# dynamic programming:
LIS := proc(L)
	local i, j;
	local index := 1;
	local output := Array(1..numelems(L), i -> Array(1..0));

	for i from 1 to numelems(L) do
		for j from 1 to i - 1 do
			if (L[j] < L[i]) and (upperbound(output[j]) > upperbound(output[i])) then
				output[i] := copy(output[j]);
			end if;
		end do;
		# append current value
		output[i] ,= L[i];
	end do;

	#output longest subsequence using loop
	for i from 2 to numelems(L) do
		if (upperbound(output[i]) > upperbound(output[index])) then
			index := i;
		end if;	
	end do;
	
	return output[index];
	
end proc: