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 {
    public static int n;
    public static int q;
    public static int[] p;
    public static int[] rank;
 
    public static boolean same(int x, int y) {
        return findSet(x) == findSet(y);
    }
 
    public static void unite(int x, int y) {
        int i = findSet(x);
        int j = findSet(y);
 
        if (i == j){
	    return;
	}
        if (rank[i] > rank[j]){
            p[j] = p[i];
        }
        else {
            p[i] = p[j];
            if(rank[i] == rank[j]){
            rank[j]++;
            }
        }	
    }
 
    public static int findSet(int i) {
       if(p[i] == i){ 
           return i;
        }else{
          return p[i] = findSet(p[i]);
        }
    }
 
    public static void DisjointSet() {
        p = new int[n];
        rank = new int[n];
 
        for (int i = 0; i < n; i++) {
            p[i] = i;
            rank[i] = 0;
        }
    }
 
 
    public static void main (String[] args){
        Scanner scanner = new Scanner(System.in);
        n = scanner.nextInt();
        q = scanner.nextInt();
 
        DisjointSet();
        for (int i = 0; i < q; i++) {
            int com = scanner.nextInt();
            int x = scanner.nextInt();
            int y = scanner.nextInt();
 
            if (com == 0){
                unite(x, y);
            }
            if (com == 1){
                if (same(x, y)){
                    System.out.println(1);
                }else{
                    System.out.println(0);
		}
            }
        }
    }
}