You have a graph of ~N~ nodes and ~Q~ queries.

Queries will be in two types:

1 x y: Add an edge between nodes ~X~ and ~Y~ ~(1 \leq X,Y \leq N, X\neq Y~).

2 k: Print the sum of the sizes of the connected components whose sizes are less than or equal to ~K~ ~(1 \leq K \leq N)~.

Input Specification

The first line will contain two integers ~N~ and ~Q~ ~(2 \leq N,Q \leq 2\cdot 10^5)~.

The next ~Q~ lines will contain a query of one of the two types described above.

Output Specification

You are to print one line for each type 2 query: the sum described in the problem statement.

Subtasks

Subtask 1 (30%)

~N,Q \leq 100~

Subtask 2 (70%)

No further constraints.

Sample Input

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

Sample Output

3
2