Marisa is conducting research on $n$ ingredients used in cooking, which can be categorized into two groups, Group $A$ and Group $B$. It is important to note that using two ingredients from different groups in a meal can be fatal.
There are $q$ events of two types that Marisa encounters:
- `1 u v`: Marisa realizes that ingredient $u$ and ingredient $v$ belong to different groups.
- `2 u v`: Marisa questions whether it is safe to use ingredient $u$ and ingredient $v$ together in a meal, based on the information she has gathered so far.
Help Marisa answer her questions!
### Input
- The first line contains two integers $n,q$.
- The next $q$ lines, each line contains three integers represent an event. It is guaranteed that all events are valid, there is no ingredient belong to both groups.
### Output
- For each event of type two, print:
+ `FATAL` if two ingredients belong to different group.
+ `SAFE` if two ingredients belong to the same group.
+ `DUNNO` if there is not enough information to conclude.
### Constraints
- $1 \le n,q \le 10^5$.
- $1 \le u, v \le n$.
### Example
Input:
```
3 5
2 1 2
1 1 2
2 1 2
1 2 3
2 1 3
```
Output:
```
DUNNO
FATAL
SAFE
```
