## Source

**This problem is adapted from [Long Long OJ](https://www.llong.tech/). All rights reserved by NOISG.**

**Problem source: <https://github.com/noisg/sg_noi_archive/tree/master/2019_prelim> (Task 3)**

**Materials compiled by [](/user/27).**

## Problem Description

There are $N$ charged particles. **Particles with opposite charges attract each other, while particles with the same charge repel each other.**

There are $Q$ operations, each represented as $T_i,A_i,B_i$, which can be divided into three types based on $T_i$:
- Operation $\tt A$ means $A_i$ and $B_i$ **attract** each other.
- Operation $\tt R$ means $A_i$ and $B_i$ **repel** each other.
- Operation $\tt Q$ asks what would happen if $A_i$ and $B_i$ are placed together, given the current information.

For each $\tt Q$ operation, if it is **determined that they attract**, output $\tt A$; if **determined that they repel**, output $\tt R$; if it cannot be determined, output $\tt ?$.

It is guaranteed that there is at least one possible configuration where all operations are consistent.

## Input Format

The first line contains two integers $N$ and $Q$.

The next $Q$ lines each contain a character $T_i$ and two integers $A_i,B_i$, representing an operation.

## Output Format

Several lines, each representing the answer to a $\tt Q$ operation.

## Samples

```input1
2 3
Q 1 2
R 1 2
Q 1 2

?
R

4 5
R 1 2
A 2 3
A 1 4
Q 2 4
Q 1 3

A
A

Sample 1 Explanation

For the first query, the relationship between $1$ and $2$ cannot be determined, so output $\tt ?$.

For the second query, it is determined that $1$ and $2$ repel each other, so output $\tt R$.

Data Range

For $100\%$ of the data:

• $1 \le N,Q \le 10^5$.
• $1 \le A_i \neq B_i \le N$.
• $T_i$ can only be $\tt A$, $\tt R$, or $\tt Q$.