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my @classes = qw( odd even );
while (...) {
   push @classes, my $class = shift @classes;
   ...
}

my $odd;
while (...) {
   my $class = ($odd++ % 2 == 0) ? 'odd' : 'even';
   ...
}

my $odd;
while (...) {
   my $class = $odd++ % 2 ? 'even' : 'odd';
   ...
}

my $odd;
while (...) {
   my $class = $odd ^= 1 ? 'odd' : 'even';
   ...
}

my $odd;
while (...) {
   my $class = ('odd','even')[$odd++ % 2];
   ...
}

my $odd;
while (...) {
   my $class = ('odd','even')[$odd ^= 1];
   ...
}

my $class = 'even';
while (...) {
   $class = ($class eq 'odd') ? 'even' : 'odd';
   ...
}

my @classes = qw( odd even );
while (...) {
   push @classes, my $class = shift @classes;
   ...
}

my $class = 'even';
while (...) {
    ($class) = grep $_ ne $class, qw( odd even );
    ...
}

my ($class, %flip_class) = qw( even odd even even odd );
while (...) {
    $class = $flip_class{$class};
    ...
}

my ($class, %flip_class) = qw( odd even )[1,1,0,0,1];
while (...) {
    $class = $flip_class{$class};
    ...
}

use Tie::Cycle qw( );

...
while (...) {
   ...
}