It may so happen again that both filters produce a positive; we apply the same idea recursively to solve this problem. Because each pair of filters only contains keys that are in the map "and" produced false positives on all previous filter pairs, the number of keys is extremely likely to quickly drop to a very small quantity that can be easily stored in an ordinary deterministic map, such as a pair of small arrays with linear search. Moreover, the average total search time is low, because almost all queries will be resolved by the first pair, almost all remaining queries by the second pair, and so on. The total space required is in practice independent of "n", and is almost entirely occupied by the first filter pair.