#!/usr/bin/perl
use 5.016;
use warnings;
use List::Util qw/shuffle/;

my $runs  = 10^3;
my $range = 1553;
my @letterRange = ( 'A' .. 'Z' );
my $i = 0;
my (@array,  @arr2, $key, $valref, $permutes);
my %permutes = ();

for ($i=1;$i<=$range;$i++) {       # C-style, start w/"1"; "0" would give 1554 elements
    @array = shuffle @letterRange for 1 ..$runs;   # @arr will hold the 1000th shuffle
    $key = "@array";
    $permutes {$key } = $i;
}

for my $key ( keys %permutes ) {
        my $value = $permutes{$key};
        push @arr2, "$value => $key";
}

print "size of hash:  " . keys( %permutes ) . ".\n";

no warnings 'numeric';
my @sorted = sort {$a <=> $b} @arr2;
use warnings;

for $_ (@sorted) {
    say $_;
}

##</code><code>##

size of hash:  1553.
1 => V Y N H D R W Q C B E F T L S I J M O U Z A G X P K
2 => W E C B M V P I Y U D K G A T Z R O N F S J L X Q H
3 => L A T Y N R C Z J O V U G Q H F B S K W I E X P M D
...