C - FF

Score : $300$ points

Problem Statement

Takahashi runs an SNS "Twidai," which has $N$ users from user $1$ through user $N$. In Twidai, users can follow or unfollow other users.

$Q$ operations have been performed since Twidai was launched. The $i$-th $(1\leq i\leq Q)$ operation is represented by three integers $T_i$, $A_i$, and $B_i$, whose meanings are as follows:

• If $T_i = 1$: it means that user $A_i$ follows user $B_i$. If user $A_i$ is already following user $B_i$ at the time of this operation, it does not make any change.
• If $T_i = 2$: it means that user $A_i$ unfollows user $B_i$. If user $A_i$ is not following user $B_i$ at the time of this operation, it does not make any change.
• If $T_i = 3$: it means that you are asked to determine if users $A_i$ and $B_i$ are following each other. You need to print Yes if user $A_i$ is following user $B_i$ and user $B_i$ is following user $A_i$, and No otherwise.

When the service was launched, no users were following any users.

Print the correct answers for all operations such that $T_i = 3$ in ascending order of $i$.

Constraints

• $2 \leq N \leq 10 ^ 9$
• $1 \leq Q \leq 2\times10 ^ 5$
• $T _ i=1,2,3\ (1\leq i\leq Q)$
• $1 \leq A _ i \leq N\ (1\leq i\leq Q)$
• $1 \leq B _ i \leq N\ (1\leq i\leq Q)$
• $A _ i\neq B _ i\ (1\leq i\leq Q)$
• There exists $i\ (1\leq i\leq Q)$ such that $T _ i=3$.
• All values in the input are integers.

Input

The input is given from Standard Input in the following format:

$N$ $Q$

$T _ 1$ $A _ 1$ $B _ 1$

$T _ 2$ $A _ 2$ $B _ 2$

$\vdots$

$T _ Q$ $A _ Q$ $B _ Q$

Output

Print $X$ lines, where $X$ is the number of $i$'s $(1\leq i\leq Q)$ such that $T _ i=3$. The $j$-th $(1\leq j\leq X)$ line should contain the answer to the $j$-th operation such that $T _ i=3$.

3 9
1 1 2
3 1 2
1 2 1
3 1 2
1 2 3
1 3 2
3 1 3
2 1 2
3 1 2

No
Yes
No
No

Twidai has three users. The nine operations are as follows.

• User $1$ follows user $2$. No other users are following or followed by any users.
• Determine if users $1$ and $2$ are following each other. User $1$ is following user $2$, but user $2$ is not following user $1$, so No is the correct answer to this operation.
• User $2$ follows user $1$.
• Determine if users $1$ and $2$ are following each other. User $1$ is following user $2$, and user $2$ is following user $1$, so Yes is the correct answer to this operation.
• User $2$ follows user $3$.
• User $3$ follows user $2$.
• Determine if users $1$ and $3$ are following each other. User $1$ is not following user $3$, and user $3$ is not following user $1$, so No is the correct answer to this operation.
• User $1$ unfollows user $2$.
• Determine if users $1$ and $2$ are following each other. User $2$ is following user $1$, but user $1$ is not following user $2$, so No is the correct answer to this operation.

2 8
1 1 2
1 2 1
3 1 2
1 1 2
1 1 2
1 1 2
2 1 2
3 1 2

Yes
No

A user may follow the same user multiple times.

10 30
3 1 6
3 5 4
1 6 1
3 1 7
3 8 4
1 1 6
2 4 3
1 6 5
1 5 6
1 1 8
1 8 1
2 3 10
1 7 6
3 5 6
1 6 7
3 6 7
1 9 5
3 8 6
3 3 8
2 6 9
1 7 1
3 10 8
2 9 2
1 10 9
2 6 10
2 6 8
3 1 6
3 1 8
2 8 5
1 9 10

No
No
No
No
Yes
Yes
No
No
No
Yes
Yes