Merge pull request #6258 from Firedrake/rogerbw-challenge-169

Solutions for challenge #169

18 files changed, 1864 insertions, 0 deletions

diff --git a/challenge-169/roger-bell-west/javascript/ch-1.js b/challenge-169/roger-bell-west/javascript/ch-1.js
new file mode 100755
index 0000000000..d1ba3034c6
--- /dev/null
+++ b/challenge-169/roger-bell-west/javascript/ch-1.js
@@ -0,0 +1,90 @@
+#! /usr/bin/node
+
+// by Frank Tan
+// https://stackoverflow.com/questions/38400594/javascript-deep-comparison
+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 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 brilliant (ct) {
+    let base = 1;
+    let out = new Set;
+    while (true) {
+        let pv = genprimes(base * 10).filter(i => i >= base);
+        for (let ai = 0; ai < pv.length; ai++) {
+            for (let bi = ai; bi < pv.length; bi++) {
+                out.add(pv[ai] * pv[bi]);
+            }
+        }
+        if (out.size >= ct) {
+            break;
+        }
+        base *= 10;
+    }
+    let o = [...out];
+    o.sort((a,b) => a-b);
+    o.length = ct;
+    return o;
+}
+
+if (deepEqual(brilliant(20),[4, 6, 9, 10, 14, 15, 21, 25, 35, 49, 121,
+                             143, 169, 187, 209, 221, 247, 253, 289,
+                             299])) {
+    process.stdout.write("Pass");
+} else {
+    process.stdout.write("FAIL");
+}
+process.stdout.write("\n");
diff --git a/challenge-169/roger-bell-west/javascript/ch-2.js b/challenge-169/roger-bell-west/javascript/ch-2.js
new file mode 100755
index 0000000000..174d0de8cd
--- /dev/null
+++ b/challenge-169/roger-bell-west/javascript/ch-2.js
@@ -0,0 +1,122 @@
+#! /usr/bin/node
+
+// by Frank Tan
+// https://stackoverflow.com/questions/38400594/javascript-deep-comparison
+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 gcd (m0,n0) {
+    let m=m0
+    let n=n0
+    while (n != 0) {
+        [m,n]=[n,m % n]
+    }
+    return m
+}
+
+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 achilles(ct) {
+    let out = [];
+    let n = 1;
+    while (true) {
+        n++;
+        let pv = [...primefactor(n).values()];
+        if (pv.length > 1 &&
+            Math.min(...pv) >= 2 &&
+            pv.reduce((acc, x) => gcd(acc,x),pv[0]) == 1) {
+            out.push(n);
+            if (out.length >= ct) {
+                break;
+            }
+        }
+    }
+    return out;
+}
+
+if (deepEqual(achilles(20),[72, 108, 200, 288, 392, 432, 500, 648,
+                            675, 800, 864, 968, 972, 1125, 1152, 1323,
+                            1352, 1372, 1568, 1800])) {
+    process.stdout.write("Pass");
+} else {
+    process.stdout.write("FAIL");
+}
+process.stdout.write("\n");
diff --git a/challenge-169/roger-bell-west/kotlin/ch-1.kt b/challenge-169/roger-bell-west/kotlin/ch-1.kt
new file mode 100644
index 0000000000..4b680bff1f
--- /dev/null
+++ b/challenge-169/roger-bell-west/kotlin/ch-1.kt
@@ -0,0 +1,62 @@
+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 brilliant(ct: Int): List<Int> {
+    var base = 1
+    var out = mutableSetOf<Int>()
+    while (true) {
+        val pl = genprimes(base * 10).filter{it >= base}
+        for (ai in 0..pl.size-1) {
+            for (bi in ai..pl.size-1) {
+                out.add( pl[ai] * pl[bi] )
+            }
+        }
+        if (out.size >= ct) {
+            break
+        }
+        base *= 10
+    }
+    return out.toList().sorted().subList(0,ct)
+}
+
+fun main() {
+    if (brilliant(20) == listOf(4, 6, 9, 10, 14, 15, 21, 25, 35, 49,
+                                121, 143, 169, 187, 209, 221, 247,
+                                253, 289, 299)) {
+        print("Pass")
+    } else {
+        print("FAIL")
+    }
+    println("")
+}
diff --git a/challenge-169/roger-bell-west/kotlin/ch-2.kt b/challenge-169/roger-bell-west/kotlin/ch-2.kt
new file mode 100644
index 0000000000..ed13770637
--- /dev/null
+++ b/challenge-169/roger-bell-west/kotlin/ch-2.kt
@@ -0,0 +1,99 @@
+import kotlin.math.*
+
+fun gcd(m0: Int,n0: Int): Int {
+    var m=m0
+    var n=n0
+    while (n != 0) {
+        val tmp=m % n
+        m = n
+        n = tmp
