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.

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.

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.

Sample Input 1

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

Sample Output 1

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.

Sample Input 2

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

Sample Output 2

Yes
No

A user may follow the same user multiple times.

Sample Input 3

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

Sample Output 3

No
No
No
No
Yes
Yes
No
No
No
Yes
Yes

见题面 Input 部分

见题面 Output 部分