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my %lookup = map { $_ => 1 << (ord($_) - ord('A')) } 'A'..'Z';

...

print('A'..'Z', "\n");
print(scalar(reverse(sprintf("%26b", $bitmap))), "\n");

ABCDEFGHIJKLMNOPQRSTUVWXYZ
111000011

my @powers = map { 1 << $_ } 0..25;

...

print('A'..'Z', "\n");
print(scalar(reverse(sprintf("%26b", $bitmap))), "\n");