Sidenote: Is this how friends work? I wouldn't know.

People in a class have friends. If people are friends, friends of friends, friends of friends of friends, and so on, they are in the same friend group. Unfortunately, this class is cursed. By the end of the year, all friendships have broken down. At a given point in time, can you tell whether 2 people are in the same friend group? (Friends are friends of themselves).

Input

The first line contains integers ~n~ and ~q~, the number of people, and the number of queries respectively.

The next ~q~ lines contains queries of the following forms:

• 1 a b indicating that the friendship between ~a~ and ~b~ has broken down. Sad.
• 2 a b asking whether ~a~ and ~b~ are currently within the same friendship group.

Output

On each line, output the answer to each query of type 2:

• A Yes if they are a part of the same friend group.
• No otherwise.

Constrainsts

• ~1 \le n \le 10^5~
• ~1 \le q \le 5\times10^5~

Example 1

Input

5 10
1 1 2
1 4 5
2 3 4
1 3 4
1 2 5
2 2 5
2 2 5
1 3 5
2 2 4
1 1 5

Output

Yes
No
No
No

Example 2

Input

10 20
2 3 9
2 6 10
1 3 10
2 4 8
1 1 9
1 2 8
2 6 10
2 4 8
1 2 9
1 6 10
1 5 8
1 2 8
1 5 6
2 7 9
1 8 10
2 7 9
2 2 4
1 3 5
1 5 8
2 1 8

Output

Yes
Yes
No
Yes
No
No
No
No
No