+    }
+    return m
+}
+
+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 achilles(ct: Int): ArrayList<Int> {
+    var out = ArrayList<Int>()
+    var n = 1
+    while (true) {
+        n += 1
+        val pv = primefactor(n).values
+        if (pv.size > 1 &&
+            pv.minOrNull()!! >= 2 &&
+            pv.reduce { acc, x -> gcd(acc,x) } == 1) {
+            out.add(n)
+            if (out.size >= ct) {
+                break
+            }
+        }
+    }
+    return out
+}
+
+fun main() {
+    if (achilles(20) == listOf(72, 108, 200, 288, 392, 432, 500, 648,
+                               675, 800, 864, 968, 972, 1125, 1152,
+                               1323, 1352, 1372, 1568, 1800)) {
+        print("Pass")
+    } else {
+        print("FAIL")
+    }
+    println("")
+}
diff --git a/challenge-169/roger-bell-west/lua/ch-1.lua b/challenge-169/roger-bell-west/lua/ch-1.lua
new file mode 100755
index 0000000000..8c0fc0b1e6
--- /dev/null
+++ b/challenge-169/roger-bell-west/lua/ch-1.lua
@@ -0,0 +1,108 @@
+#! /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 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 brilliant(n0)
+   local base = 1
+   local out = {}
+   local n = 0
+   while true do
+      pl = genprimes(base * 10)
+      for ai,av in pairs(pl) do
+         if av >= base then
+            for bi,bv in pairs(pl) do
+               if bi >= ai then
+                  c = av * bv
+                  if out[c] == nil then
+                     n = n + 1
+                  end
+                  out[c] = true
+               end
+            end
+         end
+      end
+      if n >= n0 then
+         break
+      end
+      base = base * 10
+   end
+   local o = {}
+   for k,v in pairs(out) do
+      table.insert(o,k)
+   end
+   table.sort(o)
+   while #o > n0 do
+      table.remove(o)
+   end
+   return o
+end
+
+if recursive_compare(brilliant(20), {4, 6, 9, 10, 14, 15, 21, 25, 35,
+                                     49, 121, 143, 169, 187, 209, 221,
+                                     247, 253, 289, 299}) then
+   io.write("Pass")
+else
+   io.write("FAIL")
+end
+print("")
diff --git a/challenge-169/roger-bell-west/lua/ch-2.lua b/challenge-169/roger-bell-west/lua/ch-2.lua
new file mode 100755
index 0000000000..902ce1b6bd
--- /dev/null
+++ b/challenge-169/roger-bell-west/lua/ch-2.lua
@@ -0,0 +1,154 @@
+#! /usr/bin/lua
+
+-- by hookenz at
+-- https://stackoverflow.com/questions/9168058/how-to-dump-a-table-to-console
+function dump(o)
+   if type(o) == 'table' then
+      local s = '{ '
+      for k,v in pairs(o) do
+         if type(k) ~= 'number' then k = '"'..k..'"' end
+         s = s .. '['..k..'] = ' .. dump(v) .. ','
+      end
+      return s .. '} '
+   else
+      return tostring(o)
+   end
+end
+
+-- 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 gcd(m0,n0)
+   local m,n = m0,n0
+   while n ~= 0 do
+      m,n = n,m % n
+   end
+   return m
+end
+
+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 achilles(ct)
+   local o = {}
+   local n = 1
+   while true do
+      n = n + 1
+      local pv = {}
+      for k,v in pairs(primefactor(n)) do
+         table.insert(pv,v)
+      end
+      if #pv > 1 then
+         if math.min(table.unpack(pv)) >= 2 then
+            local g = 0
+            for k,v in pairs(pv) do
+               if g == 0 then
+                  g = v
+               else
+                  g = gcd(g,v)
+               end
+            end
+            if g == 1 then
+               table.insert(o,n)
+               if #o >= ct then
+                  break
+               end
+            end
+         end
+      end
+   end
+   return o
+end
+
+if recursive_compare(achilles(20), {72, 108, 200, 288, 392, 432, 500,
+                                    648, 675, 800, 864, 968, 972,
+                                    1125, 1152, 1323, 1352, 1372,
+                                    1568, 1800}) then
+   io.write("Pass")
+else
+   io.write("FAIL")
+end
+print("")
diff --git a/challenge-169/roger-bell-west/perl/ch-1.pl b/challenge-169/roger-bell-west/perl/ch-1.pl
new file mode 100755
