Given a graph of $n$ vertices and no edge. There are $q$ queries of either form:
- `1 u v` add an edge between $u$ and $v$.
- `2 u v` determine whether $u$ and $v$ are connected.
### Input
- The first line contains 2 integers $n, q$.
- The next $q$ lines, each line contains 3 integers $t, u, v$, a query.
### Output
- For each query of type $2$, print `YES` if $u$ and $v$ are connected, otherwise print `NO`.
### Constraints
- $1 \le n, q \le 10^5$.
- $1 \le u, v \le n$.
### Example
Input:
```
6 5
1 1 2
1 1 3
2 2 3
1 5 6
2 4 5
```
Output:
```
YES
NO
```
