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sub naive_shuffle {
  my $n = my @p = @_;
...
  }
  return @p;
}

# untested
sub naive_shuffle_rec {
...
  @p[ $i, $j ] = @p[ $j, $i ]; # swap
  return ++$i < $n ? naive_shuffle_rec( $i, @p ) : @p;
}

sub naive_shuffle_traverse {
  my $i = shift;
...
    return;
  }
}

naive_shuffle_traverse(-1, undef, 1..3);

sub naive_shuffle_count {
  my $i = shift;
...
    return;
  }
}

my %tally = ();
naive_shuffle_count( -1, undef, \%tally, 1..3 );

  DB<2> x \%tally
0  HASH(0x82d7f94)
...
   '2 3 1' => 5
   '3 1 2' => 4
   '3 2 1' => 4

sub random_perm {
  my $n = my @p = @_;
...
  }
  return @p;
}