Problem: Write a program which manipulates a disjoint set S = {S1, S2, . . . , Sk}.

First of all, the program should read an integer n, then make a disjoint set where each element consists of 0, 1, ... n−1 respectively.

Next, the program should read an integer q and manipulate the set for q queries. There are two kinds of queries for different operations:

* unite(x, y): unites sets that contain x and y, say Sx and Sy, into a new set.
* same(x, y): determine whether x and y are in the same set.

Constraints

* 1 ≤ n ≤ 10000
* 1 ≤ q ≤ 100000
* x ≠ y

Input


n q
com1 x1 y1
com2 x2 y2
...
comq xq yq


In the first line, n and q are given. Then, q queries are given where com represents the type of queries. '0' denotes unite and '1' denotes same operation.

Output

For each same operation, print 1 if x and y are in the same set, otherwise 0, in a line.

Example

Input

5 12
0 1 4
0 2 3
1 1 2
1 3 4
1 1 4
1 3 2
0 1 3
1 2 4
1 3 0
0 0 4
1 0 2
1 3 0


Output

0
0
1
1
1
0
1
1

Solution (in JAVA):

Solution:
import java.util.ArrayList;
import java.util.Scanner;


public class Main {
     class UFT_Node {
int name;
UFT_Node next;
int rank;

public UFT_Node(int new_name){
	this.name = new_name;
	this.rank =0;
	this.next = this;
	}

public UFT_Node getRep(){
	UFT_Node output;
	if (this.next.name == this.name)
		return this;
	else output = this.next.getRep();
	this.next = output; 
	return output;
}

}
	UFT_Node[] nodes;
	public static void main(String[] args){
		ArrayList<Integer> output = new ArrayList<Integer>();
		Main test = new Main();
		Scanner inputScanner = new Scanner(System.in).useDelimiter("\\s");
		int n = inputScanner.nextInt();
		int q = inputScanner.nextInt();
		test.nodes = test.makeArray(n);
		
		int type = -1;
		int x= -1;
		int y= -1;
		for (int i=0;i<q;i++){
			type = inputScanner.nextInt();
			x = inputScanner.nextInt();
			y = inputScanner.nextInt();
			if(type ==0){
				test.union(x,y);
			}
			if(type ==1){
				if(test.same(x, y))
					output.add(1);
				else
					output.add(0);
			}
		} 
		for(Integer out : output){
			System.out.println(out.toString());
		}
	}
	public UFT_Node[] makeArray(int num){
		UFT_Node[] output = new UFT_Node[num];
		for (int i=0; i<num;i++){
			output[i] = new UFT_Node(i);
		}
	return output;
	}
	
	public void union(int x, int y){
		UFT_Node yRep = nodes[y].getRep();
		UFT_Node xRep = nodes[x].getRep();
		if (yRep.rank> xRep.rank){
			xRep.next= yRep;
		}
		else if(yRep.rank< xRep.rank){
			yRep.next= xRep;
		}
		else{
			yRep.next= xRep;
			xRep.rank++;
		}
	}
	
	public boolean same (int x, int y){
		return nodes[x].getRep().name==nodes[y].getRep().name;
	}
}