题目描述

There are $N$ integer variables $a_1, \ldots, a_N$. All the initial values are unspecified. You have to process $M$ events in order, each of which is an observation event, a change event or an inquiry event.

One kind of an observation event has the format,

$$\begin{aligned} &1 \ x \ y \end{aligned}$$

which represents that it is observed that $a_x$ and $a_y$ are equal. In other words, after this event it is guaranteed that these two variables have the same value unless there is a change event for either variable.

The other kind of an observation event has the format,

$$\begin{aligned} &2 \ x \ y \end{aligned}$$

which represents that it is observed that $a_x$ and $a_y$ are not equal.

A change event has the format,

$$\begin{aligned} &3 \ x \end{aligned}$$

which represents that the value of $a_x$ changes to a different integer.

Finally, an inquiry event has the format,

$$\begin{aligned} &4 \ x \ y \end{aligned}$$

which asks whether $a_x$ and $a_y$ are equal. If it can be proven from all the past events that $a_x$ and $a_y$ are equal, you have to print Yes. Similarly, if it can be proven that $a_x$ and $a_y$ are not equal, you have to print No. If neither can be proven, you have to print Unknown.

输入格式

The input consists of a single test case of the following format, where all values in the input are integers.

$$\begin{aligned} &N \ M \\ &\text{event}_1 \\ &\vdots \\ &\text{event}_M \end{aligned} $$

The integer $N$ is the number of variables ($1 \leq N \leq 10^6$). The integer $M$ is the number of events ($1 \leq M \leq 500,000$). $M$ events are given in chronological order. The format of each event is explained above. In an observation event or an inquiry event, it is guaranteed that $1 \leq x < y \leq N$. In a change event it is guaranteed that $1 \leq x \leq N$.

At any point, it is guaranteed that there is at least one assignment to all $N$ variables that contradicts none of the given information.

输出格式

For each inquiry event, print Yes, No or Unknown followed by a newline.

4 11
1 1 2
4 1 2
2 3 4
4 3 4
4 1 3
1 1 3
4 1 3
4 1 4
3 1
4 1 3
4 1 4

Yes
No
Unknown
Yes
No
No
Unknown