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.Scanner;


public class Main {

	static int[] par;
	static int[] rank;

	static void initUF(int n) {
		par = new int[n];
		rank = new int[n];
		for (int i=0;i<n;i++){
			par[i] = i;
			rank[i] = 1;
		}
	}
	
	static int root(int n) {
		if (par[n]==n) {
			return n;
		} else {
			return (par[n] = root(par[n]));
		}
	}
	
	static boolean same(int i, int j) {
		return root(i)==root(j);
	}

	static void unite(int i, int j) {
		int x = root(i);
		int y = root(j);
		
		if (rank[x]>rank[y]) {
			par[y] = x;
		} else {
			par[x] = y;
			if (rank[x]==rank[y]) rank[x]++;
		}
	}
	
	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		int n = scan.nextInt();
		int q = scan.nextInt();
		
		initUF(n);
		for (int i=0;i<q;i++) {
			int com = scan.nextInt();
			int x = scan.nextInt();
			int y = scan.nextInt();
			if (com==0) {
				unite(x, y);
			} else {
				System.out.println(same(x, y) ? 1 : 0);
			}
		}
		
	}
	
}