user
For this task, for our purposes, a cuboid is a 3 dimensional object, with six rectangular faces, where all angles are right angles, opposite faces of the cuboid are equal, and where each dimension is a positive integer unit length. It will subsequently be referred to simply as a cuboid; but be aware that it references the above definition.

The surface area of a cuboid is two times the length times the width, plus two times the length times the height, plus two times the width times the height. A cuboid will always have an even integer surface area. The minimum surface area a cuboid may have is 6; one where the **l**, **w**, and **h** measurements are all **1**.

```
  2 × ( l × w + w × h + h × l )
  2 × ( 1 × 1 + 1 × 1 + 1 × 1 ) = 6

```

Different cuboid configurations (may) yield different surface areas, but the surface area is always an integer and is always even.

A cuboid with l = 2, w = 1 h = 1 has a surface area of 10

```
  2 × ( 2 × 1 + 1 × 1 + 1 × 2 ) = 10

```

There is no configuration which will yield a surface area of 8.

There are 16 known even integer values below 1000 which can not be a surface area for any integer cuboid. It is conjectured, though not rigorously proved, that no others exist.

Task

* Find and display the sixteen even integer values larger than 6 (the minimum cuboid area) and less than 1000

that can not be the surface area of a cuboid.

See also

* Numbers Aplenty - O'Halloran numbers * OEIS:A072843 - O'Halloran numbers: even integers which cannot be the surface area of a cuboid with integer-length sides * Idoneal numbers
assistant
```
my @Area;

my $threshold = 1000; # a little overboard to make sure we get them all

for 1..$threshold -> $x {
    for 1..$x -> $y {
        last if $x × $y > $threshold;
        for 1..$y -> $z {
           push @Area[my $area = ($x × $y + $y × $z + $z × $x) × 2], "$x,$y,$z";
           last if $area > $threshold;
        }
    }
}

say "Even integer surface areas NOT achievable by any regular, integer dimensioned cuboid:\n" ~
   @Area[^$threshold].kv.grep( { $^key > 6 and $key %% 2 and !$^value } )»[0];

```

Output:

```
Even integer surface areas NOT achievable by any regular, integer dimensioned cuboid:
8 12 20 36 44 60 84 116 140 156 204 260 380 420 660 924
```