Problem8240--ABC278 —— C - FF

8240: ABC278 —— C - FF

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Time Limit : 1.000 sec  Memory Limit : 256 MiB

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Description

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≤i≤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:
$N\ Q$
$T_1\ A_1\ B_1$
$T_2\ A_2\ B_2$
$⋮$
$T_Q\ A_Q\ B_Q$

Output

Print X lines, where X is the number of i's (1≤i≤Q) such that $T_i=3$. The j-th (1≤j≤X) line should contain the answer to the j-th operation such that $T_i=3$.

Constraints

$2≤N≤10^9$
$1≤Q≤2×10^5$
$T_i=1,2,3\ (1≤i≤Q)$
$1≤A_i≤N\ (1≤i≤Q)$
$1≤B_i≤N\ (1≤i≤Q)$
$A_i\neq B_i\ (1≤i≤Q)$
There exists $i\ (1≤i≤Q)$ such that $T_i=3$.
All values in the input are integers.

Sample 1 Input 

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 1 Output 

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 2 Input 

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 2 Output 

Yes
No

Sample 3 Input 

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 3 Output 

No
No
No
No
Yes
Yes
No
No
No
Yes
Yes

Source/Category

 
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