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.*;

public class Main{
    public static void main(String[] args){
        Scanner scan = new Scanner(System.in);
        int sets = scan.nextInt(), queries = scan.nextInt();
        UnionFind uf = new UnionFind(sets);
        for(int i = 0; i < queries; i++){
            if(scan.nextInt() == 0) uf.union(scan.nextInt(), scan.nextInt());
            else System.out.println(uf.same(scan.nextInt(), scan.nextInt()) ? 1 : 0);
        }
    }
}

class UnionFind{
    int ufarr[];
    UnionFind(int sets){
        ufarr = new int[sets];
        for(int i = 0; i < sets; i++) ufarr[i] = i;
    }

    int find(int x){
        while(ufarr[x] != x) x = ufarr[x];
        return x;
    }

    int union(int x, int y){
        int x_ = find(x), y_ = find(y);
        if(x_ != y_){
            ufarr[x_] = y_;
            return 0;
        }
        return 1;
    }

    boolean same(int x, int y){
        return find(x) == find(y);
    }
}