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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.List;
import java.util.StringTokenizer;

public class Main {

	private class DisjointSet {
		
		int[] p, rank;
		
		public DisjointSet(int size) {
			p = new int[size];
			rank = new int[size];
			for (int i = 0; i < size; i++) {
				makeSet(i);
			}
		}

		private void makeSet(int x) {
			p[x] = x;
			rank[x] = 0;
		}
		
		public boolean same(int x, int y) {
			return findSet(x) == findSet(y);
		}

		private int findSet(int x) {
			List<Integer> list = new ArrayList<>();
			
			while (x != p[x]) {
				list.add(x);
				x = p[x];
			}
			
			for (int i : list) {
				p[i] = p[x];
			}
			
			return p[x];
		}
		
		public void unite(int x, int y) {
			link(findSet(x), findSet(y));
		}

		private void link(int x, int y) {
			if (rank[x] > rank[y]) {
				p[y] = x;
			} else {
				p[x] = y;
				if (rank[x] == rank[y]) {
					rank[y]++;
				}
			}
		}
	}
	
	public static void main(String[] args) throws IOException {
		new Main().run();
	}
	
	private void run() throws IOException {
		BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer(reader.readLine());
		int n = Integer.parseInt(st.nextToken());
		DisjointSet ds = new DisjointSet(n);
		int q = Integer.parseInt(st.nextToken());
		for (int i = 0; i < q; i++) {
			st = new StringTokenizer(reader.readLine());
			int c = Integer.parseInt(st.nextToken());
			int x= Integer.parseInt(st.nextToken());
			int y = Integer.parseInt(st.nextToken());
			if (c == 0) {
				ds.unite(x, y);
			} else {
				System.out.println(ds.same(x, y)?"1":"0");
			}
		}
		reader.close();
	}
}