D. Vasiliy's Multiset
time limit per test
4 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Author has gone out of the stories about Vasiliy, so here is just a formal task description.

You are given q queries and a multiset A, initially containing only integer 0. There are three types of queries:

  1. "+ x" — add integer x to multiset A.

  • "- x" — erase one occurrence of integer x from multiset A. It's guaranteed that at least one x is present in the multiset A before this query.
  • "? x" — you are given integer x and need to compute the value , i.e. the maximum value of bitwise exclusive OR (also know as XOR) of integer x and some integer y from the multiset A.
  • Multiset is a set, where equal elements are allowed.

    Input

    The first line of the input contains a single integer q (1 ≤ q ≤ 200 000) — the number of queries Vasiliy has to perform.

    Each of the following q lines of the input contains one of three characters '+', '-' or '?' and an integer xi (1 ≤ xi ≤ 109). It's guaranteed that there is at least one query of the third type.

    Note, that the integer 0 will always be present in the set A.

    Output

    For each query of the type '?' print one integer — the maximum value of bitwise exclusive OR (XOR) of integer xi and some integer from the multiset A.

    Example
    Input
    10
    + 8
    + 9
    + 11
    + 6
    + 1
    ? 3
    - 8
    ? 3
    ? 8
    ? 11
    Output
    11
    10
    14
    13
    Note

    After first five operations multiset A contains integers 0, 8, 9, 11, 6 and 1.

    The answer for the sixth query is integer  — maximum among integers , , , and .