
+    $f{$m}++;
+  }
+  return \%f;
+}
+
+sub homeprime($n0) {
+  my $n=$n0;
+  while (1) {
+    my $t = primefactor($n);
+    my @tk = sort {$a <=> $b} keys %{$t};
+    if (scalar @tk == 1 && $t->{$tk[0]} == 1) {
+      last;
+    }
+    my $ns = '';
+    foreach my $d (@tk) {
+      foreach (1..$t->{$d}) {
+        $ns .= $d;
+      }
+    }
+    $n = 0 + $ns;
+  }
+  return $n;
+}
diff --git a/challenge-168/roger-bell-west/postscript/ch-1.ps b/challenge-168/roger-bell-west/postscript/ch-1.ps
new file mode 100644
index 0000000000..a568fb7425
--- /dev/null
+++ b/challenge-168/roger-bell-west/postscript/ch-1.ps
@@ -0,0 +1,244 @@
+%!PS
+
+% begin included library code
+
+/test.end {
+    ( ) print
+    test.count 0 gt {
+        (Passed ) print
+        test.pass (...) cvs print
+        (/) print
+        test.count (...) cvs print
+        ( \() print
+        test.pass 100 mul test.count idiv (...) cvs print
+        (%\)) print
+        (\r\n) print
+    } if
+} bind def
+
+/quicksort.swap {
+    2 dict begin
+    /bi exch def
+    /ai exch def
+    arr ai get
+    arr bi get
+    arr exch ai exch put
+    arr exch bi exch put
+    end
+} bind def
+
+/test {
+    /test.count test.count 1 add def
+    {
+        /test.pass test.pass 1 add def
+    } {
+        ( ) print
+        test.count (....) cvs print
+        (-fail) print
+    } ifelse
+} bind def
+
+/quicksort.main { % lo hi -> (null)
+    3 dict begin
+    /hi exch def
+    /lo exch def
+    /xit false def
+    lo 0 lt {
+        /xit true def
+    } if
+    hi 0 lt {
+        /xit true def
+    } if
+    lo hi ge {
+        /xit true def
+    } if
+    xit not {
+        /p quicksort.partition def
+        lo p quicksort.main
+        p 1 add hi quicksort.main
+    } if
+    end
+} bind def
+
+/keys { % dict -> array of dict keys
+    [ exch
+      {
+          pop
+      } forall
+    ]
+} bind def
+
+/quicksort { % [ a c b ] -> [ a b c ]
+    1 dict begin
+    /arr exch def
+    0 arr length 1 sub quicksort.main
+    arr
+    end
+} bind def
+
+/deepeq {
+    2 dict begin
+    /a exch def
+    /b exch def
+    a type b type eq {
+        a type /dicttype eq {
+            a length b length eq {
+                <<
+                    a {
+                        pop
+                        true
+                    } forall
+                    b {
+                        pop
+                        true
+                    } forall
+                >>
+                true exch
+                {
+                    pop
+                    dup a exch known {
+                        dup b exch known {
+                            dup a exch get exch b exch get deepeq not {
+                                pop false
+                            } if
+                        } {
+                            false
+                        } ifelse
+                    } {
+                        false
+                    } ifelse
+                } forall
+            } {
+                false
+            } ifelse
+        } {
+            a type dup /arraytype eq exch /stringtype eq or {
+                a length b length eq {
+                    true
+                    0 1 a length 1 sub {
+                        dup a exch get exch b exch get deepeq not {
+                            pop false
+                            exit
+                        } if
+                    } for
+                } {
+                    false
+                } ifelse
+            } {
+                a b eq
+            } ifelse
+        } ifelse
+    } {
+        false
+    } ifelse
+    end
+} bind def
+
+/isprime {
+    4 dict begin
+    /candidate exch def
+    1 {
+        candidate 2 lt {
+            false
+            exit
+        } if
+        candidate 2 eq {
+            true
+            exit
+        } if
+        candidate 2 mod 0 eq {
+            false
+            exit
+        } if
+        candidate 3 eq {
+            true
+            exit
+        } if
+        candidate 3 mod 0 eq {
+            false
+            exit
+        } if
+        /prime true def
+        /limit candidate sqrt cvi 1 add def
+        /anchor 0 def
+        {
+            /anchor anchor 6 add def
+            anchor limit gt {
+                exit
+            } if
+            [ -1 1 ] {
