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