You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 3.0 seconds
Memory limit: 256.0 MB

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

## Examples
```input
18
+ 1
+ 2
? 1
+ 4
? 2
+ 6
? 3
+ 7
+ 8
? 1
? 2
+ 5
? 1
+ 1000000000000000000
? 1000000000000000000
- 4
? 1
? 2
```
```output
3
6
3
3
10
3
2000000000000000000
3
4
```
-----
```input
10
+ 100
? 100
+ 200
? 100
- 100
? 100
+ 50
? 50
- 50
? 50
```
```output
200
300
100
100
50
```

## 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 $$$50$$$.

Now solve the problem and return the code.