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 $i$.

The input is given from Standard Input in the following format: >$N$ $Q$\ >$T _ 1$ $A _ 1$ $B _ 1$\ >$T _ 2$ $A _ 2$ $B _ 2$\ >$\vdots$\ >$T _ Q$ $A _ Q$ $B _ Q$ #### 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.

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 $T _ i=3$.

***For Sample #1:*** 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. ***For Sample #2:*** A user may follow the same user multiple times.

AtCoder [ABC278C]