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 void main(String[] args){
        int n, q;
        Scanner scanner = new Scanner(System.in);
        n = scanner.nextInt();
        q = scanner.nextInt();
        UnionFind uf = new UnionFind(n);

        for(int i = 0; i < q; i++){
            int query, x, y;
            query = scanner.nextInt();
            x = scanner.nextInt();
            y = scanner.nextInt();
            if(query == 0){
                uf.unite(x, y);
            }
            if(query == 1){
                if(uf.same(x, y)){
                    System.out.println(1);
                }else{
                    System.out.println(0);
                }
            }
        }
    }
}

class UnionFind {
    private int n;
    private int[] root;

    UnionFind(int n){
        this.n = n;
        this.root = new int[n];
        for(int i = 0; i < n; i++){
            root[i] = i;
        }
    }

    private int find(int x){
        if(x == root[x]) {
            return root[x];
        }
        return root[x] = find(root[x]);
    }

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

    public void unite(int x, int y){
        if(same(x, y)) return;
        x = find(x);
        y = find(y);

        root[y] = x;
    }
}