A country has $n$ cities. There are two ways to move between two cities, using subway or using road. Initially, there are no connection between any two cities.
There are $q$ queries of either form:
* `1 u v`: Build a road between $u$ and $v$.
* `2 u v`: Build a subway system between $u$ and $v$.
After each query, determine if the traffic system in this country is good.
The system is called good if for every pair of cities $i$ and $j$, if one can travel from $i$ to $j$ using subway then he can also use road to travel, and vice versa.
### Input
- The first line contains two integers $n, q$.
- The next $q$ lines, each line is a query.
### Output
- For each query, if the system is good, print `YES`, otherwise print `NO`.
### Constraints
- $1 \le n, q \le 10^5$.
- $1 \le u, v \le n$.
### Example
Input:
```
2 2
1 1 2
2 1 2
```
Output:
```
NO
YES
```
