You are given ~N~ nodes that are completely separated. You must support the following operations:

• 1 a b Add an edge between node ~a~ and node ~b~. ~(1 \le a, b \le N, a \neq b)~. Note that it is not guaranteed node ~a~ and node ~b~ are not connected beforehand.
• 2 a b Output whether two nodes ~a, b~ ~(1 \le a, b \le N, a \neq b)~ are connected. Two nodes are connected if there is a path from the first node to the second.

There will be ~Q~ of these operations.

Input Specification

The first line will ~2~ integers, ~N, Q~ ~(1 \le N, Q \le 10^5)~.

The next ~Q~ lines will each contain a operation as defined above.

Output Specification

For each type ~2~ operation, print YES if the two nodes are connected, and NO otherwise. (Exact capitalization).

Subtasks

Subtask 1 [20%]

~N, Q \le 100~

Subtask 2 [80%]

No further constraints.

Sample Input

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

Sample Output

NO
YES
NO