Before revision:   We show that competitive ratio of an optimal deterministic online algorithm for OUC is at least 3 and at most 5. 
After revision:  We show that competitive ratio of an optimal deterministic online algorithm for OUC is at least 3 and at most 5. Furthermore, we show that for the input point sequences which are subsets of the infinite square or hexagonal lattices, competitive ratio of an optimal deterministic online algorithm for OUC is at least 2.5 and at most 3. The lower bounds derived in this paper are independent of computational complexity.