index 0000000000..8ee19a6e92
--- /dev/null
+++ b/challenge-169/roger-bell-west/perl/ch-1.pl
@@ -0,0 +1,61 @@
+#! /usr/bin/perl
+
+use strict;
+use warnings;
+use experimental 'signatures';
+
+use Test::More tests => 1;
+
+is_deeply(brilliant(20),
+          [4, 6, 9, 10, 14, 15, 21, 25, 35, 49, 121,
+           143, 169, 187, 209, 221, 247, 253, 289, 299],
+          'example 1');
+
+sub genprimes($mx) {
+  my %primesh=map {$_ => 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;
+    }
+    $p=shift @q;
+  }
+  return [sort {$a <=> $b} keys %primesh];
+}
+
+sub brilliant($ct) {
+  my $base = 1;
+  my %out;
+  while (1) {
+    my @pl = grep {$_ >= $base} @{genprimes($base * 10)};
+    foreach my $ai (0..$#pl) {
+      foreach my $bi ($ai..$#pl) {
+        $out{ $pl[$ai] * $pl[$bi] } = 1;
+      }
+    }
+    if (scalar keys %out >= $ct) {
+      last;
+    }
+    $base *= 10;
+  }
+  my @o = sort {$a <=> $b} keys %out;
+  splice @o,$ct;
+  return \@o;
+}
diff --git a/challenge-169/roger-bell-west/perl/ch-2.pl b/challenge-169/roger-bell-west/perl/ch-2.pl
new file mode 100755
index 0000000000..94cf5853d0
--- /dev/null
+++ b/challenge-169/roger-bell-west/perl/ch-2.pl
@@ -0,0 +1,85 @@
+#! /usr/bin/perl
+
+use strict;
+use warnings;
+use experimental 'signatures';
+use List::Util qw(min reduce);
+
+use Test::More tests => 1;
+
+is_deeply(achilles(20),
+          [72, 108, 200, 288, 392, 432, 500, 648, 675, 800, 864, 968,
+           972, 1125, 1152, 1323, 1352, 1372, 1568, 1800],
+          'example 1');
+
+sub gcd($m,$n) {
+  while ($n!=0) {
+    ($m,$n)=($n,$m % $n);
+  }
+  return $m;
+}
+
+sub genprimes($mx) {
+  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;
+    }
+    $p=shift @q;
+  }
+  return [sort {$a <=> $b} keys %primesh];
+}
+
+sub primefactor($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 achilles($ct) {
+  my @o;
+  my $n = 1;
+  while (1) {
+    $n++;
+    my @pv = values %{primefactor($n)};
+    if (scalar @pv > 1 &&
+        min(@pv) >= 2 &&
+        (reduce {gcd($a,$b)} @pv) == 1) {
+      push @o,$n;
+      if (scalar @o >= $ct) {
+        last;
+      }
+    }
+  }
+  return \@o;
+}
diff --git a/challenge-169/roger-bell-west/postscript/ch-1.ps b/challenge-169/roger-bell-west/postscript/ch-1.ps
new file mode 100644
index 0000000000..8c675e37bf
--- /dev/null
+++ b/challenge-169/roger-bell-west/postscript/ch-1.ps
@@ -0,0 +1,265 @@
+%!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.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 {
+    /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 { % [ a c b ] -> [ a b c ]
+    1 dict begin
+    /arr exch def
+    0 arr length 1 sub quicksort.main
+    arr
+    end
+} 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
+
+/filter { % array proc(bool) -> array
+    1 dict begin
+    /p exch def
+    [ exch
+      {
+          dup p not
+          {
+              pop
+          } if
+      } forall
+    ]
+    end
+} 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
+    } for
+    /q [ 3 5 7 ] def
+    /qi 0 def
+    /p 2 def
+    /mr mx sqrt cvi def
+    {
+        p mr le not {
+            exit
+        } if
+        primesh p known {
+            p dup mul p mx {
+                primesh exch undef
+            } for
+        } if
+        q length qi sub 2 le {
+            /q q q q length 1 sub get 4 add apush def
+            /q q q q length 1 sub get 2 add apush def
+        } if
+        /p q qi get def
+        /qi qi 1 add def
+    } loop
+    primesh keys
+} 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
+
+/keys { % dict -> array of dict keys
+    [ exch
+      {
+          pop
+      } forall
+    ]
+} 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
+
+/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.start {
+    print (:) print
+    /test.pass 0 def
+    /test.count 0 def
+} bind def
+
+% end included library code
+
+/brilliant {
+    6 dict begin
+    /ct exch def
+    /base 1 def
+    /out 0 dict def
+    {
+        /pl base 10 mul 1 sub genprimes { base ge } filter def
+        0 1 pl length 1 sub {
+            /a e