Score : $200$ points

Problem Statement

$N$ players numbered $1$ to $N$ will play a soccer game. When a player commits an offense, that player will receive a yellow card or a red card. A player who satisfies one of the following conditions will be removed from the game.

• Accumulates two yellow cards.
• Receives a red card.

Once a player is removed, that player will no longer receive any cards.

You will watch this game. Initially, the players have not received any cards. There will be $Q$ events. Correctly answer the questions asked in the events. There are three kinds of events, which are given in the format c x from the input, where $c$ is $1$, $2$, or $3$. The events are as follows.

• 1 x: Player $x$ receives a yellow card.
• 2 x: Player $x$ receives a red card.
• 3 x: You are asked whether player $x$ has been removed from the game. Answer Yes or No.

Constraints

• $1 \leq N \leq 100$
• $1 \leq Q \leq 100$
• $1 \leq x \leq N$ in all events.
• There is at least one event of the third kind.
• A player who has been removed will no longer receive any cards.
• All values in the input are integers.

Input

The input is given from Standard Input in the following format, where $\text{event}_i$ denotes the $i$-th event.

$N$ $Q$

$\text{event}_1$

$\text{event}_2$

$\vdots$

$\text{event}_Q$

Each event is in one of the following formats:

1 $x$

2 $x$

3 $x$

Output

Print $X$ lines, where $X$ is the number of events of the third kind in the input. The $i$-th line should contain Yes if, for the $i$-th event of the third kind, player $x$ has been removed from the game, and No otherwise.

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

No
No
Yes
No
Yes
No

Here are all the events in chronological order.

In the $1$-st event, you are asked whether player $1$ has been removed from the game. Player $1$ has not been removed, so you should print No. In the $2$-nd event, you are asked whether player $2$ has been removed from the game. Player $2$ has not been removed, so you should print No. In the $3$-rd event, player $2$ receives a yellow card. In the $4$-th event, player $1$ receives a red card and is removed from the game. In the $5$-th event, you are asked whether player $1$ has been removed from the game. Player $1$ has been removed, so you should print Yes. In the $6$-th event, you are asked whether player $2$ has been removed from the game. Player $2$ has not been removed, so you should print No. In the $7$-th event, player $2$ receives a yellow card and is removed from the game. In the $8$-th event, you are asked whether player $2$ has been removed from the game. Player $2$ has been removed, so you should print Yes.
In the $9$-th event, you are asked whether player $3$ has been removed from the game. Player $3$ has not been removed, so you should print No.