This is the hard version of the problem. The only difference is that in this version there are remove queries.

Initially you have a set containing one element — $$$0$$$. You need to handle $$$q$$$ queries of the following types:

+ $$$x$$$ — add the integer $$$x$$$ to the set. It is guaranteed that this integer is not contained in the set;
- $$$x$$$ — remove the integer $$$x$$$ from the set. It is guaranteed that this integer is contained in the set;
? $$$k$$$ — find the $$$k\text{-mex}$$$ of the set.

In our problem, we define the $$$k\text{-mex}$$$ of a set of integers as the smallest non-negative integer $$$x$$$ that is divisible by $$$k$$$ and which is not contained in the set.

Input

The first line contains an integer $$$q$$$ ($$$1 \leq q \leq 2 \cdot 10^5$$$) — the number of queries.

The following $$$q$$$ lines describe the queries.

An addition query of integer $$$x$$$ is given in the format + $$$x$$$ ($$$1 \leq x \leq 10^{18}$$$). It is guaranteed that $$$x$$$ is not contained in the set.

A remove query of integer $$$x$$$ is given in the format - $$$x$$$ ($$$1 \leq x \leq 10^{18}$$$). It is guaranteed that $$$x$$$ is contained in the set.

A search query of $$$k\text{-mex}$$$ is given in the format ? $$$k$$$ ($$$1 \leq k \leq 10^{18}$$$).

It is guaranteed that there is at least one query of type ?.

Output

For each query of type ? output a single integer — the $$$k\text{-mex}$$$ of the set.

Note

In the first example:

After the first and second queries, the set will contain elements $$$\{0, 1, 2\}$$$. The smallest non-negative number that is divisible by $$$1$$$ and is not in the set is $$$3$$$.

After the fourth query, the set will contain the elements $$$\{0, 1, 2, 4\}$$$. The smallest non-negative number that is divisible by $$$2$$$ and is not in the set is $$$6$$$.

In the second example:

Initially, the set contains only the element $$$\{0\}$$$.
After adding an integer $$$100$$$ the set contains elements $$$\{0, 100\}$$$.
$$$100\text{-mex}$$$ of the set is $$$200$$$.
After adding an integer $$$200$$$ the set contains elements $$$\{0, 100, 200\}$$$.
$$$100\text{-mex}$$$ of the set $$$300$$$.
After removing an integer $$$100$$$ the set contains elements $$$\{0, 200\}$$$.
$$$100\text{-mex}$$$ of the set is $$$100$$$.
After adding an integer $$$50$$$ the set contains elements $$$\{0, 50, 200\}$$$.
$$$50\text{-mex}$$$ of the set is $$$100$$$.
After removing an integer $$$50$$$ the set contains elements $$$\{0, 200\}$$$.
$$$100\text{-mex}$$$ of the set is $$$50$$$.

Idx	Name	Rating
A	Bestie	1000
B	Ugu	900
C1	Sheikh (Easy version)	1800
C2	Sheikh (Hard Version)	2100
D1	Balance (Easy version)	1500
D2	Balance (Hard version)	2400
E	Location	2800

Codeforces Round 830 (Div. 2)