+                anchor add candidate exch mod 0 eq {
+                    /prime false def
+                    exit
+                } if
+            } forall
+            prime false eq {
+                exit
+            } if
+        } loop
+        prime
+    } repeat
+    end
+} bind def
+
+/quicksort.partition {
+    3 dict begin
+    /pivot arr hi lo add 2 idiv get def
+    /i lo 1 sub def
+    /j hi 1 add def
+    {
+        {
+            /i i 1 add def
+            arr i get pivot ge {
+                exit
+            } if
+        } loop
+        {
+            /j j 1 sub def
+            arr j get pivot le {
+                exit
+            } if
+        } loop
+        i j ge {
+            j
+            exit
+        } if
+        i j quicksort.swap
+    } loop
+    end
+} bind def
+
+/test.start {
+    print (:) print
+    /test.pass 0 def
+    /test.count 0 def
+} bind def
+
+% end included library code
+
+/perrinprime {
+    4 dict begin
+    /n exch def
+    /out n dict def
+    /seq [ 3 0 2 ] def
+    {
+        /nv seq 0 get seq 1 get add def
+        seq 0 seq 1 get put
+        seq 1 seq 2 get put
+        seq 2 nv put
+        nv isprime {
+            out nv true put
+            out length n ge {
+                exit
+            } if
+        } if
+    } loop
+    out keys quicksort
+    end
+} bind def
+
+(perrinprime) test.start
+13 perrinprime
+[ 2 3 5 7 17 29 277 367 853 14197 43721 1442968193 792606555396977 ]
+deepeq test
+test.end
diff --git a/challenge-168/roger-bell-west/postscript/ch-2.ps b/challenge-168/roger-bell-west/postscript/ch-2.ps
new file mode 100644
index 0000000000..138a084180
--- /dev/null
+++ b/challenge-168/roger-bell-west/postscript/ch-2.ps
@@ -0,0 +1,237 @@
+%!PS
+
+% begin included library code
+
+/quicksort.main { % lo hi -> (null)
+    3 dict begin
+    /hi exch def
+    /lo exch def
+    /xit false def
+    lo 0 lt {
+        /xit true def
+    } if
+    hi 0 lt {
+        /xit true def
+    } if
+    lo hi ge {
+        /xit true def
+    } if
+    xit not {
+        /p quicksort.partition def
+        lo p quicksort.main
+        p 1 add hi quicksort.main
+    } if
+    end
+} bind def
+
+
+/test.start {
+    print (:) print
+    /test.pass 0 def
+    /test.count 0 def
+} bind def
+
+/quicksort { % [ a c b ] -> [ a b c ]
+    1 dict begin
+    /arr exch def
+    0 arr length 1 sub quicksort.main
+    arr
+    end
+} bind def
+
+
+/values { % dict -> array of dict values
+    [ exch
+      {
+          exch pop
+      } forall
+    ]
+} bind def
+
+/primefactor {
+    4 dict begin
+    /n exch def
+    /f 1 dict def
+    /m n def
+    n sqrt cvi genprimes quicksort {
+        /p exch def
+        {
+            m p mod 0 eq {
+                f p known {
+                    f p f p get 1 add put
+                } {
+                    f p 1 put
+                } ifelse
+                /m m p idiv def
+            } {
+                exit
+            } ifelse
+        } loop
+        m 1 eq {
+            exit
+        } if
+    } forall
+    m 1 gt {
+        f m known {
+            f m f m get 1 add put
+        } {
+            f m 1 put
+        } ifelse
+    } if
+    f
+    end
+} bind def
+
+/test {
+    /test.count test.count 1 add def
+    {
+        /test.pass test.pass 1 add def
+    } {
+        ( ) print
+        test.count (....) cvs print
+        (-fail) print
+    } ifelse
+} bind def
+
+/strconcat % (a) (b) -> (ab)  
+{ exch dup length
+  2 index length add string
+  dup dup 4 2 roll copy length
+  4 -1 roll putinterval
+} bind def
+
+/quicksort.swap {
+    2 dict begin
+    /bi exch def
+    /ai exch def
+    arr ai get
+    arr bi get
+    arr exch ai exch put
+    arr exch bi exch put
+    end
+} bind def
+
+/keys { % dict -> array of dict keys
+    [ exch
+      {
+          pop
+      } forall
+    ]
+} bind def
+
+
+/apush { apush.right } bind def
+
+/apush.right { % [a b] c -> [a b c]
+    exch
+    [ exch aload length 2 add -1 roll ]
+} bind def
+
+/genprimes {
+    /mx exch def
+    /primesh mx dict def
+    2 1 3 {
+        primesh exch true put
+    } for
+    6 6 mx 1 add {
+        dup 1 sub exch 1 add 2 exch {
+            dup mx le {
+                primesh exch true put
+            } {
+                pop
+            } ifelse
+        } for