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#!/usr/bin/perl

...
        }
        print "\n";
}

E(1/32) = E(1/16) & R
E(2/32) = E(1/16) = E(2/16) & R
...
E(29/32) = E(1/4) | E(7/8) = E(1/2) | E(13/16) = E(3/4) | E(5/8)
E(30/32) = E(15/16) = E(2/2) & E(15/16)
E(31/32) = E(1/2) | E(15/16) = E(3/4) | E(7/8)