repeat<n>(a) = (x:[n]) where
	if n = 1 then
		x = a
	else
		if n - (2 * (n / 2)) = 1 then
			u = repeat<n/2>(a);
			x = a . u . u
		else
			u = repeat<n/2>(a);
			x = u . u
		end if
	end if
end where

fulladder(a,b,c) = (s, r) where
  s = (a ^ b) ^ c;
  r = (a & b) + ((a ^ b) & c);
end where

adder<n>(a:[n], b:[n], c_in) = (o:[n], c_out) where
  if n = 0 then
    o = [];
    c_out = 0
  else
    (s_n, c_n1) = fulladder(a[0], b[0], c_in);
    (s_n1, c_out) = adder<n-1>(a[1..], b[1..], c_n1);
    o = s_n . s_n1
  end if
end where

equal<n, m>(a:[n]) = (eq) where
	if n = 0 then
		eq = 1
	else
		if m - (2 * (m / 2)) = 1 then
			eq = a[0] & equal<n-1, m/2>(a[1..]);
		else
			eq = (not a[0]) & equal<n-1, m/2>(a[1..]);
		end if
	end if
end where

reg_n<n>(a:[n]) = (r:[n]) where
	if n = 0 then
		r = []
	else
		r = (reg a[0]) . (reg_n<n-1>(r[1..]))
	end if
end where

and_each<n>(a, b:[n]) = (o:[n]) where
	if n = 0 then
		o = []
	else
		o = (b[0] and a) . and_each<n-1>(a, b[1..])
	end if
end where

count_mod<n, m>(in:[n]) = (out:[n]) where
	neq = not (equal<n, m>(in));
	(incr, carry) = adder<n>(in, 1 . repeat<n-1>(0), 0);
	out = and_each<n>(neq, incr)
end where

main() = (ret:[2],out:[2]) where
	out = count_mod<2, 3>(ret);
	ret = reg_n<2>(out)
end where