Cave Connectivity

Huihui is enthusiastic about cave exploration. One day, he arrives at a cave group area labeled JSZX based on a map. The area consists of \(n\) caves (numbered from 1 to n) and several channels. Each channel connects exactly two caves. Two caves are considered connected if there exists a sequence of channels linking them (this sequence is called a path connecting the caves).

The channels (or edges) are unstable and can appear or be destroyed over time. The monitoring instrument displays these changes in real time on the terminal as follows:

• Connect u v: A channel between caves \(u\) and \(v\) appears.
• Destroy u v: The channel between caves \(u\) and \(v\) is destroyed.

It is guaranteed that at any moment there is at most one path between any two caves. Initially, there are no channels. In addition, the terminal can also receive the command:

• Query u v: Check whether cave \(u\) and cave \(v\) are currently connected.

Your task is to process a sequence of \(m\) commands. For every Query command, output Yes if the specified caves are connected; otherwise output No.

inputFormat

The first line contains two integers \(n\) and \(m\) \((1 \le n, m \le 10^5)\), representing the number of caves and the number of commands, respectively.

The following \(m\) lines contain a command each, in one of the following formats:

• Connect u v
• Destroy u v
• Query u v

Note: Commands are given online. Initially, there are no channels.

outputFormat

For each Query command, output a single line: Yes if the two caves are connected, or No if they are not.

sample

5 7
Connect 1 2
Connect 2 3
Query 1 3
Query 1 4
Connect 4 5
Destroy 2 3
Query 1 3

Yes
No
No